Novel soft sensor development using echo state network integrated with singular value decomposition: Application to complex chemical processes

It is of great importance to develop advanced soft sensors for ensuring the safety and stability of complex industrial processes. Unluckily, with the increasing scale of chemical processes, it becomes more and more demanding to develop soft sensor with high accuracy. In addition, most of industrial processes are dynamic. As a result, the soft sensors developed using static models cannot achieve acceptable performance. In order to handle this problem, the Echo state network (ESN) as a kind of recurrent neural network is selected. However, the output weights of ESN are calculated linearly. On one hand, the collinear in the reserve layer outputs may decrease the performance; on the other hand, the over-fitting problem may occur. To enhance and improve the ESN performance, singular value decomposition based ESN (SVD-ESN) is presented. In the SVD-ESN method, the singular value decomposition instead of the traditional least square is adopted to calculate the weights between the output layer and the reserve layer. Through singular value analysis in the outputs of the reserve layer, appropriate defining parameters are selected to enhance the accuracy and ensure the computing speed. As a result, the collinearity and over-fitting problem is solved; then the performance of ESN is enhanced. To test and validate the performance of SVD-ESN, the proposed SVD-ESN is developed as soft sensor for the High Density Polyethylene (HDPE) production process and Purified Terephthalic Acid (PTA) production process. Compared with the conventional ESN, Extreme Learning Machine (ELM), Dynamic Window based ELM (DW-ELM) and Long Short-Term Memory (LSTM), the simulation results show that the proposed SVD-ESN model obtains better performance in terms of prediction accuracy, which conforms that the proposed SVD-ESN can be used as an effective dynamic model for developing accurate soft sensors.