Adaptive hyperball Kriging method for efficient reliability analysis

Reliability analysis techniques combining with various surrogate models have attracted increasing attention because of their accuracy and great efficiency. However, they primarily focus on the structures with continuous response, while very rare researches on the reliability analysis for structures with discontinuous response are carried out. Furthermore, existing adaptive reliability analysis methods based on importance sampling (IS) still have some intractable defects when dealing with small failure probability, and there is no related research on reliability analysis for structures involving discontinuous response and small failure probability. Therefore, this paper proposes a novel reliability analysis method called AGPC-IS for such structures, which combines adaptive Gaussian process classification (GPC) and adaptive-kernel-density-estimation-based IS. In AGPC-IS, an efficient adaptive strategy for design of experiments (DoE), taking into consideration the classification uncertainty, the sampling uniformity and the regional classification accuracy improvement, is developed with the purpose of improving the accuracy of Gaussian process classifier. The adaptive kernel density estimation is introduced for constructing the quasi-optimal density function of IS. In addition, a novel and more precise stopping criterion is also developed from the perspective of the stability of failure probability estimation.The efficiency, superiority and practicability of AGPC-IS are verified by three examples

A new unequal-weighted sampling method for efficient reliability analysis

For traditional surrogate model-based methods, the distribution parameters of random variables will change with the enrichment of the data, ultimately leading to the reconstruction of surrogate model and reassessment of reliability, which often results in a wastage of computational resources. In response, an extended Kriging model-based method is proposed in this paper for efficient reliability analysis under parameters change. Different from the standard Kriging model, in addition to random variables, variable distribution parameters are also included in the proposed method to constitute the extended input variables. In this way, the updated Kriging model with prior parameter information can be directly treated as the initial surrogate model for the posterior problem. Consequently, there is no need to reconstruct the surrogate model if the distribution parameters change, and only one Kriging model is required for this method. The efficiency, robustness and accuracy of the proposed method are demonstrated through three examples. This study contributes to dynamic assessment techniques for structural reliability analysis.

Dynamic pruning-based Bayesian support vector regression for reliability analysis

The seismic reliability calculation of complex building structures requires a lot of simulation analysis and therefore the calculation cost is high. Fitting performance function with surrogate model can improve computational efficiency, but how to ensure the calculation accuracy while improving the reliability analysis efficiency of the engineering structure is a problem worthy of study. This paper proposes a Kriging-based reliability analysis method, which establishes the Kriging surrogate model with fewer calculations of the performance function, improves the accuracy of the surrogate model of performance function by infill-sampling, and obtains the approximate failure probability combined with Monte Carlo simulation. Two numerical examples are analyzed; the results show that this method is efficient and accurate. The method is applied to the seismic reliability calculation of mega-sub controlled structural system, in which the randomness of structure and seismic action is considered. The application results show that it is an effective method for reliability analysis of complex building structures.

To improve the efficiency and accuracy of traditional least squares method–based polynomial response surface method (RSM) for reliability analysis of structure, the application of various adaptive metamodeling approaches is notable. The moving least squares method (MLSM)–based RSM is the simplest one and found to be effective in this regard. But, its performance in reliability analysis of structure largely depends on the proper choice of the parameter of weight function involved. In the present study, a generalized scheme to appropriately obtain the hyper-parameter of the MLSM-based RSM to approximate implicit responses of structure for reliability analysis is proposed. The algorithm is hinged on the fact that for reliability analysis, one is interested in the sign of the approximated limit state function (LSF) rather than its magnitude. Thereby, it is sufficient to obtain the hyper-parameter for which the first derivative of the probability of failure as obtained from the approximated LSF with respect to the hyper-parameter is zero. The effectiveness of the proposed algorithm is elucidated through three numerical examples. The improvement achieved by the proposed MLSM-based RSM has been compared with the reliability results obtained by the MLSM-based RSM considering the commonly recommended value of the hyper-parameter and also by the approach where the parameters are obtained by leave one out cross-validation procedure.

Reliability analysis based on a novel density estimation method for structures with correlations

The effect of probability distributions on the slope reliability is highlighted in this study since the lognormal distribution is often used to characterize the variability of soil properties to avoid negative values. A multiple response-surface based MCS method for slope reliability analysis in spatially variable soils is proposed. A heterogeneous slope consisting of three soil layers (including a weak layer) is studied to demonstrate the validity of the proposed method and explore the effect of probability distributions for soil shear strength parameters on the reliability of the heterogeneous slope. The results indicate that the proposed method provides a practical tool for evaluating the reliability of heterogeneous slopes. It can greatly improve the computational efficiency especially when the probability of slope failure is at relatively low levels (pf<10−3). The difference in the probabilities of failure of the heterogeneous slope associated with the lognormal, normal, gamma and beta distributions is significant when the spatial variability of soil properties is incorporated. In general, the probability of failure may be underestimated as the lognormal distribution is used for characterization of the random fields of soil properties.

Reliability is a critical indicator for evaluating the safety and performance of mechanical structures. Surrogate models are widely employed in reliability analysis to reduce computational costs; however, their accuracy strongly depends on the quality of training samples. This paper proposes an uncertainty and distance-driven sequential sampling deep neural network method (UDDS-DNN) for structural reliability analysis. First, initial training samples were generated from the Monte Carlo population (MCP) using the Minimax sampling strategy. This ensured global coverage of the random variable space. Then, the predictive uncertainty of the DNN was quantified using the Jackknife-based method. The estimated uncertainty, inter-sample distance, and probabilistic characteristics of the input random variables were considered. The adaptive learning function was constructed to guide sequential sample enrichment. The proposed method was validated through two numerical examples and three engineering case studies. Results demonstrated that UDDS-DNN achieves high accuracy and computational efficiency in multivariate, nonlinear, and complex structural reliability problems. The method provided an effective solution for reliability analysis of complex structures using DNN-based sequential sampling.

This paper researched on the static and fatigue strength of a 220-ton mining dump truck steering knuckle by the method of reliability analysis, Monte Carlo and response surface. The geometrical model of the steering knuckle was established in CATIA and this model was imported into HyperMesh to obtain the finite element model of steering knuckle. With this finite element model the static strength of the knuckle was checked in the case of uneven road condition in ANSYS in order to acquire the stress nephogram and deformation map. Taking the random influential factors of the reliability into account, the reliability analysis file was compiled by the language of APDL. Then the static and fatigue strength analysis was executed by the method of Monte Carlo and response surface in the PDS module to obtain the statistical results of residual strength and fatigue life, the failure probability and reliability. Finally the quantitative calculation of the failure probability was achieved. In order to realize lightweight design and improve the economy, the knuckle was optimized in ensuring the premise of safety and reliability.

In this work, the reliability analysis is employed to take into account the uncertainties in a structure. Reliability analysis is a tool to compute the probability of failure corresponding to a given failure mode. In this study, one of the most commonly used reliability analysis method namely first order reliability method is used to calculate the probability of failure. Since finding the most probable point (MPP) or design point is a constrained optimization problem, in contrast to all the previous studies based on the penalty function method or the preference of the feasible solutions technique, in this study one of the latest versions of the differential evolution metaheuristic algorithm named improved (μ+λ)-constrained differential evolution (ICDE) based on the multi-objective constraint-handling technique is utilized. The ICDE is very easy to implement because there is no need to the time-consuming task of fine tuning of the penalty parameters. Several test problems are used to verify the accuracy and efficiency of the ICDE. The statistical comparisons revealed that the performance of ICDE is better than or comparable with the other considered methods. Also, it shows acceptable convergence rate in the process of finding the design point. According to the results and easier implementation of ICDE, it can be expected that the proposed method would become a robust alternative to the penalty function based methods for the reliability assessment problems in the future works.

Three-dimensional fatigue crack growth based method for fatigue reliability of metallic materials

A novel fidelity selection strategy-guided multifidelity kriging algorithm for structural reliability analysis

Reliability analysis method based on determination of the performance function’s PDF using the univariate dimension reduction method

Time-dependent structural systems (TDSSs) in engineering involve high dimensionality, nonlinearity, and complex uncertainties, complicating the reliability analysis compared to time-independent assessments. To address these challenges, this paper proposes an extremum-based back propagation neural network (BPNN) method for TDSS reliability analysis. The method adopts a double-loop structure. Specifically, the inner loop finds the minimum of the time-dependent performance function for a given realization of the random variables. This transformation converts the time-dependent problem into an equivalent time-invariant one. Then, the outer loop constructs a BPNN surrogate model to map the relationship between the random variables and the performance function minima. To improve computational efficiency, an adaptive sample selection strategy is integrated into the training process. This technique selects samples near the failure boundary to iteratively update the BPNN, ensuring high accuracy with a small training set. Once the stopping criterion is satisfied, the failure probability is estimated using Monte Carlo simulation (MCS). The trained BPNN model is used to rapidly predict the extremum for the large-scale sample pool. The proposed method is verified through three practical engineering cases: a four-bar mechanism, an aero-engine turbine disc, and a cantilever tube. Results show that the method remains accurate and efficient. The successful applications confirm the rationality and engineering applicability of the proposed model.