嵌入岭回归的BP算法及其在软测量中的应用

Modified Errors Back Propagation Algorithm Based on Ridge Regression and Its Application to Soft Sensor

针对三层神经网络(ANN)最佳隐节点个数难以确定和随着隐节点个数增加ANN模型易出现过拟合等缺点,提出了嵌入岭回归(RR)的误差反传算法(BP)。BP-RR根据样本规模自适应确定隐节点个数,并通过BP算法充分提取样本数据信息。然后,针对隐含层输出可能存在的复共线性,采用RR以预测性能为指标,通过进化算法确定最佳岭参数,进而重新确定隐含层与输出层之间最佳的权值和阈值,克服ANN过拟合,建立具有良好预测性能的模型。将BP-RR应用于建立石脑油干点软测量,结果显示,BP-RR模型具有良好的预测性能。与ANN相比,BP-RR模型鲁棒性强,预测精度高。

To overcome the two main flaws of three-layer artificial neural network, i. e. tendency to overfitting and difficulty to determine the optimal number of hidden layer nodes, a modified errors back propagation algorithm containing ridge regression （BP-RR） is proposed. BP-RR determines the number of the hidden layer nodes according to the number of observed vectors in training sample. Firstly, BP is applied to learn from the training sample to the best of its abilities. Secondly, considering that there exists the outstanding correlation or multicollinearity among the hidden-layer-node output data, ridge regression is employed to obtain the optimal weights associated the hidden layer nodes with output layer nodes and the optimal thresholds of the output layer nodes instead of the original values obtained by BP; and then the model with the good predict ability is developed. The ridge regression uses an evolution algorithm to optimize ridge parameter according to the predict accuracy of the model. Further, BP-RR is employed to develop the naphtha dry point soft sensor. The results show that the good predict ability model with the robust character is obtained, and that the predict accuracy of BP-RR is superior to that of ANN.