Simulation-based Reliability Analysis Research Articles

Simulation-Based Reliability Analysis of Steel Girder Railway Bridges

Bridges are an essential component of the transportation system and safety and sustainability of bridges are critical for the efficient operation thereof. Due to scarcity of resources, an economical way should be determined to design and maintain bridges and the transportation system in general. Reliability indexes are widely used in the analysis of these concepts within a semi-probabilistic approach. However, advances in computer technology allow implementing a fully-probabilistic approach. This study represents a simulation-based reliability analysis of steel girder bridges in the railway lines. Statistical parameters of the bridges are determined both analysing the existing body of knowledge available in the literature and conducting specimen tests. The Bayesian approach is used to update the statistical properties of the steel material. Basic Monte Carlo Simulation (MCS) is used to simulate the load and resistance of the bridge. The reliability of the bridges is determined according to their ultimate limit states and statistical load distribution. By using simulation, the consistency of the log-normal marginal distribution obtained is analysed herein.

A combined shear strength reduction and surrogate model method for efficient reliability analysis of slopes

Surrogate models are often used to alleviate extensive computational burden for slope reliability analysis. How to efficiently train a surrogate model with high precision is always a nontrivial task. This paper proposes a novel method, which combines the shear strength reduction (SSR) technique, the surrogate model and the adaptive pool-based sampling strategy for efficient slope reliability analysis. The surrogate model is used to replace the time-consuming slope stability model in simulation-based reliability analysis, while the SSR technique coupled with an adaptive pool-based sampling strategy is innovatively adopted to search for the most informative samples to train the surrogate model, which can improve the computational efficiency significantly. Further, an expanded sampling method is suggested to improve the local prediction of surrogate model in other design space, enabling an efficient evaluation of the slope failure probability corresponding to different threshold safety factors. The main feature of the proposed method is that it takes advantage of SSR technique to efficiently generate training samples in the region of interest. Several slope examples are analyzed to validate the accuracy, computational efficiency as well as the applicability of the proposed method. The results show that proposed method outperforms other approaches in computational efficiency and can give accurate estimation of slope failure probability as well.

Smart Rainwater Harvesting for Sustainable Potable Water Supply in Arid and Semi-Arid Areas

This paper presents a smart rainwater harvesting (RWH) system to address water scarcity in Palestine. This system aims to improve the water harvesting capacity by using a shared harvesting system at the neighborhood level and digital technology. The presentation of this system is organized as follows: (i) identification of the challenges of the rainwater harvesting at the neighborhood level, (ii) design of the smart RWH system architecture that addresses the challenges identified in the first phase, (iii) realization of a simulation-based reliability analysis for the smart system performance. This methodology was applied to a residential neighborhood in the city of Jenin, Palestine. The main challenges of smart water harvesting included optimizing the shared tank capacity, and the smart control of the water quality and leakage. The smart RWH system architecture design is proposed to imply the crowdsourcing-based and automated-based smart chlorination unit to control and monitor fecal coliform and residual chlorine: screens, filters, and the first flush diverter address RWH turbidity. Water level sensors/meters, water flow sensors/meters, and water leak sensors help detect a water leak and water allocation. The potential time-based reliability (Re) and volumetric reliability (Rv) for the smart RWH system can reach 38% and 41%, respectively. The implication of the smart RWH system with a dual water supply results in full reliability indices (100%). As a result, a zero potable water shortage could be reached for the dual water supply system, compared to 36% for the municipal water supply and 59% for the smart RWH system. Results show that the smart RWH system is efficient in addressing potable water security, especially when combined with a dual water supply system.

Subset simulation-based reliability analysis of the corroding natural gas pipeline

In this study, a subset simulation-based methodology is developed to evaluate the time-dependent reliability of the corroding pipeline with multiple correlated corrosion defects. Two competing failure modes, namely small leak and burst, are considered in the methodology. Firstly, the time-dependent structural reliability model of the two competing failure modes is established. Then, the computational framework for implementing subset simulation for failure probability estimation of the individual corrosion defect is presented. Thereafter, a procedure to calculate the system reliability of the entire pipeline with correlated corrosion defects is proposed. Moreover, a numerical example based on a real natural gas pipeline is proposed, and the time-dependent failure probabilities of both the small leak and burst are predicted, which are compared with the evaluation results produced by the direct Monte Carlo simulation and Kriging method. By means of numerical example, the accuracy and efficiency of our methodology are demonstrated. Furthermore, a sensitivity analysis is performed to investigated the effect of the correlation of the corrosion defects on the system reliability, and the results indicate that the correlation exert great impact on system reliability.

Sensitivity of Sample for Simulation-Based Reliability Analysis Methods

In structural reliability analysis, simulation methods are widely used. The statistical characteristics of failure probability estimate of these methods have been well investigated. In this study, the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample, called ‘contribution indexes’, are proposed to measure the contribution of sample. The contribution indexes in four widely simulation methods, i.e., Monte Carlo simulation (MCS), importance sampling (IS), line sampling (LS) and subset simulation (SS) are derived and analyzed. The proposed contribution indexes of sample can provide valuable information understanding the methods deeply, and enlighten potential improvement of methods. It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples, which are the main factors to the efficiency of the methods. Moreover, numerical examples are used to validate these findings.

Reliability analysis of concrete barriers under vehicular crashes using augmented RBFs

A reliability analysis approach was studied for the assessment of roadside barriers under vehicular crashes. It was achieved using computational mechanics and a simulation-based reliability analysis method. Traditionally, the evaluation of roadside barriers has been conducted based on limited crash tests. With the development of high-performance computer hardware and software, numerical crash simulations can be performed using high-fidelity finite element (FE) methods. Based on the crash simulation results, various barrier systems can be assessed. Due to the high nonlinearity and implicit nature of crash responses, approximate models such as metamodels become useful to replace numerical crash analyses. In this work, augmented radial basis functions (RBFs) were used to generate approximate models of limit state functions, which represented crash responses exceeding certain limit values. With explicit limit state functions, failure probabilities or probabilities of exceedance were calculated using Monte Carlo simulations (MCS). The combination of crash simulations and a metamodeling technique allows an efficient reliability analysis, when expensive numerical analyses are required. A New Jersey concrete barrier example was analyzed and various crash responses and their limits were considered. The probability-based analysis method provides a useful tool to improve transportation safety. It can potentially replace the prescriptive pass/fail approach traditionally employed in barrier evaluation and design.

Proposed Algorithms for an Efficient System Reliability-Based Design Optimization of Truss Structures

AbstractThe design optimization considering the system reliability of a structural system is a computationally challenging task. This is especially the case in an indeterminate structure that has many possible modes or paths to complete failure. Accomplishing this task efficiently requires using enhanced and powerful techniques for the structural analysis, the reliability analysis, and the optimization solution. In a simulation-based reliability analysis, the actual value of the performance functions is irrelevant to the calculated probability of failure. The actual value of the performance function is merely calculated to determine whether the system failed or not. In this paper, nonlinear analysis algorithms for truss structures are proposed. These algorithms are used for determining whether the structural system failure occurs during the simulation-based system reliability analysis in a computationally efficient manner. Using these algorithms, a simulation-based system reliability design optimization o...

Reliability-Based Multidisciplinary Design Optimization Using Subset Simulation Analysis and Its Application in the Hydraulic Transmission Mechanism Design

The Monte Carlo simulation (MCS) can provide high reliability evaluation accuracy. However, the efficiency of the crude MCS is quite low, in large part because it is computationally expensive to evaluate a very small failure probability. In this paper, a subset simulation-based reliability analysis (SSRA) approach is combined with multidisciplinary design optimization (MDO) to improve the computational efficiency in reliability-based MDO (RBMDO) problems. Furthermore, the sequential optimization and reliability assessment (SORA) approach is utilized to decouple an RBMDO problem into a sequential of deterministic MDO and reliability evaluation problems. The formula of MDO with SSRA within the framework of SORA is proposed to solve a design optimization problem of a hydraulic transmission mechanism.

Efficient approach for reliability-based optimization based on weighted importance sampling approach

An efficient methodology is presented to perform the reliability-based optimization (RBO). It is based on an efficient weighted approach for constructing an approximation of the failure probability as an explicit function of the design variables which is referred to as the ‘failure probability function (FPF)’. It expresses the FPF as a weighted sum of sample values obtained in the simulation-based reliability analysis. The required computational effort for decoupling in each iteration is just single reliability analysis. After the approximation of the FPF is established, the target RBO problem can be decoupled into a deterministic one. Meanwhile, the proposed weighted approach is combined with a decoupling approach and a sequential approximate optimization framework. Engineering examples are given to demonstrate the efficiency and accuracy of the presented methodology.

Design based on reliability of naval multilayer fiber composite panels using evolutionary algorithms and stochastic structural mechanics

The complexity of sea wave loads and the number of design variables involved in the design of laminated composites for naval applications makes this a challenging problem. Traditional methodologies for engineering design and analysis are not suitable to deal with these kinds of design problems. This work presents a methodology based on evolutionary algorithms and stochastic structural mechanics to design high-reliability naval multilayer composite structural panels.. The mechanical response of structural panels was modeled by using the Multilayer First Order Shear Deformable Plate Theory and the Finite Element Method. Sea wave loads were modeled as stochastic dynamic loads by using the Simulation Based Reliability Analysis approach. The structural reliability of the panel, as a function of the composite ply’s fiber direction, was considered a design variable. In order to maximize the structural reliability, an optimization methodology based on Genetic Algorithms was proposed. For the design process, a computational code using FORTRAN® and the OpenMP® library for parallel computing was developed. The proposed methodology was applied to the design of composite naval panels and results were compared to those obtained through traditional design methodologies. The results show increased reliability of the panels in all cases analyzed. The proposed methodology is, thus, shown as a reliable engineering tool to optimize the structural performance of existing designs.

Simulation-Based Reliability Analysis for Kinematic Accuracy of Retracting Mechanism of Landing Gear

A simulation-based reliability analysis approach for kinematics accuracy of retracting mechanism is presented. The parametric variable model with linkage dimension error and joint clearance of retracting mechanism is modeled in ADAMS, adopting the Monte Carlo simulation method to analysis the influence of kinematic accuracy. The flowchart of the approach has been presented. Finally, the retracting mechanism is taken as an example to validate the proposed method. The results show that it is more accurate than the traditional methods.

Conditional probability Markov chain simulation based reliability analysis method for nonnormal variables

Based on fast Markov chain simulation for generating the samples distributed in failure region and saddlepoint approximation (SA) technique, an efficient reliability analysis method is presented to evaluate the small failure probability of non-linear limit state function (LSF) with non-normal variables. In the presented method, the failure probability of the non-linear LSF is transformed into a product of the failure probability of the introduced linear LSF and a feature ratio factor. The introduced linear LSF which approximately has the same maximum likelihood points as the non-linear LSF is constructed and its failure probability can be calculated by SA technique. The feature ratio factor, which can be evaluated on the basis of multiplicative rule of probability, exhibits the relation between the failure probability of the non-linear LSF and that of the linear LSF, and it can be fast computed by utilizing the Markov chain algorithm to directly simulate the samples distributed in the failure regions of the non-linear LSF and those of the linear LSF. Moreover, the expectation and variance of the failure probability estimate are derived. The results of several examples demonstrate that the presented method has wide applicability, can be easily implemented, and possesses high precision and high efficiency.

An Indicator Response Surface Method for Simulation-Based Reliability Analysis

An accurate and efficient Monte Carlo simulation method is presented for limit-state-based reliability analysis at both component and system levels, using a response surface approximation of the failure indicator function. The cross-validated moving least squares method is used to construct the response surface of the indicator function, based on an optimum symmetric Latin hypercube sampling technique. The proposed method can handle problems with complicated limit state(s). Also, it can easily handle implicit, highly nonlinear limit-state functions, with variables of any statistical distributions and correlations. The method appears to be particularly efficient for multiple limit state and multiple design point problems. Three structural reliability examples are used to highlight its superior accuracy and efficiency over traditional reliability methods.

Multivariate Simulation and Multimodal Dependence Modeling of Vehicle Axle Weights with Copulas

Safety assessment and rational design of bridge structures requires the uncertainty associated with vehicle loads to be modeled as accurately as possible. This modeling is rendered difficult by the presence of vehicle axle weights that involve different combinations of unimodal and multimodal probability distributions with different dependence structures. In this paper, a transformation invariant approach using copula functions is proposed for the multivariate simulation of dependent axle weights of different vehicle classes. Copula based dependence modeling, which is widely used in the financial risk analysis, is applied to model and simulate three different vehicle cases with different combinations of marginal probability distributions for axle weights. The database of observed vehicle weights is based on the data collected at five locations on national highways in India. The dependence between multimodal distributions of axle weights is accurately considered and simulations are carried out. The simulated axle weights are found to be in very good agreement with the observed data. This type of simulation is useful in carrying out simulation-based reliability analysis of bridges and pavements.

Pressure dependent stochastic reliability analysis of water distribution networks

Any reliability analysis based on just deterministic values of daily average or peak demands, cannot represent the overall system reliability realistically. Using a stochastic model in this paper variations of the system and nodal reliability values are investigated through a period of time. Considering probabilistic nature of demands, this paper combines the extended period simulation of water distribution networks with the head driven simulation based reliability analysis that presents the nodal and system reliabilities more realistically than conventional demand driven simulation based analysis. A sample network with possibility of one link failure is examined and diurnal profile of reliability values due to mechanical and hydraulic failures and known probabilities of demands is presented. It is seen that considering the probabilistic nature of demands the severity of mechanical and hydraulic failures on the hydraulic performance of the system are illustrated properly and realistically, especially at the critical times or nodes, in comparison with the deterministic values.

Comparison of Methods for Predicting Deficient-Network Performance

When a nodal demand is excessive as in a fire-flow condition or when a pump fails or a pipe breaks, a water distribution system (WDS) may temporarily become deficient and unable to satisfy all nodal demands. However, the prediction of the performance of a WDS under a temporarily-deficient condition is necessary for simulation-based reliability analysis and design of WDSs. Available methods for such prediction are reviewed herein. When the actual outlets are considered as demand nodes the methods which simultaneously consider the nodal flows and heads give fairly accurate and similar results. However, when the demands of secondary networks are assumed concentrated at the nodes of the primary WDSs, the prediction of the deficient-condition performance of a primary WDS is rather approximate. For reliability purposes, however, the method using parabolic head-discharge relationship (no flow at minimum head to required flow at desirable head), is the best for prediction of deficient-network performance.