A Compressed Sensing Method for Gear Vibration Signals Based on Adaptive Sparse Representation

Abstract

The present invention discloses a method for compressive sensing of gear vibration signals based on adaptive sparse representation, which specifically relates to the technical fields of signal processing and mechanical fault diagnosis. First, a multi-channel vibration sensor is used to collect gear vibration signals, and preprocessing is performed to obtain high-quality signals. Then, an improved K-SVD algorithm is used to construct an adaptive sparse dictionary to improve the sparse representation capability of the signal. Next, an optimized measurement matrix that satisfies the restricted isometry property (RIP) is designed, including a combination of a weighted random Toeplitz matrix and a circulant matrix, to achieve efficient compressed sampling. In the signal reconstruction stage, a regularization term is introduced and an improved orthogonal matching pursuit (OMP) algorithm is used to improve reconstruction accuracy and noise resistance. This method significantly improves signal reconstruction accuracy and processing efficiency, and is suitable for the fields of real-time monitoring and fault diagnosis.

Description

Technical Field

[0001] The invention relates to the technical field of signal processing and mechanical fault diagnosis, and in particular to a gear vibration signal compression sensing method based on adaptive sparse representation. Background Art

[0002] Gears are the core components of mechanical transmission systems, and their operating status directly affects the performance and life of the equipment. Gears will generate complex vibration signals during operation, which contain rich mechanical status information. By analyzing the gear vibration signals, potential faults can be discovered in time and major accidents can be prevented. However, gear vibration signals are usually high-frequency, high-dimensional, non-stationary and nonlinear. Traditional high-sampling rate data acquisition methods will generate a large amount of data, which increases the burden of data storage, transmission and processing, and is not conducive to real-time monitoring and online fault diagnosis.

[0003] Compressed Sensing (CS) theory provides a new idea for signal sampling and reconstruction. The theory shows that as long as the signal is sparse in a certain domain, it can be accurately reconstructed by sampling at a rate much lower than the Nyquist sampling rate. However, the traditional compressed sensing method has the following shortcomings when applied to gear vibration signals:

[0004] Inaccurate sparse representation: The complexity of the gear vibration signal makes it difficult to obtain a sufficiently sparse representation under a fixed basis (such as Fourier basis, wavelet basis), which affects the reconstruction accuracy.

[0005] The measurement matrix is ​​difficult to satisfy the restricted isometry property (RIP): Although the random measurement matrix satisfies the RIP in theory, it is difficult to implement in actual hardware and has high computational complexity, which is not conducive to real-time processing.

[0006] High complexity of reconstruction algorithms: Commonly used signal reconstruction algorithms (such as Basis Pursuit) have large computational complexity and cannot meet real-time requirements.

[0007] Insufficient noise resistance: The actual collected signals inevitably contain noise, and traditional methods are sensitive to noise, which affects the reconstruction quality. Summary of the invention

[0008] To this end, the present invention provides a gear vibration signal compression sensing method based on adaptive sparse representation to solve the problems raised in the background technology.

[0009] In order to achieve the above object, the present invention provides the following technical solution: a gear vibration signal compression sensing method based on adaptive sparse representation, comprising the following steps:

[0010] (1) Data collection and preprocessing:

[0011] 1.1) Use a multi-channel vibration sensor to collect gear vibration signals and obtain the original signal set ;

[0012] 1.2) Remove the DC component, normalize and reduce noise of the original signal to obtain the preprocessed signal set ;

[0013] (2) Adaptive sparse dictionary learning:

[0014] 2.1) Use the improved K-SVD algorithm to learn the dictionary of the preprocessed signal and construct an adaptive sparse dictionary and the sparse coefficient matrix , in order to improve the sparse representation ability of the signal; the specific algorithm steps are as follows:

[0015] 2.1.1) Initialization settings: Setting up the adaptive sparse dictionary The number of atoms ,satisfy , L is the number of signal samples, sparsity ;

[0016] 2.1.2) Initialize dictionary: Adaptive sparse dictionary , take a random Gaussian matrix and then normalize each column:

[0017] ;

[0018] in, represents the k-th column vector of the dictionary, i.e. the k-th dictionary atom, Representation vector of Euclidean norm;

[0019] 2.1.3) Sparse coding: For each preprocessed signal , by solving the following optimization objective

[0020] , solve for the sparse coefficient :

[0021] ;

[0022] The optimization goal is to find a balance between sparsity and reconstruction error:

[0023] Item 1: Try to minimize the signal Instead of sparse representation differences to ensure the accuracy of reconstruction;

[0024] Item 2: Try to minimize of norm to enforce sparsity and suppress redundant non-zero coefficients;

[0025] This form is the standard form of the LASSO (Least Absolute Shrinkage and Selection Operator) problem, which is solved by The norm is used as a regularization term to effectively approximate norm problem, while ensuring the convexity of the optimization problem, making it convenient and efficient to solve;

[0026] in, is the sparsity regularization parameter, which controls the trade-off between sparsity and reconstruction error;

[0027] 2.1.4) Dictionary update:

[0028] For each atom dictionary , the dictionary update steps are as follows:

[0029] 2.1.4.1) Calculate the error matrix: ;

[0030] in, is a sparse coefficient matrix No. OK;

[0031] 2.1.4.2) Singular value decomposition SVD: error matrix Perform SVD decomposition: ;

[0032] 2.1.4.3) Update dictionary atoms and the corresponding sparse coefficients : ;

[0033] 2.1.4.4) Iteration:

[0034] Repeat the sparse coding and dictionary updating steps until the adaptive sparse dictionary Convergence or reaching the maximum number of iterations;

[0035] (3) Optimize measurement matrix design:

[0036] 3.1) Construct a combined measurement matrix of weighted random Toeplitz matrix and circulant matrix , in order to improve the sparsity and structural characteristics of the matrix, reduce the hardware and computational complexity, and significantly improve the adaptability to the signal and the reconstruction accuracy, especially in high noise or real-time scenarios, showing better performance. The specific steps are as follows:

[0037] 3.1.1) Weighted Random Toeplitz Matrix The construction steps are as follows:

[0038] 3.1.1.1) Randomly generate a length of A random sequence , where L represents the original length of the signal, i.e., the signal dimension; m represents the target dimension of the measurement matrix, i.e., the target number of sampling points; L+M-1 represents the total length of the random sequence, ensuring that all required elements are covered when constructing the Toeplitz matrix. Obey standard normal distribution;

[0039] 3.1.1.2) Define the weight vector , used for weighting;

[0040] 3.1.1.3) Construct the Toeplitz matrix: in, Represents the Toeplitz matrix The element in the i-th row and j-th column of ; Indicates that the j-th element of the weight vector is used for weighting; Indicated by The constructed matrix elements use the indexing rule of i-j+L to extract the corresponding elements in the sequence;

[0041] 3.1.2) Circular Matrix The construction steps are as follows:

[0042] 3.1.2.1) Randomly generate length sequence , Obey standard normal distribution;

[0043] 3.1.2.2) Construct the circulant matrix: ,in, Represents a circulant matrix The element in the i-th row and j-th column of ; Represents the circular nature of the modular operation used to determine the location of an index in a matrix;

[0044] 3.1.3) Combined measurement matrix : The weighted random Toeplitz matrix With the circulant matrix Combined with: , the combined measurement matrix Satisfies the restricted isometry property RIP, where , ;

[0045] (4) Compressed sampling:

[0046] 4.1) Preprocessing signal for each channel Perform compressed sampling to obtain compressed measurement values ;in, For the Compression measurement values ​​for each channel;

[0047] (5) Signal reconstruction:

[0048] 5.1) Using the improved OMP algorithm, using the measured value , measurement matrix and adaptive sparse dictionary , solve for the sparse coefficient , reconstruct the signal , and introduce regularization terms and adaptive thresholds to improve reconstruction accuracy and noise resistance performance; the specific steps of the improved OMP algorithm are as follows:

[0049] 5.1) Initialization:

[0050] 5.1.1) Residual ;

[0051] 5.1.2) Support set ;

[0052] 5.1.3) Number of iterations ;

[0053] 5.2) Iteration process:

[0054] 5.2.1) Atom selection: ,in for No. List, Represents the atom selected in the kth iteration, that is, the dictionary matrix No. List; Represents the dictionary matrix The j-th vector of represents the residual vector of the kth iteration; represents the jth column atomic vector With the residual vector The inner product of Represents the jth column and the Naz vector norm (Euclidean length of a vector); Indicates the maximum j value of the objective function;

[0055] 5.2.2) Support set S update: ;

[0056] 5.2.3) Sparse coefficient calculation: Solve the following optimization problem: ,in, The current observation signal, that is, the measurement value, is obtained through the measurement matrix The compressed signal; Represents the signal reconstruction error, that is, the observed signal The squared error between the signal reconstructed by the dictionary and Represents the sparse coefficient norm; is an adaptive sparse dictionary The corresponding support set A subset of columns, represents the regularization parameter;

[0057] 5.2.4) Residual update: ,in, The residual at the k+1th iteration represents the unexplained part of the current signal reconstruction; represents the reconstructed signal obtained in the iteration;

[0058] 5.2.5) Termination condition: If or , then the iteration stops; among them, Residual norm, indicating the size of the residual in the current iteration; is the preset residual tolerance threshold, indicating the minimum error acceptable for iteration; Indicates the maximum number of iterations;

[0059] 5.1) Output: Reconstructed signal: ,in, represents the reconstructed signal, represents the optimal sparse coefficient;

[0060] (6) Result output:

[0061] 6.1) Output the reconstructed signal set , used for subsequent analysis and processing, the reconstructed signal is applied to spectrum analysis, feature extraction and fault diagnosis.

[0062] The invention discloses a computer-readable storage medium, wherein a program is stored in the storage medium. When the program is run on a processor, a gear vibration signal compression sensing method based on adaptive sparse representation is executed.

[0063] The present invention also discloses a processor, which is used to execute a program. When the program runs on the processor, the gear vibration signal compression sensing method based on adaptive sparse representation is executed.

[0064] The present invention has the following advantages:

[0065] 1. The improved K-SVD algorithm designed by the present invention introduces sparse regularization in sparse coding, thereby improving the robustness and accuracy of sparse representation.

[0066] 2. The present invention adopts a combination of a weighted random Toeplitz matrix and a circulant matrix, which satisfies the RIP condition while reducing the complexity of hardware implementation.

[0067] 3. The computational complexity of the algorithm designed by the present invention is reduced, meeting the needs of real-time monitoring and online fault diagnosis.

[0068] 4. The present invention adds regularization terms and adaptive thresholds to the OMP algorithm to improve reconstruction accuracy and noise resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The overall flow chart provided for the present invention;

[0070] Figure 2 A schematic diagram of the structure of the optimized measurement matrix provided by the present invention;

[0071] Figure 3 A schematic diagram of the improved K-SVD algorithm provided by the present invention;

[0072] Figure 4 A flow chart of the improved OMP reconstruction algorithm provided by the present invention;

[0073] Figure 5 This is a comparison diagram of the signal before and after reconstruction provided by the present invention. DETAILED DESCRIPTION

[0074] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] like Figure 1-Figure 5 As shown, in order to verify the effectiveness of the method of the present invention, a real gear vibration signal is processed.

[0076] Step 1: Data collection and preprocessing

[0077] Data collection:

[0078] A multi-channel accelerometer is used to collect gear vibration signals with a frequency range of 0.1 kHz to 20 kHz.

[0079] The sampling frequency is set to , the number of sampling points for each channel is point.

[0080] Get the original signal set .

[0081] Data preprocessing:

[0082] Remove DC component: For each channel signal , calculate its mean and remove: .

[0083] Normalization: Normalize the signal amplitude to the [-1,1] interval:

[0084] Noise reduction: wavelet denoising method is used, Daubechies 4 wavelet basis is selected, multi-scale decomposition and reconstruction of the signal is performed to remove high-frequency noise and obtain the preprocessed signal .

[0085] Step 2: Adaptive sparse dictionary learning:

[0086] Improved K-SVD algorithm:

[0087] Set the number of dictionary atoms , sparsity , .

[0088] Initialize the dictionary and generate randomly , and normalize the columns.

[0089] Sparse coding: For each preprocessed signal , solve for the sparse coefficient .

[0090] Dictionary update: for each dictionary atom to update.

[0091] Convergence condition: When the number of iterations reaches 50 or the dictionary change is less than the threshold, the iteration stops.

[0092] Step 3: Optimize the measurement matrix design:

[0093] Construct a matrix that satisfies the combined measurement :

[0094] Weighted Random Toeplitz Matrix :

[0095] Randomly generate sequence , the length is .

[0096] Weight vector Set to:

[0097] ,in, Control weight distribution;

[0098] Build ;

[0099] Circular Matrix :

[0100] Randomly generate sequence , the length is

[0101] Build ;

[0102] Combined to get the measurement matrix , .

[0103] Step 4: Compressed Sampling:

[0104] For each preprocessed signal , perform compressed sampling: .

[0105] Step 5: Signal reconstruction:

[0106] Improved OMP algorithm:

[0107] Parameter setting: Regularization parameters , adaptive threshold .

[0108] Iterative process: residuals ; Iteratively select atoms and update the support set and sparse coefficients.

[0109] When the residual satisfies Or the number of iterations reaches When , stop the iteration.

[0110] Reconstruct the signal:

[0111] Step 6: Output the results

[0112] Output the reconstructed signal .

[0113] Result analysis:

[0114] Performance indicators:

[0115] Mean Square Error (MSE): ;

[0116] Signal-to-noise ratio calculation:

[0117] Structural Similarity Index (SSIM): Evaluates the similarity of the reconstructed signal to the original signal in terms of structure, brightness, and contrast.

[0118] Experimental results:

[0119]

[0120] SNR (Signal-to-Noise Ratio) is an indicator that measures the relative strength of signal and noise and is often used to evaluate signal quality. The higher the SNR value, the higher the proportion of useful information in the signal and the smaller the impact of noise.

[0121] ;

[0122] in conclusion:

[0123] The method of the present invention realizes accurate reconstruction of gear vibration signals at a lower sampling rate. Through adaptive sparse representation and optimized measurement matrix design, the reconstruction accuracy and efficiency are improved, the anti-noise performance is enhanced, and the needs of real-time monitoring and fault diagnosis are met.

[0124] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A compressed sensing method for gear vibration signals based on adaptive sparse representation, comprising the following steps: (1) Data collection and preprocessing: 1.1) Use a multi-channel vibration sensor to collect gear vibration signals and obtain the original signal set ; 1.2) Remove the DC component, normalize and reduce noise of the original signal to obtain the preprocessed signal set ; It is characterized by: (2) Adaptive sparse dictionary learning: 2.1) Use the improved K-SVD algorithm to learn the dictionary of the preprocessed signal and construct an adaptive sparse dictionary and the sparse coefficient matrix , to improve the sparse representation ability of the signal; (3) Optimize measurement matrix design: 3.1) Construct a combined measurement matrix of weighted random Toeplitz matrix and circulant matrix ; (4) Compressed sampling: 4.1) Preprocessing signal for each channel Perform compressed sampling to obtain compressed measurement values ;in, For the Compression measurement values ​​for each channel; (5) Signal reconstruction: 5.1) Using the improved OMP algorithm, using the measured value , measurement matrix and adaptive sparse dictionary , solve for the sparse coefficient , reconstruct the signal , and introduce regularization terms and adaptive thresholds to improve reconstruction accuracy and noise resistance performance; the specific steps of the improved OMP algorithm are as follows: 5.1) Initialization: 5.1.1) Residual ; 5.1.2) Support set ; 5.1.3) Number of iterations ; 5.2) Iteration process: 5.2.1) Atom selection: ,in for No. List, Represents the atoms selected in the kth iteration, i.e., the dictionary matrix No. List; Represents the dictionary matrix The j-th vector of represents the residual vector of the kth iteration; represents the j-th column atomic vector With the residual vector The inner product of Represents the jth column and the Naz vector norm, which is the Euclidean length of the vector; Indicates the maximum j value of the objective function; 5.2.2) Support set S update: ; 5.2.3) Sparse coefficient calculation: Solve the following optimization problem: ,in, The current observation signal, that is, the measurement value, is obtained through the measurement matrix The compressed signal; Represents the signal reconstruction error, that is, the observed signal The squared error between the signal reconstructed by the dictionary and Represents the sparse coefficient norm; is an adaptive sparse dictionary The corresponding support set A subset of columns, represents the regularization parameter; 5.2.4) Residual update: ,in, The residual at the k+1th iteration represents the unexplained part of the current signal reconstruction; represents the reconstructed signal obtained in the iteration; 5.2.5) Termination condition: If or , then the iteration stops; among them, Residual norm, indicating the size of the residual in the current iteration; is the preset residual tolerance threshold, indicating the minimum error acceptable for iteration; Indicates the maximum number of iterations; 5.1) Output: Reconstructed signal: ,in, represents the reconstructed signal, represents the optimal sparse coefficient; (6) Result output: 6.1) Output the reconstructed signal set , used for subsequent analysis and processing, the reconstructed signal is applied to spectrum analysis, feature extraction and fault diagnosis.

2. According to the method of compressed sensing of gear vibration signals based on adaptive sparse representation in claim 1, it is characterized in that: the specific algorithm of step 2.1) is as follows: 2.1.1) Initialization settings: Setting up the adaptive sparse dictionary The number of atoms ,satisfy , L is the number of signal samples, sparsity ; 2.1.2) Initialize dictionary: Adaptive sparse dictionary , take a random Gaussian matrix and then normalize each column: ； in, represents the k-th column vector of the dictionary, i.e. the k-th dictionary atom, Representation vector of Euclidean norm; 2.1.3) Sparse coding: For each preprocessed signal , by solving the following optimization objective Solving for sparse coefficients : ; The optimization goal is to find a balance between sparsity and reconstruction error: Item 1: Try to minimize the signal Instead of sparse representation differences to ensure the accuracy of reconstruction; Item 2: Try to minimize of norm to enforce sparsity and suppress redundant non-zero coefficients; By The norm is used as a regularization term to effectively approximate norm problem, while ensuring the convexity of the optimization problem, making it convenient and efficient to solve; in, is the sparsity regularization parameter, which controls the trade-off between sparsity and reconstruction error; 2.1.4) Dictionary update: For each atom dictionary , the dictionary update steps are as follows: 2.1.4.1) Calculate the error matrix: ; in, is a sparse coefficient matrix No. OK; 2.1.4.2) Singular value decomposition SVD: error matrix Perform SVD decomposition: ; 2.1.4.3) Update dictionary atoms and the corresponding sparse coefficients : ; 2.1.4.4) Iteration: Repeat the sparse coding and dictionary updating steps until the adaptive sparse dictionary Convergence or maximum number of iterations reached.

3. The method for compressive sensing of gear vibration signals based on adaptive sparse representation according to claim 1, characterized in that: The step 3.1) constructs a combined measurement matrix of a weighted random Toeplitz matrix and a circulant matrix , the specific steps are as follows: 3.1.1) Weighted Random Toeplitz Matrix The construction steps are as follows: 3.1.1.1) Randomly generate a length of Random sequence of ,in, L represents the original length of the signal, that is, the signal dimension; m represents the target dimension of the measurement matrix, that is, the target number of sampling points; L+M-1 represents the total length of the random sequence, ensuring that all required elements are covered when constructing the Toeplitz matrix. Obey standard normal distribution; 3.1.1.2) Define the weight vector , used for weighting; 3.1.1.3) Construct the Toeplitz matrix: in, Represents the Toeplitz matrix The element in the i-th row and j-th column of ; Indicates that the j-th element of the weight vector is used for weighting; Indicated by The constructed matrix elements use the indexing rule of i-j+L to extract the corresponding elements in the sequence; 3.1.2) Circular Matrix The construction steps are as follows: 3.1.2.1) Randomly generate length sequence , Obey standard normal distribution; 3.1.2.2) Construct the circulant matrix: ,in, Represents a circulant matrix The element in the i-th row and j-th column of ; Represents the circular nature of the modular operation used to determine the location of an index in a matrix; 3.1.3) Combined measurement matrix : The weighted random Toeplitz matrix With the circulant matrix Combined with: , the combined measurement matrix Satisfies the restricted isometry property RIP, where , .

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