论文标题
使用聚类,分类和高斯过程建模学习非平稳和不连续的功能
Learning non-stationary and discontinuous functions using clustering, classification and Gaussian process modelling
论文作者
论文摘要
替代模型已证明是解决需要重复评估昂贵计算模型的工程问题的极其有效的帮助。它们是通过稀疏评估昂贵的原始模型而建造的,并提供了一种解决原本棘手的问题的方法。替代建模的关键方面是模型平滑性和规律性近似的假设。但是,这种假设在现实中并不总是满足的。例如,在民用或机械工程中,某些模型可能会呈现不连续性或非平滑度,例如,在不稳定的模式(例如屈曲或弯曲)的情况下。建立一个能够考虑这些根本不同行为或不连续性的单一替代模型并非易事。在本文中,我们提出了一种三阶段方法,用于结合聚类,分类和回归的非平滑函数的近似。这个想法是按照系统的局部行为或制度划分空间,并建立最终组装的本地替代物。使用了一系列知名的机器学习技术:Dirichlet工艺混合模型(DPMM),支持向量机和高斯工艺建模。该方法在两个分析功能和拉伸膜结构的有限元模型上进行了测试和验证。
Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have provided a way to solve otherwise intractable problems. A crucial aspect in surrogate modelling is the assumption of smoothness and regularity of the model to approximate. This assumption is however not always met in reality. For instance in civil or mechanical engineering, some models may present discontinuities or non-smoothness, e.g., in case of instability patterns such as buckling or snap-through. Building a single surrogate model capable of accounting for these fundamentally different behaviors or discontinuities is not an easy task. In this paper, we propose a three-stage approach for the approximation of non-smooth functions which combines clustering, classification and regression. The idea is to split the space following the localized behaviors or regimes of the system and build local surrogates that are eventually assembled. A sequence of well-known machine learning techniques are used: Dirichlet process mixtures models (DPMM), support vector machines and Gaussian process modelling. The approach is tested and validated on two analytical functions and a finite element model of a tensile membrane structure.