System reliability analysis of a self-anchored suspension bridge based on the integral dimension reduction method

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.

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.

The relationship between the reliability probabilities of the component and the system is hard to get. If this relationship can be obtained easily, the reliability of the system can be calculated by using the reliability structures of the components. The common method to express this relationship is using the linear correlation index, which only shows the linear correlation between the components failure rather than the relationship between high nonlinear functions. In order to describe this relationship accurately and calculate the system reliability using the component reliability structures, a Uniform Design (UD)-Saddlepoint Approximation (SA)-based system reliability analysis method is proposed. The system reliability analysis method is decomposed to three simple steps: (1) calculating the weight coefficient which represents the contribution rate of each component to system reliability, (2) approximating Cumulant Generation Function (CGF) of each component, (3) calculating CGF of the system and approximating the system reliability with SA method. The weight coefficient of each component is derived from UD method, and a variable interval selection method is developed to decrease the required number of samples and increase the accuracy of the weight coefficients. First-Order Saddlepoint Approximation (FOSA) method or Mean-Value First-Order Saddlepoint Approximation (MVFOSA) method is used to analyze the CGF of a component performance function. Then the CGF of the system can be obtained by the weighted addition law by combining the CGFs of components performance functions with the weight coefficients. Finally, the system reliability can be approximated by SA method. Four examples are employed to demonstrate that the new method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

Fault Tree Analysis (FTA) is a powerful analytical technique for analyzing system reliability and safety by enumerating any possible safety-critical failure modes, which is very useful for identifying the risks and weaknesses in the system. Therefore, FTA is widely applied to the safety evaluation of large-scale and mission-critical systems. However, the following problems are usually pointed out when building a fault tree for a complex system: 1) System modeling is a hard and time consuming work, and 2) FTA models are difficult to be validated. In this paper, we propose a new method for system reliability analysis based on Multilevel Flow Models (MFM) and Goal Tree-Success Tree (GTST) methods. We use Goal Tree (GT) methodology to model the target system at a higher and system level, and use the Success Tree (ST) together with MFM at a lower and functional level. In this way, modeling effort could be significantly reduced. In this paper, an algorithm is also presented to translate the GTST-MFM model into ST model based on which qualitative reliability analysis can be performed by the Fusell-vesely algorithm. In this paper, a Low Head Safety Injection System (LHSIS) is taken as a case study to exemplify how to apply our proposed GTST-MFM method to model the system and to validate fault trees directly built by deductive method.

This paper proposes a quantitative reliability analysis method for power systems with multi-level standby structure based on GO method. First, the GO model used to describe the multi-level standby structure is proposed. Then, the reliability analysis process for such systems based on GO method is formulated. Finally, the proposed GO method is applied in reliability analysis of AC power system for single unit with 100% capacity divisions in nuclear power plant. In order to verify the feasibility, advantage and reasonable of the proposed GO method, its analysis result compared with the analysis result of GO method without considering standby correlations among the multi-level standby structure. All in all, this study provides guidance of reliability analysis for power systems with multi-level standby structure.

Extension of Hassan and Wolff method for system reliability analysis of soil slopes

This paper presents a robust reliability analysis method for systems of multimodular redundant (MMR) controllers using the method of partitioning and parallel processing of a Markov chain (PPMC). A Markov chain is formulated to represent the N distinct states of the MMR controllers. Such a Markov chain has N2 directed edges, and each edge corresponds to a transition probability between a pair of start and end states. Because N can be easily increased substantially, the system reliability analysis may require large computational resources, such as the central processing unit usage and memory occupation. By the PPMC, a Markov chain's transition probability matrix can be partitioned and reordered, such that the system reliability can be evaluated through only the diagonal submatrices of the transition probability matrix. In addition, calculations regarding the submatrices are independent of each other and thus can be conducted in parallel to assure the efficiency. The simulation results show that, compared with the sequential method applied to an intact Markov chain, the proposed PPMC can improve the performance and produce allowable accuracy for the reliability analysis on large-scale systems of MMR controllers.

An efficient and accurate algorithm is proposed to evaluate the reliability of cable-stayed bridges accounting for soil-pile interaction. The proposed algorithm integrates the finite-element method and the response surface method. The finite-element method is used to model the cable-stayed bridge including soil-pile interaction. The reliability index is evaluated based on the response surface method. Uncertainties in the superstructure, the substructure and load parameters are incorporated in the proposed algorithm. A long span steel cable-stayed bridge with a main span length of 1088 m built in China is considered as an illustrative example. The reliability of the bridge is evaluated for the strength and serviceability performance functions. Results of the study show that when strength limit states for both girder and tower are considered, soil-pile interaction has significant effects on the reliability of steel cable-stayed bridges. Further, a detailed sensitivity study shows that the modulus of subgrade reaction is the most important soil-pile interaction-related parameter influencing the reliability of steel cable-stayed bridges.

In recent years, there often exist multiple priors from experienced experts or historical experiments with the rapid development of system structure in engineering fields. Bayesian Melding Method is commonly used for integrating multiple priors, which is based on the deterministic system structure. However, if the system model cannot be described by an explicit expression, the traditional Bayesian Melding Method is not feasible for system reliability analysis anymore. In order to describe the structure relationship clearly, Bayesian Network is applied in this paper to construct the complex system structure model and the system reliability is calculated by node probability tables rather than explicit expressions. Combining the advantages of the Bayesian Melding Method and Bayesian Network, a multi-prior integration and updating algorithm is developed for the system reliability analysis of complex system structures. Finally, a satellite attitude control system is used to demonstrate the proposed method. The system is established by the Bayesian Network and the comparison between natural prior and updated prior is discussed at length.

A new method for estimating the reliability of structural systems is proposed. The method is based on the use of Monte Carlo simulation. Monte Carlo based methods for system reliability analysis has several attractive features, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. The disadvantage of such methods is the amount of computational efforts that may be involved. However, by reformulating the reliability problem to depend on a parameter and exploiting the regularity of the failure probability as a function of this parameter, it is shown that a substantial reduction of the computational efforts involved can be obtained.

A Bayesian approach for integrating multilevel priors and data for aerospace system reliability assessment

This paper presents a Generalized Complementary Intersection Method (GCIM) that can predict system reliability for series, parallel, and mixed systems. The GCIM is an extension of the original study, referred to as the Complementary Intersection Method (CIM). The CIM was developed to assess system reliability for series systems. The contribution of this paper is to generalize the original CIM so that it can be used for system reliability analysis regardless of system structures (series, parallel, and mixed system). First, we derive a closed-form system reliability formula for a parallel system through its transformation into a series system using De Morgan’s law. Second, a unified system reliability analysis framework is proposed for mixed systems by defining a new System Structure matrix (SS-matrix) and employing the Binary Decision Diagram (BDD) technique. The SS-matrix is used to present any system structure in a comprehensive matrix form. Then the BDD technique together with the SS-matrix automates the process to identify system’s mutually exclusive path sets, of which each path set is a series system. As a result, system reliability with any system structure can be decomposed into the probabilities of the mutually exclusive path sets. Five engineering examples are used to demonstrate that the proposed GCIM can assess system reliability regardless of the system structures.

System reliability analysis by enhanced Monte Carlo simulation

According to the deficiency of traditional Markov chain approach in dynamic fault tree analysis, a new modular method for system reliability analysis is proposed. This paper focuses on dividing the fault tree of system into independent subtrees using a linear-time algorithm, and the processing method for different subtrees: Binary decision diagram solution for static subtrees and Bayesian Network solution for dynamic subtrees, respectively. In addition, an approach is also provided for mapping some dynamic logic gates into discrete-time Bayesian network. At last, the modular method has been applied to assess the reliability of a satellite key device and the results have shown that the proposed method can overcome the state explosion problem, and is useful for assessing the reliability of large and complex systems.