Transfer fault diagnosis based on local maximum mean difference and K-means

Highlights

• A novel transfer fault diagnosis framework is proposed.

• Local maximum mean difference acts on a sparse auto-encoder to achieve subdomain alignment of features.

• The K-means-based method is put forward to explore the structure information of unlabeled target samples.

Abstract

Existing feature-based transfer learning methods have achieved great performance in the transfer fault diagnosis with unlabeled data. While most of them are global alignment methods based on maximum mean difference (MMD), which ignore the differences between different faults and pay little attention to the structural information in the unlabeled target samples. This paper proposes a transfer sparse auto-encoder (SAE) based on local maximum mean difference (LMMD) and K-means to solve the above problems. Firstly, we build a deep network based on SAE and LMMD for learning a common latent feature space where source and target subdomains are aligned. Subsequently, to fully explore the target domain information, we put forward the K-means-based method which can obtain final diagnosis results by synthesizing the source and target domain information in the latent feature space. Lastly, a case study is conducted to verify the robustness and effectiveness of the proposed methods. The experimental result demonstrates that the proposed methods outperform the MMD-based methods in the transfer fault diagnosis problem.

Introduction

Bearing is an essential but easily damaged component of rotating machinery, and often works in complex and various environments (Lin et al., 2020). Once bearing fault occurs, it will substantially affect the efficiency of machines, thereby causing economic losses (Patel & Upadhyay, 2020). Thus, bearing fault diagnosis methods has emerged to address the aforementioned concerns (Fernández-Francos et al., 2013, Wang and Chen, 2011).

Recently, deep learning-based methods have achieved successful cases for fault diagnosis such as deep belief network (DBN) (Yu and Liu, 2020, Zhong et al., 2021), deep sparse auto-encoder (SAE) (Li et al., 2019b; Wang et al., 2019), convolutional neural network (CNN) (Chen et al., 2020a; Souza et al., 2021). While these methods are data greedy and need a lot of labeled data to assist training (Guo et al., 2019). In the real world, bearings often operate in numerous working conditions, it is very difficult to record the bearing failures under each working condition due to the huge consumption of human and financial resources. Moreover, the collected vibration signals undergo linearly or nonlinearly under different working conditions. That is, only some operating data without labels can be collected under some working conditions. Furthermore, the models trained under other working conditions cannot be directly applied to the working conditions owing to different data distribution.

Transfer learning (TL) (Chen et al., 2020b; Li et al., 2020) introduces an efficient means to handle the preceding problems by using knowledge learned from one working condition to solve problems in different but related working conditions. Most of the recent works are statistic moment matching-based methods (Si et al., 2021, Wei et al., 2021). They aim to seek a common feature space where the difference between target and source domains is minimized. To achieve this goal, several metrics have been raised to measure the differences between domains (Che et al., 2020, Jin et al., 2020, Lu et al., 2020). As an effective distance measurement method without parameters, the maximum mean difference (MMD) has become one of the most popular methods in transfer fault diagnosis (Li et al., 2019c; Yang et al., 2019). For example, Wen et al. (2019) successfully applied the SAE combined with the MMD penalty term to the transfer diagnosis task on the CRWU dataset.

However, these MMD-based methods are global alignment approaches without considering the differences in distribution between faults. As result, they align the differences between domains, while also confusing the differences between faults, leading to negative transfer. To take into account the differences of different domains and different categories simultaneously, Long et al. (2013) proposed joint maximum mean difference (JMMD), which achieves conditional probability alignment by generating pseudo-labels on the target domain data. This pseudo-labels-based method is not robust enough, since misalignment accumulates with pseudo-labels errors. For the robust subdomain alignment, Zhu et al. (2020) design a local maximum mean discrepancy (LMMD) which achieves subdomain alignment by assigning different weights to samples. And the weights of samples are generated iteratively according to the output probability on the classifier.

Nevertheless, since LMMD is an iterative method of generating weights, it is often affected by the initial weights. It is very meaningful to design an effective starting weight for LMMD. The SAE provides a robust way to generate the initial parameters of the network by capturing the distribution characteristics of raw data. And the previous combination of SAE and MMD worked well. Therefore, a neural network constructed by fusing LMMD and SAE is expected to achieve better results.

In addition, most of the existing methods in transfer fault diagnosis obtained the final classifier results through the trained softmax classifier (Wu et al., 2020) or support vector machine (SVM) (Zhang et al., 2020). These methods only use the data in the source domain and ignore the structure information in the unlabeled target domain. While, these unlabeled data often contain meaningful information, which can help us further enhance the accuracy of the diagnosis. To fully explore this valuable information, we resort to the K-means-based-method (Tian et al., 2020) which is proved to be an efficient and useful method in pseudo-label propagation.

In summary, the majority of the aforementioned researches are presented in Table 1.

Inspired by the preceding challenges, we proposed novel transfer SAE based on LMMD and K-means (SAE-LK) for transfer fault diagnosis. Firstly, we establish a deep network based on SAE and LMMD (SAE-MMD) to train a transfer encoder that can obtain domain-adaptive features by aligning subdomains. Then we map the source and the target domain data into a common latent feature space by the trained encoder. Moreover, to fully mine the structural information in the target domain, we employed the K-means-based method to generate fault centers of the target domain and obtained the final diagnosis results by measuring the distance between samples and the fault centers. An extensive experiment based on a bearing data set was conducted to show the superiority of the proposed SAE-LK.

The remainder of this paper is organized as follows. Section 2 introduces the basic theory of SAE and LMMD. Section 3 proposes the detail of the proposed SAE-LK. Section 4 conducts six transfer tasks based on a bearing data set to show the efficiency of the proposed TEDAE. Lastly, Section 5 draws the conclusion.