A refined feature extraction method for nonlinear recursive characteristics of friction signals

Abstract

This invention discloses a refined feature extraction method for the nonlinear recursive characteristics of friction signals, comprising the following steps: noise reduction and filtering of measured friction signals; phase space reconstruction; construction of a phase trajectory recursion matrix and plotting of a recursion graph; and extraction of texture features of the recursion graph using a local binary model. This invention applies a continuously valued membership function instead of the traditional Heaviside function to identify the recursive characteristics between phase points within the reconstructed phase trajectory, solving the problems of rigid boundaries, information loss, and deviations in recursive analysis results caused by binary values. This invention uses a local binary model to extract texture features of the gray recursion graph, achieving a quantitative description of the nonlinear recursive characteristics of friction signals and further enriching the tribological-dynamic coupling research method. This invention optimizes the recursive characteristic extraction technology for univariate time series of friction signals, thereby realizing an online identification method for the running-in state driven by friction signals, and achieving online real-time monitoring of the wear process of operating equipment.

Description

Technical Field

[0001] This invention relates to signal processing, and in particular to a method for refined feature extraction of nonlinear recursive characteristics of friction signals. Background Technology

[0002] The systemic dependence of friction and wear behavior on running-in control parameters and its time-varying characteristics with the wear process determine the typical nonlinear characteristics of time series signals such as friction coefficient, friction vibration, and temperature. This also leads to the complexity and difficulty of friction and wear research compared to general research. With the rapid development of sensor technology and data analysis methods, constructing a data-driven system for identifying running-in conditions and evaluating quality has gradually become a cutting-edge topic in tribology and related fields. Numerous research results show that, from the perspective of tribological-dynamic coupling, applying fractal and chaotic methods such as correlation dimension, entropy, Lyapunov exponent, and recursive characteristic analysis to reveal the dynamic characteristics and evolution mechanism of friction signals can provide a new perspective for the study of friction and wear behavior. Significant results have been achieved in many fields, including the characterization of chaotic characteristics of tribological behavior, identification and evaluation of running-in conditions, data-driven condition monitoring, and fault diagnosis.

[0003] Compared to traditional chaos analysis methods that rely on correlation dimension and Lyapunov exponents, recursive analysis is an attractor visualization and feature extraction method that focuses on macroscopic recursive graphs and quantitative recursive analysis parameters, considering the relative distances between phase points within the reconstructed high-dimensional phase trajectory. It does not depend on statistical analysis results, thus enabling the analysis of chaotic characteristics in short-term non-stationary time series. However, traditional recursive analysis uses the relative magnitude of the distance between phase points in the reconstructed phase trajectory and a preset recursion threshold as the criterion for whether recursive behavior occurs in the phase space. This makes the analysis results highly dependent on the value of the recursion threshold. If the preset recursion threshold is too small, there may be almost no recursive points in the reconstructed recursive graph except for the main diagonal, failing to accurately characterize the recursive characteristics of the system. Conversely, an excessively large recursion threshold will cause almost all phase points to exhibit recursive behavior with other phase points, resulting in a large amount of false information. Currently, the selection of recursion thresholds is mostly based on specific problems, and a unified method has not yet been formed, exhibiting a certain degree of subjective dependence and empirical reliance, posing challenges to the reliability, stability, and universality of recursive analysis results.

[0004] Furthermore, traditional recursive analysis is based on the expansion of a 0-1 binary recursive matrix constructed using the Heaviside function. This means that the coordinates corresponding to the two states where recursion occurs are labeled "1", and vice versa. This approach divides all phase points within the phase trajectory into two categories: one category consists of phase points located inside a hypersphere centered on a reference phase point with a preset recursion threshold as its radius; the other category consists of phase points located outside the hypersphere. This ignores the differences between the two categories of phase points, easily leading to the loss of dynamic information from the original complex system. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a refined feature extraction method for the nonlinear recursive characteristics of friction signals. Considering that the recursive matrix obtained from reconstruction has elements ranging from 0 to 1, it is treated as a grayscale value. This can be applied to grayscale images with different texture features for visualization. Furthermore, grayscale image analysis techniques such as Local Binary Model (LBP) are used to extract the texture features of the grayscale image, achieving a quantitative description of the recursive characteristics of the reconstructed phase trajectory. Based on this, the sliding window method is combined to characterize the dynamic behavior of the tribological system as it changes with the wear process, realizing data-driven tribological system state identification and monitoring.

[0006] Technical Solution: The technical problem this invention aims to solve is a refined feature extraction method for the nonlinear recursive characteristics of friction signals. Traditional recursive analysis relies heavily on preset recursion thresholds and suffers from the loss of system dynamics information due to the reconstruction of a 0-1 binary recursive matrix using the Heaviside function. This invention proposes to introduce a membership function to evaluate whether recursion occurs between phase points in a phase trajectory. This criterion satisfies the following two conditions: First, the function value is inversely proportional to the distance between phase points; that is, the closer the states of the phase points are, the closer the membership function value is to 1, and vice versa. Second, the membership function has no rigid boundaries, and the recursive state between phase points can be described by continuous values ​​within the interval [0,1], thereby more accurately measuring the recursive characteristics of the phase trajectory.

[0007] The present invention provides a method for refined feature extraction of nonlinear recursive characteristics of friction signals, comprising the following steps:

[0008] (1) Noise reduction and filtering of measured friction signals: The friction signals collected during the friction and wear experiment were filtered and denoised using the Wavelet Toolbox in MATLAB to extract the effective components.

[0009] (2) Phase Space Reconstruction: According to the embedding theorem, for a d-dimensional chaotic attractor, there can always be an m-dimensional (satisfying m≥2d+1) embedding space that is topologically equivalent to the original dynamic system. For a one-dimensional time series {x} with unknown prior information... i}, i = 1, 2, 3, ..., n, adopt the phase space reconstruction method based on coordinate delay, that is, reconstruct the sequence {x} according to the time interval τ. i Take values ​​from} and construct vector Xi:

[0010] X i =[x i ,x i+τ ,x i+2τ ,...,x i+(m-1)τ ], i = 1, 2, ..., N

[0011] m is the embedding dimension, calculated using the spurious nearest neighbor method; τ is the delay time, calculated using the mutual information method.

[0012] The m-dimensional phase space matrix is ​​constructed as follows:

[0013] X = [X1, X2, ..., X i ,...,X N ] T

[0014] In the formula, N is the number of phase space vectors after reconstruction, N = n - (m - 1)τ.

[0015] In step (2), the selection method for phase space reconstruction parameters is as follows: For a time series signal with a data volume of n, starting from the first data, take the data within a calculation window of length T to form a subsequence. Calculate the delay time and embedding dimension of the subsequence according to the mutual information method (MI) and the false nearest neighbor method (FNN). Then, slide the window backward along the time axis with a sliding step size of T to obtain the next subsequence and calculate its delay time and embedding dimension. Repeat the above process until the last point of all data. Then, use statistical methods to determine the optimal phase space reconstruction parameters for the entire sequence, that is, select the delay time and embedding dimension with the highest frequency as the final phase space reconstruction parameters.

[0016] (3) Construct the phase trajectory recursion matrix and draw the recursion graph: Apply the membership function R ij =cos[πd ij / 2max(d ij The Heaviside function replaces the relative distance between phase points in the reconstructed phase trajectory, where d ij =||X i -X j || represents the phase point X i and X j Euclidean distance between them, max(d ijThe maximum distance between all phase points within the phase trajectory is denoted as . Since the membership function is a function that can take continuous values ​​in the interval [0,1] and is inversely proportional to the distance between phase points, it can effectively eliminate the binary value and rigid boundary caused by the Heaviside function. In addition, the recursive matrix constructed based on the membership function does not contain the recursive threshold variable, which can avoid the deviation of the recursive analysis results caused by improper recursive threshold values. Thus, the recursive matrix for reconstructing the phase trajectory is constructed.

[0017] Treating each element in the reconstructed recursion matrix as a grayscale value, a grayscale recursion graph is drawn in a two-dimensional plane: State X i and X j The more similar the elements R ij The closer the value is to 1, the darker the corresponding position in the gray recursive graph; conversely, the darker the value of the state vector X... i and X j The lower the similarity, the better the R ij The closer the value is to 0, the lighter the color of the corresponding position in the image.

[0018] (4) Extracting recursive graph texture features of membership function using Local Binary Model (LBP): LBP is an operator used to describe the local texture features of an image. It is defined in a 3×3 window and consists of a center pixel and eight neighboring pixels. The center pixel of the window is the threshold. All neighboring pixels are compared with the center pixel. If a neighboring pixel is greater than the center pixel, it is marked as 1; otherwise, it is marked as 0. In this way, a string of 8-bit binary characters will be obtained in the defined 3×3 image block. These binary characters will be arranged in a certain order to generate a binary number. The decimal value corresponding to this binary value is the LBP feature value of the center pixel of the window. This LBP feature value represents the texture information of the surrounding area of ​​this center pixel. Calculating the LBP feature value for each pixel in the image can obtain the LBP feature map of the image. However, the discrimination effect is not ideal in some cases. Therefore, the LBP map is not directly used as a feature vector for classification and recognition. Instead, the statistical histogram of LBP features is used as the feature vector.

[0019] In step (4), the LBP texture feature vector can be represented by the image block LBP histogram. First, the image is divided into several N×N image sub-blocks, and the LBP value of each pixel in each sub-block is calculated. Then, histogram statistics are performed on each sub-block to obtain the histogram of the N×N image sub-blocks. Finally, the histograms of all image sub-blocks are normalized, and the normalized histograms of all sub-blocks are connected to obtain the texture features of the entire image, which is used for classification and recognition of the LBP feature vector.

[0020] A computer storage medium storing a computer program that, when executed by a processor, implements a refined feature extraction method for the nonlinear recursive characteristics of friction signals, as described above.

[0021] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described method for refining the nonlinear recursive characteristics of friction signals.

[0022] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0023] 1. This invention uses a continuously valued membership function instead of the traditional Heaviside function to identify the recursive characteristics between phase points within the reconstructed phase trajectory, thus solving the rigid boundary caused by binary value, as well as the information loss and deviation of recursive analysis results caused by improper recursive threshold values.

[0024] 2. This invention applies a local binary model to extract texture features from a gray recursive graph, thereby achieving a quantitative description of the nonlinear recursive features of friction signals and further enriching the tribological-dynamic coupling research method.

[0025] 3. This invention optimizes the recursive characteristic extraction technology of univariate time series of friction signals, and combines the sliding window method to characterize the evolution law of the dynamic recursive characteristics of friction signals with the wear process, thereby realizing the online identification method of running-in state driven by friction signals, and realizing online real-time monitoring of the wear process of operating equipment. Attached Figure Description

[0026] Figure 1 This is a flowchart of friction signal analysis and processing;

[0027] Figure 2 This is a signal diagram after noise reduction in an embodiment;

[0028] Figure 3 The delay time map is determined using the MI method;

[0029] Figure 4 The embedding dimension graph is determined using the FNN method;

[0030] Figure 5 This is a frequency statistics chart of the delay time after using the sliding window method;

[0031] Figure 6 It is a frequency statistics chart of the embedded dimensions after using the sliding window method;

[0032] Figure 7 It is a recursive graph of membership functions generated by membership functions;

[0033] Figure 8 It is a traditional recursive graph generated using the Heaviside function;

[0034] Figure 9 The texture feature histogram for the 76s–150s period of break-in wear was extracted using the LBP model based on the membership recursive graph.

[0035] Figure 10 The texture feature histogram for the 151s–225s period of break-in wear was extracted using the LBP model based on the membership recursive graph.

[0036] Figure 11 The texture feature histogram for the 901s–975s period of stable wear was extracted using the LBP model based on the membership recursion graph.

[0037] Figure 12 The texture feature histogram for the stable wear period from 976s to 1050s was extracted using the LBP model based on the membership recursion graph. Detailed Implementation

[0038] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0039] like Figure 1 As shown, a method for refined feature extraction of nonlinear recursive characteristics of friction signals includes the following steps:

[0040] Step 1: Noise Reduction and Filtering of Measured Friction Signals. The friction signals collected during the friction and wear experiment were filtered and denoised using the Wavelet Toolbox in MATLAB to extract effective nonlinear components.

[0041] Step 2: Phase Space Reconstruction. The friction signal is decomposed into several continuous, non-overlapping computational windows containing equal data lengths using the sliding window method. Based on the time-delay phase space reconstruction theory, the time delay τ and embedding dimension m of each computational window are extracted. Using statistical methods, the most frequently occurring parameters m and τ are selected as appropriate embedding dimensions and time delays. Then, the single-dimensional time series signal {x(t)|t=1,2,…,n} within each computational window is reconstructed into a high-dimensional phase space.

[0042] X t =[x t ,x t+τ ,x t+2τ ,...,x t+(m-1)τ ],t=1,2,...,N

[0043] X = [X1, X2, ..., X i ,...,X N ] T

[0044] m is the embedding dimension, τ is the delay time, and N is the number of phase space vectors after reconstruction, N = n - (m - 1).

[0045] Step 3: Construct the phase trajectory recursion matrix and draw the recursion graph. The membership function is a function that can take continuous values ​​in the interval [0,1] and is inversely proportional to the distance between phase points; that is, the larger the difference between two points, the weaker the support between them. Therefore, it can effectively eliminate the binary value and rigid boundary caused by the Heaviside function. In addition, the recursion matrix constructed based on the membership function does not contain the recursion threshold variable, which can avoid the deviation of the recursion analysis results caused by improper recursion threshold values. Thus, the recursion matrix for reconstructing the phase trajectory is constructed, and the membership function recursion graph is generated.

[0046]

[0047] Where d ij =||X i -X j ||,i,j∈{1,2,…,N}

[0048] Step 4: Use the Local Binary Model (LBP) to extract the recursive graph texture features of the membership function.

[0049] LBP texture feature vectors are generally represented by LBP histograms of image blocks. The steps are as follows:

[0050] (1) Divide the image into several N×N image sub-blocks (e.g., 16×16) and calculate the LBP value of each pixel in each sub-block.

[0051] (2) Perform histogram statistics on each sub-block to obtain the histogram of N×N image sub-blocks.

[0052] (3) Normalize the histograms of all image sub-blocks, and connect the normalized histograms of all sub-blocks to obtain the texture features of the entire image.

[0053] Example:

[0054] Run-in friction experiments were conducted using a rotary friction and wear testing machine, with annular disc specimens as the friction pair, under lubricated conditions. The annular specimen was made of bearing steel, and the disc specimen was made of carbon steel. The sliding speed was set to 0.91 m / s, the normal phase pressure to 1.05 MPa, and the sampling frequency to 20 Hz.

[0055] After integrating and processing the friction signals obtained from the experiments, the Wavelet Toolbox in MATLAB was used for filtering and noise reduction to extract the effective components. For example... Figure 2 This is a diagram of the running-in friction signal after noise reduction.

[0056] A statistical method for selecting phase space reconstruction parameters is used. For a time series signal with 22,500 data points, a subsequence is constructed by taking data within a computational window of length 1,500, starting from the first data point. The delay time and embedding dimension of this subsequence are calculated using mutual information (MI) and spurious nearest neighbor (FNN) methods. Figure 3 The delay time map is determined using the MI method, such as... Figure 4 The embedding dimension graph is determined using the FNN method.

[0057] The window is then slid backward along the time axis, with a step size of 1500, to obtain the next subsequence and calculate its delay time and embedding dimension. This process is repeated until the last point of all data is collected. Then, statistical methods are used to determine the optimal phase space reconstruction parameters for the entire sequence, i.e., selecting the delay time and embedding dimension with the highest frequency as the final phase space reconstruction parameters, such as... Figure 5 This refers to the frequency statistics of delay times after using the sliding window method, such as... Figure 6 This is a frequency statistics chart of the embedding dimensions after using the sliding window method. It can be seen that m=6 and τ=2 are the optimal phase space reconstruction parameters.

[0058] Construct the phase trajectory recurrence matrix using membership functions and draw the recurrence graph, such as Figure 7 It is a recursive graph of membership functions generated by membership functions. Figure 8 It is a traditional recursive graph generated by the Heaviside function.

[0059] contrast Figure 7 and Figure 8 As can be seen, compared with the recursive graph generated by the traditional Heaviside function, the method described in this invention can refine the differences between each pixel and can more completely preserve the time series feature information.

[0060] Local Binary Model (LBP) is used to extract recursive graph texture features based on membership functions, such as... Figure 9 This involves extracting the texture feature histogram for the 76s–150s break-in period using the LBP model based on a membership recursive graph; for example... Figure 10 Based on the membership recursive graph, the LBP model was used to extract the texture feature histogram for the 151s–225s break-in friction period; such as Figure 11 Based on the membership recursive graph, the LBP model was used to extract the texture feature histogram for the 901s–975s period of break-in friction; such as Figure 12 Based on the membership recursive graph, the LBP model was used to extract the texture feature histogram during the break-in friction period from 976s to 1050s.

Claims

1. A method for refined feature extraction of nonlinear recursive characteristics of friction signals, characterized in that, Includes the following steps: (1) Noise reduction and filtering of measured friction signals: The friction signals collected during the friction and wear experiment were filtered and denoised using the Wavelet Toolbox in MATLAB to extract the effective components; (2) Phase space reconstruction: For a one-dimensional time series {x} with unknown prior information... i }, i = 1, 2, 3, ..., n, adopt the phase space reconstruction method based on coordinate delay, that is, reconstruct the sequence {x} according to the time interval τ. i Take values ​​from} and construct vector Xi: X i =[x i ,x i+τ ,x i+2τ ,...,x i+(m-1)τ ],i=1,2,...,N m is the embedding dimension, calculated using the spurious nearest neighbor method; τ is the delay time, calculated using the mutual information method. The m-dimensional phase space matrix is ​​constructed as follows: X=[X1,X2,…,X i ,…,X N ] T In the formula, N is the number of phase space vectors after reconstruction, N = n - (m - 1)τ; (3) Construct the phase trajectory recursion matrix and draw the recursion graph: Apply the membership function R ij =cos[πd ij / 2max(d ij The Heaviside function replaces the relative distance between phase points in the reconstructed phase trajectory, where d ij =||X i -X j || represents the phase point X i and X j Euclidean distance between them, max(d ij This represents the maximum distance between all phase points within the phase trajectory. Treating each element in the reconstructed recursion matrix as a grayscale value, a grayscale recursion graph is drawn in a two-dimensional plane: State X i and X j The more similar the elements R ij The closer the value is to 1, the darker the corresponding position in the gray recursive graph; conversely, the darker the value of the state vector X... i and X j The lower the similarity, the better the R ij As the value approaches 0, the corresponding position in the image becomes lighter in color. (4) Extracting Recursive Graph Texture Features of Membership Function Using Local Binary Model: LBP is an operator used to describe the local texture features of an image. It is defined in a 3×3 pane and consists of a center pixel and eight neighboring pixels. The center pixel of the window is the threshold. All neighboring pixels are compared with the center pixel. If a neighboring pixel is greater than the center pixel, it is marked as 1; otherwise, it is marked as 0. In this way, a string of 8-bit binary characters will be obtained in the defined 3×3 image block. These binary characters will be arranged in a certain order to generate a binary number. The decimal value corresponding to this binary value is the LBP feature value of the center pixel of the window. This LBP feature value represents the texture information of the surrounding area of ​​this center pixel. Calculating the LBP feature value for each pixel in the image can obtain the LBP feature map of the image. However, the differentiation effect is not ideal in some cases. Therefore, the LBP map is not directly used as a feature vector for classification and recognition. Instead, the statistical histogram of LBP features is used as the feature vector.

2. The method for refined feature extraction of nonlinear recursive characteristics of friction signals according to claim 1, characterized in that, In step (2), the selection method for phase space reconstruction parameters is as follows: For a time series signal with a data volume of n, starting from the first data, take the data within a calculation window of length T to form a subsequence. Calculate the delay time and embedding dimension of the subsequence according to the mutual information method and the spurious nearest neighbor method. Then, slide the window backward along the time axis with a sliding step size of T to obtain the next subsequence and calculate its delay time and embedding dimension. Repeat the above process until the last point of all data. Then, use statistical methods to determine the optimal phase space reconstruction parameters for the entire sequence, that is, select the delay time and embedding dimension with the highest frequency as the final phase space reconstruction parameters.

3. The method for refined feature extraction of nonlinear recursive characteristics of friction signals according to claim 1, characterized in that, In step (4), the LBP texture feature vector can be represented by the image block LBP histogram. First, the image is divided into several N×N image sub-blocks, and the LBP value of each pixel in each sub-block is calculated. Then, histogram statistics are performed on each sub-block to obtain the histogram of the N×N image sub-blocks. Finally, the histograms of all image sub-blocks are normalized, and the normalized histograms of all sub-blocks are connected to obtain the texture features of the entire image, which is used for classification and recognition of the LBP feature vector.

4. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a method for refined feature extraction of nonlinear recursive characteristics of friction signals as described in any one of claims 1-3.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a method for refined feature extraction of nonlinear recursive characteristics of friction signals as described in any one of claims 1-3.

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