CN113551904B

CN113551904B - Gear box multi-type concurrent fault diagnosis method based on hierarchical machine learning

Info

Publication number: CN113551904B
Application number: CN202110722255.9A
Authority: CN
Inventors: 蔡志强; 陈秋安; 司书宾; 段锋; 孟学煜; 张帅
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2021-06-29
Filing date: 2021-06-29
Publication date: 2023-06-30
Anticipated expiration: 2041-06-29
Also published as: CN113551904A

Abstract

The invention relates to a multi-type concurrent fault diagnosis method of a gear box for hierarchical machine learning, which provides a brand-new hierarchical machine learning model on the basis of traditional machine learning, wherein the model comprises two layers, the first layer is a traditional machine learning model with a simple structure, and the method is used for identifying single fault types with easily-distinguished characteristics and filtering multi-type concurrent fault samples which cannot be accurately identified to the second layer, and the second layer model is used for carrying out correct classification. And the second layer adopts an extreme learning machine to establish a classification model, the extreme learning machine is a single-layer feedforward neural network, and gradient calculation in the traditional neural network negative feedback regulation process is overcome by adopting least square fitting, so that the adjustment of model parameters can be realized rapidly. Through the hierarchical machine learning, fault diagnosis is carried out, so that the accuracy of fault recognition can be improved, and the training efficiency can be greatly improved.

Description

Gear box multi-type concurrent fault diagnosis method based on hierarchical machine learning

Technical Field

The invention belongs to the field of fault diagnosis of rotary mechanical equipment, and particularly relates to a multi-type concurrent fault diagnosis method of a gear box based on hierarchical machine learning.

Background

Gearboxes are the most widely used class of rotating machinery in industrial equipment, and particularly have a significant role in aerospace equipment as an important transmission component. The research on fault diagnosis of the gearbox can improve the reliability of the gearbox and ensure the normal operation of equipment. Under the general condition, the running condition of the rotary machine is complex, the performance can be gradually degraded in the continuous long-term running process, faults are easy to occur, the quality of products is reduced or production is stopped, and huge property loss and casualties are caused by heavy weight. The gearbox plays a key role in the power transmission and motion conversion process of mechanical equipment and is also the most vulnerable part in the rotating mechanical equipment. It is counted that 70% of the malfunctions of the rotating machine are directly related to the gearbox. Therefore, related researches on state detection and fault diagnosis of mechanical equipment of the gear box are developed, fault hidden dangers existing in equipment operation are timely and accurately found, and the method has important significance in guaranteeing equipment safety and reducing accident occurrence.

Aiming at fault diagnosis and reliability research of a gear box, three modeling methods mainly exist at the present stage: a mechanism-based modeling method, a knowledge-based modeling method, and a data-driven modeling method. The modeling method based on the mechanism needs to fully know the internal structure and the mechanism of the equipment, and the established model has profound physical significance, so that the modeling method has good ductility. However, when the structure of the device is too complex and all information of the internal mechanism of the complex device cannot be obtained, it is very difficult to build an accurate model. In addition, the mechanism modeling is always based on a plurality of simplifications and assumptions, and therefore, errors are generated between the output of the model and the actual result. Knowledge-based modeling methods do not require complete knowledge of the internal mechanisms of the complex equipment, and the built models are easy to understand, but can be less versatile. Building a knowledge model requires accumulating a great deal of production experience and process knowledge, but if an unprecedented fault is encountered, false positives and false negatives occur due to the lack of corresponding experience and knowledge. The modeling method based on data driving does not need an accurate model and related prior knowledge of equipment, but directly performs fault diagnosis, reliability analysis and the like on the collected equipment data, and a machine learning algorithm is a typical representative of the data. With the rise of artificial intelligence and the massive accumulation of equipment data in recent years, data-based methods have attracted attention from more and more researchers, and have gradually become the first solution in the field of gearbox fault diagnosis.

The Chinese patent with publication number of CN108918137A discloses a gear box fault diagnosis device based on an improved WPA-BP neural network and a method thereof. However, the current fault diagnosis methods based on the neural network and the heuristic parameter optimization algorithm have the following defects: multiple iterations are required to cause inefficiency in modeling; heuristic algorithms are prone to being trapped in local optima, and results are unstable; only aiming at a plurality of single-type fault diagnosis problems, the method cannot adapt to complex multi-type concurrent fault diagnosis scenes.

Disclosure of Invention

The invention solves the technical problems that: in order to overcome the defect that modeling efficiency is low and effective diagnosis cannot be carried out on multiple types of concurrent faults in the prior art, the invention provides a gear box multiple types of concurrent faults diagnosis method based on hierarchical machine learning. The method provides a brand new hierarchical machine learning model based on traditional machine learning, wherein the model comprises two layers, the first layer is a traditional machine learning model with a simple structure, and the model is used for identifying single fault types with easily-distinguished characteristics, filtering multiple types of concurrent fault samples which cannot be accurately identified to the second layer, and carrying out correct classification by the second layer model. And the second layer adopts an extreme learning machine to establish a classification model, the extreme learning machine is a single-layer feedforward neural network, and gradient calculation in the traditional neural network negative feedback regulation process is overcome by adopting least square fitting, so that the adjustment of model parameters can be realized rapidly. Through the hierarchical machine learning, fault diagnosis is carried out, so that the accuracy of fault recognition can be improved, and the training efficiency can be greatly improved.

The technical scheme of the invention is as follows: a gearbox multi-type concurrent fault diagnosis method based on brand-new level machine learning comprises the following steps:

step 1: constructing a gearbox fault dataset comprising the sub-steps of:

step 1.1: a gear box fault diagnosis experiment platform is built, the sensor is utilized to collect the original characteristic data, wherein the original characteristic data comprises the rotation speed, the rotation acceleration and the displacement of the gear box,

step 1.2: preprocessing the original characteristic data obtained in the previous step, and constructing a fault data set for training a machine learning model; meanwhile, the samples are divided into normal samples and fault samples, and the training set and the testing set are divided according to a random mode for the data set so as to evaluate the effect of the trained model;

step 2: the processed data in the step 1 is used for establishing a traditional machine learning two-classification model for identifying the state of the gear box; then establishing a multi-classification model, wherein the model is a first-layer classification model;

step 3: evaluating the multi-classification model obtained in the step 2 and filtering out sample data which is not classified correctly, comprising the following sub-steps:

step 3.1: establishing an evaluation system of the multi-classification model in the step 2, namely comparing fault diagnosis performance of each multi-classification algorithm in the step two by using an confusion matrix, classification accuracy, classification recall and classification accuracy evaluation indexes;

step 3.2: displaying the evaluation indexes in the step 3.1 in an image mode to perform visual analysis, checking the accuracy of fault diagnosis of each category, and taking a model with highest accuracy as an optimal model; filtering fault type samples lower than an accuracy threshold in the optimal model;

step 4: establishing a fault diagnosis model which is a second layer model according to the fault samples filtered in the step 3, wherein the method comprises the following substeps:

step 4.1: diagnosing by adopting an extreme learning machine, wherein the extreme learning machine comprises three layers, namely an input layer, a hidden layer and an output layer; assume that there are N training samples (x _i ,y _i ) Wherein x is _i ＝[x _i1 ,x _i2 ,...,x _in ]∈R ⁿ Is an n-dimensional input sample, y _i ＝[y _i1 ,y _i2 ,...,y _in ] ^T ∈R ^m Is the corresponding m-dimensional output, and the goal of learning is to find the relationship between the input and the output. Assuming that the hidden layer has L nodes and the activation function is g (·), the expression of the extreme learning machine is:

wherein beta is _j Is the output weight, omega of the j-th hidden layer node _j Is a weight vector connecting the ith input node and the jth hidden node, b _j Is the bias of the j-th hidden layer node;

the output of the learning machine is finally obtained as follows:

step 4.2: introducing a kernel matrix on the output in step 4.1: k=hh ^T The output of the kernel extreme learning machine is:

step 5: the multi-classification model in the step 2 is used for obtaining a part type diagnosis result with higher precision, the extreme learning machine in the step 4 is used for obtaining a part type diagnosis result filtered out by the step 3, and the two results are summarized to obtain a final diagnosis result.

The invention further adopts the technical scheme that: the data set comprises a training set and a testing set, wherein the training set comprises 70% and the testing set comprises 30%.

The invention further adopts the technical scheme that: in the step 2, a logistic regression method is adopted for identifying the state of the gear box, and the logistic regression expression is as follows

Where g (z) represents the activation function, x is the input vector, w is the weight vector, and b is the bias vector. For convenience of representation, w and b are replaced by θ, with the following result

Then, identifying samples in a fault state by using a classification model, and dividing the specific types of each fault sample; after division, a plurality of different algorithms are adopted to establish a multi-classification model for fault diagnosis.

The invention further adopts the technical scheme that: a multi-classification model for fault diagnosis is established by adopting a support vector machine and a neural network,

the support vector machine expression is as follows:

the neural network expression is as follows: assuming that the number of layers of the neural network is K (K>1) The number of nodes of each layer from the input layer to the output layer is m ₀ ,m ₁ ,…,m _K Thereby defining the dimension of the input vector as m ₀ The dimension of the output vector is m _k . Each layer of output vector of the network is expressed as follows:

input layer:

hidden layer one:

hidden layer two:

…

output layer:

weight matrix and bias vector for each layer

The output of the network is +.>

Effects of the invention

The invention has the technical effects that:

the multi-type concurrent fault diagnosis method for the gear box based on the hierarchical machine learning is mainly based on the traditional machine learning algorithm and the extreme learning machine to complete the construction of a hierarchical machine learning model, and analysis and summarization of model effects are carried out through various evaluation indexes, so that the modeling and diagnosis processes are simple and efficient.

The multi-type concurrent fault diagnosis method for the gearbox based on the hierarchical machine learning can identify the normal state and the fault state of the gearbox, can diagnose the identified fault type, particularly can accurately and efficiently complete fault diagnosis based on a simple and easily-realized hierarchical machine learning model for complex multi-type concurrent fault diagnosis, has clear structure and clear thought, and has good effect, and can meet expected targets.

The multi-type concurrent fault diagnosis method for the gear box based on hierarchical machine learning can effectively utilize test data of the gear box to carry out fault diagnosis on the gear box, and can obtain a model with the best effect by evaluating diagnosis results of different models. In addition, the final result is a specific multi-type concurrent fault diagnosis result, which is favorable for scientific quantitative evaluation of the running state and performance of the gear box and has important significance for improving the reliability of the whole machine of the gear box.

Drawings

FIG. 1 is a flow chart of a fault diagnosis algorithm based on hierarchical machine learning.

FIG. 2 is a schematic diagram of a model and data change flow of a hierarchical machine learning algorithm in an embodiment.

Fig. 3 is a schematic diagram of fault diagnosis results based on a conventional machine learning algorithm in an embodiment.

FIG. 4 is a graph of ROC results for various algorithms as a second layer model in an embodiment.

Fig. 5 is a schematic diagram of the final effect after being processed by the hierarchical machine learning algorithm in the embodiment.

Detailed Description

In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention.

With reference to figures 1 to 5 of the drawings,

the technical scheme adopted for solving the technical problems is as follows:

the multi-type concurrent fault diagnosis method for the gearbox based on hierarchical machine learning is characterized by comprising the following steps of:

step 1, constructing a gear box fault data set;

firstly, an experimental platform is built to collect necessary original characteristic data, and characteristic variables which can reflect the performance of rotating mechanical parts best are extracted by combining actual conditions. And carrying out data preprocessing on the original data, including a series of operations such as missing value processing, data standardization, feature dimension reduction and the like, and finally constructing a fault data set for training a machine learning model. Labeling normal samples and fault samples, and dividing a training set and a testing set for the data set so as to evaluate the effect of the trained model.

Step 2, establishing a multi-type concurrent fault diagnosis model based on traditional machine learning

According to the data collected in the step 1, a traditional machine learning model is established for state identification and fault diagnosis of the gear box, samples in fault state are identified, and specific types of each fault sample are divided, such as pitting, tooth breakage, abrasion and the like, and the specific types of each fault sample represent different fault types of the gear. In order to select the classification model with the best effect, algorithms based on a support vector machine, an artificial neural network, a random forest, a gradient lifting tree and the like are used for respectively establishing a multi-classification model for fault diagnosis.

And 3, evaluating the first-layer algorithm model and filtering out sample data which are not classified correctly.

a. Firstly, an evaluation system of the fault diagnosis model in the step 2 is established, evaluation is carried out by using evaluation indexes such as confusion matrix, classification accuracy, classification recall and the like, and fault diagnosis performance of each algorithm on the first layer model is compared.

b. And visually analyzing the processing result of the first layer model, and checking the accuracy of fault diagnosis of each class. And setting a threshold value for fault diagnosis precision according to actual production requirements, filtering out fault type samples lower than the precision threshold value in each model, and carrying out processing of subsequent steps.

Step 4, establishing a fault diagnosis model according to the fault samples filtered in the step 3

The original fault data set is processed by the first layer model, the number of the data samples which are screened out and not classified correctly is only a small part, and the fault data set can be diagnosed by adopting an extreme learning machine. The extreme learning machine comprises three layers, namely an input layer, a hidden layer and an output layer. Assume that there are N training samples (x _i ,y _i ) Wherein x is _i ＝[x _i1 ,x _i2 ,...,x _in ]∈R ⁿ Is an n-dimensional input sample, y _i ＝[y _i1 ,y _i2 ,...,y _in ] ^T ∈R ^m Is the corresponding m-dimensional output, and the goal of learning is to find the relationship between the input and the output. False, falseLet the hidden layer have L nodes, and the activation function be g (), then extreme learning machine's expression is:

wherein beta is _j Is the output weight, omega of the j-th hidden layer node _j Is a weight vector connecting the ith input node and the jth hidden node, b _j Is the bias of the j-th hidden layer node.

The extreme learning machine is a special feedforward neural network, and is characterized in that the weights and the biases of hidden layer nodes are given randomly or artificially, updating is not needed, the learning process only calculates the output weights, back propagation iterative calculation is not needed, and the efficiency is greatly improved. The extreme learning machine takes each sample as an input layer node, and the theoretical training set error can be infinitely close to 0, so that the extreme learning machine as a second layer model has very good precision and efficiency on a fault data set with a small sample size. Writing equation (1) into a compact format:

Hβ＝Y (2)

wherein H is E R ^N×L Is the hidden layer output matrix and Y is the real label matrix.

The goal of an extreme learning machine is to minimize training errors, which can be expressed as the following optimization problem:

wherein C is a generalization factor, θ is a training error, and the conversion to dual optimization problem is as follows:

wherein alpha is _i Is the lagrangian multiplier for the ith training sample. Respectively calculate L _D For beta, theta _i And alpha _i And let the partial differential result be 0, namely:

the output weights can be derived as:

where I is the identity matrix. The final extreme learning machine output is:

random initialization of the extreme learning machine, while avoiding negative feedback adjustment, is less robust and generalizing the model. In order to improve the stability and generalization capability of the extreme learning machine, a kernel method is introduced, wherein the kernel method regards a hidden layer as an unknown feature, and the mapping from an input space to a feature space can be realized. The kernel matrix is defined as:

K＝HH ^T (10)

the output of the kernel extreme learning machine is:

the kernel extreme learning machine has better effect than the extreme learning machine, but the introduction of the kernel increases model parameters at the same time, and the relative optimal solution of the model can be found by optimizing the parameters by adopting a grid search strategy.

Step 5, obtaining a final hierarchical machine learning model and evaluating the effect thereof

And (3) integrating the results of the step (2), the step (3) and the step (4) to obtain a final multi-type concurrent fault diagnosis result of the gearbox based on the hierarchical machine learning model. Hierarchical machine learning is still a multi-classification problem which is basically solved, so that the multi-classification model is evaluated by adopting evaluation indexes of the multi-classification model, such as an overall confusion matrix, overall classification accuracy and fault diagnosis accuracy of each type, overall classification recall and fault diagnosis recall of each type, and the like.

The embodiment is a gearbox multi-type concurrent fault diagnosis method based on hierarchical machine learning.

Referring to fig. 1 to 5, the multi-type concurrent fault diagnosis method for a gearbox based on hierarchical machine learning according to the embodiment is applied to a gearbox for fault diagnosis, and specifically comprises the following steps:

and 1, constructing a gear box fault data set. The specific mode is as follows:

in the embodiment, the experimental data of the QPZZ-II rotary machine vibration analysis and fault diagnosis test platform system is taken as a research object, and the system can rapidly simulate various states and vibration of the rotary machine and can perform comparative analysis and diagnosis of various states. The system is widely applied to scientific research, teaching, product development, personnel training and the like in universities, industrial and mining and scientific research institutions. The international tandem organization in japan has been trained on advanced engineers for diagnosis of international equipment using a similar platform so far, with good results. The system is used for carrying out a gearbox simulation experiment, the gearbox consists of a large gear with the number of teeth of 75 and a small gear with the number of teeth of 55, and the modulus of the two gears is 2. The experiment simulates the operation process of the gearbox, and totally comprises a normal state and five fault states, wherein the five fault states comprise three single fault types and two concurrent fault types. The three single faults are a large gear pitting fault, a large gear broken tooth fault and a small gear abrasion fault, and the two concurrent faults are large gear pitting plus small gear abrasion and large gear broken tooth plus small gear abrasion. To be able to build a machine learning model for diagnosing the gearbox state, 8 characteristic variables, denoted F1, F2, F3, F4, F5, F6, F7 and F8, respectively, were collected for the experiment, and pearson correlation coefficients between the characteristic variables are shown in table 1.

TABLE 1 relationship between characteristic variables

The experiment collected 2100 valid samples in total, including 1000 normal samples, 200 large gear pitting failure samples, 200 large gear tooth breakage failure samples, 300 small gear wear samples, 200 large gear pitting plus small gear wear failure samples, and 200 large gear tooth breakage and small gear wear failure samples. The whole data set is divided into a training set and a test set, wherein the training set accounts for 70% and the test set accounts for 30%, then each state sample data is added with a label value, and the specific data distribution is shown in table 2.

TABLE 2 data set State distribution and tag case

And 2, diagnosing faults of the gear box by using a support vector machine, a random forest, a gradient lifting decision tree and an artificial neural network as classifiers according to the data collected in the step 1. Training of each model is performed with a training set, and then the results of the test set are used as a measure of model effectiveness. The diagnostic results of each model on the test set are shown in tables 3 to 6.

TABLE 3 diagnostic results of random forest on test set

TABLE 4 support of diagnostic results of vector machines on test sets

TABLE 5 gradient-lifting decision tree diagnostic results on test set

TABLE 6 diagnostic results of artificial neural networks on test sets

And 3, evaluating the first-layer algorithm model and filtering out sample data which are not classified correctly. The concrete mode is as follows:

a. firstly, according to the diagnosis result of the step two, the effect of each classifier is evaluated, and four commonly used multi-classification evaluation indexes are Average Accuracy (AA), macro accuracy (MP), macro Recall (MR) and macro F1-Measurement (MF) respectively. Their definitions are as follows:

where n represents the number of categories, 6 in this experiment, tp represents that both the real tag and the predictive tag are positive, TN represents that both the real tag and the predictive tag are negative, FP represents that the real tag is negative and the predictive tag is positive, FN represents that the real tag is positive and the predictive tag is negative. The relationship between them is shown in Table 7:

table 7 TP, TN, FP, FN relation

As shown in fig. three, scores on four different indexes of each algorithm and classification accuracy on each category can be derived from tables 3, 4, 5, 6 and 7 and formulas (1), (2), (3) and (4).

b. The third graph includes two parts, the larger part can see the scores of the algorithms on four evaluation indexes, and the smaller part can see the classification accuracy of the algorithms on each type of sample. It can be seen from the plot that the sample accuracy of

labels

4 and 6 is far lower than other categories, indicating that the characteristics of the two types of fault samples are similar, so that the classifier cannot make a correct judgment. In order to improve the overall fault diagnosis accuracy, the sample data of the two types should be filtered out and sent to the next layer of model for further diagnosis.

And 4, establishing a fault diagnosis model according to the fault sample filtered in the step 3. The concrete mode is as follows:

filtered out are the failure samples of

labels

4 and 6, so the second layer model is actually performing a classification task. Wherein there are 300 samples with a label of 4 and 200 samples with a label of 6, and the samples are equally divided into a training set of 70% and a test set of 30%. The two classification models in this experiment respectively adopt Logistic Regression (LR), extreme Learning Machine (ELM), kernel Extreme Learning Machine (KELM), kernel extreme learning machine (GKELM) using a grid search strategy for parameter optimization, and the kernel functions in this example all select gaussian kernel functions. The diagnostic results of each model on the test set are shown in tables 8 to 11.

Table 8 diagnostic results of LR on test set

TABLE 9 diagnosis of ELM on test set

Table 10 diagnosis of KELM on test set

TABLE 11 diagnostic results of GKELM on test set

For evaluation of two-class machine learning, ROC curves are generally used, and the full name of ROC is a receiver operating characteristic curve, also called a sensitivity curve. The reason for this is that each point on the curve reflects the same sensitivity, they are all responses to the same signal stimulus, but are the results obtained at several different decision criteria. The receiver operation characteristic curve is a graph formed by taking the probability of frightening as a horizontal axis (FPR), the probability of hitting as a vertical axis (TPR), and curves drawn by different results obtained by different judging standards under the specific stimulation condition. The ROC curves for the four bi-classifiers in this experiment are shown in fig. 4, where:

auc in the legend shows the area of the plane graph of each algorithm curve and the x-axis city, and according to the property of the ROC curve, the larger the area value is, the better the classifier performance is, and the best effect of the GKELM as the second layer model can be seen from the graph. In order to explore the effect of hierarchical machine learning when the second layer model is GKELM, samples filtered by the first layer model are respectively processed by the second layer GKELM model, and specific diagnosis results of each category are shown in tables 12 to 15.

TABLE 12 RFC-GKELM diagnostic results

TABLE 13 SVC-GKELM diagnostic results

TABLE 14 GBDT-GKELM diagnostic results

TABLE 15 ANN-GKELM diagnostic results

And 5, combining the step 2, the step 3 and the step 4 to obtain a final hierarchical machine learning model and evaluating the effect of the model. The concrete mode is as follows:

step 2, training a plurality of models, step 3, comparing each algorithm model of the first layer, step 4, classifying the filtered samples, and comparing each algorithm model of the second layer. The hierarchical machine learning model in this example therefore includes two layers, the first layer model for diagnosing the gearbox states 1, 2, 3 and 5 and the second layer model for diagnosing the

states

4 and 6. In this experiment, each layer of models contained multiple algorithms, and although the models in each layer were compared laterally and the best model was selected, the effect between layers was not considered, and all model combination diagnostic results were compared to determine the best model combination, as shown in table 16. It can be clearly seen from table 16 that the hierarchical machine learning model of the SVC and GKELM combination works best.

Table 16 all models combine diagnostic results

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Claims

1. A multi-type concurrent fault diagnosis method of a gear box based on hierarchical machine learning is characterized by comprising the following steps:

step 1: constructing a gearbox fault dataset comprising the sub-steps of:

step 4.1: diagnosing by adopting an extreme learning machine, wherein the extreme learning machine comprises three layers, namely an input layer, a hidden layer and an output layer; assume that there are N training samples (x _i ，y _i ) Wherein x is _i ＝[x _i1 ，x _i2 ，...，x _in ]∈R ⁿ Is an n-dimensional input sample, y _i ＝[y _i1 ，y _i2 ，...，y _in ] ^T ∈R ^m Is the corresponding m-dimensional output, and the aim of learning is to find the relationship between the input and the output; assuming that the hidden layer has L nodes and the activation function is g (·), the expression of the extreme learning machine is:

the output of the learning machine is finally obtained as follows:

2. A method for diagnosing multiple types of concurrent faults in a gearbox based on hierarchical machine learning as claimed in claim 1 in which the data set comprises a training set and a test set, wherein the training set comprises 70% and the test set comprises 30%.

3. The method for diagnosing multiple concurrent faults of a gear box with brand-new level of machine learning as claimed in claim 1, wherein in the step 2, a logistic regression method is adopted for identifying the state of the gear box, and the logistic regression expression is as follows

Where g (z) represents the activation function, x is the input vector, w is the weight vector, and b is the bias vector; for convenience of representation, w and b are replaced by θ, with the following result

4. A multi-type concurrent fault diagnosis method for a gear box based on hierarchical machine learning as claimed in claim 3, wherein a multi-classification model for fault diagnosis is established by using a support vector machine and a neural network,