线性回归模型精化方法

Linear regressive model improved by neural network

为了解决由试验观测数据建立的回归拟合模型存在的模型误差,用基于回归残差的神经网络方法精化模型.采用给定方程获得模拟数据,通过数据结构散点图建立回归模型趋势项,利用经典最小二乘法估计趋势项参数,由趋势项参数计算回归残差,借助误差分级迭代的改进BP算法对趋势项进行精化,将两部分叠加获得精化模型.试验结果验证了基于回归残差的神经网络方法精化模型的有效性:神经网络方法精化后的模型能提高回归模型的拟合及预测精度5倍以上,优于最小二乘配置法和半参数法精化结果.神经网络方法精化模型既克服了单一神经网络模型的不可解释性,使模型具有物理意义,又具有较高的预测精度.

The regression fitting model established with the experiment observation data inevitably has the model error.Thus the neural network method based on the regression residual is adopted to improve the model.The simulation data are obtained by the given equation,and the tendency item of regression model is established by the chart of scatter data structure.The tendency parameter is estimated by the classical least squares method,and the regression residual is computed through the tendency parameter.The error grade iterative method of BP（back propagation） neural networks carries on the compensation to the tendency item,and the improved model is obtained by the splicing of the two parts.The results verify the validity of the model improved by the neural network based on the regression residual.The model improved by neural network can improve the regression model fitting,and can improve the forecast accuracy by more than 5 times.It is superior to least squares collocation method and semi-parametric method.The model improved by neural network overcomes the non-explanation in single neural network model,so that the model has physical meaning,and has higher prediction accuracy.