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

This study proposes a system reliability analysis of rack storage facilities subjected to forklift colliding events. The proposed system reliability analysis consists of two steps: the first step is to identify dominant failure modes that most contribute to the failure of the whole rack facilities, and the second step is to evaluate the system failure probability. In the first step, dominant failure modes are identified by using a simulation-based selective searching technique where the contribution of a failure mode to the system failure is roughly estimated based on the distance from the origin in the space of the random variables. In the second step, the multi-scale system reliability method is used to compute the system reliability where the first-order reliability method (FORM) is initially used to evaluate the component failure probability (failure probability of one member), and then the probabilities of the identified failure modes and their statistical dependence are evaluated, which is called as the lower-scale reliability analysis. Since the system failure probability is comprised of the probabilities of the failure modes, a higher-scale reliability analysis is performed again based on the results of the lower-scale analyses, and the system failure probability is finally evaluated. The illustrative example demonstrates the results of the system reliability analysis of the rack storage facilities subjected to forklift impact loadings. The numerical efficiency and accuracy of the approach are compared with the Monte Carlo simulations. The results show that the proposed two-step approach is able to provide accurate reliability assessment as well as significant saving of computational time. The results of the identified failure modes additionally let us know the most-critical members and their failure sequence under the complicated configuration of the member connections.

본 연구에서는 다중 파괴모드를 고려한 사면의 신뢰도해석에 대하여 연구한다. 해석은 크게 두 부분으로 나뉜다. 첫 번째, Der Kiureghian과 Dakessian이 제안한 barrier method를 사용하여 시스템 신뢰도에 크게 영향을 미치는 중요 파괴모드를 연속적으로 탐색하여 찾아낸다. 둘째로, 찾아낸 중요 파괴모드들과 이에 해당하는 설계점들을 바탕으로 사면의 파괴확률을 계산한다. 다중 파괴모드를 갖는 사면의 신뢰도해석에서 파괴확률은 다중점 일차신뢰도법, Ditlevsen의 구간해법 및 몬테카를로 시뮬레이션 등을 이용하여 평가할 수 있다. 본 연구에서는 예제 해석을 통하여 이들 방법들의 비교연구를 수행하였다. 해석결과는 토사사면에 많은 수의 잠재적인 파괴면이 존재할 수 있지만, 사면의 시스템 파괴확률은 소수의 중요 파괴면에 의해 지배된다는 것을 보여준다. 따라서 토사사면의 시스템 신뢰도해석을 위해서 가장 중요한 단계는 모든 중요 파괴모드를 효율적인 방법에 의해서 탐색하여 결정하는 것이다. This work studies the reliability analysis of a slope that considers multiple failure modes. The analysis consists of two parts. First, significant failure modes that contribute most to system reliability are determined. The so-called barrier method proposed by Der Kiureghian and Dakessian to identify significant failure modes successively is employed. Second, the failure probability for the slope is estimated on the basis of the identified significant failure modes and corresponding design points. For reliability problems entailing multiple design points, failure probability can be estimated by the multi-point first-order reliability method (FORM), Ditlevsen's bounds method, and Monte Carlo simulation. In this paper, a comparative study between these methods has been made through example problems. Analysis results showed that while a soil slope may have a large number of potential slip surfaces, its system failure probability is usually governed by a few significant slip surfaces. Therefore, the most important step in the system reliability analysis for a soil slope is to identify all the significant failure modes in an efficient way.

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

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.

System reliability analysis of geosynthetic reinforced soil slope considering local reinforcement failure

System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding 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.

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

Time-dependent system reliability is computed as the probability that the responses of a system do not exceed prescribed failure thresholds over a time duration of interest. In this work, an efficient time-dependent reliability analysis method is proposed for systems with bivariate responses which are general functions of random variables and stochastic processes. Analytical expressions are derived first for the single and joint upcrossing rates based on the first-order reliability method (FORM). Time-dependent system failure probability is then estimated with the computed single and joint upcrossing rates. The method can efficiently and accurately estimate different types of upcrossing rates for the systems with bivariate responses when FORM is applicable. In addition, the developed method is applicable to general problems with random variables, stationary, and nonstationary stochastic processes. As the general system reliability can be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis of general systems with more than two responses. Three examples, including a parallel system, a series system, and a hydrokinetic turbine blade application, are used to demonstrate the effectiveness of the proposed method.

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 the development and demonstration of an efficient reliability-based tool for the reinforced earth retaining wall design in heavy haul railway. Here, two major internal failure modes, rupture and pullout, are the focus in the demonstration. The First-Order Reliability Method (FORM) is adopted to estimate the probability of failure for each failure mode, and is implemented in a spreadsheet. The reliability analysis is conducted with the consideration of the effect of uncertainty in the reinforcement length, horizontal and vertical spacing between steel strips, tensile strength of steel strips as well as the material property of the backfills. Using this design tool, a few candidate designs can be easily obtained by meeting the acceptable probability of failure and the final design is determined based on cost. The results obtained using FORM are also verified by comparing with those from Monte Carlo simulation. This design tool is shown to be simple to use in the retaining wall design of the railway engineering.

A self-anchored suspension bridge contains many interrelated and acting components. The damage of any component under load may affect the service function of the bridge. The reliability index of a single element often overestimates the safety state of the bridge. To evaluate the overall reliability of a self-anchored suspension bridge, a reliability analysis method for a self-anchored suspension bridge system based on the integral dimension reduction (IDR) method is established, which avoids the calculation of high-dimensional integral and greatly improves the analysis efficiency. Firstly, the reliability indexes and checkpoints of each potential failure element are analyzed. Secondly, the sensitivity of random variable reliability is analyzed and the corresponding safety margin equation is established. Finally, the IDR method is used to reduce the dimension of high-dimensional integral and transform it into the product of equivalent linear failure mode failure probability, which improves the analysis efficiency. Using this analysis method, the static system reliability of a three-tower self-anchored suspension bridge is analyzed, which provides a method of system reliability analysis of this kind of bridge.

PLIC-FSR-SYS: System reliability analysis based on parallel learning of influential components with filtered sample region

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.