Structural vibration signal reconstruction method combining iterative threshold method and MBCS

Abstract

The present application relates to a kind of structure vibration signal reconstruction methods of combining iterative threshold method and MBCS, when signal sparsification, the signal is compressed sampling using iterative threshold method, and the more sparse compressed observation signal of sparsity is obtained;And when signal compression, through multiple observation matrix, obtain multiple groups of observation signals, using the statistical correlation between multiple signals and the bayesian compressed sensing reconstruction algorithm, the reconstructed original signal is obtained.The method can be used for the compressed sampling and original signal reconstruction of monitoring signal, solve the problem of high cost such as transmission, storage caused by large amount of data when signal acquisition, improve the precision of structure vibration signal reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration signal processing technology, specifically relating to a structural vibration signal reconstruction method that combines iterative thresholding and multitask Bayesian Compressive Sensing (MBCS). Background Technology

[0002] To avoid signal loss during recovery, traditional structural dynamic response signal acquisition requires adherence to the Nyquist sampling theorem, which dictates that the sampling frequency must be more than twice the maximum frequency of the original signal. This results in massive amounts of real-time bridge structural health monitoring data, increasing data transmission and storage costs. The recently proposed Compressive Sensing (CS) theory combines compression and sampling, fundamentally reducing the amount of data collected and providing a new approach to solving this problem. CS theory states that for signals possessing compressibility and sparsity, or sparsity in a certain transform domain, the signal can be compressed using an observation matrix uncorrelated with the transform basis. The original signal can then be reconstructed from the compressed observation signal by solving a non-convex optimization problem. The vibration response signals of civil engineering structures exhibit approximately sparse characteristics in the frequency domain, wavelet domain, or other transform domains, meeting the signal characteristic requirements of CS theory.

[0003] For structural health monitoring signals in civil engineering, they are susceptible to environmental noise interference and are generally sparse. In compressed sensing theory, the sparsity of these signals is insufficient. Furthermore, most current Bayesian compressed sensing reconstruction methods reconstruct a set of compressed signals independently, neglecting the statistical correlation between the signals. Summary of the Invention

[0004] The purpose of this invention is to provide a structural vibration signal reconstruction method that combines the iterative thresholding method and MBCS, which is beneficial to improving the accuracy of structural vibration signal reconstruction.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a structural vibration signal reconstruction method combining iterative thresholding and MBCS, comprising the following steps:

[0006] Step S1: Select a sparse orthogonal basis Ψ, and make the signal x sparsely represented according to the formula x = Ψθ to obtain the sparse vector θ;

[0007] Step S2: Determine the number L of multiple tasks;

[0008] Step S3: Calculate the threshold T using the iterative thresholding method. k Then, based on the threshold T kHard thresholding is applied to the sparse vector θ to obtain a new sparse vector.

[0009] Step S4: Input the random observation matrix Sparse vectors are processed using L different Gaussian random matrices. Projecting yields L sets of compressed observation vectors y i Then, Φ of group L tasks i y i Add to cell arrays Φ and Y;

[0010] Step S5: Establish a multi-task Bayesian compressed sensing model and reconstruct sparse vectors.

[0011] Step S6: Utilize the reconstructed sparse vector Through formula Restore the original signal.

[0012] Furthermore, step S3 specifically includes the following steps:

[0013] Step S3.1: Set the value of parameter μ, let k = 1, calculate the sparse vector θ1 using the original signal x, and determine the maximum value Z of θ1. max and minimum value Z min Calculate the initial threshold T k =(Z min +Z max ) / 2;

[0014] Step S3.2: Based on the threshold T k For sparse vector θ k Hard thresholding is performed, setting sparse coefficients smaller than the threshold to zero while leaving the remaining sparse coefficients unchanged, resulting in a new sparse vector θ. k+1 ;

[0015]

[0016] Step S3.3: Calculate the error RE = ||θ1 - θ k+1 ||2 / ||θ1||2, and judge the result: if RE≥μ, then execute step S3.4; if RE<μ, then Perform step S3.5;

[0017] Step S3.4: Let k = k + 1, and calculate the new threshold T. k =(T k-1 +Z min ) / 2, repeat steps S3.2-S3.3;

[0018] Step S3.5: Obtain the new sparse vector.

[0019] Furthermore, step S5 specifically includes the following steps:

[0020] Step S5.1: Set parameters a, b, total number of iterations I, and error value tole; set the initial hyperparameter {α}. k Let k = 1;

[0021] Step S5.2: Based on the empirical Bayesian principle, extract Φ from the observation matrix of the i-th task. i Select a column {φ i} k And mark its position and denot it as l, i = 1, 2, ..., L, and solve the corresponding {s} according to equations (2)-(10). i} k 、{q i} k 、{g i} k 、{μ i} k 、{Σ i} k Hyperparameter {α} l} k And the logarithm of the maximized marginal likelihood function at position l, {L(α)} k ;

[0022]

[0023]

[0024]

[0025]

[0026] A = diag(α1, α2...α) N (6)

[0027]

[0028]

[0029]

[0030]

[0031] Step S5.3: Let k = k + 1, and based on the empirical Bayesian principle, extract Φ from the observation matrix of the 1st to the Lth task. i Select a new column {φ i} kand calibrate its position, denoted as l, solve the corresponding {s i} k 、{q i} k 、{g i} k ;

[0032]

[0033]

[0034]

[0035] Step S5.4: Obtain the hyperparameter {α l} k by using formula (5), and judge: if {α l} k > 0, update the hyperparameter {α} with {α l} k ; if {α k ; if {α l} k < 0, do not update the hyperparameter {α}; k ;

[0036] Step S5.5: Obtain {μ i} k and the logarithmic value {L(α)} of the maximum marginal likelihood function at position l by using formulas (8) and (10) respectively; k ;

[0037] Step S5.6: Judge: if |{L(α)} k -{L(α)} k-1 |<tole或k>I, the iteration terminates, and the obtained {μ i} k is the reconstructed sparse vector otherwise, repeat steps S5.3 to S5.6.

[0038] Compared with existing technologies, this invention has the following advantages: This invention proposes a structural vibration signal reconstruction method combining iterative thresholding and multi-task Bayesian compressed sensing. This method can be used for compressed sampling and reconstruction of monitoring signals, solving the problem of high transmission and storage costs caused by large data volumes during signal acquisition. By setting a threshold, elements in the original sparse coefficients smaller than the threshold are set to zero, while elements larger than the threshold remain unchanged. This results in a sparser vector with stronger sparsity, reducing noise interference and improving the reconstruction accuracy of the subsequent original signal. Simultaneously, by utilizing the statistical characteristics between multiple sets of observation data, information complementarity is achieved, and the estimated sparse vector preserves more information. Furthermore, this method incorporates noise parameters into the model through a multi-task Bayesian compressed sensing reconstruction algorithm. By integrating the noise parameters, only hyperparameters need to be recovered during the calculation process, making the calculation simpler and easier for engineering applications. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the method implementation of an embodiment of the present invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0042] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0043] like Figure 1 As shown, this embodiment provides a structural vibration signal reconstruction method combining iterative thresholding and MBCS, including the following steps:

[0044] Step S1: Select a sparse orthogonal basis Ψ, and make the signal x sparsely represented according to the formula x = Ψθ, so as to obtain the sparse vector θ.

[0045] Step S2: Determine the number L of multiple tasks.

[0046] Step S3: Calculate the threshold T using the iterative thresholding method. k Then, based on the threshold T kHard thresholding is applied to the sparse vector θ to obtain a new sparse vector.

[0047] In this embodiment, step S3 specifically includes the following steps:

[0048] Step S3.1: Set the value of parameter μ, let k = 1, calculate the sparse vector θ1 using the original signal x, and determine the maximum value Z of θ1. max and minimum value Z min Calculate the initial threshold T k =(Z min +Z max ) / 2;

[0049] Step S3.2: Based on the threshold T k For sparse vector θ k Hard thresholding is performed, setting sparse coefficients smaller than the threshold to zero while leaving the remaining sparse coefficients unchanged, resulting in a new sparse vector θ. k+1 :

[0050]

[0051] Step S3.3: Calculate the error RE = ||θ1 - θ k+1 ||2 / ||θ1||2, and judge the result: if RE≥μ, then execute step S3.4; if RE<μ, then Proceed to step S3.5.

[0052] Step S3.4: Let k = k + 1, and calculate the new threshold T. k =(T k-1 +Z min ) / 2, repeat steps S3.2-S3.3.

[0053] Step S3.5: Obtain the new sparse vector.

[0054] Step S4: Input the random observation matrix Sparse vectors are processed using L different Gaussian random matrices. Projecting yields L sets of compressed observation vectors y i Then, Φ of group L tasks i y i Add to cell arrays Φ and Y.

[0055] Step S5: Establish a multi-task Bayesian compressed sensing model and reconstruct sparse vectors.

[0056] In this embodiment, step S5 specifically includes the following steps:

[0057] Step S5.1: Set parameters a, b, total number of iterations I, and error value tole; set the initial hyperparameter {α}. k Let k = 1.

[0058] Step S5.2: Based on the empirical Bayesian principle, extract Φ from the observation matrix of the i-th task. i Select a column {φ i} k And mark its position and denot it as l, i = 1, 2, ..., L, and solve the corresponding {s} according to equations (2)-(10). i} k 、{q i} k 、{g i} k 、{μ i} k 、{Σ i} k Hyperparameter {α} l} k And the logarithm of the maximized marginal likelihood function at position l, {L(α)} k :

[0059]

[0060]

[0061]

[0062]

[0063] A = diag(α1, α2...α) N (6)

[0064]

[0065]

[0066]

[0067]

[0068] Step S5.3: Let k = k + 1, and based on the empirical Bayesian principle, extract Φ from the observation matrix of the 1st to the Lth task. i Select a new column {φ i} k And mark its position and denot it as l, and solve the corresponding {s} according to equations (11)-(13). i} k 、{q i} k 、{gi} k :

[0069]

[0070]

[0071]

[0072] Step S5.4: Calculate the hyperparameter {α l} k by using formula (5), and judge: if {α l} k > 0, use {α l} k to update the hyperparameter {α} k ; if {α l} k < 0, do not update the hyperparameter {α} k .

[0073] Step S5.5: Calculate {μ i} k and the logarithmic value {L(α)} of the maximized marginal likelihood function at position l k .

[0074] Step S5.6: Judge: if |{L(α)} k -{L(α)} k-1 |<tole or k>I, the iteration is terminated, and the obtained {μ i} k is the reconstructed sparse vector otherwise, repeat steps S5.3 to S5.6.

[0075] Step S6: Use the reconstructed sparse vector to recover the original signal through a formula.

[0076] In the method of the present invention, when sparsifying a signal, an iterative threshold method is used to perform compressive sampling on the signal to obtain a compressed observation signal with higher sparsity; and when compressing the signal, multiple groups of observation signals are obtained through a plurality of observation matrices, and the statistical correlation between the multiple groups of signals and a Bayesian compressed sensing reconstruction algorithm are used to obtain a reconstructed original signal with higher accuracy.

[0077] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A structural vibration signal reconstruction method combining iterative thresholding and MBCS, characterized in that, Includes the following steps: Step S1: Select sparse orthogonal basis According to the formula Make signal Sparse representation yields sparse vectors. ; Step S2: Determine the number L of multiple tasks; Step S3: Calculate the threshold T using the iterative thresholding method. k Then based on the threshold T k For sparse vectors Hard thresholding is performed to obtain a new sparse vector. ; Step S4: Input the random observation matrix , Sparse vectors are processed by L different Gaussian random matrices. Projecting yields L sets of compressed observation vectors. Then, the tasks in group L , Add to cell array and cell array middle; Step S5: Establish a multi-task Bayesian compressed sensing model and reconstruct sparse vectors. ; Step S6: Utilize the reconstructed sparse vector Through formula Restore the original signal; Step S3 specifically includes the following steps: Step S3.1: Set the value of parameter μ, let k=1, and use the original signal. Calculate the sparse vector ,Sure The maximum value Z max and minimum value Z min Calculate the initial threshold T k =(Z min +Z max ) / 2; Step S3.2: Based on the threshold T k For sparse vectors Hard thresholding is performed, setting sparse coefficients smaller than a threshold to zero while leaving the remaining sparse coefficients unchanged, resulting in a new sparse vector. ; (1) Step S3.3: Calculate the error And judge the result: if If so, proceed to step S3.4; if ,but Proceed to step S3.5; Step S3.4: Let k = k + 1, and calculate the new threshold T. k =( T k-1 + Z min ) / 2, repeat steps S3.2-S3.3; Step S3.5: Obtain the new sparse vector. .

2. The structural vibration signal reconstruction method combining iterative thresholding and MBCS according to claim 1, characterized in that, Step S5 specifically includes the following steps: Step S5.1: Set parameters a, b, total number of iterations I, and error value tole; set initial hyperparameters. Let k=1; Step S5.2: Based on the empirical Bayesian principle, extract from the observation matrix of the i-th task Select one column And mark its position and denot it as l, Solve the corresponding equations (2)-(10). , , , , Hyperparameters And the logarithm of the maximized marginal likelihood function at position l. ; (2) (3) (4) (5) (6) (7) (8) (9) (10) Step S5.3: Let k = k + 1, and based on the empirical Bayesian principle, extract the observation matrices from the first to the Lth tasks. Select a new column And mark its position and denot it as l, and solve the corresponding equations (11)-(13). , , ; (11) (12) (13) Step S5.4: Use equation (5) to calculate the hyperparameters. And determine: if Then use Update hyperparameters ;if Then the hyperparameters will not be updated. ; Step S5.5 Use equations (8) and (10) to calculate respectively And the logarithm of the maximized marginal likelihood function at position l. ; Step S5.6: determining: if <tole or k>I, the iteration terminates, and the obtained is the reconstructed sparse vector ; otherwise, repeat steps S5.3 to S5.6.

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