CN107843333B - A kind of pipeline radial direction glottis neoplasms detection system and method based on compressive sensing theory - Google Patents
A kind of pipeline radial direction glottis neoplasms detection system and method based on compressive sensing theory Download PDFInfo
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Abstract
The invention discloses a kind of pipeline radial direction glottis neoplasms detection system and method based on compressive sensing theory.The present invention is on a radius in measurement section, along the radially uniform N number of sensor arrangement position of setting of pipeline；H position is randomly choosed from N number of sensor arrangement position is respectively arranged sensor；Pipeline radial direction glottis neoplasms detection method based on compressive sensing theory breaches the limitation of Shannon-Nyquist sampling thheorem, by sensor array in large scale needed for script, it is reduced to acceptable quantitative range, and can still achieve the purpose that accurately to extract radial mode shape amplitude；Compared to traditional detection method, method proposed by the invention greatly reduces the complexity of hardware layout level and the cost of data acquisition, storage and processing, and process is succinct, it is easy to accomplish.
Description
Technical Field
The invention relates to a pipeline acoustic modal detection technology, in particular to a pipeline radial acoustic modal detection system and method based on a compressed sensing theory.
Background
In the field of noise testing, testing aiming at a pipeline sound field is a main method for determining sound source information in a pipeline and far-field noise influence outside the pipeline, and the method has important application in the related fields of aerospace, automobile, household appliance noise reduction and the like. The acoustic mode is directly related to the geometric characteristics of rotating mechanism components such as a fan, a motor and the like, and the mechanism of noise generation of the related mechanism and the distribution condition of a noise source can be inferred and analyzed after the structure of the acoustic mode is determined, so that a guidance basis is provided for noise reduction design, and therefore the acoustic mode detection method is very important for pipeline noise testing.
The acoustic modal detection of the pipeline can be divided into circumferential modal detection and radial modal detection, and the aim of the detection is to obtain the amplitude of each modal. For the radial mode detection, the circumferential mode detection is required as a precondition, and therefore, the radial mode detection is complicated. In order to detect the circumferential modes, a sensor array is generally flush mounted on the wall surface of the pipeline along the circumferential direction, and the amplitude of each circumferential mode can be obtained by performing Fourier decomposition on the obtained data based on the space. After the circumferential main mode is determined according to the amplitude, radial mode detection can be performed. In practice, a sensor array is arranged in the pipeline along the radial direction to obtain sound field data, then a radial modal coefficient is obtained based on Fourier-Bessel decomposition, and finally a radial modal spectrum of the sound field is obtained.
It should be noted that the above-mentioned circumferential mode detection must follow Shannon-Nyquist sampling theorem, which means that the total number of array elements required by the sensor array is twice the highest mode order that can be detected. In actual tests, the number of blades of a rotating part is often large, and the number of generated circumferential modal orders is generally high as known from the Taylor-Sofrin selectivity, so that a large number of sensors need to be arranged in the circumferential direction. Similarly, to obtain the radial mode, a plurality of measuring points are often required to be arranged at a plurality of circumferential positions of the pipeline along the radial direction, so that the number of radial sensors is large. The above factors coupled together tend to make the conventional radial mode detection system extremely complex, and the cost of data acquisition, storage and processing is too high. At present, although there is a counter-measure such as rotating the sensor array, the above contradiction is only alleviated to some extent, and the problem is not solved at all. Therefore, it is necessary to develop a new mode extraction method from the viewpoint of signal processing, and to control the number of sensors within an acceptable range while detecting a large-range mode.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a pipeline radial acoustic modal detection system and a detection method based on a compressed sensing theory.
The invention aims to provide a pipeline radial acoustic modal detection system based on a compressed sensing theory.
The shape of the pipeline is a circular shape with a uniform section and a radius R, a cylindrical coordinate system (x, R, theta) is adopted, the section where a component generating high-order mode sound waves is located is a sound source section, the sound source section is located at the section where x is 0, the sound waves propagate in the pipeline in the positive direction of x, and the measuring section is located at the position where x is x0Cross-section of (a).
The invention relates to a pipeline radial acoustic modal detection system based on a compressed sensing theory, which comprises: n sensor arrangement positions and H sensors; wherein, on a radius of the measuring section, N sensor arrangement positions are uniformly arranged along the radial direction of the pipeline; randomly selecting H positions from the N sensor arrangement positions to arrange the sensors respectively; the number N of the sensor arrangement positions is determined by the highest transmissible radial modal order N of the pipeline, wherein N is a natural number and is more than N; the number H of the sensors satisfies the following conditions: cslog (N/s) < H < N, where C is an empirical constant and s is modal sparsity.
The invention further aims to provide a pipeline radial acoustic modal detection method based on the compressed sensing theory.
The invention discloses a pipeline radial acoustic modal detection method based on a compressed sensing theory, which comprises the following steps:
1) determining a pipeline model: the shape of the pipeline is a circular shape with a uniform section and a radius R, a cylindrical coordinate system (x, R, theta) is adopted, the section where a component generating high-order mode sound waves is located is a sound source section, the sound source section is located on the section where x is 0, the sound waves are transmitted in the pipeline along the positive direction of x, and the measuring section is located on the section where x is x0Cross section of (a);
2) determining the highest frequency of detection, determining the highest transmittable radial mode order N of the pipeline to be detected according to the inner radius of the pipeline, determining the number N of sensor arrangement positions uniformly arranged on one radius of the measurement section along the radial direction of the pipeline according to the highest transmittable radial mode order of the pipeline, and randomly selecting H positions from the N sensor arrangement positions to respectively set the sensors;
3) synchronously acquiring signals by all sensors to obtain time domain data, performing fast Fourier transform on the time domain data to obtain a frequency spectrum, extracting frequency domain data of each sensor under the concerned frequency from the frequency spectrum, and constructing a measurement result vector;
4) constructing an H multiplied by N compressed sensing measurement matrix according to the arrangement position of the sensors selected in the step 2);
5) constructing an N multiplied by N spatial transformation matrix;
6) reconstructing the radial frequency signal under the concerned frequency according to the measurement result vector, the compressed sensing measurement matrix and the spatial transformation matrix to obtain a complete radial frequency signal;
7) and extracting the radial modal amplitude according to the reconstructed radial frequency signal.
In the step 2), N sensor arrangement positions are uniformly arranged on one radius of the measuring section along the radial direction of the pipeline; h positions are randomly selected from the N sensor arrangement positions to be respectively provided with sensors, and the number H of the sensors satisfies the following conditions: cslog (N/s) < H < N, where C is an empirical constant and s is 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 advantages of H over the prior art methods are lost.
In step 3), the time domain data is subjected to fast Fourier transform to obtain a frequency spectrum, and the frequency f of interest is determined0Extracting from the frequency spectrum at the frequency of interest f0Frequency domain data P of each sensorh(f0) H1, …, H, constructing a measurement vector y P1(f0),P2(f0),...,PH(f0)]TThis is the compressed sensing measurement.
In step 4), a random 1-0 matrix is used as a compressed sensing measurement matrix, so that an H × N compressed sensing measurement matrix is constructed:
in the case of the r-th row and the i-th column, the matrix element has a value of 1, and the rest are 0, r is 1, …, H, i ∈ [1, N ].
In step 5), since the frequency domain data obtained in step 3) is not itself sparse, it is necessary to apply a spatial transformation matrix to transform it into a sparse modal space to fill it upThe requirement of compressed sensing is satisfied. For the detection of radial mode, the mode decomposition is based on Fourier-Bessel transformation, so the required space transformation matrix psiBHas the following form:
wherein, Jm(. DEG) represents a first class Bessel function of order m, m being the order of the circumferential mode, riFor the ith radial position among N sensor arrangement positions which are radially and uniformly distributed, and riI × R/N, i 1 … N, and ki(i-1, 2, …, N) is a solution under the constraint of Bessel function second type boundary condition, and is J'm(kiR) ═ 0, where (·)' denotes the derivative; k satisfying this boundary conditioniFor multiple values, solving for a series of k1、k2…kNTo finally determine the spatial transformation matrix psiB。
In step 6), according to the measurement result vector, the compressed sensing measurement matrix and the spatial transformation matrix, adopting l1-reconstructing the radial frequency signal at the frequency of interest with norm minimization to obtain an estimated signal in the transform spaceComputingObtaining complete radial frequency signal
In step 7), the ith order radial mode amplitude is calculated as follows:
wherein,being the norm of the Bessel eigenfunction, which is defined as, under the second class of boundary conditions, when m ≠ 0:
finally obtaining the amplitude c of each order of radial modei。
The invention has the advantages that:
the pipeline radial acoustic modal detection method based on the compressive sensing theory breaks through the limitation of Shannon-Nyquist sampling theorem, reduces the originally required sensor array with large scale to an acceptable quantity range, and can still achieve the purpose of accurately extracting the radial modal amplitude; compared with the detection method in the prior art, the method provided by the invention greatly reduces the complexity of a hardware arrangement level and the cost of data acquisition, storage and processing, and is simple in process and easy to implement.
Drawings
FIG. 1 is a model diagram of a pipeline radial acoustic modal detection system based on compressive sensing theory according to the present invention;
FIG. 2 is a diagram of a comparison between a single-frequency radial frequency signal obtained by an embodiment of a pipeline radial acoustic modal detection method based on compressive sensing theory according to the present invention and a radial frequency signal obtained by the prior art;
fig. 3 is a graph of the radial frequency signal of the present invention measured with a 5-sensor versus a prior art 20-sensor.
Detailed Description
The invention will be further elucidated by means of specific embodiments in the following with reference to the drawing.
As shown in fig. 1, the duct ① is shaped as a circular cross-section with a radius R, and using a cylindrical coordinate system (x, R, θ), the sound source cross-section ④ of the component generating the high order modal sound wave is located at a cross-section with x equal to 0, the sound wave propagation direction ② is along the positive x direction in the duct, and the measurement cross-section ⑤ is located at a cross-section with x equal to x0The pipeline radial acoustic mode detection system based on the compressive sensing theory comprises H sensors, natural numbers N are determined according to the highest transmittable radial mode order N of a pipeline, N is larger than N, N sensor arrangement positions ③ are uniformly arranged on one radius of a measurement section along the radial direction of the pipeline, H sensors are randomly selected from the N sensor arrangement positions and are respectively arranged at the H positions, the number N of the sensor arrangement positions is determined according to the highest transmittable radial mode order N of the pipeline, N is a natural number and is larger than N, and the number H of the sensors is required to be Cslog (N/s) < H < N, wherein C is an empirical constant, and s is mode sparsity.
In the present embodiment, the radius R of the pipe is 0.5m, and a set of sound waves (frequency f) with a circumferential mode m of 3 and a radial mode n of (3,8) is present inside the pipe05000Hz) and both modalities are cut-on. It should be noted that in practical tests, higher-order modes beyond a certain order will be rapidly attenuated, and in the present embodiment, the radial mode n>The sound waves of 14 will be quickly attenuated and will not propagate in the axial direction inside the tube.
The pipeline radial acoustic modal detection method based on the compressed sensing theory comprises the following steps:
1) determining a pipeline model, wherein the pipeline is a circular shape with a uniform section and a radius R of 0.5m, a cylindrical coordinate system (x, R, theta) is adopted, a component generating high-order modal sound waves is positioned on a sound source section with x of 0, the sound waves propagate in the pipeline in the positive direction of x, and a measuring section is positioned on x of x0Cross section of (a);
2) determining the highest frequency of detection, wherein the circumferential mode m is 3, and then determining the maximum frequency according to the inner half of the pipelineAnd determining the highest transmittable radial modal order N of the pipeline to be detected, wherein in the embodiment, the number of the sensor arrangement positions arranged on the measurement section is determined to be N equal to 20, all possible transmittable radial modal orders are covered, and 20 sensor arrangement positions (the detectable modal N is 1-20) are arranged along the radial direction, and the numbers of the sensor arrangement positions are respectively marked as J from the position close to the center of a circlei(i is 1, …,20), and 5 sensor positions are randomly selected from the 20 sensor arrangement positions, and the 9 th, 13 th, 14 th, 15 th and 17 th sensor arrangement positions, i.e., J in this embodiment, are respectively provided9、J13、J14、J15And J17；
3) Synchronously acquiring signals by 5 sensors to obtain time domain data, performing fast Fourier transform on the time domain data to obtain a frequency spectrum, and extracting a concerned frequency f from the frequency spectrum0Amplitude P (f) of frequency domain data for each sensor at 5000Hz0) Constructing a measurement vector y ═ P9(f0),P13(f0),P14(f0),P15(f0),P17(f0)]T；
4) Constructing a 5 multiplied by 20 compressed sensing measurement matrix according to the sensor arrangement position selected in the step 2);
5) construction of a 20 x 20 spatial transformation matrix psiB：
Wherein, Jm(. cndot.) denotes a Bessel function of the first type, r, where m ═ 3iI × R/20, i 1 … 20, and kiAccording to J'm(kiSolving the equation by taking the R) as 0, and taking the first 20 solutions which satisfy the equation, namely k1～k20；
6) According to the measurement structure matrix, the compressed sensing measurement matrix and the spatial transformation matrix, a convex optimization method is used for solving l1Norm minimization problem:
to obtainRecalculationReconstructing the original integral 20 sensor arrangement positions f0Radial frequency signal of 5000 Hz:
7) extracting radial modal amplitude according to the reconstructed radial frequency signal and calculating the ith radial modal amplitude c according to the following formulai：
Wherein,
thereby ultimately obtaining the radial mode amplitude.
As shown in fig. 2, the error of the result of the radial frequency signal reconstructed by the above method is less than 0.1% compared with the result of the prior art method, which shows that the method of the present invention can accurately reconstruct the signals of all N sensor arrangement positions by using only 5 sensors (1/4 of the number of sensors in the prior art). By adopting the method, the modal detection results of all orders of radial modal amplitudes 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, so that the pipeline radial acoustic modal detection method based on the compressive sensing theory can still effectively extract all orders of modal amplitudes under the condition of greatly reducing the size of the sensors.
Finally, it is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Claims (8)
1. A pipeline radial acoustic modal detection system based on a compressed sensing theory is characterized in that a pipeline is in a shape of a circular uniform-section shape with a radius of R, a cylindrical coordinate system (x, R and theta) is adopted, a section where a component generating high-order modal sound waves is located is a sound source section, the sound source section is located on the section where x is 0, the sound waves are transmitted in the pipeline in the positive direction of x, and a measurement section is located on the section where x is x0Characterized in that said pipe radial acoustic modal detection system comprises: n sensor arrangement positions and H sensors; wherein, on a radius of the measuring section, N sensors are uniformly arranged along the radial direction of the pipelineAn arrangement position; randomly selecting H positions from the N sensor arrangement positions to arrange the sensors respectively; the number N of the sensor arrangement positions is determined by the highest transmissible radial modal order N of the pipeline, wherein N is a natural number and is more than N; the number H of sensors satisfies: cslog (N/s) < H < N, where C is an empirical constant and s is modal sparsity.
2. A pipeline radial acoustic modal detection method based on a compressed sensing theory is characterized by comprising the following steps:
1) determining a pipeline model: the shape of the pipeline is a circular shape with a uniform section and a radius R, a cylindrical coordinate system (x, R, theta) is adopted, the section where a component generating high-order mode sound waves is located is a sound source section, the sound source section is located at the section where x is 0, the sound waves propagate in the pipeline in the positive direction of x, and the measuring section is located at the section where x is x0Cross section of (a);
2) determining the highest detection frequency, determining the highest transmittable radial modal order N of the pipeline to be detected according to the inner radius of the pipeline, determining the number N of sensor arrangement positions uniformly arranged on one radius of the measurement section along the radial direction of the pipeline according to the highest transmittable radial modal order of the pipeline, and randomly selecting H positions from the N sensor arrangement positions to be respectively provided with sensors;
3) synchronously acquiring signals by all sensors to obtain time domain data, performing fast Fourier transform on the time domain data to obtain a frequency spectrum, extracting frequency domain data of each sensor under the concerned frequency from the frequency spectrum, and constructing a measurement result vector;
4) constructing an H multiplied by N compressed sensing measurement matrix according to the arrangement position of the sensors selected in the step 2);
5) constructing an N multiplied by N spatial transformation matrix;
6) reconstructing the radial frequency signal under the concerned frequency according to the measurement result vector, the compressed sensing measurement matrix and the spatial transformation matrix to obtain a complete radial frequency signal;
7) and extracting the radial modal amplitude according to the reconstructed radial frequency signal.
3. The inspection method according to claim 2, wherein in step 2), N sensor arrangement positions are uniformly arranged in a radial direction of the pipe on one radius of the measurement section; h positions are randomly selected from the N sensor arrangement positions to be respectively provided with sensors, and the number H of the sensors satisfies the following conditions: cslog (N/s) < H < N, where C is an empirical constant and s is modal sparsity.
4. The detection method according to claim 2, wherein in step 3), the frequency spectrum is obtained by subjecting the time domain data to fast fourier transform, and the frequency of interest f is determined0Extracting from the spectrum at the frequency of interest f0Frequency domain data P of each sensorh(f0) H1, …, H, constructing a measurement vector y P1(f0),P2(f0),…PH(f0)]TThis is the compressed sensing measurement.
5. The detection method according to claim 2, wherein in step 4), a random 1-0 matrix is used as the compressed sensing measurement matrix, thereby constructing an H x N compressed sensing measurement matrix:
in the case of the r-th row and the i-th column, the matrix element has a value of 1, and the rest are 0, r is 1, …, H, i ∈ [1, N ].
6. Detection method according to claim 2, characterized in that in step 5) the spatial transformation matrix ψBHas the following form:
wherein, Jm(. DEG) represents a first class Bessel function of order m, m being the order of the circumferential mode, riFor the ith radial position of N sensor arrangement positions which are radially and uniformly distributed, and riI × R/N, i 1 … N, and ki(i-1, 2, …, N) is a solution under the constraint of Bessel function second type boundary condition, and is J'm(kiR) ═ 0, where (·)' denotes the derivative; k satisfying this boundary conditioniFor multiple values, solving for a series of k1、k2…kNTo finally determine the spatial transformation matrix psiB。
7. The detection method according to claim 2, wherein in step 6), l is used according to the measurement result vector, the compressed sensing measurement matrix and the spatial transformation matrix1-norm minimization reconstructing the radial frequency signal at the frequency of interest to obtain an estimated signal in the transformed spaceComputingObtaining complete radial frequency signal
8. The detection method according to claim 7, wherein in step 7), the ith order radial mode amplitude is calculated as follows:
wherein,being the norm of the Bessel eigenfunction, which is defined as, under the second class of boundary conditions, when m ≠ 0:
finally obtaining the amplitude c of each order of radial modei。
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