Gear fault diagnosis method based on all-pole model and k-means method

Abstract

The application aims to provide a gear fault diagnosis method based on a full pole model and a K-means method, comprising establishing a full pole model of a gear box system vibration signal, extracting a fault feature parameter based on K-means, and a gear fault online diagnosis process, wherein establishing the full pole model of the gear box system vibration signal comprises a full pole model, model parameter identification, model order determination, and obtaining model poles, etc. The application gathers the poles s1 in the normal, broken tooth, and wear three states into several clusters, and identifies the center point C i and a distance threshold R i as a fault feature parameter. Based on the fault feature parameter center point C i and the distance threshold R i , a gear fault diagnosis process is established, and whether it belongs to a certain cluster is judged by using the distance between the pole position and the center point C i and R i , so as to realize the fault diagnosis of the gear health, broken tooth, and wear three states.

Description

TECHNICAL FIELD

[0001] The present application relates to a gear fault diagnosis method. BACKGROUND

[0002] Gearbox is a general component for transmitting power and movement in mechanical equipment, which has the advantages of compact structure and high transmission accuracy, and is widely used in various fields. During operation, due to the influence of alternating stress on gears for a long time, faults such as tooth breakage and tooth surface wear are prone to occur, thereby causing periodic structural impact during the operation of gear pairs. Gear faults not only cause instability of power transmission, but also affect the working stability and service life of gear shafts, bearings and other components.

[0003] The vibration signal on the gearbox contains the gear operation state information, and when the gear fails, the vibration response characteristics will change. An autoregressive model (AR model) is established based on the gearbox vibration signal, and white noise is taken as input and vibration signal is taken as output to establish a full pole model of the gear transmission system under different working conditions. When the dynamic response of the system changes, the parameters of the model will change, thereby causing the pole positions of the full pole model to change. SUMMARY

[0004] The purpose of the present application is to provide a gear fault diagnosis method based on full pole model and K-means method, which can realize online monitoring and diagnosis of gear faults.

[0005] The purpose of the present application is achieved as follows:

[0006] The gear fault diagnosis method based on full pole model and K-means method of the present application is characterized in that:

[0007] (1) Establishing a full pole model of the gearbox system vibration signal

[0008] a. Full pole model

[0009] Let the vibration signal at time k be y(k), based on the AR model principle, use n vibration signals y(k-1), …, y(k-n) before time k to represent y(k), that is

[0010]

[0011] Where n is the model order; θ i is the autoregressive parameter of the AR model; e(k) is the prediction error;

[0012] At time k, the predicted value of the vibration signal is

[0013]

[0014] Write in matrix form as

[0015]

[0016] In the formula, Where φ n (k) = -y(k-n); θ = [θ1 θ2 … θ n ] T , for linear system, θ i is constant;

[0017] The z-transform of the formula y(k) is obtained

[0018]

[0019] In the formula, Y(z) is the z-transform of y(k), E(z) is the z-transform of e(k), taking E(z) as input and Y(z) as output, the impulse transfer function of the system is

[0020]

[0021] Since H(z) has no zero point, it is called the all-pole model of the vibration signal;

[0022] F(z) represents the denominator polynomial of H(z):

[0023]

[0024] F(z) contains n to be identified autoregressive parameters θ i , i = 1, 2, …, n, here F(z) is also called the AR model of the vibration signal;

[0025] b. Model parameter identification

[0026] For the vibration signal Y T = [y(1) y(2) … y(M)] with data length M, the regression vector Φ is constructed as

[0027]

[0028] φ n (k) = -y(k-n) is brought into the above formula to obtain

[0029]

[0030] Let y(0), y(-1), …, y(1-n) all equal to 0, and use the least square method to solve the autoregressive parameters θ of the model as

[0031] θ = (Φ T Φ)-1 Φ T Y;

[0032] c. Model order determination

[0033] At time k, the prediction error e(k) is expressed as

[0034]

[0035] For M data, the sum of squares of prediction errors PE sum is:

[0036]

[0037] According to PE sum and the accuracy requirement, the order of the model is determined;

[0038] d. Obtain model poles

[0039] Let F(z) = 0, get the discrete form of the poles, z1, z2, …, z n , convert the discrete poles z i into continuous poles s i in the s plane, let s i = σ i + jω i , and the transformation formula is

[0040]

[0041]

[0042] Where Δt is the sampling time;

[0043] (2) Fault feature parameter extraction based on K-means

[0044] K in the K-means clustering algorithm represents the number of clusters, that is, the data is clustered into K clusters, and means represents the mean of all data in each cluster as the center point of the cluster;

[0045] Collect vibration signals under normal, broken tooth and wear conditions to form training samples, establish a full pole model of the gearbox system vibration signal, and obtain the poles of the training samples;

[0046] (3) Gear fault online diagnosis process

[0047] The feature parameter center point C i and distance threshold R i, establish the fault diagnosis flow based on the pole position, specifically including: collecting the vibration signal of the gear box, in each diagnosis cycle, intercepting the vibration signal with a length of M, establishing the full pole model H(z), and calculating the poles of the model H(z); calculating the distance D i (i=1, 2,..., K) of the s1 pole to each center point C i (i=1, 2,..., K); comparing the size of each D i (i=1, 2,..., K), determining the minimum value min(D i ) and the corresponding i cluster; judging whether min(D i ) exceeds the distance threshold R i of the i cluster, if within the distance threshold of the cluster, directly giving the diagnosis result, if exceeding the distance threshold of the cluster, giving the state abnormal result.

[0048] The application can also include:

[0049] 1. When the discrete form of the pole n=5, that is, the 5th order model, 5 discrete poles z1, z2,..., z5 can be obtained, which are converted into 5 continuous poles s1, s2,..., s5, for the actual physical system, 2 pairs of conjugate poles s 1,2 , s 3,4 and 1 real pole s5 should be included, by comparing and analyzing the gear box vibration signals under different operating states, the conjugate pole s 1,2 closest to the virtual axis has the greatest influence on the dynamic characteristics of the system, and the distribution positions of the pole are different under the tooth breaking, wear and healthy states, since the conjugate pole s 1,2 is symmetrical about the real axis, the pole s1 is selected as the judgment basis for the gear fault diagnosis.

[0050] 2. The poles s1 under the normal, tooth breaking and wear states are clustered into clusters, and the center point C i and the distance threshold R i of each cluster are identified as fault feature parameters, i=1, 2,..., K.

[0051] The advantages of the application are:

[0052] 1. For typical faults such as gear tooth breaking and wear, the application establishes a full pole model based on the vibration signal of the gear box body, and proposes a fault diagnosis method based on the pole position of the model. The method is characterized by simple calculation method, can be used for gear fault online monitoring, and determines the fault type.

[0053] 2. The application proposes a fault feature parameter extraction method based on K-means. The poles s1 under the normal, tooth breaking and wear states are clustered into clusters, and the center point C i and the distance threshold R ias a fault feature parameter.

[0054] 3, based on the fault feature parameter center point C i and distance threshold R i , establish a gear fault diagnosis process, use the distance between the pole position and the center point C i and R i to determine whether it belongs to a certain cluster, so as to realize the fault diagnosis of gear health, broken tooth and wear. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The clustering result when K=4;

[0056] Figure 2 The flowchart of the present application;

[0057] Figure 3 The distance from s1 to four center points;

[0058] Figure 4 The diagnosis result of the test sample. DETAILED DESCRIPTION

[0059] The present application will be described in more detail below with examples combined with the drawings:

[0060] Combined Figures 1-4 , the present application is aimed at gear broken tooth and wear fault, based on the vibration signal of gear box, a gear fault online diagnosis method based on full pole model and K-means method is designed, the specific steps are as follows:

[0061] Step 1 to establish a full pole model of gear box system vibration signal

[0062] Step 1.1 full pole model

[0063] Let the vibration signal at k time be y(k), based on the principle of AR model, y(k) can be expressed by n vibration signals y(k-1),…, y(k-n) before k time, that is

[0064]

[0065] Wherein, n is the model order; θ i is the autoregressive parameter of AR model; e(k) is the prediction error, in ideal case, e(k) is a white noise random sequence with mean 0 and variance σ 2 .

[0066] According to formula (1), the predicted value of vibration signal at k time is

[0067] ​

[0068] Write in matrix form as

[0069]

[0070] In the formula, Where θ n (k) = -y(k-n); θ = [θ1 θ2 … θ n ] T For linear systems, θ i is a constant.

[0071] The z-transform of equation (1) is obtained

[0072]

[0073] In the formula, Y(z) is the z-transform of y(k), and E(z) is the z-transform of e(k). Taking E(z) as input and Y(z) as output, the impulse transfer function of the system is

[0074]

[0075] Since H(z) has no zero point, it is called the all-pole model of the vibration signal.

[0076] Use F(z) to represent the denominator polynomial of H(z):

[0077]

[0078] F(z) contains n to be identified autoregressive parameters θ i (i = 1, 2, …, n), where F(z) is also called the AR model of the vibration signal.

[0079] Step 1.2 Model parameter identification

[0080] For the vibration signal Y T = [y(1) y(2) … y(M)] with data length M, the regression vector Φ is constructed as

[0081]

[0082] φ n (k) = -y(k-n) is brought into equation (7) to obtain

[0083]

[0084] Here let y(0), y(-1), …, y(1-n) all equal 0.

[0085] The least square method can be used to solve the autoregressive parameters θ of the model as

[0086] θ = (Φ T Φ) -1 Φ T Y (9)

[0087] Step 1.3 Model order determination

[0088] At time k, the prediction error e(k) can be expressed as

[0089]

[0090] For M data, the sum of squares of prediction errors PE sum is:

[0091]

[0092] According to PE sum and the accuracy requirement, the order of the model can be determined.

[0093] In the working condition of 1200 rpm speed and 2 N·m load, the original gear box vibration signal with data length M = 5120 is intercepted under normal state. Select n = 5, and the sum of squares of prediction errors PE sum = 1.07. According to equations (7)-(9), the autoregressive parameters θ of the model are calculated, and F(z) is obtained as

[0094] F(z) = 1 + 1.5622z -1 + 1.3417z -2 + 0.2978z -3 - 0.2897z -4 - 0.2532z -5 (12)

[0095] Step 1.4 Obtain model poles

[0096] Let F(z) = 0, and the discrete form of the poles z n is obtained. Convert the discrete poles z i into the continuous poles s i in the s plane, and let s i = σ i + jω i , then the transformation formula is

[0097]

[0098]

[0099] Where Δt is the sampling time.

[0100] For equation (12), five discrete poles z 1,2= -0.37 ± 0.82j, z 3,4 = -0.67 ± 0.41j, z5= 0.51. According to formula (13), (14), when the sampling frequency is 5.12 kHz, it is converted into continuous poles, s 1,2 = -541.66 ± 10212.67j, s 3,4 = -1236.19 ± 13273.28j, s5= -3447.52. The pole s1 is selected as the basis for fault diagnosis.

[0101] Step 2: Fault feature parameter extraction based on K-means

[0102] K-means clustering is an algorithm for clustering target points by similarity, grouping similar objects into the same cluster. In the K-means clustering algorithm, K represents the number of clusters, i.e. clustering data into K clusters, and means represents taking the mean of all data in each cluster as the center point of the cluster.

[0103] Collect vibration signals under normal, broken tooth and wear conditions to form a number of training samples. According to the method, a full pole model of the gearbox system vibration signal is established, and the poles of the training samples are obtained. Based on the K-means method, the poles s1 under the normal, broken tooth and wear conditions are clustered into several clusters, and the center point C i and the distance threshold R i are identified as fault feature parameters, where i = 1, 2, …, K.

[0104] At 1200 rpm, 0.8, 1.2, 1.6, 2 N·m load, a total of 96 groups of vibration signal training sample data are generated, including 32 groups of health, broken tooth and wear state, and each group of data length M = 5120.

[0105] According to the training samples, a full pole model is established, and the poles of each sample are calculated. The K-means method is used to analyze the clustering of the s1 poles of the training samples. When the number of center points K = 4, the s1 pole clustering result is as Figure 1 shown. From Figure 1 it can be seen that the samples are clustered into four clusters, cluster 1 is 32 healthy samples, the center point C1 is (-650.31, 9860.32); cluster 2 is 32 broken tooth samples, the center point C2 is (-716.99, 7564.06); cluster 3 is 16 wear samples, the center point C3 is (-1296.63, 10024.49); cluster 4 is 16 wear samples, the center point C4 is (-1253.62, 9027.95). There is one center point for health and broken tooth samples, and two center points for wear samples. The accuracy rate of 96 sample clustering is 100%.

[0106] In actual fault diagnosis, according to the distance from the s1 pole to each center point, it is determined whether the pole belongs to the cluster, and the working state of the gear is judged. For this purpose, the radius of each cluster (i.e. the distance threshold R i ) needs to be determined as the basis for judging whether it belongs to the cluster. According to the clustering result, the distance threshold R i of each cluster is determined.

[0107] Table 1 Distance threshold of each cluster

[0108]

[0109] Step 4 Gear fault online diagnosis process

[0110] Feature parameter center point C i and distance threshold R i based on K-means clustering, a fault diagnosis process based on pole position is established. The gear fault online diagnosis process is shown in Figure 2 . Specifically, it includes: collecting the vibration signal of the gearbox, in each diagnosis period, intercepting the vibration signal with a length of M = 5120, establishing the full pole model H(z), and calculating the poles of the model H(z); calculating the distance D i (i = 1, 2, …, K) from the s1 pole to each center point C i ; comparing the size of each D i (i = 1, 2, …, K), determining the minimum value min(D i ) and the corresponding i-th cluster; judging whether min(D i ) exceeds the distance threshold R i of the i-th cluster, if it is within the distance threshold of the cluster, the diagnosis result is directly given, if it exceeds the distance threshold of the cluster, the state abnormal result is given.

[0111] Taking a test sample as an example, the s1 = -1160.72 + 10345.23j is calculated, and the distance from s1 to the four center points is shown in Figure 3 . The distance D3 is the smallest, and D3 < R3, so the pole belongs to the i = 3 corresponding cluster 3, that is, the diagnosis result is wear failure.

[0112] The method proposed in the application is applied to analyze and diagnose 20 test samples, and the results are shown in Figure 4 . Among them, 10 groups are wear, 4 groups are broken teeth, and 6 groups are healthy. The fault diagnosis accuracy is 100%.

[0113] In conclusion, the present application is directed to gear tooth breaking, wear and tear failure, based on the vibration signal of the gear box, a gear fault online diagnosis method based on the full pole model and K-means is designed, which can realize the online real-time health monitoring of the gear, and ensure the safe and stable operation of the gear transmission system.

Claims

1. A gear fault diagnosis method based on the all-pole model and the K-means method, characterized by: (1) Establish the all-pole model of the vibration signal of the gearbox system. a. All-pole model Let the vibration signal at time k be y(k). Based on the AR model principle, y(k) is represented by the n vibration signals y(k-1), ..., y(kn) before time k, i.e. Where n is the model order; θ i Here are the autoregressive parameters of the AR model; e(k) is the prediction error. At time k, the predicted value of the vibration signal for Written in matrix form as In the formula, Where φ n (k)=-y(kn);θ=[θ1 θ2…θ n ] T For linear systems, θ i It is a constant; Taking the z-transform of y(k), we get In the formula, Y(z) is the z-transform of y(k), and E(z) is the z-transform of e(k). Taking E(z) as input and Y(z) as output, the pulse transfer function of the system is obtained as follows: Since H(z) has no zeros, it is called the all-pole model of the vibration signal; Let F(z) denote the denominator polynomial of H(z): F(z) contains n autoregressive parameters θ to be identified. i , i = 1, 2, ..., n, where F(z) is also called the AR model of the vibration signal; b. Model parameter identification For a vibration signal Y with a data length of M T =[y(1) y(2) … y(M)], construct the regression vector Φ as φ n Substituting (k) = -y(kn) into the above equation, we get Let y(0), y(-1), ..., y(1-n) all equal to 0, and use the least squares method to solve for the autoregressive parameter θ of the model. θ=(Φ T F) -1 F T Y; c. Determining the model order At time k, the prediction error e(k) is expressed as: For M data points, the sum of squared prediction errors PE sum for: According to PE sum And to meet the precision requirements, determine the order of the model; d. Find the poles of the model Setting F(z) = 0, we obtain the discrete poles, z1, z2, ..., z n Discrete poles z i Transformed into continuous poles s in the s-plane i Form, making s i =σ i +jω i Its transformation formula is Where Δt is the sampling time; (2) Fault feature parameter extraction based on K-means In the K-means clustering algorithm, K represents the number of clusters, that is, the data is clustered into K clusters, and means means that the mean of all data in each cluster is used as the centroid of the cluster. Vibration signals under three conditions—normal, broken tooth, and worn—are collected to form training samples. A full pole model of the gearbox system vibration signal is established to obtain the poles of the training samples. (3) Online Gear Fault Diagnosis Process The feature parameter C based on K-means clustering is the centroid. i and distance threshold R i A fault diagnosis process based on pole location is established, specifically including: acquiring vibration signals from the gearbox; in each diagnostic cycle, extracting a vibration signal of length M; establishing an all-pole model H(z); and calculating the poles of model H(z); calculating the distance from pole s1 to each center point C. i Distance D i (i = 1, 2, ..., K); compare each D i Given a set of values ​​(i = 1, 2, ..., K), determine the minimum value min(D). i ) and the corresponding i-th cluster; determine min(D i Does it exceed the distance threshold R of the i-th cluster? i If the distance is within the cluster's distance threshold, a diagnosis result is given directly; if the distance exceeds the cluster's distance threshold, an abnormal status result is given.

2. The gear fault diagnosis method based on the all-pole model and K-means method according to claim 1, characterized in that: When the discrete form of the poles n=5, i.e., a 5th-order model, five discrete poles z1, z2, ..., z5 can be obtained, which can be transformed into five continuous poles s1, s2, ..., s5. For a real physical system, this should include two pairs of conjugate poles s1, s2, ..., s5. 1,2 s 3,4 With one real pole s5, by comparing and analyzing the gearbox vibration signals under different operating conditions, the conjugate pole s closest to the imaginary axis is identified. 1,2 The pole has the greatest impact on the dynamic characteristics of the system, and its distribution location differs under broken tooth, worn, and healthy conditions, due to the conjugate pole s 1,2 Regarding the symmetry of the real axis, the pole s1 is selected as the basis for judging gear fault diagnosis.

3. The gear fault diagnosis method based on the all-pole model and K-means method according to claim 1, characterized in that: The poles s1 under the three conditions of normal, broken tooth, and worn tooth are clustered into groups, and the center point C of each group is identified. i and distance threshold R i As fault characteristic parameters, i = 1, 2, ..., K.

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