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INCLUSION OF PAGE METHOD WITHIN THE TWO-POINT IN SITU METHOD

FOR DETERMINING SOUND POWER LEVELS

by

Christopher R. Reynolds

A senior thesis submitted to the faculty of

Brigham Young University - Idaho

in partial fulfillment of the requirements for the degree of

Bachelor of Science

Department of Physics

Brigham Young University - Idaho

April 2018

BRIGHAM YOUNG UNIVERSITY - IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by


This thesis has been reviewed by the research advisor, research coordinator,and department chair and has been found to be satisfactory.

Date Jon Paul Johnson, Advisor

Date Richard Datwyler, Comittee Member

Date Ryan Nielson, Comittee Member

Date David Oliphant, Comittee Member

Date Stephen McNeil, Department Chair

Date R. Todd Lines, Senior Thesis Coordinator

ABSTRACT

INCLUSION OF PAGE METHOD WITHIN THE TWO-POINT IN SITU METHOD

FOR DETERMINING SOUND POWER LEVELS


Department of Physics

Bachelor of Science

The Acoustical Group at the Brigham Young University Physics department

has developed a new technique for processing sound. The Phase and Ampli-

tude Gradient Estimator (PAGE method) has been shown to correctly calcu-

late intensity and energy in a plane-wave tube[6].

Industrial manufactures currently have a few simple ways to test the sound

pollution of their large equipment. While there are International Standards in

place, they are extremely difficult to meet and follow. There has been work

done at Brigham Young University to try and implement a cheaper, faster,

and more efficient form of determining sound power level.

This thesis looks into the research and results of adding the PAGE meth-

ods into the Two-Point In Situ method, as well as an analysis of the PAGE

method’s ability to calculate energy density inside of a reverberation chamber.

It will also test the Two-Point In Situ with a less-than ideal sound source.

ACKNOWLEDGMENTS

First, I would like to acknowledge my wife, Cameo. She pushed me to

pursue Physics when I didn’t know what direction to take. Over the past 5

years she has sacrificed a lot for my educational pursuits. I would not have

achieved so much without her support.

Secondly, I would like to acknowledge the faculty of the BYU-Idaho Physics

Department. Their willingness to provide guidance in course work, research

projects and career advice has been priceless. I have developed a special skills

and abilities because of their teachings.

Thirdly, I would like to express my gratefulness towards Dr. Scott Sommer-

feldt, graduate students Caleb Goates and Travis Hoyt for their guidance and

assistance during this research. I would like to also acknowledge Dr. Kent Gee

and Dr. Tracianne Neilsen for their assistance and direction given. I would

like to express my appreciation towards the Acoustics group at Brigham Young

University for their support with facilities and equipment.

Lastly, I would like thank the National Science Foundation for providing

the funding for the REU program at Brigham Young University under the

contract PHY-194312.

Contents

Table of Contents xi

List of Figures xiii

1 Introduction 11.1 Standards for Industry . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Background 32.1 Background of the ISO 3741 Standards . . . . . . . . . . . . . . . . . 32.2 Background of the Two-Point In Situ Method . . . . . . . . . . . . . 4

2.2.1 Calculating the Room Constant . . . . . . . . . . . . . . . . . 42.2.2 Calculating the Directivity Factor . . . . . . . . . . . . . . . . 52.2.3 Calculating Sound Power . . . . . . . . . . . . . . . . . . . . . 5

2.3 Theory - PAGE Method . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Experimental Procedure 93.1 Signal Processors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Setup for the Unknown Sound Source . . . . . . . . . . . . . . . . . . 103.3 ISO 3741 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Two-Point In Situ Measurements . . . . . . . . . . . . . . . . . . . . 11

4 Results 154.1 ISO 3741 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Two-Point In Situ and PAGE . . . . . . . . . . . . . . . . . . . . . . 164.3 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.1 Addition of Water . . . . . . . . . . . . . . . . . . . . . . . . 184.3.2 Error Calculations . . . . . . . . . . . . . . . . . . . . . . . . 194.3.3 Error in Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Future Research 235.1 Error with Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2 PAGE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

xi

xii CONTENTS

5.3 Two-Point In Situ Method . . . . . . . . . . . . . . . . . . . . . . . . 25

A Two-Point In Situ AFR 27

B Two-Point In Situ - Pulse 39

C ISO 3741 57

Bibliography 64

Index 66

List of Figures

2.1 This table shows how the PAGE and Traditional methods differ incalculating the PED and KED. . . . . . . . . . . . . . . . . . . . . . 6

3.1 ISO 3741 standard measurement setup with the blender under load.The location of the 6 microphones were in accordance to the ISO 3741. 11

3.2 Microphone probe spacer is 2.5 cm for a total of 5 cm between micro-phones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 A setup for the Two-Point In Situ method. The arrow A shows theprobe’s location in the near-field for the reference source, and in the far-field for the unknown source. The arrow B shows the string connectingthe two sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 ISO 3741 results for the blender base and under load. . . . . . . . . . 164.2 ISO 3741 results are compared with the Two-Point In Situ results for

the blender under no load. At this location the calculated sound powerwas closer to the averaged for both the Traditional and PAGE methods. 17

4.3 ISO 3741 results are compared with the Two-Point In Situ methodresults for the blender under load. . . . . . . . . . . . . . . . . . . . . 18

4.4 Confirmation of the Pulse system vs Acoustic Field Recorder. Thismeasurement only validates that the computational code worked asexpected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.5 Probe was located in a resonance point both the Traditional and PAGEmethod performed poorly. . . . . . . . . . . . . . . . . . . . . . . . . 21

5.1 Two-Point In Situ calculation using the Narrow Band frequencies re-turned by the Pulse system with functions written by the PAGE team. 24

5.2 Two-Point In Situ calculation using the One-Third-Octave frequenciesreturned by the Pulse system with functions written by the PAGE team. 24

xiii

Chapter 1

Introduction

1.1 Standards for Industry

Sound power can be defined as the total sound energy emitted by a source per time[1].

Sound power is reported at different frequency levels determined from sound pressure

measurements[3]. Legislation and health administrations have set safety regulations

regarding the sound radiation produced by industrial equipment[1]. When possible,

manufacturers will measure and publish the sound power levels[2] in order to ensure

that the sound produced by the equipment they produce is in accordance with those

regulations. International Standards have been setup that dictate the necessary steps

for determining the sound power levels of equipment by using sound pressure. Manu-

facturers can take their measurements inside of a reverberation chamber that follows

the requirements listed in the International Standards[3]. If measurements are made

in accordance to the International Standards for sound pressure measurements inside

of a reverberation chamber, known as the ISO 3741, the standard deviation in the

results can be expected to be below the standard deviations given in the standard[3].

1

2 Chapter 1 Introduction

1.2 Previous Work

Brigham Young University’s Physics department has an acoustics research group with

a team working on methods to determine sound power levels that are not as difficult as

the ISO 3741. This method is called the Two-Point In Situ method[4][2][5]. They are

able to calculate the sound power levels of an ideal sound source inside a reverberant

environment with values of under 1 dB for the standard deviation[4][2].

Another team in the acoustics research group is working on developing new pro-

cessing methods to processes the data collected from the sound pressure measure-

ments. This new process is called the PAGE method (Phase and Amplitude Gradient

Estimator). Their research has shown that the PAGE method more accurately cal-

culates the sound intensity, and energy density of anechoic plane waves[7][6].

1.3 Objectives

There were two primary objectives of this research. First was to test the PAGE

method’s ability to calculate energy density inside a reverberant environment. The

second objective was testing the Two-Point In Situ method with a less-ideal sound

source.

Chapter 2

Background

2.1 Background of the ISO 3741 Standards

The properties of a room will affect the sound pressure and therefore will affect

the sound power level calculations. Ideally, a reverberation chamber creates a diffuse

environment for the sound field. In a diffuse environment, the locally averaged energy

density is distributed equally throughout the room. With these ideal conditions, the

sound power is proportional to the spatially averaged energy density[2]. However,

this ideal situation rarely exists.To correct for gaps between this ideal and the real

world, the ISO 3741 has a specific method to estimate a time-average squared sound

pressure in a reverberation chamber that meets certain requirements. It also requires

6 microphones with specific requirements on their locations[3]. The ISO 3741 also

requires that the sound source is tested under a variety of operating conditions and

loads[3].

3

4 Chapter 2 Background

2.2 Background of the Two-Point In Situ Method

A research group at Brigham Young University has been working on developing a new

method for determining the sound power using the Hopkins-Stryker equation[4][2][5].

This method is known as Two-Point In Situ method. Two refers to the two measure-

ments taken, one taken in the far-field, the other in the near-field. Instead of using

the local spatial average of the total energy density, work by Marquez et al. proved

that a time average Generalized Energy Density (GED) with a weighting factor equal

to 0.25 more accurately calculates the sound power of the source [4][2].

〈wG,β〉t = β〈wP 〉t + (1− β)〈wK〉t (2.1)

Where β represents the weighting factor, 〈wP 〉t represents the Potential Energy Den-

sity (PED) and 〈wK〉t represents the Kinetic Energy Density (KED). The GED,

〈wG,β〉t is used in the Modified Hopkins-Stryker Equation (MHSE) below.

〈wG,β〉t =〈Π〉t2c

[γ(θ0, φo)

4πr4iKi,β +

4

R

](2.2)

Where 〈Π〉t represents the sound power, c is the speed of sound, R represents the

room constant, r is the distance from the probe to the source γ(θ0, φ0) represents

the directivity factor with θ0 and φ0 as the polar and azmuthal angles of the probe’s

location as measured from the acoustical center of the sound source. The actual

values of γ(θ0, φ0) for the reference sound source used in this research were calculated

by Marquez et al. inside of an anechoic chamber[2][5]. K is the Near-Field correction.

For the full derivation see work by Jensen[4].

2.2.1 Calculating the Room Constant

Calculating the sound power of an unknown source involves jumping through some

algebraic hoops. The first hoop required is calculating the room constant using the

2.2 Background of the Two-Point In Situ Method 5

reference source.

R =16π(〈w2,G,β〉t〈w1,G,β〉t−1

)γ(θ0, φ0)

(K2,β

r22− K1,β

r21

〈w2,G,β〉t〈w1,G,β〉t

) (2.3)

The subscripts 1 and 2 represent measurements taken for the reference source inside

the near and far fields.

2.2.2 Calculating the Directivity Factor

After the room constant has been calculated, the next algebraic hoop to jump through

is calculating the directivity factor for the unknown source.

γ′(θ′

0φ′

0) =16π(〈w4,G,β〉t〈w3,G,β〉t

− 1)

R(K4,β

r24− K3,β

r23

〈w4,G,β〉t〈w3,G,β〉t

) (2.4)

Where γ′(θ′0φ

′0) represents the directivity factor and angles for the unknown sound,

and subscripts 3 and 4 represent measurements taken for the unknown source inside

the near and far fields.

2.2.3 Calculating Sound Power

The sound power of the unknown source can then be calculated by the last algebraic

hoop.

〈Π′〉t =2c〈w3,G,β〉t(

γ′(θ′0,φ

′0)

4πr43K3,β + 4

R

) (2.5)

Where 〈Π′〉t represents the sound power of the unknown source. The functions to

handle these calculations were written and updated by Jensen[4]. The code provided

in Appendix A calls on these functions but does not include their code.


2.3 Theory - PAGE Method

Brigham Young University has been developing the PAGE (Phase and Amplitude

Gradient Estimator) method over the past few years. The PAGE method is a new way

to calculate the Potential Energy Density (PED) 〈wP 〉 and Kinetic Energy Density

(KED) 〈wK〉 based on several pressure measurements with a probe. In this research,

the PAGE calculations were compared to the traditional approach for calculating

the PED and KED used in the Two-Point In Situ method. PAGE has demonstrated

distinct advantage over the traditional method when used to measure sound intensities

and energies inside a plane-wave tube[6]. For more information on the derivation on

the PAGE method see Whiting et al.[7].

Energy Densities Traditional Method PAGE Method

PEDG11+G22+2Re

{G12

}8ρc2

G11+G22+2

∣∣G12

∣∣8ρc2

KEDG22+G11−2Re

{G12

}8ωρd2

18ωρd2

[G11 +G22 − 2

∣∣G12

∣∣+G22+G11+2

∣∣G12

∣∣4

(arg{H12

})2]

Figure 2.1 This table shows how the PAGE and Traditional methods differin calculating the PED and KED.

The Traditional method uses only the real component of the cross-spectrum for

calculating the PED and KED. The PAGE method uses a different approach. It

uses the magnitude of the cross-spectrum. This requires both the real and imaginary

components of the cross-spectrum. The cross-spectrum is used as part of the fast

Fourier Transform (FFT) for signal analysis. It calculates the of the cross-correlation,

or cross-covariance, between a pair of microphones [8]. G12 represents the cross-

spectrum between microphones 1 and 2. The auto spectrum, also known as the power

spectrum, is also used as part of the FFT for signal analysis[8], and is represented as

2.3 Theory - PAGE Method 7

G11 and G22. The H12 is the ensemble-averaged transfer function and it is calculated

by dividing the cross spectrum (G12) by the auto spectrum (G11) [7].

Chapter 3

Experimental Procedure

A variety of equipment and software was used to make the measurements and pro-

cess the results. A common kitchen blender was the sound source tested. A brief

description of the process for making measurements following the ISO 3741 and the

Two-Point In Situ methods, mentioned in the previous chapter, will be discussed

further.

3.1 Signal Processors

The research team developing the PAGE Method (Phase and Amplitude Gradient

Estimator) used software created by Dr. Kent Gee and members of the BYU Acoustics

Research Group. The program is a LabVIEW VI (Virtual Instrument), called the

Acoustic Field Recorder (AFR)[6]. It receives and processes the signals received by

microphones via a National Instruments data-acquisition system (DAQ). Research on

the PAGE method extensively use the AFR when taking measurements. The research

team developing the Two-Point In Situ method extensively use a well known signal

processor, Bruel & Kjr Pulse system. The Pulse system includes both the software

9

10 Chapter 3 Experimental Procedure

and the data-acquisition system.

3.2 Setup for the Unknown Sound Source

A common kitchen blender was chosen over a speaker because it is considered a less-

ideal source. A blender is considered a less-ideal source because the position of the

acoustic center is less clear and the radiation pattern and spectra are considered to be

less uniform[4]. As mentioned in the previous chapter, ISO 3741 measurements were

taken with the blender under multiple conditions and loads[3]. The blender was tested

under a specific load and under no load, both with the same operating conditions. The

operating condition was on puree with the speed set on high. This setting was chosen

as it is a common setting used in households. The setup of the blender under no

load included only the base of the blender. The loaded test included the pitcher filled

with 4 cups of water as measured by the marker on the pitcher. Water was chosen

specifically because it would allow for the blender to be uniformly tested under load

while allowing for the most consistent sound while operating.

3.3 ISO 3741 Measurements

Following the strict guidelines, multiple measurements were taken in accordance to

ISO 3741 standards. See Figure 3.1. Six microphones were used at various locations in

the reverberation chamber. Multiple locations help ensure that the measurements are

in accordance. The blender was placed approximately 1.5 meters above the ground

on top of a stand. For each condition and location the measurement was taken for 60

seconds.

3.4 Two-Point In Situ Measurements 11

Figure 3.1 ISO 3741 standard measurement setup with the blender underload. The location of the 6 microphones were in accordance to the ISO 3741.

3.4 Two-Point In Situ Measurements

As discussed in previous work, the Two-Point In Situ method requires that 4 mea-

surements are taken [4][2][5]. A measurement is taken with the probe in the near

field, and another in the far-field, for both the reference source and the unknown

source, as discussed in the previous chapter. Shown in Figure 3.2, the vector inten-

sity probe, made up of 6 G.R.A.S. Type 50VI microphones, was used to take the

measurements[2]. The microphones were in pairs each spaced 5 centimeters apart.


Figure 3.2 Microphone probe spacer is 2.5 cm for a total of 5 cm betweenmicrophones

To reduce errors in the location of the probe, a string was stretched between the

two sources. The string was attached to each source at their estimated acoustical

center. Seen in Figure 3.3 as point B. This helped to help identify the values of the

polar and azimuthal angles (θ0, φ0), as mentioned in the previous chapter. A rotation

system for recording measurements was set up. It was typical to make a near-field

measurement for the reference source using the AFR (Acoustic Field Recorder), then

the Pulse. Leaving the probe in that location, a far-field measurement was taken for

the unknown source with the Pulse, then the AFR. The probe was moved to be in

the near-field of the unknown source, both measurements taken. Finally the far-field

of the reference source was measured for the both processors. This can be seen in

Figure 3.3.

3.4 Two-Point In Situ Measurements 13

Figure 3.3 A setup for the Two-Point In Situ method. The arrow A showsthe probe’s location in the near-field for the reference source, and in the far-field for the unknown source. The arrow B shows the string connecting thetwo sources.

Chapter 4

Results

4.1 ISO 3741 Results

After the measurements were obtained, computational codes written in MATLAB

were used to handle the processing and data analysis. See Appendix A for the MAT-

LAB code.

In the ISO 3741 standard, there is an option to achieve Engineer Grade results

called A-weighting[3]. Most industry professionals will choose to weight their results.

A weighting adjusts the One-Third Octave frequencies (OTO) to be closely related

to how we hear the sound[3]. Frequencies below the Schroder frequency and above

the Spacial Nyquist frequency are not meaningful[3].

The averaged total weighted sound power as calculated by the ISO 3741 for the

blender base and under load are 94.6 and 89.3 dBA respectfully, with a standard

deviation equal to 1 dB[3]. As shown in Figure 4.1.

15

16 Chapter 4 Results

102

103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

B r

e 1

pW

)

Blender ISO3741 Standards - Weighted

Base - ISO3741 | Lw

A = 94.6 dBA

Load - ISO3741 | Lw

A = 89.3 dBA

Schroeder Frequency

Spatial Nyquist Frequency

Figure 4.1 ISO 3741 results for the blender base and under load.

4.2 Two-Point In Situ and PAGE

Comparing the results from the multiple experiments gave an averaged total sound

power and an averaged standard deviation for those results. The averaged results for

the total sound power for the base, as calculated with the Traditional method, was

89.1 dBA with a standard deviation of 1 dB. For the total sound power for the base

calculated with the PAGE (Phase and Amplitude Gradient Estimator) method was

90.2 dBA with a standard deviation of 2.1 dB. See Figure 4.2.

4.2 Two-Point In Situ and PAGE 17

103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

BA

re

1 p

W)

Base - Traditional vs PAGE

Base - ISO3741 | Lw

A = 94.6 dBA

Traditional - | Lw

A = 89.9 dBA

PAGE | Lw

A = 90.1 dBA

Schroder Frequency

Nyquist Frequency

Figure 4.2 ISO 3741 results are compared with the Two-Point In Situ resultsfor the blender under no load. At this location the calculated sound powerwas closer to the averaged for both the Traditional and PAGE methods.

The averaged results for the total sound power for the blender under load, as

calculated with the Traditional method, was 86.1 dBA with a standard deviation of

0.5 dB. For the total sound power for the base calculated with the PAGE (Phase and

Amplitude Gradient Estimator) method was 89.7 dBA with an uncertainty of 1.7 dB.

As seen in Figure 4.3, the Traditional method and the PAGE method calculated the

total sound power was 86.5 and 85.8 dBA.


103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

B r

e 1

pW

)

Loaded Weighted - Traditional vs PAGE

Traditional | Lw

A = 86.5 dBA

PAGE | Lw

A = 85.8 dBA

Load - ISO3741 | Lw

A = 89.3 dBA

Schroeder Frequency


Figure 4.3 ISO 3741 results are compared with the Two-Point In Situmethod results for the blender under load.

The large discrepancy between the ISO 3741 and the Two-Point In Situ method

for calculating the sound power levels with less-ideal sounds still needs more research.

4.3 Error Analysis

4.3.1 Addition of Water

As mentioned in Chapter 2, deciding to use water introduced both expected and

unexpected errors. One of the expected errors introduced by water was the affect

it had on the calculated sound power. It is interesting to note how much lower the

sound power levels are for the blender when the water was added. Since the blender

was under load, measuring only the sound produced by the motors is difficult because

of the sound of the water moving. Comparing the total sound power calculated using

the ISO 3741 for the base and for the loaded blender, as seen in Figure 4.2 and 4.3, the

total sound power dropped from 94.6 dB to 89.3 dB. This drop, of 5 dB in the total

4.3 Error Analysis 19

sound power, was also seen for the Two-Point In Situ method. The water added error

in the initial measurement process as well. The acoustical center of the sound source

was thrown off by the water. It appears that the Two-Point In Situ method relies

heavily on the location of the acoustical center, the origin of the sound produced, in

order to accurately calculate the total sound power[4].

4.3.2 Error Calculations

The calculated standard deviation is not as sufficient or accurate as it could be.

A more complete error analysis needs to be considered. The human error in mea-

surements, equipment error and errors in the calculations were not included in the

computational codes provided. Fixing this problem is a future project that will be

discussed further in the next chapter.

4.3.3 Error in Code

I wrote the computational code that combined functions and methods from both

teams using the AFR system. It is very possible that this code could have introduced

error. However, the errors in the code appear to be small when the PAGE functions

are used with measurements taken by the AFR. See Figure 4.4. This figure was created

initially as a test to determine if the combination of functions worked as expected.

Unlike the previous data, this data was taken inside the small reverberation chamber

at BYU. It was part of another experiment currently being researched involving a

specific ideal sound source.


102

103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

BA

re

1e

-12

)

Pulse Results vs AFR Results

Traditional Pulse Results

ISO 3741 Pulse Results

Traditional AFR Results

PAGE AFR Results

Schroder Frequency


Figure 4.4 Confirmation of the Pulse system vs Acoustic Field Recorder.This measurement only validates that the computational code worked asexpected.

It is plausible that the large deviation in the calculated sound power levels are

correlated with errors made in the measurement recording process. Each test had

large areas of human introduced errors. The estimation of the acoustical center of

the blender could have played a large role. The locations of the probe and sound

sources inside the reverberation chamber was a critical problem. There was one test

in particular that the results directly shows the results of the probe or sound source

located in a resonance point in the room, see Figure 4.5. A resonance point in a

reverberation chamber is a position in the room that is either louder or quieter when

in that specific spot. It is difficult to avoid these points in any chamber.

4.3 Error Analysis 21

102

103

104

Frequency (Hz)

40

50

60

70

80

90

100

110

Lw

(dB

re 1

pW

)

PAGE vs Traditional - Bad Location

Base - ISO3741 | Lw

= 94.6 dB

Traditional - Weighted | Lw

= 88.3 dB

PAGE - Weighted | Lw

= 116.4 dB

Schroeder Frequency

Nyquist Frequency

Figure 4.5 Probe was located in a resonance point both the Traditionaland PAGE method performed poorly.

What is interesting in Figure 4.5, is how the resonance point affected the PAGE

(Phase Amplitude and Gradient Estimator) calculation. PAGE relies on the imagi-

nary components of the cross-spectrum, so this becomes complicated quickly.

While Figures 4.2 and 4.3 show that the PAGE and Traditional methods calculated

the total sound power to be similar, it does not provide enough evidence to prove that

the PAGE outperforms the Traditional method. This result does confirm the results

of Jensen et al., that the Two-Point In Situ method does not accurately handle less-

ideal sound sources[4].

Chapter 5

Future Research

5.1 Error with Code

Combining the two different teams’ computational codes and functions into one code

introduced a lot of complications. The PAGE (Phase and Amplitude Gradient Esti-

mator) code has functions that handle the calculation of the the auto-spectrum and

cross-spectrum from the raw data returned by the AFR (Acoustic Field Recorder).

The computer code written by the Two-Point In Situ team did not work with the

PAGE codes. See Figures 5.1 and 5.2. The Pulse system returns the data to be

further processed in two forms, Narrow-Band (NB) frequencies, or One-Third-Octave

frequencies (OTO). The processed data data which can be returned from the Pulse

is not as flexible as the data returned from the AFR.

23

24 Chapter 5 Future Research

102

103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

B r

e 1

pW

)

Pulse Narrow Band Base - Weighted

Traditional - NB

PAGE - NB

Lw

A (3745)

Schroder Frequency

Nyquist Frequency

Figure 5.1 Two-Point In Situ calculation using the Narrow Band frequenciesreturned by the Pulse system with functions written by the PAGE team.

102

103

104

Frequency (Hz)

40

50

60

70

80

90

100

Lw

(d

B r

e 1

pW

)

Pulse One-Third-Octave Base - Weighted

Traditional - NB

PAGE - NB

Lw

A (3745)

Schroder Frequency

Nyquist Frequency

Figure 5.2 Two-Point In Situ calculation using the One-Third-Octave fre-quencies returned by the Pulse system with functions written by the PAGEteam.

As seen in Figures 5.1 and 5.2, the PAGE calculation was a lot higher than ex-

pected. At higher frequency ranges, both the PAGE and the Traditional calculations

overshot the ISO 3741 expected results. This error is likely due to the fact that up

until now, the PAGE has only been extensively tested with the AFR[7][6]. Further

work is needed to determine what changes made inside the PAGE computational

calculations that will allow the Phase and Amplitude Gradient Estimator Method to

work with other data-acquisition systems.

5.2 PAGE Method 25

5.2 PAGE Method

The next step for the PAGE (Phase and Amplitude Gradient Estimator) research

team is to continue testing the PAGE method’s performance inside a reverberant

field. The functions written and used by the PAGE code, are written to handle raw

data. The PAGE team needs to look into testing the PAGE method with other

data-acquisition systems. As mentioned in the previous chapter with the imaginary

components of the cross-spectrum getting difficult to separate inside of a reverberant

field. Future research could be conducted to look at the how reverberation time affects

the PAGE method’s calculation. A significant future project is an error analysis. The

three types of error mentioned in the previous chapter: human error in measurements,

equipment error and computational error need to be accounted for in the results.

5.3 Two-Point In Situ Method

As seen in Figures 5.1 and 5.2, the processed data returned from the Pulse will

currently not work with the PAGE process. When asked about the specific processing

method of the Pulse, the team did not know. Currently, there is research on a Three-

Point In Situ Method, as mentioned by Jensen et al.[4]. There is hope that this

method might overcome the obstacles faced in measuring less-ideal sound sources.

As well as the PAGE team, the team working on the Two-Point In Situ method

needs to do a more detailed error analysis. While the work of Jensen et al. has laid

a foundation for the Two-Point and Three-Point In Situ methods, a more detailed

error analysis is needed. Another future project is the determination of the locations

for the acoustical centers of less-ideal sound sources.

26 Chapter 5 Future Research

Appendix A

Two-Point In Situ AFR

As mentioned in the previous chapters, this is the code used to process the data. To see

the details of the functions called into this code can be seen in previous work[2][4][7].

clear;

% close all;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%{

Program:

TwoPointAFR

Author:

Christopher Reynolds

Summary:

Code from the Two-Point In Situ functions and PAGE functions has...

been combined and written to work with the AFR software.

%}

27

28 Chapter A Two-Point In Situ AFR

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Constants

tests = 6; % Number of Tests/Conditions

fs = 96000; % Sampling frequency (Hz)

pref = 2e-5; % Reference pressure

ns = 2^15; % Number of samples per block

beta = 0.25; % Weighting factor

fl = 100; % Lower Probe limit

fh = (343/(2*0.025)); % Spacial Nyquist

df = fs/ns;

fss = 0:df:(fs/2-df);

% Path for files

% .bin files, Path to the folder containing data returned by the AFR

filepath = ’Path to folder’;

% Excell File contain information about position of probe and source

PosFile = ’Path Position file location ’;

% Excell file contianing information about the atmospheric conditions

Wfile = ’Path to atmospheric conditions’;

% Pre calculated reverberation time of the Large Chamber

T60File = ’Path to file’;

% Load in the 3745 Sound Power File - Directivity Factors for Ref source

load(’SmallSpeakerAn.mat’);

29

%% Constants for PAGE_func.m and TRAD_func.m

w = hann(ns)’;

% Used to scale the ASD for energy conservation

W = mean(w.*conj(w));

% Probe Configurations

% Converts spacing from microphone to center

space = 0.05/2;

probe_config = [space,0,0;-space,0,0;...

0,space,0;0,-space,0;...

0,0,space;0,0,-space];

%% Loads Atmospheric Conditions from Experiment

WD = xlsread(Wfile,’B1:B3’);

Tc = WD(1); % Celcius

Pressure = WD(2); % mbar

Hum = WD(3); % Hum (%)

RR = 287.058; % J/(kg*K)

T = 273.15+Tc;

rho = Pressure*100/(RR*T); % Density of Air

c = 20.05 * sqrt(T); % Speed of sound

%% Reference and DUT (Unknown source) Constants - position values

Positions = xlsread(PosFile,’A3:C6’);

r_ref = [Positions(1,1);Positions(2,1)];

r_dut = [Positions(3,1);Positions(4,1)];


th_ref = Positions(1,2);

ph_ref = Positions(1,3);

%% T60 Data

T60Data = xlsread(T60File);

T60f = T60Data(1,:).’;

T60 = T60Data(2,:).’;

Lx = T60Data(4,2);

Ly = T60Data(5,2);

Lz = T60Data(6,2);

V = Lx*Ly*Lz; % Volume m^3

S = 2*Lx*Ly+2*Ly*Lz+2*Lz*Lx; % Surface Area m^2

fsh = 2000*sqrt(mean(T60)./V); % Schroder frequency

%% Loads Files

file = binfileload(filepath,’ID’,1,0);

[fileffts,~] = computeBlockFFt(file,ns,w,W);

% Frequency, Autospectrum

[Gxx,f,~] = autospec(file,fs,ns);

[fc,~] = FDOTOspec(f,Gxx,[20,20000],’rect’);

% One array to hold the data from the six microphones for all four tests

x = zeros([tests,6,length(file)]);

% Creates matrix to hold all of the single sided ffts for each test

31

Xss = zeros(tests,6,size(fileffts,1),size(fileffts,2));

% Potential and Kinetic Energys

Ep = zeros([tests,length(fc)]);

Ek = zeros([tests,length(fc)]);

P_Ep = zeros([tests,length(fc)]);

P_Ek = zeros([tests,length(fc)]);

% Loop through the different test conditions

for yy = 1:tests

% Loops through each microphone in the Probe

for zz = 1:6

% Loads in microphone data

x(yy,zz,:) = binfileload(filepath,’ID’,yy,zz-1);

% Calculates the single sided ffts for each experiment

[Xss(yy,zz,:,:),~] = computeBlockFFt(x(yy,zz,:),ns,w,W);

end

% Calculates the Potential and Kinetic Energies at the 1/3 octaves

TRAD(yy) = TRAD_func(fss,squeeze(Xss(yy,:,:,:)),probe_config,rho,c);

PAGE(yy) = PAGE_func(fss,squeeze(Xss(yy,:,:,:)),...

probe_config,rho,c,0,8);

[~,Ep(yy,:)] = FDOTOspec(f,TRAD(yy).Ep,[20,20000],’rect’);

[~,Ek(yy,:)] = FDOTOspec(f,TRAD(yy).Ek,[20,20000],’rect’);

[~,P_Ep(yy,:)] = FDOTOspec(f,PAGE(yy).Ep,[20,20000],’rect’);

[~,P_Ek(yy,:)] = FDOTOspec(f,PAGE(yy).Ek,[20,20000],’rect’);


end

% Fixes the Energy densities

Ep = Ep ./ df;

Ek = Ek ./ df;

P_Ep = P_Ep ./ df;

P_Ek = P_Ek ./ df;

% Generalized Energy Density - PAGE

P_GED = (beta .* P_Ep) + ((1-beta) .* P_Ek);

%% Directivity Factor

% Finding Room Constants

[~,thIND] = min(abs(An.th-th_ref(1)));

[~,phIND] = min(abs(ph_ref(1)-An.ph));

Q = squeeze(An.Q(thIND,phIND,:)).’;

delta1 = ones(size(fc));

delta2 = ones(size(fc));

ps = Pressure/10; % mbar to kPa

ps0 = 101.325; % kPa

alpha = absorption(Tc,ps,Hum,fc);

A0 = r_dut*alpha;

delta = 10.^((A0.*(1.0053-0.0012.*A0).^1.6)/10);

delta = ones(size(delta));

%% Generalized Energy Density - Traditional

33

GED = (beta .* Ep) + ((1-beta) .* Ek);

% Finds the R value (Room Constant) for unknown source

[Rinsitu,~] = RcalcExp_Corrected_BETA(2*GED(1,:),...

2*GED(2,:),r_ref(1),r_ref(2),beta,Q,c,fc,delta(1,:),delta(2,:));

% Finds the Q Value (Directivity Factor)

% for unknown source for both tests

[~,Wdut_1] = WcalcExp_Corrected_BETA(2*GED(3,:),...

2*GED(4,:),r_dut(1),...

r_dut(2),beta,Rinsitu,c,fc,delta(1,:),delta(2,:));

[~,Wdut_2] = WcalcExp_Corrected_BETA(2*GED(5,:),...

2*GED(6,:),r_dut(1),...

r_dut(2),beta,Rinsitu,c,fc,delta(1,:),delta(2,:));

% Finds the R value (Room Constant) for unknown source

[P_Rinsitu,~] = RcalcExp_Corrected_BETA(2*P_GED(1,:),...

2*P_GED(2,:),r_ref(1),r_ref(2),beta,Q,c,fc,delta(1,:),delta(2,:));

% Finds the Q Value (Directivity Factor) for unknown source for tests

[~,P_Wdut_1] = WcalcExp_Corrected_BETA(2*P_GED(3,:),...

2*P_GED(4,:),r_dut(1),...

r_dut(2),beta,P_Rinsitu,c,fc,delta(1,:),delta(2,:));

[~,P_Wdut_2] = WcalcExp_Corrected_BETA(2*P_GED(5,:),...

2*P_GED(6,:),r_dut(1),...

r_dut(2),beta,P_Rinsitu,c,fc,delta(1,:),delta(2,:));

%% A-weighting


% From Annex F.3 ISO 3741 (2010)

fA = [50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250...

1600 2000 2500 3150 4000 5000 6300 8000 10000];

Ck = [-30.2 -26.2 -22.5 -19.1 -16.1 -13.4 -10.9 -8.6 -6.6 -4.8 -3.2 -1.9 ...

-0.8 0.0 0.6 1.0 1.2 1.3 1.2 1.0 0.5 -0.1 -1.1 -2.5];

% Sound Power Measurements not A-weighted

Lw_1 = 10*log10(abs(Wdut_1)/1e-12);

TotLw_1 = 10*log10(sum(10.^(Lw_1(:,fc>=fl&fc<=fh)*0.1),2));

LwA_1 = Lw_1(:,fc <= max(fA) & fc >= min(fA)) + ...

ones(length(beta),1)*Ck;

TotLwA_1 = 10*log10(sum(10.^(LwA_1(:,fA>=fl&fA<=fh)*0.1),2));

% Sound Power Measurements A-weighted

Lw_2 = 10*log10(abs(Wdut_2)/1e-12);

TotLw_2 = 10*log10(sum(10.^(Lw_2(:,fc>=fl&fc<=fh)*0.1),2));

LwA_2 = Lw_2(:,fc <= max(fA) & fc >= min(fA))...

+ ones(length(beta),1)*Ck;

TotLwA_2 = 10*log10(sum(10.^(LwA_2(:,fA>=fl&fA<=fh)*0.1),2));

% Sound Power Measurements PAGE - not A-weighted

P_Lw_1 = 10*log10(abs(P_Wdut_1)/1e-12);

P_TotLw_1 = 10*log10(sum(10.^(P_Lw_1(:,fc>=fl&fc<=fh)*0.1),2));

P_LwA_1 = P_Lw_1(:,fc <= max(fA) & fc >= min(fA)) ...

+ ones(length(beta),1)*Ck;

P_TotLwA_1 = 10*log10(sum(10.^(P_LwA_1(:,fA>=fl&fA<=fh)*0.1),2));

35

% Sound Power Measurements corrected - PAGE - A-weighted

P_Lw_2 = 10*log10(abs(P_Wdut_2)/1e-12);

P_TotLw_2 = 10*log10(sum(10.^(P_Lw_2(:,fc>=fl&fc<=fh)*0.1),2));

P_LwA_2 = P_Lw_2(:,fc <= max(fA) & fc >= min(fA)) +...

ones(length(beta),1)*Ck;

P_TotLwA_2 = 10*log10(sum(10.^(P_LwA_2(:,fA>=fl&fA<=fh)*0.1),2));

%% Figures

% First Condition

figure;

semilogx(fA,LwA_1,’-b’,’Linewidth’,1.25);

hold on;

semilogx(fA,P_LwA_1,’-r’,’Linewidth’,1.25);

title("Blender No Load - AFR",’Fontsize’,14);

xlim([fsh-50 10000]);

ylim([40 100]);

ylabel(’L_wA (dBA re 1 pW)’,’Fontsize’,14);

xlabel(’Frequency (Hz)’,’Fontsize’,14);

l1 = line([fsh fsh],[0 200],’color’,’k’,’linestyle’,’--’);

l2 = line([fh fh],[0 200],’color’,’k’,’linestyle’,’:’);

legendStr1 = ’’;

legendStr1 = [legendStr1;{...

[’Traditional AFR | L_w = ’ num2str(...

round(TotLwA_1(1)*10)/10) ’ dBA’]}];



legendStr2 = [...

legendStr2;{[’PAGE AFR | L_w = ’ num2str(...

round(P_TotLwA_1(1)*10)/10) ’ dBA’]}];

legendStr3 = ’Schroeder Frequency’;

legendStr4 = ’Spatial Nyquist Frequency’;

legend([legendStr1;legendStr2;legendStr3;legendStr4],...

’Fontsize’,14,’location’,’southeast’);

hold off;

% Second Test Condition

figure;

semilogx(fc,Lw_2,’-b’,’Linewidth’,1.25);

hold on;

semilogx(fc,P_Lw_2,’-r’,’Linewidth’,1.25);

xlim([fsh-50 10000]);

ylim([40 100]);

ylabel(’L_w (dBA re 1 pW)’,’Fontsize’,14);



l2 = line([fh fh],[0 200],’color’,’k’,’linestyle’,’:’);


legendStr1 = [legendStr1;{[’Traditional | L_w = ’ num2str(...

round(TotLwA_2(1)*10)/10) ’ dBA’]}];


legendStr2 = [legendStr2;{[’PAGE | L_w = ’ num2str(...

37

round(P_TotLwA_2(1)*10)/10) ’ dBA’]}];

legendStr3 = ’Schroeder Frequency’;

legendStr4 = ’Spatial Nyquist Frequency’;

legend([legendStr1;legendStr2;legendStr3;legendStr4],...


title(’Blender Under Load’,’Fontsize’,14)

hold off;

Appendix B

Two-Point In Situ - Pulse

In this appendix, the functions were written to work with the Pulse not the AFR.

clear;

% close all;

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%{

Code originally written by Zac Jensen and Travis Hoyt when using

the Pulse to measure sound power using the Hopkin-Stryker equation.

Current version author: Christopher Reynolds

Takes narrow band data with the Pulse and analyzes it to find sound

power levels. The addition to this code is the PAGE method to see

how the PAGE compares to the traditional. If a variable has "P_" it

is a PAGE variable. Also not that unlike the other PAGE vs Traditional

codes, this has a different defined distance. This code uses

the distance between microphones not center distances. There is also

39

40 Chapter B Two-Point In Situ - Pulse

factor 1/3 effecting the Potential Energy.

%}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Constants

%load in the 3745 Sound Power File to get the "An" struct for Q

load(’SmallSpeakerAn.mat’)

% Microphone spacing not Center spacing!!!!!

% Spcr = .05; % 5 cm spacer

Spcr = .025; % 2.5 cm spacer

beta = 0.25; % Weighting factor

fh = 343/(2*Spcr); % Spacial Nyquist

fl = 100;

dt = 19.53e-6;

fs = 1/dt; % Sampling frequency (Hz)

df = 3.125;

%% Loads in data from Pulse files

FileName = {’PT1_REF_CPB.Autospectrum_Base.txt’,...

’PT1_REF_CPB.CrossSpectrum_Base.txt’,...

’PT2_REF_CPB.Autospectrum_Base.txt’,...

’PT2_REF_CPB.CrossSpectrum_Base.txt’};

PathName = ’Directory Path to the files location’;

FilterIndex = 1;

41

DataFlag = 0;

if FilterIndex == 0

return

elseif FilterIndex == 2

DataFlag = 1;


DataFlag = 2;

end

%% Weather

WFile = ’Weather.xlsx’;

if isempty(WFile)

display(’Lets put in the atmospheric conditions’)

Tc = input(’Enter the temperature in celcius’);

Pressure = input(’Enter the atmospheric pressure in mbar’);

Hum = input(’Enter the percent Humidity’);

else

WD = xlsread(WFile,’B1:B3’);



Hum = WD(3); % Hum (%)

end

RR = 287.058; % J/(kg*K)


T = 273.15+Tc; % Celcius to Kelvin


% Speed of sound as defined by Standards

c = 20.05 * sqrt(T);

%% Loads in T60 file for Large Reverb Chamber

T60File = ’T60LC.xlsx’;


% Reverb Time

Trev = T60Data(2,:).’;

% Room Dimensions

Lx = T60Data(4,2);

Ly = T60Data(5,2);

Lz = T60Data(6,2);

V = Lx*Ly*Lz; % Volume

S = 2*Lx*Ly+2*Ly*Lz+2*Lz*Lx; % Surface Area

fsh = 2000*sqrt(mean(Trev)./V); % Schroder Frequency

%% Positions

PosFile = ’Positions.xlsx’;

43

Positions = xlsread(PosFile);

% Total number of distances

% Typically the number is 4 (2 for each test)

rtot = (length(Positions)-2)/2;

d = Positions(1,2);

%% Loads Reference Source Data Narrow Band

LFile = length(FileName);

switch DataFlag

case 2

cnt1 = 0;

cnt2 = 0;

for ii = 1:2:3

RefPosInd(floor(ii/3)+1) = str2double(FileName{ii}(3));

pl = 0;

cnt1 = cnt1 + 1;

for yy = 1:6

fID = fopen([PathName,FileName{ii}]);

Data = textscan(fID,’%f %f %f %f’,’HeaderLines’,yy*83+(yy-1)*pl);

fG(1,:) = Data{:,2}; % Frequency array of autospectrum

G(cnt1,:,yy) = Data{:,3}; % Autospectrum

% OTO frequency [100:10000} Hz

%[fG,~] = FDOTOspec(fG,G(1,:),[20,20000],’rect’);;

pl = length(Data{:,3})+10;

fclose(fID);


end

cnt2 = cnt2 + 1;

pl = 0;

for yy = 1:3

fID = fopen([PathName,FileName{ii+1}]);


C(cnt2,:,yy) = Data{:,3}; % Real part of cross spectrum

C_im(cnt2,:,yy) = Data{:,4}; % Imaginary part of cross spectrum


fclose(fID);

end

end

% TRAD

kG = 2*pi*ones(size(G,1),1)*fG/c;

PED = squeeze(G(:,:,1))/2/rho/c^2;

Ep = 1./(24*rho*c^2).*sum(G,3)+1./(12*rho*c^2).*(sum(C,3));

Ek = 1./(2*rho*c^2.*kG.^2*Spcr^2)...

.*sum(G,3) - 1./(rho*c^2.*kG.^2*Spcr^2).*sum(C,3);

% PAGE

H = C + 1j * C_im; % Full cross spectrum

P_Ep = 1./(24*rho*c^2)*sum(G,3) + 1./(12*rho*c^2)...

.*sum(abs(H),3);

45

P_Ek = (1./(2*rho*c^2.*kG.^2*Spcr^2).*sum(G,3) - ...

1./(rho*c^2.*kG.^2*Spcr^2).*sum(abs(H),3))...

+(1./(8*rho*c^2.*kG.^2*Spcr^2).*...

(...

(G(:,:,1)+G(:,:,2)+(2.*abs(H(:,:,1))).*angle(H(:,:,1)).^2)...

+(G(:,:,3)+G(:,:,4)+(2.*abs(H(:,:,2))).*angle(H(:,:,2)).^2)...

+(G(:,:,5)+G(:,:,6)+(2.*abs(H(:,:,3))).*angle(H(:,:,3)).^2)...

)

);

% Finds the 1/3 octave Energy densities

% Dummy Variables to hold Energy matrices

Epmat = zeros(2,length(fOTO));

Ekmat = zeros(2,length(fOTO));

P_Epmat = zeros(2,length(fOTO));

P_Ekmat = zeros(2,length(fOTO));

for uu = 1:2

[~,Epmat(uu,:)] = FDOTOspec(fG,Ep(uu,:),...

[min(fOTO),max(fOTO)],’rect’);

[~,Ekmat(uu,:)] = FDOTOspec(fG,Ek(uu,:)...

,[min(fOTO),max(fOTO)],’rect’);

[~,P_Epmat(uu,:)] = FDOTOspec(fG,P_Ep(uu,:),...

[min(fOTO),max(fOTO)],’rect’);

[~,P_Ekmat(uu,:)] = FDOTOspec(fG,P_Ek(uu,:)...

,[min(fOTO),max(fOTO)],’rect’);

end


% Changes to conventional script

Ep = Epmat ./ df;

Ek = Ekmat ./ df;

P_Ep = P_Epmat ./ df;

P_Ek = P_Ekmat ./ df;

%}

end

KED = Ek;

% PAGE

P_KED = P_Ek;

%% Solve for the room constant

% Weighted Total Energy

GED = beta*Ep + (1-beta)*KED;

P_GED = beta*P_Ep + (1-beta)*P_KED;

ps = Pressure/10; % mbar to kPa

ps0 = 101.325; % kPa

r_ref = [Positions(2+RefPosInd(1),1); ...

Positions(2+RefPosInd(2),1)];

th_ref = Positions(2+RefPosInd(1),2);

ph_ref = Positions(2+RefPosInd(1),3);

47

% Natural Absorbtion

alpha = absorption(Tc,ps,Hum,fG);

A0 = r_ref*alpha;

% Near Field Correction Term

delta = 10.^((A0.*(1.0053-0.0012.*A0).^1.6)/10);

% Finds the indeces of Known Directivty Factor

[~,thIND] = min(abs(An.th-th_ref));

[~,phIND] = min(abs(ph_ref-An.ph));

% Finds the values of Known Directivity Factor

Q = squeeze(An.Q(thIND,phIND,:)).’;

% Traditional Room Constant

[Rinsitu(1,:),W_ref(1,:)] = RcalcExp_Corrected_BETA(2*GED(1,:),...

2*GED(2,:),r_ref(1),r_ref(2),beta,Q,c,fG,delta(1,:),delta(2,:));

% PAGE Room Constant

[P_Rinsitu(1,:),P_W_ref(1,:)] = RcalcExp_Corrected_BETA(2*P_GED(1,:),...

2*P_GED(2,:),r_ref(1),r_ref(2),beta,Q,c,fG,delta(1,:),delta(2,:));

%% Load in Unknown Source measurements

%

% Point to Files

% [FileName,PathName,FilterIndex] = ...

uigetfile({’*.txt’;’*.mat’},...


% ’Choose the DUT measurements files.’,’R:/Students/Zac Jensen/Thesis/Experiments/’,’MultiSelect’,’on’);

FileName = {’PT1_DUT_NB.Autospectrum_Base.txt’,...

’PT1_DUT_NB.CrossSpectrum_Base.txt’,...

’PT2_DUT_NB.Autospectrum_Base.txt’,...

’PT2_DUT_NB.CrossSpectrum_Base.txt’};

PathName = ’Directory Path to the files’ location ’;

FilterIndex = 1;

DataFlag = 0;

if FilterIndex == 0


DataFlag = 1;


DataFlag = 2;

end

% Load in ISO 3741 data

%’Choose the ISO 3741 Sound Power File (DUT)’,’MultiSelect’,’on’);

ISO3741FileName = ’ISO3741_Lw_base 09-Aug-2017.mat’;

ISO3741PathName = ’’;

ISO3741FilterIndex = 1;

if ~ISO3741FilterIndex

ISO3741Flag = 0;

else

49

ISO3741Flag = 1;

load([ISO3741PathName,ISO3741FileName]);

end

end

%% Load DUT Measurement Data

LFile = length(FileName);

switch DataFlag

case 2

cnt1 = 0;

cnt2 = 0;

for ii = 1:2:3

DutPosInd(floor(ii/3)+1) = str2double(FileName{ii}(3));

pl = 0;

cnt1 = cnt1 + 1;

for yy = 1:6

fID = fopen([PathName,FileName{ii}]);


fG(1,:) = Data{:,2};

G(cnt1,:,yy) = Data{:,3};


fclose(fID);

end


cnt2 = cnt2 + 1;

pl = 0;

for yy = 1:3

fID = fopen([PathName,FileName{ii+1}]);

Data = textscan(fID,’%f %f %f %f’,’HeaderLines’,...

yy*83+(yy-1)*pl);

% Real part of cross spectrum Narrow Band

C(cnt2,:,yy) = Data{:,3};

% Imaginary part of cross spectrum Narrow Band

C_im(cnt2,:,yy) = Data{:,4};


fclose(fID);

end

end

kG = 2*pi*ones(size(G,1),1)*fG/c;

PED = squeeze(G(:,:,1))/2/rho/c^2;

Ep_dut = 1./(24*rho*c^2)*sum(G,3)+...

1./(12*rho*c^2).*(sum(C,3));

Ek_dut = 1./(2*rho*c^2.*kG.^2*Spcr^2)...

.*sum(G,3) - 1./(rho*c^2.*kG.^2*Spcr^2).*sum(C,3);

% PAGE

H = C + 1j * C_im; % Full cross spectrum

P_Ep_dut = 1./(24*rho*c^2).*sum(G,3) + ...

51

1./(12*rho*c^2).*(sum(abs(H),3));

P_Ek_dut = (1./(2*rho*c^2.*kG.^2*Spcr^2)...

.*sum(G,3) - 1./(rho*c^2.*kG.^2*Spcr^2).*sum(abs(H),3))...

+(1./(8*rho*c^2.*kG.^2*Spcr^2).*...

(...

(G(:,:,1)+G(:,:,2)+(2.*abs(H(:,:,1))).*angle(H(:,:,1)).^2)...

+(G(:,:,3)+G(:,:,4)+(2.*abs(H(:,:,2))).*angle(H(:,:,2)).^2)...

+(G(:,:,5)+G(:,:,6)+(2.*abs(H(:,:,3))).*angle(H(:,:,3)).^2)...

));

%{

% Finds the 1/3 octave Energy densities

% Dummy Variables to hold Energy matrices

Epmat_dut = zeros(2,length(fG));

Ekmat_dut = zeros(2,length(fG));

P_Epmat_dut = zeros(2,length(fG));

P_Ekmat_dut = zeros(2,length(fG));

for uu = 1:2

[~,Epmat_dut(uu,:)] = FDOTOspec(fG,Ep_dut(uu,:)...

,[min(fG),max(fG)],’rect’);

[~,Ekmat_dut(uu,:)] = FDOTOspec(fG,Ek_dut(uu,:)...


[~,P_Epmat_dut(uu,:)] = FDOTOspec(fG,P_Ep_dut(uu,:)...


[~,P_Ekmat_dut(uu,:)] = FDOTOspec(fG,P_Ek_dut(uu,:)...


end


% Changes to conventional script

Ep_dut = Epmat_dut ./ df;

Ek_dut = Ekmat_dut ./ df;

P_Ep_dut = P_Epmat_dut ./ df;

P_Ek_dut = P_Ekmat_dut ./ df;

%}

end

% PED = Ep_dut;

KED = Ek_dut;

% PAGE

P_KED = P_Ek_dut;

%% Solve for the sound power and directivity of the DUT

% Weighted Energy

GED = beta.*Ep_dut + (1-beta).*KED;

P_GED = beta.*P_Ep_dut + (1-beta).*P_KED;

r_dut = [Positions(rtot+2+DutPosInd(1),1); Positions(rtot+2+DutPosInd(2),1)];

alpha = absorption(Tc,ps,Hum,fG);

A0 = r_dut*alpha;

delta = 10.^((A0.*(1.0053-0.0012.*A0).^1.6)/10);

delta = ones(size(delta));

53

[Qdut(1,:),Wdut(1,:)] = WcalcExp_Corrected_BETA(2*GED(1,:),2*GED(2,:),...

r_dut(1),r_dut(2),beta,Rinsitu(1,:),c,fG,delta(1,:),delta(2,:));

[P_Qdut(1,:),P_Wdut(1,:)] = WcalcExp_Corrected_BETA(2*P_GED(1,:),...

2*P_GED(2,:),r_dut(1),r_dut(2),beta,P_Rinsitu(1,:),...

c,fG,delta(1,:),delta(2,:));

%% Hopkins-Stryker Equation

Lw = 10*log10(abs(Wdut)/1e-12);

TotLw = 10*log10(sum(10.^(Lw(:,fG>=fl&fG<=fh)*0.1),2));

P_Lw = 10*log10(abs(P_Wdut)/1e-12);

P_TotLw = 10*log10(sum(10.^(P_Lw(:,fG>=fl&fG<=fh)*0.1),2));

%% A-weighting


fA = [50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 ...

2000 2500 3150 4000 5000 6300 8000 10000];

Ck = [-30.2 -26.2 -22.5 -19.1 -16.1 -13.4 -10.9 -8.6 -6.6 -4.8 -3.2 -1.9 ...

-0.8 0.0 0.6 1.0 1.2 1.3 1.2 1.0 0.5 -0.1 -1.1 -2.5];

% If 1/3 octave has a higher minimum, it changes where Weighted Frequency

% and Weighted Constant Matrices start

if min(fG) > min(fA)


AINDmin = find(fA==min(fG));

fA = fA(AINDmin:end);

Ck = Ck(AINDmin:end);

end

LwA = Lw(:,fG <= max(fA) & fG >= min(fA)) + ones(length(beta),1)*Ck;

TotLwA = 10*log10(sum(10.^(LwA(:,fA>=fl&fA<=fh)*0.1),2));

P_LwA = P_Lw(:,fG <= max(fA) & fG >= min(fA)) + ones(length(beta),1)*Ck;

P_TotLwA = 10*log10(sum(10.^(P_LwA(:,fA>=fl&fA<=fh)*0.1),2));

%%

%%% A-weighted Plots %%%

figure

semilogx(fA,LwA,’-b’,’Linewidth’,2)

hold on

semilogx(fA,P_LwA,’-r’,’Linewidth’,2)

line1 = line([fsh fsh],[0 200],’color’,’k’,’linestyle’,’--’);

line2 = line([fh fh],[0 200],’color’,’k’,’linestyle’,’:’);

legend(’Traditional - test’,’PAGE - test’,’L_wA (3745)’,...

’Schroder Frequency’,’Nyquist Frequency’,’location’,’southeast’);

xlim([100 10000])

ylim([40 100]);

55

title(’Test of Code’);

xlabel(’Frequency (Hz)’);

hold off;

ylabel(’dB ’)

Appendix C

ISO 3741

In this appendix, the processing of the ISO 3741 standards are calculated.

clear;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%{

Program:

Standard method for Sound Power in Reverberation Chamber

Summary:

This program calculates the sound power of a source inside of the

reverberation chamber using the standard method. This program

calls functions written by the BYU Acoustics Research Group.

Functions and Authors:

Travis Hoyt and the Pulse team

binfileload.m by: Kent Gee

autospec.m by: Kent Gee, Alan Wall, and Brent Reichman

57

58 Chapter C ISO 3741

FDOTOspec.m by: Kent Gee

%}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Constants

fs = 96000; % Sampling frequency (Hz)

pref = 2e-5; % Reference pressure

ns = 2^15; % Samples per Block

tests = 1; % Number of Tests

mics = 6; % Number of Mics per test

B0 = 1.013*10^5; % Pa

A0 = 1;

fh = 6860; % Spacial Nyquist

filepath = ’Directory Path to the File’;

%% Loads Atmospheric Conditions from Experiment

IFile = ’std_ATM.xlsx’;

WD = xlsread(IFile,’B1:B3’);



Hum = WD(3); % Hum (%)

RR = 287.058; % J/(kg*K)

T = 273.15+Tc; % Converts Tc to Kelvin

% Variables calculated from data


59

c = 20.05 * sqrt(273 + Tc); % Speed of sound depending on temp

B = Pressure * 100; % Converts Pressure from mbar to Pa

%% T60

T60File = ’T60LC.xlsx’;


fOTO = rot90(T60Data(1,:).’); % 1/3 OTO frequency

Trev = rot90(T60Data(2,:).’); % Reverb time as a

% Dimensions of Chamber

Lx = T60Data(4,2);

Ly = T60Data(5,2);

Lz = T60Data(6,2);

% Variables calculated from data

V = Lx*Ly*Lz; % Volume m^3

S = 2*Lx*Ly+2*Ly*Lz+2*Lz*Lx; % Surface Area m^2

fsh = 2000*sqrt(mean(Trev)./V); % Schroder frequency

A = (55.26 / c) .* (V ./ Trev); % Absorbtion area of room

%% Load File

file = binfileload(filepath,’ID’,1,0);

[G11,f,~] = autospec(file,fs,ns);

[fc,~] = FDOTOspec(f,G11,[20,20000],’rect’);

xx = zeros([tests,mics,length(file)]); % Files

G = zeros([tests,mics,length(G11)]); % Autospectrum


OTOspec = zeros([tests,mics,length(fOTO)]); % 1/3 Octave Spectrum

for m = 1:tests

for k = 1:mics

xx(m,k,:) = binfileload(filepath,’ID’,1,k-1);

[G(m,k,:),~,~] = autospec(xx(m,k,:),fs,ns);

[~,OTOspec(m,k,:)] = FDOTOspec(f,G(m,k,:),[100,10000],’rect’);

end

end

%% Average Levels

% Uncorrected Average Sound Pressure Levels

OTOspecAvg = mean(OTOspec,2);

LpAvg = squeeze(10.*log10(OTOspecAvg(:,:,:)./ pref^2)).’;

%% Uncertainty

Lpiall = 10 .*log10(OTOspecAvg./pref^2);

Lpm = mean(10 .* log10(OTOspecAvg ./ pref^2),1);

sigR0 = 0.5; % Reproducibility Uncertainty standard deviation

sigomc = 0.5; % uncertainty due to operating and mounting conditions

sigtot = sqrt(sigR0^2+sigomc^2);

kfactor = 2; % 2 = 95% chance that Lw

%is between Lw+U and Lw - U; (Assuming a normal distribution)

61

U = sigtot*kfactor;

%% Calculates the Sound Power Level

% Dummy Variables to clear up Sound Power level Equation

Z1 = 10 .* log10(A./A0);

Z2 = 4.34 .* (A./S);

Z3 = 10 .* log10(1 + ((S*c) ./ (8*V.*fOTO)));

C1 = log10((B*427) / (B0*400));

C2 = log10(sqrt(273 / T));

% Sound Power Level Averaged over all the Tests

Lw = LpAvg + ((Z1 + Z2 + Z3) - (25*(C1+C2)) -6);

%% A-weighting


fA = [50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 ...

2000 2500 3150 4000 5000 6300 8000 10000];

Ck = [-30.2 -26.2 -22.5 -19.1 -16.1 -13.4 -10.9 -8.6 -6.6 -4.8 -3.2 -1.9 ...

-0.8 0.0 0.6 1.0 1.2 1.3 1.2 1.0 0.5 -0.1 -1.1 -2.5];

% If 1/3 octave has a higher minimum, it changes where Weighted Frequency

% and Weighted Constant Matrices start

if min(fOTO) > min(fA)


AINDmin = find(fA==min(fOTO));

fA = fA(AINDmin:end);

Ck = Ck(AINDmin:end);

end

% Calculates Weighted Standards for each test

TotLw = 10*log10(sum(10.^(Lw(:,fOTO>=fsh&fOTO<=fh)*0.1),2));

LwA = Lw + Ck(fA <= max(fOTO) & fA >= min(fOTO));

% TotLw = 10*log10(sum(10.^(Lw*0.1)));

TotLwA = 10*log10(sum(10.^(LwA*0.1)));

%% Figures

figure

semilogx(fOTO,Lw,’-^k’,’LineWidth’,1.5);

hold on;

semilogx(fOTO,LwA,’-*m’,’LineWidth’,1.5);

title(’Blender ISO3741 Standards - Weighted’,’Fontsize’,14);


ylim([40 100])

ylabel(’L_w (dB re 1 pW)’,’Fontsize’,14);



legendStr1 = [legendStr1;{[’Base - ISO3741 | L_w = ’...

num2str(round(TotLw(1)*10)/10) ’ dB’]}];

legendStr = ’’;

legendStr = [legendStr;{[’Base - ISO3741 | L_wA = ’...

63

num2str(round(TotLwA(1)*10)/10) ’ dBA’]}];

legend([legendStr1;legendStr;’Schroeder Frequency’],...


hold off;

Bibliography

[1] Occupational exposure to noise: evaluation, prevention and control (World Health

Organization, 2001).

[2] D. R. Marquez, Estimating the Acoustic Power of Sources in Nonideal Enclosures

Using Generalized Acoustic Energy Density, Master’s thesis, Brigham Young Uni-

versity (2014).

[3] A. S. of America, Acoustics - Determination of sound power levels of noise sources

using sound pressure - Precision method for reverberation rooms - ISO 3741:1999

ANSI S12.51-2002, Acoustical Society of America (2002).

[4] Z. Jensen, Improvements to the Two-Point In Situ Method for Measurement of

the Room Constant and Sound Power in Semi-Reverberant Rooms, Master’s thesis,

Brigham Young University (2016).

[5] B. Xu, Generalized Acoustic Energy Density and Its Applications, Ph.D. thesis,

Brigham Young University (2010).

[6] D. Hawks, Performance of Phase and Amplitude Gradient Estimator Method for

Calculating Energy Quantities in a Plane-Wave Tube Environment (Department

of Physics Brigham Young University - Idaho, 2016).

65

66 BIBLIOGRAPHY

[7] E. Whiting, Energy Quantity Estimation in Radiated Acoustic Fields, Master’s

thesis, Brigham Young University (2016).

[8] H. Herlufsen, Technical Review, Tech. Rep. 1 (1984).

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