Hybrid artificial neural network based on BP-PLSR and its application in development of soft sensors

A novel hybrid artificial neural network (HANN) integrating error back propagation algorithm (BP) with partial least square regression (PLSR) was proposed to overcome two main flaws of artificial neural network (ANN), i.e. tendency to overfitting and difficulty to determine the optimal number of the hidden nodes. Firstly, single-hidden-layer network consisting of an input layer, a single hidden layer and an output layer is selected by HANN. The number of the hidden-layer neurons is determined according to the number of the modeling samples and the number of the neural network parameters. Secondly, BP is employed to train ANN, and then the hidden layer is applied to carry out the nonlinear transformation for independent variables. Thirdly, the inverse function of the output-layer node activation function is applied to calculate the expectation of the output-layer node input, and PLSR is employed to identify PLS components from the nonlinear transformed variables, remove the correlation among the nonlinear transformed variables and obtain the optimal relationship model of the nonlinear transformed variables with the expectation of the output-layer node input. Thus, the HANN model is developed. Further, HANN was employed to develop naphtha dry point soft sensor and the most important intermediate product concentration (i.e. 4-carboxybenzaldehyde concentration) soft sensor in p-xylene (PX) oxidation reaction due to the fact that there exist many factors having nonlinear effect on them and significant correlation among their factors. The results of two HANN applications show that HANN overcomes overfitting and has the robust character. And, the predicted squared relative errors of two optimal HANN models are all lower than those of two optimal ANN models and the mean predicted squared relative errors of HANN are lower than those of ANN in two applications.