HALK: A hybrid active-learning Kriging approach and its applications for structural reliability analysis

Structural reliability analysis based on improved wolf pack algorithm AK-SS

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

PurposeBecause of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).Design/methodology/approachIn DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.FindingsThe computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.Originality/valueThis paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

In modern engineering, physical processes are modelled using advanced computer simulation tools (e.g. finite element models) to assess and optimize their performance. Moreover, awareness is growing on concepts like structural reliability and robust design, hence making the efficient quantification and propagation of uncertainties a key challenge. A major part of those analyses is the characterization of uncertainty in the input, which is typically done with probabilistic variables. In the case of sparse data sets, however, probability theory is often not the optimal choice. Imprecise probabilities provide a more general framework accounting for both aleatory and epistemic uncertainties. The uncertainty propagation of imprecise probabilities leads to imprecise responses. In this context, an algorithm for solving imprecise structural reliability problems is presented. The algorithm transforms the imprecise problem into two precise structural reliability problems, which opens up possibilities for using traditional structural reliability analyses techniques. An adaptive experimental design algorithm based on Polynomial-Chaos-Kriging is used to efficiently estimate imprecise failure probabilities. The capabilities of the framework are illustrated through an application using an analytical function and a realistic engineering problem setting.

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.

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

Surrogate SDOF models for probabilistic performance assessment of multistory buildings: Methodology and application for steel special moment frames

Efficient framework for structural reliability analysis based on adaptive ensemble learning paired with subset simulation

Highly efficient Bayesian updating using metamodels: An adaptive Kriging-based approach

Bayesian inference with Subset Simulation: Strategies and improvements

The constitutive equation and carrying capacity of structure will change over time under high temperature conditions. The traditional structural reliability models are inefficient to solve these time-varying structural reliability problems. A time-varying response surface method with thermal response and response threshold value changing over time was proposed. The method can be used for high-temperature structural reliability analysis. Combined with Box-Behnken experimental design,a cross quadratic function of structure's basic variables and time was introduced for establishing a time-varying model of the thermal structural response. The function of structural response threshold value and time was established by using temperature as intermediate variable. The time-varying structural reliability calculation method was proposed when basic variables are normally distributed. A study case was given to demonstrate the applicability of this method and its greatly enhanced effectiveness besides accuracy.

Physics guided wavelet convolutional neural network for wind-induced vibration modeling with application to structural dynamic reliability analysis

Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multiple failure modes, and this strategy can avoid identifying the minimum mode or the maximum mode by the initial and the in-process Kriging meta-models and eliminate the corresponding inaccuracy propagating to the final result. By analyzing three case studies, the effectiveness and the accuracy of the proposed refined U learning function are verified.

The purpose of this research is to prove the eventuality of using a novel adaptive surrogate model for optimization problems. The adaptive surrogate model is based on iteration sampling and extended radial basis function (ERBF). This method improves the precision by a means that new sample points is placed in the blank area and all the sample points is uniformly distributed in the design region. The precision of the surrogate model is checked using standard error measure to determine whether updating the surrogate model or not. Since the prediction of modal frequencies require structure modal simulations. In order to decrease the number of computer simulations, a Multi-Island GA approach is combined with the adaptive surrogate model to find the optimum modal frequencies of a strapdown inertial navigation system for electric helicopters. The strapdown inertial navigation system is comprised of damping material, counterweight material and inertial navigation sensor. This is a multi-objective functions optimization problem since the modal frequencies are considered from mode 1 to mode 6 in this paper. Several weights of multi-objective functions are utilized to research the modal frequencies. The whole number of 15 sampling points is picked to build the primary surrogate model using Latin hypercube sampling (LHS). The results of adaptive surrogate model show that two new sampling points are needed to reform the precision of the surrogate model under the condition of 2 % confidence bounds. The structure modal optimization results show that the choice of the weights for the multi-objective functions has a major effect on the final optimum modal frequencies. Time- and frequency-domain analysis indicated that the optimum modal frequencies are far away from the excitation frequencies to avoid strapdown inertial navigation system resonance as far as possible.

Efficient response surface method for high-dimensional structural reliability analysis