Reliability Analysis Of Structural Systems Research Articles

An efficient analysis method for system reliability of semi-rigid base asphalt pavement structure based on direct probability integral method

The structural design parameters of asphalt pavement inherently possess randomness. Reliability theory aids in considering the stochastic nature of these parameters in asphalt pavement design. However, as the number of considered random factors increases, the complexity of reliability calculation models and the consumption of computational resources also significantly escalate. To analyze the structural reliability of semi-rigid base asphalt pavements more efficiently and accurately, a method combining Weighted Kernel Density Estimation (Weighted-KDE) with Direct Probability Integration Method (DPIM) using sampling strategies was employed. Furthermore, integrating the equivalent extreme value principle, an asphalt pavement structural system reliability analysis method was proposed, considering multiple failure mode correlations. The numerical solution steps of this method are also outlined. Based on the typical semi-rigid asphalt pavement structure in China, this study utilized the elastic layer system method (the program Apbi) and a computational program developed in MATLAB to compare the efficiency and accuracy of calculating reliability between DPIM and the Monte Carlo Simulations (MCS). The computational outcomes indicate that, under the premise of selecting 18 random parameters, DPIM can achieve the required accuracy in assessing the reliability of asphalt pavement structure and system reliability. Analyzing how the number of samples affects the computational results reveals that using weighted-KDE and DPIM only needs a few hundred sample points to limit the relative error within 4 %, compared to the results obtained from 105 samples in MCS. The research findings demonstrate that DPIM incorporating the principle of equivalent extreme value events can serve as an efficient analytical approach for assessing the system reliability of asphalt pavement structures characterized by more complex failure modes.

Time-dependent reliability analysis of structural systems based on parallel active learning Kriging model

Time-dependent reliability analysis quantifies the failures of structural systems due to time-dependent uncertainties, such as material degradation and dynamic loads. The active learning Kriging model methods are widely used in structural reliability analysis to replace extensive time-consuming finite element simulations. However, they can only update one training sample and one failure mode per iteration, which limits their application to time-dependent, parallel computing, and multiple failure modes problems. In this study, we propose a new parallel active learning Kriging model for time-dependent reliability analysis, which can update multiple training samples and multiple failure modes per iteration. It includes the following strategies: (1) a novel parallel learning function is proposed, which combines the correlation function and U learning function to allow for the selection of multiple training samples per iteration; (2) an adaptive adjustment strategy for the number of parallel samples is proposed, which takes into account the prediction probability of parallel samples; (3) the proposed parallel learning function is integrated into time-dependent reliability analysis with multiple failure modes, enabling simultaneous updates of multiple training samples and failure modes, thus greatly reducing the number of iterations and computational time; and (4) a new stopping criterion is proposed to improve the efficiency of the estimation of failure probability. The proposed method can be applied to series or parallel time-dependent structural systems with multiple failure modes. We demonstrate the effectiveness of the proposed method through three examples, and the proposed method can achieve a balance between the computational time and function calls while maintaining a high level of accuracy in the estimation of time-dependent failure probability.

An adaptive method based on PC-Kriging for system reliability analysis of truss structures

In practice, a truss consists of a large number of members which makes it a complex system. This leads to difficulties to estimate the system reliability due to computational costs. An adaptive method is thereby proposed to deal with this issue. It constructs a global metamodel to quickly estimate the rough reliability index of a truss. According to the estimated reliability index, the differential evolution algorithm is performed to generate more samples located in an expanded domain so that more representative failure modes can be identified. Combined with AK-SYSi, local metamodels of representative failure mods are built, and updated through active learning. When the convergence criterion is satisfied, the results of system reliability analysis can be obtained. Eventually, two examples of truss structures are studied to illustrate the superiority of the proposed method in balancing accuracy and efficiency. The results indicate that the proposed method makes a good balance between accuracy and efficiency when it is applied to analyze the system reliability of the truss.

An improved active Kriging method for reliability analysis combining expected improvement and U learning functions

The reliability assessment of structures with multiple failure modes and small failure probability is challenging due to the time-consuming simulations required. Active learning Kriging methods for structural reliability with multiple failure modes have shown high computational efficiency and accuracy. However, selecting the appropriate sample and its failure mode to update the Kriging models remains a key problem. In this paper, we propose a new learning function and stopping criterion to further improve the efficiency of structural system reliability analysis. Firstly, we propose a new learning function that combines the expected improvement function and the U learning function. This function selects the most suitable samples, balancing the degree of expected improvement of samples to the limit state surface and the degree of misclassification probability of samples. Secondly, we propose a new stopping criterion that considers both the accurate construction of limit state surfaces and the probability of accurately predicting the signs of samples. This criterion avoids premature or late termination of the active learning process. Thirdly, the sequential MCS simulation method is employed in the active learning process to efficiently evaluate small failure probability problems. By analyzing four examples, we verify the accuracy and efficiency of the proposed structural reliability analysis method.

Weighted low-discrepancy samplings: A novel method for slope system reliability analysis

This paper presents an efficient method for system reliability analysis of geotechnical examples based on the low-discrepancy sequences (LDS) sampling technique in combination with probabilistic weighting of the samples, i.e., the weighted low-discrepancy samplings (WLDS). In the framework of quasi-Monte Carlo simulation (QMCS), the Sobol’s quasi-random LDS are employed to generate the basic random variable samples that can significantly improve the efficiency of probabilistic weighting for the probability of failure calculation. In particular, the most probable system failure points (MPPs) can be directly captured according to the probabilistic weighting calculation. Via Nataf transformation, the WLDS computational framework incorporating correlated random variables in soils is also illustrated. Focusing on geotechnical applications, the reliability analyses of example soil slopes are presented to verify the performance of the proposed method. It is found that the proposed WLDS method not only can accurately obtain the probability of system failure but also can capture the multi-MPPs defining different earth slope failure modes in a cost-effective manner. The results in this study demonstrate that the proposed WLDS method is a feasible and promising method for performing the system reliability analysis of complex geotechnical earth structures.

Novel methods for reliability study of multi-dimensional non-linear dynamic systems

This research presents two unique techniques for engineering system reliability analysis of multi-dimensional non-linear dynamic structures. First, the structural reliability technique works best for multi-dimensional structural responses that have been either numerically simulated or measured over a long enough length to produce an ergodic time series. Second, a novel extreme value prediction method that can be used in various engineering applications is proposed. In contrast to those currently used in engineering reliability methodologies, the novel method is easy to use, and even a limited amount of data can still be used to obtain robust system failure estimates. As demonstrated in this work, proposed methods also provide accurate confidence bands for system failure levels in the case of real-life measured structural response. Additionally, traditional reliability approaches that deal with time series do not have the benefit of being able to handle a system's high dimensionality and cross-correlation across several dimensions readily. Container ship that experiences significant deck panel pressures and high roll angles when travelling in bad weather was selected as the example for this study. The main concern for ship transportation is the potential loss of cargo owing to violent movements. Simulating such a situation is difficult since waves and ship motions are non-stationary and complicatedly non-linear. Extreme movements greatly enhance the role of nonlinearities, activating effects of second and higher order. Furthermore, laboratory testing may also be called into doubt due to the scale and the choice of the sea state. Therefore, data collected from actual ships during difficult weather journeys offer a unique perspective on the statistics of ship movements. This work aims to benchmark state-of-the-art methods, making it possible to extract necessary information about the extreme response from available on-board measured time histories. Both suggested methods can be used in combination, making them attractive and ready to use for engineers. Methods proposed in this paper open up possibilities to predict simply yet efficiently system failure probability for non-linear multi-dimensional dynamic structure.

System Reliability Analysis for Truss Structures Based on Automatic Updated�Model

Multiple failure modes tend to be identified in the reliability analysis of a redundant truss structure. This identification process involves updating the model for identifying the next potential failure members. Herein we intend to update the finite element model automatically in the identification process of failure modes and further perform the system reliability analysis efficiently. This study presents a framework that is implemented through the joint simulation of MATLAB and APDL and consists of three parts: reliability index of a single member, identification of dominant failure modes, and system-level reliability analysis for system reliability analysis of truss structures. Firstly, RSM (response surface method) combines with a constrained optimization model to calculate the reliability indices of members. Then the β-unzipping method is adopted to identify the dominant failure modes, and the system function in MATLAB, as well as the EKILL command in APDL, is used to facilitate the automatic update of the finite element model and realize load-redistribution. Besides, the differential equivalence recursion algorithm is performed to approximate the reliability indices of failure modes efficiently and accurately. Eventually, the PNET (probabilistic network evaluation technique) is used to calculate the joint failure probability as well as the system reliability index. Two illustrative examples demonstrate the accuracy and efficiency of the proposed system reliability analysis framework through comparison with corresponding references.

Decomposition method for reliability analysis of structural systems

Decomposition method for reliability analysis of structural systems

Assessment of DeepONet for time dependent reliability analysis of dynamical systems subjected to stochastic loading

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of recently proposed DeepONet in solving time dependent reliability analysis and uncertainty quantification of systems subjected to stochastic loading. Unlike conventional machine learning and deep learning algorithms, DeepONet is an operator network and learns a function to function mapping and hence, is ideally suited to propagate the uncertainty from the stochastic forcing function to the output responses. We use DeepONet to build a surrogate model for the dynamical system under consideration. Multiple case studies, involving both toy and benchmark problems, have been conducted to examine the efficacy of DeepONet in time dependent reliability analysis and uncertainty quantification of linear and nonlinear dynamical systems. Comparisons have also been drawn with Recurrent Neural Network results and with results obtained from Proper Orthogonal Decomposition based Gaussian process. The results obtained indicate that the DeepONet architecture is accurate as well as efficient. Moreover, DeepONet posses zero shot learning capabilities and hence, a trained model easily generalizes to unseen and new environment with no further training.

Probability of failure estimation for highway bridges under combined effects of uncorrelated multiple hazards

Majority of the highly populated regions of the United States are susceptible to multiple natural hazards. In such regions, the design and construction of structures under multiple hazards are critical to achieve the appropriate structural performance and infrastructure resilience. Multi-hazard reliability analysis of structural systems evaluates the system response under multiple random loads, some of which may occur simultaneously, or the effect of one may weaken the structural system before the occurrence of the next event. This paper studies the combined effects of scouring and earthquakes, as two uncorrelated extreme events, on the performance of reinforced concrete highway bridges. In a continuous effort to support future improvement in understanding the impact of multi-hazard loading scenario on bridges and to develop mitigation actions, this paper assesses the seismic vulnerability of a reinforced concrete highway bridge experiencing the effect of erosion due to the increase in frequency of flood events. The analytical fragility approach uses a three-dimensional nonlinear finite element model of the bridge cases with various levels of scouring. Because a bridge is system of components, a component level fragility curve is used to track the response of the components for a given ground motion intensity. The system fragility curves are developed to consider the vulnerability of critical components to assess the probability of bridge damage. The results indicate that under multi-hazard scenarios, the component governing the fragility of the bridge system varies depending on the level of scour sustained by the structure.

Structural system reliability assessment using generalized factorized dimensional reduction method and iterative maximum entropy method

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.

A new active learning Kriging metamodel for structural system reliability analysis with multiple failure modes

Recently, the active learning Kriging (ALK) metamodel has proved to be an efficient method for structural system reliability analysis with multiple failure modes. A key step for enhancing the accuracy and efficiency of an ALK method is to select training samples around the limit state of the performance function as fast as possible. This study develops a new ALK metamodel based on the concept of significant domain where samples contribute the most to the failure of the system, which is termed as the ALK-SD, to achieve the above purpose. First, multiple Kriging models are established based on several initial training samples for each component using a modified DACE toolbox. Then, the significant domain of an engineering system is identified according to the type of the system. Thereafter, a new learning function H is defined to sequentially update the initial Kriging models by selecting the most probable points in the significant domain. Finally, four numerical examples and one engineering example are studied to illustrate the effectiveness of the proposed method, and the corresponding results are subsequently compared with those obtained via similar methods in literature in terms of the computational efficiency and the locations of newly added training samples. The results show that the proposed method can effectively and accurately evaluate the structural system reliability by outperforming its counterparts.

A copula-function-based structural system reliability analysis method

A copula-function-based structural system reliability analysis method

System reliability analyses of static and dynamic structures via direct probability integral method

Structural system reliability analysis is of important significance for evaluating the safety of structures with many components. Since a structural system can be acted by static or dynamic load, a unified and efficient method is required to assess the system reliability of static or dynamic load induced structures. In this study, the direct probability integral method (DPIM) is proposed to uniformly attack system reliability problems of static and dynamic structures. Firstly, the static and first-passage dynamic reliability formulas of the series, parallel and mixed systems are established by the joint probability density function (PDF) of multiple performance functions. Based on the probability density integral equation (PDIE) of performance functions, the DPIM is proposed along the two approaches, i.e., DPIM-S and DPIM-H. The former computes the system reliability using the PDF of extreme value mapping of performance functions, which is obtained by smoothing Dirac delta function. In the latter, the system reliability formulas with Heaviside function are analytically derived by the PDIE of multiple performance functions. Specially, the role of smoothing of Dirac delta function in DPIM for stochastic response and reliability analyses is revealed. Finally, five typical examples, including two mathematical examples and three static and dynamic structural systems, demonstrate high efficiency and accuracy of the DPIM for system reliability computation. Because of omitting the smoothing of Dirac delta function, the DPIM-H takes less CPU time for solving system reliabilities of static and dynamic structures than DPIM-S, while the DPIM-S has a significant advantage of obtaining the PDF of performance function.

Application of generalised equivalent extreme-value event in structural system reliability analysis

To alleviate the difficulty of combination explosion, in this work, a generalised equivalent extreme-value event is presented to the problem of multi-component simultaneous failure in system reliability analysis, where m components in total l components are failed simultaneously. Firstly, the generalised equivalent extreme-value event is formulated with rigorous mathematical derivation for single boundary problem. Secondly, based on a mathematical transformation, the generalised equivalent extreme-value event is extended to double boundaries problem. Thirdly, by introducing the point estimation method (PEM) and the principle of maximum entropy to calculate the first four-order statistical moments and the failure probability of the equivalent performance function, an easy-to-implement method is proposed, which is capable of solving the multi-component simultaneous failure problem of static and dynamic systems. Finally, the feasibility of the proposed method is verified through a mathematical example and two engineering examples. The comparison to the Monte Carlo simulation shows that the proposed method is of high precision and high efficiency.

Time-dependent structural system reliability analysis model and its efficiency solution

For the widely existing time-dependent structural system (TDSS), the current model ignores the interaction among multiple modes in the minimum transformation of the performance function of each mode w.r.t. the time, it may misjudge the state of the system at some instants and result in the error of estimating the reliability. To avoid this possible mistake, this paper proposes an improved reliability analysis model for the TDSS. In the proposed model, the TDSS performance function is transformed into the single-mode time-dependent performance function firstly according to the relationship of multiple modes. Then the failure probability of the TDSS can be estimated by the single-mode time-dependent performance function. The relationship of multiple modes is strictly considered in the proposed model. On the basis of the improved model, this paper also presents the Kriging surrogate model combined with the Monte Carlo simulation method to estimate the failure probability of the TDSS. In this Kriging method, the initial training samples are uniformly selected in the sample space and a new extremum learning function is proposed. Theoretical analysis verifies the rationality of the proposed reliability analysis model, and the efficiency of the proposed method is illustrated by the results of numerical examples.

Structural system reliability analysis based on multi-modal optimization and saddlepoint approximation

This paper studies reliability analysis of structures with multiple failure modes. The analysis consists of three parts. First, the memetic animal migration optimization algorithm, applied for multiple optimum points detection in a multimodal optimization problem, is used to search for the most probable points of the limit state functions of main failure modes. Next, the multi-point first-order reliability method is used to estimate the failure probability of structures with multiple failure modes. Last, the saddlepoint approximation based second-order reliability method is further extended to system reliability analysis, aiming to improve the accuracy of system reliability prediction.

Structural System Reliability: Overview of Theories and Applications to Optimization

This paper provides an overview of theories and applications of structural system reliability (SSR). The paper defines SSR problems and discusses the growing needs for SSR analysis and technical challenges. Detailed literature reviews are provided for three subtopics: SSR methods for Boolean system events, SSR methods for sequential failures, and SSR-based design/topology optimization. Discussions of each subtopic define the target problem using mathematical formulations and categorize existing SSR methods in terms of the characteristics of the problems and approaches. The paper summarizes SSR methods that are considered critical in the history and have introduced notable technological developments in recent years. In each subtopic or category, the reviewed methods are compared with each other in terms of accuracy, computational efficiency, and implementation issues to allow identifying apposite methods for SSR applications. The paper concludes with remarks on future research needs and opportunities.

Chatter reliability prediction of side milling aero-engine blisk

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

Seismic reliability analysis of energy-dissipation structures by combining probability density evolution method and explicit time-domain method

Hysteretic dampers such as buckling restrained braces (BRBs) have been widely used for improving the performance of civil structures exposed to seismic hazard. In this study, a hybrid approach, which combines the probability density evolution method (PDEM) and the explicit time-domain method (ETDM), is proposed for system reliability analysis of energy-dissipation structures with hysteretic dampers under seismic excitations. The PDEM can capture the probability density function (PDF) of system limit-state function for a structure by constructing a virtual random process associated with the limit state. The system failure probability of the structure can be directly evaluated through the integration of the PDF of system limit-state function over the failure domain. However, hundreds of deterministic nonlinear time-history analyses corresponding to the selected representative points need to be conducted in the solution procedure of PDEM, leading to high computational cost when applied to large-scale energy-dissipation structures. To enhance the efficiency of PDEM, the ETDM with dimension-reduced iteration scheme is incorporated into PDEM to conduct the required nonlinear time-history analyses with high efficiency, in which only a small number of degrees of freedom associated with the hysteretic dampers are considered in the iteration process. A real engineering building with 32 BRBs is investigated to illustrate the accuracy and efficiency of the proposed method and its feasibility to practical structures.