Method for measuring the acoustic reflection coefficient of a material in an acoustic tube

Abstract

The application discloses a kind of methods for measuring the sound reflection coefficient of material in acoustic tube, which comprises the following steps: firstly, the sample to be tested is placed in the test environment to emit and collect signals, and discrete Fourier transform is carried out to establish the sparse matrix form of sound receiving signal; then, the Bayesian formula containing hyperparameters is determined, and the hyperparameters are recursively solved to obtain the estimation result of multipath time delay; then, single-frequency PCW signal is emitted and collected, and the least square method is used to solve the amplitude parameter to obtain the estimation result of optimal multipath amplitude; finally, according to the estimation result of multipath time delay and the estimation result of multipath amplitude, the incident direct wave and the first reflected wave are extracted and separated, and the reflection coefficient of the sample to be tested is calculated. By using the sparse Bayesian learning method and the least square method, the application realizes the time delay estimation and amplitude estimation of multipath signal in acoustic tube, and achieves the purpose of separating multipath signal and calculating the reflection coefficient of acoustic material.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of acoustic parameter testing of sound tube environment material, and particularly relates to a method for measuring the acoustic reflection coefficient of a material in a sound tube. BACKGROUND

[0002] The underwater sound tube is an important experimental platform for measuring the acoustic performance parameters of a material, but there are technical problems to be solved in low-frequency parameter testing under the limited length of the sound tube. The main problem is that under low-frequency conditions, the wavelength of the measurement signal is long, and it is difficult to separate the incident wave and the reflected wave from the obtained signal.

[0003] At present, the main methods for realizing low-frequency testing of the sound tube under laboratory conditions include the traveling wave tube method, the standing wave tube method, and the wideband pulse method. The traveling wave tube method and the standing wave tube method need to be calibrated online by a hydrophone, and the engineering implementation is difficult. The wideband pulse method provides a method of using a short pulse in the time domain, which greatly shortens the requirement for the length of the sound tube. However, due to the problem of the transducer transmission response, an ideal wideband pulse cannot be obtained in actual use, which also causes the superposition of the incident sound wave and the reflected sound wave, and the information of the sound field cannot be accurately obtained. SUMMARY

[0004] The present application aims at the deficiencies of the prior art, and provides a method for measuring the acoustic reflection coefficient of a material in a sound tube.

[0005] The purpose of the present application is achieved by the following technical scheme: a method for measuring the acoustic reflection coefficient of a material in a sound tube, comprising the following steps:

[0006] (1) placing a sample to be tested into a test environment, controlling a transducer to emit a signal through a computer system, collecting a signal through a hydrophone in the sound tube, performing discrete Fourier transform on the emitted signal of the transducer and the received signal collected by the hydrophone, and uniformly discretizing the arrival time range of the incident direct wave and the reflected wave to establish a sparse matrix form of the sound received signal;

[0007] (2) determining a Bayesian formula containing a hyperparameter according to the sparse matrix form of the sound received signal established in the step (1), and recursively solving the hyperparameter to obtain an estimation result of the multipath time delay;

[0008] (3) controlling the transducer to emit a single-frequency PCW signal through the computer system, collecting a signal through the hydrophone in the sound tube, and solving the amplitude parameter by using the least square method to obtain an estimation result of the optimal multipath amplitude;

[0009] (4) extracting and separating the incident direct wave and the first reflected wave according to the estimation result of the multipath time delay obtained in the step (2) and the estimation result of the multipath amplitude obtained in the step (3), and calculating the reflection coefficient of the sample to be tested.

[0010] Optionally, the frequency of the transmitted signal is less than the cutoff frequency of the acoustic tube.

[0011] Optionally, the sparse matrix form of the acoustic receiving signal is obtained according to the following formula:

[0012]

[0013]

[0014] β = [β0(0·Δt), β1(1·Δt), …, β M-1 ((M-1)·Δt)] T

[0015] wherein the matrix S represents the value of the discrete Fourier transform result of the transmitted signal s(nT s ) at a specific frequency point, n represents a sampling point, T s represents a sampling period; is a Fourier transform coefficient matrix, the column vectors of which are uncorrelated, Δt is the time interval between adjacent discrete points, f k represents a specific frequency point; the vector β is a sparse matrix of the acoustic receiving signal, which contains L << M non-zero elements corresponding to the amplitude of L multipaths; is noise.

[0016] Optionally, the step (2) comprises the following sub-steps:

[0017] (2.1) determining the general expression of the Bayesian formula containing hyperparameters and solving it to obtain the variance of the marginal distribution and the mean of the posterior probability according to the sparse matrix form of the acoustic receiving signal established in the step (1);

[0018] (2.2) recursively solving the hyperparameters by using the expectation-maximization algorithm, and iterating for multiple times until the termination condition of iteration is reached to obtain the variance γ of the hyperparameter vector β and the noise variance σ 2 ;

[0019] (2.3) obtaining the estimated value according to the variance of the marginal distribution and the mean of the posterior probability and the variance γ of the hyperparameter vector β and the noise variance σ 2 ; obtaining the estimation result of the multipath time delay according to the estimated value

[0020] Optionally, the termination condition of iteration depends on the convergence rate, and the expression of the convergence rate is:

[0021]

[0022] where ζ is the convergence rate, is the estimated value of the previous iteration of γ, is the estimated value of the variance of the i+1 iteration.

[0023] Optionally, the estimated value is expressed as:

[0024]

[0025] where Γ is the diagonal matrix of γ, Γ = diag(γ); H is the matrix transpose; Σ Y is the variance of the marginal distribution, ∑ Y = σ 2 I k + AΓA H , I k is the k-order identity matrix; Y is the observation, which is related to β and σ 2 .

[0026] Optionally, the expression of the estimated value of the multipath amplitude is:

[0027]

[0028]

[0029] where and are the time delay signal and amplitude corresponding to the first J multipaths, respectively, and are the time delay signal and amplitude corresponding to the remaining (L-J) multipaths, respectively, is the estimated value of the multipath amplitude, and η is the possible number of multipaths.

[0030] Optionally, the expression of the reflection coefficient is:

[0031]

[0032] where R is the reflection coefficient of the sample to be tested at the frequency point f pcw , P r (f pcw ) is the value of the incident direct wave signal at the frequency point f pcw , and P i (f pcw ) is the value of the once-reflected wave signal at the frequency point f pcw .

[0033] The beneficial effects of the present application are that the present application is suitable for low-frequency sound tube testing under limited length, and can realize the separation of multipath signals during sound tube testing; the present application adopts a sparse Bayesian learning algorithm, fuses hierarchical prior probability and likelihood probability, does not require the input and configuration of any model parameters, and adaptively realizes the solution of the compressed sensing problem; the present application adopts a least square estimation method, takes time delay as prior information, reduces the calculation amount of amplitude estimation, and can obtain more effective estimation results; and the present application calculates the reflection coefficient and the transmission coefficient of the sample on the basis of the time delay estimation and the amplitude estimation of the multipath signal, so as to achieve the consistency of the coefficient measurement value and the theoretical calculation value, and reduce the error value caused by the current signal interception method. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 A sound tube model suitable for the present application;

[0035] Figure 2 A time delay estimation result obtained by the present application using a sparse Bayesian method;

[0036] Figure 3 Amplitude estimation results at different frequency points obtained by the present application using a least square method;

[0037] Figure 4 A comparison result of the sample coefficient measurement value and the theoretical value calculated by the present application. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0039] The sound tube material acoustic reflection coefficient measurement method of the present application realizes the signal separation of the incident direct wave and the once-reflected wave in the received signal by using a sparse Bayesian learning algorithm and a constrained least square algorithm to perform multipath time delay estimation and amplitude estimation on the signals collected by the hydrophone in the sound tube, and finally calculates the acoustic reflection coefficient of the material. The specific steps include the following steps:

[0040] (1) The sample to be tested is placed in a test environment, a transducer emits a signal controlled by a computer system, a hydrophone in the sound tube collects the signal, and the sound tube model is as shown in Figure 1 The discrete Fourier transform is performed on the emitted signal of the transducer and the received signal collected by the hydrophone, and the arrival time range of the incident direct wave and the reflected wave is uniformly discretized to establish the sparse matrix form of the sound received signal.

[0041] It should be understood that the acoustic material to be tested is placed in the test environment as a test sample for testing. Both the transmitted signal and the received signal are acoustic signals.

[0042] In this embodiment, the computer system controls the transducer to transmit the signal. In actual acoustic tube testing, a commonly known NI software system is usually used to control the transducer to transmit the signal. It should be understood that other instruments or systems can also be used to control the transducer to transmit the signal as long as the signal can be transmitted.

[0043] In this embodiment, the frequency of the transmitted signal is less than the cutoff frequency of the acoustic tube.

[0044] Further, the computer system controls the transducer to transmit a wide-band sinc function signal. The sinc function signal is a waveform in the signal, and the parameters in the function can be adjusted according to the actual frequency range to make the signal meet the requirements. In the measurement of the acoustic reflection coefficient of the material, since the acoustic tube has a cutoff frequency requirement, a sinc function signal is usually transmitted for measurement.

[0045] Specifically, the computer system controls the transducer to transmit the signal. It is assumed that the transmitted signal generated at the transducer position is s(t), and the signal received at the hydrophone position after passing through L underwater acoustic channels is y(t), where the time delay generated by the lth underwater acoustic channel is represented as Correspondingly, the channel fading factor (multipath amplitude) at the frequency f is represented as e(t) is a zero-mean additive Gaussian white noise term with a variance of σ 2 , and the signal transmission-reception model can be represented as:

[0046]

[0047] where t represents time.

[0048] In actual measurement, the received signal is a digital signal, the sampling frequency is f s , the number of sampling points is N, and the sampling period is T s = 1 / f s , the signal transmission-reception model is discretized in the time domain, and is represented as:

[0049]

[0050] The discrete Fourier transform (DFT) is performed on both sides of the above discretized signal transmission-reception model formula, and the DFT result is converted into a specific frequency point f k , k = 0, 1, …, K-1, and the result is represented as:

[0051]

[0052]

[0053] where Y(f k ), S(f k ) and E(f k ) are the values of the discrete Fourier transform of y(nT s ), s(nT s ) and e(nT s ) at the specific frequency point.

[0054] Further, the result of the discrete Fourier transform is expressed as:

[0055]

[0056]

[0057] where is the frequency-independent average of the sample reflection coefficient, expressed as:

[0058]

[0059] In actual processes, is approximately equal to 0, such as in the frequency band of 3 kHz to 5 kHz, the reflection coefficient of an 8 mm steel plate is between 0.38 and 0.54, and the result of calculating does not exceed 0.08, so can be regarded as a noise quantity and added to E(f k ), and the final result is recorded as

[0060] According to the size of the sound tube, the position of the sensor and the speed of sound, the approximate signal time delay is calculated, and the range of τ l ∈ [T1, T2], the time delay τ l is uniformly discretized at M points in this time range, and satisfies T2-T1=MΔt, where Δt is the time interval between adjacent discrete points, and Δt≤1 / f s is generally selected to enable accurate sampling and estimation of the time delay quantity, the discrete Fourier transform result can be re-expressed as:

[0061]

[0062] At mΔt=τ l , it satisfies and at other sampling time points, it satisfies β m (mΔt)=0.

[0063] It should be understood that the time delay is the time required from the transmitting end to the receiving end; the range of calculating the time delay is mainly based on the sound tube size, sensor position and sound speed, such as the hydrophone is 2m away from the transducer and 0.5m away from the sample to be tested, and then the time delay is theoretically t1=2 / 1480≈1.351*10E-3, t2=3 / 1480≈2.027*10E-3; and the range of the time delay can be taken as [1.35*10E-3, 2.03*10E-3].

[0064] The K equations corresponding to the final discretized signal transmission-reception model are written in matrix form to obtain the sparse matrix form of the sound receiving signal, and the discretized signal transmission-reception model satisfies:

[0065]

[0066]

[0067] β=[β0(0·Δt),β1(1·Δt),…,β M-1 ((M-1)·Δt)] T

[0068] Wherein, the matrix is the Fourier transform coefficient matrix, and the column vectors thereof are not correlated; the vector β is a sparse matrix, which contains L<<M non-zero elements, respectively corresponding to the amplitude of L multipath. Under the premise of satisfying K and the multipath amplitude

[0069] It should be understood that the sparse matrix β contains L<<M non-zero elements, most of which are zero. It is easy to understand that since the sparse matrix β is sparse, and Y is expressed by β, finally Y is also sparse.

[0070] (2) According to the sparse matrix form of the sound receiving signal established in step (1), the Bayesian formula containing hyperparameters is determined, and the hyperparameters are recursively solved to obtain the estimation result of the multipath time delay.

[0071] (2.1) According to the sparse matrix form of the sound receiving signal established in step (1), the general expression of the Bayesian formula containing hyperparameters is determined and solved to obtain the variance of the marginal distribution and the mean of the posterior probability.

[0072] In this embodiment, the general expression of the Bayesian formula containing hyperparameters is:

[0073]

[0074] Where, σ 2 For noise The variance of , where γ is the variance of vector β, and σ is the variance of vector β. 2 Both β and γ are hyperparameters to be calculated, p(β; γ) is the prior probability containing the hyperparameter γ, and p(β|Y; σ) is the hyperparameter to be calculated. 2 ,γ) is a parameter containing the hyperparameter σ 2 The posterior probability of γ, p(Y|β;σ) 2 ) contains hyperparameter σ 2 The likelihood probability, p(Y; σ 2 ,γ) is a parameter containing the hyperparameter σ 2 The probability distribution of the actual observed values ​​of γ.

[0075] Based on the Bayesian formula above, the unknown β can be obtained by solving the optimization problem, and its expression is:

[0076]

[0077] In this context, the unknown β can be considered as a variable that depends only on γ; the observed quantity Y can be considered as a variable that depends on both β and σ. 2 Relevant quantities; p(β|Y; σ 2 mean of γ) and variance Γ is the diagonal matrix of γ, Γ = diag(γ), H is the matrix transpose, Σ Y It can be obtained from the marginal distribution below.

[0078] It is easy to understand that marginal distributions refer to those containing hyperparameter σ. 2 The probability distribution of the actual observed values ​​of γ, p(Y; σ) 2 ,γ).

[0079] The marginal distribution is obtained using the law of total probability. Specifically, the marginal distribution p(Y; σ) is... 2 ,γ) can be obtained by applying p(Y|β,σ) 2 The product of p(β; γ) and p(β; γ) is calculated by integrating it with respect to β, and is expressed as:

[0080]

[0081] Utilizing the properties of Gaussian functions, the convolution of two Gaussian functions will still result in a Gaussian function, yielding p(Y; σ). 2 The mean μ of ,γ) Y =0, variance ∑ Y =σ 2 I k +AΓA H I k It is a k-order identity matrix.

[0082] (2.2) recursively solve the hyper-parameters by using the Expectation Maximization algorithm, and iterate until the termination condition is met to obtain the variance γ of the hyper-parameter vector β and the noise variance σ 2 .

[0083] It should be understood that the Expectation Maximization (EM) algorithm is a commonly used iterative algorithm for maximum likelihood estimation or maximum a posteriori probability estimation of a probabilistic parameter model containing hidden variables.

[0084] In this embodiment, the maximum expectation algorithm is used to estimate the value of the unknown quantity as a hidden variable (Hidden variables), and the iterative update values of the hyper-parameter γ and the noise variance σ 2 can be obtained according to the following formula:

[0085]

[0086] The iterative update expression of γ is:

[0087]

[0088] wherein, is the variance iterative estimation value of the i+1th time, which can be obtained by calculating μ β and Σ β according to the i th iteration.

[0089] The iterative update expression of σ 2 is:

[0090]

[0091] wherein, is the variance iterative estimation value of the i+1th time, which can be obtained by calculating and Σ β according to the i th iteration.

[0092] The termination condition of the above iteration loop depends on the convergence rate ζ, which is a representation of the relative performance improvement in the algorithm iteration solving process, and is expressed as:

[0093]

[0094] wherein, is the iterative solution estimation value of the previous γ. When the algorithm meets the iteration termination condition, the output vector is the estimation result of the channel containing the multipath delay .

[0095] For example, MATLAB can be used to recursively solve for hyperparameters, and its algorithm flowchart is shown in Table 1. The final output estimate is... Includes multipath delay estimation results.

[0096] Table 1: MATLAB Algorithm Flow

[0097]

[0098] This invention utilizes a sparse Bayesian learning method to solve hyperparameters containing multipath delay information. The sparse Bayesian learning method integrates hierarchical prior probabilities and likelihood probabilities, eliminating the need for any model parameter input or configuration. It can adaptively solve compressed sensing problems, thereby achieving multipath delay estimation of underwater acoustic signals.

[0099] (2.3) Based on the variance of the marginal distribution and the mean of the posterior probability, as well as the variance γ of the hyperparameter vector β and the noise variance σ 2 Obtain the estimated value Based on the estimated value Obtain the estimation results of multipath delay.

[0100] In this embodiment, the estimated value of the unknown quantity The expression is:

[0101]

[0102] Where Γ is the diagonal matrix of γ, Γ=diag(γ); H is the matrix transpose; Σ Y Let ∑ be the variance of the marginal distribution. Y =σ 2 I k +AΓA H I k Let Y be the k-order identity matrix; Y be the observation, along with β and σ. 2 The relevant quantities.

[0103] In this embodiment, the final vector estimate is obtained. This refers to the multipath delay that includes the channel. The estimation result, therefore, based on the estimated value This allows us to obtain the estimation results of multipath delay.

[0104] (3) The transducer is controlled by a computer system to transmit a single-frequency PCW signal, and the signal is collected by a hydrophone in the acoustic tube. The amplitude parameter is solved by the least squares method to obtain the optimal multipath amplitude estimation result.

[0105] After obtaining the delay information, the computer system is used to control the transducer to emit a single-frequency PCW signal. It should be understood that the true delay information can be estimated based on the sparse Bayesian estimation method in the foregoing, but the amplitude information obtained is frequency-averaged multipath amplitude information. In actual processes, the reflection coefficients of the sample at different frequencies are different, so that the average multipath amplitude information obtained by the estimation cannot be applied in practice. To solve this problem, the estimated delay information is used as prior information to continue to estimate the amplitude at a fixed single frequency. Therefore, the single-frequency pulse signal, i.e., the PCW signal, can be used to obtain accurate amplitude at a fixed frequency.

[0106] In this embodiment, the MATLAB / CVX optimization toolbox can be used to solve the constrained least squares to obtain the optimal estimation result of the multipath amplitude.

[0107] It should be understood that the least squares method is a commonly used mathematical optimization technique that finds the best function match of data by minimizing the sum of squares of errors. The unknown data can be easily obtained by using the least squares method, and the sum of squares of errors between the obtained data and the actual data is minimized.

[0108] Specifically, if the time delays of the first J multipaths are obtained and the amplitude values of the remaining (L-J) multipaths can be ignored, the amplitude values of the first J multipaths can be obtained by solving the optimization function according to the principle of the least squares method. The noise term is There is uncertainty, to further improve the accuracy of the multipath amplitude estimation, a constraint term is added, and the optimization function expression of the multipath amplitude is

[0109]

[0110]

[0111] wherein, and are the time delay signals and amplitude values corresponding to the first J multipaths, and are the time delay signals and amplitude values corresponding to the remaining (L-J) multipaths, is the estimation result of the multipath amplitude, and η is the possible number of multipaths.

[0112] (4) The incident direct wave and the first reflected wave are extracted and separated based on the estimation result of the multipath time delay obtained in step (2) and the estimation result of the multipath amplitude obtained in step (3), and the reflection coefficient of the sample to be tested is calculated.

[0113] Specifically, it is assumed that the emitted single-frequency PCW signal is The estimated channel time delay and channel amplitude of the incident direct wave signal and the first reflected wave signal are τ0 and τ1, and α0 and α1, respectively. r The incident direct wave signal P i and the first reflected wave signal P

[0114]

[0115]

[0116] The discrete Fourier transform of the incident direct wave signal and the first reflected wave signal can obtain the values P r (f pcw ) and P i (f pcw ) of the incident direct wave signal and the first reflected wave signal in the frequency domain, and the reflection coefficient R of the test sample at the corresponding frequency point can be calculated according to the values of the incident direct wave signal and the first reflected wave signal, and the reflection coefficient of the test sample in a certain frequency band can be further obtained.

[0117] The expression of the reflection coefficient is:

[0118]

[0119] Wherein, R is the reflection coefficient of the test sample at the corresponding frequency point f pcw , P r (f pcw ) is the value of the incident direct wave signal at the frequency point f pcw , and P i (f pcw ) is the value of the first reflected wave signal at the frequency point f pcw .

[0120] The method for measuring the sound reflection coefficient of the material in the sound tube according to the embodiments will be described in detail below, and the purpose and effect of the present application will become more apparent.

[0121] Example 1

[0122] In order to verify the effect of the reflection coefficient calculation by using the sparse Bayesian and least square method in the present application, simulation analysis is carried out. The sound tube test environment is simulated, the length of the sound tube is 5m, the inner diameter is 208mm, the distance between the transmitting transducer and the sample is 2.5m, the distance between the hydrophone and the sample is 0.5m, the sound speed in water is set as c=1480m / s, the sample is set as structural steel material, the sampling rate fs of the simulated emission sinc function is 100kHz during time delay estimation, the cutoff frequency is 5000Hz, the signal pulse width is 2ms, and the total signal time length is 5ms. The single frequency PCW signal is simulated during amplitude estimation, and the signal sampling rate is 100kHz. Figure 2For comparison of the time delay estimation result with the theoretical value, it can be seen from the figure that the direct incident wave and the first reflection wave time delay in the sound tube can be accurately estimated by using the sparse Bayesian method. Figure 3 For comparison of the amplitude estimation result with the theoretical value, it can be seen from the figure that on the basis of the known time delay estimation, the direct incident wave and the first reflection wave amplitude at a certain frequency point can be accurately estimated by using the constrained least square method. Figure 4 For comparison of the steel plate sample simulation result with the theoretical value, it can be seen from the figure that the simulation calculation result of the application is consistent with the theoretical value.

[0123] The above examples are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the application.

Claims

1. A method for measuring the acoustic reflection coefficient of a material in a acoustic tube, characterized in that, Includes the following steps: (1) Place the test sample in the test environment, control the transducer to emit a signal through the computer system, collect the signal through the hydrophone in the acoustic tube, perform discrete Fourier transform on the emitted signal emitted by the transducer and the received signal collected by the hydrophone, and uniformly discretize the arrival time range of the incident direct wave and the reflected wave to establish a sparse matrix form of the acoustic received signal. (2) Based on the sparse matrix form of the acoustic received signal established in step (1), determine the Bayesian formula containing hyperparameters, and recursively solve the hyperparameters to obtain the estimation result of multipath delay. (3) The transducer is controlled by a computer system to transmit a single-frequency PCW signal, and the signal is collected by a hydrophone in the acoustic tube. The amplitude parameter is solved by the least squares method to obtain the optimal multipath amplitude estimation result. (4) Based on the estimation results of the multipath delay obtained in step (2) and the estimation results of the multipath amplitude obtained in step (3), the incident direct wave and the primary reflected wave are extracted and separated, and the reflection coefficient of the sample to be tested is calculated.

2. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 1, characterized in that, The frequency of the transmitted signal is less than the cutoff frequency of the acoustic tube.

3. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 1, characterized in that, The sparse matrix form of the acoustic received signal is obtained according to the following formula: β=[β0(0·Δt),β1(1·Δt),…,β M-1 ((M-1)·Δt)] T Among them, matrix S represents the transmitted signal s(nT) s The value of the Discrete Fourier Transform result at a specific frequency point, where n represents the number of sampling points and T. s Indicates the sampling period; The Fourier transform coefficient matrix has column vectors that are independent of each other, Δt is the time interval between adjacent discrete points, and f k This represents a specific frequency point; the vector β is a sparse matrix of the acoustic received signal, which contains L << M non-zero elements, corresponding to the amplitudes of the L multipaths respectively; It is noise.

4. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 1, characterized in that, Step (2) includes the following sub-steps: (2.1) Based on the sparse matrix form of the acoustic received signal established in step (1), determine the general expression of the Bayes formula containing hyperparameters and solve it to obtain the variance of the marginal distribution and the mean of the posterior probability. (2.2) The expectation-maximization algorithm is used to recursively solve the hyperparameters, and the iteration is repeated until the termination condition is met to obtain the variance γ and noise variance σ of the hyperparameter vector β. 2 ; (2.3) Based on the variance of the marginal distribution and the mean of the posterior probability, as well as the variance γ of the hyperparameter vector β and the noise variance σ 2 Obtain the estimated value Based on the estimated value Obtain the estimation results of multipath delay.

5. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 4, characterized in that, The termination condition of the iteration depends on the convergence rate, which is expressed as: Where ζ is the convergence rate. This is the estimated value of γ obtained from the previous iteration. This is the variance estimate for the (i+1)th iteration.

6. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 4, characterized in that, The estimated value The expression is: Where Γ is the diagonal matrix of γ, Γ=diag(γ); H is the matrix transpose; Σ Y Let ∑ be the variance of the marginal distribution. Y =σ 2 I k +AΓA H I k Let Y be the k-order identity matrix; Y be the observation, along with β and σ. 2 The relevant quantities.

7. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 1, characterized in that, The expression for the estimation result of the multipath amplitude is: in, and These are the time delay signals and amplitudes corresponding to the first J multipath paths, respectively. and These represent the time delay signal and amplitude corresponding to the remaining (LJ) multipath signals. This represents the estimated multipath amplitude, where η is the number of possible multipaths.

8. The method for measuring the acoustic reflection coefficient of materials in a acoustic tube according to claim 1, characterized in that, The expression for the reflection coefficient is: Where R is the frequency point f corresponding to the sample to be tested. pcw The reflection coefficient P r (f pcw () represents the frequency point f pcw The value of the incident direct wave signal, P i (f pcw () represents the frequency point f pcw The value of the next reflected wave signal.

Images