CN115459778B - Method, device and storage medium for reducing vibration signal compressed sensing reconstruction error - Google Patents

Method, device and storage medium for reducing vibration signal compressed sensing reconstruction error Download PDF

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CN115459778B
CN115459778B CN202210948233.9A CN202210948233A CN115459778B CN 115459778 B CN115459778 B CN 115459778B CN 202210948233 A CN202210948233 A CN 202210948233A CN 115459778 B CN115459778 B CN 115459778B
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康杰
谢炎龙
任伟新
赵杨平
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Abstract

The embodiment of the invention discloses a method, a device and a storage medium for reducing a compressed sensing reconstruction error of a vibration signal, wherein the method comprises the following steps: obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation; inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model; determining a relative residual error of the autoregressive model based on the model residual and the model output; and (3) performing relative residual error reduction treatment according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal. By adopting the method, any transformation base is not needed, the limitation of lack of sparsity of the vibration signal is avoided, the new reconstruction signal has higher precision compared with the original reconstruction signal, and the reconstruction precision of the vibration signal is improved. In addition, by constructing an autoregressive model to introduce the time sequence characteristics of the signals, the relative residual error of the model is reduced, the reconstruction error is reduced, and the signal reconstruction precision is further improved.

Description

Method, device and storage medium for reducing vibration signal compressed sensing reconstruction error
Technical Field
The present invention relates to the field of data transmission technologies, and in particular, to a method, an apparatus, and a storage medium for reducing a compressed sensing reconstruction error of a vibration signal.
Background
Structural health monitoring requires real-time measurement of structural features to monitor anomalies. Vibration signals are key measures to extract dynamic structural features (i.e., natural frequency, damping ratio, and mode shape). Because the sampling frequency is higher, the data volume of the vibration signal is huge in long-term structure monitoring acquisition, and huge pressure is brought to a data transmission link, in particular to wireless data transmission.
The compressed sensing technology is a data compression technology newly developed in recent years, and the unique sampling step simplifies the signal sampling compression process and reduces the data transmission quantity. Under the compression sensing frame, the vibration signal is directly transmitted to the sensor end
Figure BDA0003784643980000011
Multiplying the observation matrix->
Figure BDA0003784643980000012
Post-compression to observations +.>
Figure BDA0003784643980000013
And solving the underdetermined equation y=phix at the data receiving end to reconstruct the vibration signal.
The compressed sensing technology faces the problem of lack of sparsity of vibration signals when reconstructing the vibration signals. Compressed sensing reconstructs the vibration signal by solving a linear equation y=Φx, which contains an infinite number of solutions since the compressed value y has fewer dimensions than the vibration signal x (y has the dimension M and x has the dimension N).
The existing compressed sensing reconstruction method assumes that the vibration signal x is in a conventional transformation base
Figure BDA0003784643980000014
(e.g., fourier basis and wavelet basis) with sparsity, i.e., assuming x=θs and +.>
Figure BDA0003784643980000015
Only a small number of elements are non-zero, and then solving the optimization problem of formula (1) to obtain +.>
Figure BDA0003784643980000016
Then obtain the reconstruction signal +.>
Figure BDA0003784643980000017
It should be noted that equation (1) is an NP-hard problem, i.e., it cannot be directly solved, and the existing compressed sensing method obtains +.>
Figure BDA0003784643980000018
Figure BDA0003784643980000019
However, the structural vibration signal lacks sparsity on the conventional transformation basis, that is, the decomposition coefficient s of x on the transformation basis θ is assumed to have only a few elements and is not zero, and at this time, under the condition that the number of acquired compressed observations y is small, the existing compressed sensing method obtains a reconstructed signal by solving the equation of formula (1)
Figure BDA0003784643980000021
There will be a large error.
For the problem of lack of sparsity of vibration signals, there are currently two main types of approaches to enhance the reconstructed signals
Figure BDA0003784643980000022
Is a precision of (a). One class of methods increases sparsity of vibration signals by increasing completeness or redundancy of the transform basis, i.e., increasing the transform basis
Figure BDA0003784643980000023
Or directly set a parameter continuous atom library. Another class of methods uses joint sparsity features of structurally different site signals, e.g., signal x 1 Sum signal x 2 The decomposition coefficient of (2) on the transformation basis theta is s 1 Sum s 2 Then assume s 1 Sum s 2 The element values at the same location are larger or smaller.
From the above discussion, it can be appreciated that existing compressed sensing reconstruction requires the assumption that the vibration signal x is at a conventional transform basis
Figure BDA0003784643980000024
The sparsity is present on (e.g., fourier basis and wavelet basis) to achieve vibration signal reconstruction. The structure is used as a system, the environment excitation to which the structure is subjected is close to white noise in an actual running state, and the white noise does not have sparsity on any transformation basis, so that the vibration response of the structure output does not have obvious sparsity on a conventional transformation basis. If the number of compressed observations y is low, then the reconstruction signal +.>
Figure BDA0003784643980000025
Will contain a large error. Although the existing compressed sensing reconstruction algorithm can improve the accuracy of the reconstructed signal to a certain extent by adopting a combined structure for increasing the completeness of the transformation base theta or utilizing signals of different measuring points, the method is still limited by lack of sparsity of the vibration signal.
Disclosure of Invention
The invention mainly aims to provide a method, a device and a storage medium for reducing a compressed sensing reconstruction error of a vibration signal, which can solve the problem that a larger error exists in the reconstruction of the compressed sensing vibration signal in the prior art.
To achieve the above object, a first aspect of the present invention provides a method for reducing a vibration signal compressed sensing reconstruction error, the method comprising:
obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation;
inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
determining a relative residual of the autoregressive model based on the model residual and a model output;
and performing processing for reducing the relative residual error according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal.
In one possible implementation, the autoregressive model includes the following mathematical expression:
Figure BDA0003784643980000031
in the method, in the process of the invention,
Figure BDA0003784643980000032
is the model output; />
Figure BDA0003784643980000033
For model regression>
Figure BDA0003784643980000034
Is a model parameter, (i=1, 2, Λp), p is an order, ++>
Figure BDA0003784643980000035
Is a model residual.
In one possible implementation, the relative residual comprises the following mathematical expression:
Figure BDA0003784643980000036
in the method, in the process of the invention,
Figure BDA0003784643980000037
for model output, +.>
Figure BDA0003784643980000038
For model residual, (i=1, 2, Λp),>
Figure BDA0003784643980000039
is a norm.
In one possible implementation manner, the auto-regression model feature parameter further includes a model regression amount and a model parameter, the processing for reducing the relative residual error according to the auto-regression model parameter and the basis solution system of the under-determined equation, to obtain a new reconstructed vibration signal, including:
constructing an optimization problem for reducing the relative residual error by utilizing a basic solution system of a model regression quantity, a model output quantity, an order, model parameters and a undercurrent equation;
and solving the optimization problem to obtain a new reconstruction vibration signal.
In one possible implementation, the optimization problem includes the following mathematical expression:
Figure BDA00037846439800000310
wherein x is out ＝[x p+1 x p+2 Λ x N ]Is the model output;
Figure BDA00037846439800000311
for model regression>
Figure BDA00037846439800000312
Is a model parameter, (i=1, 2, Λp), p is an order, y=Φx T As an underdetermined equation, underdetermined equation y=Φx T Is->
Figure BDA00037846439800000313
In the formula, h is a coefficient, ">
Figure BDA00037846439800000314
Pi is the basic solution of the underdetermined equation, r is the rank of the basic solution, ++>
Figure BDA00037846439800000315
Is a norm.
In one possible implementation, the solving the optimization problem to obtain a new reconstructed vibration signal includes:
calculating a general solution of the under-determined equation in the optimization problem;
performing expression simplification processing on the optimization problem based on the general solution of the under-determined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting the model output quantity in the denominator of the optimization problem, and replacing the model regression quantity and the model output quantity in the optimization problem by using the general solution of the under-determined equation;
and obtaining a new reconstructed vibration signal by using the processed optimization problem.
In one possible implementation, the post-processing optimization problem includes the following mathematical expression:
Figure BDA0003784643980000041
wherein the underdetermined equation y=Φx T General solution to (1)
Figure BDA0003784643980000042
In the formula, h is a coefficient, ">
Figure BDA0003784643980000043
For new coefficients, ++>
Figure BDA0003784643980000044
Pi is the basis solution of the underdetermined equation, < +.>
Figure BDA0003784643980000045
r is the basic solving rank, pi out Matrix of n+1 to N rows of basic unbinding N->
Figure BDA0003784643980000046
Matrix formed by basic solving pi rows p+1-i to N-i, i=1, 2, Λp, p is order, < ->
Figure BDA0003784643980000047
Is a norm;
the new reconstructed vibration signal comprises the following mathematical expression:
Figure BDA0003784643980000048
in the method, in the process of the invention,
Figure BDA0003784643980000049
for a new reconstructed vibration signal, +.>
Figure BDA00037846439800000410
For reconstructing the vibration signal +.>
Figure BDA00037846439800000411
For new coefficients, ++>
Figure BDA00037846439800000412
Pi is the basis solution of the underdetermined equation, < +.>
Figure BDA00037846439800000413
r is the rank of the base solution.
In a possible implementation manner, the processing for reducing the relative residual error according to the characteristic parameters, the order and the basis solution of the underdetermined equation of the autoregressive model is performed to obtain a new reconstructed vibration signal, and then the method further includes:
determining the current reconstruction times of the reconstruction vibration signals;
and if the current reconstruction times are smaller than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the input of the reconstruction vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and outputting the new reconstruction vibration signal until the current reconstruction times are equal to the preset calculation cycle times.
To achieve the above object, a second aspect of the present invention provides an apparatus for reducing a vibration signal compressed sensing reconstruction error, the apparatus comprising:
and a data acquisition module: the basic solution system is used for acquiring the reconstructed vibration signal, the order and the underdetermined equation;
model construction module: the method comprises the steps of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
residual determination module: for determining a relative residual of the autoregressive model based on the model residual and a model output;
and the signal reconstruction module is used for: and the processing for reducing the relative residual error is carried out according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model, so as to obtain a new reconstructed vibration signal.
To achieve the above object, a third aspect of the present invention provides a computer-readable storage medium storing a computer program, which when executed by a processor causes the processor to perform the steps as described in the first aspect and any one of the possible implementations.
To achieve the above object, a fourth aspect of the present invention provides a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps as described in the first aspect and any one of the possible implementations.
The embodiment of the invention has the following beneficial effects:
the invention provides a method for reducing vibration signal compressed sensing reconstruction errors, which comprises the following steps: obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation; inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model; determining a relative residual error of the autoregressive model based on the model residual and the model output; and (3) performing relative residual error reduction treatment according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal. By adopting the method, any transformation base is not needed, the limitation of lack of sparsity of the vibration signal is avoided to a great extent, the new reconstruction signal has higher precision compared with the original reconstruction signal, and the reconstruction precision of the vibration signal is improved. In addition, by constructing an autoregressive model, the time sequence characteristics of the signals are introduced, and the error of the compressed sensing reconstruction signals is reduced by reducing the relative residual error of the autoregressive model, so that the reconstruction accuracy of the vibration signals is further improved.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Wherein:
FIG. 1 is a flowchart of a method for reducing compressed sensing reconstruction errors of vibration signals according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for reducing compressed sensing reconstruction errors of vibration signals according to an embodiment of the present invention;
FIG. 3 is a flowchart illustrating a method for reducing vibration signal compressed sensing reconstruction errors according to an embodiment of the present invention;
FIG. 4 is a graph comparing the relative residuals of BP and BP+ARCS reconstructed signals to construct an AR model;
FIG. 5 is a graph comparing Fourier spectra of BP and BP+ARCS reconstructed signals with reconstruction accuracy;
FIG. 6 is another comparison of the Fourier spectra and reconstruction accuracy of BP and BP+ARCS reconstructed signals;
FIG. 7 is a graph comparing Fourier spectra and reconstruction accuracy of BCS and BCS+ARCS reconstructed signals;
FIG. 8 is a graph comparing Fourier spectra and reconstruction accuracy of the SAMP and SAMP+ARCS reconstructed signals;
FIG. 9 is a block diagram illustrating an apparatus for reducing compressed sensing reconstruction errors of vibration signals according to an embodiment of the present invention;
fig. 10 is a block diagram showing the structure of a computer device according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, fig. 1 is a flowchart of a method for reducing a compressed sensing reconstruction error of a vibration signal according to an embodiment of the invention, where the method shown in fig. 1 includes the following steps:
101. obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation;
102. inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
in this embodiment, the reconstruction of the reconstruction dynamic signal is performed, so that the accuracy of the signal reconstruction is improved. Wherein the reconstructed motion signal refers to a vibration signal reconstructed by some conventional compressed sensing techniques. Conventional compressed sensing techniques include, but are not limited to, bayesian Compressed Sensing (BCS), compressed Sensing (SAMP), neural network compressed sensing (BP), and the like. Since the vibration signal has not only sparsity but also time series characteristics, an autoregressive model (AR model for short, english: autoregressive model) can be established based on the vibration signal, wherein the autoregressive model is a method for statistically processing time series by using the same variable such as previous phases of x, that is, x 1 To x t-1 To predict the present period x t And assume that they are in a linear relationship. Since this was developed from linear regression in regression analysis, only x was not used to predict y, but x (itself); so called autoregressive. Exemplary, taking the vibration signal as
Figure BDA0003784643980000071
For illustration, it is stored as a row vector x= [ x 1 x 2 Λ x N ]The p-order AR model of the vibration signal x is the following mathematical expression:
Figure BDA0003784643980000072
in the formula (2), x out ＝[x p+1 x p+2 Λ x N ]Is the model output;
Figure BDA0003784643980000073
as the regression of the model, a i Is a model parameter, (i=1, 2, Λp), p is an order, ++>
Figure BDA0003784643980000074
Is a model residual.
Further, an autoregressive model may also be built for the reconstructed vibration signal. Therefore, the method and the device establish an autoregressive model through the reconstructed vibration signals, and reconstruct the reconstructed vibration signals again. Specifically, a preset autoregressive model is input by using the reconstructed vibration signal and the order, so as to establish an autoregressive model of the reconstructed vibration signal, and autoregressive model characteristic parameters of the autoregressive model of the reconstructed vibration signal are obtained, wherein the autoregressive model characteristic parameters are used for reflecting the characteristics of the autoregressive model of the reconstructed vibration signal, and the autoregressive model characteristic parameters comprise, but are not limited to, model residues, model regression, model parameters and model output of the autoregressive model.
Exemplary, reconstructing the vibration signal
Figure BDA0003784643980000075
The autoregressive model of (a) is the following mathematical expression:
Figure BDA0003784643980000081
in the formula (3), the amino acid sequence of the compound,
Figure BDA0003784643980000082
is the model output;
Figure BDA0003784643980000083
for model regression>
Figure BDA0003784643980000084
Is a model parameter, (i=1, 2, Λp), p is an order,
Figure BDA0003784643980000085
for model residue->
Figure BDA0003784643980000086
103. Determining a relative residual of the autoregressive model based on the model residual and a model output;
104. and performing processing for reducing the relative residual error according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal.
Further, the test of the existing vibration signal shows that the model relative residual error of the reconstructed vibration signal in the formula (3)
Figure BDA0003784643980000087
Model residual error which is significantly greater than the vibration signal in formula (2)>
Figure BDA0003784643980000088
Wherein (1)>
Figure BDA0003784643980000089
For reconstructing the model output of the vibration signal, +.>
Figure BDA00037846439800000810
To reconstruct the model residue of the vibration signal, x out ＝[x p+1 x p+2 Λ x N ]For the model output of the vibration signal, < >>
Figure BDA00037846439800000811
For the model residual of the vibration signal, (i=1, 2, Λp), +.>
Figure BDA00037846439800000812
Is a norm.
Accordingly, the present application sets optimization problems according to the above phenomena, reducing the reconstructed signal by reducing the relative residual of equation (3)
Figure BDA00037846439800000813
Is a result of the error in the error correction. Thus, after the above-mentioned autoregressive model feature parameters of the reconstructed vibration signal are obtained, the autoregressive model feature parameters include model residues and model output quantities, and then the autoregressive model feature parameters are used to determine the autoregressive vibration signal in step 103Relative residuals of model. And further performing processing for reducing relative residual errors according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model through step 104 to obtain a new reconstructed vibration signal +.>
Figure BDA00037846439800000814
By reconstructing the reconstructed vibration signal, the vibration signal reconstruction precision can be improved, the accuracy of performance detection of the building structure is also improved, the safety and stability of the building structure are guaranteed, and accidents are reduced.
The invention provides a method for reducing vibration signal compressed sensing reconstruction errors, which comprises the following steps: obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation; inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model; determining a relative residual error of the autoregressive model based on the model residual and the model output; and (3) performing relative residual error reduction treatment according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal. By adopting the method, any transformation base is not needed, the limitation of lack of sparsity of the vibration signal is avoided to a great extent, the new reconstruction signal has higher precision compared with the original reconstruction signal, and the reconstruction precision of the vibration signal is improved. In addition, by constructing an autoregressive model, the time sequence characteristics of the signals are introduced, and the error of the compressed sensing reconstruction signals is reduced by reducing the relative residual error of the autoregressive model, so that the reconstruction accuracy of the vibration signals is further improved.
Referring to fig. 2, fig. 2 is another flowchart of a method for reducing a compressed sensing reconstruction error of a vibration signal according to an embodiment of the invention, where the method shown in fig. 2 includes the following steps:
201. obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation;
202. inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
203. determining a relative residual of the autoregressive model based on the model residual and a model output;
204. according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model, the relative residual error is reduced, and a new reconstruction vibration signal is obtained;
it should be noted that, steps 201 to 204 are similar to steps 101 to 104 shown in fig. 1, and detailed descriptions thereof are omitted herein for avoiding repetition, and refer to the foregoing steps 101 to 104 shown in fig. 1.
In one possible implementation, the autoregressive model feature parameters further include model regression and model parameters, and then step 204 may include the following steps A1-A2:
a1, constructing an optimization problem for reducing the relative residual error by utilizing a model regression quantity, a model output quantity, an order, model parameters and a basic solution system of a less-definite equation;
illustratively, the optimization problem of reducing the relative residuals includes the following mathematical expression:
Figure BDA0003784643980000091
in the formula (4), x out ＝[x p+1 x p+2 Λ x N ]Is the model output;
Figure BDA0003784643980000092
for model regression>
Figure BDA0003784643980000093
Is a model parameter (in the formula>
Figure BDA0003784643980000094
From equation (3)), (i=1, 2, Λp), p is the order, y=Φx T Is under-determinedEquation, underdetermined equation y=Φx T Is->
Figure BDA0003784643980000095
In the formula, h is a coefficient, ">
Figure BDA0003784643980000096
Pi is the basic solution of the underdetermined equation, r is the rank of the basic solution, ++>
Figure BDA0003784643980000097
Is a norm.
A2, solving the optimization problem to obtain a new reconstruction vibration signal.
Further, by solving the optimization problem of reducing the relative residual, namely equation (4), a new reconstructed vibration signal can be obtained
Figure BDA0003784643980000101
It should be noted that, in the expression (1), the compressed sensing needs to assume that the vibration signal x is in a conventional transformation base
Figure BDA0003784643980000102
The sparsity is present on (e.g., fourier basis and wavelet basis) to achieve vibration signal reconstruction. The structure is used as a system, the environment excitation to which the structure is subjected is close to white noise in an actual running state, and the white noise does not have sparsity on any transformation basis, so that the vibration response of the structure output does not have obvious sparsity on a conventional transformation basis. If the number of compressed observations y is low, then the reconstruction signal +.>
Figure BDA0003784643980000103
If the number of compressed observations y is low, then the reconstruction signal +.>
Figure BDA0003784643980000104
Will contain a large error. Although the existing compressed sensing reconstruction algorithm can be to a certain extent realized by adopting a combined structure of increasing the completeness of the transformation base theta or utilizing different measuring point signalsThe accuracy of the reconstructed signal is improved, but the limitation of lack of sparsity of the vibration signal is still met. However, compared with the formula (1), the method of the embodiment does not need to use any transformation basis, so that the lack of sparsity limit of the vibration signal is avoided to a large extent, and thus the acquired new reconstruction signal is->
Figure BDA0003784643980000105
Compared to the original reconstructed signal->
Figure BDA0003784643980000106
Has higher precision. In addition, the embodiment introduces the time series characteristic of the signal for the first time, namely reduces the error of the compressed sensing reconstruction signal by reducing the relative residual error of the formula (3), thereby realizing the multi-characteristic description of the vibration signal.
In one possible implementation, step A2 may include the following steps B1-B3:
b1, calculating a general solution of an underdetermined equation in the optimization problem;
b2, carrying out expression simplification processing on the optimization problem based on the general solution of the under-determined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting the model output quantity in the denominator of the optimization problem, and replacing the model regression quantity and the model output quantity in the optimization problem by utilizing the general solution of the under-determined equation;
and B3, obtaining a new reconstruction vibration signal by utilizing the processed optimization problem.
The method in this patent reconstructs vibration signals by the existing compressed sensing method
Figure BDA0003784643980000107
As input, a reconstruction signal of higher accuracy is obtained by solving equation (4)>
Figure BDA0003784643980000108
The optimization problem in formula (4) is difficult to solve directly, and for this purpose, formula (4) is treated in two ways, on the one hand, denominator +.>
Figure BDA0003784643980000109
To simplify the structure of the objective function, and on the other hand to calculate the underdetermined equation in the constraint condition, underdetermined equation y=Φx T Is->
Figure BDA00037846439800001010
(wherein, h is a coefficient,
Figure BDA00037846439800001011
pi is the formula +.>
Figure BDA00037846439800001012
Solving the basic solution of the obtained underdetermined equation, r is the rank of the basic solution, < ->
Figure BDA0003784643980000111
Is the norm) and is ∈>
Figure BDA0003784643980000112
The constraint in equation (4) is eliminated instead of x in equation (4). The optimization problem after treatment is shown in the formula (5). />
Further, the optimization problem after processing includes the following mathematical expression:
Figure BDA0003784643980000113
in equation (5), the underdetermined equation y=Φx T General solution to (1)
Figure BDA0003784643980000114
In the formula, h is a coefficient, ">
Figure BDA0003784643980000115
For new coefficients, ++>
Figure BDA0003784643980000116
Pi is the basis solution of the underdetermined equation, < +.>
Figure BDA0003784643980000117
r is the basic solving rank, pi out New matrix consisting of p+1 to N columns of basic solution matrix pi,>
Figure BDA0003784643980000118
matrix formed by the p+1-i to N-i rows of basic solution matrix pi, i=1, 2, Λp, p is order,/>
Figure BDA0003784643980000119
Is a norm.
Further, obtain
Figure BDA00037846439800001110
After that, a new reconstruction signal can be obtained>
Figure BDA00037846439800001111
Wherein (1)>
Figure BDA00037846439800001112
For a new reconstructed vibration signal, +.>
Figure BDA00037846439800001113
For reconstructing the vibration signal +.>
Figure BDA00037846439800001114
For new coefficients, ++>
Figure BDA00037846439800001115
Pi is the basis solution of the underdetermined equation,
Figure BDA00037846439800001116
r is the rank of the base solution.
In one possible implementation, step 204 is followed by the following steps 205-206:
205. determining the current reconstruction times of the reconstruction vibration signals;
206. and if the current reconstruction times are smaller than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the input of the reconstruction vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and outputting the new reconstruction vibration signal until the current reconstruction times are equal to the preset calculation cycle times.
It should be noted that the residual error of the formula (4) cannot be effectively reduced by only performing the optimization of the formula (5) once, and for this purpose
Figure BDA00037846439800001117
Carrying-in (4) obtaining new model parameters +.>
Figure BDA00037846439800001118
The method steps described above are re-executed for the reconstruction of the reconstructed vibration signal. The new reconstructed vibration signal is used as a reconstructed vibration signal, and the step of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model is performed. Specifically, the number of calculation cycles may be preset, by counting the current number of reconstruction of the reconstructed vibration signal, determining whether to output a new reconstructed vibration signal by comparing the magnitude relation between the current number of reconstruction and the number of calculation cycles, for example, if the current number of reconstruction is smaller than the preset number of calculation cycles, taking the new reconstructed vibration signal as the reconstructed vibration signal, returning to execute the step of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain an autoregressive model characteristic parameter of the autoregressive model, and outputting the new reconstructed vibration signal until the current number of reconstruction is equal to the preset number of calculation cycles.
The invention provides a method for reducing vibration signal compressed sensing reconstruction errors, which comprises the following steps: obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation; inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model; determining a relative residual error of the autoregressive model based on the model residual and the model output; according to the characteristic parameters, the orders and the basic solution system of the underdetermined equation of the autoregressive model, processing for reducing the relative residual error is carried out, and a new reconstruction vibration signal is obtained; determining the current reconstruction times of the reconstruction vibration signals; and if the current reconstruction times are smaller than the preset calculation cycle times, taking the new reconstruction vibration signal as the reconstruction vibration signal, returning to the step of inputting the reconstruction vibration signal and the order into the preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and outputting the new reconstruction vibration signal until the current reconstruction times are equal to the preset calculation cycle times. By adopting the method, any transformation base is not needed, the limitation of lack of sparsity of the vibration signal is avoided to a great extent, the new reconstruction signal has higher precision compared with the original reconstruction signal, and the reconstruction precision of the vibration signal is improved. In addition, by constructing an autoregressive model, the time sequence characteristics of the signals are introduced, and the error of the compressed sensing reconstruction signals is reduced by reducing the relative residual error of the autoregressive model, so that the reconstruction accuracy of the vibration signals is further improved.
In addition, considering the condition that the structural vibration signals are acquired at the same time at multiple measuring points, the application also provides a MAR model with multiple measuring points constructed on the basis of the formula (3) and sets a more general optimization problem to reduce the residual error of the MAR model.
Collecting compressed observation values by d measuring points
Figure BDA0003784643980000121
For example, assume that the compressed observations of each measuring point are acquired through the same compressed sensing matrix phi, and solve the reconstruction signal +.>
Figure BDA0003784643980000122
A MAR model as shown in (6) can be constructed.
Figure BDA0003784643980000123
In the formula (6), the amino acid sequence of the compound,
Figure BDA0003784643980000124
for model parameters +.>
Figure BDA0003784643980000125
Figure BDA0003784643980000126
Wherein->
Figure BDA0003784643980000127
And->
Figure BDA0003784643980000128
Reconstruction signals corresponding to the first measuring point respectively +.>
Figure BDA0003784643980000129
Output and regression of->
Figure BDA00037846439800001210
Is a residual matrix. Solving the underdetermined equation of each measuring point
Figure BDA00037846439800001211
And writing the general solution into a matrix of which the matrix is shown in a formula (7).
Figure BDA00037846439800001212
In the formula (7), the amino acid sequence of the compound,
Figure BDA0003784643980000131
for relieving the general symptoms, the drug is added>
Figure BDA0003784643980000132
The matrix of the signals is reconstructed and,
Figure BDA0003784643980000133
is a coefficient matrix. Referring to formula (5), the optimization problem shown in formula (8) can be set using formula (6) and formula (7):
Figure BDA0003784643980000134
in the formula (8), the amino acid sequence of the compound,
Figure BDA0003784643980000135
norms of +.>
Figure BDA0003784643980000136
Expansion of norms in a matrix environment. Solving (7) to obtain->
Figure BDA0003784643980000137
And then obtaining a new reconstruction signal as shown in a formula (9).
Figure BDA0003784643980000138
It should be noted that the residual error of the formula (6) is not usually effectively reduced by only performing the optimization of the formula (8) once, and for this purpose
Figure BDA0003784643980000139
Carrying-in (6) obtaining new model parameters +.>
Figure BDA00037846439800001310
Bringing the optimization problem into (8) again, and solving the +.>
Figure BDA00037846439800001311
The residual error in the formula (6) can be effectively reduced by performing the cycle for a plurality of times, so that the accuracy of the multi-measuring point reconstruction signal is effectively improved. It should be noted that, the explanation of each parameter in the formulas (7), (8) and (9) may refer to the relevant explanation of the foregoing parameters, which is described herein in detail.
Referring to fig. 3, fig. 3 is a flowchart illustrating a method for reducing compressed sensing reconstruction errors of vibration signals according to an embodiment of the present invention, wherein the input parameters are respectively as shown in fig. 3
Figure BDA00037846439800001312
Pi, p, L, wherein ∈>
Figure BDA00037846439800001313
Reconstructing a vibration signal reconstructed for a conventional compressed sensing reconstruction algorithm, wherein pi is a underdetermined equation y=Φx T P is the order of the MAR model and L is the calculated number of cycles. Output parameters->
Figure BDA00037846439800001314
And reconstructing the vibration signal for the new vibration signal with improved accuracy. Steps b) and c) are solved by a least squares method, respectively.
The method in the present invention is an optimization problem set according to the time-series characteristics of the vibration signal, as in equations (4), (5) and (8). The optimization problem does not involve any signal conversion base, and compared with the existing method, the method can avoid the limitation of lack of sparsity of vibration signals, so that the existing compressed sensing reconstruction method can be enhanced, and the vibration signals are reconstructed by the existing method
Figure BDA00037846439800001315
On the basis of (a), further obtaining a reconstruction signal with higher precision +.>
Figure BDA00037846439800001316
Reducing the compressed sensing reconstruction error by solving formula (4); or reducing the compressed sensing reconstruction error by solving equation (5); or the compressed sensing reconstruction error is reduced by solving the equation (8).
Illustratively, the method in this embodiment, referred to herein as ARCS, is validated in a five-layer frame model experiment. The model is provided with an acceleration sensor each time to acquire a structural vibration signal X, then multiplied by an observation matrix phi and compressed into an observation value, and a conventional compressed sensing BP algorithm is used for reconstructing and acquiring a reconstruction signal
Figure BDA00037846439800001317
Then the method of the embodiment is adopted for +.>
Figure BDA00037846439800001318
Optimizing acquisition Signal->
Figure BDA00037846439800001319
Referring to FIG. 4, FIG. 4 is a graph showing the relative residuals of the BP and BP+ARCS reconstructed signals to construct an AR model, wherein curves 401 and 402 are the structure acquisition Original signal X, (Original line in the figure is the structure acquisition Original signal X), and FIG. 4 is a signal +_>
Figure BDA0003784643980000141
And->
Figure BDA0003784643980000142
The relative residuals of constructing the AR model, fig. 4 illustrates that the method of the present embodiment reduces the residuals of the AR model. With continued reference to fig. 5, fig. 5 is a graph comparing fourier spectra of BP and bp+arcs reconstructed signals with reconstruction accuracy, a curve 501 shown in fig. 5 (a) is a structure-collected Original signal X, a curve 502 is a structure-collected reconstructed signal of the Original signal X, (Original signal line in the figure is a structure-collected Original signal X, reconstruction signal line is a structure-collected reconstructed signal of the Original signal X), and the following fig. 5 (b) to fig. 5 (h) are analogized with fig. 5 (a), which are not repeated, and two methods are compared under different compression ratios (M/N) as shown in fig. 5>
Figure BDA0003784643980000143
And->
Figure BDA0003784643980000144
Wherein the reconstruction accuracy employs a relative error +.>
Figure BDA0003784643980000145
Fig. 5 illustrates that the method of the present embodiment improves the accuracy of the reconstructed signal by reducing the model residual.
Wherein the actual structural acceleration signal is sampled for the ARCS. The actual structure is provided with 4 sensors for collecting vibrationThe signals are compressed into observed values firstly, then vibration signals are reconstructed through a conventional BP algorithm, a conventional BCS algorithm and a conventional SAMP algorithm, the accuracy of the reconstructed signals of the algorithms is improved by using an ARCS algorithm, and the signals are reconstructed by the algorithms
Figure BDA0003784643980000146
And ARCS reconstruction Signal->
Figure BDA0003784643980000147
The fourier spectrum and reconstruction accuracy of (a) are shown in fig. 6 to 8, and the result shows that the ARCS can improve the reconstruction signal accuracy for each algorithm. Referring to fig. 6, fig. 6 is another comparison diagram of fourier spectrum and reconstruction accuracy of BP and bp+arcs reconstruction signals, a curve 601 shown in fig. 6 (a) is a structure acquisition Original signal X, a curve 602 is a reconstruction signal of the structure acquisition Original signal X, (Original signal line in the figure is the structure acquisition Original signal X, reconstruction signal line is the reconstruction signal of the structure acquisition Original signal X), and the following fig. 6 (b) to 6 (h) are analogized to fig. 6 (a), which are not repeated herein.
Referring to fig. 7, fig. 7 is a comparison chart of fourier spectrum and reconstruction accuracy of BCS and bcs+arcs reconstruction signals, wherein a curve 701 shown in fig. 7 (a) is a structure acquisition Original signal X, a curve 702 is a reconstruction signal of the structure acquisition Original signal X, (an Original signal line in the drawing is the structure acquisition Original signal X, and a Reconstruction signal line is the reconstruction signal of the structure acquisition Original signal X), and the following fig. 7 (b) to 7 (h) are similar to fig. 7 (a), and are not repeated herein.
Referring to fig. 8, fig. 8 is a graph comparing fourier spectra of SAMP and samp+arcs reconstructed signals with reconstruction accuracy. The curve 801 shown in fig. 8 (a) is a structure acquisition Original signal X, the curve 802 is a reconstruction signal of the structure acquisition Original signal X, (the Original signal line is the structure acquisition Original signal X, and the Reconstruction signal line is the reconstruction signal of the structure acquisition Original signal X), and the following fig. 8 (b) to 8 (h) are similar to fig. 8 (a), and are not described herein.
Referring to fig. 9, fig. 9 is a block diagram of an apparatus for reducing a compressed sensing reconstruction error of a vibration signal according to an embodiment of the present invention, where the apparatus shown in fig. 9 includes:
data acquisition module 901: the basic solution system is used for acquiring the reconstructed vibration signal, the order and the underdetermined equation;
model building module 902: the method comprises the steps of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
residual determination module 903: for determining a relative residual of the autoregressive model based on the model residual and a model output;
signal reconstruction module 904: and the processing for reducing the relative residual error is carried out according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model, so as to obtain a new reconstructed vibration signal.
It should be noted that, the content of each module in the apparatus shown in fig. 9 is similar to the content of each step in the method shown in fig. 1, and reference may be made to the content of each step in the method shown in fig. 1 for avoiding repetition of the description.
The invention provides a device for reducing vibration signal compressed sensing reconstruction errors, which comprises: and a data acquisition module: the basic solution system is used for acquiring the reconstructed vibration signal, the order and the underdetermined equation; model construction module: the method comprises the steps of inputting a reconstructed vibration signal and an order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output of the autoregressive model; residual determination module: determining a relative residual error of the autoregressive model based on the model residual and the model output; and the signal reconstruction module is used for: and the method is used for carrying out the processing of reducing the relative residual error according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model so as to obtain a new reconstruction vibration signal. By adopting the device, any transformation base is not needed, the limitation of lack of sparsity of the vibration signal is avoided to a great extent, the new reconstruction signal has higher precision compared with the original reconstruction signal, and the reconstruction precision of the vibration signal is improved. In addition, by constructing an autoregressive model, the time sequence characteristics of the signals are introduced, and the error of the compressed sensing reconstruction signals is reduced by reducing the relative residual error of the autoregressive model, so that the reconstruction accuracy of the vibration signals is further improved.
FIG. 10 illustrates an internal block diagram of a computer device in one embodiment. The computer device may specifically be a terminal or a server. As shown in fig. 10, the computer device includes a processor, a memory, and a network interface connected by a system bus. The memory includes a nonvolatile storage medium and an internal memory. The non-volatile storage medium of the computer device stores an operating system, and may also store a computer program which, when executed by a processor, causes the processor to implement the method described above. The internal memory may also have stored therein a computer program which, when executed by a processor, causes the processor to perform the method described above. It will be appreciated by those skilled in the art that the structure shown in fig. 10 is merely a block diagram of some of the structures associated with the present application and is not limiting of the computer device to which the present application may be applied, and that a particular computer device may include more or fewer components than shown, or may combine certain components, or have a different arrangement of components.
In an embodiment a computer device is proposed comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of the method as shown in the embodiment.
In an embodiment a computer-readable storage medium is proposed, storing a computer program which, when executed by a processor, causes the processor to perform the steps of the method as shown in the embodiment.
Those skilled in the art will appreciate that all or part of the processes in the methods of the above embodiments may be implemented by a computer program for instructing relevant hardware, where the program may be stored in a non-volatile computer readable storage medium, and where the program, when executed, may include processes in the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples only represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the present application. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.

Claims (10)

1. A method of reducing vibration signal compressed sensing reconstruction errors, the method comprising:
obtaining a basic solution system of a reconstruction vibration signal, an order and a undercurrent equation;
inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
determining a relative residual of the autoregressive model based on the model residual and a model output;
and performing processing for reducing the relative residual error according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model to obtain a new reconstructed vibration signal.
2. The method of claim 1, wherein the autoregressive model comprises the following mathematical expression:
Figure QLYQS_1
in the method, in the process of the invention,
Figure QLYQS_2
is the model output; />
Figure QLYQS_3
For model regression>
Figure QLYQS_4
Is model parameter [ (]i=1,2,…,p），pFor the order of->
Figure QLYQS_5
Is a model residual.
3. The method of claim 1, wherein the relative residual comprises the following mathematical expression:
relative residual =
Figure QLYQS_6
In the method, in the process of the invention,
Figure QLYQS_7
is a modelOutput of->
Figure QLYQS_8
Is the model residue #i=1,2,…,p），/>
Figure QLYQS_9
Is a norm.
4. The method of claim 1, wherein the auto-regressive model feature parameters further include model regression and model parameters, and wherein the reducing the relative residual error based on the auto-regressive model parameters and the basis solution of the underdetermined equation to obtain a new reconstructed vibration signal comprises:
constructing an optimization problem for reducing the relative residual error by utilizing a basic solution system of a model regression quantity, a model output quantity, an order, model parameters and a undercurrent equation;
and solving the optimization problem to obtain a new reconstruction vibration signal.
5. The method of claim 4, wherein the optimization problem comprises the following mathematical expression:
Figure QLYQS_10
in the method, in the process of the invention,
Figure QLYQS_11
is the model output; />
Figure QLYQS_14
For model regression>
Figure QLYQS_16
Is model parameter [ (]i=1,2,…,p) P is the order, ">
Figure QLYQS_12
To be the underdetermined equation +.>
Figure QLYQS_17
Is->
Figure QLYQS_18
In which, in the process,his a coefficient of->
Figure QLYQS_19
，/>
Figure QLYQS_13
For the basis solution of the underdetermined equation, r is the rank of the basis solution, +.>
Figure QLYQS_15
Is a norm.
6. The method of claim 5, wherein solving the optimization problem to obtain a new reconstructed vibration signal comprises:
calculating a general solution of the under-determined equation in the optimization problem;
performing expression simplification processing on the optimization problem based on the general solution of the under-determined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting the model output quantity in the denominator of the optimization problem, and replacing the model regression quantity and the model output quantity in the optimization problem by using the general solution of the under-determined equation;
and obtaining a new reconstructed vibration signal by using the processed optimization problem.
7. The method of claim 6, wherein the post-processing optimization problem comprises the following mathematical expression:
Figure QLYQS_20
；
wherein the equation is underdetermined
Figure QLYQS_21
Is->
Figure QLYQS_26
In which, in the process,his a coefficient of->
Figure QLYQS_29
As a result of the new coefficients of the coefficients,
Figure QLYQS_25
，/>
Figure QLYQS_30
，/>
Figure QLYQS_31
to solve the basis of the underdetermined equation, +.>
Figure QLYQS_32
R is the rank of the base solution, +.>
Figure QLYQS_22
Is based on solving the system->
Figure QLYQS_24
First, thep+1To the point ofNMatrix of rows>
Figure QLYQS_27
Is based on solving the system->
Figure QLYQS_28
First, thep+1-iTo the point ofN-iMatrix of rows [ ]i=1,2,…,p），pFor the order of->
Figure QLYQS_23
Is a norm;
the new reconstructed vibration signal comprises the following mathematical expression:
Figure QLYQS_33
in the method, in the process of the invention,
Figure QLYQS_34
for a new reconstructed vibration signal, +.>
Figure QLYQS_35
For reconstructing the vibration signal +.>
Figure QLYQS_36
For new coefficients, ++>
Figure QLYQS_37
，/>
Figure QLYQS_38
To solve the basis of the underdetermined equation, +.>
Figure QLYQS_39
R is the rank of the base solution.
8. The method of claim 1, wherein the reducing the relative residual is performed according to the auto-regressive model feature parameters, the order, and the basis solution of the underdetermined equation to obtain a new reconstructed vibration signal, and further comprising:
determining the current reconstruction times of the reconstruction vibration signals;
and if the current reconstruction times are smaller than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the input of the reconstruction vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and outputting the new reconstruction vibration signal until the current reconstruction times are equal to the preset calculation cycle times.
9. An apparatus for reducing vibration signal compressed sensing reconstruction errors, said apparatus comprising:
and a data acquisition module: the basic solution system is used for acquiring the reconstructed vibration signal, the order and the underdetermined equation;
model construction module: the method comprises the steps of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, wherein the autoregressive model characteristic parameters at least comprise model residues and model output quantities of the autoregressive model;
residual determination module: for determining a relative residual of the autoregressive model based on the model residual and a model output;
and the signal reconstruction module is used for: and the processing for reducing the relative residual error is carried out according to the characteristic parameters, the orders and the basis solution system of the underdetermined equation of the autoregressive model, so as to obtain a new reconstructed vibration signal.
10. A computer readable storage medium storing a computer program, which when executed by a processor causes the processor to perform the steps of the method according to any one of claims 1 to 8.
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