Structural assessment for collapse is commonly approached by observing the failure or collapse of systems fully incorporating degradation. Challenges however exist in the performance indicator or damage measure due to compound impacts of uncertainties of external (seismic excitation) and internal (structural properties) characteristics with degradation behavior. To account for the impacts of uncertainties, the state-of-the-art kriging nonlinear autoregressive with exogenous (NARX) model is explored in this study to replicate the response of nonlinear single-degree-of-freedom systems. The generalized hysteretic Bouc-Wen model with internal uncertainties is selected to emulate the stiffness and strength degradation. A probabilistic stochastic ground motion model is introduced to represent the external uncertainties. The global terms of NARX model are selected by least-angle regression algorithm and the kriging model is utilized to surrogate uncertain parameters into corresponding NARX model coefficients. The predictions of kriging NARX models are further compared with that of the polynomial chaos nonlinear autoregressive with exogenous input form model as well as Monte Carlo simulation. The comparisons show that kriging NARX model presents an effective and efficient meta-model technique for uncertainty quantification of systems with degradation.

中文翻译：

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具有退化的非线性单自由度系统的不确定性量化的克里金-NARX 建模评估

崩溃的结构评估通常通过观察完全包含退化的系统的故障或崩溃来进行。然而，由于外部（地震激发）和内部（结构特性）特性的不确定性与退化行为的复合影响，性能指标或损坏测量中存在挑战。为了考虑不确定性的影响，本研究探索了最先进的克里金非线性自回归与外生 (NARX) 模型，以复制非线性单自由度系统的响应。选择具有内部不确定性的广义滞后 Bouc-Wen 模型来模拟刚度和强度退化。引入概率随机地震动模型来表示外部不确定性。通过最小角度回归算法选择NARX模型的全局项，并利用克里金模型将不确定参数替代为相应的NARX模型系数。进一步将克里金 NARX 模型的预测与具有外生输入形式的多项式混沌非线性自回归模型以及蒙特卡洛模拟的预测进行了比较。比较表明，克里金 NARX 模型为退化系统的不确定性量化提供了一种有效且高效的元模型技术。进一步将克里金 NARX 模型的预测与具有外生输入形式的多项式混沌非线性自回归模型以及蒙特卡洛模拟的预测进行了比较。比较表明，克里金 NARX 模型为退化系统的不确定性量化提供了一种有效且高效的元模型技术。进一步将克里金 NARX 模型的预测与具有外生输入形式的多项式混沌非线性自回归模型以及蒙特卡洛模拟的预测进行了比较。比较表明，克里金 NARX 模型为退化系统的不确定性量化提供了一种有效且高效的元模型技术。