Reliability Analysis of Dynamic Systems by Translating Temporal Fault Trees into Bayesian Networks

In engineering practice, structural system with dynamic output performance has gained more and more attention. Reliability analysis of these dynamic systems based on the real performance function is normally time-consuming, which is hard to accept in engineering. An SVR-NARX (Support vector machine regression-Nonlinear autoregressive with exogenous input) model is, therefore, established in this paper to replace the real performance function for reliability analysis. To further improve the efficiency for dynamic systems with small failure probability, importance sampling is combined with SVR-NARX model. Two nonlinear examples in this paper show that the established SVR-NARX model can accurately describe the dynamic behavior of the systems, and the proposed method is efficient and accurate for the reliability analysis of dynamic systems.

Solving dynamic flowgraph methodology models using binary decision diagrams

Application of Markovian models in the reliability analysis of dynamic systems is presented. In the context of the paper dynamic systems are systems whose stochastic behavior is changing with time. The reliability of control/safety systems coupled with the dynamics of protected or controlled systems is also analyzed. Markovian models are compared with static logic models like fault/event trees.

Introducing Temporal Behaviour into Binary Decision Diagrams

Improvement of the Reliability Graph with General Gates to Analyze the Reliability of Dynamic Systems That Have Various Operation Modes

Event trees are a popular technique for modelling accidents in system safety analyses. Bayesian networks are a probabilistic modelling technique representing influences between uncertain variables. Although popular in expert systems, Bayesian networks are not used widely for safety. Using a train derailment case study, we show how an event tree can be viewed as a Bayesian network, making it clearer when one event affects a later one. Since this effect needs to be understood to construct an event tree correctly, we argue that the two notations should be used together. We then show how the Bayesian Network enables the factors that influence the outcome of events to be represented explicitly. In the case study, this allowed the train derailment model to be generalised and applied in more circumstances. Although the resulting model is no longer just an event tree, the familiar event tree notation remains useful.

There are many methods applied including Bayesian network and D-S evidence theory to cope with uncertainty involving aleatory uncertainty and epistemic uncertainty in reliability analysis of complex systems. This paper introduces theories of these two methods briefly, and then conversion rules that convert fault tree into Bayesian network under uncertainty are put forward, including AND node, OR node, XOR node, NOT node and Two-out-of-three vote node. Comparing to probability importance, structural importance and criticality importance, epistemic importance is given to measure the influence of root event to top event. At last, a type of engine is taken for example. Bayesian network model is established by referring to the fault tree of the engine, and D-S evidence theory is used to determine the belief functions and plausibility functions of uncertain nodes by data fusion. Weak nodes in reliability design and distribution are pointed out after reliability assessment, importance analysis, and backward reasoning. And corresponding measures can be taken to improve the reliability of the whole system.

The aim of this paper is introducing a method based on Fuzzy Time-To Failure (FTTF) to improve reliability analysis of complex engineering systems based on fault tree analysis. This method focuses on the quantitative part of fault trees (either static or dynamic) analysis and will compute failure probabilities. FTTF model is developed to estimate the reliability of system and solve aforetime methods problems. The presented FTTF model is able to figure out any construction consist of static and dynamic gates with FTTF distributions integrated on Fuzzy Monte Carlo Simulation (FMCS) techniques to analyzing Possibilistic functions associated with the fuzzy probability distributions for each basic event. Using fuzzy algorithm, gates FTTF are generated, and Top-event TTF evaluated. Some case studies are used to demonstrate the priority of this method in exact evaluation in compared with other solving methods (like: BN, Analytical solution, Markov chain and traditional fuzzy fault tree modeling), but has much less effort while having higher accuracy. Finally, this model is implemented in an Emergency Detection System (EDS) which is a useful system in aerospace and space applications.

Dependability analysis of a dynamic system which is embedded with several complex interrelated components raises two main problems. First, it is difficult to represent in a single coherent and complete picture how the system and its constituent parts behave in conditions of failure. Second, the analysis can be unmanageable due to a considerable number of failure events, which increases with the number of components involved. To remedy this problem, in this paper we outline an analysis approach that converts failure behavioural models (state machines) to temporal fault trees (TFTs), which can then be analysed using Pandora -- a recent technique for introducing temporal logic to fault trees. The approach is compositional and potentially more scalable, as it relies on the synthesis of large system TFTs from smaller component TFTs. We show, by using a Generic Triple Redundant (GTR) system, how the approach enables a more accurate and full analysis of an increasingly complex system.

Dynamic reliability analysis using the extended support vector regression (X-SVR)

In this paper, fault tree analysis method and Bayesian network are introduced briefly. To overcome the restriction that fault tree analysis assumes the condition of an event as two-state, according to the mapping relationship between fault tree and Bayesian network, an event in fault tree is transformed to a node in Bayesian network, which will be divided into some sub-nodes corresponding to different states of an event. And connecting strength in Bayesian network corresponded to logical gate in fault tree will be expressed by conditional probability distribution. Taking foundation brake system as an example, reliability analysis on high-speed EMU bogie is presented. The research result shows that when multi-state characteristic of an event and uncertainty of logical relationship are considered, the calculation of probability distribution of bogie system fault can be more accurate. The reliability algorithm of high-speed EMU bogie based on fault tree analysis and Bayesian network is presented and developed.

In this paper, a quantitative risk analysis (QRA) model incorporating human and organizational factor is presented by integrating Fault Tree (FT) with Bayesian Network (BN). FT is used to model the factors how to contribute to the final failures. BN extends the causal chain of basic events to potential human and organizational roots and provides a more precise quantitative links between the event nodes. In order to define the conditional probability table of BN, fuzzy Analytical Hierarchy Process (AHP) is integrated with a decomposition method. The fuzzy AHP helps to reduce the subjective biases by avoiding the need to spell out explicit probability values for the variables' states. The decomposition method breaks the complexity by allowing conditioning on each of the parent nodes separately. The new QRA model is demonstrated on an offshore fire case study. By exploiting the advantages of both models, the method of combining FT and BN is normally a more detailed risk model with higher resolution, comparing with traditional QRA.

Risk analysis of collision accidents during underway STS berthing maneuver through integrating fault tree analysis (FTA) into Bayesian network (BN)

Fault tree analysis (FTA) is one of the most prominent techniques used in risk analysis, this method aimed to identify how component failures lead to system failure using logical gates (i.e. AND, OR gates). However, some limitations appear on FTA due to its static structure. Bayesian networks (BNs) have become a popular technique used in reliability analysis; it represents a set of random variables and their conditional dependencies. This paper discusses the advantages of Bayesian networks over fault tree in reliability and safety analysis. Also, it shows the ability of BN to update probabilities, to represent multi-state variables, dependent failures, and common cause failure. An example taken from the literature is used to illustrate the application and compare the results of both fault tree and bayesian networks techniques.

Probability analysis of offshore fire by incorporating human and organizational factor