标题： 非线性动力学中的不确定性量化代理模型 显示英文标题

标题： Surrogate modeling for uncertainty quantification in nonlinear dynamics

摘要： 预测工程中复杂系统的行为通常涉及对运行条件的显著不确定性，例如外部载荷、环境影响和制造变异。 因此，不确定性量化（UQ）已成为基于模型的工程中的关键工具，提供识别、表征和通过计算模型传播不确定性的方法。 然而，UQ的随机性质通常需要对这些模型进行大量评估，这可能计算成本高昂并限制可行分析的范围。 为了解决这个问题，代理模型，即在有限的一组模拟上训练的高效函数近似，已成为现代UQ实践的核心。 本章书籍介绍了用于UQ的代理建模技术的简明综述，重点在于捕捉动态系统完整时变响应这一特别具有挑战性的任务。 它根据输入激励的复杂性对时变问题进行了分类，并讨论了相应的代理方法，包括主成分分析与多项式混沌展开的组合、时间扭曲技术以及带有外生输入的非线性自回归模型（NARX模型）。 每种方法都通过简单的应用实例进行说明，以阐明基本思想和实际应用。 显示英文摘要

摘要： Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty quantification (UQ) has become a critical tool in modeling-based engineering, providing methods to identify, characterize, and propagate uncertainty through computational models. However, the stochastic nature of UQ typically requires numerous evaluations of these models, which can be computationally expensive and limit the scope of feasible analyses. To address this, surrogate models, i.e., efficient functional approximations trained on a limited set of simulations, have become central in modern UQ practice. This book chapter presents a concise review of surrogate modeling techniques for UQ, with a focus on the particularly challenging task of capturing the full time-dependent response of dynamical systems. It introduces a classification of time-dependent problems based on the complexity of input excitation and discusses corresponding surrogate approaches, including combinations of principal component analysis with polynomial chaos expansions, time warping techniques, and nonlinear autoregressive models with exogenous inputs (NARX models). Each method is illustrated with simple application examples to clarify the underlying ideas and practical use.