CN107843333B - A kind of pipeline radial direction glottis neoplasms detection system and method based on compressive sensing theory - Google Patents

Abstract

The invention discloses a pipeline radial sound mode detection system and method based on compressive sensing theory. In the present invention, N sensor arrangement positions are uniformly arranged along the radial direction of the pipeline on a radius of the measurement section; H positions are randomly selected from the N sensor arrangement positions to arrange the sensors respectively; the pipeline radial acoustic modal detection based on compressive sensing theory The method breaks through the limitation of Shannon-Nyquist sampling theorem, reduces the originally required large-scale sensor array to an acceptable range, and still achieves the purpose of accurately extracting the radial modal amplitude; compared with the traditional detection method Therefore, the method proposed by the present invention greatly reduces the complexity of the hardware arrangement level and the cost of data acquisition, storage and processing, and the process is simple and easy to implement.

Description

A pipeline radial acoustic modal detection system and method based on compressive sensing theory

technical field

The invention relates to a pipeline acoustic modal detection technology, in particular to a pipeline radial acoustic modal detection system and a detection method based on compressive sensing theory.

Background technique

In the field of noise testing, the testing of the sound field of the pipeline is the main method to determine the sound source information in the pipeline and the influence of the far-field noise outside the pipeline. It has important applications in aerospace, automobile, household appliance noise reduction and other related fields. The acoustic mode is directly related to the geometric characteristics of rotating mechanism components such as fans and motors. After the acoustic mode structure is determined, it is enough to infer and analyze the mechanism of noise generated by the relevant mechanism and the distribution of noise sources, so as to provide guidance for noise reduction design. , so the acoustic modal detection method is very important for pipeline noise testing.

The acoustic modal detection of pipeline can be divided into circumferential modal detection and radial modal detection, and its goal is to obtain the amplitude of each modal. For the radial modal detection, the circumferential modal detection is required as a precondition, so it is more complicated. In order to detect the circumferential mode, the sensor array is generally installed flush on the pipe wall along the circumferential direction, and the obtained data is decomposed by the space-based Fourier, and then the amplitude of each circumferential mode can be obtained. After the circumferential main mode is determined according to the amplitude, radial mode detection can be carried out. Actually, the sensor array is arranged radially inside the pipe to obtain the sound field data, and then the radial modal coefficients are obtained based on the Fourier-Bessel decomposition, and finally the radial modal spectrum of the sound field is obtained.

It should be pointed out that the above circumferential modal detection must follow the Shannon-Nyquist sampling theorem, which means that the total number of array elements required by the sensor array is twice the highest modal order that can be detected. In actual tests, the number of blades in rotating parts is often large. According to the Taylor-Sofrin selectivity, the circumferential modal order generated by them is generally higher. For this reason, a large number of sensors need to be arranged along the circumferential direction. Similarly, in order to obtain the radial mode, it is often necessary to arrange multiple measuring points in the radial direction at multiple circumferential positions of the pipeline, which leads to a large number of radial sensors. The above factors are coupled together, which can easily lead to the extremely complex radial modal detection system, and the high cost of data acquisition, storage and processing. At present, although there are countermeasures such as rotating sensor arrays, they only alleviate the above contradictions to some extent, but do not fundamentally solve the problem. To this end, it is necessary to develop a new mode extraction method from the perspective of signal processing, which can control the number of sensors within an acceptable range while detecting a wide range of modes.

SUMMARY OF THE INVENTION

In order to solve the above problems existing in the prior art, the present invention proposes a pipeline radial acoustic modal detection system and detection method based on compressive sensing theory.

An object of the present invention is to propose a pipeline radial acoustic mode detection system based on compressive sensing theory.

The shape of the pipe is a circle of equal section with a radius of R. The cylindrical coordinate system (x, r, θ) is used. The section where the component that generates the high-order modal sound wave is located is the sound source section. Propagating in the positive direction of x in the pipe, the measurement section is located at the section where x = x ₀ .

The pipeline radial acoustic modal detection system based on the compressed sensing theory of the present invention comprises: N sensor arrangement positions and H sensors; wherein, on a radius of the measurement section, N sensor arrangement positions are uniformly arranged along the pipeline radial direction; H positions are randomly selected from the N sensor placement positions to arrange the sensors respectively; the number N of sensor placement positions is determined by the highest transmittable radial mode order n of the pipeline, n is a natural number, and N>n; the number of sensors H satisfies: Cslog(N/s) <H<N, where C is an empirical constant, and s is the modal sparsity.

Another object of the present invention is to provide a pipeline radial acoustic mode detection method based on compressive sensing theory.

The pipeline radial acoustic modal detection method based on the compressed sensing theory of the present invention comprises the following steps:

1) Determine the pipeline model: the shape of the pipeline is a circle of equal section with a radius of R, and the cylindrical coordinate system (x, r, θ) is used, and the section where the component that generates the high-order modal sound wave is located is the sound source section, and the sound source section is located at x = 0 section, the sound wave propagates in the positive direction of x in the pipeline, and the measurement section is located at the section of x = x ₀ ;

2) Determine the highest frequency of detection, and then according to the inner radius of the pipeline, determine the highest propagable radial modal order n of the pipeline to be detected, and according to the highest propagable radial modal order of the pipeline, determine one of the measured cross-sections. The number N of sensor arrangement positions evenly arranged along the radial direction of the pipeline on the radius, and randomly select H positions from the N sensor arrangement positions to install sensors respectively;

3) All sensors collect signals synchronously, obtain time-domain data, obtain frequency spectrum by fast Fourier transform of time-domain data, extract frequency-domain data of each sensor at the frequency of interest from the frequency spectrum, and construct measurement result vector;

4) According to the sensor arrangement position selected in step 2), construct an H×N compressed sensing measurement matrix;

5) Construct an N×N space transformation matrix;

6) according to the measurement result vector, the compressed sensing measurement matrix and the space transformation matrix, the radial frequency signal under the concerned frequency is reconstructed to obtain a complete radial frequency signal;

7) Extract the radial modal amplitude from the reconstructed radial frequency signal.

Wherein, in step 2), on a radius of the measurement section, N sensor arrangement positions are evenly arranged along the radial direction of the pipeline; H positions are randomly selected from the N sensor arrangement positions to set sensors respectively, and the number H of sensors satisfies : Cslog(N/s)<H<N, where C is an empirical constant and s is the modal sparsity. The larger the value of H, the higher the success rate of accurately reconstructing the original signal, but at the same time, the obvious advantage over the prior art method will be lost.

In step 3), the time domain data is subjected to fast Fourier transform to obtain a frequency spectrum, the frequency of interest f ₀ is determined, and the frequency domain data P _h (f ₀ ), h of each sensor at the frequency of interest f ₀ is extracted from the frequency spectrum _{= 1 ,} ^. _{_ _ _}

In step 4), a random 1-0 matrix is used as the compressed sensing measurement matrix, thereby constructing an H×N compressed sensing measurement matrix:

Among them, the matrix element value of the rth row and the ith column is 1, and the rest are 0, r=1,...,H, i∈[1,N].

In step 5), since the frequency domain data obtained in step 3) is not sparse, it needs to be transformed into a sparse modal space by applying a space transformation matrix to meet the requirements of compressed sensing. For the detection of radial modes, the modal decomposition is based on Fourier-Bessel transformation, so the required spatial transformation matrix ψ _B has the following form:

Among them, J _m (·) represents the m-order Bessel function of the first kind, m is the circumferential modal order, ri is the _ith radial position among the N sensor arrangement positions that are evenly distributed in the radial direction, and ri = _i ×R/N, i=1...N, and k _i (i=1,2,...,N) is the solution under the constraint of the second type of boundary conditions of the Bessel function, which can be calculated by J' _m ( _ki R)=0 where (·)' represents the derivative; k _{i satisfying} this boundary condition is multi _- valued, and a series of k ₁ , k ₂ .

In step 6), according to the measurement result vector, the compressed sensing measurement matrix and the space transformation matrix, use l ₁ -norm minimization to reconstruct the radial frequency signal at the frequency of interest to obtain the estimated signal in the transformation space calculate Get the complete radial frequency signal

In step 7), the calculation method of the ith order radial modal amplitude is as follows:

in, is the modulus of the Bessel eigenfunction, which is defined as:

Thereby, the radial modal amplitudes c _i of each order are finally obtained.

Advantages of the present invention:

The pipeline radial acoustic modal detection method based on the compressed sensing theory of the invention breaks through the limitation of the Shannon-Nyquist sampling theorem, reduces the originally required large-scale sensor array to an acceptable number range, and can still achieve accurate extraction The purpose of radial modal amplitude; compared with the detection method in the prior art, the method proposed by the present invention greatly reduces the complexity of the hardware layout level and the cost of data acquisition, storage and processing, and the process is simple and easy to implement.

Description of drawings

1 is a model diagram of a pipeline radial acoustic modal detection system based on compressive sensing theory of the present invention;

Fig. 2 is the single-frequency radial frequency signal obtained according to an embodiment of the pipeline radial acoustic modal detection method based on compressive sensing theory according to the present invention and the radial frequency signal comparison diagram obtained by the prior art;

FIG. 3 is a diagram showing the detection results of radial frequency signals obtained by using 5 sensors in the present invention to compare with 20 sensors in the prior art.

Detailed ways

Below in conjunction with the accompanying drawings, the present invention will be further described through specific embodiments.

As shown in Figure 1, the shape of the pipe ① is a circle of equal cross-section with a radius of R. Using a cylindrical coordinate system (x, r, θ), the sound source section ④ of the component that generates high-order modal sound waves is located at the section of x=0, at The propagation direction of the sound wave in the pipeline ② is along the positive direction of x, and the measurement section ⑤ is located at the section of x=x ₀ . The pipeline radial acoustic modal detection system based on compressive sensing theory in this embodiment includes: H sensors; a natural number N is determined according to the highest propagable radial modal order n of the pipeline, N>n; N sensor arrangement positions are evenly arranged along the radial direction of the pipeline ③, and H sensors are randomly selected from the N sensor arrangement positions to arrange H sensors respectively; The number n is determined, n is a natural number, and N>n; the number H of sensors must satisfy: Cslog(N/s)<H<N, where C is an empirical constant, and s is the modal sparsity.

In this embodiment, the radius of the pipe is R=0.5m, and there are a group of sound waves (frequency f ₀ =5000Hz) with circumferential mode m = 3 and radial mode n = (3, 8) in its interior, and two modes All are in cut-on state. It should be pointed out that in the actual test, high-order modes exceeding a certain order will decay rapidly. In this embodiment, the sound wave with radial mode n>14 will decay rapidly and cannot propagate in the axial direction in the tube.

The method for detecting the radial acoustic mode of a pipeline based on the compressed sensing theory of this embodiment includes the following steps:

1) Determine the pipeline model. The pipeline is a circle of equal cross-section with a radius of R=0.5m. The cylindrical coordinate system (x, r, θ) is used. The components that generate high-order modal sound waves are located at the sound source section of x=0. Propagating along the positive direction of x, the measurement section is located at the section of x=x ₀ ;

2) Determine the highest frequency of detection, the circumferential mode m=3, and then according to the inner radius of the pipeline, determine the highest propagation radial mode order n of the pipeline to be detected. The number of sensor placement positions N=20, which has covered all possible radial mode orders of propagation, and 20 sensor placement positions (detectable modes n=1 to 20) are arranged along the radial direction, and their numbers are from close to the center of the circle. Starting from , and denoted as J _i (i=1, . and 17 sensor placement positions, namely J ₉ , J ₁₃ , J ₁₄ , J ₁₅ and J ₁₇ ;

3) ₅ sensors collect signals synchronously, obtain time domain data, obtain frequency spectrum by fast Fourier transform of time domain data, and extract the frequency domain data amplitude P( f ₀ ), construct the measurement result vector y=[P ₉ (f ₀ ), P ₁₃ (f ₀ ), P ₁₄ (f ₀ ), P ₁₅ (f ₀ ), P ₁₇ (f ₀ )] ^T ;

4) According to the sensor arrangement position selected in step 2), construct a 5×20 compressed sensing measurement matrix;

5) Construct a 20×20 spatial transformation matrix ψ _B :

Among them, J _m (·) represents the Bessel function of the first kind with m=3, ri = _i ×R/20, i=1...20, and _ki is solved according to J' _m ( _ki R)=0, take The first 20 solutions that satisfy this equation are k ₁ ～k ₂₀ ;

6) According to the measurement structure matrix, the compressed sensing measurement matrix and the space transformation matrix, the convex optimization method solves the l ₁ -norm minimization problem:

get recalculate The radial frequency signal of f ₀ =5000Hz at the original complete 20 sensor placement positions can be reconstructed:

7) Extract the radial modal amplitude according to the reconstructed radial frequency signal and calculate the i-th order radial modal amplitude c _i as follows:

in,

From this, the radial modal amplitude is finally obtained.

As shown in FIG. 2 , the comparison between the results of the radial frequency signal reconstructed by the above method and the results of the prior art method has an error of less than 0.1%, indicating that the method in the present invention only uses 5 sensors (the number of sensors in the prior art). 1/4), the signals of all N sensor placement positions can be accurately reconstructed. Using the method of the present invention, the radial modal amplitudes of each order obtained by using 5 sensors are almost the same as the modal detection results of 20 sensors in the prior art, and the error is less than 0.1dB, as shown in Figure 3, thus It can be proved that the radial acoustic modal detection method of the pipeline based on the compressed sensing theory of the present invention can still effectively extract the modal amplitudes of various orders under the condition of greatly reducing the scale of the sensor.

Finally, it should be noted that the purpose of publishing the embodiments is to help further understanding of the present invention, but those skilled in the art can understand that various replacements and modifications can be made without departing from the spirit and scope of the present invention and the appended claims. It is possible. Therefore, the present invention should not be limited to the contents disclosed in the embodiments, and the scope of protection of the present invention is subject to the scope defined by the claims.

Claims (8)

1. A pipeline radial acoustic modal detection system based on compressive sensing theory. The shape of the pipeline is an equal-section circle with a radius of R, and a cylindrical coordinate system (x, r, θ) is used to locate the components that generate high-order modal acoustic waves. The cross-section is the sound source cross-section, the sound source cross-section is located at the cross-section of x=0, the sound wave propagates in the forward direction of x in the pipeline, and the measurement cross-section is located at the cross-section of x=x _0. It is characterized in that the radial acoustic modal detection of the pipeline The system includes: N sensor arrangement positions and H sensors; wherein, on a radius of the measurement section, N sensor arrangement positions are evenly arranged along the radial direction of the pipeline; H positions are randomly selected from the N sensor arrangement positions to arrange the sensors respectively ; The number N of sensor arrangement positions is determined by the highest radial mode order n that can be propagated in the pipeline, n is a natural number, and N>n; the number H of sensors satisfies: Cslog(N/s)<H<N, where C is an empirical constant, and s is the modal sparsity. 2. a pipeline radial acoustic modal detection method based on compressive sensing theory, is characterized in that, described detection method comprises the following steps: 1) Determine the pipeline model: the shape of the pipeline is a circle of equal section with a radius of R, and the cylindrical coordinate system (x, r, θ) is used, and the section where the component that generates the high-order modal sound wave is located is the sound source section, and the sound source section is located at x = 0 section, the sound wave propagates in the positive direction of x in the pipeline, and the measurement section is located at the section of x = x ₀ ; 2) Determine the highest frequency of detection, and then according to the inner radius of the pipeline, determine the highest propagable radial modal order n of the pipeline to be detected, and according to the highest propagable radial modal order of the pipeline, determine one of the measured cross-sections. The number N of sensor arrangement positions evenly arranged along the radial direction of the pipeline on the radius, and randomly select H positions from the N sensor arrangement positions to install sensors respectively; 3) All sensors collect signals synchronously, obtain time-domain data, obtain frequency spectrum by fast Fourier transform of time-domain data, extract frequency-domain data of each sensor at the frequency of interest from the frequency spectrum, and construct measurement result vector; 4) According to the sensor arrangement position selected in step 2), construct an H×N compressed sensing measurement matrix; 5) Construct an N×N space transformation matrix; 6) According to the measurement result vector, the compressed sensing measurement matrix and the space transformation matrix, reconstruct the radial frequency signal at the frequency of interest to obtain a complete radial frequency signal; 7) Extract the radial modal amplitude from the reconstructed radial frequency signal. 3. The detection method according to claim 2, characterized in that, in step 2), on a radius of the measurement section, N sensor arrangement positions are evenly arranged along the radial direction of the pipeline; randomly from the N sensor arrangement positions Select H positions to set sensors respectively, and the number H of sensors satisfies: Cslog(N/s)<H<N, where C is an empirical constant, and s is the modal sparsity. 4. detection method as claimed in claim 2, is characterized in that, in step 3) in, time domain data is obtained frequency spectrum through fast Fourier transform, determine concerned frequency f ₀ , extract from frequency spectrum at concerned frequency f _{0 The} frequency domain data P _{h ( f 0 )} of each sensor _{under the} )] ^T , which is the compressed sensing measurement result. 5. detection method as claimed in claim 2, is characterized in that, in step 4), utilizes random 1-0 matrix as compressed sensing measurement matrix, thus constructs H×N compressed sensing measurement matrix: Among them, the matrix element value of the rth row and the ith column is 1, and the rest are 0, r=1,...,H, i∈[1,N]. 6. detection method as claimed in claim 2, is characterized in that, in step 5) in, space transformation matrix ψ _B has following form: Among them, J _m (·) represents the m-order Bessel function of the first kind, m is the circumferential modal order, ri is the _ith radial position among the N sensor arrangement positions that are evenly distributed in the radial direction, and ri = _i ×R/N, i=1...N, and k _i (i=1,2,...,N) is the solution under the constraint of the second type of boundary conditions of the Bessel function, which is obtained by J' _m ( _ki R)=0 where (·)' represents the derivative; k _{i satisfying} this boundary condition is multi _- valued, and a series of k ₁ , k ₂ . 7. detection method as claimed in claim 2, is characterized in that, in step 6) in, according to measurement result vector, compressed sensing measurement matrix and space transformation matrix, adopt l ₁ -norm to minimize the radial direction under the frequency of interest. The frequency signal is reconstructed to obtain the estimated signal in the transformed space calculate Get the complete radial frequency signal 8. detection method as claimed in claim 7 is characterized in that, in step 7) in, the calculation method of i-th order radial modal amplitude is as follows: in, is the modulus of the Bessel eigenfunction, which is defined as: Thereby, the radial modal amplitudes c _i of each order are finally obtained.