Seismic Control of Tall Buildings Using Distributed Multiple ...Seismic Control of Tall Buildings...

Research ArticleSeismic Control of Tall Buildings Using Distributed MultipleTuned Mass Dampers

Hamid Radmard Rahmani and Carsten Konke

Institute of Structural Mechanics Bauhaus-Universitat Weimar Marienstr 15 D-99423 Weimar Germany

Correspondence should be addressed to Hamid Radmard Rahmani radmardrahmanigmailcom

Received 5 March 2019 Revised 16 July 2019 Accepted 29 July 2019 Published 19 September 2019

Guest Editor Eden Bojorquez

Copyright copy 2019 Hamid Radmard Rahmani and Carsten Konke is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

e vibration control of tall buildings during earthquake excitations is a challenging task because of their complex seismicbehavior is paper investigates the optimum placement and properties of the tuned mass dampers (TMDs) in tall buildingswhich are employed to control the vibrations during earthquakes An algorithm was developed to spend a limited mass eitherin a single TMD or in multiple TMDs and distribute it optimally over the height of the building e nondominated sortinggenetic algorithm II (NSGA-II) method was improved by adding multivariant genetic operators and utilized to simulta-neously study the optimum design parameters of the TMDs and the optimum placement e results showed that underearthquake excitations with noticeable amplitude in higher modes distributing TMDs over the height of the building is moreeffective in mitigating the vibrations compared to the use of a single TMD system From the optimization it was observed thatthe locations of the TMDs were related to the stories corresponding to the maximummodal displacements in the lower modesand the stories corresponding to the maximum modal displacements in the modes which were highly activated by theearthquake excitations It was also noted that the frequency content of the earthquake has significant influence on theoptimum location of the TMDs

1 Introduction

Given the modern development plans of large cities whichare designed to answer the needs of their fast-growingpopulation it is anticipated that the buildings in such citieswill become taller and more expensive [1] As result the areaof investigating solutions to provide safety and serviceabilityof tall buildings in case of natural hazards such as strongwinds and earthquakes has gained much attention in the lastdecade

e current seismic design codes allow the structures toundergo inelastic deformations during strong earthquakesSuch structures would experience larger deformations butless seismic forces otherwise the structure should sustainmuch larger earthquake loads

On the contrary the deformations under wind andearthquake loads are limited because of stability and ser-viceability provisions e resultant structures are stiffenough to withstand the wind loads without forming

noticeable deformations while simultaneously being ductileenough to withstand strong earthquakes by adopting non-linear behaviors

However particularly for controlling the vibrations intall buildings the code-based approaches do not necessarilylead to an applicable and affordable solution as thesestructures need to withstand much larger wind and earth-quake loads even though they have much lower lateralstiffness compared to low- and midrise buildings Moreoverbecause of their very high construction costs they are usuallydesigned to endure for longer time periods which increasetheir risk of experiencing strong earthquakes over the courseof their service life

A modern answer to these issues is the idea of structuralcontrol systems that include a variety of techniques whichcan be classified into four main categories passive activesemiactive and hybrid

From a historical point of view passive control systemssuch as base isolations and tuned mass dampers (TMDs)

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 6480384 19 pageshttpsdoiorg10115520196480384

were the first of these techniques to be implementedConsiderable research has focused on the passive controllersystems and they are already utilized in many countries[2 3] As these systems need no external power supply theyare easier to implement and design when compared to otheradvanced controllers In structural control problems TMDshave been successfully implemented in different structuressuch as bridges [4 5] and buildings [6ndash11] to reduceearthquake- and wind-induced vibrations Observations ofTMDs show that they can effectively reduce vibrations instructures that are excited by high winds high-speed trainsand traffic loads and also help decrease the discomfort of theinhabitants during minor earthquakes [5 12 13] Underearthquake excitations the literature shows that the per-formance of the TMDs decreases as the duration of exci-tation shortens erefore the TMDs are more effective forstructures subjected to narrowband long-duration far-fault(FF) excitations compared to pulse-like near-fault (NF)ground motions As single TMD systems can be tuned to aparticular frequency they are very sensitive to mistuningand uncertainties As a solution multiple tuned massdampers (MTMDs) were first introduced by Xu et al in 1990[14] after which they have been studied in several researchstudies [8 9 11 15ndash19] Li and Qu [20] considered thestructure as a single-degree-of-freedom (SDOF) systemwhen connected to multiple TMDs and studied the opti-mum design parameters for those TMDs With respect tousingMTMD systems inmultistory buildings Chen andWu[8] studied the efficiency of using multiple TMDs in miti-gating the seismic responses in a six-story building Afterthat Sakr [15] used partial floor loads as MTMDs eseresearch studies show that the MTMD systems cover a widerfrequency range and are less sensitive to the uncertainties ofthe system

In addition to multistory buildings several tall buildingshave benefited from the utilization of TMDs in controllingtheir vibrations (see Figure 1)

As has been shown most of them are equipped with asingle TMD which is placed on the top level of the buildinge studies also showed that using a single TMD on the toplevels of the tall buildings can effectively reduce wind-in-duced motions [22 23] is is because the structures re-spond to the wind excitation with respect to their firststructural mode in which the top levels of the building havemaximum modal displacement erefore placing a singleTMD on the top level with a tuning frequency closer to thefundamental structural frequency can efficiently reduce thestructural responses In another research Elias andMatsagar[9] studied the use of distributed MTMD systems in re-ducing wind-induced vibrations in a tall building eyconcluded that the distributedMTMDs aremore effective ascompared to a single TMD system and an MTMD system inwhich all the TMDs are placed on the top level

e research studies show that TMDs are also effective inmitigating earthquake vibrations in buildings Arfiadi andHadi [6] used a hybrid genetic algorithm method to find theoptimum properties and the location of a TMD for a 10-story building under earthquake excitation In another re-search Pourzeinali et al [24] utilized multiobjective

optimization to outline the design parameters of a TMD in a12-story building under earthquake excitation Li [11]proposed a novel optimum criterion to optimize theproperties of double TMDs for structures under groundacceleration In another research Elias et al studied theeffectiveness of a distributed TMD system in vibrationcontrol of a chimney [25] e research developments inpassive control of structures using TMDs are summarized byElias and Matsagar [26]

In all the research studies about tall buildings cited hereeither the parameters of the TMDs have mainly been studiedunder wind-induced vibrations or a single TMD has beenstudied under earthquake excitation currently studying theoptimum parameters of TMDs under earthquake excitationwithout limiting the number and location of TMDs is still achallenging task because of the stochastic nature of theearthquakes and the complex seismic behavior of suchbuildings which mandate extensive and thorough studies

Additionally in contrast to the wind loads duringearthquakes the higher modes may have more noticeableparticipation in the total response of tall buildings is ismainly because of the (1) low frequency of the higher modesin these structures compared to low- and midrise buildingsand (2) wide frequency content of the earthquakes that mayactivate multiple modes in such buildings erefore onlycontrolling the lower modes by placing TMDs on the toplevels would not necessarily lead to the optimum solution forcontrolling the motions in these buildings duringearthquakes

11 ProblemDefinition is paper addresses the mentionedissues by studying the optimum placement and properties ofTMDs in a 76-story benchmark building as the case studywhich is subjected to seven scaled earthquake excitationse variables of the resultant optimization problem includethe positions and properties of the TMD e goal of theoptimization is to reduce the controlled-to-uncontrolledratio of the displacement velocity and acceleration seismicresponses In order to solve such multiobjective optimiza-tion problem an improved revision of the nondominatedsorting genetic algorithm II (NSGA-II) is developed andutilized

In each loop the algorithm generates an arrangementand properties of the TMDs using the NSGA-II method andsends them to the analyzer module to determine the re-sponses of the building equipped with such a TMD ar-rangement under different earthquake excitations Based onthe responses the algorithm assigns a fitness value for suchTMD arrangements e fitness value is an index that showshow good or bad the obtained responses are e NSGA-IIthen utilizes a refined history of the TMD arrangements andcorresponding fitness values for its next suggestion in thenext loop In this study the algorithm was allowed to spendan applicable mass in a single TMD or distribute it throughmultiple TMDs over the height of the building

12 Contributions is research incorporates several con-tributions in the field of passive control of tall buildings and

2 Advances in Civil Engineering

optimization problems First the issues with a single TMDsystem in controlling tall buildings are addressed and im-provements are proposed by studying multimode control viadistribution of the TMDs over the height of the buildingLikewise it investigates how the frequency content of theearthquake can aect the optimum position and propertiesof the TMDs Moreover the performance of the NSGA-IIalgorithm is enhanced by adding multivariant genetic op-erations and the resulting algorithms are presented Finallythe optimum hyperparameters of the genetic algorithm fortackling similar problems are proposed by performingsensitivity analysis

13 Outlines shye mathematical settings of a structuraldynamic problem are mentioned in Section 2 shyen theNSGA-II method is described in Section 3 After that thecase study is presented in Section 4 and the selection andscaling of the earthquakes are noted shyen the results of thesensitivity analysis of the GA hyperparameters for opti-mizing the performance of the GA algorithm are presentedand the optimization process is then detailed in Section 7Finally the obtained results are presented and discussed inSections 8 and 9 and the relevant conclusions are drawn

2 Mathematical Model of the Building

shye governing equation of the motion of a tall buildingunder earthquake excitation is as follows

[M] euroU +[C] _U +[K] U Pt (1)

where M K and C represent the mass the stiness and thedamping matrices of the structure and the TMDs

[M] Mst[ ] + Mt[ ][C] Cst[ ] + Ct[ ][K] Kst[ ] + Kt[ ]

(2)

Indexes st and t indicate the degree of freedom (DOF) ofthe building and the TMDs respectively

shye external load vector Pt in Equation (1) comprisesinertial forces due to ground accelerations as follows

Pt minus euroug[M] 1t (3)

where 1t (N+n)times1 [1 1 1]T and the term euroug represents

the ground accelerationsshye structural responses including displacement

velocity and acceleration matrices can be expressed asfollows

U ust1 ust2 ustN ut1 ut2 utn V vst1 vst2 vstN vt1 vt2 vtn A ast1 ast2 astN at1 at2 atn

(4)

where N and n represent the number of DOFs (DOF) forthe building and the TMDs respectively shyerefore thedimensions of the M K and C matrices are(N + n) times (N + n)

150 m

300 m

450 m

600 m

Shanghai TowerShanghai 2015

Building height 632 mDamper position

125F581 mType of damper TMD

Ping An Finance CenterShenzhen 2017

Building height 599 mDamper position 113F556 m

Type of damper TMD

Shanghai World Financial CenterShanghai 2008


Type of damper ATMD

Petronas Twin Towers 1 and 2Kuala Lumpur 1998

Building height 452 mDamper position within four legs under

skybridge (approx 150 m above ground floor)Type of damper TMD

Princess TowerDubai 2012

Building height 413 mDamper position 98F363 m (estimated)

Type of damper TLD

23 MarinaDubai 2012


Type of damper TMD

Almas towerDubai 2008


48-49F212 mType of damper TMD

TAIPEI 101Taipei 2004


88F378 mType of damper TMD 432 park avenue

New York City 2015 Building height 426 m

Damper position 85F397 m

Type of damper TMD

Figure 1 Tallest completed buildings with dampers [21]

Advances in Civil Engineering 3

shye design parameters of a TMD include its dampingtuning frequency and mass Generally the ratios of theseparameters to the corresponding values of the structureshave more importance and are utilized in the designprocedures

m0 mt

mst

β ]t]st

ψ ctcst

(5)

where the parameters m0 β and ψ refer to mass frequencyand damping ratios while the indexes t and st indicate theTMD and the structural properties

In order to solve the equations of themotion Newmarkrsquosβ method is utilized shye average acceleration method isconsidered by setting c 12 and β 14 in the relatedformulations [27]

3 The Fast and Elitist Multiobjective GeneticAlgorithm NSGA-II

31 Introduction In this paper the NSGA-II method [28] isutilized to investigate the optimum arrangement andproperties of TMDs in a tall building NSGA-II is a non-domination-based genetic algorithm invented for multi-objective optimization problems In this method the initialpopulation is randomly generated as in a normal GAprocedure and then the algorithm sorts the population withrespect to the nondomination rank and the crowdingdistance

In general X dominates Y if X is no worse than Y in allthe objectives and if X is better than Y in at least oneobjective

Among the nondominated solutions or a union of therst ranks of nondominated solutions NSGA-II seeks abroad coverage shyis will be achieved by crowding distancewhich is the Manhattan distance between the left and rightneighboring solutions for two objectives

32 Repair shye repair method makes infeasible solutionsfeasible Figure 2 schematically shows the repair approachfor a solution space with an infeasible solution and twosolutions in the feasible region In this research an infeasiblesolution includes the out-of-limit properties for TMDs As isshown the repair function would project each of theseinfeasible solutions to the closest feasible solution shyedeveloped repair function calculates the shortest distance ofthe TMD properties (m0 β andψ) in the infeasible solutionand corrects the chromosome with respect to the calculateddistance (see Algorithm 1)

33 Selection shye objective of selection is to choose the tterindividuals in the population to create osprings for the nextgeneration and then place them in a group commonly

known as the mating poolshyemating pool is then subjectedto further genetic operations that result in advancing thepopulation to the next generation and hopefully closer to theoptimal solution In this research the roulette wheel se-lection method was utilized for developing the selectorfunction As is also shown in Algorithm 2 the algorithmselects the individuals based on a probability proportional tothe tness As is schematically illustrated in Figure 3 theprinciple of roulette selection is a linear search through aroulette wheel with the slots in the wheel weighted inproportion to the individualrsquos tness values All the chro-mosomes (individuals) in the population are placed on theroulette wheel according to their tness value [30] In thisalgorithm a probability value is assigned to each individualin the population Based on these probabilities the ranges [01] are divided between the individuals so that each indi-vidual obtains a unique range shye winning individual isthen selected by generating a random number between zeroand one and nding the individual whose range includes thisrandom number

In this algorithm the ADDRANGE function assigns arange to each individual based on their tness value andtheir position on the wheel and the RND(1) function gen-erates a random value between zero and one

34 Optimization Variables In this study three variableswere dened to be optimized by the NSGA As is sche-matically shown in Figure 4 the variables are as follows

Constraint boundary

Infeasiblesolution space

Closest

Feasiblesolution spaceFittest

Optimum

Figure 2 Repair of an infeasible solution [29]

procedure REPAIR(individual)stDECODER(individual)for each tmd in stfor each property in tmdif not property in acceptableRange

propertyCLOSESTINRANGE(property)end if

tmdRENEW(tmd property)end for

newIndividualCODER(st)end forreturn newIndividual

end procedure

ALGORITHM 1 Repairing individuals


(1) Number of TMDs(2) Position of the TMDs ⟶ story number(3) TMDsrsquo properties ⟶ m0 β andψ

shye variation domain for m0 β and ψ is considered tobe in an applicable range as shown in Table 1 shyemaximum value of the total mass ratio of TMDsmt sum

ni1m0i is limited to 3 which is equal to the

considered limit for each TMD shyis allows the GA al-gorithm to either spend the allowable mass in a singleTMD or divide it among multiple TMDs and distributethem over the height of the building As is shown thedamping and the frequency ratio of the TMDs are alsolimited to applicable values

35 Encoding In this research binary coding has beenconsidered for creating genesshyerefore the design variablesof each TMD are coded into a binary string with a constantnumber of genes as shown in Figure 5 Each ospringcontains the design parameters for the TMD as follows

m0 mt

mst

β ]t]st

ξ ctcst

(6)

where the t and st indexes correspond to the TMD and thestructure respectively

ut1

ut2

K1

K2

m1

m2

C1

C2

utiKim2

Ci

utnKnmn

Cn

us1

us2

usi

usN

Figure 4 Building equipped with TMDs

37individual E

24 individual D

15individual C

14individual B

10individual A

Figure 3 Roulette wheel selection

procedure MAKINGSELECTION(population)tPop FITNESS(population)sumFit SUM(tPop)percentFit tPopsumFitrangeFitAddedADDRANGE(tPop percentFit)randNRND(1)for each individual in populationr rangeFitAdded(individual)if randN in range r

selectedIndv individualexit

end ifend forreturn selectedIndv

end procedure

ALGORITHM 2 Making individual selection


After developing the genes for each TMD the chro-mosomes are then created by combining all genes for eachsolution As a result each chromosome contains the codeddata of all TMDs in the building Using this definition theposition of each TMD is represented by the position of therelated genes in the chromosome

36 Genetic Operators

361 Crossover Function In the crossover operation twoselected parents exchange random parts of their chromo-some to create new offsprings An appropriate strategy forselecting locations of the split points and the length of thetransferred genes depends on the problem characteristicsthat highly affect the performance of the algorithm and thequality of the final results

In this regard different alternatives have been studied inthis research to develop an appropriate crossover functionExamples of crossover operation forms that have beenutilized in other research studies but were not appropriatefor this research are discussed as follows

(1) Singlek-Point Crossover Random Points in WholeChromosome In the initial steps a completely random se-lection of the genes for crossover has been considered as acommonly used crossover function In this crossover typeafter the parents are nominated by the algorithm one or kpoints in the chromosome are randomly selected and thenew offsprings are created by splitting and combining theparentsrsquo chromosomes at the selected points is processhas often resulted in producing too many meaningless andlow-quality offsprings consequently reducing the perfor-mance of the algorithm dramatically Examples of mean-ingless offsprings can include TMDs without one or moreproperties (eg without mass or stiffness)

(2) Singlek-Point Crossover Random Points in TMD GenesPreventing the production of meaningless offsprings thecrossover function was improved in this study so that the

genes related to the TMDs in each parent could be selectedfor performing a k-point crossover Although the chance ofcreating meaningless offsprings was noticeably reduced theresults showed that the efficiency of the operator in im-proving the results was not acceptable as following thisprocess all the genes within the considered range for a TMDwould be subjected to the same operations regardless of thegenesrsquo positions

For example the genes related to the stiffness of a TMDin a parent were exchanged with those related to thedamping properties in another parent which is not logicalAs a result despite its improvements compared to the firsttype the second crossover type leads to a very low con-vergence rate because of the production of low-qualityoffsprings In addition one possible shortcut for reaching anoptimum solution was missed this step involves attachingthe TMD of one parent to a story in another parent

However the maximum convergence rate obtained bydeveloping a two-variant crossover function is presented inAlgorithm 3 As is shown in this function in each call oneof the two developed crossover variants would be selectedrandomly ese variants are described as follows

(i) Variant 1 in the first variation the crossover op-erator acts on each of the parameters of the TMDsseparately using the k-point crossover methodmeaning that in each call the crossover operatoracts on the stiffness mass or damping of the parentsand exchanges the related properties using thek-point crossover function e produced offspringshave TMDs in the same locations as their parentsbut with different properties Investigation of theperformance of this function showed that this var-iant improves the parameters of the TMDs re-gardless of their positions

(ii) Variant 2 the second crossover variation acts on thelocation of TMDs in the parents e resultantoffsprings include TMDs with the same properties astheir parents but in other stories ese two cross-over variations are demonstrated in Figure 6

362 Mutation Function In the genetic algorithm themutation operator randomly changes one or multiple genesof a parent to produce new offsprings Generally in thebinary coded chromosome the following function is utilizedto change the genes

Binarymutation(gen) 1 if gen value 0

0 if gen value 11113896 (7)

In GA problems the mutation function helps thealgorithm to explore the solution space more broadly andprevents it from sticking to the local minimums In ad-dition a proper mutation function improves the con-vergence speed In this research in order to develop anappropriate mutation function different variants werestudied It is understood that developing the mutationfunction without considering the characteristics ofthe problem would result in producing meaningless

1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi

Figure 5 Binary coding the TMDrsquos properties

Table 1 Parameter variation domain for TMDs

Parameters Min value Max valuemt () mdash 3m0 () 02 3β 08 13ψ 5 40


offsprings Keeping this in mind a two-variant mutationfunction was developed which acted on the (1) genesrelated to TMD parameters and (2) group of genes relatedto the location of the TMDs (See Algorithm 4)

37 Fitness Function During the GA procedure each so-lution comprised an arrangement of TMDs with differentparameters In order to evaluate an individual solution threeobjective functions were defined to shape the fitness func-tion e objectives of the optimization were taken to be themaximum ratios of displacement velocity and accelerationresponses in controlled condition to their uncontrolledvalues as follows

J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)

where i is the story number andN is the number of stories inthe building e pseudocode of the developed fitnessfunction is presented in Algorithm 5

4 Benchmark Building

As a case study a 76-story 306m tall official buildingconsisting of the concrete core and concrete frames wasconsidered e total mass of the building was 153000tonnes e initial mathematical model of the building in-cluded 76 transitional and 76 rotational degrees of freedomin which the rotational degrees of freedom were then re-moved by the static condensation method to create a 76-

degree-of-freedom model e damping matrix of thebuilding was calculated by considering a 1 damping ratiofor the first five modes using Rayleighrsquos approach

e first five natural frequencies of the building were016 0765 1992 379 and 639Hz e first five modeshapes of the building are presented in Figure 7

5 Ground Motion Selection

In this research the ground motions were selected andscaled using an intensity-based assessment procedureconsidered according to ASCESEI 07-10 In this regardseven earthquakesrsquo real acceleration records were selectedfrom the Pacific Earthquake Engineering Research Center(PEER) NGA strong motion database [31] (see Figure 8) andthen scaled using a design response spectrum [32 33] epeak ground acceleration (PGA) and other seismic pa-rameters of the considered design response spectrum areshown in Table 2

e specifications of the nonscaled and scaled selectedearthquakes are presented in Tables 3 and 4 e spectra ofthe nonscaled and scaled excitations are shown in Figure 9

6 Sensitivity Analysis of GeneticAlgorithm Parameters

As the parameters of GAs are highly dependent on thecharacteristics of each particular problem [34] the sensitivityanalysis on the GA parameters was performed and the op-timum values were studied Utilization of the obtained valuesfor the GA parameters resulted in improving the quality of thesolutions and the performance of the algorithm As is shownin Table 5 during the sensitivity analysis the crossover andmutation probabilities were iterated and the GA results werecompared for the El Centro earthquake excitation

e results were then sorted using the NSGA functionand the pareto fronts were obtained as shown in Table 6Considering the first pareto set in this table the resultantoptimum values for crossover and mutation probabilitieswere 07 and 02 respectively

As a result the parameters of the NSGA-II were con-sidered as they are shown in Table 7 e sufficiency of 500generations as the limit for the number of generations wasthen evaluated as shown in Figure 10

7 Optimization Process

In order to study the optimum arrangement and propertiesof the TMD in the benchmark building a computer codewas developed based on the previously discussed theoriesand functions e pseudocode of the program is presentedin Algorithm 6 In order to improve the performance of thedeveloped code and reduce the computation time someadvanced computer programming techniques such asparallel computing were utilized As a result the codeutilized multiple CPU cores to produce multiple populationsin parallel and then all the populations were combined andsorted in each generation

(1) procedure CROSSOVER(individual1individual2)(2) if rnd(1)lt 05(3) rndTmd1RANDOMSELECT TMD in individual1(4) rndTmd2RANDOMSELECT TMD in individual2(5) k rndint(3)(6) tmd1NewK-POINTCROSSOVER(rndTmd1)(7) tmd2NewK-POINTCROSSOVER(rndTmd2)(8) offspring1REBUILD(individual1 tmd1New)(9) offspring2REBUILD(individual2 tmd2New)(10) else(11) rndTmd1 RANDOMSELECT TMD in individual1(12) rndTmd2RANDOMSELECT TMD in individual2(13) tmd1New rndTmd2(14) tmd2New rndTmd1(15) offspring1REBUILD(individual1 tmd1New)(16) offspring2REBUILD(individual2 tmd2New)(17) end if(18) return (offspring1 offspring2)(19) end procedure

ALGORITHM 3 Crossover operator


8 Results

e results of the optimization process including the op-timum arrangement of the TMDs and their properties areshown in Figures 11ndash17e drift and acceleration responses

for the top story as the critical story are summarized inTable 8 As shown the optimum number of TMDs is morethan one for some of the excitations

e maximum number of TMDs is three which cor-responds to Bam and Manjil excitations placed in 76 75

0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2

Figure 6 Crossover types

(1) procedure MUTATION(individual)(2) if rnd(1)lt 05(3) rndTmdRANDOMSELECT TMD in individual(4) newStory rndint(76)(5) tmdNewMOVETMD(rndTmd newStory)(6) offspringREBUILD(individual tmdNew)(7) else(8) rndTmdRANDOMSELECT TMD in individual(9) targetGenCount rndint(10)(10) for i 1 to targetGenCount(11) targetGenRANDOMSELECTGEN(rndTmd)(12) mutTmdBINARYMUTATION(rndTmd targetGen)(13) end for(14) offspringREBUILD(individual tmdNew)(15) end if(16) return (offspring)(17) end procedure

ALGORITHM 4 Mutation operator

(1) procedure FITNESS(benchmarkData individualTmdAdded excitation)(2) ucontrolled

max vcontrolledmax acontrolledmax1113864 1113865 MAXRESPONSE(benchmarkData individualTmdAdded excitation)

(3) type uuncontrolledmax vuncontrolledmax auncontrolled

max1113864 1113865as constant(4) j1 ucontrolled

max uuncontrolledmax

(5) j2 vcontrolledmax vuncontrolledmax(6) j3 acontrolled

max auncontrolledmax

(7) indvFitnessAdded [individualTmdAdded j1 j2 j31113864 1113865](8) return (indvFitnessAdded)(9) end procedure

ALGORITHM 5 Fitness of individuals


75

70

65

60

55

50

45

40

35

30

25

20

15

10

5

0ndash05ndash1 0 105

Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz

Figure 7 Five mode shapes of the 76-story building

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402

0ndash02ndash04ndash06ndash08

(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

ndash06ndash04ndash02

020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

ndash08ndash06ndash04ndash02

002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)

Figure 8 Earthquake acceleration records obtained from Pacific Earthquake Engineering Research Center (PEER) [31] (a) Bam Iran 2003(b) El Centro USA 1940 (c) Kobe Japan 1995 (d)Manjil Iran 2002 (e) Northridge USA 1971 (f ) Landers USA 1992 (g) San FernandoUSA 1994

Table 2 Parameters of the design response spectrum

Site class PGA Ss S1 Fa Fv SMS SM1 SDS SD1

B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g


Table 3 Original earthquakesrsquo specifications

Accelerogram Max acceleration (g) Max velocity(cmsec) Max displacement (cm) Effective design

acceleration (g)Predominantperiod (sec)

Significantduration (sec)

Bam 080 12412 3394 069 020 800El Centro 044 6701 2789 030 006 1146Kobe 031 3080 747 028 042 620Manjil 051 4245 1487 047 016 2866Northridge 045 6014 2189 045 042 1062Landers 072 13340 11392 052 008 1315San Fernando 022 2171 1591 020 000 1315

Table 4 Scaled earthquakesrsquo specifications

Accelerogram Max acceleration (g) Max velocity (cmsec) Max displacement (cm) Effective designacceleration (g)

Predominantperiod (sec)



0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)

Mean matched spectrumTarget spectrum

Figure 9 Mean matched spectrum compared to the target spectrum

Table 5 Crossover and mutation variations

Variation no Crossover Mutation J1 J2 J31

06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939


and 64th floors in both cases Under both sets of excitationsmost of the mass for the TMDs was dedicated to those on thetop two floors e tuned frequency of the TMDs was closeto the fundamental frequency of the building for the top twoTMDs and about 124 times the fundamental frequency forthe TMD in the 64th-floor building e damping ratio ofthe TMDs placed on the top two stories was close to themaximum allowed value which was 40 while it was about 14for the TMD in the 64th-floor building

It was observed that the controlled displacement re-sponses of the building improved substantially by about 65under the Manjil earthquake excitation On the contrary theobjective J1 for the Bam earthquake had a value of about 095which means to about 5 improvement in reducing max-imum displacements compared to the uncontrolled re-sponse is low objective value was also obtained under theLanders earthquake with a value of about 093 for J1 im-plying 7 improvement in reducing the displacement

responses However the displacement response showssubstantial improvements in damping further oscillationscompared to uncontrolled buildings

For Landers Northridge and San Fernando earth-quakes the TMDs were placed on stories 76 and 74 andmost of the allowed mass was dedicated to the TMD on theroof e optimum tuning frequency of the TMDs was closeto the fundamental frequency of the building e dampingvalues of the TMDs were between 3639 and 3978 whichwere close to the maximum considered damping ratio

For the El Centro and Kobe earthquakes the optimumresults were obtained by placing a single TMD system on theroof In both cases all the allowed mass was utilized in theTMD Under these excitations the frequency ratios of theTMDs were registered as 106 and 105 which indicated atuning frequency closer to the fundamental frequency of thebuilding the damping ratios of the TMDs were 3953 and3978 which were close to the maximum allowed value

9 Discussion

As mentioned in Results the optimum target stories forplacing the TMDs included the top two stories for all of theearthquake excitations and some other stories such as 74 and64 for some of the earthquakes In order to understand thereasons behind this optimum arrangement the buildingrsquosmode shapes are again presented in Figure 18 but in eachmode the stories with maximum displacements are alsomarked As shown for the first three modes the top threestories have the maximum displacements e roof and the75th and 61st stories for the 4th mode and the roof and the75th and 64th stories for the 5th mode were the stories withmaximum modal displacements

Consequently it can be concluded that placing a TMDon the top stories would improve the modal displacementsin all five modes an observation which agrees with theoptimization results

On the contrary for some earthquakes TMDs wereplaced in the lower stories which implies that the optimumplacement of the TMDs may also be related to some exci-tation parameters For this reason fast Fourier trans-formation (FFT) was performed for each earthquakersquosexcitation record and amplitudes for each buildingrsquos modefrequency were then specified to investigate the effectiveproperties of the excitations as shown in Figure 19

As shown here unlike other earthquakes for the Bamand Manjil earthquakes the amplitude of the excitation inthe 4th and 5th modes is more than that in the lower modesAs a result although these higher modes have lower massparticipation factors their participation in the total responseof the earthquake is increased by higher excitation ampli-tudes In order to theoretically study these results thedisplacement response of the building under the groundmotion is presented in equation (9) as sum of the modalnodal displacements

u(t) 1113944N

n1un(t) (9)

Table 6 NSGA of crossover and mutation variations

Pareto front Crossover variation no Mutation variation no1 6 mdash2 16 mdash3 4 114 1 mdash5 8 mdash6 5 127 3 78 2 149 9 mdash10 13 mdash11 10 15

Table 7 Initial parameters of NSGA-II

Number ofgenerations

Populationsize

Crossoverprobability

Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1

San FernandoNorthridgeLanders

El CentroBam

ManjilKobe

Figure 10 Trend of objectives during the generations


where un represents the nth modersquos displacements econtribution of the nth mode to the nodal displacement u(t)is

un(t) ϕnqn(t) (10)

where qn refers to the modal coordinate which can becalculated from the following equation

euroqn + 2ζnωn _qn + ω2nqn minus Γn euroug(t) (11)

where Γn is the modal participation factor of the nth modeand is the degree to which the nth mode participates in thetotal response e modal participation factor can be cal-culated based on the modal displacements and masses asfollows

(1) population INITIALIZEPOPULATION()(2) repeat(3) repeat(4) parent1 parent2MAKESELECTION (population)(5) if rnd(1) ge crossoverProbability(6) offspring1 offspring2CROSSOVER(parent1 parent2)(7) REPAIR(offsprint1 offspring2)(8) COMPUTEFITNESS(offsprint1 offspring2)(9) end if(10) if rnd(1) ge mutationProbability(11) offspring1 offspring2MUTATION(parent1 parent2)(12) REPAIR(offsprint1 offspring2)(13) COMPUTEFITNESS(offsprint1 offspring2)(14) until size(population) le M(15) tempPopulation population(16) newPopulation [ ](17) repeat(18) p PARETOFRONT(tempPopulation)(19) psCROWDINGDISTANCE(p)(20) newPopulation newPopulation + ps(21) tempPopulation tempPopulation-ps(22) until size(tempPopulation)gt 2(23) population newPopulation(24) until generationNumber le N

ALGORITHM 6 NSGA-II

UncontrolledControlled

10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)

Story m0 szlig395339461837

767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)

Figure 11 Uncontrolledcontrolled responses under the Bam earthquake (a) Roof displacement response (b) TMD specifications(c) Objective values


ΓN ϕn [M] 1

ϕn T[M] ϕn sumNj1mjϕjnsumNj1mn

jϕ2jn

(12)

Equation (11) is related to a single-degree-of-freedom(SDOF) system with frequency and damping correspondingto the nth mode

As shown here in each mode n the nodal displacementun(t) has a direct relationship with the modal displacementsϕn which means that the stories with maximum modal dis-placements would have greater participation in the buildingrsquosmodal response In addition it is obvious that the modalresponse in the nth mode is also related to the frequency

content of the earthquake excitation euroug which means that alarger acceleration amplitude at that modersquos frequency wouldresult in larger modal responses for that mode

shyerefore the participation of a particular story in thetotal response of the building would be more than that of theother stories if the following conditions are met

(1) shye story has maximum modal displacement in themodes with a larger modal participation factor

(2) shye story has maximum modal displacement in thenth mode with a lower participation factor but theground motion has a larger Fourier transformationamplitude in the nth modersquos frequency (fn)

10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)

Figure 12 Uncontrolledcontrolled responses under the El Centro earthquake (a) Roof displacement response (b) TMD specications(c) Objective values

10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)

Figure 13 Uncontrolledcontrolled responses under the Kobe earthquake (a) Roof displacement response (b) TMD specications(c) Objective values


shyese derivations validate the possibility of placing theTMDs in stories other than the top stories a conclusion thatagrees with the optimization results

10 Conclusion

Considering the obtained results and related discussions inprevious sections the following conclusions can be drawn

(1) Compared to a single TMD on the roof level adistributed MTMD system is more eyencient in im-proving structural responses with the same amount

of masses under excitation for earthquakes that havenoticeable amplitude at the structurersquos frequencies athigher modes a scenario likely to happen within thelifetime of a tall building

(2) shye optimum stories for placement of the TMDsincludes

(a)shye stories withmaximummodal displacementsin the lower structural modes(b) shye stories with maximum modal displace-ments in modes with frequencies at which theearthquake excitation has noticeable amplitudes

10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)

Figure 14 Uncontrolledcontrolled responses under the Landers earthquake (a) Roof displacement response (b) TMD specications(c) Objective values

10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)

Figure 15 Uncontrolledcontrolled responses under the Manjil earthquake (a) Roof displacement response (b) TMD specications(c) Objective values


10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)

Figure 16 Uncontrolledcontrolled responses under the Northridge earthquake (a) Roof displacement response (b) TMD specications(c) Objective values

10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)

Figure 17 Uncontrolledcontrolled responses under the San Fernando earthquake (a) Roof displacement response (b) TMD speci-cations (c) Objective values

Table 8 Comparison between controlled and uncontrolled drifts and absolute accelerations of the top story for dierent earthquakeexcitations

Earthquake Max drift (uncontrolled) Max drift (controlled) Max absolute acceleration(uncontrolled ms2)

Max absolute acceleration(controlled ms2)

Bam 00184 00172 3494 1732El Centro 00128 00111 2099 1611Kobe 00079 00066 2572 2140Manjil 00159 00074 2851 930Northridge 00178 00146 2387 1555Landers 00282 00262 2894 1479San Fernando 00092 00075 2161 1235


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

ndash1 ndash05 0 05 1Mode 1 f = 0159 Hz

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


Figure 18 shyree stories with maximum modal displacements in the rst ve natural modes

0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued


(3) shye optimum parameters for the TMDs that controlthe vibrations in the lower modes include themaximum allowed damping ratioshyis indicates thatincreasing the damping ratio would improve theperformance of such TMDs

(4) shye results showed that the performance of theTMDs was not good in reducing the initial maxi-mums in displacement responses compared to theirreduction of the later maximums that occurred aftersome initial oscillations

(5) Even in the cases with immediate maximum dis-placement responses the MTMD system signi-cantly improves the damping

Data Availability

shye data used to support the ndings of this study areavailable from the corresponding author upon request

Conflicts of Interest

shye authors declare that they have no consecticts of interest

References

[1] M M Ali and K S Moon ldquoStructural developments in tallbuildings current trends and future prospectsrdquo ArchitecturalScience Review vol 50 no 3 pp 205ndash223 2007

[2] B F Spencer and M K Sain ldquoControlling buildings a newfrontier in feedbackrdquo IEEE Control Systems Magazine vol 17no 6 pp 19ndash35 1997

[3] T T Soong and B F Spencer ldquoSupplemental energy dissi-pation state-of-the-art and state-of-the-practicerdquo EngineeringStructures vol 24 no 3 pp 243ndash259 2002

[4] S J Moon L A Bergman and P G Voulgaris ldquoSliding modecontrol of cable-stayed bridge subjected to seismic excitationrdquoJournal of Engineering Mechanics vol 129 no 1 pp 71ndash782003

[5] J F Wang C C Lin and B L Chen ldquoVibration suppressionfor high-speed railway bridges using tuned mass dampersrdquoInternational Journal of Solids and Structures vol 40 no 2pp 465ndash491 2003

[6] Y Aradi and M N S Hadi ldquoOptimum placement andproperties of tuned mass dampers using hybrid genetic al-gorithmsrdquo International Journal of Optimization in CivilEngineering vol 1 no 1 pp 167ndash187 2011

10ndash2 10ndash1 100 101 102Frequency (Hz)

0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)

Figure 19 Fourier transformof earthquake excitations (a) Bam (b) El Centro (c) Kobe (d) Landers (e)Manjil (f) Northridge (g) San Fernando


[7] A Y T Leung and H Zhang ldquoParticle swarm optimization oftuned mass dampersrdquo Engineering Structures vol 31 no 3pp 715ndash728 2009

[8] G Chen and JWu ldquoOptimal placement of multiple tunemassdampers for seismic structuresrdquo Journal of Structural Engi-neering vol 127 no 9 pp 1054ndash1062 2001

[9] S Elias andVMatsagar ldquoDistributedmultiple tunedmass dampersfor wind vibration response control of high-rise buildingrdquo Journalof Engineering vol 2014 Article ID 198719 11 pages 2014

[10] C-L Lee Y-T Chen L-L Chung and Y-PWang ldquoOptimaldesign theories and applications of tuned mass dampersrdquoEngineering Structures vol 28 no 1 pp 43ndash53 2006

[11] C Li and B Zhu ldquoEstimating double tuned mass dampers forstructures under ground acceleration using a novel optimumcriterionrdquo Journal of Sound and Vibration vol 298 no 1-2pp 280ndash297 2006

[12] R N Jabary and S P G Madabhushi ldquoTuned mass dampereffects on the response of multi-storied structures observed ingeotechnical centrifuge testsrdquo Soil Dynamics and EarthquakeEngineering vol 77 pp 373ndash380 2015

[13] H-C Tsai and G-C Lin ldquoOptimum tuned-mass dampers forminimizing steady-state response of support-excited anddamped systemsrdquo Earthquake Engineering amp Structural Dy-namics vol 22 no 11 pp 957ndash973 1993

[14] Y L Xu J Chen C L Ng and W L Qu ldquoSemiactive seismicresponse control of buildings with podium structurerdquo Journalof Structural Engineering vol 131 no 6 pp 890ndash899 2005

[15] T A Sakr ldquoVibration control of buildings by using partialfloor loads as multiple tuned mass dampersrdquo HBRC Journalvol 13 no 2 pp 133ndash144 2017

[16] L Zuo and S A Nayfeh ldquoOptimization of the individualstiffness and damping parameters in multiple-tuned-mass-damper systemsrdquo Journal of Vibration and Acoustics vol 127no 1 p 77 2005

[17] N Hoang and P Warnitchai ldquoDesign of multiple tuned massdampers by using a numerical optimizerrdquo Earthquake Engi-neering amp Structural Dynamics vol 34 no 2 pp 125ndash144 2005

[18] M Jokic M Stegic and M Butkovic ldquoReduced-order mul-tiple tuned mass damper optimization a bounded real lemmafor descriptor systems approachrdquo Journal of Sound and Vi-bration vol 330 no 22 pp 5259ndash5268 2011

[19] AY Pisal andR S Jangid ldquoSeismic response ofmulti-story structurewith multiple tuned mass friction dampersrdquo International Journal ofAdvanced Structural Engineering vol 6 no 1 pp 1ndash13 2014

[20] C Li and W Qu ldquoOptimum properties of multiple tunedmass dampers for reduction of translational and torsionalresponse of structures subject to ground accelerationrdquo En-gineering Structures vol 28 no 4 pp 472ndash494 2006

[21] ldquoTallest 10 completed buildings with dampersrdquo CTBUHJournal vol 48 no 3 2018 httpswwwgooglecomurlsa=tamprct=jampq=ampesrc=sampsource=webampcd=1ampcad=rjaampuact=8ampved=2ahUKEwiZv-L82JvkAhXKI1AKHbMDBIwQFjAAegQIABACampurl=http3A2F2Fglobalctbuhorg2Fpaper2F3788ampusg=AOvVaw2F_KHUsmgWNYnY_pgGXE1f

[22] C C Chang andW L Qu ldquoUnified dynamic absorber designformulas for wind-induced vibration control of tall build-ingsrdquo Ie Structural Design of Tall Buildings vol 7 no 2pp 147ndash166 1998

[23] S N Deshmukh and N K Chandiramani ldquoLQR control ofwind excited benchmark building using variable stiffnesstuned mass damperrdquo Shock and Vibration vol 2014 ArticleID 156523 12 pages 2014

[24] S Pourzeynali S Salimi and H E Kalesar ldquoRobust multi-objective optimization design of TMD control device to

reduce tall building responses against earthquake excitationsusing genetic algorithmsrdquo Scientia Iranica vol 20 no 2pp 207ndash221 2013

[25] S Elias V Matsagar and T K Datta ldquoEffectiveness of dis-tributed tuned mass dampers for multi-mode control ofchimney under earthquakesrdquo Engineering Structures vol 124pp 1ndash16 2016

[26] S Elias and V Matsagar ldquoResearch developments in vibrationcontrol of structures using passive tuned mass dampersrdquoAnnual Reviews in Control vol 44 pp 129ndash156 2017

[27] N M Newmark ldquoA method of computation for structuraldynamicsrdquo Journal of the Engineering Mechanics Divisionvol 85 no 3 pp 67ndash94 1959

[28] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[29] O Kramer Genetic Algorithm Essentials Springer PublishingCompany New York NY USA 1st edition 2017

[30] D E Goldberg and K Deb ldquoA comparative analysis of se-lection schemes used in genetic algorithmsrdquo Foundations ofGenetic Algorithms vol 1 pp 69ndash93 1991

[31] PEER Center PEER Ground Motion Database PEER CenterUniversity of California Berkeley CA USA httpsngawest2berkeleyedu

[32] I Iervolino C Galasso and E Cosenza ldquoREXEL computeraided record selection for code-based seismic structuralanalysisrdquo Bulletin of Earthquake Engineering vol 8 no 2pp 339ndash362 2010

[33] F Weber J Distl L Meier and C Braun ldquoCurved surfacesliders with friction damping linear viscous damping bow tiefriction damping and semiactively controlled propertiesrdquoStructural Control and Health Monitoring vol 25 no 11p e2257 2018

[34] M Gen and R Cheng Genetic Algorithms and EngineeringOptimization John Wiley amp Sons Hoboken NJ USA 2000


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were the first of these techniques to be implementedConsiderable research has focused on the passive controllersystems and they are already utilized in many countries[2 3] As these systems need no external power supply theyare easier to implement and design when compared to otheradvanced controllers In structural control problems TMDshave been successfully implemented in different structuressuch as bridges [4 5] and buildings [6ndash11] to reduceearthquake- and wind-induced vibrations Observations ofTMDs show that they can effectively reduce vibrations instructures that are excited by high winds high-speed trainsand traffic loads and also help decrease the discomfort of theinhabitants during minor earthquakes [5 12 13] Underearthquake excitations the literature shows that the per-formance of the TMDs decreases as the duration of exci-tation shortens erefore the TMDs are more effective forstructures subjected to narrowband long-duration far-fault(FF) excitations compared to pulse-like near-fault (NF)ground motions As single TMD systems can be tuned to aparticular frequency they are very sensitive to mistuningand uncertainties As a solution multiple tuned massdampers (MTMDs) were first introduced by Xu et al in 1990[14] after which they have been studied in several researchstudies [8 9 11 15ndash19] Li and Qu [20] considered thestructure as a single-degree-of-freedom (SDOF) systemwhen connected to multiple TMDs and studied the opti-mum design parameters for those TMDs With respect tousingMTMD systems inmultistory buildings Chen andWu[8] studied the efficiency of using multiple TMDs in miti-gating the seismic responses in a six-story building Afterthat Sakr [15] used partial floor loads as MTMDs eseresearch studies show that the MTMD systems cover a widerfrequency range and are less sensitive to the uncertainties ofthe system

In addition to multistory buildings several tall buildingshave benefited from the utilization of TMDs in controllingtheir vibrations (see Figure 1)

As has been shown most of them are equipped with asingle TMD which is placed on the top level of the buildinge studies also showed that using a single TMD on the toplevels of the tall buildings can effectively reduce wind-in-duced motions [22 23] is is because the structures re-spond to the wind excitation with respect to their firststructural mode in which the top levels of the building havemaximum modal displacement erefore placing a singleTMD on the top level with a tuning frequency closer to thefundamental structural frequency can efficiently reduce thestructural responses In another research Elias andMatsagar[9] studied the use of distributed MTMD systems in re-ducing wind-induced vibrations in a tall building eyconcluded that the distributedMTMDs aremore effective ascompared to a single TMD system and an MTMD system inwhich all the TMDs are placed on the top level

e research studies show that TMDs are also effective inmitigating earthquake vibrations in buildings Arfiadi andHadi [6] used a hybrid genetic algorithm method to find theoptimum properties and the location of a TMD for a 10-story building under earthquake excitation In another re-search Pourzeinali et al [24] utilized multiobjective

optimization to outline the design parameters of a TMD in a12-story building under earthquake excitation Li [11]proposed a novel optimum criterion to optimize theproperties of double TMDs for structures under groundacceleration In another research Elias et al studied theeffectiveness of a distributed TMD system in vibrationcontrol of a chimney [25] e research developments inpassive control of structures using TMDs are summarized byElias and Matsagar [26]

In all the research studies about tall buildings cited hereeither the parameters of the TMDs have mainly been studiedunder wind-induced vibrations or a single TMD has beenstudied under earthquake excitation currently studying theoptimum parameters of TMDs under earthquake excitationwithout limiting the number and location of TMDs is still achallenging task because of the stochastic nature of theearthquakes and the complex seismic behavior of suchbuildings which mandate extensive and thorough studies

Additionally in contrast to the wind loads duringearthquakes the higher modes may have more noticeableparticipation in the total response of tall buildings is ismainly because of the (1) low frequency of the higher modesin these structures compared to low- and midrise buildingsand (2) wide frequency content of the earthquakes that mayactivate multiple modes in such buildings erefore onlycontrolling the lower modes by placing TMDs on the toplevels would not necessarily lead to the optimum solution forcontrolling the motions in these buildings duringearthquakes

11 ProblemDefinition is paper addresses the mentionedissues by studying the optimum placement and properties ofTMDs in a 76-story benchmark building as the case studywhich is subjected to seven scaled earthquake excitationse variables of the resultant optimization problem includethe positions and properties of the TMD e goal of theoptimization is to reduce the controlled-to-uncontrolledratio of the displacement velocity and acceleration seismicresponses In order to solve such multiobjective optimiza-tion problem an improved revision of the nondominatedsorting genetic algorithm II (NSGA-II) is developed andutilized

In each loop the algorithm generates an arrangementand properties of the TMDs using the NSGA-II method andsends them to the analyzer module to determine the re-sponses of the building equipped with such a TMD ar-rangement under different earthquake excitations Based onthe responses the algorithm assigns a fitness value for suchTMD arrangements e fitness value is an index that showshow good or bad the obtained responses are e NSGA-IIthen utilizes a refined history of the TMD arrangements andcorresponding fitness values for its next suggestion in thenext loop In this study the algorithm was allowed to spendan applicable mass in a single TMD or distribute it throughmultiple TMDs over the height of the building

12 Contributions is research incorporates several con-tributions in the field of passive control of tall buildings and






[M] euroU +[C] _U +[K] U Pt (1)



(2)








(4)


150 m

300 m

450 m

600 m






Type of damper TMD



Type of damper ATMD






Type of damper TLD

23 MarinaDubai 2012


Type of damper TMD









Type of damper TMD




m0 mt

mst

β ]t]st

ψ ctcst

(5)












Constraint boundary


Closest


Optimum






end procedure








m0 mt

mst

β ]t]st

ξ ctcst

(6)


ut1

ut2

K1

K2

m1

m2

C1

C2

utiKim2

Ci

utnKnmn

Cn

us1

us2

usi

usN


37individual E

24 individual D

15individual C

14individual B

10individual A





end procedure
















0 if gen value 11113896 (7)


1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi







J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






[M] euroU +[C] _U +[K] U Pt (1)



(2)








(4)


150 m

300 m

450 m

600 m






Type of damper TMD



Type of damper ATMD






Type of damper TLD

23 MarinaDubai 2012


Type of damper TMD









Type of damper TMD




m0 mt

mst

β ]t]st

ψ ctcst

(5)












Constraint boundary


Closest


Optimum






end procedure








m0 mt

mst

β ]t]st

ξ ctcst

(6)


ut1

ut2

K1

K2

m1

m2

C1

C2

utiKim2

Ci

utnKnmn

Cn

us1

us2

usi

usN


37individual E

24 individual D

15individual C

14individual B

10individual A





end procedure
















0 if gen value 11113896 (7)


1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi







J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



m0 mt

mst

β ]t]st

ψ ctcst

(5)












Constraint boundary


Closest


Optimum






end procedure








m0 mt

mst

β ]t]st

ξ ctcst

(6)


ut1

ut2

K1

K2

m1

m2

C1

C2

utiKim2

Ci

utnKnmn

Cn

us1

us2

usi

usN


37individual E

24 individual D

15individual C

14individual B

10individual A





end procedure
















0 if gen value 11113896 (7)


1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi







J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







m0 mt

mst

β ]t]st

ξ ctcst

(6)


ut1

ut2

K1

K2

m1

m2

C1

C2

utiKim2

Ci

utnKnmn

Cn

us1

us2

usi

usN


37individual E

24 individual D

15individual C

14individual B

10individual A





end procedure
















0 if gen value 11113896 (7)


1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi







J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia















0 if gen value 11113896 (7)


1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0

m0 β ξ

ktct

mtTMDi







J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




J1 maxuC

i

uUCi

1113888 1113889i1N

J2 maxvC

i

vUCi

1113888 1113889i1N

J3 maxaC

i

aUCi

1113888 1113889i1N

(8)


















8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


8 Results




0 0 0 0

0 0

0000 0

00 0 0 0 0 0 0

00 0

0 0 0 0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

000

0 0 0

0

00

0 0

0 00

0 0 0 01 1

0 01 1 1

1

1 1

1

1

1 11 1 1

11 1 1 1 1

111

1 1 1 1

11

1 1 0

0 0

0 01 0 011 0 0 11

1 0 1

1 1 1 1 1 1 1

1 111

1111

1 1 1 1 1

TMD n

TMD n

Parent 1

Parent 2 TMD 20

TMD 20TMD 1

TMD 1

Offspring 1

Offspring 2














75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 1 f = 016Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 076Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 3 f = 199Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 4 f = 379Hz

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5


Mode 5 f = 639Hz


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

Acc

eler

atio

n (g

)

08060402


(a)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


020

040608

Acc

eler

atio

n (g

)

(b)

Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120

0


02040608

Acc

eler

atio

n (g

)

(c)

Figure 8 Continued


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Time (sec)54 56 58 6046 48 50 5238 40 42 4430 32 34 3622 24 26 2814 16 18 2042 6 8 10 120


002040608

Acc

eler

atio

n (g

)

(d)

604 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5820Time (sec)


002040608

Acc

eler

atio

n (g

)

(e)


002040608

Acc

eler

atio

n (g

)

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)

(f )

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 600Time (sec)


002040608

Acc

eler

atio

n (g

)

(g)




B 0919 2431 g 0852 g 1 1 2431 g 0852 g 1621 g 0568 g












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












0 05 1 15

05

1

15

2 25 3 35 4Period (s)

Acce

lera

tion

(g)





06

01 0845 0917 09412 02 0860 0926 09503 03 0855 0924 09484 04 0839 0915 09425

07

01 0862 0925 09466 02 0835 0913 09397 03 0861 0925 09478 04 0846 0919 09449

08

01 0869 0929 095010 02 0876 0932 095211 03 0842 0915 094112 04 0852 0922 094713

09

01 0871 0930 095114 02 0866 0927 094715 03 0874 0932 095316 04 0839 0913 0939







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







9 Discussion





u(t) 1113944N

n1un(t) (9)





Populationsize


Mutationprobability

500 100 07 02

00

010203040506070809

1

50 100 150 200 250 300 350 400 450 500Generation

J1


El CentroBam

ManjilKobe




un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



un(t) ϕnqn(t) (10)





ALGORITHM 6 NSGA-II


10 20 30 40 50 600Time (s)

ndash15

ndash1

ndash05

0

05

1

15

Disp

lace

men

t(m

)

(a)


767564

143093064

098101124

ψ

(b)

J3J1 J2

095 088 083

(c)



ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ΓN ϕn [M] 1


jϕ2jn

(12)







10 20 30 40 50 600Time (s)


ndash1

ndash08

ndash06

ndash04

ndash02

0

02

04

06

08

1D

ispla

cem

ent(

m)

(a)

Story m0 β395376 299 106ψ

(b)

J3J1 J2084 091 093

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t(m

)

ndash05

ndash04

ndash03

ndash02

0

01

02

03

04

(a)

Story m0 β397876 300 105ψ

(b)

J3J1 J2086 090 097

(c)




10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



10 Conclusion






10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2

3

4

(a)

Story m0 β370776 201

100 101 3713101

ψ

74

(b)

J3J1 J2093 089 098

(c)


10 20 30 40 50 600Time (s)


Disp

lace

men

t (m

)

ndash2

ndash15

ndash1

ndash05

0

05

1

15

2

(a)

Story m0 β ψ

76 150 102 351231341492

101121

0957564 055

(b)

J3J1 J2

036 057 095

(c)



10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


10 20 30 40 50 600Time (s)

ndash15

ndash1

0

ndash05

05

15

1

Disp

lace

men

t (m

)


(a)

Story m0 β370576 226

075 104 3698104

ψ

74

(b)

J3J1 J2

081 084 095

(c)


10 20 30 40 50 600Time (s)

Disp

lace

men

t (m

)


ndash08

ndash06

ndash04

ndash02

0

04

02

06

08

(a)

Story m0 β362776 228

072 103 3639103

ψ

74

(b)

J3J1 J2080 084 097

(c)







0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75



0

005

01

015

02

025

03

Am

plitu

de

10ndash2 10ndash1 100 101 102

003

017

013

016

011

016

076

199

378

639

Frequency (Hz)

(a)

003016

003076 005

639

011378

018199

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

(b)

016

10ndash2 10ndash1 100 101 102

Frequency (Hz)

015

011076

199 639

378004

007077

0

005

01

015

02

025

Am

plitu

de

(c)

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

03

Am

plitu

de 016

199

639009

076 378005005

012

017

(d)

Figure 19 Continued





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Data Availability




References








0

005

01

015

02

025

03A

mpl

itude

016

076

199

378

639

011

017

021

018

02

(e)


002

011011 01

003016

076199 378

639

0

005

01

015

02

025

03

035

(f )

10ndash2 10ndash1 100 101 102

Frequency (Hz)

0

005

01

015

02

025

Am

plitu

de

004

01

014

005

005016

076

199

378

639

(g)



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Seismic Control of Tall Buildings Using Distributed Multiple ...Seismic Control of Tall Buildings...

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Transcript of Seismic Control of Tall Buildings Using Distributed Multiple ...Seismic Control of Tall Buildings...