基于支持向量机的可靠性分析自适应学习

Nick Pepper, Luís Crespo, F. Montomoli
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引用次数: 16

摘要

提出了一种新的自适应学习算法,用于分割一个域的两个区域的未知函数。在可靠性分析的上下文中,这两个区域代表故障域,其中违反了一组约束或要求,以及满足这些约束或要求的安全域。极限状态函数(LSF)将这两个区域分开。评估给定参数点的约束条件需要评估计算模型,这很可能是昂贵的。出于这个原因,我们希望构建一个元模型,它可以使用有限数量的训练数据尽可能准确地估计LSF。这项工作提出了一种自适应策略,采用支持向量机(SVM)作为元模型来提供LSF的半代数近似。我们描述了一个优化过程,用于在每次迭代中选择信息参数点添加到训练数据中,以提高该近似的准确性。引入了一种限定元模型预测的公式;通过这种方式,我们试图将高斯过程模型(gpm)的这一方面纳入支持向量机元模型。最后,我们将我们的算法应用于两个基准测试用例,展示了与使用gpm的可靠性分析的标准技术相媲美(如果不是更好的话)的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Adaptive learning for reliability analysis using Support Vector Machines
A novel algorithm is presented for adaptive learning of an unknown function that separates two regions of a domain. In the context of reliability analysis these two regions represent the failure domain, where a set of constraints or requirements are violated, and a safe domain where they are satisfied. The Limit State Function (LSF) separates these two regions. Evaluating the constraints for a given parameter point requires the evaluation of a computational model that may well be expensive. For this reason we wish to construct a meta-model that can estimate the LSF as accurately as possible, using only a limited amount of training data. This work presents an adaptive strategy employing a Support Vector Machine (SVM) as a meta-model to provide a semi-algebraic approximation of the LSF. We describe an optimization process that is used to select informative parameter points to add to training data at each iteration to improve the accuracy of this approximation. A formulation is introduced for bounding the predictions of the meta-model; in this way we seek to incorporate this aspect of Gaussian Process Models (GPMs) within a SVM meta-model. Finally, we apply our algorithm to two benchmark test cases, demonstrating performance that is comparable with, if not superior, to a standard technique for reliability analysis that employs GPMs.
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