Usually, within stochastic framework, a testing dataset is used to evaluate the approximation error between a surrogate model (e.g., a polynomial chaos expansion) and the exact model. We propose here another method to estimate the quality of an approximated solution of a stochastic process, within the context of structural dynamics. We demonstrate that the approximation error is governed by an equation based on the residue of the approximate solution. This problem can be solved numerically using an approximated solution, here a coarse Monte Carlo simulation. The developed estimate is compared to a reference solution on a simple case. The study of this comparison makes it possible to validate the efficiency of the proposed method. This validation has been observed using different sets of simulations. To illustrate the applicability of the proposed approach to a more challenging problem, we also present a problem with a large number of random parameters. This illustration shows the interest of the method compared to classical estimates.

中文翻译：

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瞬态结构动力学中多项式混沌近似的误差估计

通常，在随机框架内，测试数据集用于评估代理模型（例如，多项式混沌扩展）与精确模型之间的近似误差。我们在这里提出了另一种方法来估计随机过程的近似解的质量，在结构动力学的背景下。我们证明了近似误差由基于近似解的残差的方程控制。这个问题可以使用近似解在数值上解决，这里是粗略的蒙特卡罗模拟。将开发的估计与简单案例的参考解决方案进行比较。这种比较的研究使得验证所提出方法的效率成为可能。已使用不同的模拟集观察到此验证。为了说明所提出的方法对更具挑战性的问题的适用性，我们还提出了一个具有大量随机参数的问题。该图显示了该方法与经典估计相比的兴趣。