Reliability analysis of dynamic systems based on SVR-NARX model and importance sampling

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.

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

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures.

Solving dynamic flowgraph methodology models using binary decision diagrams

Reliability assessment in structural dynamics

Modified subset simulation method for reliability analysis of structural systems

Reliability analysis techniques combining with various surrogate models have attracted increasing attention because of their accuracy and great efficiency. However, they primarily focus on the structures with continuous response, while very rare researches on the reliability analysis for structures with discontinuous response are carried out. Furthermore, existing adaptive reliability analysis methods based on importance sampling (IS) still have some intractable defects when dealing with small failure probability, and there is no related research on reliability analysis for structures involving discontinuous response and small failure probability. Therefore, this paper proposes a novel reliability analysis method called AGPC-IS for such structures, which combines adaptive Gaussian process classification (GPC) and adaptive-kernel-density-estimation-based IS. In AGPC-IS, an efficient adaptive strategy for design of experiments (DoE), taking into consideration the classification uncertainty, the sampling uniformity and the regional classification accuracy improvement, is developed with the purpose of improving the accuracy of Gaussian process classifier. The adaptive kernel density estimation is introduced for constructing the quasi-optimal density function of IS. In addition, a novel and more precise stopping criterion is also developed from the perspective of the stability of failure probability estimation.The efficiency, superiority and practicability of AGPC-IS are verified by three examples

An adaptive parallel learning dependent Kriging model for small failure probability problems

An efficient simulation method for reliability analysis of linear dynamical systems using simple additive rules of probability

Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation

PurposeDegraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.Design/methodology/approachThe research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.FindingsThe proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.Research limitations/implicationsThe models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.Practical implicationsThese models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.Originality/valueA unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

PurposeThis paper aims to deal with the problems of failure dependence and common cause failure (CCF) that arise in reliability analysis of complex systems.Design/methodology/approachFirstly, a dynamic fault tree (DFT) is used to capture the dynamic failure behaviours and converted into an equivalent generalized stochastic petri net (GSPN) for quantitative analysis. Secondly, an efficient decomposition and aggregation (EDA) theory is combined with GSPN to deal with the CCF problem, which exists in redundant systems. Finally, Birnbaum importance measure (BIM) is calculated based on the EDA approach and GSPN model, and it is used to take decisions for system improvement and fault diagnosis.FindingsIn this paper, a new reliability evaluation method for dynamic systems subject to CCF is presented based on the DFT analysis and the GSPN model. The GSPN model is easy to capture dynamic failure behaviours of complex systems, and the movement of tokens in the GSPN model represent the changes in the state of the systems. The proposed method takes advantage of the GSPN model and incorporates the EDA method into the GSPN, which simplifies the reliability analysis process. Meanwhile, simulation results under different conditions show that CCF has made a considerable impact on reliability analysis for complex systems, which indicates that the CCF should not be ignored in reliability analysis.Originality/valueThe proposed method combines the EDA theory with the GSPN model to improve the efficiency of the reliability analysis.

This paper proposes a new goal-oriented (GO) method for reliability analysis of repairable systems with multiple-input and multi-function component (MIMFC). First, a new GO operator combination, which is composed of a new function GO operator and a new auxiliary GO operator, is created to represent MIMFC. The new function GO operator named as Type 22 operator is created to represent MIMFC itself, and the auxiliary GO operator named as Type 15B operator is created to represent multi-condition control signals of MIMFC. Then, GO operation formulas of the new GO operator combination are deduced based on logical relationships among inputs, outputs, and the component itself. The reliability analysis process of the new GO method is formulated. Furthermore, this new GO method is applied for the first time in steady availability analysis and qualitative analysis of the fan drive system of a power-shift steering transmission. Finally, the results obtained by the new GO method are compared with the results of fault tree analysis (FTA) and Monte Carlo simulation (MCS), and the comparison results show that this new GO method is reasonable and advantageous in reliability analysis of repairable systems with MIMFC. Moreover, the analysis process shows that it is more advantageous in the aspect of building system models and conducting reliability analysis. Overall, this paper not only improves the basic theory of the GO method and expands the application of the GO method, but it also provides a new approach for reliability analysis of repairable systems with MIMFC.

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort.

This paper presents a novel and simple approach to reliability analysis of phased-mission systems. The technique presented in this paper transforms a phased-mission system into several non-phased-mission systems, and thus allows each phase to be modeled separately. The mission succeeds as long as every phase successively executes its requirements, and failed component(s) of any phase is(are) repaired so that the system is in a successful state before as well as after it begins the next phase. Alternative mission success scenarios are also readily definable within this context. The benefit of this simplified approach is that it provides a practical implementation for the reliability analysis of phased-mission systems. The different phases of the system are computed independently, and the duration and the structure of the phases are left to the designer or manager. If the requirements of the mission change during execution of the mission (duration of a phase or the sequence of phases), the impact of the change in mission objectives is easily found without recomputing the applicable or operative Markov model. This is due to the fact that all of the reliability analysis data are presented over the entire mission duration consisting for all phases, and the initial and final probabilities can easily be found by examining the output reliability data instead of recomputing the model