概率积分法参数辨识的多尺度核偏最小二乘回归方法

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摘要针对传统的偏最小二乘回归(PLS)、人工神经网络(ANN)、支持向量机(SVM)等非线性建模方法在概率积分法参数辨识中存在着预测效果差的不足，提出概率积分法参数辨识的多尺度核偏最小二乘回归(multi-scale KPLS)方法。首先，构建满足容许条件的多尺度高斯核函数；然后，对学习样本进行模糊聚类，以最优分类个数作为多尺度高斯核函数的尺度个数，并采用10次10折交叉验证按照网格搜索方法确定核函数的宽度；最后，详细论述multi-scale KPLS的建模过程。通过实例将multi-scale KPLS的预测结果与3种传统的PLS方法、径向基神经网络(RBF-NN)和SVM模型进行对比分析。结果表明：multi-scale KPLS顾及建模样本的多尺度特性，其预测精度明显高于其他预测模型；multi-scale KPLS有效地克服了各影响因素之间的多重共线性对预测结果的不利影响，具有较强的稳健性；multi-scale KPLS适用于多个因变量对多个自变量的概率积分法参数辨识问题，其建模参数均可自适应确定，在建模效率上优于RBF-NN和SVM。

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关键词 ：采矿工程, 概率积分法, 偏最小二乘回归, 多尺度核, 模糊聚类, 地表移动参数, 开采沉陷

Abstract：Aiming at the prediction shortcomings of the traditional nonlinear modeling methods，including partial least-squares regression(PLS)，artificial neural network(ANN) and support vector machines(SVM) using probability-integral method，a novel method named multi-scale kernel partial least-squares regression(multi-scale KPLS) is proposed to identify parameters of the probability-integral method. Firstly，an admissible multi-scale Gaussian kernel function is constructed. Secondly，fuzzy clustering is applied to determine the optimal number of categories，which is regarded as scale parameter，and then，all kernel widths are optimized by 10 times 10-fold cross-validation and grid search method. Finally，the modeling process was discussed detailedly. Contrasting the prediction results of multi-scale KPLS with other methods of PLS，RBF neural network(RBF-NN) and SVM respectively，it shows that the former?s prediction accuracy is obviously better than the others? because of considering the characteristic of multi-scale in modeling samples；multi-scale KPLS has a stronger robustness and efficiently overcomes the multicollinearity between factors effecting on prediction results disadvantageously；multi-scale KPLS is suitable for parameters identification of probability-integral method with several induced variables versus several independent variables and its parameters could be determined by self-adaptive，so by terms of modeling efficiency，it is better than RBF-NN and SVM.

Key words： mining engineering probability-integral method partial least-square(PLS) multi-scale kernel fuzzy clustering parameters of surface movement mining subsidence

收稿日期: 2010-10-28

引用本文:

王正帅1，2，邓喀中1，2. 概率积分法参数辨识的多尺度核偏最小二乘回归方法[J]. 岩石力学与工程学报, 2011, 30(S2): 3863-3870.
WANG Zhengshuai1，2，DENG Kazhong1，2. PARAMETERS IDENTIFICATION OF PROBABILITY-INTEGRAL METHOD BASED ON MULTI-SCALE KERNEL PARTIAL LEAST-SQUARES REGRESSION METHOD. , 2011, 30(S2): 3863-3870.

链接本文:

http://www.rockmech.org/CN/Y2011/V30/IS2/3863

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