Gear fault diagnosis method based on hierarchical distribution Katz dimension

Abstract

The invention discloses a gear fault diagnosis method based on hierarchical distribution Katz dimensions, and belongs to the field of gear faults, and the method comprises the steps: firstly, collecting time domain vibration signals of a gear under different working conditions through a sensor, and carrying out the normalization processing of the signals; secondly, extracting the characteristics of the gear under different working conditions by using a hierarchical distribution Katz dimension; then, classification labels are added to the feature data, and the whole feature data are divided into training samples and test samples; and finally, training a classifier by using the training sample, and carrying out classification test on the test sample by means of the trained classifier, thereby realizing effective diagnosis of the gear fault type. The gear fault diagnosis method based on the hierarchical distribution Katz dimension provided by the invention realizes identification of different fault modes of the gear, and has the advantages of high accuracy and high reliability. Compared with a traditional fault diagnosis method based on fractal dimensions, the gear fault information can be extracted more comprehensively, and the gear fault diagnosis effect is better.

Description

Technical Field

[0001] The invention relates to the technical field of gear faults, and in particular to a gear fault diagnosis method based on hierarchical dispersion Katz dimension. Background Art

[0002] As the core component of mechanical transmission systems, gears play a vital role, especially in many key areas such as wind power generation and transportation. However, in actual operation, gears often experience long-term continuous operation, which is inevitably accompanied by various fault problems, such as wear, cracks, and even broken teeth. In particular, once the key part of the tooth root is damaged, it will pose a significant threat to the reliability and stability of the entire equipment. Therefore, it is particularly important to use scientific and effective methods to diagnose gear faults in a timely and accurate manner. This is not only related to the safe operation of the equipment, but also directly related to the stability and efficiency of the entire production system.

[0003] With the continuous advancement of fault diagnosis technology, gear fault diagnosis has entered a new stage of development. At present, the main means of gear fault diagnosis include machine learning, time domain analysis, and frequency domain analysis. When machine learning methods lack experience and historical data support, they need to comprehensively consider multiple process variables and build effective mathematical models. However, with the increase in model complexity and the number of parameters, the model may face the risk of overfitting, resulting in a decrease in its generalization ability on new data. Gear fault signals usually have nonlinear characteristics, which makes it difficult for traditional linear fault diagnosis techniques to accurately classify faults. Therefore, nonlinear dynamic indicators are introduced to improve the accuracy of diagnosis. These indicators include: Katz dimension, Lempel-Ziv complexity, Lyapunov index, and scatter entropy. Among these indicators, Katz dimension is not only computationally efficient, but also shows higher fault recognition accuracy and stronger feature differentiation ability in distinguishing different fault types.

[0004] As a classic nonlinear dynamics indicator, Katz dimension is often used to detect dynamic changes in signals. However, its dimension value is easily affected by outliers in the signal. Summary of the invention

[0005] The purpose of the present invention is to provide a gear fault diagnosis method based on hierarchical dispersion Katz dimension, introduce the normal cumulative distribution function and round function in the dispersion entropy into the calculation process of Katz dimension, and propose the dispersion Katz dimension to enhance the robustness of Katz dimension. In addition, hierarchical decomposition is introduced into the dispersion Katz dimension, and the hierarchical dispersion Katz dimension is proposed to extract the characteristics of gear signals in different frequency bands and realize the comprehensive characterization of its fault characteristics.

[0006] To achieve the above object, the present invention provides a gear fault diagnosis method based on hierarchical scatter Katz dimension, comprising the following steps:

[0007] S1. Collect the time domain vibration signals of the gear under different working conditions. Use the sensor to collect five time domain vibration signals under the working conditions of gear wear, gear root crack, gear tooth breakage, normal gear and gear defect. Divide each time domain vibration signal into n samples, each sample length is N, and a total of 5n samples;

[0008] S2, hierarchical decomposition, hierarchical decomposition is performed on each sample, and the p-th level decomposition includes 2 p level components;

[0009] S3, calculate the scattered Katz dimension of all hierarchical components of the p-th layer of each sample, and form a feature vector with the scattered Katz dimension values ​​of all hierarchical components of the p-th layer to obtain the feature vectors of all samples, forming a 5n×2 p The feature matrix of

[0010] S4, KNN classifier design, for each type of gear signal, randomly select the feature vectors of some samples from the feature matrix of S3 as the training samples of the KNN classifier, and the feature vectors of the remaining samples as the test samples of the classifier; input the training samples into the KNN classifier for training, and obtain the trained KNN classifier;

[0011] S5. Gear fault diagnosis, the trained KNN classifier is used to classify the test samples to obtain the fault diagnosis results.

[0012] Preferably, the calculation formula of the spread Katz dimension in S3 is as follows:

[0013]

[0014] Where X is the input signal; c is the number of categories; N is the length of the input signal; L and d are the length and maximum distance of the sequence after normal cumulative distribution mapping and linear mapping, respectively.

[0015] Preferably, the feature vector in S3 is as follows:

[0016]

[0017] Where, X p,e Decompose the hierarchical components of the e-th node at the p-th level of X.

[0018] Preferably, the scattered Katz dimension in S3 is an improvement on the Katz dimension, and the improvement steps are as follows:

[0019] A1. For the time series X = {x i, i=1,2,...,N}, and use the normal cumulative distribution function to map it to Y={y i ,i=1,2,...,N}, where y i ∈(0,1),y i The calculation formula is:

[0020]

[0021] Where λ is x i The average value of i The standard deviation of

[0022] A2. Use linear mapping to transform Y={y i ,i=1,2,...,N} is mapped to P={p i ,i=1,2,...,N},p i The calculation formula is:

[0023] p i =round(c×y i +0.5);

[0024] Among them, c is the number of categories; round is the rounding function;

[0025] A3. Calculate the length L of sequence p:

[0026]

[0027] A4. Calculate the maximum distance d between the first point and the i-th point in sequence P:

[0028] d=max(|p i -p1|),1 <i≤N;

[0029] A5. The spread Katz dimension is expressed as:

[0030]

[0031] Preferably, the scattered Katz dimension is further improved, and a hierarchical scattered Katz dimension is proposed. The improvement steps are as follows:

[0032] B1. For a given time series X = {x i ,i=1,2,...,N}, satisfying N=2 u , then the average operator Q0 and difference operator Q1 of the time series X are defined as:

[0033]

[0034] Where u is a positive integer; Q0 and Q1 represent the low-frequency and high-frequency components of the first-level decomposition of the time series X, respectively; the operator at the pth level (j=0 or 1) is expressed as:

[0035]

[0036] B2. The e-th node after the p-th layer decomposition is expressed as:

[0037]

[0038] In the formula, {l p ,p=1,2,…,u}∈{0,1} represents the average operator or difference operator of the pth layer;

[0039] B3. The hierarchical components of the e-th node after the p-th layer decomposition are:

[0040]

[0041] B4. Calculate the scattered Katz dimension of all hierarchical components of the p-th layer, and finally obtain the hierarchical scattered Katz dimension of the p-th layer of X, expressed as:

[0042]

[0043] Therefore, the present invention adopts the above-mentioned gear fault diagnosis method based on hierarchical distribution Katz dimension, and combines normal cumulative distribution function, round function and hierarchical decomposition on the basis of Katz. It realizes the identification of different gear fault modes, obtains fault feature information more comprehensively from multiple frequency bands, and improves the recognition accuracy of traditional fractal dimension for gear faults.

[0044] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is an overall flow chart of an embodiment of the present invention;

[0046] Figure 2 Schematic diagrams of five normalized gear signals according to an embodiment of the present invention; wherein (a) is a schematic diagram of a gear wear signal, (b) is a schematic diagram of a gear root crack signal, (c) is a schematic diagram of a gear broken tooth signal, (d) is a schematic diagram of a gear normal signal, and (e) is a schematic diagram of a gear defect signal;

[0047] Figure 3 It is a schematic diagram of the gear fault diagnosis results of an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. 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.

[0049] See also Figure 1 , a gear fault diagnosis method based on hierarchical scatter Katz dimension, the steps are as follows:

[0050] S1. Collect the time domain vibration signals of the gear under different working conditions. Use the sensor to collect five time domain vibration signals under the working conditions of gear wear, gear root crack, gear tooth breakage, normal gear and gear defect. Divide each signal into n samples, each sample length is N, and a total of 5n samples;

[0051] S2, hierarchical decomposition, hierarchical decomposition is performed on each sample, and the p-th level decomposition includes 2 p level components;

[0052] S3. Calculate the scattered Katz dimension of all hierarchical components of the pth layer of each sample. The calculation formula of the scattered Katz dimension is as follows:

[0053]

[0054] In the formula, X is the input signal, c is the number of categories, N is the length of the input signal, L and d are the length and maximum distance of the sequence after normal cumulative distribution mapping and linear mapping, respectively. The scattered Katz dimension values ​​of all hierarchical components of the pth layer form a feature vector:

[0055]

[0056] Among them, X p,e For the hierarchical component of the e-th node of the p-th layer decomposition, repeat S1 to S3 to obtain the feature vectors of all samples, consisting of 5n×2 p The feature matrix of .

[0057] The scattered Katz dimension is an improvement on the Katz dimension. The specific steps are as follows:

[0058] A1. For the time series X = {x i , i=1,2,...,N}, and use the normal cumulative distribution function to map it to Y={y i ,i=1,2,...,N}, where y i ∈(0,1),y i The calculation formula is:

[0059]

[0060] Where λ is x i The average value of i The standard deviation of

[0061] A2. Use linear mapping to transform Y={y i ,i=1,2,...,N} is mapped to P={p i ,i=1,2,...,N},p i The calculation formula is:

[0062] p i =round(c×y i +0.5);

[0063] Among them, c is the number of categories, and round is the rounding function;

[0064] A3. Calculate the length L of sequence P:

[0065]

[0066] A4. Calculate the maximum distance d between the first point and the i-th point in sequence P:

[0067] d=max(|p i -p1|),1 <i≤N;

[0068] A5. The spread Katz dimension can be expressed as:

[0069]

[0070] In order to overcome the shortcoming that the scattered Katz dimension cannot analyze the high and low frequency bands of the signal at the same time, the scattered Katz dimension is improved and the hierarchical scattered Katz dimension is proposed. The specific steps are as follows:

[0071] B1. For a given time series X = {x i ,i=1,2,...,N}, satisfying N=2 u , then the average operator Q0 and difference operator Q1 of the time series X are defined as:

[0072]

[0073] Where u is a positive integer, Q0 and Q1 represent the low-frequency and high-frequency components of the first-level decomposition of the time series X, respectively. (j=0 or 1) can be expressed as:

[0074]

[0075] B2. The e-th node after the p-th layer decomposition can be expressed as:

[0076]

[0077] Among them, {l p ,p=1,2,…,u}∈{0,1} represents the average operator or difference operator of the pth layer;

[0078] B3. The hierarchical components of the e-th node after the p-th layer decomposition are:

[0079]

[0080] B4. Calculate the scattered Katz dimension of all hierarchical components of the pth layer, and finally obtain the hierarchical scattered Katz dimension of the pth layer of X, which can be expressed as:

[0081]

[0082] S4, KNN classifier design, for each type of gear signal, randomly select the feature vectors of some samples from the feature matrix of S3 as the training samples of the KNN classifier, and the feature vectors of the remaining samples as the test samples of the classifier; input the training samples into the KNN classifier for training, and obtain the trained KNN classifier;

[0083] S5. Gear fault diagnosis, the trained KNN classifier is used to classify the test samples to obtain the fault diagnosis results.

[0084] Implementation Cases

[0085] Step 1: Collect the time domain vibration signals of the gear under different working conditions. Use the sensor to collect five time domain vibration signals under the working conditions of gear wear, gear root crack, gear tooth breakage, normal gear and gear defect. Each signal is divided into 100 samples, each sample length is 8192, a total of 500 samples, and the normalized five signals are as follows: Figure 2 As shown;

[0086] Step 2, hierarchical decomposition, hierarchical decomposition is performed on each sample, and the fourth level of decomposition includes 16 hierarchical components;

[0087] Step 3, calculate the scattered Katz dimension of all hierarchical components of the fourth layer of each sample to form a feature vector: HDKatz = [DKatz (X 4,0 ,3),…,DKatz(X 4,e ,3),…,DKatz(X 4,15 ,3)], repeat steps 1 to 3 to obtain the feature vectors of all samples, forming a 500×16 feature matrix;

[0088] Step 4, KNN classifier design. For each type of gear signal, 50 sample feature vectors are randomly selected from the feature matrix in step 3 as training samples of the KNN classifier, and the feature vectors of the remaining samples are used as test samples of the classifier. The training samples are input into the KNN classifier for training to obtain the trained KNN classifier.

[0089] Step 5, gear fault diagnosis, use the trained KNN classifier to classify the test samples and obtain the fault diagnosis results. The recognition rate is 80.8%. The diagnosis results are as follows Figure 3 shown.

[0090] Therefore, the present invention adopts the above-mentioned gear fault diagnosis method based on hierarchical scatter Katz dimension, which realizes the identification of different gear fault modes. Compared with the traditional fault diagnosis method based on fractal dimension, the present invention can more comprehensively extract gear fault information and improve the diagnosis effect of gear fault.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A gear fault diagnosis method based on hierarchical distribution Katz dimension, characterized in that: The following steps are involved: S1. Collect the time domain vibration signals of the gear under different working conditions. Use the sensor to collect five time domain vibration signals under the working conditions of gear wear, gear root crack, gear tooth breakage, normal gear and gear defect. Divide each time domain vibration signal into n samples, each sample length is N, and a total of 5n samples; S2, hierarchical decomposition, hierarchical decomposition is performed on each sample, and the p-th level decomposition includes 2 p level components; S3, calculate the scattered Katz dimension of all hierarchical components of the p-th layer of each sample, and form a feature vector with the scattered Katz dimension values ​​of all hierarchical components of the p-th layer to obtain the feature vectors of all samples, forming a 5n×2 p The feature matrix of S4, KNN classifier design, for each type of gear signal, randomly select the feature vectors of some samples from the feature matrix of S3 as the training samples of the KNN classifier, and the feature vectors of the remaining samples as the test samples of the classifier; input the training samples into the KNN classifier for training, and obtain the trained KNN classifier; S5. Gear fault diagnosis, the trained KNN classifier is used to classify the test samples to obtain the fault diagnosis results.

2. A gear fault diagnosis method based on hierarchical distribution Katz dimension according to claim 1, characterized in that: The calculation formula for the spread Katz dimension in S3 is as follows: Where X is the input signal; c is the number of categories; N is the length of the input signal; L and d are the length and maximum distance of the sequence after normal cumulative distribution mapping and linear mapping, respectively.

3. A gear fault diagnosis method based on hierarchical distribution Katz dimension according to claim 2, characterized in that: The feature vector in S3 is as follows: Where, X p,e Decompose the hierarchical components of the e-th node at the p-th level of X.

4. A gear fault diagnosis method based on hierarchical distribution Katz dimension according to claim 3, characterized in that: The scattered Katz dimension in S3 is an improvement on the Katz dimension. The improvement steps are as follows: A1. For the time series X = {x i , i=1,2,...,N}, and use the normal cumulative distribution function to map it to Y={y i ,i=1,2,...,N}, where y i ∈(0,1),y i The calculation formula is: Where λ is x i The average value of i The standard deviation of A2. Use linear mapping to transform Y={y i ,i=1,2,...,N} is mapped to P={p i ,i=1,2,...,N},p i The calculation formula is: p i =round(c×y i +0.5); Among them, c is the number of categories; round is the rounding function; A3. Calculate the length l of the sequence p: A4. Calculate the maximum distance d between the first point and the i-th point of sequence p: d=max(|p i -p1|),1<i≤N; A5. The spread Katz dimension is expressed as:

5. A gear fault diagnosis method based on hierarchical distribution Katz dimension according to claim 4, characterized in that: The scattered Katz dimension is further improved, and the hierarchical scattered Katz dimension is proposed. The improvement steps are as follows: B1. For a given time series X = {x i ,i=1,2,...,N}, satisfying N=2 u , then the average operator Q0 and difference operator Q1 of the time series X are defined as: Where u is a positive integer; Q0 and Q1 represent the low-frequency and high-frequency components of the first-level decomposition of the time series X, respectively; the operator at the pth level (j=0 or 1) is expressed as: B2. The e-th node after the p-th layer decomposition is expressed as: In the formula, {l p ,p=1,2,…,u}∈{0,1} represents the average operator or difference operator of the pth layer; B3. The hierarchical components of the e-th node after the p-th layer decomposition are: B4. Calculate the scattered Katz dimension of all hierarchical components of the p-th layer, and finally obtain the hierarchical scattered Katz dimension of the p-th layer of X, expressed as:

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