An Engineering-Statistical Approach to Predictive Modeling and Robust Optimization with Applications to Machining

本研究的目的是开发一个通用的框架，预测建模和鲁棒优化与加工过程中的应用。该方法是使用贝叶斯方法将基于物理的工程模型与基于实验的统计模型相结合。由此产生的模型被称为工程统计模型。机械加工中的工程模型本质上大多是确定性的，并且由于模型假设和未知参数而经常遭受不确定性，而统计模型开发成本高，并且在实验范围之外具有较差的预测能力。该项目的工程统计建模方法克服了这些局限性，因此预计将有更好的表现。该方法将使用两种加工工艺进行开发和验证：激光辅助机械微加工和常规车削。如果成功，该研究将导致一种新的建模方法，可用于更好地预测，控制和优化加工过程。该研究预计将在工业应用中产生巨大影响，因为工业工程师通常没有时间识别工程模型基本假设中的错误，开发新理论并对预测进行修正。该方法可以根据过程数据快速修正工程模型，并可用于预测和优化。此外，该方法可以用于模型的细化，可以精确指出错误可能发生的地方，并帮助研究人员开发更好的理论。该方法具有通用性，适用于成形、连接等其它制造工艺。 由于通过模拟和实验有效利用信息，预计该方法将有助于通过提高产量和减少浪费来降低制造成本。该项目的跨学科性质将导致在制造科学和统计方法的不同群体的学生的严格培训，从而满足制造业的关键需求。

The objective of this research is to develop a general framework for predictive modeling and robust optimization with applications to machining processes. The approach is to use Bayesian methods to integrate physics-based engineering models with experiment-based statistical models. The resulting models are called engineering-statistical models. The engineering models in machining are mostly deterministic in nature and often suffer from uncertainties due to model assumptions and unknown parameters, whereas the statistical models are expensive to develop and have poor predictive capability outside the experimental range. This project's engineering-statistical modeling approach overcomes these limitations and thus is expected to perform better. The approach will be developed and validated using two machining processes: laser assisted mechanical micromachining and conventional turning.If successful, the research will lead to a new modeling approach that can be used for making better prediction, control, and optimization of machining processes. The research is expected to make a great impact in industrial applications, because engineers in industries often do not have the time to identify the mistakes in the underlying assumptions of engineering models, develop new theory, and make corrections to the prediction. The new approach can be quickly applied to correct the engineering model based on the data from their processes and can be used for prediction and optimization. Moreover, the approach can be used for model refinement and can pin-point where the mistake might have happened and help the researchers to develop a better theory. The approach is general and is applicable to other manufacturing processes such as forming and joining. Because of the efficient use of information through simulations and experiments, it is envisaged that the approach will help in cutting down manufacturing costs by improving yield and reducing waste. The interdisciplinary nature of the project will result in rigorous training of a diverse group of students in manufacturing science and statistical methods, and thereby meet a critical need of the manufacturing industry.