Structural Reliability Analysis Method 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.

An Adaptive Kriging-Based Fourth-Moment Reliability Analysis Method for Engineering Structures

The fourth-moment method can accurately perform a reliability analysis when it is challenging to determine the distribution of the random variable due to limited available samples. This method only utilizes the first four moments of the random variable and constructs the fourth-moment reliability index. However, it cannot be applied in engineering cases where the state function cannot be expressed explicitly, as it becomes difficult to establish a correlation between the first four moments of the random variable and the state function. Simplifying the state function forcefully may result in significant reliability prediction errors. To address this limitation, this study proposes an adaptive Kriging-based fourth-moment method for reliability analysis under complex state equations. The proposed method demonstrates better applicability and efficiency compared to existing methods. Several numerical examples are provided to validate the effectiveness and accuracy of the proposed method.

Meta-model based sequential importance sampling method for structural reliability analysis under high dimensional small failure probability

Reliability analysis poses a significant challenge for complex structures with stringent reliability requirements. While Sequential Importance Sampling (SIS) and Subset Simulation (SUS) have proven highly effective in addressing high-dimensional problems with small failure probabilities, the computational burden of mechanical simulations remains substantial due to the time-consuming nature of numerical simulation processes. Consequently, this paper introduces a novel approach, denoted as AK-SIS, which combines SIS with Kriging metamodeling specifically designed to address computational challenges associated with small failure probabilities. The fundamental principle of this approach involves utilizing AK-MCS technology (Echard et al., 2011) [1] as a precursor to the SIS approach to initially generate metamodels. These metamodels are then employed in lieu of performance functions in subsequent steps, significantly reducing the number of function calls required to simulate complex engineering problems when applying SIS techniques directly. By inheriting the advantages of SIS, AK-SIS has demonstrated its suitability for reliability analysis in scenarios involving high-dimensional spaces and small fault probabilities. Furthermore, AK-SIS is not limited by the shape of the failure domain, eliminates the need to solve the design point, and is particularly well-suited for analyzing reliability in cases of discontinuous failure domains, multiple failure domains, as well as complex failure domains and rare events. The efficacy of AK-SIS is substantiated through rigorous evaluation encompassing nonlinear, high-dimensional examples, and an engineering application. These empirical validations collectively contribute to a robust methodological framework for reliability analysis of intricate structures characterized by stringent reliability requirements.

A mixed uncertain structural reliability analysis method considering random and convex set variables with correlation

AbstractIn this paper, a mixed model reliability analysis method is put forward for the problem of assessing the reliability of complex engineering structures containing both random and convex aggregate variables. By integrating the ellipsoidal model with correlation and the interval model, the uncertainty region characterized by the ellipsoidal model with correlation is optimized with full consideration of the limited amount of engineering structure sample data, and the risk region represented by the reliability model is redefined, a new mixed reliability assessment criterion is established, and the minimum safe nonprobability reliability index of the structure is built. A key reference is offered by the safety limit diagram of constant reliability indexes set for the first time for the optimal design of engineering structure reliability. The proposed mixed reliability model is compared and analyzed with three classical models. The sensitivity of nonprobability reliability indexes, influenced by random variable parameters and correlation coefficients, is analyzed. This verification confirms that the new reliability model not only provides an accurate assessment of engineering structures' reliability but also lowers the computational demands of engineering design. In this paper, aero‐engine blades and wind turbine blades are taken as examples to expound the validity of the reliability model built using this method and its importance to the structural safety analysis of actual engineering.

A Structural Reliability Analysis Method Considering Multiple Correlation Features

The paper analyzes the correlation features between stress strength, multiple failure mechanisms, and multiple components. It investigates the effects of different correlation features on reliability and proposes a method for structural reliability analysis that considers the joint effects of multiple correlation features. To portray the stress–strength correlation structure, the Copula function is utilized and the influence of the correlation degree parameter on reliability is clarified. The text describes the introduction of time-varying characteristics of structural strength and correlation parameters. A time-varying Copula is then constructed to calculate the structural reliability under the stress–strength correlation characteristics. Additionally, a time-varying hybrid Copula is constructed to characterize the intricate and correlation features of multiple failure mechanisms and components. The article proposes the variational adaptive sparrow search algorithm (VASSA) to obtain optimal parameters for the time-varying hybrid Copula. The effectiveness and accuracy of the proposed method are verified through actual cases. The results indicate that multiple correlation features significantly influence structural reliability. Incorporating multiple correlation features into the solution of structural reliability yields safer results that align with engineering practice.

Bayesian active learning line sampling with log-normal process for rare-event probability estimation

Line sampling (LS) stands as a powerful stochastic simulation method for structural reliability analysis, especially for assessing small failure probabilities. To further improve the performance of traditional LS, a Bayesian active learning idea has recently been pursued. This work presents another Bayesian active learning alternative, called ‘Bayesian active learning line sampling with log-normal process’ (BAL-LS-LP), to traditional LS. In this method, we assign an LP prior instead of a Gaussian process prior over the distance function so as to account for its non-negativity constraint. Besides, the approximation error between the logarithmic approximate distance function and the logarithmic true distance function is assumed to follow a zero-mean normal distribution. The approximate posterior mean and variance of the failure probability are derived accordingly. Based on the posterior statistics of the failure probability, a learning function and a stopping criterion are developed to enable Bayesian active learning. In the numerical implementation of the proposed BAL-LS-LP method, the important direction can be updated on the fly without re-evaluating the distance function. Four numerical examples are studied to demonstrate the proposed method. Numerical results show that the proposed method can estimate extremely small failure probabilities with desired efficiency and accuracy.

Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy

Efficient structural reliability analysis method is crucial to solving reliability analysis of complex structural problems. High-computational cost and low-failure probability problems greatly limit the efficiency in structural reliability analysis problems, causing the safety and reliability of the structure to be questioned. In this work, a highly efficient structural reliability analysis method coupling active Kriging algorithm with conjugate first order reliability method (AK-CFORM) is proposed. Specifically, the resample strategy is considered to reduce the number of samples evaluated in each active learning process; the uniform sampling is used to better balance global and local optimal problems; the conjugate map is used to improve the robustness of analytical first order reliability method; and the approximate numerical differential formula is proposed to solve the problems of non-convergence when solving the gradient of the Kriging surrogate model. Finally, three numerical cases and four engineering cases are used to illustrate the effectiveness and robustness of the proposed method. The results show that the proposed AK-CFORM has greater advantages in the number of calling system response and surrogate model with robust and accurate performance.

Importance sampling enhanced by adaptive two-stage Kriging model and active subspace for analyzing rare probability with high dimensional input vector

For the high dimensional and small failure probability events widely existing in engineering, structural reliability analysis method still faces challenges at present. Since active subspace (AS) method can effectively reduce the dimension of input vector space, and metamodel-based importance sampling (IS) can efficiently estimate small failure probability, this paper combines AS with IS to propose an adaptive two-stage Kriging model method (AS-IS-AK2) for rare failure event with high dimensional problem. The proposed AS-IS-AK2 includes two stages. In the first stage, a new learning function is proposed to construct the Kriging model for roughly estimating the performance function values of all IS samples, and the gradient information is provided as a by-product for AS. In the second stage, an adaptive Kriging method is constructed in the reduced dimension space to accurately judge the states of all IS samples. Since AS reduces the dimension of input vector space, and IS reduces the required size of candidate sample pool for obtaining the convergent failure probability estimation, the computational complexity is reduced in reconstructing the Kriging model to judge the states of IS samples. The results of three examples verify the advantage of the proposed method for high dimensional problem with small failure probability.

Three-dimensional creep calculation model for reliability analysis of concrete-filled steel tubular (CFST) structure

For long-span concrete-filled steel tube (CFST) structure, it is essential to implement efficient and realistic prediction models for the long-term processes of core concrete creep. In order to systematically study the main influential factors in CFST structure creep effects, a probabilistic analysis can be performed. The objective of this paper is to analyse the long-term response of CFST structure by using time-dependent reliability method. To address the problem of creep calculation, a novel and comprehensive presentation was developed. By converting the integral-type creep law to a differential-type form with internal variables, based on the Kelvin chain model, an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains was established. We have compiled a three-dimensional (3-D) finite-element analysis programme that considers the creep Poisson effect of core concrete to analyse the long-term performance of the CFST structure. This is achieved by developing a commercial finite element code, such as Usermat in ANSYS. As calculation examples, several time-dependent analyses of a CFST stub column and long-span CFST arch bridge were performed. The calculated results of long-term behaviour agree well with experimental and measured data. Considering the randomness of various input parameters, such as physical dimensions and materials of the CFST structure, we have analysed the uncertainty using the Latin-hypercube-sampling (LHS) stochastic finite-element method. The results of creep sensitivity analysis revealed that coefficient of creep model uncertainty, steel and concrete elastic modulus were the three most influential parameters for CFST stub columns’ creep, and load, coefficient of creep model uncertainty, relative humidity, steel and concrete elastic modulus were the five for CFST arch bridges’ long-term deflection. In addition, the use of Monte Carlo (MC) and response surface (RS) methods for structural stochastic reliability analysis demonstrates the ability of these approaches to assess the reliability index of long-span CFST arch bridges. This provides a valuable reference for the design and performance evaluation of CFST structures.

A Novel Adaptive Bayesian Model Averaging-Based Multiple Kriging Method for Structural Reliability Analysis

A Novel Adaptive Bayesian Model Averaging-Based Multiple Kriging Method for Structural Reliability Analysis

An efficient and versatile Kriging-based active learning method for structural reliability analysis

An efficient and versatile Kriging-based active learning method for structural reliability analysis

P-AK-MCS: Parallel AK-MCS method for structural reliability analysis

In recent years, the active learning reliability method that combines the Kriging model and Monte Carlo simulation (AK-MCS) has emerged as a promising approach due to its computational efficiency and accuracy. However, the commonly used learning functions, such as the expected feasibility function (EFF), U function, H function, and expected risk function (ERF), can only select one training point at each iteration which is time-wasteful when parallel computing is available. Therefore, this paper proposes a parallel active learning Kriging strategy, namely P-AK-MCS, for structural reliability analysis. By introducing an influence function that reflects the impact of the added point on the original learning function, four parallel learning functions are constructed: pseudo-U (PU) function, pseudo-EFF (PEFF), pseudo-H (PH) function, and pseudo-ERF (PERF). These functions aim to identify multiple training points at each iteration without requiring additional functional evaluations. The effectiveness of the proposed method is validated using four examples. The results demonstrate that compared to the standard AK-MCS, the proposed P-AK-MCS significantly reduces the number of computation loops and greatly decreases computational costs. Moreover, the total number of functional evaluations required is similar to that of the standard AK-MCS and remains insensitive to the number of multiple training points.

Reliability assessment of carbon/epoxy micro-fiber subject to compressive stress

PurposeThis study addresses the reliability of a composite fiber (carbon fibers/epoxy matrix) at microscopic level, with a specific focus on its behavior under compressive stresses. The primary goal is to investigate the factors that influence the reliability of the composite, specifically considering the effects of initial fiber deformation and fiber volume fraction.Design/methodology/approachThe analysis involves a multi-step approach. Initially, micromechanics theory is employed to derive limit state equations that define the stress levels at which the fiber remains within an acceptable range of deformation. To assess the composite's structural reliability, a dedicated code is developed using the Monte Carlo method, incorporating random variables.FindingsResults highlight the significance of initial fiber deformation and volume fraction on the composite's reliability. They indicate that the level of initial deformation of the fibers plays a crucial role in determining the composite reliability. A fiber with 0.5% initial deformation exhibits the ability to endure up to 28% additional stress compared to a fiber with 1% initial deformation. Conversely, a higher fiber volume fraction contributes positively to the composite's reliability. A composite with 60% fiber content and 0.5% initial deformation can support up to 40% additional stress compared to a composite containing 40% fibers with the same deformation.Originality/valueThe study's originality lies in its comprehensive exploration of the factors affecting the reliability of carbon fiber-epoxy matrix composites under compressive stresses. The integration of micromechanics theory and the Monte Carlo method for structural reliability analysis contributes to a thorough understanding of the composite's behavior. The findings shed light on the critical roles played by initial fiber deformation and fiber volume fraction in determining the overall reliability of the composite. Additionally, the study underscores the importance of careful fiber placement during the manufacturing process and emphasizes the role of volume fraction in ensuring the final product's reliability.

Statistical evaluation of tubular joint SCFs from test data and finite element analyses

Stress concentration factors (SCF) derived from both FEA and measurements from laboratory experiments are associated with uncertainties. To understand these uncertainties, SCF values can be determined from a series of tests or possibly also several SCF-values estimated from converged finite element analysis. The challenge is to determine a recommended value for the SCF based on these tests or analysis, ensuring that the resulting SCF along with the SN-curve meets the code required 2.3% exceedance probability. In this paper, structural reliability analysis (SRA) methods are employed to model the combined uncertainty of the parameters representing the SN-curve and the measured SCFs from experimental test joints. Based on this analysis, the SCF that, when paired with the design SN-curve, provides the minimum fatigue life is established. From this analysis, a method to provide characteristic values of the SCF is suggested. Finally, FEA of the same detail, with and without modelling the weld, using both first and second-order elements are performed. From these analyses the SCF is estimated using linear extrapolation and direct extraction. Based on these findings and their comparison to the characteristic SCF, a suggested method to extract SCFs from FEA is provided.

Human and organizational factors influencing structural safety: A review

A broad review of the existing literature concerning Human and Organizational Factors (HOFs) and human errors influencing structural safety is presented in this study. Publications on this research topic were collected from the Scopus database. Two research focal points of this topic, namely modelling and evaluating the human error effects on structural reliability, and identifying causal factors for structural defects and failures, have been recognized and discussed with an in-depth literature review. The review of studies with a model focus summarizes the models and methods that have been developed to evaluate structural reliability considering human error effects. Besides, the review of publications on the factor subject outlines the most acknowledged HOFs that influence structural safety. Moreover, an additional spotlight was given to the studies from the offshore industry for the advanced development in HOFs and contributing the first complete Human Reliability Analysis (HRA) method for structural reliability analysis. In conclusion, this study provides a holistic overview of the knowledge developed in existing research on the topic of HOFs and human error influencing structural safety. Furthermore, current developments and challenges are reflected, and future research directions are explored for academics entering and working in this field. Additionally, the insights into HOFs generated from this review can assist engineers with better hazard identification and quality assurance in practice.

SS-MASVM: An advanced technique for assessing failure probability of high-dimensional complex systems using the multi-class adaptive support vector machine

The integrity of structures in contemporary engineering practices is heavily influenced by inherent uncertainties, which necessitates the development of reliable structural reliability analysis methods for uncertainty quantification and probabilistic analysis. This paper investigates the integration of surrogate models and subset simulation (SS) to accurately compute the failure probabilities of high-dimensional complex systems. Focus is placed on enhancing the computational efficiency and accuracy through using the multi-class adaptive support vector machine (MASVM). The proposed SS-MASVM method incorporates more efficient learning functions, integrates K-means clustering, and employs SS technology for precise estimation of failure probabilities of high-dimensional complex systems. Numerical and engineering structural examples validate the effectiveness of the proposed method and highlight its potential in practical reliability analysis, and the results disclose that the SS-MASVM is efficient and accurate for assessing the complex system reliability.

RBIK-SS: A parallel adaptive structural reliability analysis method for rare failure events

RBIK-SS: A parallel adaptive structural reliability analysis method for rare failure events

Fast convergence strategy for adaptive structural reliability analysis based on kriging believer criterion and importance sampling

The kriging-based adaptive structural reliability analysis method has become widely used, and various learning functions have been proposed. In this study, a fast convergence strategy (FCS) for adaptive structural reliability analysis is proposed based on the Kriging Believer criterion and importance sampling. FCS considers the improvement in the accuracy of the failure probability estimation instead of overemphasizing the approximation accuracy of the limit state function. Contribution of samples to the accuracy of failure probability estimation is quantified based on the Kriging Believer criterion. FCS can implement sequence and parallel additions. The optimal importance sampling function is constructed to further improve the efficiency of the FCS. Several examples are used to demonstrate that FCS can efficiently and accurately handle complex limit state function and the engineering problem of implicit functions.

Aerospace structural reliability analysis method based on regular vine copula model with the asymmetric tail correlation

Considering the asymmetric tail correlations between variables in reliability analysis, an effective aerospace structural reliability analysis method based on regular vine copula models is proposed. Firstly, a product of multiple pair-copula functions and marginal density functions based on regular vine copula models are used to construct the joint probability density function. Secondly, the asymmetric copula functions are introduced into the candidate construction sets of pair-copula functions for capturing asymmetric tail correlations between variables. Meanwhile, the akaike information criterion (AIC) is adopted to select the optimal pair-copula functions. Thirdly, taking the difference of multi-dimensional correlations into account, six different regular vine copula models are used to construct the multivariate joint probability density function. And the corresponding regular vine copula-first order reliability method (RVC-FORM) considering the asymmetric tail correlation is proposed. Finally, three numerical examples and an aerospace turbine blade example are investigated to demonstrate the validity of the proposed method.

Reliability assessment of civil structures with incomplete probability distribution information

The probability distribution of random variables is usually incomplete owing to a limited amount of data, making it a challenging problem for structural reliability assessments. This paper presents a novel reliability analysis method for civil structures with incomplete data. The probability distributions of the random variables were estimated using an improved Bayesian inference method. In the proposed inference method, the frequencies and mode shapes were selected as the observation data. The likelihood function is replaced by homogeneous chaos, and the computational efficiency of Bayesian inference is improved. The affine invariant ensemble algorithm was used to generate samplers for the posterior distribution. After estimating the probability distribution of the incomplete random variables, a reliability analysis was performed, and the failure probability of the structure was estimated. Numerical studies on a two-span, two-story reinforced concrete building and a five-span bridge are presented. Experimental studies were also performed on an eight-story steel frame structure. The results show that the probability distributions of random variables can be significantly updated using the proposed technique and modal properties. The proposed technique was more efficient than the Gibbs sampling method. The failure probabilities of the structures were estimated using the estimated probability distributions.