An enhanced classification approach for reliability estimation of structural systems
An enhanced classification approach for reliability estimation of structural systems
复制标题
结构系统可靠性评估的增强分类方法
DOI：
10.1007/s10845-012-0702-1
复制
发表时间：
2012
影响因子：
8.3
通讯作者：
Seung
中科院分区：
文献类型：
--
作者：
Jiten Patel;Seung
在半监督学习方法中，利用大量未标记数据（未知响应数据）对训练数据（标记数据或已知响应数据）进行扩充，可以提高基于分类的代理模型可靠性评估的准确性。在这项研究中，提出了一种增强的概率神经网络（PNN）算法，在每个标记点的高斯不被假定为球形。每个高斯函数都有一个“完整”的协方差矩阵，而不是简单地假设高斯函数有一个“球形”协方差矩阵。首先，期望最大化算法应用于标记和未标记的数据，同时假设“全”高斯的数量等于标记的数据点的数量。这些“完整”高斯分布在特定数据点的贡献是通过使用贝叶斯定理发现的。贝叶斯决策准则，然后使用在PNN的最后输出层的测试模式分类到安全或故障类。所提出的方法的主要好处来自于利用未标记的数据更好地估计构成高斯聚类的基础数据的“完整”协方差矩阵，然后将其用于估计分类的类的概率密度函数。该过程不需要额外的计算成本来提高分类结果的准确性，因为未标记数据的成本通常可以忽略不计。两个例子，包括一个解析问题和桁架问题，以验证所提出的可靠性估计过程。结果反映了相当大的改进的分类器性能估计的可靠性，同时保持足够的准确性。
The accuracy of a classification-based surrogate model for reliability assessment can be improved by augmenting the training data (labeled data or data with known responses) with a large number of unlabeled data (data with unknown responses) in semi-supervised learning methods. In this research, an enhanced Probabilistic Neural Network (PNN) algorithm is proposed where the Gaussians at each labeled point are not assumed to be spherical. Each of the Gaussians has a ‘full’ covariance matrix instead of simply assuming the Gaussian with a ‘spherical’ covariance matrix. First, the Expectation-Maximization algorithm is applied on the labeled and unlabeled data while assuming that the number of ‘full’ Gaussians is equal to the number of labeled datapoints. The contribution of each of these ‘full’ Gaussians at a particular datapoint is found by using the Bayes Theorem. The Bayes decision criterion is then used in the final output layer of the PNN to classify test patterns into either the safe or the failure class. The primary benefit of the proposed method comes from utilizing unlabeled data for better estimation of ‘full’ covariance matrices of constituting Gaussian clusters of underlying data, which are then used to estimate the Probability Density Functions of classes for classification. This procedure does not require additional computational costs to improve the accuracy of the classification results since the cost of unlabeled data is negligible in general. Two examples including an analytic problem and a truss problem are presented in order to validate the proposed reliability estimation process. The results reflect considerable improvements of the classifier performance for estimating reliability while maintaining sufficient accuracy.