递阶偏最小二乘回归在大坝安全监测中的应用

Hierarchical Partial Least-square Regression and Its Application to Dam Safety Monitoring

偏最小二乘回归能有效地消除因子间的多重相关性,但从其算法特点和实际应用来看,也存在不足。例如,在算法方面,偏最小二乘提取的主成分不一定能同时保证方差和相关程度最大;在应用方面,含有较多自变量的偏最小二乘回归模型的可解释性不高。递阶偏最小二乘回归是偏最小二乘回归后续研究的成果之一,在一定程度上克服了上述不足。算例表明,递阶偏最小二乘回归模型较其他回归模型的可解释性强,较为合理。

Partial least-square regression （PLSR） can effectively avoid multicollinearity among variables. However, considering its arithmetic and application characteristics, PLSR also has some demerits. For instance, in the aspect of arithmetic, the principal components that PLSR distilled can not guarantee the maximal square deviation and its related degree, and in the aspect of application, the interpretability of least square regression models including many variables is not high. Hierarchical PLSR （Hi-PLSR） is one of the research results of PLSR, and it can overcome the above-mentioned demerits. The result of case study shows that the models based on Hi-PLSR are reasonable and highly interpretable compared with stepwise regression and PLSR.