Elsevier

Knowledge-Based Systems

Volume 67, September 2014, Pages 270-277
Knowledge-Based Systems

A new BRB based method to establish hidden failure prognosis model by using life data and monitoring observation

https://doi.org/10.1016/j.knosys.2014.04.045Get rights and content

Abstract

It is important to predict the hidden failure of a complex engineering system. In the current methods for establishing the failure prognosis model, the qualitative knowledge and quantitative information (life data and monitoring observation) cannot be used effectively and simultaneously. In order to predict the hidden failure by using the qualitative knowledge, life data and monitoring observation, a new model for hidden failure prognosis is proposed on the basis of belief rule base (BRB). In the newly proposed model, there are some unknown parameters whose initial values are usually given by experts and may not be accuracy, which may lead to the inaccuracy prediction. In order to tune the parameters of the failure prognosis model according to the life data and monitoring observation, an optimal algorithm for training the parameters is further developed on the basis of maximum likelihood (ML) algorithm. The proposed model and optimal algorithm can operate together in an integrated manner to improve the precision of failure prognosis by using the qualitative knowledge and quantitative information effectively. A case study is examined to demonstrate the ability and potential applications of the newly proposed failure prognosis model.

Introduction

It is important to establish the failure prognosis models of complex systems. For example, in some systems such as nuclear power stations and rocket control loops that have the high requirements for safety, it is necessary to predict their failures [1], [3], [4], [8], [15], [16], [17], [19], [20], [21]. In the engineering practice, some failures are hidden and cannot be observed directly. For example, the inertial platform is an important device in the navigation system and the gyro is the key component of the platform. In order to assess the performance of the rocket, it is necessary to establish the failure prognosis model of the platform. As the main factor to affect the performance of the inertial platform, the gyro drift is not directly observable and can only be assessed via other monitoring observation such as voltage or electricity. Compared with the observable failure, the prognosis model of the hidden one is often difficult to establish [8], [19]. This paper focuses on establishing the prognosis model of the hidden failure.

In order to establish the prognosis model of hidden failure, two types of methods that include model based method and data-driven based method have been proposed. In the model based method, two steps are usually needed: firstly, a state or parameter that can reflect the hidden failure is chosen when the mathematical model is known. Then the filter based predictors including Kalman predictor [15], [17], strong tracking predictor [3], fuzzy Kalman predictor [20] and particle predictor [4] are chosen to establish the forecasting model of the state or parameter. Thus, the failure prognosis model is established. The principle to choose the appropriate filter is determined by the characteristics of system and noise.

The data-driven based method mainly includes the qualitative knowledge based method and quantitative data based method. When the qualitative knowledge about a system is available, the qualitative knowledge based method can be used to establish the hidden failure prognosis model. The expert system based method [1] and Petri net based method [16] both belong to the qualitative knowledge based method. When the quantitative information can be obtained, the hidden Markov model (HMM) based method is used to predict the hidden failure [2], [7], [18], [23].

Although the above methods have been used to establish the prognosis model of hidden failure, some problems may exist. When it is difficult to establish the accurate mathematical or statistical model of a complex system, the model based methods are not applicable. In the data-driven based methods, either qualitative knowledge or quantitative information is used but not both to establish the prognosis model. However, because the qualitative knowledge is usually simply, combinatorial explosion and inaccurate prediction may exist. In the HMM based method, enough quantitative information is needed to train the failure prognosis model, so it is not applicable in cases where a lot of quantitative information may not be available. In engineering, the quantitative information often includes the monitoring observation and the life data. However, in the current HMM based method, the qualitative knowledge and life data are not used.

From above analysis, it can be seen that the qualitative knowledge and quantitative information cannot be used simultaneously and effectively to establish the failure prognosis model. In order to solve the problems, a model for predicting hidden behavior has been proposed by Zhou et al. [25] on the belief rule base (BRB) which has been developed recently [13], [14], [21], [22], [24]. However, when the proposed model is established for failure prognosis, only qualitative knowledge and monitoring observation that belongs to quantitative information are used, and the life data is not considered. As such, a new BRB based failure prognosis model is further developed in this paper. In the newly proposed BRB based model, there are some unknown parameters whose initial values are usually given by experts and may not be accuracy, which may lead to the inaccuracy prediction. Therefore, an optimal algorithm for training the parameters of the failure prognosis model is developed further on the basis of maximum likelihood (ML) algorithm [6]. The proposed model and optimal algorithm can operate together in an integrated manner to improve the forecasting precision of hidden failure by using the qualitative knowledge, life data and monitoring observation effectively.

This paper is organized as follows. In Section 2, the problem for predicting the hidden failure is formulated on the basis of BRB. Section 3 proposes a new BRB based model for failure prognosis. An optimal algorithm for training the parameters of the failure prognosis model is developed in Section 4. A case study is presented to verify the proposed forecasting model and optimal algorithm in Section 5. The paper is concluded in Section 6.

Section snippets

Notations

The notations that will be used in this paper are listed as follows:

xa key parameter which cannot be observed directly
y = [y1, …, ym]Tmonitoring observation
sf‘Failure’ state of the system
Ω(t  1)all the available information about the system up to time instant (t  1)
Pthpre-set threshold
Djjth consequent of BRB
θkrule weight of the kth rule
gnonlinear function modeled by BRB
ψ1parameter vector composed of rule weights and belief degrees
hmapping function
ν(t)m-dimensional noise vector contaminating the

New BRB based model for failure prognosis

In this paper, the available information Ω(t  1) mainly includes three types of information: monitoring observation, life data and qualitative knowledge. In order to effectively use the available information to improve the precision of failure prognosis, the belief rule base (BRB) [13], [14] is chosen to establish the prognosis model. The main reasons to use BRB are as follows:

  • (1) For some complex systems, it is usually difficult to obtain complete and accurate data beforehand to train the model

BRB based algorithm for failure prognosis

In this Section, an algorithm for estimating the parameters of the BRB based failure prognosis model is developed firstly, and then the BRB based failure prognosis algorithm is proposed further.

A case study

In order to demonstrate that the proposed BRB based failure prognosis may be applied in engineering, the failure prognosis model of the inertial platform will be constructed in this Section.

Conclusions

In order to use qualitative knowledge and quantitative information that includes life data and monitoring observation to establish the prognosis model of hidden failure, a new BRB based model is proposed in this paper. Moreover, in the BRB based model, there are some parameters whose initial values are usually given by experts and may be inaccurate, so it is necessary to train them. As such, an optimal algorithm is further proposed for parameter learning on the basis of maximum likelihood (ML)

Acknowledgements

The authors would like to thank the editor and four anonymous referees for their constructive comments and suggestions, which have been very help in improving the paper.

Jiang J. thanks the partial support by National Natural Science Foundation of China under Grant 71201168. Zhou Z.J. thanks the partial support by National Natural Science Foundation of China under Grants 61004069 and 61370031, the open funding programme of Joint Laboratory of Flight Vehicle Ocean-based Measurement and Control

References (25)

  • M.Z. Chen et al.

    An adaptive failure prediction method based on strong tracking filter

    J. Shanghai Maritime Univ. (in Chinese)

    (2001)
  • M.Z. Chen et al.

    A new particle predictor for failure prediction of nonlinear time-varying systems

    Develop. Chem. Eng. Mineral Process.

    (2005)
  • Cited by (10)

    • Fault diagnosis and prognosis based on physical knowledge and reliability data: Application to MOS Field-Effect Transistor

      2020, Microelectronics Reliability
      Citation Excerpt :

      Rules are formulated as If-Then statements. Fuzzy logic based approaches in combination with Bayesian networks, Markovian and semi-Markovian processes are the most used methods [6–8]. The implementation of expert methods is relatively easy compared to other approaches.

    • A disjunctive belief rule-based expert system for bridge risk assessment with dynamic parameter optimization model

      2017, Computers and Industrial Engineering
      Citation Excerpt :

      Thus, the number of fuzzy rules is exponential based on the number of fuzzy numbers and/or antecedent attributes. Due to these limitations, the belief rule-based (BRB) expert system (Yang, Liu, Wang, Sii, & Wang, 2006), which has been widely used for different purposes such as failure prognosis (Jiang, Zhou, Han, Zhang, & Ling, 2014; Liu, Liu, & Lin, 2013; Zhou et al., 2015), oil pipeline leak detection (Xu et al., 2007; Yang, Wang, Lan, Chen, & Fu, 2017), clinical disease diagnosis (Hossain, Ahmed, Fatema, & Andersson, 2017; Zhou et al., 2015; Kong, Xu, Yang, & Ma, 2015), Forex trading prediction (Dymova, Sevastjanov, & Kaczmarek, 2016), consumer preference prediction (Tang, Yang, Chin, Wong, & Liu, 2011; Yang, Fu, Chen, Xu, & Yang, 2016), and basic classification problem (Calzada, Liu, Wang, & Kashyap, 2015; Yang, Wang, Su, Fu, & Chin, 2016), is applied to model bridge risks in this study. To date, the most common belief rule in a BRB is based on the conjunctive relationship between antecedent attributes, namely conjunctive belief rules (CBRs), which is required to cover all combinations of each referential value for each antecedent attribute.

    • A data envelopment analysis (DEA)-based method for rule reduction in extended belief-rule-based systems

      2017, Knowledge-Based Systems
      Citation Excerpt :

      The system's foundation includes the Dempster-Shafer theory of evidence [5,6], Bayesian probability theory [7] and fuzzy-set theory [8]. To date, BRBS has been applied in many areas, such as safe evaluation of engineering systems [9–11], military capability evaluation [12], pipeline leak detection [13,14], risk analysis [15,16], prediction of consumer preferences [17–19], residual-life probability prediction of metalized film capacitors [20] and basic classification problems [21–23]. In optimisation studies of BRBS, rule reduction is also a research focus such that many techniques, such as statistical utility [24], principal component analysis [25] and error analysis [26], have been applied in many attempts and produced promising rule reduction methods.

    • Dynamic rule adjustment approach for optimizing belief rule-base expert system

      2016, Knowledge-Based Systems
      Citation Excerpt :

      Calzada et al. [17] formulated a dynamic rule activation method to optimize the rule-inference process. Now, the RIMER approach has been applied in many areas, such as in the safe evaluation of engineering systems [18–20], military capability evaluation [21], pipeline leak detection [22,23], risk analysis [24,25], prediction of consumer preferences [26,27], residual-life probability prediction of metalized film capacitors [28], and basic classification problem [29–31]. As an expert system using the RIMER approach, BRB is employed for storing various types of uncertain knowledge in the form of belief structure.

    • A model for online failure prognosis subject to two failure modes based on belief rule base and semi-quantitative information

      2014, Knowledge-Based Systems
      Citation Excerpt :

      Under the degradation failure and multiple shock failures, the problem of competitive failure is solved using the Wiener model when the degradation process is assumed to be linear [2–4]. Based on the assumption that the shock failure is considered as the external attack whose strength is the function of performance degradation and stress, a competitive failure model is proposed [9,10,13]. This paper focuses on failure prognosis when two failure processes are dependent and competitive.

    View all citing articles on Scopus
    View full text