Bridge expansion joint acoustic monitoring method based on beam forming microphone array

Abstract

The invention discloses a bridge expansion joint acoustic monitoring method based on a beam forming microphone array, and the method comprises the steps: synchronously collecting acoustic signals through multiple channels, and achieving the high-precision signal alignment through clock offset compensation; the noise analysis module is started by combining a pre-triggering signal of a vehicle passing through the detection unit, the optimal microphone distance is dynamically determined according to sound field coherence and a signal-to-noise ratio maximization model, and a stepping motor drives a movable microphone to achieve real-time adjustment. On the basis, a spatial filtering weight is generated by adopting a self-adaptive beam forming algorithm, and directional enhancement and interference suppression of the expansion joint sound source are realized. Through collaborative optimization of a hardware structure and a signal processing method, the sensitivity and accuracy of acoustic monitoring of the bridge expansion joint are effectively improved, the abnormal sound source recognition capability can be remarkably enhanced, the environmental noise interference is reduced, and the method is suitable for intelligent monitoring and diagnosis of the long-term service state of the bridge expansion joint.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent monitoring of bridge expansion joints, and particularly relates to a bridge expansion joint acoustic monitoring method based on a beamforming microphone array. BACKGROUND

[0002] The expansion joint is an important connecting device between bridge spans or between the bridge span and the abutment, and its function is to adapt to the displacement of the bridge structure caused by factors such as temperature changes, concrete shrinkage and creep, and loads. The health condition of the expansion joint is directly related to the driving comfort and the safety of the bridge structure. Once diseases such as loosening, fracture, and jamming occur, not only will a huge impact noise be produced, but also irreversible damage will be caused to the main structure of the bridge. Therefore, long-term, continuous, and reliable state monitoring of the bridge expansion joint has great engineering significance.

[0003] At present, the monitoring technology of the bridge expansion joint mainly includes the following two types: (1) manual inspection and visual detection method: relying on technical personnel to conduct regular on-site inspection or using a vehicle-mounted or unmanned aerial vehicle-mounted camera to collect and identify images. This method is highly subjective, inefficient, and cannot achieve real-time monitoring, and it is difficult to find hidden or small structural damage; contact sensor monitoring method: including installing acceleration sensors, displacement meters, strain gauges, and the like near the expansion joint. These methods can usually provide direct structural response data, but the installation process often requires invasive operations such as drilling on the bridge structure, which is complex and costly, and the sensors themselves are easily damaged in harsh road environments, and long-term reliability is challenging; (2) acoustic monitoring method: this is a new non-contact and low-cost monitoring method, and its basic principle is that when a vehicle passes through the expansion joint, a unique acoustic signal will be generated, and the time domain and frequency domain characteristics of the signal are closely related to the health status of the expansion joint. By analyzing the sound signal, the state of the expansion joint can be evaluated and fault diagnosis can be performed.

[0004] The existing acoustic monitoring method still has significant limitations in practical application: (1) the acoustic environment of the bridge is complex, and the monitoring signal is easily overwhelmed by strong traffic noise (such as engine roar, tire rolling noise), wind noise, rain noise, etc., resulting in a very low signal-to-noise ratio (SNR) and difficulty in extracting effective features; (2) the existing microphone array structure is rigid, and some studies attempt to use a microphone array for sound source enhancement and positioning, but the spacing between the microphones is usually fixed and cannot be adjusted. Since the coherence of the sound field is closely related to the frequency and the spacing between the microphones, a fixed array geometry cannot adapt to the changing environmental noise field and different types of expansion joint sound sources, resulting in a decline in the performance of the beamforming algorithm in some frequency bands, and the ability to suppress noise and enhance the target sound source is limited.

[0005] In summary, the prior art lacks a bridge expansion joint acoustic monitoring system that can adapt to complex noise environments, dynamically optimize array configuration to maximize signal-to-noise ratio, and has high-precision synchronous acquisition capability. The present application aims to overcome the above shortcomings and provide an efficient, reliable, non-contact automated monitoring solution. SUMMARY

[0006] Technical problem: In view of the shortcomings of the prior art, the present application provides a bridge expansion joint acoustic monitoring method based on a beamforming microphone array. Through mechanical structure optimization, adaptive array adjustment, high-precision signal processing and closed-loop control, accurate acquisition and analysis of expansion joint acoustic signals in complex environments are achieved, and the anti-interference ability, positioning accuracy and environmental adaptability of the monitoring system are improved, solving the problems of large noise interference, low positioning accuracy and poor environmental adaptability in bridge expansion joint monitoring.

[0007] Technical solution: The present application is a bridge expansion joint acoustic monitoring method based on a beamforming microphone array, comprising the following steps: S1, arranging at least one fixed microphone and at least two movable microphones near the bridge expansion joint; S2, synchronously acquiring acoustic signals of each microphone through a multi-channel analog-to-digital conversion module, and measuring and compensating clock offset between channels using a digital signal processing unit to ensure signal synchronization; S3, receiving a pre-trigger signal of the vehicle passing detection unit to start the noise analysis module; S4, dynamically determining the optimal microphone spacing based on sound field coherence calculation and signal-to-noise ratio maximization model; S5, driving the movable microphones through a stepper motor and encoder to realize real-time adjustment of the microphone spacing; S6, using an adaptive beamforming algorithm to generate spatial filtering weights to directionally enhance and suppress interference of the expansion joint sound source, thereby realizing monitoring and analysis of the expansion joint acoustic signals.

[0008] wherein, In step S2, the digital signal processing unit uses a clock offset estimation method based on the cross-correlation algorithm, and the compensation accuracy reaches within 1% of the sampling period; In step S4, the method for determining the optimal microphone spacing comprises the following steps: S41, sound field modeling and data acquisition: control the microphone to move along the guide rail and acquire sound pressure time domain signals at the encoder positioning points; separate the pure noise period without expansion joint sound source and the mixed sound period with expansion joint sound source through sound energy threshold judgment; S42, dynamic noise template library construction: store noise spectrum templates in different weather conditions such as wind, rain and sunny, match the current environment to quickly output pure noise estimation; dynamically update the template library through the online noise spectrum learning module; the noise analysis module uses Welch's Method for spectral analysis of environmental noise signals, outputs the noise spectrum characteristics in the frequency band of 50Hz~2kHz, and simultaneously calls the dynamic noise template library storing typical noise spectra in three weather conditions of wind, rain and sunny, quickly matches the current environment and outputs pure noise estimation; the template library is updated once a month through the online noise spectrum learning module; S43, frequency domain coherence calculation: define the coherence function of the target sound source in the expansion joint at frequency , interval ; , the coherence function of the environmental noise at frequency , interval ; , and focus on the frequency band weight function of the expansion joint characteristic frequency band ; S44, modeling based on frequency domain coherence calculation and SNR maximization, the specific formula is as follows: Frequency domain coherence calculation: ; ; In the formula, is the spatial position, is the sound pressure or signal of the sound pressure signal of the target sound source in the expansion joint at frequency and position , is the sound pressure or signal of the sound pressure signal of the target sound source in the expansion joint at frequency and position , is the sound pressure signal of the environmental noise at frequency and position , is the sound pressure signal of the environmental noise at frequency and position , and respectively represent the complex conjugate of and , expectation operator; ; represents the optimal interval, take the maximum value in the expansion joint characteristic frequency band , the weight of the environmental noise dominant frequency band decays to , wherein the weight allocation strategy Dynamic adjustment according to environmental sensor data.

[0009] In step S5, the stepper motor adopts high-precision positioning control mode, and can realize micro-step subdivision control through pulse width modulation waveform driving, so as to ensure the accuracy and stability of the microphone spacing adjustment.

[0010] In step S6, a minimum variance distortionless response (MVDR) adaptive beamformer is adopted: a fixed-pointing Decomposition algorithm, that is, improved Gram-Schmidt algorithm is used to solve the inverse of the covariance matrix, and the specific steps are as follows: S61, receiving a microphone signal matrix , represents the complex domain, is the number of sampling points, is the number of microphones; S62, decomposing : wherein is a unitary matrix, is an upper triangular matrix; S63, generating a steering vector formula based on the bridge joint linear sound source model: ; wherein are the absolute propagation time delays of sound waves from the sound source to the first microphone, is the signal frequency, , , are the distances from the sound source to the first microphone, wherein ; is the speed of sound, ; S64, solving the beam weight: according to the beam weight satisfying the optimization problem: (constraint condition ), the solution is: ; In the formula, is the covariance matrix of the input signal, wherein , is an upper triangular matrix, is the conjugate transpose of .

[0011] The bridge joint acoustic monitoring device based on the beamforming microphone array used in the method comprises: (1) fixed microphone and movable microphone: used for collecting acoustic signals of the bridge joint;​ (2) Vehicle passing detection unit: for outputting a pre-trigger signal when the vehicle approaches the expansion joint; (3) Multi-channel analog-to-digital conversion module: for synchronously collecting multi-channel acoustic signals; (4) Digital signal processing unit: for clock offset measurement and compensation, sound field coherence calculation, and signal-to-noise ratio maximization analysis; (5) Stepping motor and encoder: for driving the movable microphone and realizing real-time adjustment of the microphone spacing; (6) Beamforming processing module: for executing an adaptive beamforming algorithm and generating spatial filtering weights to realize directional enhancement and interference suppression of the expansion joint sound source.

[0012] Advantages: Compared with the prior art, the present application has the following advantages: By analyzing the environmental noise spectrum characteristics in real time and calculating the optimal microphone spacing based on the signal-to-noise ratio maximization model, the spatial filtering performance of the array is always optimally configured for the current noise environment.

[0013] Combined with the high-precision MVDR adaptive beamforming algorithm, the main beam can be extremely accurately formed in the direction of the expansion joint, and a null is formed in the direction of the noise arrival, thereby maximally suppressing strong environmental interference (such as traffic flow noise, wind and rain noise).

[0014] The system can automatically distinguish the noise characteristics under different weather conditions (sunny, rainy, windy), and adjust the optimal spacing calculation model and beamforming weight distribution strategy accordingly. This makes the present application not a rigid system with fixed parameters, but an intelligent solution that can adapt to local conditions, ensuring long-term stability and monitoring effectiveness in various complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 Bridge expansion joint acoustic monitoring method based on beamforming microphone array technical flowchart; Figure 2 Optimization of microphone array spacing flowchart; Figure 3 Microphone array beamforming flowchart; Figure 4 Bridge expansion joint acoustic monitoring device based on beamforming microphone array layout diagram; Figure 5 Bridge expansion joint acoustic monitoring device based on beamforming microphone array working schematic diagram. DETAILED DESCRIPTION

[0016] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0017] The device used in the bridge expansion joint acoustic monitoring method based on a beamforming microphone array comprises: (1) fixed microphone and movable microphone: used for collecting acoustic signals of the bridge expansion joint; (2) vehicle passing detection unit: used for outputting a pre-trigger signal when a vehicle approaches the expansion joint; (3) multi-channel analog-to-digital conversion module: used for synchronously collecting multi-channel acoustic signals; (4) digital signal processing unit: used for clock offset measurement and compensation, sound field coherence calculation, and signal-to-noise ratio maximization analysis; (5) stepper motor and encoder: used for driving the movable microphone and realizing real-time adjustment of the microphone spacing; (6) beamforming processing module: used for executing an adaptive beamforming algorithm and generating spatial filtering weights to realize directional enhancement and interference suppression of the expansion joint sound source.

[0018] Referring to Figure 4 , it is a typical arrangement of the bridge expansion joint acoustic monitoring device based on a beamforming microphone array of the present application. The arrangement is as follows: The extension direction of the microphone guide rail is substantially perpendicular to the length direction of the bridge expansion joint, and is fixedly installed on the bridge side or the maintenance passage. The microphone is installed on the guide rail and is precisely driven by the stepper motor to move along the guide rail to realize real-time adjustment of the microphone spacing. The vehicle passing detection unit (such as a laser radar or a ring coil detector) is arranged at a certain distance upstream of the road from the expansion joint to generate a pre-trigger signal in advance when a vehicle approaches.

[0019] The signal processing unit is the control core of the system and is electrically connected with the stepper motor on the guide rail, the microphone array, and the vehicle passing detection unit. Referring to Figure 5 , the working process is as follows: receiving the pre-trigger signal from the vehicle passing detection unit, starting the noise analysis module; based on the real-time collected acoustic signals and the built-in algorithm, dynamically calculating the optimal microphone spacing in the current environment; generating a control instruction to drive the stepper motor to adjust the microphone position; then executing the adaptive beamforming algorithm to enhance and suppress the expansion joint sound source signal, and finally outputting the monitoring result.

[0020] The application provides a bridge expansion joint acoustic monitoring method based on a beamforming microphone array, which takes monitoring of a D80 expansion joint (a design displacement amount is ±80 mm) as an example, and the main technical process of the implementation scheme is as follows (see Figure 1 ): S1, see Figure 4 The device is installed in the above manner, a fixed microphone and at least two movable microphones are arranged near the bridge expansion joint; the microphones are installed on the guide rail and are driven to move along the guide rail by a stepping motor to adjust the distance between the microphones in real time. A vehicle passing detection unit (such as a laser radar or a ring coil detector) is arranged on the road upstream of the expansion joint at a distance from the expansion joint, and is used to generate a pre-trigger signal in advance when a vehicle approaches.

[0021] Specifically, all the microphones are installed on a straight guide rail with a total length of 2.5 meters. The guide rail is made of corrosion-resistant aluminum alloy, and the extension direction of the guide rail is perpendicular to the length direction of the D80 expansion joint, and the guide rail is installed on the outside of the bridge shoulder or the crash barrier, and is about 5 meters away from the center line of the expansion joint. The vehicle passing detection unit adopts a laser ranging sensor, and is installed 10 meters in front of the expansion joint, and is used to output a pre-trigger signal when a vehicle approaches.

[0022] S2, the acoustic signals of the microphones are synchronously collected by a multi-channel analog-to-digital conversion module, and the clock offset between the channels is measured and compensated by a digital signal processing unit to ensure signal synchronization; Specifically, the multi-channel analog-to-digital conversion module adopts a 24-bit ADC (analog-to-digital converter), and the sampling frequency is set to 44.1 kHz, and the microphone signals are synchronously collected. The digital signal processing unit adopts an FPGA (field programmable gate array), and the clock offset estimation method based on the cross-correlation algorithm has a compensation accuracy of within 1% of the sampling period.

[0023] S3, receiving the pre-trigger signal of the vehicle passing detection unit, starting the noise analysis module.

[0024] Specifically, when a vehicle passes through the laser radar detection area, the system is triggered. The noise analysis module is immediately started, and a dynamic noise template library is called. For example, when the current weather is rainy, the system matches the “rainy day” noise template (the characteristic is that the energy in the 200-500 Hz frequency band is significantly high).

[0025] S4, based on the environmental noise spectrum characteristics, the noise analysis module identifies the pure noise period and the mixed sound period (the period containing the expansion joint sound source and the environmental noise), and dynamically determines the optimal microphone distance by combining the sound field coherence calculation and the signal-to-noise ratio maximization model.

[0026] See Figure 2 , specifically, the method for determining the optimal distance between the microphones comprises the following steps: S41, Sound Field Modeling and Data Acquisition: Control the microphone to move along the guide rail, at the encoder positioning point ( Acquire sound pressure time-domain signals; separate pure noise periods (sound sources without expansion joints) and mixed sound periods (sound sources including expansion joints) by judging sound energy threshold. S42, Dynamic Noise Template Library Construction: Stores noise spectrum templates for different weather conditions (wind, rain, sunny), quickly outputs pure noise estimates by matching the current environment; the template library is dynamically updated through an online noise spectrum learning module; the noise analysis module uses Welch's Method to perform spectrum analysis on environmental noise signals, outputting noise spectrum characteristics in the 50Hz~2kHz frequency band, and simultaneously calls the "Dynamic Noise Template Library" (stores typical noise spectra for wind, rain, and sunny weather), quickly matches the current environment and outputs pure noise estimates (the template library is updated monthly through the "Online Noise Spectrum Learning Module"); S43, Frequency Domain Coherence Calculation: Define the target sound source of the expansion joint at a frequency... ,spacing coherence function under Environmental noise at frequency ,spacing coherence function under The frequency band weighting function focuses on the characteristic frequency band of the expansion joint. ; S44, based on frequency domain coherence calculation and SNR (signal-to-noise ratio) maximization modeling, has the following specific formula: Frequency domain coherence calculation: ; ; In the formula, It is spatial location. At frequency and location The sound pressure or signal of the target sound source (expansion joint) at the location. At frequency and location The sound pressure or signal of the target sound source (expansion joint) at the location. At frequency and location The sound pressure signal of the ambient noise at the location, At frequency and location The sound pressure signal of the ambient noise at the location, and They represent and The complex conjugate, It is the expectation operator.

[0027] ; represents the optimal distance, The maximum value is taken in the characteristic band of the expansion joint , the band weight of the ambient noise dominant band is attenuated to , wherein the weight allocation strategy is dynamically adjusted according to the environmental sensor data.

[0028] Specifically, focusing on the characteristic band (800-1600 Hz) of the D80 expansion joint, the band weight function is set 1 in this interval, and attenuated to 0.2 in other frequency bands (especially 200-500 Hz where rain noise is significant).

[0029] S5, driving the movable microphone through the stepper motor and encoder to realize real-time adjustment of the microphone distance; Specifically, the stepper motor adopts a high-precision positioning control mode, which can realize micro-step subdivision control through pulse width modulation waveform driving, and ensure the accuracy and stability of the microphone distance adjustment.

[0030] S6, using an adaptive beamforming algorithm to generate spatial filtering weights to directionally enhance and interfere with the expansion joint sound source, thereby realizing the monitoring and analysis of the expansion joint acoustic signal.

[0031] Referring to Figure 3 , specifically, an MVDR adaptive beamformer is used: a fixed-point decomposition algorithm (improved Gram-Schmidt algorithm) is used to solve the covariance matrix inverse, and the specific steps are as follows: S61, receiving the microphone signal matrix , represents the complex domain, is the number of sampling points, is the number of microphones; S62, decomposing : , wherein is a unitary matrix, is an upper triangular matrix; S63, generating a steering vector formula based on the expansion joint linear sound source model ; , wherein are the absolute propagation time delays of the sound waves from the sound source to the th microphone, is the signal frequency, , , ​are the distances from the sound source to the 0th, 1st, 2nd microphones, respectively, wherein, is the sound speed, taking 340 m / s; S64, solving the beam weight: according to the beam weight satisfies the optimization problem: (constraint ), the solution is: wherein, is the covariance matrix of the input signal, wherein, , is an upper triangular matrix, is the conjugate transpose of

[0032] After the spatial filtering weight is calculated, a main beam is formed in the direction of the expansion joint to enhance the signal, and nulls are formed in the directions of the traffic noise and the wind and rain noise. After processing, the target signal gain is improved by about 12 dB, the main interference noise is suppressed by more than 15 dB, and the signal-to-noise ratio is significantly improved, which facilitates subsequent state diagnosis and abnormality identification.

[0033] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of helping the reader to understand the principles of the present application, and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspirations disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the scope of protection of the present application.​​​

Claims

1. A method of acoustic monitoring of a bridge expansion joint based on a beamforming microphone array, characterized in that, The method specifically comprises the following steps: S1, arranging at least one fixed microphone and at least two movable microphones near the bridge expansion joint; S2, synchronously collecting acoustic signals of each microphone through a multi-channel analog-to-digital conversion module, and measuring and compensating clock offset between channels by using a digital signal processing unit to ensure signal synchronization; S3, receiving a pre-trigger signal of a vehicle passing detection unit, and starting a noise analysis module; S4, dynamically determining an optimal microphone spacing based on a sound field coherence calculation and a signal-to-noise ratio (SNR) maximization model; S5, driving the movable microphones through a stepper motor and an encoder to realize real-time adjustment of the microphone spacing; S6, generating spatial filtering weights by using an adaptive beamforming algorithm to realize directional enhancement and interference suppression of the expansion joint sound source, thereby realizing monitoring and analysis of the expansion joint acoustic signal.

2. A method of acoustic monitoring of a bridge expansion joint based on a beamforming microphone array according to claim 1, characterized in that, In step S2, the digital signal processing unit adopts a clock offset estimation method based on a cross-correlation algorithm, and the compensation accuracy reaches within 1% of the sampling period.

3. The method of claim 1, wherein, In step S4, the method for determining the optimal microphone spacing comprises the following steps: S41, sound field modeling and data collection: controlling the microphone to move along the guide rail, collecting sound pressure time domain signals at the encoder positioning points; separating the pure noise period without the expansion joint sound source and the mixed sound period containing the expansion joint sound source through sound energy threshold judgment; S42, dynamic noise template library construction: storing noise spectrum templates under different weather conditions such as wind, rain and fine weather, matching the current environment to quickly output pure noise estimation; dynamically updating the template library through an online noise spectrum learning module; the noise analysis module performs frequency spectrum analysis on the environmental noise signal by using Welch's Method, and outputs the noise spectrum characteristics in the frequency band of 50Hz~2kHz, and simultaneously calls the dynamic noise template library storing typical noise spectra under three weather conditions of wind, rain and fine weather, quickly matches the current environment and outputs the pure noise estimation; the template library is updated once a month through the online noise spectrum learning module; S43, frequency domain coherence calculation: define the coherence function of the target sound source of the expansion joint at frequency , interval , the coherence function of the environmental noise at frequency , interval , and the frequency band weight function of focusing the frequency band of the expansion joint characteristic frequency . ;​ S44, modeling based on frequency domain coherence calculation and signal-to-noise ratio (SNR) maximization, and the specific formula is as follows: Frequency domain coherence calculation: ; ； wherein is a spatial position, is an acoustic pressure signal of a target sound source at a frequency and a position , is an acoustic pressure signal of a target sound source at a frequency and a position , is an acoustic pressure signal of ambient noise at a frequency and a position , is an acoustic pressure signal of ambient noise at a frequency and a position , and denote the complex conjugate of and , is a desired operator; ； represents the optimal spacing, maximizing at the expansion joint characteristic frequency band , the ambient noise dominant frequency band weight decays to where the weight allocation strategy is dynamically adjusted according to ambient sensor data.

4. The method of claim 1, wherein, In step S5, the stepper motor adopts a high-precision positioning control mode, and can realize micro-step subdivision control through pulse width modulation waveform driving, thereby ensuring the accuracy and stability of the microphone spacing adjustment.

5. The method of claim 1, wherein, In step S6, a minimum variance distortionless response (MVDR) adaptive beamformer is used: a fixed-pointing The solution algorithm, i.e., the improved Gram-Schmidt algorithm, is used to solve the inverse of the covariance matrix, and the specific steps are as follows: S61, receive a microphone signal matrix , denotes the complex domain, is the number of samples, is the number of microphones; S62, to perform decomposition: wherein is a unitary matrix, is an upper triangular matrix; S63, generating a steering vector formula based on the linear sound source model of the expansion joint as follows: ， wherein respectively the absolute propagation time of the sound wave from the sound source to the first microphone, is the signal frequency, , , are the distances of the sound source to the first microphone, respectively, wherein ; is the sound velocity, ; S64, solve beam weights: according to beam weights satisfy optimization problem: (constraint ), whose solution is: ; wherein is the covariance matrix of the input signals, wherein , is an upper triangular matrix, is the conjugate transpose of 6. A bridge joint acoustic monitoring device based on a beamforming microphone array for use in the method of any one of claims 1 to 5, characterized in that, It comprises: (1) fixed microphone and movable microphone: used for collecting acoustic signals of the bridge expansion joint; (2) vehicle passing detection unit: used for outputting a pre-trigger signal when a vehicle approaches the expansion joint; (3) multi-channel analog-to-digital conversion module: used for synchronously collecting multi-channel acoustic signals; (4) digital signal processing unit: used for measuring and compensating clock offset, sound field coherence calculation and signal-to-noise ratio (SNR) maximization analysis; (5) stepper motor and encoder: used for driving the movable microphone and realizing real-time adjustment of the microphone spacing; (6) beamforming processing module: used for executing an adaptive beamforming algorithm and generating spatial filtering weights to realize directional enhancement and interference suppression of the expansion joint sound source.

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