Mechanical Fault Diagnosis Method Based on Multi-Scale Symbolic Dynamic Entropy High-Density Wavelet

Abstract

A mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelet transform is proposed. This method performs high-density wavelet transforms of different levels on the mechanical fault signal to obtain low-frequency, mid-frequency, and high-frequency components at different levels. At each level, the multi-scale symbolic dynamic entropy values ​​of the low-frequency and mid-frequency components are calculated. The cosine distance between the two multi-scale symbolic dynamic entropy vectors at each level is calculated and used to measure the similarity between the two vectors. The level with the highest similarity between the two entropy vectors is identified, and this level is adaptively determined as the optimal decomposition scale. The mechanical fault signal is then subjected to high-density wavelet transform, and the low-frequency components are reconstructed. The reconstructed signal is analyzed, and the fault type is determined based on fault feature information. This invention effectively solves the problem of adaptively determining the decomposition level based on mechanical fault signal features, has a stronger ability to extract fault feature frequencies, and has broad application prospects in the field of fault diagnosis.

Description

Technical Field

[0001] This invention relates to mechanical fault diagnosis technology, and in particular to a mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelets. Background Technology

[0002] In the field of mechanical fault diagnosis, signal processing is a crucial technique. Vibration signal analysis is one of the most commonly used methods, with the key being the extraction of fault features. High-density wavelet transform (HDW) is an emerging wavelet analysis technique that can achieve high-precision time-frequency analysis and has the advantage of near-translation invariance. HDW is implemented using a three-channel filter bank, with each channel outputting the low, mid, and high-frequency components of the signal, allowing for a more comprehensive acquisition of vibration characteristics and achieving a higher time-frequency sampling rate. Furthermore, HDW can perform inter-scale analysis, enabling better analysis of signal characteristics for each component and significantly improving the distortion-free nature of the reconstructed signal. Using HDW to process mechanical fault signals can reduce interference from various noise sources, aiding in the identification of fault types and severity, and improving the accuracy of fault diagnosis. Therefore, HDW is widely used in mechanical fault diagnosis. However, in HDW, the decomposition level has a significant impact on the decomposition effect; the selection of the optimal decomposition level is one of the key factors determining the HDW result. In wavelet transform, users typically determine the decomposition scale in advance based on signal characteristics and their own experience. However, determining the scale based on subjective experience is highly unreasonable, as it often fails to achieve good results for different signals. Therefore, the decomposition scale should be determined based on the characteristics of the signal itself. Some scholars have researched how to rationally select the wavelet decomposition scale and proposed several approaches and methods; however, these methods are all based on wavelet transform and are not suitable for high-density wavelets.

[0003] Information entropy, as a quantitative indicator, describes the randomness of a system and can be used as a criterion for parameter selection. Commonly used entropies in vibration signal analysis include sample entropy, permutation entropy, and symbolic dynamic entropy. Among these, symbolic dynamic entropy has many advantages over sample entropy and permutation entropy, such as higher computational efficiency and robustness to noise. However, for a given time series, directly applying symbolic dynamic entropy can only generate a single scale value. This makes it difficult to comprehensively describe the fault characteristics. Multi-scale symbolic dynamic entropy (MSDE) combines the advantages of multi-scale analysis, improving the performance of symbolic dynamic entropy and enabling better complexity estimation. Therefore, using multi-scale symbolic dynamic entropy to construct a high-density wavelet adaptive method for determining the decomposition scale is feasible and necessary. Summary of the Invention

[0004] Based on the above technical background, this invention provides a mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelet. It uses multi-scale symbolic dynamic entropy for the adaptive selection of high-density wavelet decomposition series, and proposes an adaptive high-density wavelet transform mechanical fault diagnosis method to extract fault features of fault signals, which has good feature extraction capability.

[0005] This invention achieves the above objectives using the following technical solution: A mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelets, with the following specific steps:

[0006] Step 1: Perform high-density wavelet transforms of different levels on the mechanical fault signal to obtain the low-frequency, mid-frequency, and high-frequency components of the signal at different levels. Calculate the multi-scale symbolic dynamic entropy (MSDE) values ​​of the low-frequency and mid-frequency components at each level, following the steps below:

[0007] A: Select a scaling factor τ, where τ is a positive integer, and perform coarse-grained segmentation on the mechanical fault signal X{x(i), i=1,2,...,N} of signal length N according to the given scaling factor to obtain several coarse-grained vectors. Forming sub-time series;

[0008]

[0009] B: Select an appropriate number of symbols ε, where ε is a positive integer. Based on the Laplace criterion, divide the sub-time series into ε intervals. Replace the numerical values ​​of the elements in the time series with symbols σ to obtain the symbol sequence Z{z(r),r=1,2,...,N1}, where N1 represents the length of the sub-time series, N1=N-τ+1, and z(r) represents the symbol σ corresponding to the r-th value after symbolization.

[0010] C: Select a suitable dimension m and time delay λ, segment the above symbol sequence Z{z(r), r=1,2,...,N1}, and construct the mode vector.

[0011]

[0012] D: Calculate each state mode probability

[0013]

[0014] In the formula, a is a positive integer, a = 1, 2, 3, ..., ε m type(·) represents mapping the symbol space to the state-mode space, and ||·|| represents the cardinality of a set;

[0015] E: For a symbolic time series with embedding dimension m and number of symbols ε, there are a total of ε m A state pattern; the probability of utilizing the state pattern. Constructing the state pattern matrix

[0016] F: Calculate the probability of state transitions, i.e., the observed state pattern q. ε,m,λ When, the probability of the sign σ appearing later is:

[0017]

[0018] In the formula, b is a positive integer, b = 1, 2, 3, ..., ε;

[0019] G: Calculate the symbolic dynamic entropy of each sub-time series, which is the sum of the state pattern probability entropy and the state transition probability entropy:

[0020]

[0021] In the formula, x is the input signal; normalization is performed to ensure that 0 ≤ SDE norm (x,m,λ,ε)≤1:

[0022]

[0023] H: Calculation of multi-scale symbolic dynamic entropy from symbolic dynamic entropy:

[0024]

[0025] Step 2: Calculate the cosine distance between the two multi-scale symbolic dynamic entropy vectors at each level in Step 1, and use this distance to measure the similarity between the two vectors;

[0026] Step 3: Find the level with the highest similarity between the two entropy vectors in Step 1, that is, find the level corresponding to the first minimum value of the cosine distance in Step 2, and adaptively determine this level as the optimal decomposition scale.

[0027] Step 4: Perform high-density wavelet transform on the mechanical fault signal at the optimal decomposition scale; reconstruct the low-frequency components; analyze the reconstructed signal; and determine the fault type based on the fault characteristic information.

[0028] This invention introduces multi-scale symbolic dynamic entropy into high-density wavelet transform. Addressing the problem that high-density wavelet transform cannot adaptively determine the decomposition scale, it first uses high-density wavelets to decompose the signal level by level. Then, it calculates the cosine distance between the multi-scale symbolic dynamic entropy vectors of the low-frequency and mid-frequency coefficients at each level. Finally, the level where the distance first reaches its minimum value is determined as the optimal decomposition level. This effectively solves the problem of adaptively determining the optimal decomposition level in high-density wavelet transform and has broad prospects for engineering applications. Attached Figure Description

[0029] Figure 1 This is a diagram of the high-density wavelet transform process;

[0030] Figure 2 This is a flowchart of the present invention;

[0031] Figure 3 This is the time-domain diagram of the source signal in this invention;

[0032] Figure 4 This is the frequency domain diagram of the source signal in this invention;

[0033] Figure 5 This refers to the cosine distance between the multi-scale symbol dynamic entropy vectors of the low-frequency and mid-frequency components of each layer after the signal is decomposed layer by layer in this invention.

[0034] Figure 6 This is the frequency domain diagram of the low-frequency components reconstructed after high-density wavelet transform in this invention, under the optimal decomposition level.

[0035] Figure 7 This is the frequency domain diagram of the low-frequency components reconstructed after high-density wavelet transform of the signal when the decomposition level is too large in this invention;

[0036] Figure 8 This is the frequency domain diagram of the low-frequency components reconstructed after high-density wavelet transform of the signal in this invention when the decomposition level is too small. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. See also Figures 1 to 8 High-density wavelet transform is a commonly used redundant wavelet transform. Its decomposition and reconstruction are achieved through a three-channel filter bank. Figure 1 The diagram illustrates the multi-level decomposition process. In high-density wavelet transform, the number of decomposition levels significantly impacts the decomposition effect; the selection of the optimal decomposition level is a key factor determining the high-density wavelet transform result. In engineering applications, the decomposition scale should be adaptively determined based on the characteristics of the signal itself. Therefore, this invention proposes a mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelets.

[0038] To verify the effectiveness of the mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelets, this invention uses an aerospace bearing as an example for illustration, and the steps are as follows: Figure 2 As shown in Table 1, fault diagnosis was performed on the inner ring of a rolling bearing using data collected from the high-speed aerospace bearing test bench at the Polytechnic University of Turin. The specifications of the test bearing are shown in Table 1 below.

[0039] Table 1 Specifications of the test rolling bearings

[0040] Pitch circle diameter Contact angle rolling element diameter Number of rolling elements 40.5mm 0° 9mm 10

[0041] During the test, the motor drives the test bearing to rotate, and the vibration signal is collected at a rotation frequency of 100Hz. The signal sampling frequency is 51200Hz, and the number of sampling points N = 51200. Based on the bearing specifications and rotation frequency, the characteristic frequency of the rolling element failure of the test bearing is calculated as: f r =611.11Hz.

[0042] The specific operation steps of this embodiment are as follows (e.g.) Figure 2 As shown):

[0043] Step 1. The data acquisition device acquires the vibration signal f(t) of the test rolling bearing, and its time-domain waveform is shown below. Figure 3 As shown, due to various interfering factors, such as noise, the periodic impacts are obscured, making it difficult to observe the impact characteristics; the frequency domain diagram is as follows. Figure 4 As shown, the fault characteristic frequency is not prominent, and there is a lot of interference from other frequencies around it, which makes it difficult to accurately identify the bearing fault characteristic frequency.

[0044] Step 2. Perform high-density wavelet transform on the fault signal step by step to obtain the low-frequency, mid-frequency and high-frequency components of each level;

[0045] Step 3. After each level of transformation, calculate the multi-scale symbol dynamic entropy values ​​of the low-frequency component and the mid-frequency component of this level respectively;

[0046] Step 4. Calculate the cosine distance between the two MSDE vectors at each level in Step 3, such as... Figure 5 As shown;

[0047] Step 5. Find the series corresponding to the first minimum value of the cosine distance in Step 3, and obtain 4 as the optimal series.

[0048] Step 6. Perform a 4-level high-density wavelet transform on the fault signal;

[0049] Step 7. Reconstruct the low-frequency components of layer 4 to restore their signal length to the same as the original signal. Perform spectral analysis on the reconstructed signal, such as... Figure 6Mechanical faults were identified based on prominent frequencies and their harmonics in the spectrum. The extracted fault frequency was 601 Hz. Considering the resolution issue, the experimental results were basically consistent with the actual fault frequency and effectively suppressed high-frequency noise. Thus, it could be determined that there was a fault in the inner ring of the test bearing. The diagnostic results were consistent with the experimental scheme, proving the effectiveness of the embodiment.

[0050] To further illustrate the advantages of the method of the present invention, Figure 7 and Figure 8 Frequency domain plots of the reconstructed low-frequency signal are presented for scaling transformations with excessively large and small decomposition levels. Figure 7 As can be seen, when the number of levels is too large, due to the excessive degree of decomposition, only the fault characteristic frequency remains in the spectrum, while harmonics and other frequencies are all eliminated; from Figure 8 As can be seen, when the number of classification levels is too small, although the fault characteristic frequencies are still apparent, they are not as obvious as in the 4-level decomposition, and the low-frequency components of the last level still contain a lot of useless noise. Therefore, it is clear that the embodiment is more effective in bearing fault diagnosis.

Claims

1. A mechanical fault diagnosis method based on multi-scale symbolic dynamic entropy high-density wavelets, characterized in that, The specific steps are as follows: Step 1: Perform high-density wavelet transforms of different levels on the mechanical fault signal to obtain the low-frequency, mid-frequency, and high-frequency components of the signal at different levels. Calculate the multi-scale symbolic dynamic entropy (MSDE) values ​​of the low-frequency and mid-frequency components at each level, following the steps below: A: Select a scaling factor τ, where τ is a positive integer, and scale the mechanical fault signal of length N according to the given scaling factor. Perform coarse-grained segmentation to obtain several coarse-grained vectors. This forms a sub-time series; （1） B: Select a suitable number of symbols ε, where ε is a positive integer. Based on the Laplace criterion, divide the sub-time series into ε intervals. Replace the numerical values ​​of the elements in the time series with symbols σ to obtain the symbol sequence. ,in N 1 indicates the length of the sub-time series. ，z ( r ) represents the symbolized first... r The symbol σ corresponds to each numerical value; C: Selecting an appropriate dimension m And the time delay λ, the above symbol sequence Segmentation, constructing pattern vectors ; D: Calculate each state mode probability ; （2） In the formula, a It is a positive integer. a= 1,2,3...,ε m type(·) indicates mapping the symbol space to the state-mode space. The cardinality of a set; E: For an embedding dimension of m A symbol time series with ε symbols has a total of ε symbols. m A state pattern; the probability of utilizing the state pattern. Constructing the state pattern matrix ; F: Calculate the probability of state transitions, i.e., the observed state pattern. When, the probability of the sign σ appearing later is: （3） In the formula, b It is a positive integer. b=1,2,3,...,ε ; G: Calculate the symbolic dynamic entropy of each sub-time series, which is the sum of the state pattern probability entropy and the state transition probability entropy: （4） In the formula, x The input signal is normalized so that... : （5） H: Calculation of multi-scale symbolic dynamic entropy from symbolic dynamic entropy: （6） Step 2: Calculate the cosine distance between the two multi-scale symbolic dynamic entropy vectors at each level in Step 1, and use this distance to measure the similarity between the two vectors; Step 3: Find the level with the highest similarity between the two entropy vectors in Step 2, that is, find the level corresponding to the first minimum value of the cosine distance in Step 2, and adaptively determine this level as the optimal decomposition scale. Step 4: Perform high-density wavelet transform on the mechanical fault signal at the optimal decomposition scale; reconstruct the low-frequency components; analyze the reconstructed signal; and determine the fault type based on the fault characteristic information.

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