An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory
An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory
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DOI：
10.1016/j.strusafe.2003.05.002
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发表时间：
2004-07
影响因子：
5.8
通讯作者：
J. Hurtado
中科院分区：
文献类型：
--
作者：
J. Hurtado
极限状态函数的隐式性质阻碍了复杂结构的可靠性分析。对于他们的近似使用已作出的响应面法（RSM），最近，神经网络。从统计学的观点来看，这相当于一种回归方法。然而，在结构可靠性文献中，很少有人注意到将该问题作为一个分类任务来处理的可能性。这就扩大了最终对手头的目的有用的方法的清单，并证明有必要全面审查其显著特点。本文从统计学习理论的角度来完成这项任务，该理论为所有回归，分类和概率密度估计提供了一个统一的框架。分类方法分为三类，它表明，只有一组是有用的结构可靠性，根据一些特定的标准。在这一类别中是多层感知器和支持向量机，它们是推荐的方法，因为（a）它们可以根据一些样本估计函数，（B）它们使用灵活和自适应的模型，（c）它们可以克服维数灾难。本文还从统计学习的角度对响应面模型进行了深入的分析。结果表明，经验发现的不稳定性，这种方法的解释与统计学习的概念。
The reliability analysis of complex structures is hindered by the implicit nature of the limit-state function. For their approximation use has been made of the Response Surface Method (RSM) and, more recently, of Neural Networks. From the statistical viewpoint this corresponds to a regression approach. In the structural reliability literature little attention has been paid, however, to the possibility of treating the problem as a classification task. This enlarges the list of methods that are eventually useful to the purpose at hand and justifies an overall examination of their distinguishing features. This task is performed in this paper from the point of view of the Theory of Statistical Learning, which provides a unified framework for all regression, classification and probability density estimation. The classification methods are grouped into three categories and it is shown that only one group is useful for structural reliability, according to some specific criteria. In this category are the Multi-Layer Perceptrons and the Support Vector Machines, which are the recommended methods because (a) they can estimate the function on the basis of a few samples, (b) they use flexible and adaptive models and (c) they can overcome the curse of dimensionality. The paper also includes an in-depth analysis of the RSM from the point of view of statistical learning. It is shown that the empirically found instability of this method is explained with statistical learning concepts.