A method for diagnosing failure of a reducer under multiple working conditions

Abstract

The present application aims at the problem that the performance of the diagnosis model is unstable in the auxiliary transfer training using single working condition source domain sample data, and proposes a reducer fault diagnosis method under multiple working conditions. The method uses the probability latent semantic analysis model to mine the implicit features between the reducer fault vibration signals under different working conditions, introduces the multi-source domain labeled auxiliary feature samples under different working conditions, constructs the Fisher kernel function based on the fault feature dictionary, establishes the multi-source domain transfer LSSVM fault diagnosis model based on the probability latent semantic analysis, improves the stability of the diagnosis effect, and realizes the fault diagnosis of the reducer under multiple working conditions in the actual production environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fault diagnosis of rotating machinery, and particularly relates to a fault diagnosis method for a reducer under multiple working conditions. BACKGROUND

[0002] The reducer is mainly composed of rotating components such as gear bearings. At present, many intelligent diagnosis methods have been proposed to solve the difficulty of fault diagnosis of rotating machinery components. These methods can be roughly divided into two forms: one is to use artificial feature extraction and machine learning; the other is to use deep learning or transfer learning. Unlike the diagnosis method of artificial feature extraction, deep learning usually constructs a deep neural network to adaptively learn the features in the data through training data, and trains a diagnosis model. It can realize an end-to-end fault diagnosis process. When the classification model is trained, the reducer vibration signal is input into the diagnosis model as test data to identify the reducer fault features. However, the traditional deep learning network has made great progress in the field of mechanical fault diagnosis, which depends on two reasons: first, most of the data are labeled and available; second, the training data and test data are of the same distribution. Once a reducer fails seriously, it will cause serious consequences, so there are few labeled sample data. In addition, due to the variability of the working conditions of the reducer, even if the labeled reducer vibration signal data is collected, it cannot be guaranteed that the training data collected this time and the target data next time are of the same distribution, which leads to low generalization ability of the fault diagnosis model obtained by deep learning. Transfer learning is to use source domain samples with different but similar sample distributions to train the model, and then migrate the model to the target domain through transfer strategy to complete the fault recognition of the target domain data.

[0003] Although various intelligent diagnosis methods have achieved remarkable results, most algorithms still have certain limitations in processing one-dimensional signals such as reducer vibration signals, which have strong nonlinearity and non-stationarity. For example, there are problems such as strong background noise interference, unclear input data features, insufficient labeled data, and poor generalization ability of diagnosis models under complex working conditions. Therefore, it is necessary to propose a fault diagnosis method for reducers under variable working conditions to solve the above problems. SUMMARY

[0004] The application aims at the problem of unstable performance of a diagnostic model assisted by a single working condition source domain sample data in migration training, and proposes a reducer fault diagnosis method based on multi-working condition migration learning. The method uses a probability latent semantic analysis model to mine the implicit features between reducer fault vibration signals under different working conditions, introduces multi-source domain labeled auxiliary features under different working conditions, constructs a Fisher kernel function based on a fault feature dictionary, establishes a multi-source domain migration LSSVM fault diagnosis model based on probability latent semantic analysis, improves the stability of the diagnosis effect, and realizes the fault diagnosis of the reducer under multi-working conditions in the actual production environment.

[0005] The technical scheme of the application is a reducer fault diagnosis method under multi-working conditions, which comprises the following steps:

[0006] Step 1: according to the probability latent semantic analysis model, the hidden variables between the reducer vibration signal samples and the fault features under different working conditions are constructed;

[0007] Step 1.1: define the related variables of the probability latent semantic analysis model;

[0008] The reducer vibration signal set is D={d1,d2,…,d N} and the corresponding reducer fault type set is W={w1,w2,…,w m}, the joint frequency matrix of the co-occurrence of the vibration signal and the fault type is N={n(d,w)}, (d,w) represents that the fault type of the reducer vibration signal d is w, n(d,w) represents the frequency of the specific reducer vibration signal d being the fault type w, the shared hidden variable Z={z1,z2,…,z K} is introduced, and under the condition of the hidden variable Z, the vibration signal set D and the fault type set W are independent of each other;

[0009] Step 1.2: generate a joint distribution sample;

[0010] According to the probability distribution P(d) of the vibration signal D, N samples d are randomly selected from the vibration signal set D; under each sample d, a topic z is randomly selected from the hidden variable Z according to the conditional probability P(z|d); then under each topic, a fault type w is randomly selected from the fault type set W according to the conditional probability P(w|z), and at this time a joint sample (d,w) is generated;

[0011] The generation probability of the entire co-occurrence sample set is:

[0012] wherein, N represents the number of samples, n(d, w) represents the frequency of a specific reducer vibration signal d being of fault type w, P(z) represents the probability distribution of the latent variable, and P(d|z) represents the probability of the vibration signal sample being d under the condition that the selected latent variable is z;

[0013] Step 2: Establishing a LSSVM fault diagnosis model y based on source domain assisted migration Mul (x) is;

[0014]

[0015] wherein, N t is the number of samples under the s-th working condition, λ ij and b are model parameters set, is the classification hyperplane of the s-th working condition; is the classification hyperplane of the t-th working condition, K(·) represents a kernel function, represents the i-th fault feature sample in the sample D and belongs to the t-th working condition; represents the i-th fault feature sample in the sample D and belongs to the s-th working condition;

[0016] Step 3: Calculate the values of P(z), P(d|z) and P(w|z) so that the corresponding generation probability P(d, w) is maximum when the reducer vibration signal d contains the fault type w;

[0017] Step 3.1: Constructing a maximum likelihood function;

[0018] Step 3.2: Calculating P(z), P(d|z) and P(w|z) by using the following formula;

[0019]

[0020]

[0021]

[0022] Step 3.3: Combining the formulas in steps 3.1, 3.2 and the formula in step 2.2 to obtain P(z, d) = P(d|z)P(z) through iterative calculation;

[0023] Step 4: Constructing a fault feature dictionary;

[0024] First, a feature sample is generated according to the original reducer vibration signal, and then the obtained feature sample is clustered, and a feature dictionary is constructed according to the clustering result;

[0025] Step 5: Obtain the reducer vibration signal and the sample data of the corresponding fault type, combine steps 2, 3 and 4 to train the fault diagnosis model of step 2, and use the trained fault diagnosis model to detect the reducer fault type.

[0026] Further, the reducer fault type is divided into gear normal, tooth surface crack, tooth surface wear, tooth fracture and missing tooth.

[0027] The present application has good diagnostic accuracy and diagnostic stability in the fault diagnosis of the reducer under multiple working conditions. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The present application is a specific embodiment flowchart of the method;

[0029] Figure 2 It is an algorithm schematic diagram based on weight migration;

[0030] Figure 3 It is a flowchart of LSSVM fault diagnosis algorithm based on source domain auxiliary migration;

[0031] Figure 4 It is a schematic diagram of generating samples through reducer vibration signals;

[0032] Figure 5 It is the mapping relationship of document-hidden variable-word;

[0033] Figure 6 It is a flowchart of constructing a fault feature dictionary;

[0034] Figure 7 It is a graph of the number of hidden variables and the average fault diagnosis accuracy under different source domains;

[0035] Figure 8 The source domain is 3 working condition data fault diagnosis result;

[0036] Figure 9 The source domain is 4 working condition data fault diagnosis result;

[0037] Figure 10 The source domain is 5 working condition data fault diagnosis result. DETAILED DESCRIPTION

[0038] The embodiments of the present application will be described in detail below Figure 1 ), the present embodiment is implemented on the premise of the technical solution of the present application, and gives a detailed implementation and specific operation process, but the protection scope of the present application is not limited to the following embodiment.

[0039] The embodiment mainly can be divided into the following steps:

[0040] Step 1: Establishing LSSVM fault diagnosis based on source domain assisted migration;

[0041] Step 1.1: When the target domain sample data is insufficient, introduce the model learning strategy of source domain sample data assisted migration. In the process of training the target diagnosis model, adjust the weight of the source domain sample data to make the model parameters closer to the parameters of the target diagnosis model, and finally train the classification model most suitable for the target task.

[0042] The specific process is shown in Figure 2 . The red circles and triangles in the figure represent two classes of sample data in the target domain, and the blue circles and triangles represent two classes of sample data in the source domain. When the target domain data is less, the target domain model cannot be fully trained, resulting in a target domain classification model with poor performance, as shown in Figure 2 (A). When the source domain auxiliary sample data is added, the sample data is increased and the model can be properly trained, and the corresponding classification model can be trained, as shown in Figure 2 (B). However, since the source domain sample data distribution is only similar to the target domain sample data distribution and is not completely the same, there will be some interference samples affecting the classification performance of the model, and some incorrect classification sample data will appear, such as Figure 2 (B) samples circled in red. At this time, by constructing the objective function, find the low-quality source domain samples that affect the performance of the target domain classification model, such as Figure 2 (C) samples circled in light blue, reduce their weight, and reduce the influence of low-quality source domain samples on the target model, as shown in Figure 2 (D), so as to adjust the classification decision function and improve the model performance.

[0043] Substitute into the specific LSSVM objective function and add constraint conditions:

[0044]

[0045] In the formula: ω is the normal vector of the plane; b is the bias coefficient; represents the confidence risk of the model; γ t is the regularization coefficient, balancing the parameters of algorithm accuracy and generalization ability; e i is the error function; is a certain sample in the source domain; N s is the number of source domain samples; is a certain sample in the target domain; N t is the number of target domain samples; is a certain classification hyperplane in the source domain; is a certain classification hyperplane in the target domain.

[0046] Step 1.2: For the constraint problem of formula (1), the solution steps are as follows:

[0047] (1) First, construct the Lagrange equation of formula (2):

[0048]

[0049] In the formula: λ i ∈R belongs to the Lagrange multiplier.

[0050] (2) Then, according to the Kuhn-Tucker conditions, take the partial derivative of L with respect to ω, b, e, and λ respectively, and set each partial derivative to zero and simplify, which can obtain:

[0051]

[0052] (3) Use the substitution elimination method to arrange the above formula (3), and simplify to obtain:

[0053]

[0054] In the formula: Ω represents the (N t +N s )×(N t +N s ) symmetric matrix, K(·) represents the kernel function, y i , y j ∈Y; Y represents the label set of the training samples, I represents an (N t +N s )×1 column vector, I = [1, 1, …, 1] T ; λ represents the Lagrange multiplier vector, γ represents the regularization coefficient,

[0055] (4) Solve the parameters b and λ:

[0056]

[0057] Finally, the LSSVM fault diagnosis model based on source domain auxiliary transfer is obtained:

[0058]

[0059] The above gives the establishment process of the LSSVM fault diagnosis model based on source domain auxiliary transfer. Figure 3 The flowchart of the LSSVM fault diagnosis method based on source domain auxiliary transfer.

[0060] Step 2: Establishing the probabilistic latent semantic analysis model to build the hidden variables between the reducer vibration signal samples and the fault characteristics, and to mine the implicit relationship between the reducer vibration signals under different working conditions;

[0061] Step 2.1: Defining the related variables of the probabilistic latent semantic analysis model;

[0062] The document D = {d1, d2, …, d N} is the reducer vibration signal sample data, and the generation mode of the sample is shown in Figure 4 The corresponding word is W = {w1, w2, …, w m} is the fault type of the reducer, and the joint frequency matrix of the "document-word" co-occurrence is N = {n(d, w)}, (d, w) represents a certain reducer vibration signal sample for a certain fault type, and n(d, w) represents the frequency of a certain vibration signal sample d for a certain fault type w. In order to realize the mutual independence between the document D and the word W, the shared hidden variable Z = {z1, z2, …, z K} is introduced. Under the condition of the hidden variable Z, the document D and the word W are independent of each other.

[0063] Step 2.2: Generating a joint distribution sample;

[0064] First, according to the probability distribution P(d) of the document set D, randomly select N documents d from D; under each document d, randomly select a topic z from the topic hidden variable according to the conditional probability P(z|d); then under each topic, randomly select a word w from the word set according to the conditional probability P(w|z), at this time a joint sample (d, w) is generated. The mapping relationship of the three is shown in Figure 5 The specific expression formula is:

[0065] P(d, w) = P(d)P(w|d) (7)

[0066]

[0067] According to Bayes' theorem, we can get:

[0068] P(z, d) = P(d)P(z|d) = P(z)P(d|z) (9)

[0069] At this time, the co-occurrence probability of a certain vibration signal sample d and a certain fault type w can be expressed as:

[0070]

[0071] Then from the above process, it can be concluded that the generation probability of the entire co-occurrence sample set is:

[0072]

[0073] Step 3: Solve the parameters of the Probabilistic Latent Semantic Analysis model according to the maximum likelihood algorithm.

[0074] Solve the values of the parameters P(z), P(d|z) and P(w|z) so that the corresponding generation probability P(d, w) is maximum when the document d contains the word w.

[0075] Step 3.1: Construct the maximum likelihood function;

[0076]

[0077] Step 3.2: Simplify the expression of Le at the back;

[0078]

[0079] In the formula: X represents the "document-word" co-occurrence sample (d, w); θ represents the parameters P(z), P(w|z) and P(d|z).

[0080] Step 3.3: Solve the lower bound of formula (1-27) according to Jensen's inequality;

[0081]

[0082] In the formula: P * (z) represents the probability distribution related to the latent variable; represents the mathematical expectation of P * (z).

[0083] Further available:

[0084]

[0085] As can be seen from formula (15), when the value of the parameter θ is determined, P * (z) = P(z|X, θ) can be allowed to maximize the minimum value Le0 of the maximum likelihood function Le in the current iteration.

[0086] Step 3.4: Convert the above problem into a constrained extremum solving problem by combining the implicit constraint condition;

[0087]

[0088] Step 3.5: Solve by using the Lagrange multiplier method.

[0089]

[0090] Take the partial derivative of P(z), P(w|z) and P(d|z) respectively and set it to 0. Let the number of latent variables be R, then the detailed solving process of the maximum likelihood algorithm is as follows:

[0091] (1) Initialize P(z) = 1 / R, and randomly assign values to parameters P(w|z) and P(d|z).

[0092] (2) E-step, calculate the posterior probability of hidden variable z:

[0093]

[0094] (3) M-step, obtain P(z), P(w|z) and P(d|z) according to formula (18) and the posterior probability obtained in the E-step:

[0095]

[0096]

[0097]

[0098] (4) Substitute the results in step (3) into formula (10) to update the value of P(d, w), and substitute it into the likelihood function of formula (12) to calculate its value. Repeat steps 2 and 3 until the value of the likelihood function in formula (12) converges or the maximum number of iterations is reached.

[0099] Through the above steps, the parameters of the probabilistic latent semantic analysis model are finally obtained. The probability of hidden variable z under the condition of document d is obtained by Bayes formula:

[0100]

[0101] Step 4: Constructing a fault feature dictionary to determine the fault feature vocabulary. The entire process of constructing a fault feature dictionary is shown in the flow chart as Figure 6 The K-means clustering method is used to construct the fault feature dictionary, with the goal of minimizing the Euclidean distance from the samples within the class to the cluster center:

[0102]

[0103] where c ij is defined as follows:

[0104]

[0105] The detailed process of constructing the fault feature dictionary is as follows:

[0106] (1) First, randomly select k sample data as k cluster centers w i ;

[0107] (2) Calculate the Euclidean distance between the k cluster centers w i and each sample data x j , and then determine c ij according to formula (24).

[0108] (3) Update the cluster centers according to the following formula:

[0109]

[0110] (4) Repeat steps (2) and (3) until the cluster centers no longer change or the maximum number of iterations is reached, and the cluster centers are the fault feature words.

[0111] After constructing the fault feature dictionary, the Euclidean distance is minimized to determine each sample data x j whether the fault feature word w i appears:

[0112]

[0113] If the fault feature word w i appears in the original reducer vibration signal the number of times is:

[0114]

[0115] Step 5: Establish a multi-source domain transfer LSSVM fault diagnosis model based on probability latent semantic analysis;

[0116] According to the semantic analysis model and the maximum likelihood criterion, the values of P(z), P(d|z) and P(w|z) are obtained, and the joint probability P(d,w) of the "document-word" co-occurrence sample can be calculated by formula (10). Finally, the multi-source domain transfer LSSVM diagnosis model based on latent semantic analysis is obtained:

[0117]

[0118] In the formula: D represents the fault feature sample set of the reducer vibration signal under m kinds of working conditions, D = {D1, D, …D s ,D s+1 ,…D m}; represents the i-th fault feature sample in the sample D and belongs to the s-th working condition; represents the Fisher kernel function of LSSVM:

[0119]

[0120] Step 6: Use the vibration signal data of the reducer gear box under different working conditions, and the working condition details are shown in Table 1. The fault types include normal gear, tooth surface crack, tooth surface wear, tooth fracture and missing tooth.

[0121] Table 1 Working condition details

[0122]

[0123] Firstly, the relationship between the number of hidden variables and the average fault diagnosis accuracy under multiple working conditions needs to be analyzed to determine the number of hidden variables, Figure 7 The relationship between the number of hidden variables and the average fault diagnosis accuracy for source domain samples under different numbers of working conditions is shown in the figure. Figure 7 It can be observed that when the number of hidden variables is between 24 and 28, the average fault diagnosis accuracy reaches a maximum value. In order to reduce the computational complexity, the number of hidden variables is taken as 24. It can also be observed from the figure that under the condition of determining the number of hidden variables, the more working conditions the source domain sample contains, the higher the corresponding average fault diagnosis accuracy. Because the less working condition information the source domain data contains, the less implicit information can reflect the implicit characteristics of the target domain, therefore, the more working condition information the source domain sample data contains, the higher the corresponding average fault diagnosis accuracy.

[0124] Further explore the influence of multiple working conditions on the algorithm diagnosis results, select the reducer gearbox vibration signal data of E working condition from table 1 as the migration target domain sample set, randomly select 3, 4, 5 kinds of working condition data (i.e. 3, 4, 5 kinds of source domain) from the remaining eight kinds of working condition data as source domain sample set, each selection method is executed for 20 times, and 20 source domain auxiliary sample sets composed of reducer gearbox vibration signal data under different working conditions are constructed, that is, 20 fault diagnosis experiments are performed.

[0125] Tables 2, 3 and 4 are the diagnosis results of using 3, 4, 5 kinds of working condition data of reducer gearbox vibration signal as source domain auxiliary sample for migration. It can be observed that the diagnosis accuracy of each specific fault type using 4 and 5 kinds of working condition data is slightly higher than that using 3 kinds of working condition data. From the volatility of 20 diagnosis results, the volatility of diagnosis result accuracy using 5 kinds of working condition data is relatively small.

[0126] Table 2 specific fault type diagnosis accuracy (%) using 3 kinds of source domain

[0127]

[0128]

[0129] Table 3 specific fault type diagnosis accuracy (%) using 4 kinds of source domain

[0130]

[0131] Table 4 specific fault type diagnosis accuracy (%) using 5 kinds of source domain

[0132]

[0133]

[0134] To avoid the contingency of the diagnosis results of a certain type of fault, the average of the diagnosis results of each source domain feature set is calculated, and to analyze the stability of the diagnosis results more accurately, the standard deviation and variance are introduced to quantitatively represent the stability of the diagnosis results of the algorithm under multiple working conditions:

[0135]

[0136] In the formula: x i and respectively represent the average fault diagnosis accuracy using the i th source domain feature set and the overall mean value. The diagnosis results are shown in Figs. Figure 8 、 9 and 10.

[0137] From the diagnosis results of Figure 8 、 9 and 10, it can be observed that the average fault diagnosis accuracy using 3, 4, and 5 working condition data as source domain feature sample sets is not much different, but since more working condition data can be used as source domain feature sample sets to mine more implicit information as transferable knowledge to enhance the model, it can also be observed from the results that the standard deviation and variance of the diagnosis results when 5 working condition data are selected as the source domain feature sample set are smaller than those when 3 and 4 working condition data are selected. Based on this, it can be found that when considering the implicit features between the reducer fault vibration signals under different working conditions, the diagnosis results of the diagnosis model are more stable when using the reducer gear vibration signal data under multiple working conditions as the source domain transfer.

Claims

1. A method for diagnosing gearbox faults under multiple operating conditions, the method comprising: Step 1: Construct latent variables between the vibration signal samples and fault characteristics of the reducer under different operating conditions based on the probabilistic latent semantic analysis model; Step 1.1: Define the relevant variables for the probabilistic latent semantic analysis model; The vibration signal set of the reducer is D = {d1, d2, ..., d...} N The corresponding set of fault types for the reducer is W = {w1, w2, ..., w}. m The joint frequency matrix of "vibration signal-fault type" co-occurrence is N = {n(d,w)}, where (d,w) represents the fault type w for the reducer vibration signal d, and n(d,w) represents the frequency of a specific reducer vibration signal d with fault type w. A shared latent variable Z = {z1,z2,…,z} is introduced. K Under the condition of the hidden variable Z, the vibration signal set D and the fault type set W are independent of each other; Step 1.2: Generate joint distribution samples; Based on the probability distribution P(d) of the vibration signal D, N samples d are randomly selected from the vibration signal set D; under each sample d, a topic z is randomly selected from the latent variable Z according to the conditional probability P(z|d); then under each topic, a fault type w is randomly selected from the fault type set W according to the conditional probability P(w|z), and a joint sample (d,w) is generated. The generation probability of the entire co-occurrence sample set is obtained as follows: in, N represents the number of samples, n(d,w) represents the frequency of a specific reducer vibration signal d being fault type w, P(z) represents the probability distribution of the latent variable, and P(d|z) represents the probability that the vibration signal sample is d given that the latent variable is z. Step 2: Establish an LSSVM fault diagnosis model based on source domain-assisted migration. Mul (x) is; Where, N t Let λ be the number of samples under the s-th working condition. ij b are the model parameters that are set. Let be the classification hyperplane for the s-th working condition; Let K(·) be the classification hyperplane for the t-th working condition, and let K(·) denote the kernel function. This indicates that the i-th fault feature sample in sample D belongs to the t-th working condition; This indicates that the i-th fault feature sample in sample D belongs to the s-th working condition; Step 3: Calculate the values ​​of P(z), P(d|z), and P(w|z) to maximize the generation probability P(d,w) when the reducer vibration signal d contains fault type w; Step 3.1: Construct the maximum likelihood function; Step 3.2: Calculate P(z), P(d|z), and P(w|z) using the following formulas; Step 3.3: Combine the formulas from Step 3.1 and Step 3.2 with the formula from Step 2.2: By combining these methods and performing iterative calculations, we obtain P(z,d)=P(d|z)P(z); Step 4: Construct a fault feature dictionary; First, feature samples are generated based on the original reducer vibration signal. Then, the obtained feature samples are clustered, and a feature dictionary is constructed based on the clustering results. Step 5: Obtain sample data of the reducer vibration signal and corresponding fault type, and train the fault diagnosis model of Step 2 in combination with Steps 2, 3 and 4. Use the trained fault diagnosis model to detect the fault type of the reducer.

2. The method for diagnosing reducer faults under multiple operating conditions as described in claim 1, characterized in that, The types of gear reducer failures are classified as normal gear, tooth surface cracks, tooth surface wear, tooth breakage, and missing teeth.

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