观测数据拟合分析中的多重共线性问题

Research on the Multicollinearity Existing in Observation Data Simulation and Analysis

为有效克服在工程安全监测数据及统计数据的拟合与预测研究中,采用最小二乘回归法难以有效识别自变量因子间的多重共线性并消除其对回归模型精度影响的不足,引进偏最小二乘回归(PLSR)方法,对观测数据变量及其影响因子进行拟合与预测分析。将模型拟合预测与非模型式的数据内涵分析有机结合,可同时实现回归建模、数据结构简化以及因子间的多重共线性分析,并通过交叉有效性检验来控制模型精度。结果表明:PLSR方法对系统信息和噪声有良好的辨识能力,能有效克服因子多重共线性对模型精度的影响,使模型结果对实测变量的物理成因解释更趋合理,因而比最小二乘回归方法更具广泛适用性。

In order to overcome deficiencies in the simulation and forecast for engineering safety monitor and statistics data induced by the least-square method which cannot effectively identify the multicollinearity of independent variables and eliminate its effects on model precision, the partial least-squares regression （PLSR） method is advanced to analyze observation data and their influencing variables. The PLSR method is well integrated with non-model-style data connotation analyses, thus the regression modeling, data structure simplifing and the multicollinearity analyzing could be simultaneously carried out, and the model precision is controlled by the method of cross validation test. Model results show that the PLSR method has a wider applicability than the least-square regression method, for the former can satisfactorily identify system information or noise and effectively eliminate the multicollinearity effects on model accuracy of simulation and forecast, which makes the model tend to be more reasonable in physical genesis analyses on observation data.