CN115459778A - Method and device for reducing vibration signal compressed sensing reconstruction error and storage medium - Google Patents

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

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CN115459778A
CN115459778A CN202210948233.9A CN202210948233A CN115459778A CN 115459778 A CN115459778 A CN 115459778A CN 202210948233 A CN202210948233 A CN 202210948233A CN 115459778 A CN115459778 A CN 115459778A
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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 vibration signal compressed sensing reconstruction error, wherein the method comprises the following steps: acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 residuals and the model outputs; and (4) carrying out treatment of reducing relative residual errors according to the characteristic parameters and the order of the autoregressive model and a basic solution system of an underdetermined equation 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, the time series characteristics of the signals are introduced by constructing an autoregressive model, the relative residual error of the model is reduced, the reconstruction error is reduced, and the signal reconstruction precision is further improved.

Description

Method and device for reducing vibration signal compressed sensing reconstruction error and storage medium
Technical Field
The invention relates to the technical field of data transmission, in particular to a method and a device for reducing a vibration signal compressed sensing reconstruction error and a storage medium.
Background
Structural health monitoring requires real-time measurement of structural features to monitor anomalies. The vibration signal is a key measure to extract dynamic structural features (i.e., natural frequency, damping ratio, and mode shape). Due to the fact that the sampling frequency is high, the data volume of vibration signals acquired by long-term structure monitoring is huge, and huge pressure is brought to a data transmission link, particularly 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 framework of compressed sensing, the vibration signal is directly transmitted at the sensor end
Figure BDA0003784643980000011
Multiplication by an observation matrix
Figure BDA0003784643980000012
Post-compression into an observed value
Figure BDA0003784643980000013
And solving an underdetermined equation y = phi x at the data receiving end to reconstruct the vibration signal.
The compressed sensing technology faces the problem that the vibration signal is lack of sparsity when the vibration signal is reconstructed. Compressed sensing reconstructs the vibration signal by solving a linear equation y = Φ x, which contains an infinite number of solutions since the compressed value y has a smaller dimension than the vibration signal x (y has a dimension M and x has a dimension N).
The existing compressed sensing reconstruction method assumes that a vibration signal x is in a conventional transformation base
Figure BDA0003784643980000014
Sparsity (e.g., fourier and wavelet bases), i.e., x = θ s and
Figure BDA0003784643980000015
only a small number of elements are nonzero, and then solving the optimization problem of the formula (1) to obtain
Figure BDA0003784643980000016
Then obtaining a reconstructed signal
Figure BDA0003784643980000017
It should be noted that equation (1) is an NP-hard problem, i.e. it cannot be solved directly, and the existing compressed sensing method obtains the NP-hard problem by approximately solving the NP-hard problem
Figure BDA0003784643980000018
Figure BDA0003784643980000019
However, structural vibration signals lack sparsity on a conventional transformation base, that is, assuming that a decomposition coefficient s of x on a transformation base theta only has a few nonzero elements, when the number of acquired compression observation values y is small, a reconstructed signal obtained by solving the equation (1) in the existing compression sensing method
Figure BDA0003784643980000021
There will be a large error.
For the problem of lack of sparsity of vibration signals, there are two main approaches to improve the reconstructed signals
Figure BDA0003784643980000022
The accuracy of (2). One class of methods increases the sparsity of the vibration signal by increasing the completeness or redundancy of the transform basis, i.e., increasing the transform basis
Figure BDA0003784643980000023
Or directly setting a parameter continuous atom library. Another class of methods utilizes joint sparsity features of structurally different measured point signals, e.g. signal x 1 Sum signal x 2 Has a decomposition coefficient s on the transform basis theta 1 And s 2 Then assume s 1 And s 2 The numerical values of the elements at the same positions are larger or smaller.
From the above theoryAs can be seen, the existing compressed sensing reconstruction needs to assume that the vibration signal x is in a conventional transformation base
Figure BDA0003784643980000024
Sparsity (e.g., fourier and wavelet bases) to enable vibration signal reconstruction. The structure is used as a system, the environment excitation borne by the structure is close to white noise in the actual running state, and the white noise does not have sparsity on any transformation basis, so that the vibration response output by the structure does not have obvious sparsity on the conventional transformation basis. Reconstructing the signal when the number y of compressed observations is less
Figure BDA0003784643980000025
Will contain large errors. Although the existing compressed sensing reconstruction algorithm can improve the accuracy of a reconstructed signal to a certain extent by adopting a joint structure of increasing the completeness of a transformation base theta or utilizing different measuring point signals, the existing compressed sensing reconstruction algorithm is still limited by the lack of sparsity of a vibration signal.
Disclosure of Invention
The invention mainly aims to provide a method, a device and a storage medium for reducing a vibration signal compressed sensing reconstruction error, which can solve the problem that the reconstruction of a compressed sensing vibration signal has a large error in the prior art.
To achieve the above object, a first aspect of the present invention provides a method for reducing a compressed sensing reconstruction error of a vibration signal, the method comprising:
acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 quantity of the autoregressive model;
determining a relative residual of the autoregressive model based on the model residuals and model outputs;
and carrying out treatment of reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal.
In one possible implementation, the autoregressive model includes the following mathematical expression:
Figure BDA0003784643980000031
in the formula (I), the compound is shown in the specification,
Figure BDA0003784643980000032
the output quantity of the model is taken;
Figure BDA0003784643980000033
in order to be the regression quantity of the model,
Figure BDA0003784643980000034
for model parameters, (i =1,2, Λ p), p is the order,
Figure BDA0003784643980000035
is the model residual.
In one possible implementation, the relative residual includes the following mathematical expression:
Figure BDA0003784643980000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003784643980000037
in order to be the output quantity of the model,
Figure BDA0003784643980000038
as model residuals, (i =1,2, Λ p),
Figure BDA0003784643980000039
is a norm.
In a feasible implementation manner, the auto-regression model feature parameters further include model regression quantities and model parameters, and the processing of reducing the relative residual errors is performed according to the auto-regression model parameters and a basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal, including:
constructing an optimization problem for reducing the relative residual error by using a model regression quantity, a model output quantity, an order, a model parameter and a basic solution system of an underdetermined equation;
and solving the optimization problem to obtain a new reconstructed vibration signal.
In one possible implementation, the optimization problem includes the following mathematical expression:
Figure BDA00037846439800000310
in the formula, x out ＝[x p+1 x p+2 Λ x N ]The output quantity of the model is taken;
Figure BDA00037846439800000311
in order to be the regression quantity of the model,
Figure BDA00037846439800000312
for model parameters, (i =1,2, Λ p), p is the order, y = Φ x T For underdetermined equations, underdetermined equation y = Φ x T General solution of
Figure BDA00037846439800000313
In the formula, h is a coefficient,
Figure BDA00037846439800000314
pi is the basic solution system of the underdetermined equation, r is the rank of the basic solution system,
Figure BDA00037846439800000315
is a norm.
In a possible implementation manner, the solving the optimization problem to obtain a new reconstructed vibration signal includes:
calculating a general solution of an underdetermined equation in the optimization problem;
performing expression simplification processing on the optimization problem based on the general solution of the underdetermined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting a model output quantity in a denominator of the optimization problem, and replacing a model regression quantity and the model output quantity in the optimization problem by using the general solution of the underdetermined equation;
and obtaining a new reconstructed vibration signal by utilizing the processed optimization problem.
In one possible implementation, the processed optimization problem includes the following mathematical expression:
Figure BDA0003784643980000041
wherein the underdetermined equation y = Φ x T General solution of
Figure BDA0003784643980000042
In the formula, h is a coefficient,
Figure BDA0003784643980000043
in order to be a new coefficient of the data,
Figure BDA0003784643980000044
pi is the fundamental solution system of the underdetermined equation,
Figure BDA0003784643980000045
rank, Π, of r-based solution system out Based on the solution of the matrix formed by the nth rows p +1 to N,
Figure BDA0003784643980000046
a matrix formed by pi p +1-i to N-i rows is solved as a basis, i =1,2, Λ p, p is the order,
Figure BDA0003784643980000047
is a norm;
the new reconstructed vibration signal includes the following mathematical expression:
Figure BDA0003784643980000048
in the formula (I), the compound is shown in the specification,
Figure BDA0003784643980000049
in order to reconstruct the vibration signal newly,
Figure BDA00037846439800000410
in order to reconstruct the vibration signal,
Figure BDA00037846439800000411
in order to be a new coefficient of the signal,
Figure BDA00037846439800000412
pi is the fundamental solution system of the underdetermined equation,
Figure BDA00037846439800000413
r is the rank of the base solution.
In a feasible implementation manner, the processing for reducing the relative residual error according to the auto-regression model feature parameter, the order, and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal further includes:
determining the current reconstruction times of the reconstructed vibration signal;
and if the current reconstruction times are less than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the step of inputting the reconstruction vibration signal and the order into a preset autoregressive model to obtain the 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 compressed sensing reconstruction errors of a vibration signal, the apparatus comprising:
a data acquisition module: a basic solution system for obtaining a reconstructed vibration signal, an order and an underdetermined equation;
a model construction module: the system comprises a reconstruction module, a model residual module, a model output module, a model parameter generation module and a model parameter generation module, wherein the reconstruction module is used for inputting the reconstruction vibration signal and the order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and the autoregressive model characteristic parameters at least comprise model residual and model output quantity of the autoregressive model;
a residual determination module: for determining a relative residual of the autoregressive model based on the model residuals and model outputs;
a signal reconstruction module: and the processing unit is used for reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation 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 shown in the first aspect and any possible implementation manner.
To achieve the above object, a fourth aspect of the present invention provides a computer device, including a memory and a processor, the memory storing a computer program, the computer program, when executed by the processor, causing the processor to perform the steps as shown in the first aspect and any possible implementation manner.
The embodiment of the invention has the following beneficial effects:
the invention provides a method for reducing a compressed sensing reconstruction error of a vibration signal, which comprises the following steps: acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 of the autoregressive model and model output quantity; determining a relative residual error of the autoregressive model based on the model residuals and the model output quantities; and (4) carrying out treatment of reducing relative residual errors according to the characteristic parameters and the order of the autoregressive model and a basic solution system of an underdetermined equation to obtain a new reconstructed vibration signal. By adopting the method, any transformation base is not needed, the limitation that the vibration signal lacks sparsity 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, the time series characteristics of the signals are introduced by constructing the autoregressive model, 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 precision of the vibration signals is further improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Wherein:
FIG. 1 is a flowchart illustrating a method for reducing a reconstruction error of compressed sensing of a vibration signal according to an embodiment of the present invention;
FIG. 2 is another flowchart of a method for reducing reconstruction errors of compressed sensing of a vibration signal according to an embodiment of the present invention;
FIG. 3 is a further flowchart illustrating a method for reducing a compressed sensing reconstruction error of a vibration signal 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 and reconstruction accuracy of BP and BP + ARCS reconstructed signals;
FIG. 6 is another comparison of 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 the Fourier spectra and reconstruction accuracy of SAMP and SAMP + ARCS reconstructed signals;
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;
fig. 10 is a block diagram of a computer device according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, fig. 1 is a flowchart illustrating a method for reducing a reconstruction error of compressed sensing of a vibration signal according to an embodiment of the present invention, where the method shown in fig. 1 includes the following steps:
101. acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 quantity of the autoregressive model;
in the present embodiment, the reconstruction of the reconstructed signal is performed again to improve the accuracy of signal reconstruction. Wherein, the reconstructed motion signal refers to the vibration signal reconstructed by some conventional compressed sensing technology. Conventional compressive sensing techniques include, but are not limited to, bayesian Compressive Sensing (BCS), compressive Sensing (SAMP), neural network compressive sensing (BP), and the like. Since the vibration signal has not only sparsity but also time series characteristics, an Autoregressive model can be established based on the vibration signal, wherein the Autoregressive model (AR model for short) is a statistical method for processing time series, and the former stages of the same variable, such as x, namely x 1 To x t-1 To predict the current period x t And assume that they are in a linear relationship. Since this is developed from linear regression in regression analysis, but instead of predicting y with x, x predicts x (itself); so called autoregressive. Illustratively, the vibration signal is
Figure BDA0003784643980000071
For illustration, it is stored as a row vector x = [ x ] 1 x 2 Λ x N ]Then, 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 ]The output quantity of the model is taken;
Figure BDA0003784643980000073
as model regressions, a i For model parameters, (i =1,2, Λ p), p is the order,
Figure BDA0003784643980000074
is the model residual.
Further, an autoregressive model may also be established for the reconstructed vibration signal. Therefore, the autoregressive model is established through the reconstructed vibration signal, and the reconstructed vibration signal is reconstructed again. Specifically, a preset autoregressive model is input by using a reconstructed vibration signal and an order, so as to establish an autoregressive model of the reconstructed vibration signal and obtain autoregressive model characteristic parameters of the autoregressive model of the reconstructed vibration signal, 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 include, but are not limited to, model residuals, model regression quantities, model parameters and model output quantities of the autoregressive model.
Illustratively, reconstructing the vibration signal
Figure BDA0003784643980000075
The autoregressive model of (a) is the following mathematical expression:
Figure BDA0003784643980000081
in the formula (3), the reaction mixture is,
Figure BDA0003784643980000082
the output quantity of the model is taken;
Figure BDA0003784643980000083
in order to be the regression quantity of the model,
Figure BDA0003784643980000084
for model parameters, (i =1,2, Λ p), p is the order,
Figure BDA0003784643980000085
the residual of the model is the residual of the model,
Figure BDA0003784643980000086
103. determining a relative residual of the autoregressive model based on the model residuals and model outputs;
104. and carrying out treatment of reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal.
Further, the test of the existing vibration signal shows that the relative residual error of the model of the reconstructed vibration signal in the formula (3)
Figure BDA0003784643980000087
Is significantly larger than the model residual of the vibration signal in equation (2)
Figure BDA0003784643980000088
Wherein the content of the first and second substances,
Figure BDA0003784643980000089
to reconstruct the model output of the vibration signal,
Figure BDA00037846439800000810
to reconstruct the model residual of the vibration signal, x out ＝[x p+1 x p+2 Λ x N ]Is the output quantity of the model of the vibration signal,
Figure BDA00037846439800000811
as model residual of the vibration signal, (i =1,2, Λ p),
Figure BDA00037846439800000812
is a norm.
The present application therefore sets the optimization problem according to the above phenomena, reducing the reconstructed signal by reducing the relative residual of equation (3)
Figure BDA00037846439800000813
Error in (2). Therefore, after the autoregressive model characteristic parameters of the reconstructed vibration signal are obtained, the relative residual error of the autoregressive model of the reconstructed vibration signal is determined by using the model residual and the model output quantity included in the autoregressive model characteristic parameters in step 103. And further, the step 104 is carried out to reduce the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal
Figure BDA00037846439800000814
Through reconstructing the reconstructed vibration signal again, the reconstruction precision of the vibration signal can be improved, the performance detection precision of the building structure is also improved, the safety and the stability of the building structure are favorably ensured, and the occurrence of accidents is reduced.
The invention provides a method for reducing a compressed sensing reconstruction error of a vibration signal, which comprises the following steps: acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 of the autoregressive model and model output quantity; determining a relative residual error of the autoregressive model based on the model residuals and the model output quantities; and (4) carrying out treatment of reducing relative residual errors according to the characteristic parameters and the order of the autoregressive model and a basic solution system of an underdetermined equation to obtain a new reconstructed vibration signal. By adopting the method, any transformation base is not needed, the limitation that the vibration signal lacks sparsity 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, the time series characteristics of the signals are introduced by constructing the autoregressive model, 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 precision 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 present invention, where the method shown in fig. 2 includes the following steps:
201. acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 residue and model output quantity of the autoregressive model;
203. determining a relative residual of the autoregressive model based on the model residuals and model outputs;
204. according to the characteristic parameters and the order of the autoregressive model and a basic solution system of the underdetermined equation, carrying out treatment of reducing the relative residual error to obtain a new reconstructed vibration signal;
it should be noted that, the contents of steps 201 to 204 are similar to the contents of steps 101 to 104 described in fig. 1, and for avoiding repetition, details are not repeated here, and the contents of steps 101 to 104 described in fig. 1 may be referred to specifically.
In a possible implementation manner, the autoregressive model feature parameters further include a model regression quantity 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 using a model regression, a model output quantity, an order, a model parameter and a basic solution system of an underdetermined equation;
illustratively, the optimization problem of reducing the relative residual includes the following mathematical expression:
Figure BDA0003784643980000091
in the formula (4), x out ＝[x p+1 x p+2 Λ x N ]The output quantity of the model is taken;
Figure BDA0003784643980000092
in order to be the regression quantity of the model,
Figure BDA0003784643980000093
as model parameters (in the formula)
Figure BDA0003784643980000094
From formula (3)), (i =1,2, Λ p), p is the order, y = Φ x T For underdetermined equations, underdetermined equation y = Φ x T General solution of
Figure BDA0003784643980000095
In the formula, h is a coefficient,
Figure BDA0003784643980000096
pi is the basic solution system of the underdetermined equation, r is the rank of the basic solution system,
Figure BDA0003784643980000097
is a norm.
And A2, solving the optimization problem to obtain a new reconstructed vibration signal.
Then, by solving the optimization problem of reducing the relative residual error, namely the equation (4), a new reconstructed vibration signal can be obtained
Figure BDA0003784643980000101
It should be noted that the compressed sensing in equation (1) requires the assumption that the vibration signal x is in the conventional transformation base
Figure BDA0003784643980000102
(e.g., fourier basis and SmallWave basis) to achieve vibration signal reconstruction. The structure is used as a system, the environment excitation borne by the structure is close to white noise in the actual running state, and the white noise does not have sparsity on any transformation basis, so that the vibration response output by the structure does not have obvious sparsity on the conventional transformation basis. Reconstructing the signal when the number y of compressed observations is less acquired
Figure BDA0003784643980000103
Reconstructing the signal when the number y of compressed observations is less acquired
Figure BDA0003784643980000104
Will contain large errors. Although the existing compressed sensing reconstruction algorithm can improve the accuracy of a reconstructed signal to a certain extent by adopting a joint structure of increasing the completeness of a transformation base theta or utilizing different measuring point signals, the existing compressed sensing reconstruction algorithm is still limited by the lack of sparsity of a vibration signal. However, compared with the formula (1), the method of the embodiment does not need to use any transformation basis, thereby largely avoiding the lack of sparsity limitation of the vibration signal, and acquiring a new reconstruction signal
Figure BDA0003784643980000105
Compared with the original reconstructed signal
Figure BDA0003784643980000106
With higher accuracy. In addition, the embodiment introduces the time series characteristics 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), and realizes multi-characteristic description of the vibration signal.
In one possible implementation, step A2 may comprise the following steps B1-B3:
b1, calculating a general solution of an underdetermined equation in the optimization problem;
b2, performing expression simplification processing on the optimization problem based on the general solution of the underdetermined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting a model output quantity in a denominator of the optimization problem, and replacing a model regression quantity and the model output quantity in the optimization problem by using the general solution of the underdetermined equation;
and B3, obtaining a new reconstructed vibration signal by utilizing the processed optimization problem.
The method in the patent is a vibration signal reconstructed by the existing compressed sensing method
Figure BDA0003784643980000107
As an input, a reconstructed signal with higher accuracy is obtained by solving equation (4)
Figure BDA0003784643980000108
The optimization problem in the formula (4) is difficult to directly solve, and the formula (4) is processed in two aspects, on one hand, the denominator in the formula (4) is omitted
Figure BDA0003784643980000109
To simplify the structure of the objective function and, on the other hand, to calculate the underdetermined equations y = Φ x in the constraints T General solution of
Figure BDA00037846439800001010
(in the formula, h is a coefficient,
Figure BDA00037846439800001011
pi is the equation of passage
Figure BDA00037846439800001012
Solving the basic solution system of the underdetermined equation, wherein r is the rank of the basic solution system,
Figure BDA0003784643980000111
is a norm) and are calculated by
Figure BDA0003784643980000112
The constraint in equation (4) is removed instead of x in equation (4). The optimization problem after treatment is shown as formula (5).
Further, the processed optimization problem includes the following mathematical expression:
Figure BDA0003784643980000113
in equation (5), underdetermined equation y = Φ x T General solution of
Figure BDA0003784643980000114
In the formula, h is a coefficient,
Figure BDA0003784643980000115
in order to be a new coefficient of the signal,
Figure BDA0003784643980000116
pi is the fundamental solution system of the underdetermined equation,
Figure BDA0003784643980000117
rank, Π, of r-based solution system out A new matrix is formed by the p +1 th to N th rows of the basic solution matrix Π,
Figure BDA0003784643980000118
a matrix formed by p +1-i to N-i rows of the N < th > matrix is solved as a basis, i =1,2, lambdap, p is the order,
Figure BDA0003784643980000119
is a norm.
Further, obtain
Figure BDA00037846439800001110
Then a new reconstructed signal can be obtained
Figure BDA00037846439800001111
Wherein the content of the first and second substances,
Figure BDA00037846439800001112
in order to reconstruct the vibration signal newly,
Figure BDA00037846439800001113
in order to reconstruct the vibration signal,
Figure BDA00037846439800001114
in order to be a new coefficient of the signal,
Figure BDA00037846439800001115
pi is the basic solution system of the underdetermined equation,
Figure BDA00037846439800001116
r is the rank of the base solution.
In a possible implementation, step 204 is followed by the following steps 205-206:
205. determining the current reconstruction times of the reconstructed vibration signal;
206. and if the current reconstruction times are less than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the step of inputting the reconstruction vibration signal and the order into a preset autoregressive model to obtain the 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 equation (4) cannot be reduced effectively by optimizing equation (5) only once, and for this reason, the residual error can be reduced
Figure BDA00037846439800001117
Carry-in (4) acquisition of new model parameters
Figure BDA00037846439800001118
And re-executing the steps of the method to reconstruct the reconstructed vibration signal. Namely, 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 the preset autoregressive model to obtain the autoregressive model characteristic parameter of the autoregressive model is returned to be executed. Specifically, the number of cycles may be calculated in advance, the current number of reconstruction of the reconstructed vibration signal may be counted, and whether a new reconstructed vibration signal is output may be determined by comparing the magnitude relationship between the current number of reconstruction and the number of cycles calculated, for example, if the current number of reconstruction is smaller than the preset number of reconstructionAnd calculating the cycle number, namely taking the new reconstructed vibration signal as a reconstructed vibration signal, returning to the step of inputting the reconstructed vibration signal and the order into a preset autoregressive model to obtain the characteristic parameters of the autoregressive model, and outputting the new reconstructed vibration signal until the current reconstruction number is equal to the preset calculated cycle number.
The invention provides a method for reducing a compressed sensing reconstruction error of a vibration signal, which comprises the following steps: acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 of the autoregressive model and model output quantity; determining a relative residual error of the autoregressive model based on the model residuals and the model output quantities; according to the characteristic parameters and the order of the autoregressive model and a basic solution system of an underdetermined equation, carrying out relative residual error reduction treatment to obtain a new reconstructed vibration signal; determining the current reconstruction times of the reconstructed vibration signal; and if the current reconstruction times are less than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of inputting the reconstruction vibration signal and the order into a preset autoregressive model to obtain the 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 that the vibration signal lacks sparsity 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, the time series characteristics of the signals are introduced by constructing the autoregressive model, 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 precision of the vibration signals is further improved.
In addition, in consideration of the situation that the structural vibration signals are acquired at multiple measuring points at the same time, the application also provides a method for constructing the MAR model at the multiple measuring points on the basis of the formula (3) and setting a more general optimization problem to reduce the residual error of the MAR model.
Collecting compressed observed values by d measuring points
Figure BDA0003784643980000121
For example, assuming that the compressed observed values of the measuring points are acquired by the same compressed sensing matrix phi, the reconstructed signal of each channel is solved
Figure BDA0003784643980000122
The MAR model shown in (6) can be constructed.
Figure BDA0003784643980000123
In the formula (6), the reaction mixture is,
Figure BDA0003784643980000124
in order to be the parameters of the model,
Figure BDA0003784643980000125
Figure BDA0003784643980000126
wherein
Figure BDA0003784643980000127
And
Figure BDA0003784643980000128
respectively corresponding to the first measuring point to reconstruct signals
Figure BDA0003784643980000129
The output quantity and the regression quantity of (2),
Figure BDA00037846439800001210
is a residual matrix. Underdetermined equation for each measuring point
Figure BDA00037846439800001211
And writing the general solution into a matrix form to obtain a matrix shown in formula (7).
Figure BDA00037846439800001212
In the formula (7), the reaction mixture is,
Figure BDA0003784643980000131
in order to realize the general solution,
Figure BDA0003784643980000132
in order to reconstruct the signal matrix,
Figure BDA0003784643980000133
is a matrix of coefficients. Referring to equation (5), the optimization problem shown in equation (8) can be set using equations (6) and (7):
Figure BDA0003784643980000134
in the formula (8), the reaction mixture is,
Figure BDA0003784643980000135
norm of
Figure BDA0003784643980000136
Extension of the norm in a matrix environment. Solving for equation (7) acquisition
Figure BDA0003784643980000137
Then, a new reconstruction signal can be obtained as shown in the formula (9).
Figure BDA0003784643980000138
It should be noted that the residual error of equation (6) cannot be reduced effectively by optimizing equation (8) only once, and for this reason, the residual error can be reduced
Figure BDA0003784643980000139
Carry-in (6) acquisition of new model parameters
Figure BDA00037846439800001310
The optimization problem is updated in the formula (8), and then the solution is carried out
Figure BDA00037846439800001311
The residual error in the formula (6) can be effectively reduced by circulating for multiple times, so that the precision of the multi-point reconstruction signal is effectively improved. It should be noted that, for the explanation of each parameter in the formulas (7), (8) and (9), reference may be made to the related explanation of the aforementioned parameter, which is described herein for details.
Referring to fig. 3, fig. 3 is a flowchart illustrating a method for reducing a reconstruction error of compressed sensing of a vibration signal according to another embodiment of the present invention, as shown in fig. 3, the input parameters are
Figure BDA00037846439800001312
Pi, p, L, wherein,
Figure BDA00037846439800001313
reconstructing a vibration signal reconstructed by a conventional compressed sensing reconstruction algorithm, wherein pi is an underdetermined equation y = phi x T P is the order of the MAR model and L is the number of calculation cycles. Parameters of the output
Figure BDA00037846439800001314
And reconstructing the vibration signal for the new vibration signal after the precision is improved. And the steps b) and c) are respectively solved by adopting a least square method.
The method of the invention is an optimization problem set according to the time series characteristics of the vibration signal, as shown in formulas (4), (5) and (8). The optimization problem does not involve any signal transformation base, and compared with the existing method, the method can avoid the limitation that the vibration signal lacks sparsity, so that the existing compressed sensing reconstruction method can be strengthened, and the vibration signal is reconstructed in the existing method
Figure BDA00037846439800001315
On the basis, a reconstructed signal with higher precision is further obtained
Figure BDA00037846439800001316
Reducing compressed sensing reconstruction errors by solving equation (4);or reducing the compressed sensing reconstruction error by solving equation (5); or the compressed perceptual reconstruction error is reduced by solving equation (8).
Illustratively, the method of this embodiment, referred to herein as ARCS, was validated in a five-layer framework model experiment. An acceleration sensor is arranged in the model each time to acquire a structural vibration signal X, the structural vibration signal X is multiplied by an observation matrix phi to be compressed into an observation value, and a conventional compressed sensing BP algorithm is used for reconstructing to acquire a reconstructed signal
Figure BDA00037846439800001317
The method pair of the embodiment is adopted again
Figure BDA00037846439800001318
Performing optimized acquisition of signals
Figure BDA00037846439800001319
Referring to FIG. 4, FIG. 4 is a graph comparing the relative residuals of the BP and BP + ARCS reconstructed signals for AR model construction, wherein curves 401 and 402 are the structure-acquired Original signal X (the Original line in the graph is the structure-acquired Original signal X), and FIG. 4 is a graph comparing the two methods
Figure BDA0003784643980000141
And
Figure BDA0003784643980000142
to construct the relative residuals of the AR model, fig. 4 illustrates that the method of this embodiment reduces the residuals of the AR model. Please refer to fig. 5, fig. 5 is a graph comparing the fourier spectrum and the Reconstruction accuracy of the BP and BP + ARCS reconstructed signals, where a curve 501 shown in fig. 5 (a) is a structure acquisition Original signal X, a curve 502 is a structure acquisition Original signal X reconstructed signal, (in the figure, an Original signal line is a structure acquisition Original signal X, and a Reconstruction signal line is a structure acquisition Original signal X), and similarly, please refer to fig. 5 (a) and follow-up fig. 5 (b) to fig. 5 (h), which are not repeated herein, as shown in fig. 5, compare the two methods under different compression ratios (M/N), which are shown in fig. 5
Figure BDA0003784643980000143
And
Figure BDA0003784643980000144
the reconstruction accuracy adopts 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 ARCS is tested by sampling the actual structural acceleration signal. The actual structure is provided with 4 sensors, vibration signals are collected and compressed into an observed value, then the vibration signals are reconstructed through a conventional BP algorithm, a BCS algorithm and an SAMP algorithm respectively, the accuracy of signal reconstruction of each algorithm is improved by utilizing an ARCS algorithm, and the signals are reconstructed through each algorithm
Figure BDA0003784643980000146
And ARCS reconstructed signals
Figure BDA0003784643980000147
The fourier spectrum and reconstruction accuracy of (a) are shown in fig. 6 to 8, and the results show that the ARCS can improve the accuracy of the reconstructed signal for each algorithm. Please refer to fig. 6, fig. 6 is another comparison diagram of the fourier spectrum and the Reconstruction accuracy of the BP and BP + ARCS reconstructed signals, a curve 601 shown in fig. 6 (a) is a structure-collected Original signal X, a curve 602 is a reconstructed signal of the structure-collected Original signal X, (in the figure, an Original signal line is the structure-collected Original signal X, and a Reconstruction signal of the structure-collected Original signal X), and similarly, the following fig. 6 (b) to fig. 6 (h) are referred to in fig. 6 (a), which is not repeated herein.
Please refer to fig. 7, fig. 7 is a comparison diagram of fourier spectrums and Reconstruction accuracy of BCS and BCS + ARCS reconstructed signals, wherein a curve 701 shown in fig. 7 (a) is a structure-collected Original signal X, a curve 702 is a reconstructed signal of the structure-collected Original signal X, (in the figure, an Original signal line is the structure-collected Original signal X, and a Reconstruction signal of the structure-collected Original signal X), and similarly, fig. 7 (a) is used to compare the subsequent fig. 7 (b) to fig. 7 (h), which is not repeated herein.
Referring to fig. 8, fig. 8 is a graph comparing the fourier spectra and reconstruction accuracy of the SAMP and SAMP + ARCS reconstructed signals. In fig. 8 (a), a curve 801 and a curve 802 are shown for a structure-collected Original signal X and a reconstructed signal of the structure-collected Original signal X, where an Original signal line and a Reconstruction signal of the Original signal X are shown, and similarly, fig. 8 (a) is used to compare the following fig. 8 (b) to fig. 8 (h), which is not repeated 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:
the data acquisition module 901: a basic solution system for obtaining a reconstructed vibration signal, an order and an underdetermined equation;
model building module 902: the autoregressive model characteristic parameters at least comprise model residues and model output quantity of the autoregressive model;
residual determination module 903: for determining a relative residual of the autoregressive model based on the model residuals and model outputs;
the signal reconstruction module 904: and the processing unit is used for reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal.
It should be noted that the contents of each module in the apparatus shown in fig. 9 are similar to the contents of each step in the method shown in fig. 1, and for avoiding repetition, no further description is provided here, and the contents of each step in the method shown in fig. 1 may be referred to specifically.
The invention provides a device for reducing the compressed sensing reconstruction error of a vibration signal, which comprises: a data acquisition module: a basic solution system for obtaining a reconstructed vibration signal, an order and an underdetermined equation; a model construction module: the system comprises a model input module, a model output module, a vibration signal reconstruction module, a vibration signal analysis module and a vibration signal reconstruction module, wherein the model input module is used for inputting a reconstructed vibration signal and an order into a preset autoregressive model to obtain autoregressive model characteristic parameters of the autoregressive model, and the autoregressive model characteristic parameters at least comprise model residue and model output quantity of the autoregressive model; a residual determination module: determining a relative residual error of the autoregressive model based on the model residuals and the model outputs; a signal reconstruction module: and the method is used for reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and a basic solution system of an underdetermined equation to obtain a new reconstructed vibration signal. By adopting the device, any transformation base is not needed, the limitation that the vibration signal lacks sparsity 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, the time series characteristics of the signals are introduced by constructing the autoregressive model, 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 precision of the vibration signals is further improved.
FIG. 10 is a diagram illustrating an internal structure of a computer device in one embodiment. The computer device may specifically be a terminal, and may also be 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 comprises 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 the processor, causes the processor to carry out the above-mentioned method. The internal memory may also have a computer program stored thereon, which, when executed by the processor, causes the processor to perform the method described above. It will be appreciated by those skilled in the art that the configuration shown in fig. 10 is a block diagram of only a portion of the configuration associated with the present application, and is not intended to limit the computing device to which the present application may be applied, and that a particular computing device may include more or less components than those 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 perform the steps of the method shown in the present embodiment.
In one embodiment, a computer-readable storage medium is provided, in which a computer program is stored, which, when executed by a processor, causes the processor to perform the steps of the method of the present embodiment.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a non-volatile computer-readable storage medium, and can include the processes of the embodiments of the methods described above when the program is executed. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile 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), rambus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method for reducing compressed sensing reconstruction errors of a vibration signal, the method comprising:
acquiring a basic solution system of a reconstructed vibration signal, an order and an underdetermined 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 quantity of the autoregressive model;
determining a relative residual of the autoregressive model based on the model residuals and model outputs;
and carrying out treatment of reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal.
2. The method of claim 1, wherein the autoregressive model comprises the following mathematical expression:
Figure FDA0003784643970000011
the regression of the form factor is determined,
Figure FDA0003784643970000012
for model parameters, (i =1,2, Λ p), p is the order,
Figure FDA0003784643970000013
is the model residual.
3. The method of claim 1, wherein the relative residual error comprises the following mathematical expression:
Figure FDA0003784643970000014
in the formula (I), the compound is shown in the specification,
Figure FDA0003784643970000015
in order to be the output quantity of the model,
Figure FDA0003784643970000016
as model residuals, (i =1,2, Λ p),
Figure FDA0003784643970000017
is a norm.
4. The method according to claim 1, wherein the auto-regressive model characteristic parameters further include model regression quantities and model parameters, and the processing of reducing the relative residuals is performed according to the auto-regressive model parameters and a basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal, including:
constructing an optimization problem for reducing the relative residual error by using a model regression quantity, a model output quantity, an order, a model parameter and a basic solution system of an underdetermined equation;
and solving the optimization problem to obtain a new reconstructed vibration signal.
5. The method of claim 4, wherein the optimization problem comprises the following mathematical expression:
Figure FDA0003784643970000021
in the formula, x out ＝[x p+1 x p+2 Λx N ]The output quantity of the model is taken;
Figure FDA0003784643970000022
in order to be the regression quantity of the model,
Figure FDA0003784643970000023
for model parameters, (i =1,2, Λ p), p is the order, y = Φ x T For underdetermined equations, underdetermined equation y = Φ x T General solution of
Figure FDA0003784643970000024
In the formula, h is a coefficient,
Figure FDA0003784643970000025
pi is the basic solution system of the underdetermined equation, r is the rank of the basic solution system,
Figure FDA0003784643970000026
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 an underdetermined equation in the optimization problem;
performing expression simplification processing on the optimization problem based on the general solution of the underdetermined equation to obtain a processed optimization problem, wherein the simplification processing comprises omitting a model output quantity in a denominator of the optimization problem, and replacing a model regression quantity and the model output quantity in the optimization problem by using the general solution of the underdetermined equation;
and obtaining a new reconstructed vibration signal by utilizing the processed optimization problem.
7. The method of claim 6, wherein the processed optimization problem comprises the following mathematical expression:
Figure FDA0003784643970000027
wherein the underdetermined equation y = Φ x T General solution of
Figure FDA0003784643970000028
In the formula, h is a coefficient,
Figure FDA0003784643970000029
in order to be a new coefficient of the signal,
Figure FDA00037846439700000210
pi is the fundamental solution system of the underdetermined equation,
Figure FDA00037846439700000211
rank, Π, of r-based solution system out Based on the solution of the matrix formed by the nth rows p +1 to N,
Figure FDA00037846439700000212
a matrix formed by pi p +1-i to N-i rows is solved as a basis, i =1,2, Λ p, p is the order,
Figure FDA00037846439700000213
is a norm;
the new reconstructed vibration signal includes the following mathematical expression:
Figure FDA00037846439700000214
in the formula (I), the compound is shown in the specification,
Figure FDA00037846439700000215
for the purpose of a new reconstruction of the vibration signal,
Figure FDA00037846439700000216
in order to reconstruct the vibration signal,
Figure FDA00037846439700000217
in order to be a new coefficient of the signal,
Figure FDA00037846439700000218
pi is the fundamental solution system of the underdetermined equation,
Figure FDA00037846439700000219
r is the rank of the base solution.
8. The method according to claim 1, wherein the processing for reducing the relative residual is performed according to the auto-regression model feature parameters, the order and a basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal, and then further comprising:
determining the current reconstruction times of the reconstructed vibration signal;
and if the current reconstruction times are less than the preset calculation cycle times, taking the new reconstruction vibration signal as a reconstruction vibration signal, returning to the step of executing the step of inputting the reconstruction vibration signal and the order into a preset autoregressive model to obtain the 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 compressed sensing reconstruction error of a vibration signal, the apparatus comprising:
a data acquisition module: a basic solution system for obtaining a reconstructed vibration signal, an order and an underdetermined equation;
a model construction module: the autoregressive model characteristic parameters at least comprise model residues and model output quantity of the autoregressive model;
a residual determination module: for determining a relative residual of the autoregressive model based on the model residuals and model outputs;
a signal reconstruction module: and the processing unit is used for reducing the relative residual error according to the characteristic parameters and the order of the autoregressive model and the basic solution system of the underdetermined equation to obtain a new reconstructed vibration signal.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, causes the processor to carry out the steps of the method according to any one of claims 1 to 8.
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