Series System Reliability Analysis Research Articles

Application of first-order reliability method with orthogonal plane sampling for high-dimensional series system reliability analysis

The increasing complexity of modern engineering systems has motivated a shift of research focus from component-level reliability to system reliability with interdependent components. There is a growing demand for efficient reliability methods to analyze high-dimensional systems that involve numerous dependent components and component variables. The first-order reliability method (FORM), which is widely used for component-level reliability analysis, becomes inaccurate for high-dimensional systems composed of numerous components, each with a nonlinear high-dimensional limit state function. By integrating the orthogonal plane sampling, this paper proposes an improved FORM-based method to tackle the curse of dimensionality for series systems. The idea is to construct secant hyperplanes using the orthogonal plane samples so as to reduce the FORM error for high-dimensional nonlinear limit state functions. The design points of secant hyperplanes are projected to high-dimensional system space using an efficient procedure based on the specified correlation matrix of variables. Finally, the series system reliability is computed as high-dimensional multi-normal integral, which is addressed by the equivalent component method. Four numerical examples are investigated to demonstrate the accuracy and efficiency of the proposed method. Results indicate that the proposed method is significantly more efficient than the Monte Carlo simulation and more accurate than the conventional FORM.

An integrated damage modeling and assessment framework for overhead power distribution systems considering tree-failure risks

The overhead power distribution system (OPDS) is vulnerable to strong winds, such as hurricanes. Due to the challenges of including tree damage risks to the OPDS, tree failures are usually ignored in the risk assessment of the OPDS against strong winds. In the present study, an integrated damage modeling and assessment framework for the OPDS is proposed considering tree failure risks. The geographical information of trees surrounding the OPDS is extracted from satellite images using computer vision techniques, including CNN-based (convolutional neural network) image classifier and sliding window approach. The tree failure risk models are developed using tree geographical information in conjunction with tree height data, tree allometry and finite element analysis. With further integration of the conditional probability failure of poles under fallen tree impacts, the pole’s failure probability considering the combined wind and fallen trees is obtained using series system reliability analysis. The failure probability of the pole is obtained using physics-based modeling facilitated by Bayesian regularisation neural network (BRNN) algorithm. The poles and wires are connected for system reliability assessment using connectivity-based theory. When the wind direction is counterclockwise from the east and the wind speed is 57 m/s, tree-failure can introduce 68.6% differences in OPDS’ failure probabilities compared with that without consideration of fallen trees.

Adaptive Monte Carlo Simulation Method and Its Applications to Reliability Analysis of Series Systems with a Large Number of Components

AbstractIt is not uncommon to encounter engineering structures that can be modeled as series systems with a large, even unlimited, number of correlated components (e.g., component number greater th...

System Reliability Framework for Design of Flexible Pavements

AbstractThe paper presents a methodology to carry out the series system reliability analysis of multilayered flexible pavements with respect to correlated fatigue and rutting failure modes. The imp...

State dependent Girsanov’s controls in time variant reliability estimation in randomly excited dynamical systems

The problem of time variant reliability estimation of structural dynamical systems subjected to nonstationary, Gaussian, random excitations is considered. The system equations are cast in the form of Ito’s stochastic differential equations and the problem of reliability estimation is tackled based on Monte Carlo simulations with a Girsanov transformation based sampling variance reduction scheme. The problem of time variant reliability analysis is first cast as an equivalent problem in series system reliability analysis. Novel contribution of the work lies in proposing procedures to arrive at state dependent (closed loop) Girsanov’s controls. Suboptimal Girsanov’s controls for estimating the time variant reliability are derived based on component level ideal controls, which are exactly obtainable for linear systems, and, via a local linearization step for nonlinear systems. It is shown that a simplified version of the above closed loop controls, that avoids linearization step for nonlinear systems, can be deduced by minimizing a distance measure similar to what has been done for arriving at open loop controls. Illustrations on multi-degree of freedom linear/nonlinear systems demonstrate the superior performance of the proposed method vis-à-vis the existing open loop control based methods. Limited largescale Monte Carlo simulations are used to verify the acceptability of solutions based on the proposed scheme.

Extension of quasi-Newton approximation-based SORM for series system reliability analysis of geotechnical problems

The quasi-Newton approximation-based second-order reliability method is extended, through the incorporation of a linearization approach, to analyze the series system reliability of geotechnical problems. Two types of quasi-Newton approximations are applied to identify the design point and to compute the second-order probability of failure, respectively. The equivalent second-order reliability index is obtained using an approximation hyperplane for each limit state function. Then, the computed equivalent second order reliability indices can be employed, together with the corresponding unit direction vectors, to estimate the series system probability of failure using a linearization approach. Three geotechnical problems are employed to demonstrate the efficiency and accuracy of the suggested procedure, and advantages with respect to alternative computational tools are discussed.

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.

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.

Time-Independent Reliability Analysis of Bridge System Based on Mixed Copula Models

The actual structural systems have many failure modes. Due to the same random sources owned by the performance functions of these failure modes, there usually exist some nonlinear correlations between the various failure modes. How to handle the nonlinear correlations is one of the main scientific problems in the field of structural system reliability. In this paper, for the two-component systems and multiple-component systems with multiple failure modes, the mixed copula models for time-independent reliability analysis of series systems, parallel systems, series-parallel systems, and parallel-series systems are presented. These obtained mixed copula models, considering the nonlinear correlation between failure modes, are obtained with the chosen optimal copula functions with the Bayesian selection criteria and Monte Carlo Sampling (MCS) method. And a numerical example is provided to illustrate the feasibility and application of the built mixed models for structural system reliability.

Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method

The paper presents a computationally efficient method for system reliability analysis of mechanisms. The reliability is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. This mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. The extreme event distribution is derived using the principle maximum entropy (MaxEnt) along with the constraints specified in terms of fractional moments. To optimize the computation of fractional moments of a multivariate response function, a multiplicative form of dimensional reduction method (M-DRM) is developed. The main benefit of the proposed approach is that it provides full probability distribution of the maximal output error from a very few evaluations of the trajectory of mechanism. The proposed method is illustrated by analyzing the system reliability analysis of two planar mechanisms. Examples presented in the paper show that the results of the proposed method are fairly accurate as compared with the benchmark results obtained from the Monte Carlo simulations.

System-Reliability Evaluation Based on Series Chain Model under Exponential Distribution

In the general reliability analysis of series systems, the components which compose the system are assumed independent of each other. However, for most mechanical series systems, dependent failure is their common feature. If neglecting dependent failures where CCF(Common Cause Failure) plays an important role, it will lead to considerable errors or even misleading conclusions. In this article, the concept of series chain model is put forward in consideration of the CCF. By using the load—strength interference model, the order statistic theory and the knowledge of statistical distribution, the author develops a specific method to evaluate the reliability of series systems under exponential distribution. In the last part, by using Monte Carlo simulation, a group of specific data are given to verify the series chain model and compare the two different series system model. The results show that the reliability calculation under the classic series model is relatively conservative, while the reliability calculation under the series chain model is convincing. And thus, the series chain model is more applicable in engineering.

First-order reliability analysis of slope considering multiple failure modes

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 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), which gives the probability of the union of approximate events. FORM approximations at each design point and a subsequent series system reliability analysis are employed to estimate failure probability. Application of the procedure is illustrated through example problems. The results show that the applied procedure is able to efficiently consider various failure modes caused by stratifications and variations in soil properties in probabilistic slope stability assessments.

System reliability analysis of the robotic manipulator with random joint clearances

The paper presents an innovative method for computing reliability of a robotic manipulator such that the positional error in the entire trajectory remains within acceptable limits. This problem is equivalent to a series system reliability analysis that can be solved using the extreme value distribution of the positional error. The principle of maximum entropy is applied to derive this distribution. A novel feature of the analysis is the use of fractional moments, instead of integer moments commonly used in the entropy literature. The fractional moments are obtained from a small, simulated sample of positional error. Examples are presented to illustrate accuracy and efficiency of the proposed method.

An efficient method for system reliability analysis of planar mechanisms

This article presents an efficient method for system reliability analysis of planar mechanisms with random dimensions and joint clearances. The reliability of the mechanism is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. Since the currently used methods for system reliability analysis are approximate in nature, this article presents a more efficient and innovative method based on the minimum cross-entropy principle for probabilistic analysis used in the information theory. The mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. To derive this distribution, fractional moments of the output error are estimated from a small simulated sample of trajectories of mechanism motion which serve as constraints in the minimization of cross entropy. The proposed method is illustrated by analyzing the reliability slider–crank and a four-bar function generator. The comparison of the results with those obtained from the Monte Carlo simulations confirms the high accuracy of the proposed method.

Reliability analysis of series systems with multiple failure modes under epistemic and aleatory uncertainties

Uncertainty exists widely in engineering practice. An engineering system may have multiple failure criteria. In the current paper, system reliability analysis with multiple failure modes under both epistemic and aleatory uncertainties is presented. Epistemic uncertainty is modelled using p-boxes, while aleatory uncertainty is modelled using probability distributions. A first-order reliability method is developed and non-linear performance functions are linearized by the sampling method instead of the commonly used Taylor’s expansion at the most probable point. Furthermore, multiple failure modes in a system are often correlated because they depend on the same uncertain variables. In order to consider these correlated failure modes, the methods proposed by Feng and Frank are extended in this paper in order to calculate the joint probability of failure for two arbitrary failure modes under both aleatory and epistemic uncertainties. The Pearson correlation coefficient of two arbitrary failure modes is determined by the sampling method. Since two types of uncertainty exist in the system, the probability of system failure is an interval rather than a point value. The probability of failure of the system can be obtained by the combination of the extension ‘narrow’ bound method and the interval arithmetic. A numerical example is presented to demonstrate the applicability of the proposed method.

Multiple design points in first and second-order reliability

A method is developed to successively find the multiple design points of a component reliability problem, when they exist on the limit-state surface. FORM or SORM approximations at each design point followed by a series system reliability analysis is shown to lead to improved estimates of the failure probability. Three example applications show the generality and robustness of the method.

First-excursion probability of uncertain structures

The first-order reliability method (FORM) is used to estimate the first-excursion probability of uncertain structures subjected to deterministic dynamic loading. The limit-state function for the first-excursion event is formulated. A general purpose finite element code is used to compute the limit-state function and its gradient with respect to random structural properties. An algorithm is developed that successively finds the locally minimum distance points on the limit-state surface in the order of increasing distance from the origin in the standard normal space. A standard series system reliability analysis is then performed to compute the first-excursion probability. Two example inelastic structures are used to demonstrate the application and validity of the proposed method.

Bayesian Reliability Analysis of Series Systems of Binomial Subsystems and Components

Bayesian Reliability Analysis of Series Systems of Binomial Subsystems and Components

Bayesian Reliability Analysis of Series Systems of Binomial Subsystems and Components

A Bayesian procedure is presented for estimating the reliability of a series system of independent binomial subsystems and components. The method considers either test or prior data (perhaps both or neither) at the system, subsystem, and component level. Beta prior distributions are assumed throughout. Inconsistent prior judgments are averaged within the simple-to-use procedure. The method is motivated by the following practical problem. It is required to estimate the overall reliability of a certain air-to-air heat-seeking missile system containing five major subsystems with up to nine components per subsystem. The posterior distribution of the overall missile-system reliability from which the required estimates are obtained is computed.

Structural Reliability Analysis of Series Systems

Reliability analysis of chain‐like series structural systems was performed for the special cases of lognormal stress and both Weibull and lognormal component strength. The goal was to relate component reliability to system reliability. This problem has application to establishment of design requirements, e.g. for fatigue avoidance in tethering components for marine structures or disks for turbine engines. When the events of failure of each member in a series system are assumed to be mutually independent, a simple expression for risk results. But component failure events are not independent, because of the presence of the same stress term in each event. Correction factors to be applied to the simple expression are derived for the stress and strength distributions considered. It is demonstrated, that the conservative assumption of independent component failure events can produce weight penalties of 10% or more. An example is provided which illustrates application of the results to establish a design requirement for a tendon of a tension leg platform.