AI 中文总结
研究针对非侵入式降阶模拟器在认证级应用中需严格误差评估的问题，提出基于POD - GPR的验证框架，制定误差预算并评估。该框架应用于碳 - 碳飞机刹车盘，实现代理到代码保真度，还给出两项次要贡献。
AI 中文摘要
虽然非侵入式降阶模拟器成功替代了昂贵的有限元模拟，但认证级应用需要相对于求解器自身离散化不确定性进行严格的误差评估。本文介绍了一个验证框架，该框架直接针对数值不确定性下限评估预测准确性。我们在碳 - 碳飞机刹车盘的拒绝起飞场景中进行了演示，预测峰值温度和峰值冯·米塞斯应力场。模拟器基于60914个节点的固定网格运行，依赖于由5个输入参数化的管道耦合本征正交分解（POD）和高斯过程回归（GPR）。我们制定了代数精确的后验误差预算，将模拟器的符号误差在极值处分离为不同的截断和回归分量。然后根据通过对感兴趣的峰值量进行网格收敛研究建立的离散化下限来评估此误差。在一个完全独立的测试集上，我们的模拟器在两个场的自身离散化不确定性范围内与高保真求解器的峰值匹配，这一基准我们定义为代理到代码保真度。值得注意的是，残余误差主要源于线性降阶限制而非回归不准确。除了主要框架，我们还提出了两个次要贡献：热和机械峰值的并发非侵入式预测，以及这些极值的空间区域定位的概率方法。该方法适用于参数化有限元模拟的非侵入式降阶模型，只要能获得感兴趣量的离散化误差估计。
英文摘要
While non-intrusive reduced-order emulators successfully substitute for costly finite-element simulations, certification-grade applications demand a rigorous error assessment relative to the solver's own discretization uncertainty. This work introduces a verification framework designed to evaluate prediction accuracy directly against this numerical uncertainty floor, rather than physical observation. We demonstrate this approach on a carbon-carbon aircraft brake disc during a rejected take-off scenario, predicting peak temperature and peak von Mises stress fields. Operating over a fixed mesh of 60914 nodes, the emulator relies on a pipeline coupling proper orthogonal decomposition (POD) and Gaussian process regression (GPR) parameterized by 5 inputs. We formulate an algebraically exact, a posteriori error budget that isolates the emulator's signed error into distinct truncation and regression components at the extremum. This error is then evaluated against a discretization floor established via mesh-convergence studies on the peak quantities of interest. On a completely independent test set, our emulator matches the high-fidelity solver's peak values within its own discretization uncertainty for both fields, a benchmark we define as surrogate-to-code fidelity. Notably, the residual error stems primarily from linear reduction limits rather than regression inaccuracies. Beyond the main framework, we present two secondary contributions: the concurrent, non-intrusive prediction of the thermal and mechanical peaks, and a probabilistic approach to spatial zone localization for these extrema. This methodology applies to non-intrusive reduced-order models of parameterized finite-element simulations wherever a discretization-error estimate for the quantity of interest can be obtained.
Comments32 pages, 8 figures, 11 appendix figures
