A Hybrid Approach to Noise-Reduced Pods in Urban Areas Arjun Agarwal Lasya Balachandran [email protected][email protected]Hannah Cherry John Kellaher Ethne Laude [email protected][email protected][email protected]Michael J. DiBuono* Nicholas J. Calzaretto* [email protected][email protected]New Jersey’s Governor’s School of Engineering and Technology July 24, 2020 *Corresponding Author Abstract—Urban environments generate intense and incessant noise, oftentimes creating distractions for city inhabitants and contributing to various health issues. To address the concerns created by short-term exposure to acute noise pollution in a streamlined and non-intrusive manner, this project proposes a noise-reduced pod. This pod integrates passive and active noise cancellation technology to effectively reduce high and low frequency signals, respectively. For the passive approach, 3D pods were modeled with highly noise absorbent and reflective materials and were structured to most effectively attenuate sound waves. For the active approach, electronic components were utilized to collect and output signals, and a Filtered-x Least Mean Square (LMS) Finite Impulse Response (FIR) adaptive filter was created to process the input noise and produce the anti-noise. It was determined that polyurethane foam and double-glazed plexiglass are the best materials for sound absorption, rounded edges are the best structure for sound reflection, and μ =0.008 is the best step size for adaptive filtering. The aforementioned technology was combined in a final pod model, designed for single person use in smart cities. I. INTRODUCTION Rapid urbanization has introduced a host of problems in modern cities, one of which is environmental noise pollution, a major concern that is often overlooked. Noise pollution is defined by the Environmental Pollution Centers as “exposure to elevated sound levels that may lead to adverse effects in humans or other living organisms,” usually caused by street traffic, construction, air traffic, and train stations in cities [1]. In an urban environment, noise pollution not only distracts city inhabitants but can also cause detrimental health effects. According to the World Health Organization, 1 out of 3 people are ”annoyed during the daytime” due to noise pollution [2]. Thus, for city inhabitants who are taking a phone call or reading a book on busy streets or in urban parks, environmental noise pollution serves as a distraction. With no convenient escape from city noise, city inhabitants are forced to sacrifice productivity. Noise pollution also comes with a number of health impacts. While continual exposure to noise pollution is a separate issue, acute noise events are also damaging to the human auditory system and body as a whole. Studies show that there is a positive correlation between noise pollution level and systolic and diastolic blood pressure, as well as a positive correlation between noise pollution level and heart rate [3]. Because the human auditory system is constantly analyzing background acoustics, regardless of conscious attention to the sounds themselves, acute noise events can trigger acute responses of the autonomic nervous and the endocrine system. Repeated exposure to acute noise events in cities can lead to long- term damage, making it desirable to offer an escape, albeit temporary, from a constant influx of noise pollution. At the moment, the two most prominent solutions to per- sonal noise cancellation are earplugs and noise-cancelling headphones, both of which come with their own set of disadvantages. Earplugs can not only force ear wax further down the ear canal, which can cause tinnitus (a ringing in the ears), but also have been found to result in ear infections due to repeated usage of unsanitized earplugs. Earplugs also inadvertently prevent desired noise, such as music or phone audio, from being heard without being muffled due to their use of passive noise cancellation. Passive noise cancellation is sound attenuation caused by the material and geometry of the structure. This makes earplugs inconvenient in many scenarios. Noise-cancelling headphones address the issue of having desired sounds blocked out by using active noise cancellation (ANC). ANC is noise cancellation caused by anti- noise sound waves generated to create destructive interference. However, noise-cancelling headphones are typically expensive, ranging from $200 to $400, making them unaffordable for 1
Transcript
A Hybrid Approach to Noise-Reduced Pods inUrban Areas
New Jersey’s Governor’s School of Engineering and TechnologyJuly 24, 2020
*Corresponding Author
Abstract—Urban environments generate intense and incessantnoise, oftentimes creating distractions for city inhabitants andcontributing to various health issues. To address the concernscreated by short-term exposure to acute noise pollution in astreamlined and non-intrusive manner, this project proposesa noise-reduced pod. This pod integrates passive and activenoise cancellation technology to effectively reduce high and lowfrequency signals, respectively. For the passive approach, 3D podswere modeled with highly noise absorbent and reflective materialsand were structured to most effectively attenuate sound waves.For the active approach, electronic components were utilized tocollect and output signals, and a Filtered-x Least Mean Square(LMS) Finite Impulse Response (FIR) adaptive filter was createdto process the input noise and produce the anti-noise. It wasdetermined that polyurethane foam and double-glazed plexiglassare the best materials for sound absorption, rounded edges arethe best structure for sound reflection, and µ = 0.008 is the beststep size for adaptive filtering. The aforementioned technologywas combined in a final pod model, designed for single personuse in smart cities.
I. INTRODUCTION
Rapid urbanization has introduced a host of problems inmodern cities, one of which is environmental noise pollution,a major concern that is often overlooked. Noise pollution isdefined by the Environmental Pollution Centers as “exposureto elevated sound levels that may lead to adverse effects inhumans or other living organisms,” usually caused by streettraffic, construction, air traffic, and train stations in cities [1].In an urban environment, noise pollution not only distractscity inhabitants but can also cause detrimental health effects.
According to the World Health Organization, 1 out of3 people are ”annoyed during the daytime” due to noisepollution [2]. Thus, for city inhabitants who are taking a phonecall or reading a book on busy streets or in urban parks,environmental noise pollution serves as a distraction. With no
convenient escape from city noise, city inhabitants are forcedto sacrifice productivity.
Noise pollution also comes with a number of health impacts.While continual exposure to noise pollution is a separate issue,acute noise events are also damaging to the human auditorysystem and body as a whole. Studies show that there is apositive correlation between noise pollution level and systolicand diastolic blood pressure, as well as a positive correlationbetween noise pollution level and heart rate [3]. Because thehuman auditory system is constantly analyzing backgroundacoustics, regardless of conscious attention to the soundsthemselves, acute noise events can trigger acute responses ofthe autonomic nervous and the endocrine system. Repeatedexposure to acute noise events in cities can lead to long-term damage, making it desirable to offer an escape, albeittemporary, from a constant influx of noise pollution.
At the moment, the two most prominent solutions to per-sonal noise cancellation are earplugs and noise-cancellingheadphones, both of which come with their own set ofdisadvantages. Earplugs can not only force ear wax furtherdown the ear canal, which can cause tinnitus (a ringing inthe ears), but also have been found to result in ear infectionsdue to repeated usage of unsanitized earplugs. Earplugs alsoinadvertently prevent desired noise, such as music or phoneaudio, from being heard without being muffled due to theiruse of passive noise cancellation. Passive noise cancellationis sound attenuation caused by the material and geometryof the structure. This makes earplugs inconvenient in manyscenarios. Noise-cancelling headphones address the issue ofhaving desired sounds blocked out by using active noisecancellation (ANC). ANC is noise cancellation caused by anti-noise sound waves generated to create destructive interference.However, noise-cancelling headphones are typically expensive,ranging from $200 to $400, making them unaffordable for
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many people [4]. Because there is no current technology thatcomprehensively addresses the issue of noise pollution, thepod offers a solution that combines both passive and activetechnology to achieve efficient noise-cancellation.
II. BACKGROUND
A. Sound Wave Interference
Sound waves are longitudinal waves that are created whenmatter vibrates parallel to the direction of energy transfer.They are formed when a vibrating body causes a surroundingmedium (e.g. air, water) to vibrate. When two or more soundwaves pass through the same space at the same time, theiramplitudes add and interference occurs.
Fig. 1. Constructive and Destructive Interference
Constructive interference is the superposition of waves tocreate a wave with a greater amplitude, while destructiveinterference creates a wave with a smaller amplitude. In Figure1, the waves on the left, which have the same frequency, are inphase, meaning the waves are perfectly aligned. These wavesconstructively interfere to create a larger amplitude, whichresults in a louder sound in the case of sound waves. The waveson the right are out of phase, meaning one wave is offset halfa wavelength from the other. When the two waves combine,they completely cancel, creating destructive interference [5].This phenomenon is ideal for noise cancellation because thereis no resulting sound wave.
B. Passive Noise Cancellation
A crucial component of the noise-reduced pods are thesound attenuating capabilities of the materials that comprisethe installation, as well as the geometry of the installation.
1) Sound Absorption Through Materials: One means ofsound attenuation is sound absorption. All materials reduce theenergy and intensity of sound waves at varying amounts. Aloss in energy is created when the waves propagate through themediums, creating vibrations in the material and frictional heatenergy. This heat energy is subtracted from the total energyof the sound wave. The rate at which the sound wave energypropagates through the medium is given by the equation:
P =1
2ρvω2As2 (1)
where P represents the power of the sound wave, ρ represents
density of the medium, v represents the velocity of the soundwave, ω represents the angular frequency of the sound wave,A represents the area of the sound wave, and s represents themaximum amplitude of the sound wave.
Two metrics are utilized to observe the sound-absorbingproperties of the possible materials: the Noise Reduction Coef-ficient (NRC) and the Sound Transmission Class (STC) rating.The Noise Reduction Coefficient is “the ratio of absorbedenergy to incident energy and is represented by α,” [6] and iscalculated using the equation:
α =EaEi
= 1− EτEi
(2)
In Equation 2, Ea represents the absorbed energy, Ei repre-sents the incident energy of the sound wave, and Eτ representsthe transmitted energy. Sound Absorption Coefficient valuesrange from 0 to 1,
The second of these metrics is the Sound TransmissionClass (STC) rating, an integer representation of how soundwave intensity is reduced. The STC is calculated by takingthe average transmission loss over 16 standard frequenciesranging from 125 Hz to 4,000 Hz. The value represents thedecibel reduction of sound waves through a medium. It shouldbe noted that NRC and STC values represent an average soundreduction over multiple frequencies, and most materials absorba greater amount of energy from higher frequency soundwaves. Figure 2 demonstrates the noise reduction coefficientvalues for different materials and how the value changes overvarious frequencies.
Fig. 2. Absorption Coefficients for Different Wood Types [6]
Another means to reduce the energy of sound waves isreflection. Soft and porous materials, such as foam, primarilyattenuate sound waves through absorption; however, harderand smoother materials, such as steel, have low NRC and STCvalues. These materials attenuate sound waves through wavereflection. Sound waves approach the material at the incidentangle, and are reflected at the reflection angle [7]. The incidentand reflection angle are equivalent, as demonstrated in Figure3.
2) Sound Attenuation Through Geometry: The shape of astructure, or the geometry, changes the noise-reducing capa-bilities of the installation as well. Rounded surfaces are likely
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to provide greater incident angles, increasing the reflectionangle and dissipated energy. Greater incident angles increasethe distance traveled by the wave through the medium. Thisincreases the effective thickness of the absorbent material,maximizing the absorbed energy. Figure 4 demonstrates thiseffect. Minimizing the profile of a structure reduces thepossibility of sound waves contacting the structure as well.
Fig. 3. Incident vs Reflected Angle for Sound Waves
Fig. 4. Effective Thickness Relative to Theta
C. Active Noise Cancellation
Active noise control (ANC) involves the electro-acousticgeneration of “anti-noise” sound waves to cancel out anunwanted existing sound wave. Ideally, the “anti-noise” soundwave is an inverted version of the unwanted sound wave,meaning that the anti-noise wave is offset by half a wave-length. When the two waves are superimposed together, theyinterfere destructively.
The active noise control system used in the pod is an “adap-tive” system that self-adjusts based upon the characteristics ofthe noise to be cancelled and any environmental conditionsaffecting the acoustic field. This system contains three maincomponents: a reference microphone to sense noise from thesource, a speaker to provide the anti-noise source, and an errormicrophone to gauge any remaining noise through the system.
Reference microphones pick up the existing unwanted noisewhich is then cancelled out by the anti-noise from the speakers
using an adaptive filter. Due to the distance between the anti-noise speakers and the error microphone, the noise and anti-noise do not cancel perfectly. The error microphone picks upany residual noise and sends a feedback error signal to theadaptive filter [8]. An adaptive filter is a digital filter capableof self-adjusting its filter parameters, or coefficients, automat-ically over time via an algorithm in response to feedback.
1) Feedback Control: Noise cancellation with adaptivefilters employs closed loop control, also known as feedbackcontrol, which creates a feedback loop between output andinput signals. This loop continuously monitors the system’soutput signal and compares it with the desired signal tocalculate the error signal. This calculated error is then fedback to the adaptive filter which then updates to reduce errorin future iterations. This constant looping back of the errorsignal for filter adaptation is shown in Figure 4.
Fig. 5. Block Diagram of the Noise Signals
2) Anti-Noise Signal Generation: The sound received bythe error microphone is dependent on the reference micro-phones and the anti-noise speakers. This sound, e(t), isrepresented as
e(t) = r(t) + a(t) (3)
where r(t) and a(t) represent the existing unwanted noise andanti-noise provided by the speakers at the error microphone,respectively. For ideal cancellation, the error microphoneshould receive no noise, meaning the anti-noise speakersshould be completely out of phase with the noise source.However, in real-life applications, it is highly unlikely toachieve near perfect noise cancellation.
The received noise at the error microphone can be repre-sented as r(t) = cne(t) ∗ n(t), where cne(t) represents thechannel between the noise source and the error microphone,n(t) represents the noise signals, and ∗ denotes a convolution,i e., two functions, cne(t) and n(t), produce a third function(r(t)) through the weighted sum of decaying shifts of thesecond signal. This convolution can be expanded using theintegral below, where u denotes a running variable for thetime shift [9].
r(t) =
∫ t
0
cne(u)n(t− u)du (4)
Similarly, the noise received by the reference microphoneis the combination of all the signals received from the noisesource. All of the signals form the reference microphone passthrough the adaptive filter for the anti-noise speakers and arereceived by the error microphone. Using the same logic, thesound received by the anti-noise speakers is:
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a(t) = cse(t) ∗ (h(t) ∗ (cnr(t) ∗ n(t))) (5)
where cnr(t) represents the channel between the noise sourceand the reference microphone, h(t) represents the adaptivefilter, and cse represents the channel between the speaker andthe error microphone. Equation 5 can be expanded as thefollowing equations:
m(t) = cnr(t) ∗ n(t) =∫ t
0
cnr(u)n(t− u)du (6)
s(t) = h(t) ∗m(t) = h(t) ∗ (cnr(t) ∗ n(t))
=
∫ t
0
h(u)m(t− u)du (7)
a(t) = cse(t) ∗ (h(t) ∗ (cnr ∗ n(t)))
=
∫ t
0
cse(u)s(t− u)du (8)
Equation 6 is the represents combination of all of the noisesignals from the source to the reference microphone. Equation7 denotes the combination of signals through the varyingadaptive filter. Equation 8 describes the combination of anti-noise signals based on the adaptive filter.
The goal of the ANC algorithm is to create a h(t) suchthat e(t) is minimized. If the signals from the noise sourcereceived by the error microphone are represented as cne(t),e(t) is represented as:
Solving for the value h(t) from Equation 9, h(t) can be writtenas:
h(t) = −c−1se (t) ∗ cne(t) ∗ ∗c−1
nr (t) (10)
D. Alternative Noise Cancellation Methods
Another method to reduce the intensity of incoming soundwaves is to utilize a high pass filter. These electronic filterscreate a frequency threshold, where high frequency soundwaves transmit to the listener, while low frequency soundwaves are attenuated. This is accomplished by absorbing soundwave energy with an array of microphones, transforming thewaves into an electronic signal, and using an RC circuit toeliminate low-frequency signals. A high pass filter can beused in tandem with a low pass filter to create a bandpass,or a select range of transmitted frequencies. However, thissystem requires the use of large microphone arrays, making itexpensive and difficult to implement in an urban environment[10].
E. Software
MATLAB and its wide array of digital signal processingsupport makes it the most suitable environment for the devel-opment and simulation of the ANC algorithm used in the pod[11]. Specifically, MATLAB is a technical computing environ-ment that combines algorithm development, data analysis andvisualization, and numeric computation.
OnShape, a solid modeling computer-aided design program,is used to design the electronic components of the pod,specifically the speaker and microphone systems. To makesolids, a two-dimensional sketch is created and then extrudedinto a three-dimensional field.
To assist in the 3D CAD model of the pod itself, SketchUpis used. SketchUp is a 3D modeling computer program for awide range of drawing applications such as architectural, civiland mechanical engineering.
III. PROCEDURE
A. Hybrid Approach
A hybrid approach to noise cancellation, utilizing bothpassive and active technologies, is implemented in this podin order to optimize its functionality over a wide range ofnoise signals and frequencies. Passive noise control, or the useof materials and geometry to achieve sound absorption andreflection, appears to be most effective for middle and highfrequency noise [12]. Meanwhile, active noise control has hadextensive success with low frequency noise control below 500Hz. By using both approaches, the pod has the capability toaccount for a range of frequencies. Another major benefit ofthe hybrid approach is that it minimizes the need for specificmaterials and designs, allowing for a pod design that is cost-effective and efficient. For this reason, bringing together bothtechniques provides for a comprehensive noise cancellationpod.
B. Pod Design
1) Selecting Materials for Sound Absorption: Plexiglass,”a synthetic polymer of methyl methacrylate,” is a type ofacrylic sheeting with favorable noise-reducing properties [13].Double glazed plexiglass varies from traditional plexiglassframes in that two plexiglass panels are fitted into a singleframe, separated by a thin cavity of air. This empty space isoften pressurized using inert gases such as argon for thermalinsulation benefits. Additionally, the plexiglass panels are un-equal in width to mitigate the negative effects of resonance. Assound waves travel through a medium, particular frequenciesare amplified. These frequencies match the natural frequencyof the medium: the frequency at which a medium oscillateswithout external forces. It is modeled by Equation 11.
fc =5.2e10
h
ρ
E(11)
h represents plate thickness (in.), ρ represents the density(lb/in3), and E represents elastic modulus (psi). When thenatural frequency and sound wave frequency are equal, theintensity of the sound wave is increased. The natural frequency
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of a medium varies with width, meaning that resonance can becontrolled. The differing natural frequencies of the plexiglasspanels effectively reduces the intensity of frequencies thatwould otherwise be amplified with a single panel. Figure 6depicts the noise-reducing capabilities of different plexiglassvariants in terms of Sound Transmission Class. The doubleglazed variant was evidently the most effective at this task.
Fig. 6. Sound Transmission Class for Plexiglass [14]
Open-cell polyurethane foam was used for its sound ab-sorbing properties. The open cell structure reflects and trapssound waves within the materials, scattering and more effec-tively absorbing the sound wave energy. Pure polyurethanefoam has a NRC value of 0.297. This variant of the foammost effectively attenuates sound waves in the 800-1200Hzfrequency range, but is much less effective in other frequencyranges. To combat the loss of sound absorption ability incertain frequency ranges, a composite mixture of polyurethanefoam and textile waste was used. A 3:2 ratio of polyurethanefoam to textile waste was implemented, increasing the NRCvalue to 0.593. This mixture also attenuates sound muchmore effectively at lower and higher frequency ranges incomparison to the 800-1200Hz range of pure polyurethanefoam. Figure 7 displays the noise reduction capabilities ofdifferent polyurethane foam and textile waste composites. The3:2 composite was represented by the 60-RPF function.
Fig. 7. Graph of Sound Absorption Coefficients of Different PolyurethaneFoam and Textile Waste Composites [15]
Steel has poor sound attenuation properties, but was nec-essary for the structure of the pod. The material bears aNRC value of 0.1, significantly lower than the other primarymaterials. To combat the reduced noise attenuation ability,
steel and polyurethane foam were used in tandem. In eachinterior corner of the pod, the foam was attached to therounded steel edges and load-bearing steel bars. The foamattenuates transmitted and reverberated sound waves withinthe corners. A similar design tactic was used in the roof ofthe pod.
Using MATLAB, the absorption coefficients forpolyurethane and steel were run through a simulationcreated to model sound waves traveling through the respectivematerials. (Appendix B, Figure 27) Two random sine waveswere generated with a frequency of 1000 Hz and processed.The absorption coefficient of polyurethane foam is 0.593while that of steel is 0.1. These absorption coefficients wereput into the following equation:
waveA(i) = sin(1000 ∗ t(i)) ∗ exp(−a ∗ t(i)) (12)
where a represents the absorption coefficient. As seen inFigure 8, it was evident that polyurethane foam shows greatersound absorption properties compared to steel as the amplitudeof the wave traveling through polyurethane foam decreases farmore over the x-axis, time.
Fig. 8. Effect of Different Absorption Coefficients for Various Materials
2) Selecting 3D Structure for Sound Attenuation: The podswere constructed using a simple rounded square base profileand a concentric roof. The profile curves where the soundattenuation was weakest in order to maximize incident angles.The concentric roof accounts for external factors as well,proactively addressing weather concerns, including that ofsnow and rain. It should be noted that the design placed anemphasis on a visually pleasing design, rather than soundattenuation via pod geometry. This means that only the cornersof the pods are rounded, and not the sides. Other designchoices were too complex to realistically construct or imple-ment in city environments.
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C. Electronic Components
1) Raspberry Pi: The Raspberry Pi is a single-board com-puter used for software and hardware projects that is bothsmall in size and affordable. For this project, the most recentmodel of the Raspberry Pi, the Raspberry Pi 4 Model B,was used not only for its computational efficiency but alsoits compatibility with MATALB. Using the MATLAB Sup-port Package for Raspberry Pi Hardware, two programmingmethods can be utilized: standalone execution and interactivecommunication. The first is standalone execution, which al-lows a MATLAB algorithm to be developed independentlyand then translated into equivalent C code that can be runon the Raspberry Pi as a standalone application. The secondprogramming method is interactive communication, whichallows remote control of the Raspberry Pi through MATLABrunning on a desktop or browser [16]. This project usesthe standalone execution programming method in order tosimplify the signal processing. While this project currentlydoes not employ this programming method, it does recognizethe viability of this option for further enhancements of thepod relating to an Internet of Things (IoT) model in whichinformation about ambient noise is wirelessly sent to a centralcity information system.
2) Microphones: This pod system used a USB LavalierMicrophone made by the audio hardware company MAONO.The USB connection allowed this mic to easily connect tothe Raspberry Pi 4 Model B, and its omnidirectional audiosensitivity made it suitable for capturing incoming noise froma broad surrounding zone [17].
3) Speakers: The sound pressure level (SPL) in the podwas considered when selecting suitable speakers. This valuerepresents the sound pressure in an area and is measured indecibels (dB). The SPL value decreases exponentially as thesound wave propagates over an increasing distance, an effectattributed to the inverse square law [18]. The speaker mustproduce sound waves greater in intensity than those recordedby the error microphone. Taking this into consideration, thepod used speakers that are capable of producing 60 dB soundwaves at the source point in order to effectively attenuate evenhigh-intensity sound waves that transmit through the sound-absorbing plexiglass and polyurethane foam.
This system used a 3 watt 8 ohm speaker made by CQRobot[19]. A 3W speaker was chosen because that was the amountof power necessary to produce a sound pressure level of at least60dB about one meter from the speakers, where one meter isthe average distance from the listener in the pod to any oneof the four speakers placed in the upper corners of the pod.
D. Hardware Placement
1) Microphones: The reference microphones must beplaced in such a way that they do not receive any of the anti-noise provided by the speakers. Placing the reference micro-phones in this way would cause the microphones to receiveonly the ambient noise. For this reason, four microphoneswere placed outside the pods near the corners to minimize
the interference caused by the anti-noise and maximize thesignals received from the noise sources.
The error microphone was placed within a light casinghanging from the ceiling close to the occupant of the pod. Themicrophone must be able to accurately determine the sum ofthe sound from the noise source and the anti-noise from thespeakers in order to provide accurate feedback to the adaptivefilter in order to adjust the anti-noise signals played by thespeakers.
2) Speakers: In order to maximize the space covered by thespeakers, the speakers were placed at the top four corners ofthe pod and tilted down slightly to cover the regions of spacethat may be occupied (refer to figure 4). The speaker downtiltsmust be adjusted to cover the auditory range of the occupant(i.e., where noise cancellation must occur) regardless of theirheight and whether the person is standing or sitting.
Fig. 9. Region Covered by the Anti-Noise from the Speakers
E. ANC System
The ANC algorithm was designed to account for the pres-ence of multiple reference microphones and speakers. In theproposed noise-cancelling pods, 4 reference microphones, 4adaptive filters, 4 speakers, and 1 error microphone wereemployed. For simplicity, it is assumed that a weightedcombination of the noise signals received by the referencemicrophones is provided to a bank of adaptive filters, eachfilter providing an anti-noise audio signal to be transmittedby a corresponding speaker. The noise x(t) received by thereference microphones is given by:
x(t) =
R∑i=1
βicnri(t) ∗ n(t)
=
R∑i=1
βi
∫ t
0
cnri(u)n(t− u)du withR∑i=1
βi = 1 (13)
where R denotes the number of reference microphones, βidenotes the weight given to the ith reference microphone,cnri(t) represents the channel between the noise source andthe ith reference microphone, and n(t) represents the noise
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signals. If all reference microphones are weighted equally, thenβi =
1R ∀ i.
In the frequency domain, this may be simply representedas:
X(f) =
R∑i=1
βiCnri(f)N(f) withR∑i=1
βi = 1 (14)
where X(f), Cnri(f), and N(f) denote the frequency domainrepresentations of x(t), cnri(t), and n(t), respectively.
For a given speaker j, the anti-noise signal, sj(t), generatedby the jth adaptive filter, hj(t), is given by:
sj(t) = hj(t) ∗ x(t) =∫ t
0
hj(u)x(t− u)du (15)
where x(t) is obtained from Equation 13. In the frequencydomain, we have:
Sj(f) = Hj(f)X(f) (16)
where Sj(f) and Hj(f) denote the frequency domain rep-resentations of sj(t) and hj(t), respectively. The combinedanti-noise signal provided by the speakers can be representedas:
a(t) =
S∑k=1
csek(t) ∗ sk(t) =S∑k=1
∫ t
0
csek(u)sk(t− u)du
(17)where S represents the number of speakers and csek(t)
represents the channel between the kth speaker and the errormicrophone. In the frequency domain, this may be expressedas:
A(f) =
S∑k=1
Csek(f)Sk(f) =
S∑k=1
Csek(f)Hk(f)X(f)
=
S∑k=1
Csek(f)Hk(f)(
R∑i=1
βiCnri(f)N(f)) (18)
where Sj(f) and X(f) are substituted from Equation 16 andEquation 14, respectively. The flow of signals throughout theANC system is illustrated using the block diagram in Figure10.
F. Digital Signal Processing in MATLABDigital signal processing was employed after collecting the
signals gathered through the reference microphones and errormicrophone. As the primary input signal continues throughthe adaptive filter, the filter weights, or coefficients, are self-adjusted using an algorithm in order to reduce the errorbetween the sampled output signal received by the errormicrophone, e(n), and the desired signal, d(n). To achieveperfect noise-cancellation, the desired signal d(n) must bezero.
Fig. 10. Mapping of Noise Signals Between the Microphones and Speakers
1) Finite Impulse Response (FIR) Filter: The adaptive filterused for ANC in this pod was the Finite Impulse Response(FIR) filter. The coefficients for the FIR filter arise from feed-back control using the mean square error between the desiredsignal and the output signal [20]. After several iterations, theadaptive filter learns noise characteristics and cancels the inputsignal. In general, a FIR filter has the following format:
y(n) = w(n) ∗ x(n) (19)
where w(n) is the filter coefficient, x(n) is the input signal,and * denotes a convolution. The filter coefficient is updatedusing a Least Mean Squares algorithm.
2) Least Mean Squares (LMS) Algorithm: Because the errorsignal must be held as low as possible to achieve the mostaccurate active noise cancellation, the Least Mean Squaresalgorithm was determined to be the most suitable approach forthe ANC system. The algorithm updates the FIR filter weights,or coefficients, in order to minimize the error e(n) between theoutput signal y(n) and the desired signal d(n), and converge tothe optimum filter weight. After multiple iterations, the meansquared error (MSE) should be minimized.
The LMS algorithm uses gradient descent in order to updatefilter weights. The algorithm starts by assuming small weights(zero in most cases) and, at each step, by finding the gradientof the mean square error, the weights are updated. That is, ifthe MSE gradient is positive, it implies the error would keepincreasing positively if the same weight is used for furtheriterations, which means that the weights must be reduced. Inthe same way, if the gradient is negative, the weights must beincreased.
The LMS algorithm uses closed loop control, allowingthe algorithm to compensate for dynamic variations in noisesignals and environmental conditions.
3) Filtered-x LMS FIR Adaptive Filter: The Digital SignalProcessing (DSP) System Toolbox software in MATLABoffers support for active noise control and adaptive filtering.Among these filters, it was determined that the Filtered-xLMS FIR (FXLMS) adaptive filter algorithm offered the best
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approach [21]. This decision was based on the fact that theFIR filter provides better stability than the Infinite ImpulseResponse (IIR) filter, and the LMS algorithm requires lowcomputational and hardware complexity [22].
The filter coefficients w(n) were adjusted based on the LMSalgorithm in the following equation:
w(n+ 1) = w(n) + 0.01e(n)x(n) (20)
where e(n) is the error, w(n) is the coefficient used currently,and w(n + 1) is the coefficient obtained from the LMSalgorithm, which will be used for the next coming inputsample. The value of µ, or 0.01, is the step-size parameter orthe convergence factor. It controls the speed of the coefficientchange and is the basis for the convergence speed of theLMS algorithm. If µ is chosen to be very small then thealgorithm converges very slowly. Together, the FIR filter andLMS algorithm lead to:
y(n) = w(n)x(n) (21)
e(n) = d(n)− y(n) (22)
w(n+ 1) = w(n) + 0.01e(n)x(n) (23)
G. MATLAB Program
Using MATLAB functions and the DSP Toolbox, fxlms= dsp.FilteredXLMSFilter() returned a Filtered-x LMS FIRadaptive filter system object, fxlms. This system object wasused to compute the filtered output and the filter error fora given input signal and desired signal. In the program, theinput signal was simulated by a randomly generate sine wave,which is representative of the noise that would be picked upby the reference microphones in the pods. Meanwhile, thedesired signal was 0 as that would indicate complete noisecancellation. Variables that were modified to optimize outputincluded initial filter coefficients, leakage factor, and step sizefactor [23]. The leakage factor controlled the weight updateof the LMS algorithm and bounds the parameter estimate,eliminating the problem of drifting in the algorithm andstabilizing the system [24]. The step size factor, or adaptationconstant, determined the rate of convergence to the optimalfilter weights. (Appendix B, Figure 28)
IV. RESULTS
A. Noise-Reduced Pod Model
1) Materials: The base structure of the pod was createdusing steel, making the structure sturdy. As steel has a lowabsorption coefficient, the steel beams were hollow. Thehollowed out steel structure was lined with polyurethane foam.This foam is incredibly sound absorbent and thus will furtherprevent the sound from entering the pod. Plexiglass wasutilized so that there is a way to see inside the pod, increasingvisual appeal.
2) 3D Structure: The pod’s structure was modeled usingSketchUp, a 3D modeling program. To start, the pod was givenan inside area of 4’ x 4’ x 8’ for there to be enough roomfor an adult to comfortably stand inside, as the average heightfor an American adult is 5’ 6” [25]. On the outside, the podwas 4’8 3/16” x 4’ 8 3/16” x 9’ to allow for the material tobe thicker and thus more sound absorbent, as seen in Figure11. The four corners of the pod were rounded, and extendto 8’ tall. The insides of the corners were perforated, as toprevent the voice of someone inside from echoing throughoutthe pod. Three of the sides of the pod were identical, with aframe of steel on the bottom and top extending 7 3
16” towardseach other. The space between the steel was occupied by thedouble glazed plexiglass, with dimensions of 3’ 5 3
4” x 6’ 958”. This gives the pod an open appearance. The fourth sideof the pod maintained the same structural design as the otherthree sides, but also added a hinge on the right edge in orderto act like a door when viewed from the outside.
The door was sloped slightly inwards, causing the widthof the entrance to be 2’ 9 3
8”, as seen in Figure 12. Thisdimension was based on the average width of shoulders forAmerican men, 19” [25]. As the walls were made of soundabsorbent materials to prevent sound from entering the pod,the electronic components could not be placed in the wallsthemselves. For this reason, the pod had a domed roof madeto hold the technical components involved in active noisecancellation. The ceiling of the pod also contained the wiringfor the light and motion sensor, ensuring that the pod couldbe used at all times of day.
Fig. 11. Back View of 3D Model of Pod
3) Ventilation System: As the pod is an enclosed structure,there needed to be a way for fresh air to flow in, while
8
Fig. 12. Front View of 3D Model of Pod
Fig. 13. Top View of 3D Model of Pod
still preventing sound from entering. An effective method ofdoing so was utilizing a sound maze, which creates a complexpath surrounded by foam, as seen in Figure 26. The foamsurrounds plywood barriers that run horizontally across thevent, absorbing the sound as it travels though and preventingit from reaching the inside of the pod. These barriers onlyextended down 3
4 of the vent, leaving a small open space forair to travel. The gaps alternated sides (Figure 16) to allowthe air and sound to travel a further distance, absorbing soundvia the foam on the sides. The vent had dimensions of 4 5
16”x 2’ 1 11
16” on the outside. Inside, the vent was 3 1316” x 2’ 1
316”. The vent was 4” thick, as that was the thickness of thewalls of the pod. There were 4 foam coated barriers inside thevent, alternating which side had the opening. They extended20” into the vent and were 1
8” thick. They were placed every
.675”. The front and back of the vent were covered, as seenin Figure 15.
Fig. 14. Arrangement of Acoustic Foam on the Plywood [26]
Fig. 15. Front View of 3D Model of Vent
Fig. 16. Back View of 3D Model of Vent
4) Power Source: In order to power the electrical compo-nents used for active noise cancellation, the pod needs a powersource. For that reason, the pods will be connected to the city’spower grid using a 3-prong grounded plug.
B. Electronic Components Mounting
1) Inner Corner Speaker Mounting Case: In order to housethe speaker, a mounting case was needed for the upper cornersof the pod itself. Designed in OnShape, this mounting case,as shown in Figure 17, was developed in order to fit the 3watt 8 ohm speaker that was chosen for this project. Not onlydoes the mounting case extend to the height of the steel beamthat surrounds the upper portion of the pod, but also preciselyfits into the rounded corners of the pod. The spot for thespeaker to be placed in the mounting case has a length of
9
2.755”, height of 1.220”, and depth of 0.630”. The inside ofthe mounting case was intentionally made hollow to providespace for the Raspberry Pi 4 Model B, which is connected toboth one speaker, which is inside the pod, and one referencemicrophone, which is outside the pod.
Fig. 17. 3D Model of Speaker Mounting Case
2) Microphone with Mounting Case: In order to properlyaffix the reference microphones to the outside of the pod, amounting case, as shown in Figure 18, was designed usingOnShape. First, the USB Lavalier Microphone was modeledusing a number of cylinders that were put together using filletsand chamfers. Then, a case with a height of 4”, length of 0.75”,and width of 0.75” was developed to house the microphone.Using a revolute mate, the microphone and its case wereplaced together to produce a finished design. It was developedin such a manner that it would be placed through the walland reach through the pod’s walls and into the hollow speakermounting case. Thus, the Raspberry Pi 4 Model B can beconnected to both the speaker and the reference microphone.This microphone mounting case will also be used for thesingular error microphone placed inside the pod in the centerof the ceiling.
C. MATLAB Simulation
In order to evaluate the performance of the Filtered-x LMSFIR adaptive filter and the fxlms system object that wascreated, extensive simulations were performed in MATLAB.(Appendix B, Figure 29) Because the LMS step size controlsthe convergence speed of the algorithm and plays an essentialrole in designing an ANC algorithm, the step size was thevariable modified in the simulation. In order to simulatethe effect of the step size on the algorithm with respect toconvergence speed and remaining MSE, the input sound signalhad to first be simulated. This was done by by randomlygenerating a sine wave with a frequency of 2000 Hz. Thissignal was then processed by the filter created. After runningsimulations with variable step sizes, it was determined that a
Fig. 18. 3D Model of Microphone Mounting Case
small step size, required for small excess MSE, resulted inslow convergence. (Figures 19, 20, 21) Meanwhile, a largestep size, needed for fast adaption, resulted in loss of stabilityand had a negative effect on the system’s steady-state MSE.(Figure 22) The optimal step size was determined to be µ =0.008. (Figure 23)
Fig. 19. Active Noise Control of a Noise Signal, µ = 0.0006
10
Fig. 20. Active Noise Control of a Noise Signal, µ = 0.001
Fig. 21. Active Noise Control of a Noise Signal, µ = 0.004
V. CONCLUSION
A. Significance of Findings
This project explored an innovative hybrid approach tonoise-reduced pods in urban areas to provide an escape forcity inhabitants from the chaos of noise pollution on citystreets. With accelerating urbanization, the challenge of noisepollution and its related health concerns will only continueto grow. Exposure to noise of both high and low frequenciescan be addressed through passive and active noise cancellationtechnologies, respectively. For passive cancellation, an analysisof materials revealed that polyurethane foam and double-glazed plexiglass are optimal for sound absorption, while ananalysis of structure revealed that rounded edges not onlyprovide aesthetic benefit, but also provide a greater incidentangle for sound absorption. For active cancellation, extensivesimulations run in MATLAB through the Filtered-x LMS FIR
Fig. 22. Active Noise Control of a Noise Signal, µ = 0.008
Fig. 23. Active Noise Control of a Noise Signal, µ = 0.037
adaptive filter with variable step sizes showed that the best stepsize to converge upon the optimal filter weights and minimizeMSE was µ=0.008.
B. Applications
Data collected about user hotspots and daily pod usagewill be gathered and sent to city officials to assist in betterplacement of pods around the city. Noise pollution data gath-ered through each pod’s microphones will also be analyzed inorder to direct attention to areas critically affected by noise.The pods themselves will be applicable in a wide range oflocations, including city streets, urban parks, subway stations,and industrial plants.
C. Future Developments
An application for mobile devices will be created to assistusers in locating the nearest available pod that is not in use,
11
data provided using the motion sensor located within the pod.Solar panels will also be integrated into the pod design inorder to have the pods operate apart from the city powergrid. Additionally, the algorithm will be modified in order toincrease the convergence rate.
.
12
APPENDIX A
Fig. 24. Technical Drawing of Microphone and Case
Fig. 25. Technical Drawing of Raspberry Pi Case for Speaker
Fig. 26. Technical Drawing of Vent
.
13
APPENDIX B
1 clear2
3 t = 0:0.001:30;4 size = numel(t);5
6 a = 0.593; %polyurethane absorption coefficient7 b = 0.1; %steel absorption coefficient8
9 waveA = [];10 waveB = [];11
12 for i = 1:1:size13 waveA(i) = sin(1000*t(i))*exp(-a*t(i));14 waveB(i) = sin(5*t(i))*exp(-b*t(i));15 end16
Fig. 29. MATLAB FXLMS Simulation of Step Size [27]
.
14
VI. ACKNOWLEDGMENTS
The authors of this paper gratefully acknowledge the follow-ing: Research Coordinator and Residential Teaching Assistant(RTA) Project Liaison Benjamin Lee for his supervision andinvaluable assistance in conducting proper research; HeadRTA Rajas Karajgikar; project coordinators Michael DiBuonoand Nicholas Calzaretto for organizing this project; projectmentors Jack Russ, Xavier Johnson, Julia Ma, Kaitlin Taylor,and Allison Boyd for their valuable expertise and guidance;Dean Jean Patrick Antoine, the Director of the NJ Governor’sSchool of Engineering and Technology (GSET), and DeanIlene Rosen, the Director Emeritus of GSET, for their man-agement and guidance; Rutgers University, Rutgers School ofEngineering, and the State of New Jersey for the chance toadvance knowledge, explore engineering, and open up newopportunities; Lockheed Martin and the NJ Space Grant Con-sortium for funding our scientific endeavours; and lastly NJGSET Alumni, for their continued participation and support.
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