Interpretable sparse learned weights and their entropy based quantification for online machine health monitoring

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Abstract

Incipient fault detection and diagnosis provide a firm grounding for machine health monitoring. Nevertheless, fault signatures at the time of an incipient fault are extremely weak and easily submerged by interference. Currently, signal processing based approaches and machine learning based approaches have been studied for incipient fault detection and diagnosis. However, the former requires relevant technicians with expert knowledge, while the latter needs a substantial volume of labeled samples without model interpretability. In this study, a physics-informed learning framework that integrates weight-based sparse degradation modeling with entropy based indicators is proposed to realize online incipient fault detection and diagnosis. Firstly, based on available normal baseline data and real-time data, a weight-based sparse degradation model is proposed to continually update physics-informed model weights so that weak fault characteristics indicated by learned weights can be considerably enhanced. Meanwhile, this study introduces a family of entropy based indicators for machine health monitoring and their performances are thoroughly investigated based on simulation and experimental studies, which aims to quantify amplified fault characteristics revealed by the continuously updated model weights for online incipient fault detection. Two case studies show that the proposed methodology has better detection ability and sensitivity than classical health indicators for incipient bearing faults. Since the proposed methodology does not demand fault data for model establishment, it is closer to real engineering applications and has more engineering meanings. Moreover, physics-informed model weights can automatically capture informative frequencies for immediate diagnosis and further analysis.

Introduction

Incipient fault detection and diagnosis are mandatory measures for machine health monitoring [1]. Herein, incipient fault detection methodologies monitor an incipient machine fault while fault diagnosis methodologies judge the type and location of the fault. Once the time of incipient fault initiation is determined, some quick diagnosis technologies should be carried out to confirm fault types. Therefore, it is essential to detect the time of incipient fault initiation and diagnose failure modes as soon as possible so that a timely and appropriate maintenance can be arranged in advance to avoid major disasters. Moreover, incipient fault detection and diagnosis play a fundamental role in machine performance degradation assessment (PDA) and prognostics [2]. The time of incipient fault initiation can be regarded as a trigger moment of PDA and remaining useful life (RUL) prediction [3], [4]. This is because performing prognostic technologies need to know any possible event as more as possible that is likely to affect its future degradation trend and evolution for RUL prediction modeling. Further, the confirmation of fault types is beneficial to fault severity and progression analysis. Nevertheless, there are many challenges of incipient fault detection and diagnosis. Firstly, incipient cyclic impulses are generated from vibration data in the presence of slight defects on rolling bearing surfaces. Thus, incipient signatures are weak for extraction because they are easily submerged in strong background noise. Secondly, incipient bearing faults usually trigger broad-bandwidth informative frequency bands and their energy is weakened and not so concentrated, which is difficult to locate and is severely overwhelmed by in-band noise. Therefore, incipient fault detection and diagnosis are emerging topics and they have been widely investigated during recent years [5], [6].

Given non-Gaussian and nonstationary characteristics of vibration signals in the presence of incipient bearing faults, some professional indices have been designed to detect incipient bearing faults and they have been combined with signal processing technologies to locate informative frequency bands for fault diagnosis [7]. For example, spectral kurtosis developed by Antoni [8] is a milestone health indicator for incipient bearing fault detection and a Fast kurtogram [9] was accordingly proposed to determine an optimal frequency band for fault diagnosis. However, the Fast kurtogram guided by maximization of spectral kurtosis is sensitive to impulsive noise and leads to a wrong decision of an optimal frequency band location. Aiming at this issue, many variants of spectral kurtosis and many solutions were proposed as summarized in [10]. Moreover, other advanced indicators, such as Gini index [11], [12] and smoothness index [13], were then put forward to replace kurtosis and they can achieve satisfactory results in incipient fault detection and diagnosis. The aforementioned indicators are typical sparsity measures [14] and they have been used to quantify sparsity properties of fault vibration signals to realize early fault monitoring and diagnosis. Meanwhile, Antoni et al. [15] proposed a general and statistical framework to develop health indicators for machine health monitoring based on a maximum likelihood ratio. A family of complexity measures, such as correlation dimension [16], permutation entropy [17], approximate entropy [18], etc., have been also investigated for machine health monitoring and fault diagnosis. Although these indicators with specific properties for incipient fault detection and diagnosis have been successfully applied in incipient fault detection and diagnosis, performances of these indicators are unstable in different application scenarios. Usually, it requires a lot of expert knowledge and engineering experience to select proper indicators and their theoretical studies are very complex. To get rid of dependence on domain and expert knowledge, machine learning based approaches have gradually become appealing topics to achieve incipient fault detection and diagnosis. For example, Ye et al. [19] proposed a graph-based modeling methodology to construct a health indicator and a hypothesis test was conducted on the health indicator to monitor incipient bearing faults. Mao et al. [20] utilized a stacked denoising autoencoder to extract useful features and obtained features were put into support vector data description (SVDD) for incipient bearing fault discovery. Chen et al. [21] presented a novel probability-relevant principal component analysis (PRPCA) and integrated PRPCA with test statistics for incipient fault detection. Zhang et al. [22] firstly established a baseline normal Gaussian cloud model and then Kullback-Leibler divergence was applied to develop a health indicator for early anomaly detection. Cheng et al. [23] combined deep slow feature analysis with a belief rule methodology to discover incipient gear faults. Zhou et al. [24] gave a thorough review of machine health monitoring based on health indicators. However, most existing data-driven incipient fault detection and diagnosis methodologies used a large number of historical and fault data for model training and estabilishment. Since pure data-driven approaches do not have any physical meanings and explicit explanations, they are not reliable and convincing in engineering applications. Therefore, there is a growing trend to develop a physics-informed data-driven modeling methodology that combines advantages of signal processing based approaches and machine learning based approaches. Currently, many researchers proposed physics-informed fault diagnosis modeling methodologies by simply using signal processing technologies as data preprocessing means [25], [26], [27]. Some works embedded signal processing technologies into an architecture of neural networks to develop a physics-informed or interpretable data-driven modeling methodology [28], [29]. Nevertheless, their model weights or outputs still have no physical meanings and model training demands a large amount of fault data.

Currently, statistical complexity measures have been widely studied for machine health monitoring and many applications indicate their effectiveness to quantify nonlinear fault characteristics and underlying dynamic changes [16], [17], [30]. In this study, a family of entropy based indicators is introduced to quantify interpretable model weights and construct health indicators for machine health monitoring. Their mathematical definition is equal to the interplay between entropy measures, such as Shannon entropy and distance measures, such as Euclidean distance in a normalized form, which is intuitive and computationally efficient. Currently, these entropy based indicators have been successfully applied in time series analysis of stock markets [31], song recognition [32], brain networks [33], etc. Wang et al. [34] used these entropy based indicators to select informative intrinsic mode function (IMF) components based on Empirical mode decomposition (EMD). In this study, we attempt to explore these entropy based indicators to generate health indicators for machine health monitoring. Further, a physics-informed learning framework that integrates weight-based sparse degradation modeling with entropy based indicators is proposed to realize online incipient fault detection and diagnosis. Meanwhile, their performances for incipient bearing fault detection are thoroughly presented based on simulation and experimental studies. The main contributions of this paper are summarized as follows.

  • 1)

    Firstly, a physics-informed sparse degradation modeling methodology is proposed to continuously learn interpretable weights that directly capture and amplify fault characteristics, such as fault characteristic frequencies and their harmonics. The proposed methodology can realize online incipient fault detection and diagnosis without any fault data for model building.

  • 2)

    Secondly, a family of entropy based indicators is introduced in this study to directly quantify the physics-informed model weights for incipient bearing fault detection. Moreover, their performances for machine health monitoring are thoroughly investigated based on simulation data and experiment data.

  • 3)

    Thirdly, experimental results show that the proposed physics-informed learning framework is more sensitive to incipient bearing faults than some famous health indicators. Moreover, useful and informative frequency components located and revealed by updated model weights do not need any prior and expert knowledge, which has potential applications in blind diagnosis scenarios.

The structure of this paper is summarized as follows. In Section 2, a physics-informed sparse degradation modeling methodology that uses square envelope spectra to online learn interpretable weights without needing any fault data is proposed. Section 3 introduces the definition of entropy based indicators and their performance for machine health monitoring is investigated based on simulation data. Finally, a whole picture of the proposed framework to realize online incipient fault detection and diagnosis is presented. Two bearing run-to-failure datasets are studied to validate the proposed framework and investigate the performances of proposed health indicators in Section 4. Conclusions are drawn in a final section.

Section snippets

Proposed physics-informed sparse degradation modeling methodology

It has been widely recognized that machine degradation is a slow and gradual performance deterioration process. It is difficult to obtain a large amount of degradation data and fault data for model training and establishment. Therefore, developing machine degradation models without requiring degradation or fault data for machine health monitoring has significant engineering applications. In this section, a physics-informed sparse degradation modeling methodology is proposed to online learn

Proposed learning framework that integrates sparse degradation modeling with entropy based indicators for online incipient fault detection and diagnosis

In this section, a physics-informed learning framework that integrates weight-based sparse degradation modeling with entropy based indicators is presented to realize online incipient fault detection and diagnosis. Firstly, the basic definition of entropy based indicators is introduced. Next, their performances for machine health monitoring are thoroughly investigated based on simulation data. Finally, a whole flowchart of the proposed weight learning framework for online incipient fault

Proposed methodology for online incipient fault detection and diagnosis of NASA bearing

Firstly, a popular bearing run-to-failure dataset that is one of the commonly used vibration-oriented datasets is introduced to indicate the feasibility and advantages of the proposed weight learning framework based on sparse degradation modeling and entropy based indicators for online incipient fault detection and diagnosis. The test rig that implemented a bearing run-to-failure experiment and collected life cycle vibration signals is depicted in Fig. 7 [40]. It can be observed from Fig. 7

Conclusions

This paper proposed a novel physics-informed weight learning framework that integrated sparse degradation modeling with entropy based indicators to realize online incipient fault detection and diagnosis. Firstly, a weight-based sparse degradation model was proposed to online learn interpretable weights for effectively extracting and enhancing fault characteristics. Based on interpretable weights learned from degradation data, intuitive fault detection and immediate fault diagnosis were

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.

Acknowledgment

The research work was fully supported by the National Natural Science Foundation of China under Grant No. 51975355, Grant No. 11632011 and No. 12121002). The authors would like to thank all valuable comments from three reviewers to improve the quality of this paper.

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