Ensemble deep contractive auto-encoders for intelligent fault diagnosis of machines under noisy environment

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Abstract

Intelligent fault diagnosis methods based on deep auto-encoder have achieved great success in the past several years. However, these methods cannot effectively handle the data collected under noisy environment. Therefore, this paper proposes a new ensemble deep contractive auto-encoder (EDCAE) to address the problem. First, we design fifteen deep contractive auto-encoders (DCAE) to learn invariant feature representation automatically. Due to the Jacobian penalty term in DCAE and different characteristics, these models can deal with various noisy data effectively. Second, fisher discriminant analysis is applied to select low-dimensional features with the maximum class separability. Softmax classifier is adopted to identify the selected features and produce fifteen classification results. Finally, a new combination strategy is developed to combine these individual results. Benefitting from the combination strategy, it can produce accurate diagnosis results even under strong background noise. Additionally, to prove the effectiveness of EDCAE, theory analysis about error bound is conducted. The proposed method is verified on three case studies including bearing, gear box and self-priming centrifugal pump. Experiments are conducted under seven different signal-to-noise-ratios. Results show that EDCAE is better than other intelligent diagnosis methods, including individual DCAE, deep auto-encoder, sparse deep auto-encoder, deep denoising auto-encoder and several ensemble methods.

Introduction

Fault diagnosis of machine is of utmost importance, because early detection of emerging fault significantly improves operational continuity and equipment safety [1]. Among the existing methods, intelligent diagnosis methods do not need to model the physical systems and is very suitable for modern complex equipment [2]. Therefore, it has attracted widespread research interest recently.

Deep auto-encoder (DAE) is a promising intelligent diagnosis algorithm due to its ability to learn salient feature representations automatically [3], [4]. Such ability overcomes the weakness of traditional manual feature engineering that it is ad-hoc, labor-intensive, and may not generalize to multiple contexts [5]. Benefiting from the above advantage, intelligent diagnosis methods based on DAE have achieved great success [6]. Standard DAE was applied to the fault diagnosis of roller bearing [7]. DAE with a new maximum correntropy cost function was applied to fault diagnosis of gearbox [8]. As a variant of DAE, sparse deep auto-encoder (SDAE) encourages sparsity of feature representation. An extension SDAE was proposed for induction motor fault diagnosis [9]. However, in real engineering applications, environment noise corrupts signals [10]. DAE and SDAE cannot learn invariant features from such corrupted data, leading to seriously degraded diagnosis accuracies. Deep denoising auto-encoder (DDAE) provides an access to deal with the noisy data, which is achieved by adding noise with specified intensity to training samples [11]. But in real industrial applications, noise intensity usually varies and is unknown, which limits the application of DDAE. Therefore, it is still urgent to develop powerful intelligent diagnosis methods that have better adaptability to noise.

Deep contractive auto-encoder (DCAE) is a variant of DAE [12]. It explicitly encourages invariance and robustness of feature representation by penalizing the sensitivity to input [13]. DCAE provides an effective way to handle noisy data without knowing noise intensity. However, due to single network structure and difficulty in selecting activation functions, individual DCAE model has low generalization performances in different contexts. To alleviate this problem, ensemble learning provides an approach, which uses some certain strategies to combine the results from multiple individual learners and improves the generalization performances. To the best of our knowledge, aiming at fault diagnosis, only Shao et al. [14] combined ensemble learning with SDAE model. Although their method yielded better diagnosis accuracies than other diagnosis methods, they did not consider the influence of noise. Additionally, their method has several obvious drawbacks (see Section 2.1). Considering that the research of DAE with ensemble learning is still in its infancy, it is meaningful to develop ensemble DAE by taking advantage of both modules.

In this research, a novel ensemble deep contractive auto-encoders (EDCAE) is proposed for intelligent fault diagnosis of machines under noisy environment. It includes three steps: (1) Fifteen different activation functions are adopted to design fifteen DCAE models. These member models learn invariant feature representation from the noisy data. (2) Fisher discriminant analysis selects the low-dimensional features with the maximum class separability and softmax classifier outputs fifteen classification results. (3) A new ensemble strategy is developed to combine the fifteen classification results. Additionally, theory analysis about error bound of the ensemble strategy is conducted to prove its effectiveness. The proposed method is evaluated on three cases including bearing, gear box and Self-priming centrifugal pump. Experiments are conducted under seven different signal-to-noise-ratios (SNR). Results demonstrate that EDCAE is superior to individual DCAE model, DAE, SDAE, DDAE and several ensemble methods.

The rest of this paper is organized as follows. Related works are described in Section 2. In Section 3, the proposed EDCAE is detailed. In Section 4, the experiments and comparisons are conducted. Finally, conclusions and future work are drawn.

Section snippets

Related works

This section provides a brief introduction of related works, including literature review in Section 2.1 and principle of DCAE in Section 2.2.

The proposed EDCAE for intelligent fault diagnosis

This section details the proposed EDCAE method for intelligent fault diagnosis of machines. It contains four parts: (1) DCAE models design; (2) feature learning, selection and identification; (3) combination strategy design; (4) overall procedure of the proposed method.

Experimental verification

Section 4.1 presents the experiment scheme design. Based on the scheme, the proposed method is verified on three case studies, including bearing fault diagnosis, gear box fault diagnosis and self-priming centrifugal pump fault diagnosis.

Conclusion and future work

This paper proposes a new EDCAE method for intelligent fault diagnosis of machine under noisy environment. The main contributions are designing fifteen DCAE models with different characteristics, fusing DCAE model with FDA for feature learning and selection, developing a new combination strategy. Additionally, theory analysis about error bound is implemented to prove the effectiveness of EDCAE. EDCAE is evaluated on three case studies, including motor bearing, gear box and self-priming

CRediT authorship contribution statement

Yuyan Zhang: Methodology, Software, Writing - original draft, Validation, Data curation. Xinyu Li: Formal analysis, Writing - review & editing. Liang Gao: Conceptualization, Supervision, Resources, Funding acquisition. Wen Chen: Visualization, Investigation. Peigen Li: Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by National Key Research and Development Project [Grant Number 2019YFB1704603], National Natural Science Foundation of China [Grant Number 51775216], Natural Science Foundation of Hubei Province [Grant Number 2018CFA078], and Program for HUST Academic Frontier Youth Team [Grant Number 2017QYTD04].

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