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Strongly nonlinear structural systems exhibit high computational errors when dependability is calculated using conventional approaches such as the primary second-order method of moments and the secondary second-order method of moments. The combination of the proxy model and Monte Carlo simulation is an effective method to solve the structural failure probability problem. However, existing studies on the active learning methods of proxy models for reliability calculation mainly focus on the kriging model, while for radial basis interpolation, the existing research results are relatively few. Based on the above analysis, this paper proposes to combine the cross-validation method with multiple kernel functions to evaluate the uncertainty at the prediction points. The mathematical expression of the active learning function considering three factors is proposed: the linear combination of the distance from the surface of limit state and the uncertainty of the predicted value of the proxy model as the optimization objective function, and the distance between the sample to be selected and the initial sample point as the constraint condition. Meanwhile, using the idea of the penalty function, the constrained problem is transformed into the unconstrained problem to get the final active learning function PLF. Finally, the efficiency, accuracy, and robustness of the PRBFM method are verified by classical cases and compared with other methods. It provides a new method and a new idea for the reliability analysis of complex structures. [ABSTRACT FROM AUTHOR]

Structural reliability analysis has an inherent contradiction between efficiency and accuracy. The metamodel can significantly reduce the computational cost of reliability analysis by a simpler approximation. Therefore, it is crucial to build a metamodel, which achieves the minimum simulations and accurate estimation for reliability analysis. Aiming at this, an effective adaptive metamodel based on the combination of radial basis function (RBF) model and Monte Carlo simulation (MCS) is proposed. Different shape parameters are first used to generate the weighted prediction variance, and the search for new training samples is guided by the active learning function that achieves a tradeoff of (1) being close enough to limit state function (LSF) to have a high reliability sensitivity; (2) keeping enough distance between the existing samples to avoid a clustering problem; and (3) being in the sensitive region to ensure the effectiveness of the information obtained. The performance of the proposed method for a nonlinear, non-convex, and high dimensional reliability analysis is validated by three numerical cases. The results indicate the high efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Metamodels in lieu of time-demanding performance functions can accelerate the reliability analysis effectively. In this paper, we propose an efficient collaborative active learning strategy-based augmented radial basis function metamodel (CAL-ARBF), for reliability analysis with implicit and nonlinear performance functions. For generating the suitable samples, a CAL function is first designed to constrain the new samples being generated in sensitivity region, near limit state surface and keep certain distances mutually. Then by adjusting the adjustment coefficient of CAL function, the CAL-ARBF is mathematically modeled and the corresponding reliability analysis theory is developed. The effectiveness of the proposed approach is validated by four numerical samples, including global nonlinear problem, local nonlinear problem, nonlinear oscillator and truss structure. Through comparison of several state-of-the-art methods, the proposed CAL-ARBF is demonstrated to possess the computational advantages in efficiency and accuracy for reliability analysis.

Structural reliability analysis has an inherent contradiction between efficiency and accuracy. The metamodel can significantly reduce the computational cost of reliability analysis by a simpler approximation. Therefore, it is crucial to build a metamodel, which achieves the minimum simulations and accurate estimation for reliability analysis. Aiming at this, an effective adaptive metamodel based on the combination of radial basis function (RBF) model and Monte Carlo simulation (MCS) is proposed. Different shape parameters are first used to generate the weighted prediction variance, and the search for new training samples is guided by the active learning function that achieves a tradeoff of (1) being close enough to limit state function (LSF) to have a high reliability sensitivity; (2) keeping enough distance between the existing samples to avoid a clustering problem; and (3) being in the sensitive region to ensure the effectiveness of the information obtained. The performance of the proposed method for a nonlinear, non-convex, and high dimensional reliability analysis is validated by three numerical cases. The results indicate the high efficiency and accuracy of the proposed method.

Surrogate models combined with Monte Carlo simulation (MCS) are effective ways to address failure probability problems, which involve time-consuming computer codes, in structural reliability analysis. Recently, many active learning functions based on the Kriging model have been developed to conduct adaptive sequential sampling due to its predicted value and variance. However, effective methods for learning functions based on other surrogate models to address failure probability problems remain sparse. Hence, this paper presents a new adaptive sampling function that combines the radial basis function (RBF) approximate model with MCS to calculate the failure probability of structures. The new learning function is named the active RBF method with multiple kernel functions and Monte Carlo simulation (ARBFM-MCS). It uses several RBF kernel functions to estimate the local uncertainty of the predicted values based on interquartile range (IQR) to formulate the active learning function. This method can establish several surrogate models simultaneously for application to different problems. The stopping criterion of this method is that if one of the errors calculated by the various RBF models meets the demand, the learning process stops automatically. Furthermore, the method is also compared with the k-fold cross-validation approach based on a single RBF kernel function and some other approaches presented in the literature. Six numerical examples are considered to verify the accuracy and the efficiency of the proposed method. The results reveal that the multiple kernel function method is effective and has the same accuracy level as other methods. Moreover, for these examples, the method often calls the limit state function in fewer times to obtain accurate failure probabilities. [ABSTRACT FROM AUTHOR]