Fault Diagnosis of Rolling Bearing Based on Modified Deep Metric Learning Method

Zengbing Xu,Xiaojuan Li,Tao Peng,Zhigang Wang,Hui Lin,Riccardo Rubini

doi:10.1155/2021/6635008

Abstract

A novel fault diagnosis method of rolling bearing based on deep metric learning and Yu norm is proposed in this paper, which is called a deep metric learning method based on Yu norm (DMN-Yu). In order to solve the misclassification caused by the traditional deep metric learning based on distance metric function, a similarity criterion based on Yu norm is introduced into the traditional deep metric learning. Firstly, the deep metric learning neural network (DMN) is used to adaptively extract the fault feature parameters. Secondly, considering that the data samples at the boundary between different fault categories can be misclassified, the marginal Fisher analysis method based on Yu norm is used to optimize the features. And then, BPNN classifier of DMN-Yu method is used to fine tune the network parameters and diagnose the fault category. Finally, the effectiveness and feasibility of the proposed DMN-Yu method is verified with the rolling bearing fault diagnosis test. And the superiority of the proposed diagnosis method is validated by comparing its diagnosis accuracy with the deep metric learning method based on Euclidean distance (DMN-Euc), traditional deep belief network (DBN), and support vector machine (SVM) combined with the common time-domain statistical features.

Highlights

A novel fault diagnosis method of rolling bearing based on deep metric learning and Yu norm is proposed in this paper, which is called a deep metric learning method based on Yu norm (DMN-Yu)
The superiority of the proposed diagnosis method is validated by comparing its diagnosis accuracy with the deep metric learning method based on Euclidean distance (DMN-Euc), traditional deep belief network (DBN), and support vector machine (SVM) combined with the common time-domain statistical features
In order to evaluate the superiority of the deep metric learning neural network (DMN)-Yu model, the deep metric learning method based on Euclidean distance (DMN-Euc), the traditional DBN, and the traditional support vector machine (SVM) combined with extracted manually feature parameters are used to diagnose the fault category of bearings

Summary

Theory of Deep Metric Learning

Where Z(1) is the weighted sums of the input of the first layer, W(1) ∈ RP(1)×d is the projection matrix learned in the first layer, b(1) ∈ RP(1) is the bias vector in the first layer, and s is the nonlinear activation function of each layer, which can be a sigmoid function or a tanh function. e tanh function was used as the nonlinear activation function in this paper. en, the output h(1) of the first layer is used as the input of the second layer, and the output h(2) of the second layer can be computed as. Where Z(1) is the weighted sums of the input of the first layer, W(1) ∈ RP(1)×d is the projection matrix learned in the first layer, b(1) ∈ RP(1) is the bias vector in the first layer, and s is the nonlinear activation function of each layer, which can be a sigmoid function or a tanh function. Where Z(2) is the weighted sums of the input of the second layer and W(n) ∈ R , b P(2)×P(1) (2) ∈ RP(2), and s are the projection matrix, bias, and activation function of the second layer, respectively. If f(X) is the output of input X, the Euclidean distance of the data points xi and xj in the deep metric network space is written as follows: df􏼐xi, xj􏼑 d􏼐f xi􏼁 − f􏼐xj􏼑􏼑 f xi􏼁 − f􏼐xj􏼑 2, (9). Where the goal of the deep metric learning is to establish the mapping function f under some certain constraints

Deep Metric Learning Model Based on Yu Norm

Case Analysis

Method

Findings

Conclusion