Running-in wear dynamic behavior characterization method based on gray texture recurrence plot

Abstract

The invention discloses a running-in and wear dynamic behavior characterization method based on a gray texture recurrence plot, and relates to the technical field of complex nonlinear signal processing, and the method comprises the steps: S1, carrying out the preprocessing of a friction signal outputted in a running-in and wear process, obtaining a pure friction signal, and storing the pure friction signal in a computer in a time sequence format; s2, setting a window length, and decomposing all the friction signal time sequences into a plurality of continuous and non-overlapped calculation windows; s3, time delay and embedded dimension parameters are calculated for the friction signals in each window, the frequency of two sets of parameters in all the windows is counted, the parameter with the highest occurrence frequency is selected as the same parameter, and phase-space reconstruction is conducted on the friction signal time sequence in all the windows. According to the macroscopic mode and quantitative parameters, the dynamic characterization research of the running-in wear behavior is carried out from the tribology-dynamics coupling angle, and a new perspective is provided for running-in state identification.

Description

Technical Field

[0001] The present invention relates to the technical field of complex nonlinear signal processing, and in particular to a method for characterizing running-in wear dynamics behavior based on a grayscale texture recursive graph. Background Art

[0002] The dynamics of tribological systems dictate that the friction and wear behaviors or phenomena occurring within them exhibit time-varying characteristics, necessitating the study of the system's dynamic characteristics and laws at an appropriate time scale. Furthermore, friction and wear behavior exhibits complex characteristics such as strong nonlinearity, randomness, and chaos. Therefore, coupled tribological and dynamic research methods, exemplified by chaos and attractor theory, have become an important means and method for characterizing friction and wear behavior.

[0003] When using chaos and attractor theory to study the problem of running-in wear, it is usually necessary to divide the entire running-in wear process into several stages (calculation windows), and then reveal the intrinsic characteristics of the evolution law of the friction and wear process based on the change law of the phase trajectory morphology or characteristic parameters. However, the time-varying nature of the running-in pattern process determines that the fluctuation degree and trend component of the friction signal in different stages are significantly different, resulting in the problem of inconsistent optimal input parameters when calculating some characteristic parameters. Taking the running-in wear study based on the recursive characteristics of the attractor as an example, it can be seen from the definition that the macroscopic pattern, microstructure and quantitative recursive parameters of the recursive graph output are highly dependent on the selection of input parameters such as embedding dimension, time delay, neighborhood radius, etc. The determination of the above parameters still relies on the subjective judgment or experience of the researchers. This leads to the possibility that the recursive analysis results may be highly subjective, which has a significant impact on the stability and reliability of the research results.

[0004] To this end, the present invention proposes a method for characterizing the dynamic behavior of running-in wear based on grayscale texture recursive graphs, aiming to construct a recursive characteristic criterion that is independent of the neighborhood radius value, which is used to identify whether recursion occurs in the attractor phase trajectory; at the same time, to facilitate subsequent visualization and quantitative characterization, the function value output by the criterion is set to a grayscale value from 0 to 1; in addition, statistical analysis will be introduced to further reduce the influence of embedding dimension and time delay parameters on the analysis results, and the dynamic characterization study of running-in wear behavior will be realized with the help of grayscale texture recursive graphs and corresponding quantitative parameters. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems in the prior art and to propose a method for characterizing the running-in wear dynamics behavior based on grayscale texture recursive graph.

[0006] A method for characterizing running-in wear dynamics behavior based on grayscale texture recursive graphs comprises the following steps:

[0007] S1, pre-process the friction signal output in the running-in wear process to obtain a pure friction signal and store the pure friction signal in a time sequence format to a computer;

[0008] S2, set a window length, and decompose all friction signal time sequences into a plurality of continuous and non-overlapping calculation windows;

[0009] S3, calculate the time delay and embedding dimension parameters of the friction signal in each window, and count the frequencies of the two groups of parameters in all windows, select the parameter with the highest occurrence frequency as the same parameter, and reconstruct the friction signal time sequence in all windows in a phase space;

[0010] S4, analyze the recursive characteristics of the reconstructed phase space trajectory, extract the macroscopic features and quantitative parameters of the gray texture recursive graph, and reveal the evolution law of the running-in wear dynamics behavior according to the change law of the macroscopic mode and the quantitative parameters of the recursive graph with the calculation window, and then realize the online identification of the running-in state.

[0011] Preferably, in the step S1, the pre-processing of the friction signal comprises:

[0012] Interval sampling: using the equal interval sampling function x c =downsample(x t ,n) of MATLAB to reduce the sampling frequency of the analysis sequence by an integer multiple of 1 / n, wherein x t , x c are the original sequence and the calculation sequence obtained by interval sampling respectively, and n represents the ratio of the test sampling data amount to the calculation sequence data amount;

[0013] Noise reduction filtering: using the wavelet toolbox of MATLAB, under the premise of reasonably selecting the wavelet basis and the decomposition layer number M, performing multi-scale decomposition on the calculation sequence x c , threshold quantizing the high-frequency detail components from the first to the Mth layer, and combining the low-frequency components to obtain the denoising sequence x cd .

[0014] Preferably, in the step S2, the specific steps of dividing the friction signal calculation window comprise: setting a reasonable sub-interval length s according to the data amount of the calculation sequence and the interval sampling rate, and decomposing all analysis sequences with a sequence length of N into continuous and non-overlapping calculation windows, is a ceiling function; for the first to the N s -1th window, the data contained in each window can be expressed as:

[0015] data(i)=x cd [(i-1)·s+1:i·s];

[0016] The data contained in the last window can be expressed as:

[0017] data(N s )=x cd [(N s -1)·s+1:end].

[0018] Preferably, in step S3, the specific steps of reconstructing the phase space of the friction signal time series include:

[0019] (1) For each calculation window, the time delay τ is calculated using the mutual information method and the false nearest neighbor method. i and embedding dimension m i ;

[0020] (2) The two sets of parameters calculated in all calculation windows are statistically analyzed, and the time delay τ with the highest frequency and the largest embedding dimension m are selected as the final phase space reconstruction parameters. On this basis, the phase space reconstruction of the friction signal is realized.

[0021] Preferably, in step S4, the specific steps of extracting the friction signal grayscale texture recursive map and quantization parameters include:

[0022] (1) For the high-dimensional phase space matrix reconstructed in each calculation window, the relative distance between two phase points is calculated using the maximum norm to obtain the distance matrix d ij =||X i -X j || ∞ , where X i 、X j are the coordinates of the two phase points at time i and j in the phase space trajectory respectively;

[0023] (2) Applying Gaussian function GR ij =exp[-(d ij ) 2 / (2σ 2 )], where σ represents {d ij The distance between each phase point in the phase trajectory is mapped to the interval [0,1] to obtain the gray recursive matrix GR. The colormap(flipud(gray)) function is then used to complete the grayscale recursive matrix visualization and obtain the corresponding grayscale texture recursive map to achieve the quantitative expression of the recursive degree between phase points.

[0024] (3) The obtained grayscale recursive matrix is ​​subjected to singular value decomposition, and its singular spectral entropy is calculated. Combined with the above-mentioned grayscale texture recursive map macro pattern, the dynamic characterization of the friction and wear behavior during the running-in wear process is realized.

[0025] A computer storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for characterizing the running-in wear dynamics behavior based on a grayscale texture recursive graph.

[0026] 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, the method for characterizing the dynamic behavior of running-in wear based on a grayscale texture recursive graph is implemented.

[0027] Compared with the existing technology, the advantages of the present invention are:

[0028] 1. The present invention fully considers the time-varying characteristics of the running-in wear process, proposes a method for determining phase space reconstruction parameters based on statistical analysis results, and a method for identifying attractor recursive characteristics that avoids the neighborhood radius threshold, which significantly improves the accuracy of the recursive analysis results.

[0029] 2. The present invention establishes a grayscale texture recursive map of friction signals and reconstructed phase trajectories, and conducts a dynamic characterization study of running-in wear behavior from the perspective of tribology-dynamics coupling based on its macroscopic pattern and quantitative parameters, providing a new perspective for running-in state identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Flowchart of the present invention.

[0031] Figure 2 This is the original output of the running-in wear test of an embodiment of the present invention and the time domain diagram of the friction signal obtained after preprocessing.

[0032] Figure 3 It is the optimal phase space reconstruction parameter calculated based on mutual information and false neighbor method within four calculation windows in the present invention.

[0033] Figure 4 It is the distribution histogram of the optimal phase space reconstruction parameters in all calculation windows in the present invention.

[0034] Figure 5 This is a visualization result diagram of the distance matrix of a calculation window (Window 34) and the grayscale recursive matrix based on the Gaussian function in the present invention.

[0035] Figure 6 Partial results of the grayscale texture recursive graph of the friction signal in an embodiment of the present invention.

[0036] Figure 7 This is a diagram showing the evolution of the singular spectral entropy of the grayscale texture recursive graph of the friction coefficient signal during the running-in process in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to make the technical means, creative features, purposes and effects of the present application easy to understand, the present application is further described below in conjunction with specific embodiments.

[0038] Referring to Figure 1 The method for characterizing the running-in wear dynamics behavior based on the gray texture recursive graph, as shown in the figure, comprises the following steps:

[0039] S1, pre-process the friction signal output in the running-in wear process to obtain a pure friction signal and store it in a time sequence format to a computer;

[0040] The pre-processing of the friction signal comprises:

[0041] Interval sampling: use the equal interval sampling function x c = downsample(x t , n) of MATLAB to reduce the sampling frequency of the sequence to be analyzed by an integer multiple of 1 / n, wherein x t , x c are the original sequence and the calculation sequence obtained by interval sampling, respectively, and n represents the ratio of the test sampling data amount to the calculation sequence data amount;

[0042] Noise reduction filtering: use the wavelet toolbox of MATLAB to perform multi-scale decomposition on the calculation sequence x c under the premise of reasonable selection of wavelet basis and decomposition layer number M, threshold quantization is performed on the high-frequency detail components from the first to the Mth layer, and wavelet reconstruction is performed in combination with the low-frequency components to obtain the denoising sequence x cd ;

[0043] First, use the wavelet toolbox in MATLAB for signal denoising: for the original friction signal obtained by the experiment, first use the wavedec(x t , 5, 'db4') function to perform 5-layer decomposition on the converted signal x t with 'db4' as the wavelet, secondly use the thselect('x t ','minimaxi') function to obtain the fixed threshold value of the signal, and according to the fixed value, use the wdencmp('gbl', c, l, 'db4', 5, thr,'s', 1) function to complete the denoising processing of the signal x t , and finally use the downsample(x t , n) function to perform frequency reduction (i.e. interval) sampling on the original signal x t , wherein n is the multiple of reducing the original sampling frequency, i.e. the denoised signal sequence x cd is obtained.

[0044] More specifically, the original signal is decomposed by 5 layers using db4 as the wavelet base, the signal is denoised according to the minimaxi threshold method, and the friction signal is downsampled by the function x t ,30) to obtain a denoised and downsampled signal with a frequency of 20 Hz as the subsequent research object.

[0045] S2, setting the window length, decomposing the entire friction signal time sequence into several continuous and non-overlapping calculation windows;

[0046] In the step S2, the specific steps of dividing the friction signal calculation window include: setting a reasonable sub-interval length s according to the data amount and interval sampling rate of the calculation sequence, decomposing the entire sequence with a sequence length of N into continuous and non-overlapping calculation windows, is a ceiling function; for the first to the N s th window, the data contained in each window can be expressed as:

[0047] data(i)=x cd [(i-1)·s+1:i·s];

[0048] The data contained in the last window can be expressed as:

[0049] data(N s )=x cd [(N s -1)·s+1:end]。

[0050] S3, calculating the time delay and embedding dimension parameters of the friction signal in each window, and counting the frequencies of the two groups of parameters in all windows, selecting the parameter with the highest frequency as the same parameter, and reconstructing the phase space of the friction signal time sequence in all windows;

[0051] In the step S3, the specific steps of reconstructing the phase space of the friction signal time sequence include:

[0052] (1) for each calculation window, the mutual information method and the false nearest neighbor method are used to calculate the time delay τ i and the embedding dimension m i in turn;

[0053] (2) statistically analyzing the two groups of parameters calculated in all calculation windows, selecting the time delay τ with the highest frequency and the maximum embedding dimension m as the final phase space reconstruction parameters, and realizing the phase space reconstruction of the friction signal on this basis, obtaining a high-dimensional space equivalent to the original system in topological sense to reproduce the dynamic characteristics of the running-in wear process.

[0054] The constructed high-dimensional phase space X=[X1,X2,…,X k ,…,X N ] T , where X k =[x k ,x k+τ ,…,x k+(m-1)τ ], k=1,2,…,n-(m-1)τ;

[0055] More specifically, the mutual information method is used to determine the time delay. For a univariate time series {x i ,i=1,2,3,…,n}, x can be obtained according to the following formula n and x n+τ The average mutual information between

[0056]

[0057] Where S=x(t), Q=(x+τ), P s (s i ), P q (q j ) and P sq (s i ,q j ) represent the probability densities of the discrete sequences S and Q, and the joint probability of their simultaneous measurement, respectively. Clearly, I(Q,S) is a function of τ, denoted as I(τ). The optimal delay time is chosen by selecting τ at the first local minimum of I(τ). The embedding dimension is determined using the false nearest neighbor method. When the embedding dimension is small, false nearest neighbors exist in the phase space. As m increases, false nearest neighbors are gradually eliminated. When the proportion of false nearest neighbors no longer changes with dimension, the phase space is considered fully expanded. Therefore, the dimension at which the proportion of the first false nearest neighbor is zero is selected as the optimal embedding dimension.

[0058] S4. Perform recursive characteristic analysis on the reconstructed phase space trajectory to extract the macroscopic features and quantitative parameters of the grayscale texture recursive graph; based on the change pattern of the macroscopic pattern and quantitative parameters of the recursive graph with the calculation window, reveal the evolution law of the running-in wear dynamic behavior, and then realize the online identification of the running-in state.

[0059] In step S4, the specific steps of extracting the friction signal grayscale texture recursive map and quantization parameters include:

[0060] (1) For the high-dimensional phase space matrix reconstructed in each calculation window, the relative distance between two phase points is calculated using the maximum norm to obtain the distance matrix d ij =||X i -X j || ∞ =max{|xi -x j |,…,|x i+(m-1)τ -x j+(m-1)τ |}, where X i 、X j are the coordinates of the two phase points at time i and j in the phase space trajectory respectively;

[0061] (2) Applying Gaussian function GR ij =exp[-(d ij ) 2 / (2σ 2 )], where σ represents {d ij The distance between each phase point in the phase trajectory is mapped to the interval [0,1] to obtain the gray recursive matrix GR. The colormap(flipud(gray)) function is then used to complete the grayscale recursive matrix visualization and obtain the corresponding grayscale texture recursive map to achieve the quantitative expression of the recursive degree between phase points.

[0062] In the grayscale texture recursion diagram, the horizontal and vertical coordinates of the graph represent the time corresponding to the phase point, and the corresponding position in the diagram is a gray pixel, which describes the relative distance between the phase points at the two corresponding time points. The darker the pixel color, the closer the state between the phase points at the corresponding time points is, and the higher the probability of the recursion phenomenon. Conversely, the lighter the color of the pixel, the lower the probability of the recursion phenomenon between the two phase points at the corresponding time points.

[0063] (3) The obtained grayscale recursive matrix is ​​subjected to singular value decomposition, and its singular spectral entropy is calculated. Combined with the above-mentioned grayscale texture recursive map macro pattern, the dynamic characterization of the friction and wear behavior during the running-in wear process is realized.

[0064] According to the recursive gray matrix GR, all its singular values ​​λ are calculated by singular value decomposition method, and the probability density function P(λ) is obtained by calculating the proportion of each non-zero singular value to the sum of all singular values. i ), the corresponding singular spectrum entropy can be calculated by the following formula:

[0065]

[0066] Where λ i is the non-zero singular value of the gray matrix, P(λ i ) represents its probability distribution function. The larger the singular spectrum entropy value, the more information of the matrix is ​​contained in the singular values, the smaller the correlation between the row and column vectors of the matrix, and the more divergent the element distribution. On the contrary, the more singular the grey recursive matrix is, the fewer singular values ​​are needed to reflect most of the matrix information, the smaller its entropy value, and the more concentrated the distribution of matrix elements. Therefore, the intrinsic mechanism of the evolution of the system dynamic behavior can be revealed based on the change of the singular spectrum entropy.

[0067] A computer storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for characterizing the running-in wear dynamics behavior based on a grayscale texture recursive graph.

[0068] 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, the method for characterizing the dynamic behavior of running-in wear based on a grayscale texture recursive graph is implemented.

[0069] Example

[0070] The sliding friction test was carried out on the self-developed friction and wear testing machine (sampling frequency is 600Hz), and the time domain diagram of the original friction coefficient signal output by the sensor is as follows: Figure 2 (a) shows that by applying the wavelet toolbox in MATLAB to perform noise reduction filtering, the noise reduction signal containing effective information is extracted. The timing diagram of the friction signal after noise reduction and frequency reduction is shown in Figure 2 (b) shown.

[0071] The preprocessed signal is divided into several independent calculation windows of equal length with 6000 data points as the unit. The optimal embedding parameters of each independent window are calculated based on the mutual information method and the false nearest neighbor method. Some of the results are shown in the figure. Figure 3 As shown in the figure; the delay time τ and embedding dimension m with the highest frequency of occurrence in the full sequence window are obtained by statistics as the final embedding parameters, and the results are shown in the figure. Figure 4 As shown, τ = 15 and m = 6 are finally selected to complete the reconstruction of the phase space.

[0072] According to the phase space reconstruction results, the distance matrix d between phase points is obtained ij =||X i -X j || ∞ =max{|x i -x j |,…,|x i+(m-1)τ -x j+(m-1)τ |}, by introducing the Gaussian function GR ij =exp[-(d ij ) 2 / (2σ 2 )], map the distance to the [0,1] interval again, and complete the two-dimensional visualization of the [0,1] grayscale matrix to obtain the following Figure 5-6 The grayscale recurrence graph shown, Figure 7 Shown is the evolution law of the singular spectral entropy extracted by the grey recursive matrix and the recursive grayscale image during the running-in process.

[0073] from Figure 6-7It can be seen that: in the initial stage of friction, the surfaces of the friction pairs support each other through very few micro-asperities, and the system is in an extremely unstable state. The darker pixels in the gray texture recursive map are concentrated on both sides of the main diagonal, and the singular spectrum entropy value is large; as the running-in process continues, the friction pairs gradually form a mutually adaptive surface, and the system enters the self-organization stage. The number of phase points experiencing recursive phenomena in the phase trajectory increases, and the dispersion is relatively uniform. The distribution of pixels at different depths in the gray texture recursive map becomes more uniform, and the singular spectrum entropy value shows an oscillating and increasing trend, indicating that the values ​​of the elements in the gray recursive matrix gradually tend to be average; when the system enters the stable wear stage (chaotic stage), the gray texture recursive map exhibits a checkerboard-like structure, indicating that the output friction signal fluctuates relatively smoothly and relatively evenly, and the singular spectrum entropy gradually stabilizes at a certain value.

[0074] Overall, throughout the running-in process, the system's singular spectral entropy shows a pattern of first decreasing dramatically, then increasing continuously, and then stabilizing around a constant value. This completes the behavioral characterization of the running-in wear dynamics of the friction system.

[0075] It is understood from common technical knowledge that the present invention may be implemented by other embodiments that do not depart from its spirit or essential features. Therefore, the embodiments disclosed above are, in all respects, merely illustrative and not exclusive. All modifications within the scope of the present invention or equivalent to the scope of the present invention are intended to be encompassed by the present invention.

Claims

1. A method for characterizing the dynamic behavior of running-in wear based on grayscale texture recursive graph, characterized by: The following steps are involved: S1. Preprocess the friction signal output during the running-in and wear process to obtain a pure friction signal and store it in a computer in a time series format; S2. Set the window length to decompose the entire friction signal time series into several continuous and non-overlapping calculation windows; S3. Calculate the time delay and embedding dimension parameters of the friction signal in each window, count the frequencies of the two sets of parameters in all windows, select the parameter with the most occurrences as the same parameter, and perform phase space reconstruction on the friction signal time series in all windows; S4, performing recursive characteristic analysis on the reconstructed phase space trajectory to extract macroscopic features and quantitative parameters of the grayscale texture recursive graph; Based on the macroscopic pattern of the recursive graph and the variation of quantitative parameters along the calculation window, the evolution law of the running-in wear dynamics behavior is revealed, thereby realizing the online identification of the running-in state.

2. The method for characterizing running-in wear dynamics behavior based on grayscale texture recursive graph according to claim 1, characterized in that: In step S1, preprocessing the friction signal includes: Interval sampling: Use MATLAB's equally spaced sampling function x c =downsample(x t ,n) Reduce the sampling frequency of the sequence to be analyzed by an integer multiple of 1 / n, where x t 、x c are the original sequence and the calculation sequence obtained by interval sampling, respectively; n represents the ratio of the amount of experimental sampling data to the amount of calculation sequence data; Denoising filter: Using the wavelet toolbox of MATLAB, under the premise of reasonably selecting the wavelet basis and the number of decomposition layers M, the calculation sequence x c Perform multi-scale decomposition, perform threshold quantization on the high-frequency detail components from the first to the Mth layer, and combine them with the low-frequency components for wavelet reconstruction to obtain the denoised sequence x cd .

3. The method for characterizing running-in wear dynamics behavior based on grayscale texture recursive graph according to claim 1, characterized in that: In step S2, the specific steps of dividing the friction signal calculation window include: setting a reasonable sub-interval length s according to the data volume and interval sampling rate of the calculation sequence, decomposing all the sequences to be analyzed with a sequence length of N into continuous and non-overlapping calculation windows, is the rounding function; for the first to Nth s -1 window, the data contained in each window can be expressed as: data(i)=x cd [(i-1)·s+1:i·s]; The data contained in the last window can be expressed as: data(N s )=x cd [(N s -1)·s+1:end]。 4. The method for characterizing running-in wear dynamics behavior based on grayscale texture recursive graph according to claim 1, characterized in that: In step S3, the specific steps of reconstructing the phase space of the friction signal time series include: (1) For each calculation window, the time delay τ is calculated using the mutual information method and the false nearest neighbor method. i and embedding dimension m i ; (2) The two sets of parameters calculated in all calculation windows are statistically analyzed, and the time delay τ with the highest frequency and the largest embedding dimension m are selected as the final phase space reconstruction parameters. On this basis, the phase space reconstruction of the friction signal is realized.

5. The method for characterizing running-in wear dynamics behavior based on grayscale texture recursive graph according to claim 1, characterized in that: In step S4, the specific steps of extracting the friction signal grayscale texture recursive map and quantization parameters include: (1) For the high-dimensional phase space matrix reconstructed in each calculation window, the relative distance between two phase points is calculated using the maximum norm to obtain the distance matrix d ij =||X i -X j || ∞ , where X i 、X j are the coordinates of the two phase points at time i and j in the phase space trajectory respectively; (2) Applying Gaussian function GR ij =exp[-(d ij ) 2 / (2σ 2 )], where σ represents {d ij The distance between each phase point in the phase trajectory is mapped to the interval [0,1] to obtain the gray recursive matrix GR. The colormap(flipud(gray)) function is then used to complete the grayscale recursive matrix visualization and obtain the corresponding grayscale texture recursive map to achieve the quantitative expression of the recursive degree between phase points. (3) The obtained grayscale recursive matrix is ​​subjected to singular value decomposition, and its singular spectral entropy is calculated. Combined with the above-mentioned grayscale texture recursive map macro pattern, the dynamic characterization of the friction and wear behavior during the running-in wear process is realized.

6. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for characterizing the running-in wear dynamics behavior based on a grayscale texture recursive graph as claimed in any one of claims 1 to 5 is implemented.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, it implements a method for characterizing the running-in wear dynamics behavior based on a grayscale texture recursive graph according to any one of claims 1 to 5.

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