Nowadays, numerical models are widely used in most of engineering fields to simulate the behaviour of complex systems, such as for example power plants or wind turbine in the energy sector. Those models are nevertheless affected by uncertainty of different nature (numerical, epistemic) which can affect the reliability of their predictions. We develop here a new method for quantifying conditional parameter uncertainty within a chain of two numerical models in the context of multiphysics simulation. More precisely, we aim to calibrate the parameters $\theta$ of the second model of the chain conditionally on the value of parameters $\lambda$ of the first model, while assuming the probability distribution of $\lambda$ is known. This conditional calibration is carried out from the available experimental data of the second model. In doing so, we aim to quantify as well as possible the impact of the uncertainty of $\lambda$ on the uncertainty of $\theta$. To perform this conditional calibration, we set out a nonparametric Bayesian formalism to estimate the functional dependence between $\theta$ and $\lambda$, denoted by $\theta(\lambda)$. First, each component of $\theta(\lambda)$ is assumed to be the realization of a Gaussian process prior. Then, if the second model is written as a linear function of $\theta(\lambda)$, the Bayesian machinery allows us to compute analytically the posterior predictive distribution of $\theta(\lambda)$ for any set of realizations $\lambda$. The effectiveness of the proposed method is illustrated on several analytical examples.

翻译：当前，数值模型广泛应用于工程领域（如能源行业的核电站或风力发电机）以模拟复杂系统行为。然而，这些模型受数值不确定性及认知不确定性等多重因素影响，可能降低其预测可靠性。本文针对多物理场仿真场景下两级链式数值模型，提出一种条件参数不确定性的量化新方法。具体而言，我们旨在以第一模型参数λ的概率分布已知为前提，基于第二模型的实验数据，对链中第二模型参数θ进行条件标定。通过此过程，我们力求尽可能精确地量化λ的不确定性对θ不确定性的影响。为实现条件标定，我们构建非参数贝叶斯框架以估计θ与λ之间的函数依赖关系θ(λ)。首先，假设θ(λ)的每个分量均为高斯过程先验的实现；继而，当第二模型可表示为θ(λ)的线性函数时，贝叶斯框架允许我们对任意λ的实现在解析层面计算θ(λ)的后验预测分布。多个解析算例验证了所提方法的有效性。