Engineering-Driven Statistical Adjustment and Calibration

Engineering model development involves several simplifying assumptions for the purpose of mathematical tractability, which are often not realistic in practice. This leads to discrepancies in the model predictions. A commonly used statistical approach to overcome this problem is to build a statistical model for the discrepancies between the engineering model and observed data. In contrast, an engineering approach would be to find the causes of discrepancy and fix the engineering model using first principles. However, the engineering approach is time consuming, whereas the statistical approach is fast. The drawback of the statistical approach is that it treats the engineering model as a black box and therefore, the statistically adjusted models lack physical interpretability. This article proposes a new framework for model calibration and statistical adjustment. It tries to open up the black box using simple main effects analysis and graphical plots and introduces statistical models inside the engineering model. This approach leads to simpler adjustment models that are physically more interpretable. The approach is illustrated using a model for predicting the cutting forces in a laser-assisted mechanical micro-machining process. This article has supplementary material online.工程模型开发为实现数学可处理性，通常会引入若干简化假设，而这些假设在实际场景中往往并不贴合真实情况，由此会导致模型预测结果出现偏差。针对该问题，学界常用的统计学解决方案是针对工程模型与观测数据间的偏差构建统计校正模型。与之相对，工程学路径则会通过探究偏差产生的根源，基于第一性原理对原有工程模型进行修正。不过工程学修正路径耗时冗长，而统计学校正路径则更为高效。但统计学方法的弊端在于，其将工程模型视为黑箱进行处理，因此经统计校正后的模型往往缺乏物理可解释性。本文提出了一种全新的模型校准与统计校正框架，该框架通过简单主效应分析与可视化绘图拆解黑箱，并在工程模型内部引入统计模型。该方法可得到结构更简洁、物理可解释性更强的校正模型。文中以激光辅助机械微加工过程的切削力预测模型为例，对所提方法进行了演示验证。本文附带在线补充材料。