An improved response surface method for the determination of failure probability and importance measures

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High-order limit state functions in the response surface method for structural reliability analysis (2008, methodology): “The value of the true limit state function is evaluated at a number of samples of X, to determine the unknown coefficients such that the error of approximation at the samples of X is minimized.”
Second‐order reliability method‐based inverse reliability analysis using Hessian update for accurate and efficient reliability‐based design optimization (2014, background): “When multiple MPPs exist, SORM based on the single MPP might fail to estimate the probability of failure accurately [19–22].”
A sequential surrogate method for reliability analysis based on radial basis function (2017, methodology): “Therefore, the iterative response surface reliability analysis methods are proposed [20-30], which increases the samples in the important region near the MPP, and gradually improves the accuracy of the approximation model.”
Reliability analysis of randomly vibrating structures with parameter uncertainties (2006, methodology): “An alternative procedure of computing gradients, and which has been used in response surface-based reliability analyses [48] [49] [50] [51], is to fit a polynomial for the function whose gradients we seek and subsequently, differentiate the polynomial at the desired location.”