# 不确定性量化模块

“不确定性量化模块”可用于理解模型不确定性的影响——研究关注量与模型输入变化的相关性。其中提供的通用接口可用于筛选、灵敏度分析、不确定性传播和可靠性分析。

“不确定性量化模块”可以有效地测试模型假设的有效性，可靠地简化模型，帮助您了解关注量的关键输入，探索关注量的概率分布以及确认设计的可靠性。模型的准确性得到保障以及对关注量的深入理解可以帮助您降低生产、开发和制造成本。

## 灵敏度分析

Sobol 法用于分析整个输入参数分布，并将每个关注量的方差分解为输入参数及其相互作用的贡献之和。

Sobol 法可以计算每个输入参数的 Sobol 指数。一阶 Sobol 指数显示由各个输入参数的方差产生的关注量的方差。总 Sobol 指数显示由每个输入参数的方差及其与其他输入参数的相互作用而产生的关注量的方差。每个关注量和所有参数的 Sobol 指数都显示在专用的 Sobol 图中，其中直方图按总 Sobol 指数排序。关注量对具有最高总 Sobol 指数的输入参数最敏感。输入参数的总 Sobol 指数和一阶 Sobol 指数之间的差异可以衡量该输入与其他输入之间相互作用的效果。

## Inverse Uncertainty Quantification

Inverse uncertainty quantification (inverse UQ) is used when some of the input parameters have unknown probability distributions, known as calibration parameters. Using inverse UQ, experimental data can be propagated backward to gain insight into the statistical properties of these calibration parameters. In order to apply inverse UQ, a prior probability distribution is required for each calibration parameter before the analysis can be conducted.

Experimental data is typically available for the quantities of interest and the parameters used in experiments. There are also calibration input parameters that cannot be directly measured. For instance, consider an experiment where we want to calibrate the Young's modulus of a mechanical part. We should conduct an experiment that measures the tensile stress as a function of the specified material displacement. An inverse UQ study should then be set up to use the experimental data and prior knowledge of the Young's modulus to calibrate the probability distribution that would best reproduce the measured values of the tensile stress from the experiments. Inverse UQ can be applied to a wide range of physics-based models, including those related to structural mechanics, fluid flow, acoustics, heat transfer, electromagnetics, and chemical engineering.

To make the computation of the calibration parameters' posterior probability distributions feasible, a surrogate model is used together with a Markov chain Monte Carlo (MCMC) method. After the computation, the joint and marginal probability distributions of the calibrated input parameters can be visualized. Additionally, a confidence interval table is generated that provides information such as the mean; the standard deviation; the minimum and maximum values; and the lower- and upper-bound values corresponding to confidence levels of 90%, 95%, and 99% for each calibrated input parameter.

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