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 PDF

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CN107843333B
CN107843333B CN201710580385.7A CN201710580385A CN107843333B CN 107843333 B CN107843333 B CN 107843333B CN 201710580385 A CN201710580385 A CN 201710580385A CN 107843333 B CN107843333 B CN 107843333B
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于文君
马征宇
卜焕先
黄迅
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Peking University
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Abstract

本发明公开了一种基于压缩感知理论的管道径向声模态检测系统及方法。本发明在测量截面的一个半径上,沿管道径向均匀设置N个传感器布置位置;从N个传感器布置位置中随机选择H个位置分别布置传感器;基于压缩感知理论的管道径向声模态检测方法突破了Shannon‑Nyquist采样定理的限制,将原本所需的规模庞大的传感器阵列,缩减至可以接受的数量范围,且依然能达到精确提取径向模态幅值的目的;相比传统检测方法,本发明所提出的方法大大降低了硬件布置层面的复杂度和数据采集、存储以及处理的成本,过程简洁,易于实现。

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

一种基于压缩感知理论的管道径向声模态检测系统及方法A pipeline radial acoustic modal detection system and method based on compressive sensing theory

技术领域technical field

本发明涉及管道声模态检测技术,具体涉及一种基于压缩感知理论的管道径向声模态检 测系统及检测方法。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.

背景技术Background technique

在噪声测试领域,针对管道声场的测试是确定管道内声源信息以及管道外远场噪声影响 的主要方法,在航空航天、汽车、家电降噪等相关领域都有重要的应用。声模态与风扇、电 机等旋转机构部件的几何特征直接相关,确定出声模态结构后就足以推断和分析相关机构产 生噪声的机理以及噪声源的分布情况,从而为降噪设计提供指导依据,因此声模态检测方法 对于管道噪声测试非常重要。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.

管道声模态检测可分为周向模态检测和径向模态检测,其目标在于获得各模态的幅值。 对于其中的径向模态检测,需要以周向模态检测作为前提条件,因此较为复杂。为了检测周 向模态,一般在管道壁面沿周向齐平安装传感器阵列,将获得的数据进行基于空间的Fourier 分解,即可得到各周向模态的幅值。根据幅值大小确定周向主模态之后,可进行径向模态检 测。实际会在管道内部沿径向布置传感器阵列获得声场数据,然后基于Fourier-Bessel分解得 到径向模态系数,最终获得声场的径向模态谱。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.

需要指出的是,上述周向模态检测必须遵循Shannon-Nyquist采样定理,即意味着传感器 阵列需要的阵元总数是能够检测的最高模态阶数的两倍。而在实际测试中,转动部件的叶片 数量往往较多,由Taylor-Sofrin选择率可知,其产生的周向模态阶数一般较高,为此需要沿 周向布置大量的传感器。同理,为获得径向模态,往往需要在管道多个周向位置沿径向布置 多个测点,由此导致径向传感器也数量庞大。上述因素耦合于一起,易导致常规的径向模态 检测系统异常复杂,数据采集、存储和处理的成本过高。目前尽管有旋转传感器阵列等应对 方式,但也只是从某种程度上缓解了上述矛盾,并未从根本解决问题。为此,需要从信号处 理的角度,发展新的模态提取方法,在检测较大范围模态的同时把传感器的个数控制在可接 受范围内。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.

发明内容SUMMARY OF THE INVENTION

为了解决以上现有技术中存在的问题,本发明提出了一种基于压缩感知理论的管道径向 声模态检测系统及检测方法。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.

本发明的一个目的在于提出一种基于压缩感知理论的管道径向声模态检测系统。An object of the present invention is to propose a pipeline radial acoustic mode detection system based on compressive sensing theory.

管道的形状为半径为R的等截面圆形,采用圆柱坐标系(x,r,θ),产生高阶模态声波的部 件所在的截面为声源截面,声源截面位于x=0的截面,声波在管道中沿x正向传播,测量截 面位于x=x0的截面。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 .

本发明的基于压缩感知理论的管道径向声模态检测系统包括:N个传感器布置位置和H 个传感器;其中,在测量截面的一个半径上,沿管道径向均匀布置N个传感器布置位置;从 N个传感器布置位置中随机选择H个位置分别布置传感器;传感器布置位置的个数N由管道 最高可传播径向模态阶数n确定,n为自然数,且N>n;传感器的个数H满足:Cslog(N/s) <H<N,其中C为经验常数,s为模态稀疏度。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.

本发明的另一个目的在于提供一种基于压缩感知理论的管道径向声模态检测方法。Another object of the present invention is to provide a pipeline radial acoustic mode detection method based on compressive sensing theory.

本发明的基于压缩感知理论的管道径向声模态检测方法,包括以下步骤:The pipeline radial acoustic modal detection method based on the compressed sensing theory of the present invention comprises the following steps:

1)确定管道模型:管道的形状为半径为R的等截面圆形,采用圆柱坐标系(x,r,θ),产生 高阶模态声波的部件所在的截面为声源截面,声源截面位于x=0的截面,声波在管道中 沿x正向传播,测量截面位于x=x0的截面;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)确定检测的最高频率,再根据管道的内半径,确定所需检测的管道最高可传播径向模 态阶数n,根据管道最高可传播径向模态阶数,确定在测量截面的一个半径上沿管道径 向均匀布置的传感器布置位置的个数N,并从N个传感器布置位置中随机选择出H个位置分别设置传感器;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)所有传感器同步采集信号,获得时域数据,将时域数据经过快速傅里叶变换得到频谱, 从频谱中提取各传感器在关心频率下的频域数据,构建测量结果向量;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)根据步骤2)中选择的传感器布置位置,构建H×N压缩感知测量矩阵;4) According to the sensor arrangement position selected in step 2), construct an H×N compressed sensing measurement matrix;

5)构建N×N空间变换矩阵;5) Construct an N×N space transformation matrix;

6)根据测量结果向量、压缩感知测量矩阵和空间变换矩阵,对关心频率下径向频率信号 进行重构,得到完整的径向频率信号;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)根据重构的径向频率信号提取径向模态幅值。7) Extract the radial modal amplitude from the reconstructed radial frequency signal.

其中,在步骤2)中,在测量截面的一个半径上,沿管道径向均匀设置N个传感器布置 位置;从N个传感器布置位置中随机选择H个位置分别设置传感器,传感器的个数H满足:Cslog(N/s)<H<N,其中C为经验常数,s为模态稀疏度。H的取值越大,则精确重构原始信号的成功率越高,但同时也会失去其相对现有技术方法的明显优势。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.

在步骤3)中,将时域数据经过快速傅里叶变换得到频谱,确定关心频率f0,从频谱中提 取在关心频率f0下的各传感器的频域数据Ph(f0),h=1,…,H,构建测量结果向量y=[P1(f0),P2(f0),...,PH(f0)]T,此为压缩感知测量结果。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 , . _ _ _

在步骤4)中,利用随机1-0矩阵作为压缩感知测量矩阵,由此构建H×N压缩感知测量 矩阵: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:

其中,第r行第i列的矩阵元素值为1,其余为0,r=1,…,H,i∈[1,N]。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].

在步骤5)中,由于步骤3)中获得的频域数据本身并不稀疏,需要作用空间变换矩阵将 其变换到稀疏的模态空间,以满足压缩感知的要求。对于径向模态的检测,其模态分解基于 Fourier-Bessel变换,故所需的空间变换矩阵ψB具有如下形式: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:

其中,Jm(·)表示m阶第一类Bessel函数,m为周向模态阶数,ri为径向均布的N个传感 器布置位置中第i个径向位置,且有ri=i×R/N,i=1…N,而ki(i=1,2,…,N)为Bessel函数第二类 边界条件约束下的解,由J'm(kiR)=0求得,其中(·)'表示求导数;满足此边界条件的ki为多 值的,求解获得一系列k1、k2…kN,从而最终确定空间变换矩阵ψBAmong 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 .

在步骤6)中,根据测量结果向量、压缩感知测量矩阵和空间变换矩阵,采用l1-范数最 小化对关心频率下径向频率信号进行重构,得到变换空间中的估计信号计算得到完 整的径向频率信号 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

在步骤7)中,第i阶径向模态幅值的计算方法如下:In step 7), the calculation method of the ith order radial modal amplitude is as follows:

其中,为贝塞尔本征函数的模方,在第二类边界条件下,且m≠0时其定义为:in, is the modulus of the Bessel eigenfunction, which is defined as:

由此最终获得各阶径向模态幅值ciThereby, the radial modal amplitudes c i of each order are finally obtained.

本发明的优点:Advantages of the present invention:

本发明基于压缩感知理论的管道径向声模态检测方法突破了Shannon-Nyquist采样定理 的限制,将原本所需的规模庞大的传感器阵列,缩减至可以接受的数量范围,且依然能达到 精确提取径向模态幅值的目的;相比现有技术的检测方法,本发明所提出的方法大大降低了 硬件布置层面的复杂度和数据采集、存储以及处理的成本,过程简洁,易于实现。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.

附图说明Description of drawings

图1为本发明的基于压缩感知理论的管道径向声模态检测系统的模型图;1 is a model diagram of a pipeline radial acoustic modal detection system based on compressive sensing theory of the present invention;

图2为根据本发明的基于压缩感知理论的管道径向声模态检测方法的一个实施例得到的单频 径向频率信号与现有技术得到的径向频率信号对比图;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;

图3为本发明采用5传感器对比现有技术20传感器得到的径向频率信号的检测结果图。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.

具体实施方式Detailed ways

下面结合附图,通过具体实施例,进一步阐述本发明。Below in conjunction with the accompanying drawings, the present invention will be further described through specific embodiments.

如图1所示,管道①的形状为半径为R的等截面圆形,采用圆柱坐标系(x,r,θ),产生高 阶模态声波的部件声源截面④位于x=0的截面,在管道中声波传播方向②沿x正向,测量截 面⑤位于x=x0的截面。本实施例的基于压缩感知理论的管道径向声模态检测系统包括:H个 传感器;根据管道最高可传播径向模态阶数n,确定自然数N,N>n;在测量截面的一个半 径上,沿管道径向均匀设置N个传感器布置位置③,从N个传感器布置位置中随机选择H个 位置分别布置H个传感器;传感器布置位置的个数N由管道最高可传播径向模态阶数n确定, n为自然数,且N>n;传感器的个数H需满足:Cslog(N/s)<H<N,其中C为经验常数,s 为模态稀疏度。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.

在本实施例中,管道的半径R=0.5m,其内部存在周向模态m=3,径向模态n=(3,8)的一 组声波(频率f0=5000Hz),且两模态均处于截通状态(cut-on)。需要指出,在实际测试中,超过 一定阶数的高阶模态会迅速衰减,在本实施例中,径向模态n>14的声波将迅速衰减,无法在 管内沿轴向方向传播。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.

本实施例的基于压缩感知理论的管道径向声模态检测方法,包括以下步骤: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)确定管道模型,管道为半径R=0.5m的等截面圆形,采用圆柱坐标系(x,r,θ),产生高 阶模态声波的部件位于x=0的声源截面,声波在管道中沿x正向传播,测量截面位于x=x0的截面;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)确定检测的最高频率,周向模态m=3,再根据管道的内半径,确定所需检测的管道最 高可传播径向模态阶数n,本实施例中,确定布置在测量截面上的传感器布置位置的个 数N=20,已经涵盖所有可能传播的径向模态阶数,沿径向布置了20个传感器布置位置(可 检测模态n=1~20),其编号从靠近圆心处开始,分别记为Ji(i=1,…,20),并从20个传感 器布置位置中随机选择出5个位置分别设置传感器,此实施例中选择了第9、13、14、15和17个传感器布置位置,即J9、J13、J14、J15和J172) 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个传感器同步采集信号,获得时域数据,将时域数据经过快速傅里叶变换得到频谱, 从频谱中提取关心频率f0=5000Hz处的各传感器的频域数据的幅值P(f0),构建测量结果 向量y=[P9(f0),P13(f0),P14(f0),P15(f0),P17(f0)]T3) 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)根据步骤2)中选择的传感器布置位置,构建5×20压缩感知测量矩阵;4) According to the sensor arrangement position selected in step 2), construct a 5×20 compressed sensing measurement matrix;

5)构建20×20空间变换矩阵ψB5) Construct a 20×20 spatial transformation matrix ψ B :

其中,Jm(·)表示m=3的第一类Bessel函数,ri=i×R/20,i=1…20,而ki根据J'm(kiR)=0求 解,取满足此方程的前20个解,即为k1~k20Among 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)根据测量结构矩阵、压缩感知测量矩阵和空间变换矩阵,凸优化方法求解l1-范数最 小化问题: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:

得到再计算可重构原来完整的20个传感器布置位置上f0=5000Hz的径向频率信 号:get recalculate The radial frequency signal of f 0 =5000Hz at the original complete 20 sensor placement positions can be reconstructed:

7)根据重构的径向频率信号提取径向模态幅值按下式计算第i阶径向模态幅值ci7) 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:

其中, in,

由此最终获得径向模态幅值。From this, the radial modal amplitude is finally obtained.

如图2所示,采用上述方法重构的径向频率信号的结果与现有技术方法结果进行对比误 差<0.1%,表明本发明中方法仅采用5个传感器(现有技术中传感器的个数的1/4)便可准确 重构所有N个传感器布置位置的信号。采用本发明中方法,使用5个传感器所获得的各阶径 向模态幅值同现有技术下20个传感器的模态检测结果几乎一致,误差小于0.1dB,如图3所 示,由此可证明本发明的基于压缩感知理论的管道径向声模态检测方法在大幅削减传感器规 模的情况下,依然能够有效地提取各阶模态幅值。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.

最后需要注意的是,公布实施例的目的在于帮助进一步理解本发明,但是本领域的技术 人员可以理解:在不脱离本发明及所附的权利要求的精神和范围内,各种替换和修改都是可 能的。因此,本发明不应局限于实施例所公开的内容,本发明要求保护的范围以权利要求书 界定的范围为准。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)

1.一种基于压缩感知理论的管道径向声模态检测系统,管道的形状为半径为R的等截面圆形,采用圆柱坐标系(x,r,θ),产生高阶模态声波的部件所在的截面为声源截面,声源截面位于x=0的截面,声波在管道中沿x正向传播,测量截面位于x=x0的截面,其特征在于,所述管道径向声模态检测系统包括:N个传感器布置位置和H个传感器;其中,在测量截面的一个半径上,沿管道径向均匀布置N个传感器布置位置;从N个传感器布置位置中随机选择H个位置分别布置传感器;传感器布置位置的个数N由管道最高可传播径向模态阶数n确定,n为自然数,且N>n;传感器的数量H满足:Cslog(N/s)<H<N,其中C为经验常数,s为模态稀疏度。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. 2.一种基于压缩感知理论的管道径向声模态检测方法,其特征在于,所述检测方法包括以下步骤: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)确定管道模型:管道的形状为半径为R的等截面圆形,采用圆柱坐标系(x,r,θ),产生高阶模态声波的部件所在的截面为声源截面,声源截面位于x=0的截面,声波在管道中沿x正向传播,测量截面位于x=x0的截面;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)确定检测的最高频率,再根据管道的内半径,确定所需检测的管道最高可传播径向模态阶数n,根据管道最高可传播径向模态阶数,确定在测量截面的一个半径上沿管道径向均匀布置的传感器布置位置的个数N,并从N个传感器布置位置中随机选择出H个位置分别设置传感器;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)所有传感器同步采集信号,获得时域数据,将时域数据经过快速傅里叶变换得到频谱,从频谱中提取各传感器在关心频率下的频域数据,构建测量结果向量;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)根据步骤2)中选择的传感器布置位置,构建H×N压缩感知测量矩阵;4) According to the sensor arrangement position selected in step 2), construct an H×N compressed sensing measurement matrix; 5)构建N×N空间变换矩阵;5) Construct an N×N space transformation matrix; 6)根据测量结果向量、压缩感知测量矩阵和空间变换矩阵,对关心频率下径向频率信号进行重构,得到完整的径向频率信号;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)根据重构的径向频率信号提取径向模态幅值。7) Extract the radial modal amplitude from the reconstructed radial frequency signal. 3.如权利要求2所述的检测方法,其特征在于,在步骤2)中,在测量截面的一个半径上,沿管道径向均匀布置N个传感器布置位置;从N个传感器布置位置中随机选择H个位置分别设置传感器,传感器的个数H满足:Cslog(N/s)<H<N,其中C为经验常数,s为模态稀疏度。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.如权利要求2所述的检测方法,其特征在于,在步骤3)中,将时域数据经过快速傅里叶变换得到频谱,确定关心频率f0,从频谱中提取在关心频率f0下的各传感器的频域数据Ph(f0),h=1,…,H,构建测量结果向量y=[P1(f0),P2(f0),…PH(f0)]T,此为压缩感知测量结果。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.如权利要求2所述的检测方法,其特征在于,在步骤4)中,利用随机1-0矩阵作为压缩感知测量矩阵,由此构建H×N压缩感知测量矩阵: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: 其中,第r行第i列的矩阵元素值为1,其余为0,r=1,…,H,i∈[1,N]。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.如权利要求2所述的检测方法,其特征在于,在步骤5)中,空间变换矩阵ψB具有如下形式:6. detection method as claimed in claim 2, is characterized in that, in step 5) in, space transformation matrix ψ B has following form: 其中,Jm(·)表示m阶第一类Bessel函数,m为周向模态阶数,ri为径向均布的N个传感器布置位置中第i个径向位置,且有ri=i×R/N,i=1…N,而ki(i=1,2,…,N)为Bessel函数第二类边界条件约束下的解,由J'm(kiR)=0求得,其中(·)'表示求导数;满足此边界条件的ki为多值的,求解获得一系列k1、k2…kN,从而最终确定空间变换矩阵ψBAmong 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.如权利要求2所述的检测方法,其特征在于,在步骤6)中,据测量结果向量、压缩感知测量矩阵和空间变换矩阵,采用l1-范数最小化对关心频率下径向频率信号进行重构,得到变换空间中的估计信号计算得到完整的径向频率信号 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.如权利要求7所述的检测方法,其特征在于,在步骤7)中,第i阶径向模态幅值的计算方法如下: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: 其中,为贝塞尔本征函数的模方,在第二类边界条件下,且m≠0时其定义为:in, is the modulus of the Bessel eigenfunction, which is defined as: 由此最终获得各阶径向模态幅值ciThereby, the radial modal amplitudes c i of each order are finally obtained.
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