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Summary Accurate estimation of extreme structural responses is important for ensuring the safe operation of civil infrastructure systems. However, structural response data, such as vessel motions, often provide limited information. Thus, extrapolation becomes essential to predict extreme responses having low-occurrence probabilities. In this study, we investigate a data-driven machine learning approach for accurately predicting extreme responses of a structure using polynomial chaos expansion (PCE). We use PCE to learn the mapping between input-output data pairs for supervised learning. Existing PCE relies on parametric orthogonal polynomial families defined only for specific types of independent random variables. As a result, a nonlinear probabilistic transformation is necessary for random variables beyond these parametric distributions, which can lead to slow convergence of a surrogate model to the truth model. To address the issue, the Gram-Schmidt orthogonalization is used to derive orthogonal polynomial functions for random variables that are not defined in the Askey scheme. This is achieved by solving a linear equation involving the sequence of joint raw moments of the underlying random variables. Subsequently, the coefficients of the basis functions are determined using the least squares method. Numerical examples, including an offshore structural dynamics problem and several analytical equations, are provided to demonstrate the accuracy and efficiency of the proposed method in comparison with brute force Monte Carlo simulations (MCSs). Results indicate that the proposed approach can achieve better efficiency (103 vs. 106 model evaluations) than the traditional method without compromising accuracy.