Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

Innovative techniques for structural assessment: The case of theHoly Shroud Chapel in Turin

A. De Stefano, D. Enrione & G. RuocciPolitecnico di Torino, Turin, Italy

ABSTRACT: Environmental degradation, inevitable aging, negligence and extreme events are some of themost frequent factors that can threaten the structural integrity of historical constructions. Hence, architecturalheritage owners and administrators urgently require cheap and effective tools for structural health assessment.Restoration works on the Holy Shroud Chapel in Turin, Guarino Guarini’s masterpiece which was extensivelydamaged by a fire in 1997, offered the authors the opportunity to test some innovative techniques that are ableto provide an exhaustive picture of the Chapel’s structural health. Dynamic tests were carried out by applyingseveral exciting actions and the signals were acquired to perform a modal identification of the dome in thetime-frequency domain. A stochastic multiple model approach, used to update a FE model of the Chapel, isalso presented. The PGSL algorithm, implemented in the model updating procedure, is able to define differentgroups of models, each one referring to a particular damage scenario that the building is probably undergoing.Theimproved knowledge about the structure is the starting point for the development of symptom-based structuralhealth assessments.

1 INTRODUCTION

Italy, like many other countries throughout the world,has inherited an extraordinary historical treasure fromthe past. This architectural heritage represents a fun-damental resource and a sign of the national culturalbackground, but the high costs for its maintenanceand repairs cause concern. In the last few years, thedemand for cheap and effective tools designed forthese purposes has increased.

Researchers soon became aware of the need to intro-duce the concept of “structural health” and to identifysome instruments and techniques to assess it in areliable way. This growing interest is demonstratedby the huge number of publications and conferencesexpressly devoted to these topics.

The term “structural health” stands for the condi-tion in which the structure assures a suitable levelof safety. The definition of this safety level in turnimplies the knowledge of a set of all those parameterswhich could affect it. Hence, the necessity of identify-ing sensitive elements arises and, more in general, it isimportant to acquire as much information as possibleabout the construction conditions. Monitoring systemsbecome in this sense essential elements in strategic andmonumental structures.

The structural health assessment problem can beseen under a different light. The structure to be moni-tored can be considered as a “patient” whose diseases

have to be diagnosed through a meticulous analy-sis of the surveyed symptoms. This symptom-basedapproach has been extensively adopted and improvedin the mechanical and aerospace fields. Ancient build-ings have to bear damage that arise during theirlife-cycle from different concurring causes, such asmaterial quality degradation, environmental injuries,inaccurate human interventions and modifications ofthe structural body. All these situations representexamples of so-called “damage scenarios”, i.e., theprovoking causes which lead to damage symptoms onthe construction.

Identifying damage scenarios and their probabil-ity of occurrence requires that the existing knowledgebases, whenever available, should be explored andrealistic simulations, capable of relating each possiblescenario to the severity of its consequences and themeaningfulness of its symptoms should be conducted.Dynamical tests and modal identification are power-ful tools that can provide this required knowledge.In addition, simulations performed with stochasticallyupdated models supply reliable estimations of theresidual performance a building is still able to provideafter structural changes inferred by each particulardamage scenario. This kind of information allows thehealth condition of the construction to be predicted foreach damage hypothesis.

In the following chapters, a more detailed discus-sion is given with some innovative techniques which

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have been applied as the starting point for the develop-ment of symptom-based structural health assessments:the Holy Shroud Chapel is presented as an example.

2 STRUCTURAL HEALTH ASSESSMENTTECHNIQUES

The monitoring of common structures represents awell established and widespread practice, whereas thesituation of monumental buildings is rather different.Only a few cases can be found referring to researchdue to the strict constrains necessary to preserve thecultural and artistic value of the buildings.Tools whichcombine a suitable level of reliability with less invasiveinterventions are preferred. Dynamic system identifi-cation in this sense constitutes an optimal compromisewhich is finding widespread approval among experts.Dynamic tests are very powerful identification tech-niques which are able to reveal global quantities suchas natural frequencies, modal shapes and dampingfeatures of the structure under examination. Theseparameters are closely related to the variations instiffness of the system and are therefore extremely sen-sitive to damage and deterioration phenomena. Manymodal identification techniques are now available butthe complexity and uncertainty that affect ancientmasonry constructions drastically reduce their appli-cation possibilities. Time-frequency domain methodshave proved to be accurate in treating non-stationarysignals and they are robust against noise. Further-more, some instantaneous estimators, obtained as autoand cross-correlation of bi-linear time-frequency sig-nal transforms, allow the modal features of systems tobe reliably detected.

In the structural health assessment field FE mod-elling also plays a very important role, even thought inmany cases the lack of numerical modelling accuracyand a deficient correspondence to reality representdecisive limitations. There is the risk of choosingmodel parameters which do not fit real structure prop-erties well. Model Updating (MU) provides a valuablesolution to the problem. It can be considered as themissing link between structural identification and FEmodelling since it gives a model calibration crite-rion on the basis of the experimental results. Modelupdating techniques have undergone an exponentialgrowth during the last few years due to their latentpotentialities. Recently, stochastic approaches havebecome more and more popular and can be distin-guished from traditional deterministic methods dueto their capacity to deal with behaviour uncertaintiesand problem complexity in a robust way. Deterministicmethods, whether direct or parametric, focus on modelcalibration through the minimization of a target func-tion obtained as the difference between experimentalresults and analytical data. Since Model Updatingrepresents an inverse problem, the solution that is

obtained cannot be considered as the only possibleone. Furthermore, there are many error and uncertaintysources that condition the final result. These should beconsidered in order to obtain a consistent estimationof the model parameters and consequently a reliablestructural health assessment.

On the basis of the remarks made so far, the authorsfocused attention on the development of a modelupdating method which could meet monumental build-ing requirements:

– the treatment of errors obtained from the acquisi-tion of experimental measures;

– the treatment of uncertainties due to constructioncomplexity (mechanical properties, constructivemethodologies, unknown design details, etc.);

– the management of information redundancyobtained from many distributed sensors;

– extrapolation ability in the definition of numericalmodels.

Solution accuracy is the main problem which theauthors tried to solve in a convincing way. As a uniqueoptimal solution for this problem cannot be found,the authors concentrated on the possibility of generat-ing a set of different but sufficiently reliable models.The adopted approach is generally referred to as the“multiple-model” due to the fact that it generatesa huge number of models to solve the problem ofthe solution uniqueness. Application of the adoptedmethod to the case study has allowed some modelsto be defined and has made them able to accuratelypredict its structural behaviour. An interesting devel-opment the authors intend putting into practice regardsthe identification of possible damage scenarios foreach model obtained using the updating procedure.The natural consequence is the estimation of the resid-ual performance a building is still able to supply, i.e.,its structural health.

The case of the Holy Shroud Chapel in Turin is pre-sented in order to clarify the concepts introduced so far.

3 CASE STUDY: THE HOLY SHROUD CHAPELIN TURIN

3.1 The experimental campaign

The Holy Shroud Chapel in Turin (Fig. 1) is univer-sally recognized as a outstanding example of ItalianBaroque architecture. Emanuale Filiberto di Savoiaentrusted its design to the famous Italian architectGuarino Guarini, who built the Chapel from 1667 to1694. Since the very beginning, the monarch’s intentwas that of housing the precious relic of Christianityin a more prestigious seat. The architectural resultsobtained by Guarini are extraordinary. The wholebuilding conveys the Guarini’s obsession for architec-tonic originality and a sense of mystery which are well

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Figure 1. Section of the dome.

expressed by the structural complexity and the rich-ness of perfect shapes and theological, astronomic andmathematical symbols. The chapel is composed of atambour bored by six large windows and surmountedby three big arches which sustain the dome. On theinside, a series of small arches overlapped and dis-posed on six levels, creates an hexagonal geometrywhich diminishes towards the top where it becomes thecircular base of a lantern. On the outside, another seriesof small arches creates a complex plaiting effect andthe alternation of black marble and grey stone grantsa particular sense of dynamicity.

The recent history of the Holy Shroud Chapel hasbeen marked by a tragic event.A fire broke out in 1997during some restoration works and it seriously dam-aged the structure, producing incalculable economicand artistic loss.

In the following months, the Sovraintendenzadei Beni Architettonici encharged the Politecnico diTorino with the project to carry out a general experi-mental campaign on the materials and structure (Prof.P. Napoli) and a dynamic test program (Prof. A. DeStefano).

Mainly in situ investigations were performed inorder to obtain detailed knowledge of the structuralmorphology in term of geometry, marble and masonryorganization, position of metal ties, etc. The investi-gations, conducted through topographic and camerasurveys and deep extraction of samples, allowed theexperts to detect some structural elements that had

previously been covered over. As a result of theseinvestigations, a 3D computer geometrical model ofthe entire building was set up and more detailedknowledge in the structural morphology was acquired.

The mechanical properties of the materials weremeasured both in laboratory and in situ tests, in thelatter case using cross-hole ultrasonic measurements.The tests revealed the chemical degradation inducedby the heat on the surface of the elements and a reduc-tion in the material load carrying capacity in the zonesaffected by stresses caused by the effect of constrainedthermal deformations.

Local inspections provided useful information con-cerning about the mechanical properties of the mate-rials and structural configuration and allowed a firstpreliminary estimation of extent of the damage to beobtained. However, due to their spatial limitation, thesetests were not able to completely identify the globalbehaviour of the construction. They therefore had tobe integrated with other techniques that were capa-ble of predicting the residual structural capacity of thebuilding considered as a whole.

In order to achieve a complete overall image of theChapel’s structural health, the Research Unit to whichthe authors belong, in association with the Universityof Kassel (Prof. M. Link), designed a dynamic test-ing programme, prepared a FE model and adjusted itaccording to the acquired experimental knowledge.

In order to perform the dynamic experiments, 25accelerometers were positioned on six different lev-els to measure the response of the structure alongthree different orthogonal directions: radial, verticaland horizontal normal to the radius. The dynamic testswere realized adopting four different exciting actions:

– environmental excitation (traffic, wind, micro-quakes);

– impulsive excitation produced by hammering;– impulsive excitation caused by a sphere dropped to

the ground near the foot of the building;– wind turbulence produced by a Fire-Brigade heli-

copter flying around the top of the dome.

The obtained signals were used to identify the struc-ture of the dome using the TFIE (Time FrequencyInstantaneous Estimators) method.

3.2 Modal identification

The results obtained from the dynamic tests performedon the chapel provided the starting point for the subse-quent structural identification phase. A well-designedstructural health monitoring programme cannot disre-gard this fundamental step which supplies informationconcerning the overall behaviour of the system and itis the basis for the FE model calibration.

Many effective techniques are now available forstructural identification, but in the case of complex

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monumental buildings not all are suitable to robustlyface the several uncertainties that can affect this kindof structure. Generally, output-only methods are pre-ferred to input-output ones since they are less invasive.Identification techniques can also be distinguished onthe basis of the parameters that need to be identified. Itis therefore possible to choose between direct methods,which try to determine the [M], [C] and [K] matricesof motion equation (1):

and indirect methods working on modal parameterssuch as the frequencies, damping and modal shapes.Another classification criterion concerns the domainin which the data are numerically treated and thusprovides three possibilities:

– frequency domain;– time domain;– time-frequency domain.

Frequency domain methods (for example FDD,PSD, etc.) have gradually been replaced by timedomain ones (for example ARMAV, ERA, RandomDecrement, etc.) in order to solve problems concern-ing frequency resolution and modal density. Methodsdeveloped in time-frequency domain offer severaladvantages which are here summarized:

– precise accuracy in parameter estimation;– the possibility of effectively managing non-

stationary signals;– the ability to handle moderate non-linearities;– high robustness against noise.

The main drawback that affects both time-domainand frequency-domain methods concerns the assump-tion that the modal parameters do not evolve versustime and vibration amplitude and that the input is atleast weakly stationary. Since in the civil engineer-ing area the excitation is generally non stationaryand the presence of noise during the data acquisitionphase is unavoidable, the structural response cannotbe regarded as an unvarying-versus-time signal. Theseconsiderations forced the authors to adopt an adap-tive and robust identification technique, that is able tohandle these types of non-stationary excitations. Theimplemented method is based on special amplitudeand phase estimators defined in the time-frequencydomain known in literature as Time-Frequency Instan-taneous Estimators (TFIE).

The Amplitude Ratio and PHase difference estima-tors are expressed by equations (2) and (3), respec-tively:

Figure 2. Phase difference standard deviation versus fre-quency. (50 pts/s, 10.24s); f2 = 2.344 Hz.

where Dsi(t,f) and Dsi,sj(t,f) are the auto and crossbi-linear time – frequency transforms of two compo-nents of the same vibration mode belonging to signalsacquired in two different nodes of the structure. Thethus defined estimators maintain time dependencyand, in this way, they make it possible to ascertainwhether a certain frequency could be a possible vibra-tion mode.At the modal frequency the phase differencein (3) becomes almost constant in time and its stan-dard deviation along the time axis approaches 0, ifthe noise level is low (Fig. 2). However a downwardpeak in the standard deviation of the phase differenceprocess, plotted versus frequency, marks an expectedmodal frequency. If this occurs, the AR in equation (2)computed at that frequency also remains almost con-stant versus time and marks the amplitude ratio of amodal shape.

The TFIE method has been applied to several setsof signals, generated by the different types of excita-tion adopted in the dynamic tests performed on theHoly Shroud Chapel. Modal frequencies were iden-tified using all the consistent signal pairs in all thecombinations of the following sampling parameters:

– sampling frequency: 25 or 50 pts/s– signal length: 256, 512 and 1024 pts.

The TFIE diagrams computed from signals withidentical sampling frequencies and lengths were aver-aged in order to make the downward peaks that markthe modal frequencies clearly visible. The recordsobtained from the excitation of the dropped sphere,with a sampling rate of 25 pts/s and length of 1024 pts,

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Table 1. Subdivision of the elements in the FE model.

Type of element Total number of elements

Shell with 3 or 4 nodes 11871Beam 3D 1646Truss 483D solid 28177Spring 277

provided the best results. The TFIE potential is evidentas it is able to detect the two first flexional modes ofthe chapel, whose modal frequencies are very close toeach other (f1 = 2.246 Hz and f2 = 2.344 Hz).

The modal shapes were identified using the samedata pairs and sampling conditions which allowed thebest results in the frequency search. The first flexionalshape is oriented in the NE-SW direction, the secondin the NW-SE direction. In general, it is convenient touse signals in cylindrical coordinates to identify modeswhere torsion prevails whilst Cartesian coordinateswork better to extract modal shapes with prevailingtranslation.

3.3 The finite element model

A FE model of the Chapel was prepared adopt-ing geometrical data of the model created using theRhinoceros3D programme by Arch. Abrardi and Arch.Gallo (May 2001). Their very accurate geometricalmodel, reproduced for the Sopraintendenza dei BeniArchitettonici, was simplified to build a numericalmodel with ADINA.

The bottom part of the model has a lower degreeof detail than the upper one. The base of the Chapelwas modelled to have a simplified distribution of themass and stiffness necessary to reproduce the iterationbetween the upper and the lower parts. The internalprovisional steel structure has not been modelled forthe sake of simplicity. The model is constituted of17334 nodes and 42019 elements, divided as reportedin Table 1.

The model was divided into 28 sub-structures.The assonometric projection of the model and itssubdivision in sub-structures are shown in Fig. 3.

The modal frequencies and mode shapes depend onvarious factors:

– the geometry and typology of the model;– the finite element mesh;– the mass and stiffness distribution.

The calibration of a numerical model cannot be con-duced adopting an arbitrary number of variables. Thenumber of parameters is influenced by the amountof experimental information. Choosing a larger num-ber of parameters than the identified frequencies and

Figure 3. Assonometric projection of the model and sub-division in sub-structures. Indication of the most sensitiveparameters.

Figure 4. The results of the parameters sensitivity analysis.

mode shapes leads to an ill-conditioned problem withresulting unreliable solutions.

For this reason, a preliminary sensitivity analysiswas performed to reduce the number of parameters.The elimination of some insensitive parameters alsopermits, on the one hand, to reduce the computationalweight and, on the other, to reduce the noise level.

The sensitivity analysis was performed modifyingthe parameters one by one, in a uniform way over adefined range and the obtained values were recorded.

The results are reported in Figure 4; the shown quan-tities are calculated as the mean of the ratio between thevariation of the modal properties (the first 5 frequen-cies) with respect to that of the parameters. The mostsensitive parameters are the numbers 19 (3DLivello02-2), 11 (Tamburo Esterno), 6 (Timpani) and, to lessextent, 18 (3DLivello03) and 12 (Tamburo Interno).

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All these parameters are found in the central and lowerpart of the structure. These parts in fact have a greaterinfluence on the global behaviour of the structure,mainly for the first modal shapes.

All the selected parameters are the Young’s Mod-ula of different sub-structures into which the modelwas previously divided. Each substructure is an axial-symmetric structure; this fact influences the behaviourof the structure, making it more regular in everydirection. To avoid this, a further subdivision of eachsub-structure into four different ones was made. Thissubdivision leads to an increase in the number ofselected parameters from 5 to 20 and is necessarybecause the data obtained in the identification stagehighlight a non axial-symmetric behaviour of thestructure.

3.4 The stochastic model updating

In order to solve the intrinsic problem of the solutionuniqueness and to treat error and uncertainty sourcesa stochastic “multiple-model” approach has beenadopted to update model parameters. This method canbe divided into the three following phases:

1. generation of a huge number of models varied onthe basis of some structural parameters through theminimization of objective functions that are able toexplore a consistent part of the solutions space;

2. selection, among all the generated models, ofthose which best fit the system behaviour with aprescribed level of accuracy;

3. analysis of the detected model properties and theirclassification through clustering techniques.

The adopted method implements the PGSL algo-rithm introduced by Smith (1998) which creates themodels and assigns them parameter values derivedfrom probability distributions. The principal assump-tion is that better points are likely to be found in theneighbourhood of families of good points. Hence, thesearch is intensified in regions containing good solu-tions. The search space is sampled by means of aPDF defined over the entire search space. Each axisis divided into a fixed number of intervals and a uni-form probability distribution is initially assumed. Asthe search progresses, the intervals and probabilitiesare dynamically updated so that sets of points are gen-erated with a higher probability in regions containinggood solutions.The search space is gradually narroweddown so that convergence is achieved.

The algorithm includes four nested cycles:

1. the Sampling Cycle, where a certain number ofmodels is generated and analysed through thetarget function, using the actual probability distri-bution. The Best Sample is selected, memorizedin the database and then used to recalculate theprobability distribution;

2. the Probability Updating Cycle, in which all theprobability distributions are updated as follows:the probability values of the sub-interval containingthe Best Sample selected in the preceding cycle andits neighbours are increased, while, the probabilitiesin the other regions are decreased.

3. the Focusing Cycle, which modifies the structureof the variation interval of each parameter in orderto focus the search near the actual best solution.

4. the SubDomain Cycle, which works on the solutionspace and increase the resolution in order to easethe confluence.

Each operation performed by the algorithm is man-aged by specific parameters which have to be cho-sen carefully because some of them present a highdependence on the considered problem.

In the case study, the Root Mean Square Errorbetween the identified and calculated frequencies isutilized as the objective function which has to be min-imized. At each step, a new parameter distribution iscreated by the algorithm and new model outputs areobtained. In order to match the numerical and exper-imental modal shapes, the MAC function, that givesa measure of similarity between two different modalshapes, is calculated.

The model generation procedure has been dividedinto two different phases, each one referred to a partic-ular objective functions. Firstly, the PGSL algorithmgenerates a huge number of models through the mini-mization of a function set on the first modal frequency,which is the best-identified in the dynamic tests. Thesecond objective function instead utilizes the firstthree model frequencies and mode shapes matched bymeans of the MAC function.This second step allows toselect only some of all generated models, while mod-els that have a higher value than a certain threshold areneglected.

All these selected models can be considered as rea-sonable candidates to represent the real building, buttheir large number makes necessary the application ofsome data mining techniques that can be applied todiscover different types of patterns in the model data.

The PCA (Principal Component Analysis) is per-formed to generate a new set of variables calledprincipal components that are linear combinations ofthe original ones. The goal of the PCA is to find asystem of principal components that are sorted so thatthe first components can explain most of the data vari-ance. In this way the number of dimensions can bereduced by choosing only the first two or three princi-pal components. Thus the original data are representedby a linear combination of the original parameters in anew and lower dimensional space. The application ofthe PCA and the examination of the first three prin-cipal components supplied an important result. Thefirst three principal components are not sufficient toexplain most of the data variance. For this reason it

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Figure 5. Percentage of the selected models which belongto each group.

is not possible to represent all data in a 3D referencesystem.

Finally, some clustering techniques have beenapplied to identify and collect models into groups. Theadoption of the k-means algorithm, which sub-dividesthe data into k subsets minimizing the distances withineach group and maximizing the distances between thek different groups, allowed the definition of 9 models.These models are the centroids of the 9 groups identi-fied by the k-means algorithm and can be consideredas the best candidates to represent the real structure.

The obtained results are reported in Figure 5, wherethe percentage of the selected models which belong toeach group is shown.

4 CONCLUSIONS

Some innovative techniques, which are able to assessthe structural health of monumental buildings, havebeen presented in this article. The application of thesemethods to the Holy Shroud Chapel in Turin was car-ried out in order to identify both their potentialitiesand limitations.

A brief description of the experimental campaign,carried out to acquired more detailed knowledge ofthe structural morphology, is first given. The dynamictest programme designed by the research group theauthors belong to is also presented and the differ-ent exciting sources adopted are listed. The resultsobtained with the TFIE modal identification methodare shown in the subsequent part of the paper. Thepowerfulness of this adaptive and robust tool is mainlydemonstrated by its ability to handle the non-stationaryacquired signals and to detect the first two flexionalmodes of the chapel, whose frequencies are very closeto each other. The numerical model of the building,

its subdivision into sub-structures and the sensitiv-ity analysis, performed in order to reduce the num-ber of the subsequently updated parameters, are alsoshown.

The last part of this study is focused on the devel-opment of a stochastic model updating technique. Theadopted approach is known as “multiple-model” dueto the fact that it generates a huge number of modelsto solve the problem of the impossibility to find anoptimal unique solution and to treat error and uncer-tainty sources. The PGSL algorithm is implementedin order to create these models and to assign parame-ter values derived from their probability distributions,progressively recalculated around those values whichminimize a target function.The application of this kindof model updating procedure raises the problem ofinformation redundancy, which can be faced throughthe adoption of some data mining techniques suchas the PCA and clustering. The final obtained resultsare some models that can be considered as reasonablecandidates to represent the real structure.

The models obtained from the updating procedurecan be considered as the starting point for the followingphase of damage detection and structural health assess-ment. It is now important to underline that these resultsare obtained from a linear analysis while damage anddegradation effects are strictly non-linear phenom-ena. Therefore, the subsequent numerical simulations,applied to identify symptoms which can reveal pos-sible damage scenarios on the construction, cannotdisregard these non-linear implications. The updatedmodels supplied by the multi-model approach repre-sent a useful resource in order to estimate the healthcondition of the building. Non-linear analyses per-formed on the obtained models can reveal the effectiveresidual performance the construction is still able toprovide for each damage scenario.

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