Efficient Reliability Analysis Research Articles

Seismic reliability analysis using Subset Simulation enhanced with an explorative adaptive conditional sampling algorithm

Reliability analysis of structures under earthquake loading represents a significant engineering challenge. This is due to the required and rather numerically involving non-linear dynamic analysis, the large computational burden when targeting small failure probabilities, and the synthetic earthquake model representation that may contain thousands of random variables. Subset Simulation is an efficient reliability analysis technique that can handle the challenge of a high-dimensional space with a reduced number of structural analysis calls compared to crude Monte Carlo Simulation. In this contribution, firstly, we investigate the conditions for which Subset Simulation performs efficiently. Thereafter we propose an enhancement to the existing Subset Simulation schemes that shows significant potentials for enhancing the strategy for the starting of the Markov Chain Monte Carlo simulations whenever a new level is reached in the Subset Simulation. Finally, the information gathered from the simulations is investigated to verify that Subset Simulation provides meaningful results from a physical point of view.

Efficient reliability analysis of generalized [formula omitted]-out-of-[formula omitted] phased-mission systems

A k-out-of-n phased-mission system (PMS) is a PMS where the system structure is k-out-of-n: G in each phase. This paper investigates k-out-of-n PMSs with phase-K-out-of-N requirement, where the entire mission is successful if at least K out of the N phases achieve success. Such system is referred to as a generalized k-out-of-n PMS (k/n-GPMS). The k/n-GPMSs are prevalent in applications such as satellites, unmanned aerial vehicles (UAVs), wireless sensor networks and so on. In this paper, a novel method based on multi-valued decision diagram (MDD) is proposed to analyze the reliability of k/n-GPMSs, where the number of available components n, the required number of components k, and the components failure behaviors in different phases may vary. Distinguishing from the traditional phase-by-phase MDD generation method, the proposed method considers the behavior of all phases simultaneously and generates only one MDD model in a top-down manner. To illustrate the application of the proposed method, the reliability and the sensitivity of a four UAVs system which conducts supplies delivery mission is analyzed. The complexity analysis is performed. The correctness and efficiency are verified and demonstrated by several case studies. The proposed method is also compared with Monte Carlo simulation method.

Efficient reliability analysis of stochastic dynamic first-passage problems by probability density evolution analysis with subset supported point selection

This study introduces a novel point selection procedure for the Probability Density Evolution Method (PDEM) to estimate time-dependent reliability and failure probabilities in dynamic systems under first-passage failure conditions. The method integrates and modifies features of the Subset simulation procedure to adaptively generate dependent sample sets suitable for a reliability analysis by a direct probability integration approach levering PDEM. Performance function assessments are used as weighting factors in the Subset supported Point Selection (S-PS), enhancing the ultimate failure probability estimation accuracy. The presented approach effectively identifies samples in the failure region, particularly benefiting for dynamic systems under stochastic excitation, tested with random dimensions up to 60. It also offers a computationally efficient structural reliability estimation procedure by analyzing full time–history responses. The proposed method provides deeper insights into rare failure events and mechanisms through the visualization of intermediate results. This research presents an advanced framework for estimating structural reliability and understanding critical events in dynamic systems.

Dimension-Reduction Spectral Representation of Soil Spatial Variability and Its Application in the Efficient Reliability Analysis of Seismic Response in Tunnels

Reliability analysis of tunnels considering soil spatial variability was traditionally carried out using Monte Carlo simulations, which are computationally expensive. This study proposes a dimension-reduction spectral representation method (SRM) for simulating parameter stochastic fields to capture uncertainties in soil properties, which can be coupled with the probability density evolution method (PDEM). Additionally, the PDEM is employed to conduct seismic reliability assessments of tunnels in a more efficient manner. By integrating a non-intrusive dynamic random finite element method (FEM), this study explores the horizontal drift angle and vertical relative settlement of tunnel dynamic response under different coefficient of variations (COVs) and horizontal autocorrelation lengths of elastic modulus (E). Results show the changes in COVs have more pronounced effects on the mean and standard deviation of horizontal drift angle and vertical relative settlement of tunnel than alterations in horizontal autocorrelation lengths. A limit state pertaining to the horizontal drift angle and vertical relative settlement is established through the use of a probability density function (PDF) and cumulative distribution function (CDF). The results suggest that the combination of soil spatial variability and PDEM can serve as an effective approach for practical tunnel design.

Reliability analysis of tunnels considering the rock-support interaction using a metamodel-based reliability method

The convergence-confinement method (CCM) is an important approach to analysis the rock-support interaction and to design tunnel and its support. To make an effort on efficient reliability analysis of tunnels integrated with CCM, of which performance functions are mostly highly nonlinear and implicit, a hybrid intelligent algorithm combing uniform design (UD) and Gaussian process regression (GPR) is proposed. Based on the generated UD samples, GPR-parameter metamodels to predict the important parameters of CCM and GPR-probability metamodels to approximate the real performance functions are constructed consequently. Then sensitivity analysis, determination of the optimal preliminary support timing and failure probabilities calculations can be performed in conjunction with Monte Carlo simulation (MCS) based on the constructed GPR-parameter metamodels and GPR-probability metamodels. To verify the efficiency and accuracy of the proposed method, a typical circle tunnel is analyzed and good results are achieved. Finally, a practical hydraulic tunnel is analyzed using the proposed method and some beneficial conclusions are drawn.

Simulation-free reliability analysis with importance sampling-based adaptive training physics-informed neural networks: Method and application to chloride penetration

Surrogate model-based reliability analysis aims at building a cheap-to-evaluate mathematical model as a substitute for the original performance function to enhance computational efficiency. Data-driven surrogate models have been popularly studied from a perspective of active learning. On the other hand, Physics-informed Neural Networks, called PINNs, have recently gained much attention as a physics-informed surrogate model to directly solve partial differential equations. Building on the capability of avoiding the simulation of traditional numerical solvers such as the finite element analysis, the PINN-based reliability analysis can achieve highly efficient simulation-free uncertainty quantification. This paper focuses on the development of the PINN-based reliability analysis method and its application in practical engineering applications. Reliability analysis with Importance Sampling-based Adaptive Training Physics-informed Neural Networks (IAT-PINN-RA) is proposed in this work. Compared with the existing PINN-based reliability analysis methods, IAT-PINN-RA introduces a pre-training stage for the establishment of the importance sampling distribution, and therefore achieves better performance when handling rare events. The modeling and reliability analysis of chloride penetration, which can pose serious challenges to the durability of concrete structures, are investigated. A practical example demonstrates the feasibility of using PINNs to model this physical phenomenon and the performance of the proposed method to achieve accurate and efficient reliability analysis results.

Reliability assessment of freight wagon passing through railway turnouts using adaptive Kriging surrogate model

ABSTRACT Railway turnout (RT) is a crucial component of railway infrastructure that consists of several components. Assessing the derailment probability of freight wagons passing through the turnout is crucial for quantifying failure risks and optimizing the performance of the freight wagon-turnout system (FWTS). However, existing assessment methods often require extensive model evaluations and impose substantial computational costs. To address this issue, an efficient reliability analysis method is established for assessing the derailment risk at RTs. Firstly, a dynamic model is developed to capture the wheel-rail dynamic interaction and the numerical model is validated by field tests. Secondly, to reduce the computational cost in the reliability analysis, an efficient adaptive Kriging method based on an error stopping criteria and a learning function is adopted to estimate the failure probabilities under multiple failure modes of wheel derailments. Based on the efficient learning function and convergence criterion, accurate failure probability results can be obtained with a small number of multibody and finite element coupled dynamic simulations. Furthermore, the prediction accuracy of the proposed method in capturing random characteristics for FWTS is evaluated. Finally, the influence of the evolution of rail wear on the failure probability is further discussed.

Logical Resolving-Based Methodology for Efficient Reliability Analysis.

With the CMOS technology downscaling to the deep nanoscale, the aging effects of devices degrade circuit performance and even lead to functional failure. The stress analysis is critical to evaluate the influence of aging effects on digital circuits. Some related analytical work has recently focused on reliability-aware circuit analysis. Nevertheless, the aging dependence among different devices is not considered, which will induce errors of degradation evaluation in the digital circuit. In order to improve the accuracy of reliability-aware static timing analysis, an improved analytical method is proposed by employing logical resolving. Experimental results show that the proposed method has a better evaluation accuracy of aging path delay than traditional strategies. For aging timing evaluation on aging paths, excessive pessimism can be reduced by employing the proposed method. And, a 378× speedup is achieved while having a 0.56% relative error compared with precise SPICE simulation. Moreover, the circuit performance sacrifice of an aging-aware synthesis flow with the proposed method can be decreased. Due to the high efficiency and high accuracy, the proposed method can meet the speed demands of large-scale digital circuit reliability analysis while achieving transistor simulation accuracy.

A multi-fidelity approach for reliability-based risk assessment of single-vehicle crashes

Road vehicles are highly susceptible to single-vehicle crashes (SVCs) under complex road geometry and inclement weather, which can significantly threaten traffic safety and mobility of the whole traffic system. Most existing studies involve various simplifications and approximations to assess the associated SVC risks promptly, and therefore the assessment accuracy is often compromised. A novel multi-fidelity approach is developed for the reliability-based risk assessment of SVCs to balance the simulation accuracy and efficiency. Specifically, a high-fidelity transient dynamic vehicle model is introduced for a robust estimation of the vehicle dynamics under various driving environments, assisted by a low-fidelity simplified physics-based vehicle model to improve the computational efficiency. Based on the simulations of the two models, a new multi-fidelity improved cross entropy-based importance sampling (MFICE) algorithm is proposed for integrating multi-fidelity information and facilitating accurate and efficient reliability analysis. Five demonstrative cases are studied to evaluate the performance of the proposed approach, including the comparison with existing representative approaches. The results show that the proposed innovative multi-fidelity approach can provide a reliability evaluation of SVCs both accurately and efficiently, with obviously superior performance over typical state-of-the-art counterparts. Therefore, the proposed approach bears great potential on developing proactive and near real-time intelligent traffic operation and management strategies against SVCs in both normal and hazardous conditions.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently, reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering. However, for deep foundation pit, evaluating the system safety of retaining structures and finding cost-effective design points are main challenges. To address this, this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou, China. The proposed method included two parts: system reliability model and robust design method. Back Propagation Neural Network (BPNN) is used to fit limit state functions and conduct efficient reliability analysis. The common source random variable (CSRV) model are used to evaluate correlation between failure modes and determine the system reliability. Furthermore, based on the system reliability model, a robust design method is developed. This method aims to find cost-effective design points. To solve this problem, the third generation non-dominated genetic algorithm (NSGA-III) is adopted. The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm. The proposed method has a good performance in locating the balanced design point between safety and construction cost. Moreover, the proposed method can provide design points with reasonable stiffness distribution.

Phase reduction for efficient reliability analysis of dynamic k-out-of-n phased mission systems

Phase reduction for efficient reliability analysis of dynamic k-out-of-n phased mission systems

An Efficient Reliability Analysis Method Based on the Improved Radial Basis Function Neural Network

Abstract This paper develops an efficient reliability analysis method based on the improved radial basis function neural network (RBFNN) to increase the accuracy and efficiency of structural reliability analysis. To solve the problems of low computational accuracy and efficiency of the RBFNN, an improved RBFNN method is developed by transferring the sampling center of Latin hypercube sampling (LHS) from the mean values of random variables to the most probable point (MPP) in the sampling step. Then, the particle swarm optimization algorithm is adopted to optimize the shape parameters of RBFNN, and the RBFNN model is assessed by the cross-validation method for subsequent reliability analysis using Monte Carlo simulation (MCS). Four numerical examples are investigated to demonstrate the correctness and effectiveness of the proposed method. To compare the computational accuracy and efficiency of the proposed method, the traditional radial basis function method, hybrid radial basis neural network method, first-order reliability method (FORM), second-order reliability method (SORM), and MCS method are applied to solve each example. All the results demonstrate that the proposed method has higher accuracy and efficiency for structural reliability analysis. Importantly, one practical example of an industrial robot is provided here, which demonstrates that the developed method also has good applicability and effectiveness for complex engineering problems.

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

Efficient model‐correction based reliability analysis of uncertain dynamical systems

AbstractIn this contribution, a model‐correction‐based strategy is applied 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 the 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 (MPP) 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 (MSD) system, however increasing the computational effort of the limit state function evaluations. The failure probabilities evaluated with the model‐correction approach are contrasted and discussed with the failure probabilities of the sophisticated bridge‐train interaction model. It is shown that the model‐correction‐based approach provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort.

Application of state‐space models with frequency‐dependent uncertainty for efficient reliability analysis of complex structures

AbstractIn this work, we introduce a commonly used framework to model uncertain dynamical systems and adapt it to propagate both parameters uncertainty and model mismatches through a dynamically excited railway bridge system. The approach considers the system inherent uncertainties in the frequency domain and leads to a significant reduction of the computational effort when performing an uncertainty quantification tasks. In an application example the proposed approach is utilized for efficient reliability analysis of the uncertain railway bridge system. The utilized technique allows for an efficient generation of structural responses, and thus enables a fast evaluation of failure probabilities by crude Monte Carlo sampling. Accuracy of the uncertain prediction model is ensured by comparing the failure probabilities with failure probability simulations based on a semi‐analytical Euler‐Bernoulli bridge beam model.

Efficient model-correction-based reliability analysis of uncertain dynamical systems

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.

Reliability analysis of structures using probability density evolution method and stochastic spectral embedding surrogate model

AbstractThis study presents an efficient reliability analysis method using probability density evolution method (PDEM) and stochastic spectral embedding (SSE) based surrogate model. The PDEM is used to estimate the structural response's probability density function (PDF). The PDEM is derived based on the principle of probability conservation where generalized density evolution equations (GDEEs) are decoupled from the physical system. The GDEEs are solved using finite difference method coupled with total variation diminishing, in which a set of representative points of random parameters are generated using the generalized F‐discrepancy scheme. To obtain satisfactory accuracy of the numerical solution, representative points are needed, which becomes computationally expensive for complex structures. To reduce the computation burden, the SSE is used, which approximates the original response surface. The SSE is a class of supervised machine learning algorithm where it is trained by few observations and enables output prediction as spectral representation. This is achieved by minimizing the residual using domain decomposition technique. To illustrate the proposed SSE‐based PDEM, three numerical examples are investigated, including the reliability analysis of four‐branch problem and shear building frame subjected to ground acceleration, and the reliability‐based design optimization of a moment‐resisting frame coupled with the nonlinear energy sink with negative stiffness and sliding friction. Numerical results show that the proposed SSE‐based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs.

Highly efficient reliability analysis of anisotropic heterogeneous slopes: machine learning-aided Monte Carlo method

Machine learning (ML) algorithms are increasingly used as surrogate models to increase the efficiency of stochastic reliability analyses in geotechnical engineering. This paper presents a highly efficient ML-aided reliability technique that is able to accurately predict the results of a Monte Carlo (MC) reliability study and yet performs 500 times faster. A complete MC reliability analysis on anisotropic heterogeneous slopes consisting of 120,000 simulated samples is conducted in parallel to the proposed ML-aided stochastic technique. Comparing the results of the complete MC study and the proposed ML-aided technique, the expected errors of the proposed method are realistically examined. Circumventing the time-consuming computation of factors of safety for the training datasets, the proposed technique is more efficient than previous methods. Different ML models, including random forest, support vector machine and artificial neural networks, are presented, optimised and compared. The effects of the size and type of training and testing datasets are discussed. The expected errors of the ML predicted probability of failure are characterised by different levels of soil heterogeneity and anisotropy. Using only 1% of MC samples to train ML surrogate models, the proposed technique can accurately predict the probability of failure with mean errors limited to 0.7%. The proposed technique reduces the computational time required for our study from 306 days to only 14 h, providing 500 times higher efficiency.

CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. We propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.

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.