A method and device for estimating and separating frequency components of a multi-source signal

Abstract

The application discloses a kind of multi-source signal frequency component estimation and accurate separation method and device, the application multi-source signal frequency component estimation and accurate separation method includes the number of independent sources and principal component signal based on fitting entropy determination for the sampling data of multiple channels, using variable step Newton iteration method to principal component signal unmixed aliasing obtains unmixed aliasing matrix and pre-separation signal, using error back propagation correction unmixed aliasing matrix separates multi-source mixed signal into accurate separation signal, based on the accurate separation signal of each channel carries out frequency estimation.The application aims at solving the problems that traditional signal frequency estimation and signal separation method are unknown in the number of independent sources, are easy to fall into local optimum and signal separation error accumulation, improves the problems that traditional method is easy to fall into local optimum, poor flexibility, improves accuracy in frequency estimation and signal separation.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and signal monitoring and identification, and specifically to a method and apparatus for frequency component estimation and accurate separation of multi-source signals. Background Technology

[0002] Wind power generation is a clean and renewable energy source, and its power generation process involves multiple key components such as blades, transmission systems, bearings, and generators. However, due to variable operating conditions and the influence of external environmental factors, wind turbines are prone to problems such as loose connections, damage to bearings and gearboxes, and changes in gear meshing clearance. These issues can lead to various abnormal noises and fault signals in the wind turbine. If two or more faults occur at one or more locations, multi-source composite fault signals are generated, which seriously affect its operational performance and reliability.

[0003] Because personnel cannot enter wind turbines while they are running, inspection and troubleshooting are extremely difficult. Even if some abnormal noises do not affect the operation of the wind turbine in the short term, they can become a safety hazard that leads to damage to major components and ultimately a major failure. Fault diagnosis using abnormal sound signals during wind turbine operation has advantages such as being non-invasive, conveying the overall status of the equipment, and identifying different types of faults. Therefore, estimating and accurately separating frequency components based on abnormal sound signals during wind turbine operation is of great significance for determining the type and severity of single or multi-source complex faults.

[0004] Existing technologies include frequency estimation and signal separation algorithms based on nonnegative matrix factorization (NMF) and fast independent component analysis (CFI). However, NMF-based methods are only suitable for low-computational-complexity scenarios, real-time performance is difficult to guarantee, and the decomposition form and structure are not unique; different NMF algorithms may produce different results, leading to difficulties in interpreting the signal separation. CFI-based methods, using Newton's iteration method to iteratively calculate near the initial solution, may fail to converge and are prone to getting trapped in local optima, resulting in the propagation and accumulation of solution errors. In the scenario of frequency estimation and signal separation fault diagnosis of multi-source acoustic signals from wind turbines, which is sensitive to noise and lacks a high-precision separation calculation scheme for multi-source mixed signals, there is still room for technological development. Currently, some progress has been made in frequency estimation and signal separation methods for wind turbine acoustic signals both domestically and internationally, but most studies are prone to getting trapped in local optima or do not address the backpropagation correction of signal separation errors. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and apparatus for frequency component estimation and accurate separation of multi-source signals, which addresses the above-mentioned problems of the prior art. The present invention aims to solve the problems of traditional signal frequency estimation and signal separation methods being prone to local optima and signal separation error accumulation when the number of independent sources is unknown. It improves the traditional methods by addressing the problems of being prone to local optima and lacking flexibility, thereby improving the accuracy of frequency estimation and signal separation.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for frequency component estimation and accurate separation of multi-source signals includes the following steps:

[0008] S101, for sampled data from multiple channels, determine the number of independent sources and principal component signals based on the fitting entropy;

[0009] S102, the variable step-size Newton iteration method is used to dealias the principal component signals to obtain the dealiasing matrix and the pre-separated signal;

[0010] S103 uses error backpropagation to correct the aliasing matrix and separate the multi-source mixed signal into a precise separated signal;

[0011] S104 performs frequency estimation based on the precisely separated signals of each channel.

[0012] Optionally, step S101 includes:

[0013] S201, construct an observation data matrix x of dimension N×M from the sampling data collected at M times from N channels; standardize the observation data matrix x to obtain a standardized observation data matrix X; calculate the covariance coefficients between each channel based on the standardized observation data matrix X to obtain a covariance coefficient matrix R of dimension N×N; perform eigenvalue decomposition on the covariance coefficient matrix R, arrange the eigenvalues ​​in descending order to obtain the N eigenvalues ​​of the covariance coefficient matrix R and their corresponding eigenvectors.

[0014] S202, starting from 1 and ending at N, calculate the fitting entropy for different numbers of independent sources, and determine the number of independent sources B from the calculated N fitting entropies according to the following formula:

[0015]

[0016] In the above formula, b is the number of independent sources traversed, b = 1, 2, ..., N-1, E f (b+1) is the fitting entropy when there are b+1 independent source signals, E f (b) is the fitting entropy when there are b independent source signals;

[0017] S203, select the eigenvectors corresponding to the first B largest eigenvalues ​​of the covariance coefficient matrix R as the projection matrix, and use the projection matrix to project the standardized observation data matrix X onto the low-dimensional principal component signal V with dimension B×M.

[0018] Optionally, the expression for the function to calculate the fitting entropy in step S202 is:

[0019]

[0020] In the above formula, E f (c) represents the fitting entropy when there are c independent sources, M is the number of sampling times, N is the number of channels, and λ i Let be the i-th eigenvalue of the covariance coefficient matrix R.

[0021] Optionally, in step S203, the function expression for projecting the standardized observation data matrix X onto the low-dimensional principal component signal V of dimension B×M using the projection matrix is:

[0022] V = P T X,

[0023] In the above formula, P represents a projection matrix of dimension N×B, X is the standardized observation data matrix, and we have:

[0024] P = [a ：，1 a ：，2 , ..., a ：，B ],

[0025] In the above formula, a ：，1 ~a ：，B These are the eigenvectors corresponding to the first B largest eigenvalues ​​of the covariance coefficient matrix R.

[0026] Optionally, step S102 includes:

[0027] S301, The principal component signal is centered and whitened to obtain the centered and whitened principal component signal v;

[0028] S302, Construct the nonlinear equations for resolving aliasing:

[0029]

[0030] In the above equation, F(W) is the nonlinear equation for solving aliasing, E is the expected value, and v is the principal component signal after centering and whitening. For pre-separation signal, To compare the first derivative of the function G′(u) in The values ​​at the given position are determined, and G(u) = ln(cosh(u)) and G′(u) = tanh(u), where u is the independent variable of the comparison function; the iteration step number k = 1 is initialized, and the step size parameter μ for the first step is set. (1) =1; Randomly initialize the dealiasing matrix W = [W ：，1 W ：，2 …W ：，B ], where W ：，1 ~W ：，B Let i be the first to B column vectors of the dealiasing matrix W, respectively. Initialize the column variable i = 1, and use the i-th column vector of the dealiasing matrix W as the initial i-th column vector of the first step.

[0031] S303, solve for the i-th column vector in step k+1 according to the following formula.

[0032]

[0033] In the above formula, μ (k) Let E be the step size parameter for the k-th step, and E be the expected value. For the i-th pre-separation signal, To compare the first derivative of the function G′(u) in The value at that location, To compare the second derivative G″(u) of the function in The value at that location, For the i-th column vector at step k; update the step size parameter μ at step (k+1). (k+1) ; Calculate the i-th column vector at the (k+1)-th step after iteration using the following formula. And the i-th column vector of the (k+1)-th step after iteration As the i-th column vector of the new (k+1)-th step

[0034]

[0035]

[0036] In the above formula, W ：，j This is the j-th column vector of the aliasing matrix W; This is the i-th column vector after the (k+1)-th iteration;

[0037] S304, if the number of iterations k equals the preset threshold or If so, proceed to step S305; otherwise, increment the iteration number k by 1 and proceed to step S303 to continue iterating.

[0038] S305, If column variable i is less than the number of independent sources B, increment column variable i by 1 and jump to step S303 to find the next column vector of the unaliasing matrix W; otherwise, obtain the unaliasing matrix W and jump to step S306.

[0039] S306, the pre-separation signal is obtained according to the following formula:

[0040]

[0041] In the above formula, denoted as the pre-separated signal, W as the dealiasing matrix, and v as the principal component signal after centering and whitening.

[0042] Optionally, in step S303, the step size parameter μ of the (k+1)th step is updated. (k+1) The function expression is:

[0043]

[0044] In the above formula, μ (k+1) μ is the step size parameter for the (k+1)th step. (k) Let μ be the step size parameter for the k-th step. T For the threshold, For the i-th column vector at step k The L2 norm of the computational results of the nonlinear equations for solving aliasing. For the i-th column vector at step k-1 The L2 norm of the nonlinear equations for solving the aliasing problem; where:

[0045] The function expression for condition 1 is:

[0046]

[0047] The function expression for condition 2 is:

[0048]

[0049] threshold μ T The expression for the computation function is:

[0050]

[0051] In the above formula, B represents the number of independent sources.

[0052] Optionally, step S103 includes:

[0053] S401, initialize the iteration count s to 1, and de-aliasing matrix W = [W ：，1 W ：，2 …W ：，B The i-th column vector W in ] ：，iAs the i-th column vector in the s-th iteration

[0054] S402, the aliasing matrix is ​​corrected by backpropagation of the error using the following formula:

[0055]

[0056] In the above formula, Let i be the i-th column vector in the (s+1)-th iteration. Let be the i-th column vector in the s-th iteration, α be the learning factor, and e be the learning vector. ij For the i-th pre-separation signal and the j-th principal component signal v j，： Error between;

[0057] S403, if the number of iterations s equals the set threshold or If the condition is met, proceed to step S404; otherwise, increment the iteration count s by 1 and proceed to step S402; where ε2 is a preset threshold.

[0058] S404, if column variable i is less than the number of independent sources B, increment column variable i by 1, and jump to step S402 to find the next column vector of the unaliased matrix W. Otherwise, proceed to step S405;

[0059] S405, combine all the iterated column vectors to obtain the corrected dealiasing matrix W′, and obtain the accurate separation signal based on the corrected dealiasing matrix W′ and the following formula:

[0060]

[0061] In the above formula, To accurately separate the signals, W′ is the corrected dealiasing matrix, and v is the principal component signal after centering and whitening.

[0062] Optionally, the i-th pre-separation signal in step S402 and the j-th principal component signal v j，： The expression for the calculation function of the error between them is:

[0063]

[0064] In the above formula, For the i-th pre-separation signal and the j-th principal component signal v j，： The squared correlation coefficient between them is given by:

[0065]

[0066] In the above formula, M represents the number of sampling times. For the i-th pre-separation signal The signal at time m, v j，m For the j-th principal component signal v j，： The signal at time m in the sequence.

[0067] Furthermore, the present invention also provides a frequency component estimation and accurate separation device for multi-source signals, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the frequency component estimation and accurate separation method for the multi-source signals.

[0068] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program that is programmed or configured by a microprocessor to perform the frequency component estimation and accurate separation method for the multi-source signal.

[0069] Compared with the prior art, the present invention has the following advantages: The method of the present invention can solve the problem of the difficulty in determining the number of independent sources in signal separation. It obtains an accurate dealiasing matrix through the variable step-size Newton iteration method and back propagation error, which can accurately separate the fault sound signals in the operation of wind turbine units and extract the accurate time-domain and frequency-domain characteristics of independent signals. It can be used for tasks such as fault diagnosis and anomaly detection, thereby identifying potential single faults or compound faults. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0071] Figure 2 This is the result of fault audio separation using the method described in this embodiment of the invention.

[0072] Figure 3 This is a detailed flowchart illustrating the method of an embodiment of the present invention.

[0073] Figure 4 These are the time-domain and frequency-domain features extracted in the embodiments of the present invention. Detailed Implementation

[0074] like Figure 1 As shown, the frequency component estimation and accurate separation method for multi-source signals in this embodiment includes the following steps:

[0075] S101, for sampled data from multiple channels, determine the number of independent sources and principal component signals based on the fitting entropy;

[0076] S102, the variable step-size Newton iteration method is used to dealias the principal component signals to obtain the dealiasing matrix and the pre-separated signal;

[0077] S103 uses error backpropagation to correct the aliasing matrix and separate the multi-source mixed signal into a precisely separated signal. Figure 2 This is the result of fault audio separation using the method in this embodiment;

[0078] S104 performs frequency estimation based on the precisely separated signals of each channel.

[0079] In this embodiment, a signal generator is used to generate four test signals based on a wind turbine fault signal sample library, which serve as the original audio signals. The sampling rate of the wind turbine fault signals in this embodiment is 44.1kHz, the quantization precision is 16bit, and the sampling duration is 2 seconds. The receiver uses a DSP platform of model SM320C6457 for signal processing. The original signals are linearly mixed to generate six channels (N=6) of observation signals, and Gaussian noise is introduced as a noise environment to achieve an SNR of 8dB. Let the observation signal under the noise environment be x, and the dimension of x is N×M, which can be expressed as follows:

[0080]

[0081] In the above formula, x 1，1 ~x 1，M Let x be the signal at M time points of the first channel. 2，1 ~x 2，M Let x be the signal at M time points of the second channel. N，1 ~x N，M This represents the signal at M time points of the Nth channel.

[0082] like Figure 3 As shown, step S101 in this embodiment includes:

[0083] S201, construct an observation data matrix x of dimension N×M from the sampling data collected at M times from N channels; standardize the observation data matrix x to obtain a standardized observation data matrix X; calculate the covariance coefficients between each channel based on the standardized observation data matrix X to obtain a covariance coefficient matrix R of dimension N×N; perform eigenvalue decomposition on the covariance coefficient matrix R, arrange the eigenvalues ​​in descending order to obtain the N eigenvalues ​​of the covariance coefficient matrix R and their corresponding eigenvectors.

[0084] S202, starting from 1 and ending at N, calculate the fitting entropy for different numbers of independent sources, and determine the number of independent sources B from the calculated N fitting entropies according to the following formula:

[0085]

[0086] In the above formula, b is the number of independent sources traversed, b = 1, 2, ..., N-1, E f(b+1) is the fitting entropy when there are b+1 independent source signals, E f (b) is the fitting entropy when there are b independent source signals;

[0087] S203, select the eigenvectors corresponding to the first B largest eigenvalues ​​of the covariance coefficient matrix R as the projection matrix, and use the projection matrix to project the standardized observation data matrix X onto the low-dimensional principal component signal V with dimension B×M.

[0088] In step S201 of this embodiment, the standardized observation data matrix X can be represented as:

[0089]

[0090] In the above formula, each element in the observation data matrix X represents the result of standardizing the observation data matrix x. For any X... n，m This represents the element at time m in the nth channel of the standardized observation signal data matrix X. The standardization process can be performed using the desired method, for example, in this embodiment:

[0091]

[0092] In the above formula, x n，m The element at time m in the nth channel of the observed data matrix x. σ represents the mean of the observation data of the nth channel. n Let represent the standard deviation of the observation data of the nth channel, and we have:

[0093]

[0094] In step S201 of this embodiment, the N×N covariance coefficient matrix R can be expressed as:

[0095]

[0096] Wherein, the element R in the i-th row and j-th column of matrix R i，j Let X be the covariance of the i-th and j-th rows of the observed data matrix. Since the observed data has been standardized, we have:

[0097]

[0098] Among them, X i，m Let X be the element at time m of the i-th channel in the standardized observation signal data matrix X. j，m Let X be the element of the j-th channel at time m in the standardized observation signal data matrix. Since N = 6, then:

[0099]

[0100] In step S201 of this embodiment, the covariance coefficient matrix R is decomposed into eigenvalues ​​to obtain the eigenvalues ​​λ1, λ2, ..., λ3 of R. N and the corresponding eigenvector a ：，1 a ：，2 , ..., a ：，N Let N be the total number of eigenvalues ​​of matrix R, and we have:

[0101]

[0102] Since N=6, in this embodiment, the covariance matrix R is decomposed into eigenvalues, and the eigenvalues ​​are sorted in descending order to obtain the eigenvalues ​​λ1, λ2, ..., λ6 of R and the corresponding eigenvectors a. ：，1 a ：，2 , ..., a ：，6 .

[0103] Based on the positive correlation between the energy of independent source signals and their eigenvalues, independent source signals can be distinguished from low-noise signals based on the distribution characteristics of the eigenvalues ​​of the observed data, and the number of independent sources and principal components can be extracted. This embodiment proposes using fitting entropy as a measure of the degree of fit between the number of independent signals and the principal component signals to the source signals. By calculating the fitting entropy for c independent sources, it can be measured whether the current number of independent sources and the principal components have reached a balance in their fit and contribution to the source signals. When the fitting entropy suddenly decreases and gradually converges, showing an inflection point, it indicates that the statistical distribution characteristics of the number of independent sources and the source signals match. The calculation function expression for the fitting entropy in step S202 of this embodiment is:

[0104]

[0105] In the above formula, E f (c) represents the fitting entropy when there are c independent sources, M is the number of sampling times, N is the number of channels, and λ i Let be the i-th eigenvalue of the covariance coefficient matrix R. The first term in the equation is the logarithmic estimator of the probability density of the source signal under maximum likelihood estimation, and the second term is the bias correction, ensuring that the average KL divergence between the probability density of the mixed source signal and the estimated density of the separated independent signals is an unbiased estimate. To ensure the robustness of the independent source number estimation, N fitting entropies are selected such that:

[0106]

[0107] The minimum value of b is taken as the final number of independent sources, and the estimated number of independent sources is denoted as B, which can be expressed as:

[0108]

[0109] In the above formula, b is the number of independent sources, b = 1, 2, ..., N-1, E f (b+1) is the fitting entropy when there are b+1 independent source signals, E f (b) is the fitting entropy when there are b independent source signals. Specifically, in this embodiment, when b = 4, we have:

[0110]

[0111] The minimum number of sources is chosen, so the estimated number of sources is denoted as B = 4.

[0112] In step S203 of this embodiment, the eigenvectors corresponding to the first B largest eigenvalues ​​of the covariance matrix R are selected as the projection matrix. The observed signal is projected to a lower dimension to extract the principal components containing independent signals, reducing redundant information and parameters to be solved between the observed signals, and accelerating the efficiency and accuracy of subsequent calculations. The function expression for projecting the standardized observation data matrix X to the lower-dimensional principal component signal v of dimension B×M using the projection matrix in step S203 is as follows:

[0113] V = P T X,

[0114] In the above formula, P represents a projection matrix of dimension N×B, X is the standardized observation data matrix, and we have:

[0115] P = [a ：，1 a ：，2 , ..., a ：，B ],

[0116] In the above formula, a ：，1 ~a ：，B Let be the eigenvectors corresponding to the first B largest eigenvalues ​​of the covariance coefficient matrix R.

[0117] like Figure 3 As shown, step S102 in this embodiment includes:

[0118] S301, The principal component signal is centered and whitened to obtain the centered and whitened principal component signal v;

[0119] S302, Construct the nonlinear equations for resolving aliasing:

[0120]

[0121] In the above equation, F(W) is the nonlinear equation for solving aliasing, E is the expected value, and v is the principal component signal after centering and whitening. For pre-separation signal, To compare the first derivative of the function G′(u) in The values ​​at the given position are determined, and G(u) = ln(cosh(u)) and G′(u) = tanh(u), where u is the independent variable of the comparison function; the iteration step number k = 1 is initialized, and the step size parameter μ for the first step is set. (1) =1; Randomly initialize the dealiasing matrix W = [W ：，1 W ：，2 …W ：，B ], where W ：，1 ~W ：，B Let i be the first to B column vectors of the dealiasing matrix W, respectively. Initialize the column variable i = 1, and use the i-th column vector of the dealiasing matrix W as the initial i-th column vector of the first step.

[0122] S303, solve for the i-th column vector in step k+1 according to the following formula.

[0123]

[0124] In the above formula, μ (k) Let E be the step size parameter for the k-th step, and E be the expected value. For the i-th pre-separation signal, The first derivative of the comparison function is the i-th pre-separation signal. The value of , The second derivative of the comparison function is the i-th pre-separation signal. The value of , For the i-th column vector at step k; update the step size parameter μ at step (k+1). (k+1) ; Calculate the i-th column vector at the (k+1)-th step after iteration using the following formula. And the i-th column vector of the (k+1)-th step after iteration As the i-th column vector of the new (k+1)-th step

[0125]

[0126]

[0127] In the above formula, W ：，j This is the j-th column vector of the aliasing matrix W; For the i-th column direction in the (k+1)-th step after iteration;

[0128] S304, if the number of iterations k equals the preset threshold or If so, proceed to step S305; otherwise, increment the iteration number k by 1 and proceed to step S303 to continue iterating.

[0129] S305, If column variable i is less than the number of independent sources B, increment column variable i by 1 and jump to step S303 to find the next column vector of the unaliasing matrix W; otherwise, obtain the unaliasing matrix W and jump to step S306.

[0130] S306, the pre-separation signal is obtained according to the following formula:

[0131]

[0132] In the above formula, denoted as the pre-separated signal, W as the dealiasing matrix, and v as the principal component signal after centering and whitening.

[0133] Step S301, centering and whitening the principal component signals, greatly simplifies the calculation. The principal component signals are centered by subtracting the mean of each channel from the observed signal, using the following formula:

[0134]

[0135] in, V represents the i-th row vector in the centered principal component signal. i，： V represents the i-th row vector in the principal component signal. i，m Let m represent the m-th element in the i-th row vector of the principal component signal. Solve for the covariance matrix of the centered matrix:

[0136]

[0137] In the above formula, The signal is the principal component signal after centralization;

[0138] Covariance matrix C v It has an eigenvalue decomposition form:

[0139] C v =QΛQ T ,

[0140] Where Q and Λ are respectively derived from the covariance matrix C v The orthogonal matrix and diagonal matrix are formed by the unit eigenvectors and eigenvalues. Based on the orthogonal matrix Q and the diagonal matrix Λ, the whitening matrix is ​​obtained:

[0141] H = Λ -1 / 2 Q T ,

[0142] Multiplying the whitening matrix and the principal component signal matrix yields the centered and whitened principal component signals v:

[0143]

[0144] The principle of constructing the nonlinear equation for dealiasing in step S302 is as follows: Randomly initialize the dealiasing matrix W = [W ：，1 W ：，2 …W ：，B ], where W ：，i Let W be the i-th column vector. Since each column vector in the dealiasing matrix is ​​a weight vector, and its norm only affects the amplitude of the separated signal and not the separation effect, we take the dealiasing matrix ||W ：，i ||=1, ||·|| represents the 2-norm of the matrix. Then, the independent signals... It can be obtained from the following formula:

[0145]

[0146] The i-th independent separation signal It can be obtained from the following formula:

[0147]

[0148] in, Let i be the i-th row vector of the separated signals, i.e., the i-th separated signal. To solve the transpose of the i-th column vector of the aliasing matrix W. When the separated signal has the maximum non-Gaussianity, it can be considered that the separated signal is closest to the real signal. The objective function based on negative entropy is used as the measure of non-Gaussianity. According to the Kuhn-Tucker condition, the optimization problem is equivalent to solving the zero-point problem of the following equation F(W) = 0.

[0149]

[0150] In the formula, G(·) is the comparison function, and G′(·) is the first derivative of G(·). Without loss of generality, we can choose G(u) = ln(cosh(u)) and G′(u) = tanh(u).

[0151] In this embodiment, a variable step size parameter μ is introduced, and the variable step size Newton iteration method is used to solve the zeros of the nonlinear equation F(W)=0 to ensure convergence.

[0152]

[0153] Where, μ (k) It is the step size parameter for the k-th iteration, with an initial value of μ. (1) Set to 1, W represents the i-th column vector of the dealiasing matrix W. ：，i The result of the k-th iteration of the variable-step-size Newton iteration method. To ensure the convergence speed of solving for the root of F(W), this invention adopts the variable-step-size Newton iteration method, adding a line search in the original search direction. When μ (k)When the value is small, the iterative scheme exhibits much better convergence stability, ensuring both the descent direction of the search and the convergence of Newton's iteration method. This is achieved through calculation... and Furthermore, standardization is performed after each iteration to further improve convergence stability and simplify the solution W. ：，i Iterative formula:

[0154]

[0155]

[0156]

[0157] In the above formula, μ (k) Let E be the step size parameter for the k-th step, and E be the expected value. For the i-th pre-separation signal, The first derivative of the comparison function G′(u) is given by the i-th pre-separation signal. The value at that location, The second derivative of the comparison function G″(u) is given by the i-th pre-separation signal. The value at that location, For the i-th column vector at step k; update the step size parameter μ at step (k+1). (k+1) ; Calculate the i-th column vector at the (k+1)-th step after iteration using the following formula. And the i-th column vector of the (k+1)-th step after iteration As the i-th column vector of the new (k+1)-th step Thus, step S203 is obtained by solving for the i-th column vector in the (k+1)-th step. The function model, Let G″(·) be the new value after iteration, and let G″(u) be the second derivative of the comparison function G(·). G″(u) = 1 - tanh 2 (u).

[0158] In step S303 of this embodiment, the step size parameter μ of the (k+1)th step is updated. (k+1) The function expression is:

[0159]

[0160] In the above formula, μ (k+1) μ is the step size parameter for the (k+1)th step. (k) Let μ be the step size parameter for the k-th step. T For the threshold, For the i-th column vector at step k The L2 norm of the computational results of the nonlinear equations for solving aliasing. For the i-th column vector at step k-1 The second norm of the nonlinear equations for solving the aliasing problem; as mentioned above, when the norm difference of the iterative update is greater than the threshold, μ (k+1) Keep it unchanged; otherwise, update the step size μ according to the above formula. (k+1) .in:

[0161] The function expression for condition 1 is:

[0162]

[0163] The function expression for condition 2 is:

[0164]

[0165] threshold μ T The expression for the computation function is:

[0166]

[0167] In the above formula, B represents the number of independent sources. In this embodiment, the previous iteration process F(W) is selected. ：，i The updated average difference of the B independent sources is used as the threshold μ. T When F(W) is in this iteration ：，i When the difference comparison is small, change the iteration step size μ. k+1 This ensures the descent property of Newton's iteration method. After k iterations, it satisfies... (Considering the convergence speed, this invention selects ε1 = 10) -5 Alternatively, after reaching a certain number of iterations, stop the iteration to obtain the i-th column vector of the current unaliasing matrix.

[0168] like Figure 3 As shown, step S103 in this embodiment includes:

[0169] S401, initialize the iteration count s to 1, and de-aliasing matrix W = [W ：，1 W ：，2 …W ：，B The i-th column vector W in ] ：，i As the i-th column vector in the s-th iteration

[0170] S402, the aliasing matrix is ​​corrected by backpropagation of the error using the following formula:

[0171]

[0172] In the above formula, Let i be the i-th column vector in the (s+1)-th iteration. Let be the i-th column vector in the s-th iteration, α be the learning factor, and e be the learning vector. ijFor the i-th pre-separation signal and the j-th principal component signal v j，： The error between them; considering the convergence speed of the gradient descent method, in this embodiment, α = 0.01 / B = 0.01 / 4 is selected;

[0173] S403, if the number of iterations s equals the set threshold or If the condition is met, proceed to step S404; otherwise, increment the iteration count s by 1 and proceed to step S402. Here, ε2 is a preset threshold. Considering the accuracy of the dealiasing matrix calculation, this embodiment selects ε2 = 10. -6 ;

[0174] S404, if column variable i is less than the number of independent sources B, increment column variable i by 1, and jump to step S402 to find the next column vector of the unaliased matrix W. Otherwise, proceed to step S405;

[0175] S405, combine all the iterated column vectors to obtain the corrected dealiasing matrix W′, and obtain the accurate separation signal based on the corrected dealiasing matrix W′ and the following formula:

[0176]

[0177] In the above formula, To accurately separate the signals, W′ is the corrected dealiasing matrix, and v is the principal component signal after centering and whitening.

[0178] In step S402 of this embodiment, the i-th pre-separation signal and the j-th principal component signal v j，： The expression for the calculation function of the error between them is:

[0179]

[0180] In the above formula, For the i-th pre-separation signal and the j-th principal component signal v j，： The squared correlation coefficient between the signals is used to evaluate the dealiasing effect; the closer the squared correlation coefficient is to 1, the better the signal separation effect. Furthermore, we have:

[0181]

[0182] In the above formula, M represents the number of sampling times. For the i-th pre-separation signal The signal at time m, v j，m For the j-th principal component signal v j，： The m-th time-of-time signal in the dataset. In this embodiment, the maximum value is selected. For the corresponding i and j, the i-th pre-separation signal and the j-th principal component signal are matched in order. The matching results of the pre-separation signal and the principal component signal are shown in Table 1.

[0183] Table 1: Matching results between pre-separated signals and principal component signals.

[0184] principal component signal 3 2 4 1 Correlation coefficient squared 0.814 0.8468 0.8172 0.8547

[0185] As shown in Table 1, the squared correlation coefficient between the fourth pre-separated signal and the first principal component signal is the largest.

[0186] Select the largest For the corresponding i and j, the i-th separated signal and the j-th principal component signal are in the same order. The separation signal error at this time is defined as... Calculation error e ij For W ：，i The gradient can be obtained as follows:

[0187]

[0188] in,

[0189]

[0190] Figure 2 The fault audio separation results of this embodiment are shown below. In this embodiment, the correlation coefficients between the final separated signal and the original audio signal are calculated, and the correlation coefficients are 0.9298, 0.9107, 0.9054, and 0.9166, respectively. Therefore, it can be seen that the efficient dealiasing analysis method based on error backpropagation in this embodiment can effectively separate fault audio signals and has a good fault audio separation effect.

[0191] In step S104, when performing frequency estimation based on the accurate separated signals of each channel, the required frequency estimation method can be used as needed, including but not limited to short-time Fourier transform and S-transform, to extract the time-frequency characteristics of the separated signals. For example, the calculation formula for time-frequency analysis of the separated signals using short-time Fourier transform is as follows:

[0192]

[0193] Among them, TF i (n, ω) represents the time-domain and frequency-domain feature matrices of the i-th separated signal output. Let w(nt) be the final, precisely separated signal, and let w(nt) be the window function. The time-domain and frequency-domain characteristics of all separated signals are obtained by iteratively calculating B times. Figure 4These are the time-domain and frequency-domain features extracted in this embodiment. Based on the method of this embodiment, fault signal separation and the extraction of time-domain and frequency-domain features can be achieved, thereby aiding in the diagnosis of wind turbine faults. As an optional implementation, the obtained frequency estimation results (time-domain and frequency-domain feature matrices) can be input into a pre-trained machine learning classifier (e.g., a convolutional neural network) to determine the type of wind turbine fault and further assess the severity of the fault.

[0194] In summary, to address the technical challenges of frequency estimation and accurate signal separation for multi-source signals in the field of audio signal processing and signal monitoring and identification for wind turbine generators, this embodiment presents a method for frequency component estimation and accurate separation of multi-source signals. Based on observed multi-source mixed signal sequence data, it uses fitting entropy as a criterion for balancing the number of independent sources and the contribution of principal component signals to the source signals, determining the number of independent signal sources and extracting principal component signals. Using maximizing non-Gaussian negative entropy as the objective function, an iterative format is established based on the principal component signals and the variable-step-size Newton iteration method, updating the iteration step size to achieve pre-separation of independent signals. The squared correlation coefficient between the pre-separated signal and the principal component signals is used as an evaluation index for the separation effect. An error function is defined, and the gradient of the error function with respect to the dealiasing matrix is ​​calculated. The dealiasing matrix is ​​updated and corrected along the gradient direction of the error function to obtain an accurate dealiasing matrix, completing the separation of independent source signals. Finally, frequency estimation is performed on the separated independent source signals to obtain an accurate time-frequency characteristic matrix, thereby achieving the extraction of time-domain and frequency-domain features of each independent source signal in the multi-source mixed signal (e.g., short-time Fourier transform to extract time-domain and frequency-domain features). The key aspects of this embodiment's method include: It proposes using fitting entropy as a measure of the number of independent sources and the contribution of the principal component signal to the source signal. The number of independent sources is extracted at the inflection point of the fitting entropy, and the first B eigenvectors are selected to project onto the observed signal to obtain the principal component signal. This embodiment employs an efficient dealiasing analysis method, designing a variable-step-size Newton iteration method to solve for zeros. A new iterative approach is constructed, updating the iteration step size during the iteration process to ensure the convergence of the iterative solution of the dealiasing matrix, resulting in a pre-separated signal. This embodiment feeds back the pre-separated signal and uses the square of the correlation coefficient as an evaluation function to assess the separation effect. A separation error function is defined, and the gradient of the error function with respect to the dealiasing matrix is ​​calculated. The error is propagated in the back direction, and the dealiasing matrix is ​​corrected in the direction of the error gradient to obtain an accurate dealiasing matrix and an accurate separated signal. This embodiment of the frequency component estimation and accurate separation method for multi-source signals effectively solves the problems of traditional signal frequency estimation and signal separation methods, such as the unknown number of independent sources, the tendency to get trapped in local optima, and the accumulation of signal separation errors. By calculating the inflection point of the fitting entropy, the number of independent sources in the observed signal is determined. The principal component signals are extracted from the observed signal using the projection matrix. The variable step-size Newton iteration method is used to update the iteration step size and dealias the observed signal. Finally, the dealiasing matrix is ​​corrected in the direction of the error function gradient to accurately separate the source signals. This improves the traditional method's tendency to get trapped in local optima and its lack of flexibility, thus improving the accuracy of frequency estimation and signal separation.The method in this embodiment effectively solves the problem of determining the number of independent sources in signal separation. By using the variable step-size Newton iteration method and backpropagation error, an accurate dealiasing matrix is ​​obtained, which can accurately separate fault sound signals in wind turbine operation and extract the accurate time-domain and frequency-domain characteristics of independent signals. It can be used for tasks such as fault diagnosis and anomaly detection, thereby identifying potential single or compound faults.

[0195] Furthermore, this embodiment also provides a frequency component estimation and accurate separation device for multi-source signals, including a microprocessor and a memory interconnected thereto. The microprocessor is programmed or configured to execute the frequency component estimation and accurate separation method for multi-source signals. Additionally, this embodiment also provides a computer-readable storage medium storing a computer program for being programmed or configured by the microprocessor to execute the frequency component estimation and accurate separation method for multi-source signals.

[0196] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0197] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for frequency component estimation and accurate separation of multi-source signals, characterized in that, Includes the following steps: S101, for the sampling data of multiple channels of wind turbine fault signal, the number of independent sources and principal component signals are determined based on the fitting entropy; S102, the variable step-size Newton iteration method is used to dealias the principal component signals to obtain the dealiasing matrix and the pre-separated signal; S103 uses error backpropagation to correct the aliasing matrix and separate the multi-source mixed signal into a precise separated signal; S104, frequency estimation is performed based on the accurately separated signals of each channel; Step S102 includes: S301, The principal component signals are centered and whitened to obtain the centered and whitened principal component signals. ; S302, Construct the nonlinear equations for resolving aliasing: ， In the above formula, To solve the aliased nonlinear equations, E For mathematical expectation, The principal component signals are those after centering and whitening. For pre-separation signal, To compare the first derivative of the function exist The value at that location, and has , ,in u The independent variable of the comparison function is defined; the iteration step number k=1 and the step size parameter for the first step are initialized. Randomly initialize the dealiasing matrix. ,in ~ These are the dealiasing matrices. The 1st ～ Given B column vectors, initialize the column variables. i =1, dealiasing matrix The i The column vectors are used as the initial first step's... i column vectors ; S303, solve for the k+1th step according to the following formula. i column vectors : ， In the above formula, Let k be the step size parameter. E For mathematical expectation, For the first i One pre-separated signal, For the first derivative of the comparison function In the i Pre-separation signal The value at that location, The second derivative of the comparison function In the i Pre-separation signal The value at that location, , For the k-th step i Column vectors; update the step size parameter at step k+1. ; Calculate the k+1th step after iteration according to the following formula i column vectors And the k+1th step after iteration i column vectors As the new k+1th step i column vectors ; In the above formula, To solve the aliasing matrix The j Column vectors; For the (k+1)th step after iteration, the... i Column vectors; S304, if the number of iterations k equals the preset threshold or If the iteration is successful, proceed to step S305; otherwise, increment the iteration number k by 1 and proceed to step S303 to continue iterating. S305, if column variables i Less than the number of independent sources B Then the column variable i Add 1, then jump to step S303 to solve the unaliasing matrix. The next column vector; otherwise, the unaliasing matrix is ​​obtained. Proceed to step S306; S306, the pre-separation signal is obtained according to the following formula: In the above formula, For pre-separation signal, To solve the aliasing matrix, The principal component signals after centering and whitening; Step S103 includes: S401, Initialize the iteration count s to 1, and de-aliasing matrix Each of the following i column vectors As the s-th iteration i column vectors ; S402, the aliasing matrix is ​​corrected by backpropagation of the error using the following formula: In the above formula, For the (s+1)th iteration, the... i column vectors, For the s-th iteration, the th i column vectors, As a learning factor, For the first i Pre-separation signal and the j One principal component signal Error between; S403, if the number of iterations s equals the set threshold or If the condition is met, proceed to step S404; otherwise, increment the iteration count s by 1 and proceed to step S402. The preset threshold; S404, if column variables i Less than the number of independent sources B Then the column variable i Add 1, then jump to step S402 to solve the unaliasing matrix. The next column vector Otherwise, proceed to step S405. S405, combine all the iterated column vectors to obtain the corrected dealiasing matrix. According to the corrected dealiasing matrix The precise separation signal is obtained by combining the following formula: In the above formula, To accurately separate the signal, This is the corrected unaliasing matrix. The principal component signals are those after centering and whitening.

2. The method for frequency component estimation and accurate separation of multi-source signals according to claim 1, characterized in that, Step S101 includes: S201. Construct an N×M observation data matrix x from the sampling data of M time points collected from N channels of the wind turbine fault signal; standardize the observation data matrix x to obtain a standardized observation data matrix X; calculate the covariance coefficients between each channel based on the standardized observation data matrix X to obtain a covariance coefficient matrix R of dimension N×N; perform eigenvalue decomposition on the covariance coefficient matrix R, arrange the eigenvalues ​​in descending order to obtain the N eigenvalues ​​of the covariance coefficient matrix R and their corresponding eigenvectors. S202, starting from 1 and ending at N, calculate the fitting entropy for different numbers of independent sources, and determine the number of independent sources from the calculated N fitting entropies according to the following formula. B : ， In the above formula, b The number of independent sources traversed. b =1,2,…,N-1, for b The fitting entropy with +1 independent source signals for b Fitting entropy for each independent source signal; S203, Select the first covariance coefficient matrix R B The eigenvectors corresponding to the largest eigenvalues ​​are used as the projection matrix. The standardized observation data matrix X is then projected onto the low-dimensional principal component signal V with dimensions B×M using the projection matrix.

3. The method for frequency component estimation and accurate separation of multi-source signals according to claim 2, characterized in that, The function expression for calculating the fitting entropy in step S202 is: ， In the above formula, Indicates the number of independent sources c The fitting entropy over time, where M is the number of sampling times and N is the number of channels. The first covariance coefficient matrix R is the first... i Each feature value.

4. The method for frequency component estimation and accurate separation of multi-source signals according to claim 2, characterized in that, In step S203, the function expression for projecting the standardized observation data matrix X onto the low-dimensional principal component signal V of dimension B×M using the projection matrix is: ， In the above formula, P represents a projection matrix of dimension N×B, X is the standardized observation data matrix, and we have: ， In the above formula, ~ The first part of the covariance coefficient matrix R B The eigenvectors corresponding to the largest eigenvalues.

5. The method for frequency component estimation and accurate separation of multi-source signals according to claim 1, characterized in that, In step S303, the step size parameter of step k+1 is updated. The function expression is: In the above formula, The step size parameter for the (k+1)th step. Let k be the step size parameter. For the threshold, For the k-th step i column vectors The L2 norm of the computational results of the nonlinear equations for solving aliasing. For the (k-1)th step i column vectors The L2 norm of the nonlinear equations for solving the aliasing problem; where: The function expression for condition 1 is: ， The function expression for condition 2 is: ， threshold The expression for the computation function is: ， In the above formula, B The number of independent sources.

6. The method for frequency component estimation and accurate separation of multi-source signals according to claim 1, characterized in that, In step S402 i Pre-separation signal and the j One principal component signal The expression for the calculation function of the error between them is: ， In the above formula, For the first i Pre-separation signal and the j One principal component signal The squared correlation coefficient between them is given by: ， In the above formula, M represents the number of sampling times. For the first i Pre-separation signal The first in m A signal at a given moment. For the first j One principal component signal The signal at time m in the sequence.

7. A device for frequency component estimation and precise separation of multi-source signals, comprising a microprocessor and a memory interconnected thereon, characterized in that, The microprocessor is programmed or configured to perform the frequency component estimation and accurate separation method for multi-source signals according to any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program is used to be programmed or configured by a microprocessor to perform the frequency component estimation and accurate separation method for multi-source signals according to any one of claims 1 to 6.

Images