Reliability assessment in structural dynamics

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.

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.

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

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

Many practical systems are phased-mission systems (PMSs), where the mission consists of multiple, consecutive, and non-overlapping phases of operation. An accurate reliability analysis of a PMS must consider statistical dependence of component states across phases, as well as dynamics in system configurations, success criteria, and component behavior. This paper proposes a new method based on multiple-valued decision diagrams (MDDs) for the reliability analysis of a non-repairable binary-state PMS. Due to its multi-valued logic nature, the MDD model has recently been applied to the reliability analysis of multistate systems. In this work, we present a novel way to adapt MDDs for the reliability analysis of systems with multiple phases. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for PMS analysis. Empirical results show that the MDD-based method can offer lower computational complexity as well as a simpler model construction and improved evaluation algorithms over those used in the BDD-based method.

This paper outlines an improved simulation method for a time-dependent reliability analysis of structural systems subjected to stochastic loads. Strengths of structural elements are assumed to degrade with time proportionally during the life cycle of the structural system, and stochastic load events are modeled as Poisson processes. The structural failure probabilities are estimated through the life cycle simulation, in which the directional simulation method is applied just to sample random load variables to execute each life cycle simulation efficiently. Numerical examples are presented and results are compared with those obtained by the crude Monte Carlo simulation to show the effectiveness of the proposed method. It is shown that the proposed method is effective for the assessment of the time-dependent failure probability of structural systems.

Efficient response surface method for high-dimensional structural reliability analysis

Non-linear 3D piping analysis under stochastic dynamic loads

In the present paper, a framework of dimension-reduction modeling method is developed for a dual stochastic dynamic structural system of spectrum-compatible non-stationary stochastic ground motion processes and stochastic structures. With the aid of the proposed method, the random variables used to describe the stochastic characteristics of the non-stationary ground motion processes and the structural parameters are respectively represented by the one-elementary-random-variable functions, contributing to an entire stochastic dynamic structural system readily described by merely two elementary random variables. Owing to the fact that the number of the elementary random variables needed is extremely small, the set of the representative points associated with the elementary random variables can thus be selected by the widely-used number theoretical method, and then the probability density evolution method can be conveniently combined to conduct the dynamic response analysis and dynamic reliability evaluation of nonlinear stochastic structures. In the numerical examples, the probability density evolution analysis of an eight-storey reinforced concrete frame structure with random parameters subjected to spectrum-compatible non-stationary stochastic ground motion processes is investigated as a case study. Numerical results fully demonstrated the effectiveness and robustness of the proposed method.

A new unequal-weighted sampling method for efficient reliability analysis

This paper presents a general mechanical system reliability modeling and analysis method, which consider the correlations of failure modes. Firstly, the performance functions which mathematically represent the failure modes are linearized based on FORM (First Order Reliability Methods), and the correlation coefficient matrix of those functions is calculated. Then, the PFTA (Probabilistic Fault Tree Analysis) method is adopted to establish the system reliability model which can take the correlations into account. Finally, effective algorithms such as G-FOMN (General First Order Multinormal Method) are used to quantify the system reliability, and the sensitivities of the system reliability index with respect to each failure mode, as well as the mean value and standard deviation of each random variable are also calculated. An engineering example demonstrates the applicability of the proposed method.

In this paper, the authors demonstrate how fault tree analysis could be used to perform reliability analysis of hardware-software systems. The functional dependency of the hardware components on the interfacing software components is appropriately modeled using fault trees. The MIT (Massachusetts Institute of Technology)-CSR's (Center for Space Research) ACIS (Advanced X-ray Astrophysics Facility Imaging Charge Couple Device Imaging Spectrometer) system is used to illustrate the fault tree analysis method in reliability analysis of complex hardware-software systems. The ACIS science instrument system is a space borne system to acquire and process X-ray images over the sky, and sends them to earth. It has hardware and software components with interfaces between them making it a very good example of a complex hardware software system. This approach could be used in analyzing other complex systems being designed today and in identifying the critical components to make the system safe and more reliable.

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

An overview is presented of the methods available to quantify uncertainties and to combine them in a systems reliability analysis. The different sources of uncertainty are identified and a discussion is provided to illustrate their different nature. The methods of reliability analysis are then described showing how they can incorporate parameter and model uncertainty. Finally Bayesian methods are presented illustrating how to update probabilistic statements with new information and how to incorporate parameter and model uncertainty in the reliability predictions.