A novel support vector regression method for online reliability prediction under multi-state varying operating conditions

Highlights

• A data-driven method is proposed for prognostics in multi-state operating condition.

• Features are developed to assess different reliability evolution trends.

• A sequential Monte Carlo framework is adopted for the online prediction.

• The proposed method is applied with several electrical and mechanical applications.

• The prediction accuracy, robustness and speed are evaluated.

Abstract

Modeling the evolution of system reliability in the presence of Condition Monitoring (CM) signals is an important issue for improved reliability assessment and system lifetime prediction. In practice, during its lifetime, a system usually works under varying operating conditions due to internal or external factors such as the ambient environments, operational profiles or workloads. In this context, the system reliability can show varying evolution behaviors (follow changing underlying trajectories), which presents new challenges to describe precisely the dynamics of system reliability. Thus, this paper proposes a novel data-driven approach to address the problems including the identification of varying operating conditions, the construction and dynamical updating of evolution model, and finally the online prediction of system reliability, focusing on systems under one common and typical case of varying operating conditions, the multi-state operating condition. Experiments based on artificial data and some widely studied real reliability cases reveal that the proposed method has superior performance compared with some existing benchmark approaches, in the case under consideration. This improved reliability prediction provides fundamental basis for advanced prognostics such as the Remaining Useful Life (RUL) estimation.

Introduction

Generally, reliability assessment focuses on predicting the future system reliability or State of Health (SOH) based on Condition Monitoring (CM) signals (observable indicators used to infer the unobservable underlying SOH, e.g., the capacity of a battery or the bearing vibration of a gear-box) [1]. It provides fundamental analysis for failure prognostics methods such as Remaining Useful Life (RUL) estimation or other methodologies aiming at avoiding system sudden shutdowns, increasing system availability and safety, and reducing the cost of accident and maintenance [2].

Traditional reliability assessment methods regard the degradation process of system reliability or SOH as determined and seek to construct the underlying degradation model from a large number of historical data of similar equipments, without taking account the dynamics of operating conditions or specificity for a individual equipment [3], [4], [5], [6], [7], [8]. Actually as noted by Bian, by now the majority of reliability prediction models are based on the assumption that the prevailing operating conditions are regarded as temporarily constant or irrelevant to the evolution process [9]. However, the engineering equipments in practical industrial systems, especially in the modern complex systems, usually work under varying operating conditions caused by not only the uncontrollable external environment such as ambient temperature or other circumstance factors, but also the controllable operating profiles or workloads. In this situation, it is indispensable to consider the effect of varying conditions for advanced reliability assessment.

Recently, reliability assessment and SOH prediction for equipment under varying conditions have been investigated [10] and a dynamic multi-state condition is proposed as a typical model to depict general varying conditions [11]. Under the dynamic multi-state condition:

• The system is regarded as operating at one of several discrete candidate states.

• The concerned time series consisting of CM signals evolve following different underlying degradation models under different state.

• The transition between states is randomly happened and can be regarded as a hopping process but not a gradual change.

This modeling framework is mostly appropriate when the operating conditions can be clearly distinguished and their effects on the reliability evolution processes are significant. For instance, consider the workload induced from an aircraft engine in different flight conditions as: takeoff, maximum climb, maximum cruise, loiter, flight idle, taxi, ground idle, and cutoff [9]. The evolution of workload in these conditions will be totally different and the switching of conditions is sudden and can be regarded as random, thus distinct dynamic multi-state conditions can be recognized in this case.

Reliability assessment and SOH prediction with reference to equipments operating under this dynamic multi-state condition have been investigated from the perspective of statistical modeling and priori inference. The works of [[9], [12], [13]–14] are some examples representing the state of art on this branch of methodologies.

The inherent drawbacks of the statistical modeling based methodologies derives from its two strong premises: (1) the degradation process of system state should follow a certain statistical model, such as the continuous-time Markov chain, the hidden Markov model, the hidden semi-Markov model or the Wiener process, .etc.; (2) the statistical property of the degradation model, for example the transition probability matrix for Markov-based models, should be a priori known or estimated. However, for practical instances, theoretical statistical models such as Markov chain are very hard to be verified and estimating its transition probability matrix is often time consuming or even inaccessible. Thus the applicability of such methods is limited in engineering practitions.

Another trajectory to address the reliability assessment and SOH prediction resorts to posterior estimation methodologies, e.g. machine learning, which asserts system state and system reliability or SOH through a “black box” constructed upon massive historical CM data and current measurement [[15], [16]–17]. Nevertheless, this kind of methods have not yet been explored in depth for online SOH prediction under the dynamic multi-state condition, because of the difficulties lying in three aspects: (1) how to identify different system state by CM signals, in other words, how to effectively select the feature from CM signals; (2) how to efficiently classify the selected features into classes and (3) how to dynamically adapt the “black box” -like prediction model to meet the realtime demand for online tasks.

In this paper, we develop a novel multi-state dynamic SVR approach to deal with the online reliability assessment and SOH prediction problems under the dynamic multi-state conditions. To the authors’ knowledge, this is the first time that such type of problems is solved with an online machine learning structure. To begin with, premises of this paper are listed in following:

• The whole historical training reliability data are assumed known.

• The measured CM signals get updated at each new time step.

• Only the effects of different states are concerned. The effects posed by the state transition are regarded beyond the discussion of this paper.

As Fig. 1 shows, the proposed multi-state dynamic SVR is a framework to posteriorly estimate the system state from recent measurements and recursively update the SOH prediction model according to the state estimation through a sequential Monte Carlo (SMC) paradigm.

As we shall show, novelties and contributes of the present work exhibit in the following aspects:

• The effect of operating condition on system reliability evolution is analyzed. Especially, the dynamic multi-state operating condition is modeled and investigated.

• An online machine learning framework is proposed to deal with the realtime reliability assessment and SOH prediction problems under the dynamic multi-state operating condition. It improves the existing statistical modeling based methods in two points: (1) the priori information of system states and state transition is not required, so it is more universal for practical applications and (2) it defines different operating states directly from the posterior degradation model of measurements but not from the preset operational profiles (though, of course, the alteration of degradation model of measurements is often caused by the change of operational profiles). This state classification and identification result shall be more efficient to improve the prediction model.

• A novel feature of “optimal SVR hyper-parameters” with superior representing capacity and implementing efficiency is proposed to classify reliability evolution trajectories under different state. The feasibility of this feature derives from a notable fact that since the hyper-parameters of SVR are critically decisive to its prediction performance, the optimal SVR hyper-parameters filtered by SMC for training degradation trajectories under different state will distribute to different zone in the parameters space. In another word, the distribution of the particles (distributed candidate solutions in SMC paradigm) can be actually regarded as a statistical description or a feature about the system state. Compared with features obtained from traditional feature selection methods such as K-means or Principle Component Analysis (PCA), this “optimal SVR hyper-parameters” feature possesses enough representability of depicting the degradation models under different state, but cost fewer computation.

• On the basis of “optimal SVR hyper-parameters” feature, an online prediction framework involving recursive SMC and a novel Replacement Operation is proposed to dynamically update the prediction model based on the state estimation. This implementing framework significantly decrease the computational burden on the online stage.

• Improved prediction performance under the multi-state operating condition is achieved by the proposed method. On one hand, when the concerned system is recognized as working under a stable state, the PF-SVR will maintain convergence to the corresponding clustering center, which leads to a more accurate and stable prediction results in this case. On the other hand, when the concerned system is recognized as experiencing a transition between multi-state, the system state estimation can effectively help to capture the changing evolution trend and adapt to the new trend much quicker, so finally avoids losing tracking and results in better prediction performance.

• It is noteworthy that all the online procedures including the system state estimation and prediction model updating are performed recursively, meaning that at each time step only the latest measurement are requested to be manipulated but not the total historical data. That is to say, the computational cost of the proposed method could be considerable.

To illustrate the aforementioned strengths, the proposed approach is applied to real reliability case studies including two cases regarding typical CM signals of Li-ion battery: I) the inner temperature; II) the capacity of full charged, and more cases based on standard databases from NASA PCoE (Prognostics Center of Excellence) [18]. Through these case studies, the performance of the proposed approach is evaluated with respect to the metric as Root Mean Square Error (RMSE) and is compared with the original PF-SVR method and another benchmark approach, the FGAPSO-SVR, from literature [19].

The remainder of the paper is organized as follows. Section 2 introduces some reviewing background knowledge about PF-SVR and the PCC method. The proposed novel model is presented in Section 3. Section 4 illustrates the case studies. Section 5 provides some conclusions on the findings of the research.