Experimental Investigation of the Feasibility of Using Acoustic Waves to Determine the Location of a...

8/9/2019 Experimental Investigation of the Feasibility of Using Acoustic Waves to Determine the Location of a Sound Source

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SkyGuard Enterprises253 Humpty WaySpringfield, NM 38492

October 15, 2013

To: Fred Armton, Vice President of Engineering Development

From: Ali Alhamaly

Subject: Experimental Investigation of the Feasibility of Using Acoustic Waves toDetermine the Location of a Sound Source

Summary and Introduction

As requested by the memo sent to us on August 27, 2013, we performed several teststo investigate the effectiveness of using acoustics waves to find the location of a soundsource. Based on our analysis, we came up with a calibrated algorithm that is both accurateand precise and is able to find the location of a sound source based on acoustics signals ofthree microphones. The algorithm is believed to be applicable for scaled-up applications withsome modifications. In addition, we have conducted a simple study to decide on the bestmethod to find the speed of sound. The study shows that the theoretical calculation of speedof sound is more accurate and also more practical.

The motivation behind this experimental work is to investigate the feasibility of usingacoustics measurements to detect the nuclear weapons testing in North Korea. The UnitedStates Air Force (USAF) has proposed an idea of using high altitude microphones to locatethe position of the nuclear testing. USAF has hired us to make investigations on small scalesetup to assess the feasibility of the proposed idea.

The main experiments that we have conducted are the speed of sound measurementand the determination of the location of a sound source using small microphones that arefraction of the size that will be used by USAF. The speed of sound measurement utilizes twosmall microphones that are mounted at a certain distant apart. In the location of a soundsource experiment, three microphones are used to detect the location of a sound source that ismounted on a wooden panel with the measuring microphones. In both experiments, theresults can be obtained by analyzing the acoustic signals of the small microphones involvedin each experiment.

The main result of our experimental investigation is the algorithm for finding thelocation of a sound source. The algorithm utilizes the acoustic signals of the measuringmicrophones along with simple mathematical relations that relate the location of themicrophones through the speed of sound in the medium to the actual location of the soundsource. In addition, speed of sound determination and analyzing acoustic signature of anaircraft are part of the results of this investigation.

This report presents the detailed experimental approach that was used to measure thespeed of sound and to conduct the sound source location experiment. The report starts bydescribing the experimental setup for all the experiments that were done including the testapparatus and the data acquisition system. Next, the report discusses the different methods ofcalculating the speed of sound with the uncertainty analysis for each method. The next

section presents our proposed algorithm and describes how it works and how it’simplemented. The section also presents the results of the algorithm and discusses the overall


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accuracy. In addition, full uncertainty analysis is provided for all the results of the algorithm. Next, we present the results of frequency decomposition of a sound signal. Finally, the reportdiscusses the extension of our algorithm into scaled-up applications.

Experimental Setup

This section presents the experimental apparatus and the test procedures that wereused to determine the location of a sound source. The section discusses the data acquisitionsystem, the speed of sound experiment and the microphone arrays experiment.

Exper iment Appara tus . The experiment that we have conducted is divided into twomain sections: the determination of the speed of sound and the determination of a soundsource spatial location. The basic idea behind the two experiments is the transmission andreceiving of acoustic waves. Several microphones were used to receive the sound wavesgenerated by different sources. The sound wave output signals from the microphones wereconnected to the National Instruments SC-2345 signal conditioning card. The output of theSC-2345 was connected to a data acquisition device in which the analog signals from themicrophones were sampled at 15 kHz. The digitized sampled data were recorded and stored

by using LabVIEW.The speed of sound experiment consists of two microphones mounted on a PVC

pipe and located 84 inches away from each other. The two microphones are connected to theDAQ system in order to record their output signals for later data processing. Figure 1 shows a

picture of the two microphones with the PVC pipe.

The sound source location experiment consists of 8’ x 4’ wooden panel in whichseveral small speakers are mounted behind it. In addition, 15 known location microphonesare also mounted on the wooden panel. The microphones are installed in three sets in whicheach set consists of five microphones. The output signal of the microphones can be connectedto the DAQ card to record the signals in LabVIEW. The maximum number of microphonesthat can be connected at the same time is three microphones. Figure 2 shows a picture of thewooden panel with the location of the 15 microphones.

Figure 1. Speed of sound test apparatus


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Test Procedu res . One of the objectives of the current investigation is to measure thespeed of sound. The speed of sound was measured utilizing the speed of sound apparatusshown in figure 1. The procedure for the test was fairly simple. A sound perturbation insidethe PVC pipe was produced by hitting the beginning the pipe with a wooden block. The hitcause a sound wave to propagate through the pipe. The sound wave is captured by the twomicrophones and the signal from the two microphones is recorded as well in LabVIEW. Thistest was repeated for five different times. The signal analysis of this experiment and the

calculation of the speed of sound will be discussed in the next section of this report.Additional to measure the speed of sound as discussed in the previous paragraph, the

speed of sound can be calculated theoretically by knowing the temperature of the air inlocation were the speed of sound is needed to be determined. For this reason, we recorded thetemperature of the lab room using a thermometer. Calculation of the theoretic speed of soundalong with a discussion of which method is preferred to obtain the speed of sound is includedin the next section of this report.

The second experiment that we conducted was the determination of a sound sourcelocation. The procedure of this experiment is as follows. From the different 15 microphonesthat we have on the wooden panel (figure 2), we chose a set of three microphones (onemicrophone from each section). These three microphones were then connected to the DAQcard to record their output signals. A small speaker mounted behind the wooden panel wasused to produce a sound wave and the three microphones set to record that sound wave. This

procedure was repeated again for five different times and all the data from the output signalswere record and stored by LabVIEW. Once we finished recording the five trials, a new set ofthree different microphones were used and the experiment was repeated again for the newmicrophones set. The two different microphone combinations that we have used were:(1,7,11) and (3,6,13).

The location of the small speaker was known for the first week of the experiment inwhich we used the known location to calibrate our algorithm that finds the location of thespeaker. In the second week of the experiment, the location of the speaker was unknown andit was our job to locate the speaker location using our calibrated algorithm.

Figure 2. Wooden panel with the mounted microphones for the sound source locationexperiment


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Speed of Sound Calculations

This section presents the calculations of the speed of sound using both the theoreticaland experimental methods. The section includes discussion about the use of the two

microphone signals to determine the speed of sound. In addition, this section presents thecalculation of the random and systematic uncertainties associated with measuring the speedof sound for both methods. The section concludes with our recommendation of which methodshould be used to find the speed of sound.

Experiment al Determin at ion of t he Speed of Soun d . The experimental techniqueof measuring the speed of sound relies on the simple concept of measuring the timedifference of arrival between two microphones. The time difference of arrival can be obtainedeasily by analyzing the output acoustic signals of the two microphones that were recordedduring the speed of sound experiment. Once the time difference between the twomicrophones is determined then the speed of sound can be calculated by dividing the distance

between the two microphones by the time difference of arrival. Mathematically the speed ofsound is given by

=∆ Where d is the distance apart between the two microphones and Δt is the time difference ofarrival between the acoustic signals between the two microphones. The distance between thetwo microphones was 84 inches.

As mentioned earlier, the time difference in equation 1 can be obtained by looking atthe acoustic signals form the two microphones and what we expect to see is a two verysimilar signals that are shifted slightly in time from each other and hence the time difference

between the two signals can be found by comparing two similar pattern between the twowaves like a valley for instance. It’s known that a sound wave propagating through a mediumcreates a low pressure region upstream of the wave front, and hence whenever we notice adrop in the signal amplitude for any microphone we can tell that the sound wave just passed

by that particular microphone. This observation is used to find the sound wave time of arrivalfor each microphone. An important comment here is that knowing the exact time of arrivalfrom the signal is a little bit tricky because it’s hard to know what value of drop in magnitudeshould be used to identify the arrival of the sound wave because it’s dependent on the actualresponse of each microphone. For this reason we used the first valley in the signal for each

microphone to find the time difference of arrival and this should be sufficient to find the timedifference because we noticed the same valley pattern for both microphones. Figure 3 showsthe output signal of the two microphones from the speed of sound experiment. The figureshows that the two signals are similar and that they are shifted by some time, this timedifference is found by locating the time of first valley in the both signals as marked in thefigure.

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The speed of sound experiment was repeated for five different times as mentionedearlier in the test procedures. The results of the five trials are summarized in table 1. Table 1shows the time difference between the two signals for each trail along with the calculatedspeed of sound using equation 1. It’s worth to notice that the five different signals that weobtained are very similar and they show the same pattern as figure 3. For this reason, thesignals for the other four trials are not shown and only the time difference results are givenwithin table 1. The results of table 1 indicate that the mean value of the speed of sound is13830 in/s. Sample calculation of the results shown in table 1 is included in appendix A.

Table1. Main results of the speed of sound experiment for the five different trials

Trial#

Time differenceΔt (s)

Speed ofsound c (in/s)

1 0.00607 13838.552 0.00612 13725.493 0.006048 13888.894 0.0060699 13838.785 0.0060609 13859.09

Theoret ical Determinat ion of th e Speed of Soun d . The speed of sound for an idealgas is derived from the assumptions that the pressure and temperature variations of the gasacross the sound wave are vanishingly small because the sound wave is assumed to beinfinitesimally thin and has infinitesimal strength. These assumptions lead the sound wave to

be an isentropic perturbation process. The speed of sound theoretic relation with the abovementioned assumptions for ideal gas is given by

= Where c is the speed of sound, γ is the specific heat ratio and for the case of air within thetemperature range that we conducted our experiment it’s equal to 1.4, R is the gas constantand for air its 287 J/kg K and T is the absolute temperature of the air. From equation 2 it can

be seen that the only parameter that need to be measured is the temperature of the room in

Figure 3. Near and far microphone output signals for speed of sound experiment.

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which the experiment is held at. The temperature of the room in which we performed theexperiment was 25 C which corresponds to 298 K. this leads using equation 2 to a speed ofsound of 13623 in/s. sample calculation of using equation 2 to find the speed of sound can befound in appendix A.

Unc ertain ty Calculat ions of the Experimen tal Speed of Sound . Due to thelimitation in accuracy of the instruments that we used in the lab to measure the speed ofsound, there is definitely uncertainties associated with the final reported numbers. Theseuncertainties are divided into random and systematic uncertainties. The random uncertainty isa measure of the precision of the data collected, where the systematic uncertainty is ameasure of the accuracy of the measurement.

The measurement uncertainty of the measured speed of sound comes from the factthat we had uncertainties in the measuring instruments. From equation 1, it can be seen thatthe speed of sound depends on the measurements of the distance and time. The uncertainty inthe measured distance between the two speakers was 1/32 inches. The uncertainty of themeasured time in our instrumentation was 1/30000 seconds. This can is found from thesampling frequency that we used. The sampling frequency that we used was 15 kHz, whichmeans that there is a time difference of 1/15000 seconds between each time measurement inthe DAQ system we used. Since the uncertainty in the measurement is half the resolution ofthe instrument, hence the time uncertainty will be .5*(1/15000) which is 1/30000 seconds asmentioned above. From these uncertainties, we need to find the total propagated error in themeasurement of the speed of sound. In order to do this we need to use the error propagationformula which is given by

= ±∑

Where u c is the measurement uncertainty of the speed of sound, is the derivative of the

speed of sound with respect to an independent variable (in our case the variables are eitherthe distance or the time) and is the measurement uncertainty of the independent variable.As mentioned above u d = 1/32 inches and u Δt = 1/30000 seconds. Equation 3 appliedspecifically to the speed of sound formula (equation 1) yields the following expression

= ± ∆ 2 ∆∆ We can see from equation 4 that the uncertainty of the speed of sound will have differentvalue for each trail that we conducted. This is because of the term ∆ in the equation inwhich it varies from trail to trail. However, this variation is very small and any trialcalculation will yield almost the same value of the uncertainty. Table 2 shows the calculationof the uncertainty in the speed of sound for each trial. Sample calculation of the uncertainty is

provided in appendix A.

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Table2. Measurement uncertainty of the speed of sound for the five different trials

Trial # Speed of sounduncertainty u c (in/s)

1 107.59

2 105.843 108.374 107.595 107.91

As can be seen from table 2, all the uncertainties are very close to each other as expected. Inorder to be conservative, we decided to take the largest value as the representativemeasurement uncertainty, and hence the measurement uncertainty in the speed of sound is108.4 in/s.

The random uncertainty in the measurement of the speed of sound can be found usingthe standard error. The standard error is given by

=√ Where is the standard error in the speed of sound measurement, σ is the standard deviationof the speed of sound measurements and N is the number of trials. The standard error in ourmeasurement of speed of sound is 27.8 in/s. sample calculation of the standard error can befound in appendix A.

The mean value of the speed of sound from our measurement is 13830 in/s. this valueis accompanied by measurement uncertainty of 108.37 in/s and random uncertainty of 27.8in/s. the low value of the random uncertainty indicates high precision in the measurement ofthe speed of sound. The measurement uncertainty is a reflection of the accuracy of theinstruments that we have used to measure the speed of sound and the value 108.37 in/s can beimproved by increasing the accuracy of the used instrumentation.

Unc ertain ty Calculat ions of th e Theoret ical Speed of Soun d . The uncertaintycalculation of the theoretical speed of sound follows exactly same procedure as theuncertainty in the experimental speed of sound. The only difference is the parameters thatlead to uncertainty in the speed of sound. To find the measurement uncertainty, equation 3 isapplied again but this time to equation 2. The expression of the measurement uncertainty is

= ± √ uT is the measurement uncertainty of the thermometer we used and it has a value of 1K. Inequation 6 we assumed that the measurement uncertainty in γ is very negligible. This is

justifiable because γ has a constant value over the range of temperatures that we performedthe experiment. This means that the derivative of γ with respect to temperature is almost zeroand hence we can ignore its uncertainty.

The measured temperature was 298 K , γ = 1.4 and R = 287 J/kg K . these values givemeasurement uncertainty in the theoretic speed of sound of 23 in/s. using equation 2 the

theoretic speed of sound is 13623 in/s. During the experiment that we have conducted, wemonitored the thermometer to see if the temperature changed from 298 K, but the

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1= 1 0 2= 2 0 3= 3 0

Where c is the speed of sound, t0 is the time that the sound source emits the sound wave andt1, t2 and t3 are the times that microphones 1, 2 and 3 received the sound wave that wasemitted by the sound source. Substituting equations 10-12 into 7-9 gives

1 1 = 1 0 2 2 = 2 0 3 3 = 3 0

What is unique about equations 13-15 is that they contain only three unknowns, namely xs,ys and t0. The speed of sound can be found using temperature measurements as wasdescribed in the speed of sound calculations section. The three times t1, t2 and t3 can befound by analyzing the output signals from the three microphones. As described in the speedof sound calculations section, the time of arrival of the sound wave can be known by locatingthe time of the first drop in the amplitude of the output time series signal. It was alsoexplained in the same section that finding the time of arrival from the time series signal istricky and has large uncertainty due to the unknown precise criteria for choosing the locationof first drop. The same argument holds for this situation as well and hence the time of arrivalfor each signal is hard to know. For this reason, the times t1, t2 and t3 will be modified byadding a constant time to each one them. This modification allows us to choose a time on theoutput signal of the microphones that is easily recognizable and can be repeatedly chosenfrom a different set of measurements. This modification in the timing can be justified by thefollowing argument. In equations 13-15, the right hand side is always a function of thedifference between the receiving time and the transmitting time. Hence, if we add a constanttime to both the reviving time (t1 for example) and the transmitting time t0, then thedifference t1-t0 will still be the same and hence for equations 13-15 the right hand side willalways have the same value whether we added a constant time or not. From this we can seethat the values of xs and ys will be the same with or without the constant addition. It is worthto notice here that this modification will alter the value of t0 for its true value and will makeit larger than reality, but in our case we are not interested in the value of t0 and we are onlyconcerned with the values of xs and ys because they give the location of the unknown sourcedirectly. It’s important in this modification that the added time constan t be the same for thethree signals, otherwise this method won’t work and will yield to wrong results. The way thatwe insured that the added time is the same for all the three signals is by choosing a distinctivefeature in the signal that shows up in all the microphone signals. Figure 4 shows a plot of thetime series signal for the three microphones and points out the time locations that we chosefor each of the three microphones.

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The values of the three times that we get from the output signals are given as inputs toequations 13-15, where t1 is the time for the right microphone, t2 is the time for the middlemicrophone and t3 is the time for the left microphone. With these inputs, equations 13-15 areready to be solved for the values of xs and ys. Since equations 13-15 are nonlinear, then ananalytical solution to these equations is hard to obtain. For this reason, equations 13-15 are

solved using a nonlinear numeric solver in MATLAB.Known Speaker Loca t ion Resul t s . The first part of the determination of a sound

source expriment was to test the algorithm with known source location to see how accuratethe algorithm is in finding the source location. The source location was at (47,38) inches. Asdescribed in the test producers section, we used two different microphone sets (1,7,11) and(3,6,13) to test our algorithm and for each microphone set we repeated the expriment for 5different times to assess the precision of our algorithm. Table 3 shows the results of thealgorithm for the two set of microphones and all the trials. While processing the 5 differenttrials for both microphone sets, we noticed a bad output signal for each set of microphones.The results of these trials are not included because they are outlier due to the odd behavior of

the signal for that particular trial. Hence table 3 shows only 4 trials of the data instead of 5.

Table3. Results of the location of the sound source

Trial#

Set 1microphones xs

(in)

Set 1microphones ys

(in)

Set 2microphones

xs (in)

Set 2microphones

ys (in)1 47.1 38.4 47.7 36.02 47.1 38.4 47.1 36.53 47.5 36.2 47.1 36.54 47.6 36.2 47.7 36.0

Figure 4. Output signals form the three microphones.


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As can be seen from the results in table 3, the algorithm shows a good accuracy infinding the actual location of the sound source for both microphone sets with set 1 (1,7,11)

being advantageous on set 2 (3,6,13). In addition, the algorithm shows a consistency in theresults from trial to trial.

Unc ertain ty Calcu lat ions of th e Know n Speaker Locat ion . The measurementuncertainty of the calculated position of the sound source comes from the uncertainty ofspeed of sound and the uncertainty in the measured time. Equations 13-15 can be seen as ageneral function in which it takes four inputs (c,t1,t2 and t3) and gives two outputs (xs andys). Since each input has uncertainty in it, then we would expect that these uncertainties

propagate through the output results. Let’ s denote our general function that is represented bythe solution of equations 13-15 by f(c,t1,t2,t3) where f is a two dimensional vector valuedfunction since it gives two outputs for the same set of inputs, then the uncertainty in f due touncertainties in its inputs argument is given by the general equation

= ±∑

Where u xi is (u c , u t1, ut2, ut3). From the uncertainty calculations of the speed of sound, we gotthat u c = 23 in/s and u t = 1/30000 seconds. In order to use equation 16 to get the measurementuncertainty in the calculated position of the sound source, the derivative of f with respect toeach input variables need to be found. Since f is not known analytically, then these derivativeneed to be estimated numerically. The method we chose to estimate the derivative is thesequential perturbation method. The sequential perturbation method estimates the change inmultivariate functions by perturbing each independent input variable by its own uncertainty.For instance, this method estimates the term (which is the change of f due to the

uncertainty in the speed of sound) in equation 16 by

≈+, , ,−−, , , Similarly, the term is estimated by

≈, +, ,−, − , , Equations 17 and 18 can be applied to the rest of the variables in the function f, and by doingthat the terms in equation 16 can be all estimated and hence the measurement uncertainty inthe position of the sound source can be obtained. The sequential perturbation calculations isobtained using a simple code in MATLAB that we developed, this code utilizes the nonlinearnumerical solver function provided by MATLAB. A copy of the code is included inAppendix B. Table 4 shows the results of measurement uncertainty calculations for thelocation of the sound source for both microphone sets and for each trial. u xs is themeasurement uncertainty in the x position of the source and u ys is the measurementuncertainty in the y position of the source.

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Table4. Measurement uncertainty in the known location sound source using perturbationmethod

Trial#

Set 1microphones u xs

(in)

Set 1microphones u ys

(in)

Set 2microphones

uxs (in)

Set 2microphones

uys (in)1 0.358 0.682 0.352 0.6322 0.358 0.683 0.353 0.6413 0.351 0.642 0.353 0.6414 0.351 0.641 0.352 0.632

The random uncertainty in the results can be found using equation 5 which is the standarderror in the measurement. Table 5 summarizes the random uncertainty calculations of theresults from table 3. Table 5 shows the mean value of the position of the sound source fromthe different trials reported in table 3 along with the standard error in each calculated meanvalue.

Table5. Uncertainty summary from the results in table 3

Set 1microphones xs

(in)

Set 1microphones ys

(in)

Set 2microphones

xs (in)

Set 2microphones

ys (in)Meanvalue 47.35 37.37 47.43 36.29

Standarderror .1434 0.6243 .1679 0.1274

We would like to summarize the uncertainty calculations by finding the random, systematicand measurement uncertainties in the radius instead of the x and y coordinate. The radius ofthe sound source location is given by

= Using equation 19 and the results of table 3, we can get the calculated radius of the soundsource location. Table 6 summarizes the results

Table6. The radius of the sound source

Trial#

Set 1microphones Rs

(in)

Set 2microphones Rs

(in)1 60.8 59.82 60.8 59.63 59.8 59.64 59.8 59.8

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The random uncertainty in the results of table 6 can be found using equation 5. Themeasurement uncertainty of the radius can be found by using equation 16 applied to equation19. The measurement uncertainty expression is given by

=( +) ( +)

Where u Rs is the measurement uncertainty in the radius. The values in the right hand side ofequation 20 are obtained from table 4 for the trial that has the largest measurementuncertainty. The systematic uncertainty of the radius is defined as the absolute value meanvalue of the radius minus the true value. The true value of the radius for the sound source is60.44 in. table 7 summarizes the uncertainty calculation for the radius.

Table7. Uncertainty summary of the sound source radius

Set 1microphones

(in)

Set 2microphones

(in)Mean value 60.32 59.72

Standarderror .27 0.06

Measurementuncertainty .51 .48Systematic

uncertainty .11 .72

At the end of this section, we want to show that our choice of the speed of sound methodwhich is the theoretical calculation is justified by comparing the results of the radius usingthe experimental speed of sound and the theoretical speed of sound. Table 8 shows thecomparison in radius for set 1 microphone using both calculation methods.

Table8. Comparison of speed of sound calculation method

Trial

#

Theoretical

speed of soundRs (in)

Experimental

speed of soundRs (in)

1 60.8 59.72 60.8 60.73 59.8 59.74 59.8 59.7

Meanvalue

60.32 60

From table 8, we can see that the radius results obtained using the theoretical speed of sound

are more accurate that the results obtained by experimental speed of sound. For this reason

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and for the reasons discussed earlier in the uncertainty of the speed of sound, we recommendusing the theoretical speed of sound.

Unk nown Speaker Loca t ion Resul t s . The second part of the determination of a soundsource expriment was to use the calibrated algorithm with known source location to locate the

position of the unknown speaker. The experiment was done identical to the known speakerexpriment in terms of the number of trials and the microphone sets that was used. Similar tothe known speaker data, we have found bad signals while processing the output microphonesignals and hence the results of only four trials are shown because the fifth trials led to outlierresult. Table 9 shows the results of the algorithm for four trials and both microphone sets.

Table9. Results of the position of the unknown location sound source

Trial#

Set 1microphones xs

(in)

Set 1microphones ys

(in)

Set 2microphones

xs (in)

Set 2microphones

ys (in)1 60.26 36.01 60.17 35.842 59.87 35.61 60.17 35.843 63.06 32.29 59.59 36.544 59.65 36.70 63.27 31.16

Unc ertain ty Calculat ions of the Unk now n Speaker Locat ion . Following the samecalculation methods as in the known speaker experiment, table 10 summarizes themeasurement uncertainty calculations.

Table10. Measurement uncertainty in the unknown location sound source using perturbation method

Trial#

Set 1microphones u xs

(in)

Set 1microphones u ys

(in)

Set 2microphones

uxs (in)

Set 2microphones

uys (in)1 0.376 0.677 0.387 0.6582 0.375 0.666 0.387 0.6583 0.422 0.670 0.382 0.6604 0.373 0.682 0.432 0.671

The random uncertainty calculations are done identically to what has been done in the known

speaker location. Table 11 summarizes the random uncertainty calculations.Table11. Random uncertainty summary from the results in table 9

Set 1microphones xs

(in)

Set 1microphones ys

(in)

Set 2microphones

xs (in)

Set 2microphones

ys (in)Meanvalue 60.71 35.16 60.81 34.85

Standarderror .7946 0.6243 .9797 1.24


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demonstrated in the previous sections the feasibility of our approach to find the location of asound source. Furthermore, we have shown that the method is both accurate and precise (theaccuracy is less than 1 inch). That being said, we believe that more investigation is needed

before the method be completely suitable for scaled up application. In the following paragraph, we discuss some of the areas that need carful investigation before calling the

algorithm suitable.With the small-scale setup, we have seen how accurate the algorithm is, but it is hard

to estimate the accuracy in scaled-up application because we cannot just simply assume thatthe accuracy scale linearly. This means that the ratio of how off the algorithm was from thetrue value compared to the total area covered by the microphones is probably not constant,and hence we cannot scale the ratio to find what the accuracy would be in the case of scaled-up applications. Another issue with scaled-up application is the variation of the temperature

between the sound source location and the microphone reviving location. This temperaturevariation will lead to different sound speed between the source and reviving station whichwill ultimately leads to inaccuracy in the location detection. For this reason, the sensitivity ofthe speed of sound on the results needs to be investigated to determine how to account for thevariation in the sound speed. Another issue that needs to be addressed is the attenuation anddistortion of the sound wave through large distances, which is a factor we didn’t investigatedue to the small-scale setup that we have . It’s necessarily to know the properties of the waveform received at large distance from the source location. One last comment that needs to beconsidered for scaled-up application is the need to use four microphones instead of three.This is necessary because the sound source and the reviving microphones lay in differentvertical planes, and hence a fourth microphone is needed to capture the out of plane distance.

With carful investigation of the above mentioned factors, our algorithm presents a fastway to determine the location of a sound source. The advantage of our method is that it can

be fully automated and hence instant feedback can be obtained easily.We want also to mention the fact that our algorithm can be used with some

modifications in other applications such as in exploration geophysics, in which sound wavesreflected from different surfaces from the earth ground can be analyzed to determine thesurface location.

Conclusions

The main focus of this experimental work was to investigate the effectiveness ofusing acoustics waves to find the location of a sound source. Several testing have beenconducted in order to assess the feasibility of the proposed method. I t was shown that the

acoustics waves can be used effectively to find the location of a sound source.Speed of sound was determined experimentally and theoretically. The experimentalmean value of the speed of sound was 13830 in/s while the theoretical calculation of thespeed of sound indicated a value of 13623 in/s. uncertainty study has been done on both theexperimental and theoretical speed of sound and we showed that the theoretical speed ofsound has less measurement uncertainty than the experimental speed of sound. In addition, itwas shown that the accuracy of determining the sound source location is higher when thetheoretic speed of sound is used. For these two reasons, we recommend using the theoreticalspeed of sound on the experimental approach.

We presented an algorithm in which it uses the acoustic signals of severalmicrophones to detect the location of a sound source. We showed that the algorithm has

location error of less than 1 inch based on a known source calibration study. The algorithmwas used to determine unknown speaker location and the result of the location was found to


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be (60.71,35.16) inches. The extension of our algorithm to scaled-up applications wasdiscussed and it was recommended that more investigation is needed before applying thisalgorithm into scaled-up application. Some of the issues we have identified with scaled-upapplications include: accuracy estimation, variation of the speed of sound between the sourceand microphone and the need of four microphones instead of only three. Once these are

resolved and accounted for, then our algorithm should be a fast way to determine the locationof a sound source. In addition, the algorithm has the advantage of being able to be fullyautomated by clever signal processing techniques.

Finally, we identified aircraft type and its component using the acoustic signature of arecorded sound of an aircraft. The aircraft was found to be the USSR Antonvov. Thefrequency decomposition of the acoustic signal indicated also a Weldon fuel pump andAirborne fuel pump.

Attachments:

Appendix A: Sample calculationsAppendix B: MATLAB codes


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Appendix A: Sample Calculations

This appendix presents sample calculations for the speed of sound using both theexperimental and theoretical techniques. In addition, the appendix provides sample

calculations for the measurement and random uncertainties of the speed of sound.

A-1: Experimental Speed of Sound Calculations

This sample calculation is based on the numbers in the first trial of table 1. The speedof sound is given by

=∆=. =13838.55 A-2: Theoretical Speed of Sound Calculations

The theoretical speed of sound is given by

= = 1.4 287 25 273. =13623 A-3: Measurement Uncertainty of the Experimental Speed of SoundCalculations

This sample calculation is based on the numbers in the first trial of table 1. The

measurement uncertainty is given by

= ± ∆ 2 ∆∆ =± 1320.00607 s2841300000.00607 s=107.59

A-4: Standard Error of the Experimental Speed of Sound Calculations

This sample calculation is based on the numbers in table 1. The standard error is given by

= −∑

=13838.55 13725.49 135 =13830

(A-1)

(A-2)

(A-3)

A-4


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= 14 5[13838.55 1383013725.49 1383013888.89 1383013838.78 1383013859.09 138] =27.8

A-5: Measurement Uncertainty of the Theoretical Speed of Sound Calculations

The measurement uncertainty is given by

= ± √ =±. + 1 . =22.85 (A-5)


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Appendix B: MATLAB Codes

This appendix presents the MATLAB code that was used in the location findingalgorithm. In addition, this appendix presents the MATLAB code for doing the sequential

perturbation.

clear all clc close all % comb1 11,7,1 % comb2 13,6,3 % comb3 15,9,5

% 1 = right

% 2 = middle % 3 = left

% load the sound signals load acoustic.mat

X = zeros(5,2); Y = zeros(5,2); uX = zeros(5,2); uY = zeros(5,2); %%

data = comb2run4; t =data(:,1); spanplus = .005; spanminus = .01; %% this removes the unwanted signal and define new time and amplitudevectors

diffe1 = diff(data(:,2))./diff(data(:,1)); [C,idx] = max(diffe1); idx2 = find(t>t(idx)+spanplus, 1, 'first' ); idx1 = find(t>t(idx)-spanminus, 1, 'first' ); sig1 = data(idx1:idx2,2);

tnew1 = data(idx1:idx2,1); diffe2 = diff(data(:,4))./diff(data(:,1)); [C,idx] = max(diffe2); idx2 = find(t>t(idx)+spanplus, 1, 'first' ); idx1 = find(t>t(idx)-spanminus, 1, 'first' ); sig2 = data(idx1:idx2,4); tnew2 = data(idx1:idx2,1);

diffe3 = diff(data(:,6))./diff(data(:,1)); [C,idx] = max(diffe3); idx2 = find(t>t(idx)+spanplus, 1, 'first' ); idx1 = find(t>t(idx)-spanminus, 1, 'first' );

sig3 = data(idx1:idx2,6); tnew3 = data(idx1:idx2,1);


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%% plot the three signals to choose the time location figurehold on plot(sig1, '-xr' ) plot(sig2, '-xb' ) plot(sig3, '-xk' ) legend( 'right =1' , 'middle =2' , 'left =3' ) %%

% the time values for each of the microphone in.t1 = tnew1(159); in.t2 = tnew2(159); in.t3 = tnew3(160);

% speed of sound in/s in.c = sqrt(1.4*287*(25+273))*39.3701; in.comb = 2; % random uncertainty in timein.ut = 1/30000 ;% random uncertainty in speed of sound in.uc = 22.86;

% function that calculates the location of the speaker and performsequential perturbation to find random uncertainty in the found location[x,deltaR] = locaation(in)

Locaation function

function [x,deltaR] = locaation(in)

options = optimset( 'Display' , 'off' );

comb = in.comb; % the function takes the three times + the speed of sound to find the % speaker locationt1 = in.t1; t2 = in.t2; t3 = in.t3; c = in.c; ut = in.ut; uc = in.uc;

if comb ==1

% comb 1 x0=[47;38;1.71]; % 3 equations to solve for the location F = @(x)[sqrt((89-x(1))^2 + ((39+(3/8))-x(2))^2)-c*(t1-x(3)); ...

sqrt((53-x(1))^2 + (8-x(2))^2)-c*(t2-x(3)); ... sqrt((9-x(1))^2 + ((21)-x(2))^2)-c*(t3-x(3))];

x = fsolve(F,x0,options);

% sequential perturbation calculations% t1 perturbation t1 = in.t1 + ut;

x0=[47;38;1.71];


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F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ... sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ... sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))];

y= fsolve(F,x0,options); deltaR1P = y; t1 = in.t1 - ut;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ... sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ... sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))];

y= fsolve(F,x0,options); deltaR1N = y; deltaR1 = .5*(deltaR1P - deltaR1N); t1=in.t1;

% t2 perturbation t2 = in.t2 + ut;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ...

sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ... sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))]; y= fsolve(F,x0,options); deltaR2P = y; t2 = in.t2 - ut;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ...

sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ... sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))];

y= fsolve(F,x0,options); deltaR2N = y; deltaR2 = .5*(deltaR2P - deltaR2N); t2=in.t2;

% t3 perturbation t3 = in.t3 + ut;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ...


y= fsolve(F,x0,options); deltaR3P = y; t3 = in.t3 - ut;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ...

sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ...

sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))]; y= fsolve(F,x0,options); deltaR3N = y; deltaR3 = .5*(deltaR3P - deltaR3N); t3=in.t3;

% c perturbation c = in.c + uc;

x0=[47;38;1.71]; F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ...


y= fsolve(F,x0,options); deltaR4P = y; c = in.c - uc;

x0=[47;38;1.71];


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F = @(y)[sqrt((89-y(1))^2 + ((39+(3/8))-y(2))^2)-c*(t1-y(3)); ... sqrt((53-y(1))^2 + (8-y(2))^2)-c*(t2-y(3)); ... sqrt((9-y(1))^2 + ((21)-y(2))^2)-c*(t3-y(3))];

y= fsolve(F,x0,options); deltaR4N = y; deltaR4 = .5*(deltaR4P - deltaR4N);

c=in.c; deltaR = (deltaR1. 2̂ + deltaR2.^2 + deltaR3.^2 + deltaR4.^2).^.5;

Experimental Investigation of the Feasibility of Using Acoustic Waves to Determine the Location of a...

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