4-CBA Concentration Soft Sensor Based on Modified Back Propagation Algorithm Embedded with Ridge Regression

Algorithm Embeded with Ridge Regression Xuefeng Yan Weixiang Zhao 1(Automation Institute, College of Information Science and Engineering, East China University of Science and Technology, MeiLong Road 130, Shanghai 200237, P. R. China) 2(Department of Chemical Engineering and Center for Air Resources Engineering and Science, Clarkson University, Potsdam, NY 13699-5708, USA) Abstract Considering that there exist many factors having highly nonlinear effect on the concentration of the 4-carboxybenzaldehyde (4-CBA), which is the most important intermediate product of p-xylene (PX) oxidation reaction, a modified back propagation algorithm embedded with ridge regression (BP-RR) was proposed to develop a soft sensor of the 4-CBA concentration. To overcome the two main flaws of regular multi-layer neural networks, i.e. the tendency of overfitting and the difficulty to determine the optimal number of neurons for the hidden layer, firstly, a three-layer network is selected and the number of the hidden-layer neurons is determined according to the number of the training samples and the number of the neural network parameters. Then, BP is applied to learn from the training samples. In sequel, the ridge regression is employed to remove the multicollinearity among the hidden-layer-node outputs and obtain the optimal weights (and thresholds) between the hidden layer and the output layer to replace the original values obtained by BP. Thus the neural network model with good prediction ability is developed. In addition, the ridge regression uses heuristic differential evolution algorithm to optimize ridge parameter according to the prediction accuracy of the model. The results show that the optimal value of ridge parameter is adaptively determined according to the degree of multicollinearity among the hidden-layer-node output, and then the good prediction ability model with the robust character is obtained by BP-RR. The best and the mean prediction accuracies of the neural network models developed by BP-RR are higher than those of the neural network models trained by BP alone and obtained by pruning algorithms based on principle component analysis.