CN108599773B - Vibration signal data compression acquisition method based on deterministic measurement matrix - Google Patents

Vibration signal data compression acquisition method based on deterministic measurement matrix Download PDF

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CN108599773B
CN108599773B CN201810336121.1A CN201810336121A CN108599773B CN 108599773 B CN108599773 B CN 108599773B CN 201810336121 A CN201810336121 A CN 201810336121A CN 108599773 B CN108599773 B CN 108599773B
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郭俊锋
党姜婷
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Lanzhou University of Technology
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Abstract

The invention discloses a vibration signal data compression acquisition method based on a deterministic measurement matrix, which comprises the following steps: extracting an acquired vibration signal, and performing sparsity analysis under a discrete cosine transform base DCT orthogonal base to obtain a sparsity K; according to the sparsity K, establishing a first orthogonal symmetrical deterministic measurement matrix based on the deterministic measurement matrix; iterating the obtained first orthogonal symmetrical deterministic measurement matrix by adopting a threshold iterative shrinkage algorithm to obtain a second orthogonal symmetrical deterministic measurement matrix; and optimizing the obtained second orthogonal symmetrical deterministic measurement matrix by using a singular value decomposition algorithm to obtain a third orthogonal symmetrical deterministic measurement matrix. The vibration signal data compression acquisition method based on the deterministic measurement matrix provided by the invention solves the problem that the reconstruction error of the deterministic measurement matrix is large and the vibration signal data compression acquisition method cannot be widely applied.

Description

Vibration signal data compression acquisition method based on deterministic measurement matrix
Technical Field
The invention belongs to the field of data compression and acquisition, and particularly relates to a vibration signal data compression and acquisition method based on a deterministic measurement matrix.
Background
The vibration signal acquisition widely adopted at present is analog-to-digital (A/D) sampling guided by the Nyquist sampling theory, but the signal can be accurately reconstructed only if the sampling frequency is not lower than twice of the highest frequency of the original signal. However, nowadays, mechanical equipment is becoming faster and larger in size, and the vibration frequency is becoming higher and higher, and the equipment is characterized by nonlinearity and non-stationarity. If the traditional sampling theorem is still used for sampling, higher sampling frequency is necessarily required, massive monitoring data are generated at the same time, and the real-time transmission, synchronous storage and post-processing of the data are difficult.
The solution to the above problem is suggested by the theory of compressed sensing, which states that if the original signal is sparse or compressible in some transform domain, the signal can be simultaneously compressed while being sampled at a rate well below nyquist. Compressed sensing is mainly composed of two parts, namely acquisition and reconstruction of signals, and a measurement matrix serving as the most core content of compressed sensing plays an important role in the two parts: the better the measurement matrix performance, the fewer the number of samples required and the smaller the reconstruction error. The current measurement matrix is mainly divided into two categories, namely a randomness matrix and a certainty matrix. At the initial stage of the compressive sensing theory, a random measurement matrix represented by a Gaussian matrix is favored because of small required measurement number and high reconstruction precision, but the random measurement matrix has a complex structure, occupies a large storage space, has a plurality of random variables and is not realized by hardware. On the contrary, the deterministic measurement matrix has a simple structure, greatly reduces the hardware construction difficulty, and is beneficial to engineering realization, so many scholars at home and abroad research the deterministic matrix such as a Toeplitz matrix, a cyclic measurement matrix and the like, but the deterministic measurement matrix cannot be widely applied due to larger reconstruction error.
Aiming at the problem that the reconstruction error of a deterministic measurement matrix in the compressed sensing is large, an effective solution is not provided at present.
Disclosure of Invention
Aiming at the defect of larger reconstruction error of a deterministic measurement matrix in the prior art, the vibration signal data compression acquisition method based on the deterministic measurement matrix is provided, and comprises the following steps: extracting an acquired original vibration signal, and performing sparsity analysis on the original vibration signal under a discrete cosine transform basis (DCT) orthogonal basis to obtain sparsity K;
according to the sparsity K, establishing a first orthogonal symmetrical deterministic measurement matrix based on the deterministic measurement matrix;
iterating the obtained first orthogonal symmetrical deterministic measurement matrix by adopting a threshold iterative shrinkage algorithm to obtain a second orthogonal symmetrical deterministic measurement matrix;
and optimizing the second orthogonal symmetrical deterministic measurement matrix by using a singular value decomposition algorithm to obtain a third orthogonal symmetrical deterministic measurement matrix.
Further, in the above technical solution, the method further includes:
performing compression measurement on the original vibration signal according to the third orthogonal symmetrical deterministic matrix to obtain a measured value;
reconstructing a sparse coefficient according to the measured value, the third orthogonal symmetry certainty measurement matrix and the DCT orthogonal basis;
and obtaining a reconstructed vibration signal according to the sparse coefficient.
Further, in the above technical solution, the step of establishing the first orthogonal symmetric deterministic measurement matrix based on the deterministic measurement matrix includes:
selecting a sequence from among Bernoulli sequences
Figure BDA0001629298850000021
Adding N-1 elements after the sequence to form a first sequence of (sigma)1,σ2,...,σN)＝(γ,ε1,...,εN/2-1,β,εN/2-1,...,ε1) Wherein N is a sequence
Figure BDA0001629298850000022
The number of elements in (1);
obtaining a second sequence by performing inverse Fourier transform on the first sequence, wherein the second sequence is a head row element of the first orthogonal symmetric deterministic measurement matrix, and the head row element obtains the rest other rows of the first orthogonal symmetric deterministic measurement matrix by cyclic shift;
randomly selecting M rows of a first orthogonal symmetric deterministic measurement matrix and multiplying by a coefficient
Figure BDA0001629298850000031
Normalization yields an MxN first orthometric, deterministic measurement matrix phi, i.e.
Figure BDA0001629298850000032
Wherein, the relation between M and the sparsity K needs to satisfy the formula
Figure BDA0001629298850000033
Where c ≈ 0.28.
Further, the step of iterating the obtained first deterministic measurement matrix by using a threshold iterative shrinkage algorithm to obtain a second orthogonal symmetric deterministic measurement matrix includes:
performing column unitization on the first orthogonal symmetry certainty measurement matrix phi to obtain an initial matrix phi0；
According to the sparsity K of the image data,
Figure BDA0001629298850000034
determining phi0The number of rows of (1), i.e. the measured value M;
solving a perceptual matrix D from DCT orthogonal basesq＝ψDCTΦqColumn unitizing the sensing matrix to obtain
Figure BDA0001629298850000035
Wherein phiqFor an iterative matrix, #DCTIs DCT orthogonal base, q is iteration number;
perceptual matrix unitized by columns
Figure BDA0001629298850000036
Using a formula
Figure BDA0001629298850000037
Obtaining a gram matrix, wherein T is a rotation rank matrix of the matrix;
updating the gram matrix G according to the threshold value t and the scale reduction factor gammaqObtaining an updated Graham matrix
Figure BDA0001629298850000038
Figure BDA0001629298850000039
Reducing updated gram matrices using singular value decomposition algorithms
Figure BDA00016292988500000310
Rank to M;
order to
Figure BDA0001629298850000041
Inverse solving of the perception matrix Dq(Dq∈RM×N) Obtaining a perception matrix D after threshold iterative shrinkageq；
To be provided with
Figure BDA0001629298850000042
Update phi for the targetq+1I.e. when the norm is minimum
Figure BDA0001629298850000043
The matrix Φ' is measured for a second orthogonal symmetric certainty.
Further, the step of optimizing the obtained second orthogonal symmetric deterministic measurement matrix Φ' by using a singular value decomposition algorithm to obtain a third orthogonal symmetric deterministic measurement matrix includes:
passing the second orthometric symmetric deterministic measurement matrix through the equation Φ ═ U Λ PTThe diagonalization decomposition is carried out,
wherein U is E.RM×MAnd P ∈ RN×NAre all orthogonal arrays, and are epsilon to RM×NIs a diagonal matrix and the elements on the diagonal of Λ are the singular values of the measurement matrix Φ'. Now, a limit is made to Λ: if only the factor of M before the absolute value on the positive angle line of Lambda is kept and the rest are set to be 0, then
Figure BDA0001629298850000044
Wherein Δ ═ diag (σ)1,σ2,…,σM) And obtaining a third orthometric symmetry certainty measurement matrix phi ″ ═ UΛ' P after optimizationT。
Further, according to the measured value, the third orthogonal symmetry certainty measurement matrix phi' and the DCT orthogonal basis, an OMP algorithm is adopted in the process of reconstructing the sparse coefficient.
According to an aspect of the present invention, there is also provided a storage medium including a stored program, wherein the program executes the data compression acquisition method.
According to another aspect of the present invention, there is also provided a processor, configured to execute a program, where the program executes the data compression and acquisition method.
The technical scheme adopted by the invention has the advantages that: extracting vibration signals, performing sparsity analysis to obtain sparsity K, orthogonalizing and symmetrizing the deterministic measurement matrix according to the sparsity K, reducing independent variables, and constructing a first orthometric symmetric deterministic measurement matrix easy for hardware implementation. In order to improve the reconstruction accuracy of the first orthogonal symmetrical determinacy measurement matrix, a threshold value iterative shrinkage algorithm and a singular value decomposition algorithm are combined from the non-coherence, firstly, the first orthogonal symmetrical determinacy measurement matrix is optimized through the threshold value iterative shrinkage algorithm to obtain a second orthogonal symmetrical determinacy measurement matrix so as to reduce the coherence between the first orthogonal symmetrical determinacy measurement matrix and a sparse basis, secondly, a singular value decomposition algorithm is adopted to further improve the column vector independence of the second orthogonal symmetrical determinacy measurement matrix, and finally, a third orthogonal symmetrical determinacy measurement matrix suitable for vibration signals is obtained. The vibration signal compression and acquisition algorithm provided by the text is high in operation speed, and the calculation complexity is greatly reduced while the compression performance of the measurement matrix is improved.
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FIG. 1 is a diagram illustrating the steps of implementing deterministic measurement matrix optimization by a vibration signal data compression acquisition method based on a deterministic measurement matrix according to the present invention;
fig. 2 shows steps of implementing vibration signal reconstruction by the vibration signal data compression and acquisition method based on the deterministic measurement matrix according to the present invention.
Detailed Description
The following embodiments are merely examples for illustrating the technical solutions of the present invention more clearly, and therefore, the technical solutions of the present invention are not limited to the following embodiments.
Fig. 1 shows the steps of implementing deterministic measurement matrix optimization by the vibration signal data compression and acquisition method based on the deterministic measurement matrix of the present invention.
With reference to fig. 1, a vibration signal data compression acquisition method based on a deterministic measurement matrix realizes the step of optimizing the deterministic measurement matrix, which includes the following steps:
step 102: extracting an acquired original vibration signal, and performing sparsity analysis on the original vibration signal under a discrete cosine transform basis (DCT) orthogonal basis to obtain sparsity K;
step 104: according to the sparsity K, establishing a first orthogonal symmetrical deterministic measurement matrix based on the deterministic measurement matrix;
step 106: iterating the obtained first orthogonal symmetrical deterministic measurement matrix by adopting a threshold iterative shrinkage algorithm to obtain a second orthogonal symmetrical deterministic measurement matrix;
step 108: and optimizing the second orthogonal symmetrical deterministic measurement matrix by using a singular value decomposition algorithm to obtain a third orthogonal symmetrical deterministic measurement matrix.
Fig. 2 is a step of implementing vibration signal reconstruction by the vibration signal data compression and acquisition method based on the third orthogonal symmetric deterministic measurement matrix of the present invention.
Further, in one embodiment, the method further comprises:
step 202, carrying out compression measurement on the original vibration signal according to a third orthogonal symmetrical deterministic matrix to obtain a measured value M;
204, according to the measured value M, the third orthogonal symmetrical deterministic measurement matrix and the DCT orthogonal basis psiDCTReconstructing a sparse coefficient;
and step 206, obtaining a reconstructed vibration signal according to the sparse coefficient.
Further, the step of establishing a first orthogonal symmetric deterministic measurement matrix based on the deterministic measurement matrix according to an embodiment of the present invention comprises:
selecting a sequence from among Bernoulli sequences
Figure BDA0001629298850000061
Adding N-1 elements after the sequence to form a first sequence of (sigma)1,σ2,...,σN)＝(γ,ε1,...,εN/2-1,β,εN/2-1,...,ε1) Wherein N is a sequence
Figure BDA0001629298850000062
The number of elements in (1);
obtaining a second sequence by performing inverse Fourier transform on the first sequence, wherein the second sequence is a head row element of the first orthogonal symmetric deterministic measurement matrix, and the head row element obtains the rest other rows of the first orthogonal symmetric deterministic measurement matrix by cyclic shift;
randomly selecting M rows of a first orthogonal symmetric deterministic measurement matrix and multiplying by a coefficient
Figure BDA0001629298850000063
Normalization yields an MxN first orthometric, deterministic measurement matrix phi, i.e.
Figure BDA0001629298850000064
Wherein, the relation between M and the sparsity K needs to satisfy the formula
Figure BDA0001629298850000065
Where c ≈ 0.28.
Further, the step of obtaining a second orthometric symmetric deterministic measurement matrix by iterating the obtained first deterministic measurement matrix using a threshold iterative shrinkage algorithm according to the embodiment of the present invention includes:
performing column unitization on the first orthogonal symmetry certainty measurement matrix phi to obtain an initial matrix phi0；
According to the sparsity K of the image data,
Figure BDA0001629298850000071
determining phi0The number of rows of (1), i.e. the measured value M;
solving a perceptual matrix D from DCT orthogonal basesq＝ψDCTΦqColumn unitizing the sensing matrix to obtain
Figure BDA0001629298850000072
Wherein phiqFor an iterative matrix, #DCTIs DCT orthogonal base, q is iteration number;
unitization according to columnsOf the sensing matrix
Figure BDA0001629298850000073
Using a formula
Figure BDA0001629298850000074
Obtaining a gram matrix, wherein T is a rotation rank matrix of the matrix;
updating the gram matrix G according to the threshold value t and the scale reduction factor gammaqObtaining an updated Graham matrix
Figure BDA0001629298850000075
Figure BDA0001629298850000076
Reducing updated gram matrices using singular value decomposition algorithms
Figure BDA0001629298850000077
Rank to M;
order to
Figure BDA0001629298850000078
Inverse solving of the perception matrix Dq(Dq∈RM×N) Obtaining a perception matrix D after threshold iterative shrinkageq；
To be provided with
Figure BDA0001629298850000079
Update phi for the targetq+1I.e. when the norm is minimum
Figure BDA00016292988500000710
The matrix Φ' is measured for a second orthogonal symmetric certainty.
It will be appreciated that the threshold iterative shrinkage algorithm optimizes the first deterministic measurement matrix Φ on the basis of the non-coherence: first, a mutual coherence coefficient mu is introduced, which represents the column vector of a first orthometric symmetric deterministic measurement matrix phi and the DCT orthonormal basis psiDCTThe maximum value of the inner product of the column vector,the smaller the value, the better the non-correlation property. Defining a perception matrix Dq＝ψDCTΦqPerforming column unitization processing on the sensing matrix to obtain a new matrix
Figure BDA0001629298850000081
The mutual coherence coefficient μ (D) of the column vector of the perceptual matrix is:
Figure BDA0001629298850000082
wherein d isiAnd
Figure BDA0001629298850000083
are each DqAnd
Figure BDA0001629298850000084
column vector of, order gram matrix
Figure BDA0001629298850000085
Then based on the matrix, the mutual coherence coefficient μ can now be defined as:
Figure BDA0001629298850000086
in the formula
Figure BDA0001629298850000087
Is a factor in the gram matrix, and is the column vector of the first orthometric symmetric deterministic measurement matrix phi and the DCT orthonormal basis psiDCTThe inner products of the different columns represent the maximum of the non-diagonal elements in the gram matrix. However, the two equivalent definitions μ describe only local correlation, so that an average cross-correlation coefficient μ based on a threshold t is usedt(D) Averaging the moduli of the elements on the off-diagonal line of which the gram matrix of the sensing matrix is not less than the threshold t, that is:
Figure BDA0001629298850000088
the goal of the optimization is then to reduce the first orthometric, symmetric deterministic measurement matrix phi and the DCT orthogonal basis phiDCTT-average cross correlation coefficient mu oft(D) To obtain a second orthometric symmetric deterministic measurement matrix phi'
Compared with the first orthogonal symmetrical deterministic measurement matrix phi, the second orthogonal symmetrical deterministic measurement matrix phi 'is obtained through the threshold iterative algorithm, the reconstruction performance is improved to a certain extent, but the optimal perception effect is not achieved, namely the obtained matrix is not optimal, and therefore the second orthogonal symmetrical deterministic measurement matrix phi' is continuously optimized through the singular value decomposition algorithm in the next step.
Further, according to the above embodiment of the present invention, the step of optimizing the obtained second orthogonal symmetric deterministic measurement matrix Φ' by using a singular value decomposition algorithm to obtain a third orthogonal symmetric deterministic measurement matrix Φ ″ includes:
passing the second orthometric symmetric deterministic measurement matrix Φ' through the formula Φ ═ U Λ PTThe diagonalization decomposition is carried out,
wherein U is E.RM×MAnd P ∈ RN×NAre all orthogonal arrays, and are epsilon to RM×NIs a diagonal matrix, the elements on the diagonal of Λ are the singular values of the second orthogonal symmetric deterministic measurement matrix Φ'. Now, a limit is made to Λ: if only the factor of M before the absolute value on the positive angle line of Lambda is kept and the rest are set to be 0, then
Figure BDA0001629298850000091
Wherein Δ ═ diag (σ)1,σ2,…,σM) And obtaining a third orthometric symmetry certainty measurement matrix phi ″ ═ UΛ' P after optimizationT。
It can be understood that the second orthogonal symmetric deterministic measurement matrix Φ 'can increase the minimum singular value of the second orthogonal symmetric deterministic measurement matrix Φ' through a singular value decomposition algorithm, and the larger the minimum singular value is, the stronger the column vector independence of the third orthogonal symmetric deterministic measurement matrix is, and the stronger the performance of the third orthogonal symmetric deterministic measurement matrix Φ ″ when used for signal compressed sensing is.
Further, based on the measured value M, the third orthometric symmetric deterministic measurement matrix phi' and the DCT orthometric basis psiDCTAnd q, adopting an OMP algorithm in the process of reconstructing the sparse coefficient.
According to experimental verification, compared with the measurement of the optimized first orthogonal symmetrical deterministic measurement matrix, the reconstruction error of the first orthogonal symmetrical deterministic measurement matrix optimized by the singular value decomposition algorithm can be reduced, the reconstruction accuracy of the first orthogonal symmetrical deterministic measurement matrix optimized by the threshold iteration algorithm is improved, and meanwhile, the cost of time is required.
In the description of the present invention, numerous specific details are set forth. It is understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (5)

1. A vibration signal data compression acquisition method based on a deterministic measurement matrix is characterized by comprising the following steps:
extracting an acquired original vibration signal, and performing sparsity analysis on the original vibration signal under a discrete cosine transform base DCT orthogonal basis to obtain sparsity K;
according to the sparsity K, establishing a first orthogonal symmetrical deterministic measurement matrix based on a deterministic measurement matrix;
iterating the obtained first orthogonal symmetrical deterministic measurement matrix by adopting a threshold iterative shrinkage algorithm to obtain a second orthogonal symmetrical deterministic measurement matrix;
optimizing the second orthogonal symmetrical deterministic measurement matrix by using a singular value decomposition algorithm to obtain a third orthogonal symmetrical deterministic measurement matrix;
said step of establishing a first orthogonal symmetric deterministic measurement matrix based on a deterministic measurement matrix comprises:
selecting a sequence from among Bernoulli sequences
Figure FDA0002352821560000011
Adding N-1 elements after the sequence to form a first sequence, wherein the first sequence is in the form of (sigma)1,σ2,...,σN)＝(γ,ε1,...,εN/2-1,β,εN/2-1,...,ε1)
Wherein N is a sequence
Figure FDA0002352821560000012
The number of elements in (1);
obtaining a second sequence by performing inverse Fourier transform on the first sequence, wherein the second sequence is a first row element of the first orthogonal symmetric deterministic measurement matrix, and the first row element obtains the rest other rows of the first orthogonal symmetric deterministic measurement matrix by cyclic shift;
randomly selecting M rows of a first orthogonal symmetric deterministic measurement matrix and multiplying by a coefficient
Figure FDA0002352821560000013
Normalization to obtain a M N first orthogonal symmetry determinationThe sexual measurement matrix phi, i.e.
Figure FDA0002352821560000014
Wherein the relation between M and the sparsity K needs to satisfy the formula
Figure FDA0002352821560000015
Wherein c ≈ 0.28;
the step of obtaining a second orthogonal symmetric deterministic measurement matrix by iterating the obtained first deterministic measurement matrix by using a threshold iterative shrinkage algorithm comprises:
performing column unitization on the first orthometric symmetry certainty measurement matrix phi to obtain an initial matrix phi0；
According to the sparsity K, the method comprises the following steps of,
Figure FDA0002352821560000021
determining phi0The number of rows of (1), i.e. the measured value M;
solving a perception matrix D according to the DCT orthogonal basisq＝ψDCTΦqColumn unitizing the sensing matrix to obtain
Figure FDA0002352821560000022
Wherein phiqFor an iterative matrix, #DCTIs DCT orthogonal base, q is iteration number;
a perceptual matrix unitized according to the columns
Figure FDA0002352821560000023
Using a formula
Figure FDA0002352821560000024
Obtaining a gram matrix, wherein T is a rotation rank matrix of the matrix;
updating the gram matrix G according to the threshold value t and the scale reduction factor gammaqObtaining an updated Graham matrix
Figure FDA0002352821560000025
Figure FDA0002352821560000026
Reducing the updated gram matrix using a singular value decomposition algorithm
Figure FDA0002352821560000027
Rank to M;
order to
Figure FDA0002352821560000028
Inverse solving of the perception matrix Dq(Dq∈RM×N) Obtaining a perception matrix D after threshold iterative shrinkageq；
To be provided with
Figure FDA0002352821560000029
Update phi for the targetq+1I.e. when the norm is minimum
Figure FDA00023528215600000210
(ii) determining a second orthogonal symmetric deterministic measurement matrix Φ' for the second signal;
optimizing the obtained second orthogonal symmetrical deterministic measurement matrix phi' by using a singular value decomposition algorithm to obtain a third orthogonal symmetrical deterministic measurement matrix, wherein the step of obtaining the third orthogonal symmetrical deterministic measurement matrix comprises the following steps:
passing the second orthometric symmetric deterministic measurement matrix through the equation Φ ═ U Λ PTThe diagonalization decomposition is carried out,
wherein U is E.RM×MAnd P ∈ RN×NAre all orthogonal arrays, and are epsilon to RM×NIs a diagonal matrix, the elements on the diagonal of Λ are the singular values of the measurement matrix Φ', now the definition is made for Λ: only the factor of M is kept before the absolute value on the positive angle line of the lambda, and the rest is set to be 0, namely
Figure FDA0002352821560000031
Wherein Δ ═ diag (σ1,σ2,…,σM) And obtaining the third orthometric symmetrical deterministic measurement matrix phi ″ ═ UΛ' P after optimizationT。
2. The data compression collection method according to claim 1, further comprising:
performing compression measurement on the original vibration signal according to the third orthogonal symmetrical deterministic matrix to obtain a measured value;
reconstructing a sparse coefficient according to the measured value, the third orthometric symmetric deterministic measurement matrix and the DCT orthogonal basis;
and obtaining a reconstructed vibration signal according to the sparse coefficient.
3. The data compression collection method of claim 1, wherein an OMP algorithm is used in the process of reconstructing sparse coefficients according to the measured values, the third orthometric symmetric deterministic measurement matrix Φ ", and the DCT orthobases.
4. A storage medium comprising a stored program, wherein the program executes the data compression acquisition method of any one of claims 1-3.
5. A processor, characterized in that the processor is configured to run a program, wherein the program is configured to execute the data compression acquisition method according to any one of claims 1 to 3 when the program is run.
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