System Reliability Analysis Method Research Articles

System-reliability-based design and topology optimization of structures under constraints on first-passage probability

For the purpose of reliability assessment of a structure subject to stochastic excitations, the probability of the occurrence of at least one failure event over a time interval, i.e. the first-passage probability, often needs to be evaluated. In this paper, a new method is proposed to incorporate constraints on the first-passage probability into reliability-based optimization of structural design or topology. For efficient evaluations of first-passage probability during the optimization, the failure event is described as a series system event consisting of instantaneous failure events defined at discrete time points. The probability of the series system event is then computed by use of a system reliability analysis method termed as the sequential compounding method. The adjoint sensitivity formulation is derived for calculating the parameter sensitivity of the first-passage probability to facilitate the use of efficient gradient-based optimization algorithms. The proposed method is successfully demonstrated by numerical examples of a space truss and building structures subjected to stochastic earthquake ground motions.

Multivariate system reliability analysis considering highly nonlinear and dependent safety events

Most of the existing system reliability analysis methods have focused on series and parallel systems whose components are weakly nonlinear and dependent. This paper proposes a new system reliability analysis method, named multivariate system reliability analysis (MSRA), for complex engineered systems with highly nonlinear and dependent components that are connected in series, parallel, and mixed configurations. The proposed method first employs multivariate Gaussian process (MGP) to sequentially construct a single surrogate jointly over the performance functions of all components and then performs Monte Carlo simulation on the surrogate model for system reliability analysis. The joint surrogate is updated adaptively using a novel acquisition function named multivariate probability of improvement (MPI). MGP considers the correlations between the component performance functions and provides a joint Gaussian prediction of these functions. This joint Gaussian surrogate model allows the use of MPI to achieve a dynamic trade-off between exploring the regions in the input space with high prediction uncertainty and exploring those that are close to the system limit-state function. The results of three abstract and two practical case studies show that MSRA is capable of achieving better accuracy in estimating the system reliability than the existing surrogate-based methods.

An improved TRPD method for time-variant reliability analysis

In this paper, an improved time-variant reliability analysis method based on stochastic process discretization (iTRPD) is proposed. Firstly, the time-variant reliability problem is transformed into a time-invariant series system reliability problem. Then the first order reliability method (FORM) is employed to analyze the reliability of each component of the system, and a corresponding approach is given to calculate the correlation coefficient matrix of all the components’ performance functions. Finally, the target time-variant reliability can be obtained with the reliability index vector and the correlation coefficient matrix of the involved components. In this study, the iTRPD is further applied to the system reliability problems, and hence a corresponding time-variant system reliability analysis method is also developed. Four numerical examples are investigated to demonstrate the effectiveness of the proposed methods.

Integration of Statistics- and Physics-Based Methods—A Feasibility Study on Accurate System Reliability Prediction

Component reliability can be estimated by either statistics-based methods with data or physics-based methods with models. Both types of methods are usually independently applied, making it difficult to estimate the joint probability density of component states, which is a necessity for an accurate system reliability prediction. The objective of this study is to investigate the feasibility of integrating statistics- and physics-based methods for system reliability analysis. The proposed method employs the first-order reliability method (FORM) directly for a component whose reliability is estimated by a physics-based method. For a component whose reliability is estimated by a statistics-based method, the proposed method applies a supervised learning strategy through support vector machines (SVM) to infer a linear limit-state function that reveals the relationship between component states and basic random variables. With the integration of statistics- and physics-based methods, the limit-state functions of all the components in the system will then be available. As a result, it is possible to predict the system reliability accurately with all the limit-state functions obtained from both statistics- and physics-based reliability methods.

Simplified framework for system reliability analysis of slopes in spatially variable soils

This paper proposes a simplified framework based on multiple response surface method (MRSM) and Monte Carlo simulation for efficient system reliability analysis of slopes in spatially variable soils. Equivalent spatially constant parameters, which are calculated from an explicit random variable model, are used within this framework to characterise the soil spatial variability such that conventional MRSM can be efficiently performed. In addition, a variance reduction strategy is proposed to enable the framework to be applicable to slope reliability problems that involve more than one type of shear strength. Two slope examples are studied to illustrate the accuracy and efficiency of the proposed framework, based on which the robustness of the proposed framework against various statistics, such as the anisotropic spatial variability, is fully demonstrated by numerous parametric studies. Results show that the proposed framework accurately evaluates the slope reliability considering spatially variable soils in a relatively efficient manner. The proposed framework provides a promising tool for an efficient slope reliability analysis.

A new reliability analysis method for repairable systems with closed‐loop feedback links

AbstractA new reliability analysis method for repairable systems with closed‐loop feedback link (CLFL) is proposed based on GO methodology. A method for creating new function GO operators is used to describe the CLFL. Next, methods for deducing the formulae of the new GO function are proposed. In addition, a 2‐level GO model is proposed for the GO operation of repairable systems with CLFL. And then, quantitative and qualitative analysis methods for repairable systems with CLFL based on the GO method are proposed, and a process for analyzing repairable systems with CLFL based on the new GO method is formulated. Finally, we used this new GO method to analyze the reliability of an electro‐hydraulic servo speed control system and a power‐shift steering transmission control system for a heavy vehicle. To verify the feasibility, advantages, and reasonability of the new GO method, we compared our results with those obtained by fault tree analysis, Monte Carlo Simulation, and an existing GO method using serial and parallel structures to represent the CLFL. All in all, the proposed method overcomes the limitations of the existing methods as well as increasing its applicability. And it provides a new approach for reliability analysis of repairable systems with CLFL.

Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers

This paper presents a new practical method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average (TA) (Abbasi et al. in J Intell Fuzzy Syst 29:851–861, 2015) on Rational-linear patchy fuzzy numbers. The concept of fuzzy numbers is extended by idea of Rational-linear patchy fuzzy numbers. Then, we have introduced fuzzy arithmetic operations of TA between two Rational-linear patchy fuzzy numbers. Finally, a new method has been developed for analyzing the fuzzy system reliability of series and parallel systems based on the fuzzy arithmetic operations of TA, where the reliability of each component is represented by a Rational-linear patchy fuzzy number. A technical example is given to illustrate applying the method and comparing the results of the new method with the previous methods. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.

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

This paper investigates Bayesian methods for aerospace system reliability analysis using various sources of test data and expert knowledge at both subsystem and system levels. Four scenarios based on available information for the priors and test data of a system and/or subsystems are studied using specific Bayesian inference techniques. This paper proposes the Bayesian melding method for integrating subsystem-level priors with system-level priors for both system- and subsystem-level reliability analysis. System and subsystem reliability outcomes are compared under different scenarios. Computational challenges for posterior inferences using the sophisticated Bayesian melding method are addressed using Markov Chain Monte Carlo (MCMC) and adaptive Sampling Importance Re-sampling (SIR) methods. A case study with simulation results illustrates the applications of the proposed methods and provides insights for aerospace system reliability analysis using available multilevel information.

System reliability assessment with multilevel information using the Bayesian melding method

This paper investigates the Bayesian melding method (BMM) for system reliability analysis by effectively integrating various available sources of expert knowledge and data at both subsystem and system levels. The integration of multiple priors is investigated under both linear and geometric pooling methods. The aggregated system prior distributions using various pooling methods including the BMM are evaluated and compared. Based on these integrated and updated prior distributions and three scenarios of data availability from a system and/or subsystems, methods for posterior system reliability inference are proposed. Computational challenges for posterior inferences using the sophisticated BMM are addressed using the adaptive sampling importance re-sampling (SIR) method. A numerical example with simulation results illustrates the applications of the proposed methods and provides insights for system reliability analysis using multilevel information.

System reliability analysis of soil slopes stabilized with piles

Piles are widely used to increase the stability of piles. Probabilistic methods can be used to explicitly consider the uncertainties involved in a slope stability analysis. Currently, most probabilistic slope stability analyses focus on the reliability of slopes without reinforcement. In this paper, an existing method for system reliability analysis of unreinforced slopes is extended to slopes reinforced with piles. The described procedure may potentially be used to convert other methods for reliability analysis of slopes without reinforcement to slopes reinforced with piles. Two examples are used to illustrate the suggested method. It is found that the location of the most critical slip surface of the reinforced slope generally differs from that of the unreinforced slope, and may change with the pile location and the pile spacing. The optimal locations of the piles with and without considering the uncertainties in the soil property are different. For slopes in layered soils, the system failure probability may be governed by several representative slip surfaces even when piles are installed. The system effect is more obvious when the pile spacing increases. To maximize the effectiveness of slope stabilization, the stabilizing piles should intersect with all representative slip surfaces with significant failure probabilities.

System Reliability Analysis Method Based on Fuzzy Probability

Conventional methods for analyzing system reliability involve the use of unit reliability and system composition. However, these methods have limitation on considering the type of failure distribution that exists in unit of system, resulting in inaccurate evaluation of system reliability as the bathtub curve. The process in which unit and system go from a normal working state to a failure state can be described as a fuzzy process. The fuzzy probability of unit reliability is defined in formula, and its curve is drawn based on bathtub curve, reliability function curve and fuzzy probability. For two systems that have the same system reliability, conventional methods also fail to take into account the effect of differences in unit reliability on system reliability. In this study, we introduce a novel method to analyze system reliability that based on fuzzy probability. This method is an assumption that unit reliability is a fuzzy probability-based event, and then these concepts of system failure probability and integrated system reliability are proposed. The system failure probability is a characteristic quantity used to measure the effect of different unit in system reliability. The integrated system reliability is a characteristic quantity that evaluated the comprehensive system reliability. These proposed concepts are applied in the reliability analysis of series system, parallel system and compound system. These results verify the effectiveness of the proposed method by the application and comparison in these examples.

An efficient method of system reliability analysis of steel cable-stayed bridges

The IHS-EIS method is developed for reliability analysis of steel cable-stayed bridges by integrating the improved Latin Hypercube (IHS) and a proposed effective importance sampling (EIS). All nonlinearity sources of bridges are directly captured by the proposed practical advanced analysis (PAA) using catenary elements for cables and beam-column elements for pylons, girders, and cross beams. The innovation of the proposed method comes from both PAA for performing structural analysis and IHS-EIS for solving reliability analysis. Compared to commercial software ABAQUS, the computational cost of structural analysis is significantly reduced by using the proposed PAA method. IHS-EIS can accurately capture the failure probability of structure and considerably decrease the number of samples in comparison with Monte Carlo simulation, importance sampling, Latin hypercube, and subset simulation methods. Three mathematical examples and two steel frames are first presented to demonstrate the accuracy and efficiency of IHS-EIS. This method is then applied for the semi-harp type of a steel cable-stayed bridge. The reliability sensitivity of the bridge is also investigated.

A new reliability analysis method for repairable systems with multifunction modes based on goal‐oriented methodology

AbstractThis paper proposes a new systematic reliability analysis method for repairable systems with multifunction modes based on the goal‐oriented (GO) method. First, we create a new function GO operator, a new logical GO operator, and a new auxiliary GO operator, deduce their GO operation formulas, and propose some new rules of the GO operation and an exact algorithm with shared signal of the GO method for such systems. Then, we formulate the analysis process of repairable systems with multifunction modes based on the new GO method. Finally, we apply this new GO methodology to reliability analysis of the control system for a heavy vehicle. To verify the feasibility, advantage, and reasonableness of the new GO methodology, we compare its analysis results with those of fault tree analysis and Monte Carlo simulation. We show that the proposed GO method has clear advantages in system reliability modeling and analysis. All in all, this study not only improves the theory of the GO method and widens its application but also provides a new approach for conducting reliability analysis of complex systems quickly and efficiently.

System reliability analysis of slopes using multilayer perceptron and radial basis function networks

SummaryThis paper presents a system reliability analysis method for soil slopes on the basis of artificial neural networks with computer experiments. Two types of artificial neural networks, multilayer perceptrop (MLP) and radial basis function networks (RBFNs), are tested on the studied problems. Computer experiments are adopted to generate samples for constructing the response surfaces. On the basis of the samples, MLP and RBFN are used for establishing the response surface to approximate the limit state function, and Monte Carlo simulation is performed via the MLP and RBFN response surfaces to estimate the system failure probability of slopes. Experimental results on 3 examples show the effectiveness of the proposed methodology.

A method for estimating the reliability of structural systems with moment-matching and copula concept

ABSTRACTIt is aimed to propose a copula based systematic quantitative method for system reliability analysis of engineering structures considering multiple dependent failure modes. The principles of the moment matching method, the copula theory and the bound theory are combined to achieve the purpose. As the very first step, the moment estimation of the limit state function of each component is calculated by anchored ANOVA (Analysis of Variance) expansion. The third moment saddle point approximation is then applied to derive the distribution of each performance function and evaluate the reliability index with obtained moments. By introducing copula functions into the narrow bounds theory, the traditional reliability method is improved. The best-fitting copula function is determined to ensure the accuracy of the joint probabilistic modeling between the dependent failure modes. A novel feature of the proposed method is the use of the copula concept, instead of traditional numerical integration commonly used in the joint failure probability estimation. Examples are presented to illustrate the accuracy and applicability of the presented method.

Efficient Kriging surrogate modeling approach for system reliability analysis

AbstractCurrent limit state surrogate modeling methods for system reliability analysis usually build surrogate models for failure modes individually or build composite limit states. In practical engineering applications, multiple system responses may be obtained from a single setting of inputs. In such cases, building surrogate models individually will ignore the correlation between different system responses and building composite limit states may be computationally expensive because the nonlinearity of composite limit state is usually higher than individual limit states. This paper proposes a new efficient Kriging surrogate modeling approach for system reliability analysis by constructing composite Kriging surrogates through selection of Kriging surrogates constructed individually and Kriging surrogates built based on singular value decomposition. The resulting composite surrogate model will combine the advantages of both types of Kriging surrogate models and thus reduce the number of required training points. A new stopping criterion and a new surrogate model refinement strategy are proposed to further improve the efficiency of this approach. The surrogate models are refined adaptively with high accuracy near the active failure boundary until the proposed new stopping criterion is satisfied. Three numerical examples including a series, a parallel, and a combined system are used to demonstrate the effectiveness of the proposed method.

Optimization of Spare Number for Series and Parallel Systems

An optimal model for determining minimum-cost spare number for systems with components connected in series and parallel is presented. The component availability with a certain number of spares is derived through Poisson process theory. Then the availability of series-parallel system is obtained with system reliability analysis method. Consequently, the optimization model is established to minimize the total spare cost of the system under the requirement of specified system availability. Genetic algorithms are applied to find the optimal amount of spares for each component and two illustrative examples are given.

Time-Dependent Series System Reliability Analysis Method and Application to Gear Transmission Systems

A gear transmission system such as a gear train is a series system in sense of reliability evaluation, while it is different from a traditional series system such as a chain. Therefore, the conventional series system reliability model is not appropriate for gear transmission system. Based on the time-dependent configuration and the time-dependent loading path of a gear train, system specific reliability modeling technique is presented, by which a gear train is taken as a time-dependent series system, consisting of different components (gear teeth) in different time intervals. To illustrate the application of the reliability analysis method, several time-dependent series system reliability models are developed for different types of gear trains, the reliability estimation results are compared with those obtained by traditional series system reliability model.

An Outcrossing Rate Model and Its Efficient Calculation for Time-Dependent System Reliability Analysis

Time-dependent reliability problems widely appear in the engineering practice when the material properties of the structure deteriorate in time or random loading modeled as random processes is involved. Among existing methods to the time-dependent reliability problems, the most dominating one is the outcrossing rate method. This paper presents an outcrossing rate model and its efficient calculation approach for system problems, and based on the presented model, a time-dependent system reliability analysis method is proposed. The main idea of the method is to transform the evaluation of the system outcrossing rates into the calculation of a time-invariant system reliability. Three numerical examples are used to demonstrate the effectiveness of the proposed method.

System reliability analysis of slope stability using generalized Subset Simulation

Slope failure mechanisms (e.g., why and where slope failure occurs) are usually unknown prior to slope stability analysis. Several possible failure scenarios (e.g., slope sliding along different slip surfaces) can be assumed, leading to a number of scenario failure events of slope stability. How to account rationally for various scenario failure events in slope stability reliability analysis and how to identify key failure events that have significant contributions to slope failure are critical questions in slope engineering. In this study, these questions are resolved by developing an efficient computer-based simulation method for slope system reliability analysis. The proposed approach decomposes a slope system failure event into a series of scenario failure events representing possible failure scenarios and calculates their occurrence probabilities by a single run of an advanced Monte Carlo simulation (MCS) method, called generalized Subset Simulation (GSS). Using GSS results, representative failure events (RFEs) that are considered relatively independent are identified from scenario failure events using probabilistic network evaluation technique. Their relative contributions are assessed quantitatively, based on which key failure events are determined. The proposed approach is illustrated using a soil slope example and a rock slope example. It is shown that the proposed approach provides proper estimates of occurrence probabilities of slope system failure event and scenario failure events by a single GSS run, which avoids repeatedly performing simulations for each failure event. Compared with direct MCS, the proposed approach significantly improves computational efficiency, particularly for failure events with small failure probabilities. Key failure events of slope stability are determined among scenario failure events in a cost-effective manner. Such information is valuable in making slope design decisions and remedial measures.