A robust hybrid model integrating enhanced inputs based extreme learning machine with PLSR (PLSR-EIELM) and its application to intelligent measurement

In this paper, a robust hybrid model integrating an enhanced inputs based extreme learning machine with the partial least square regression (PLSR-EIELM) was proposed. The proposed PLSR-EIELM model can overcome two main flaws in the extreme learning machine (ELM), i.e. The intractable problem in determining the optimal number of the hidden layer neurons and the over-fitting phenomenon. First, a traditional extreme learning machine (ELM) is selected. Second, a method of randomly assigning is applied to the weights between the input layer and the hidden layer, and then the nonlinear transformation for independent variables can be obtained from the output of the hidden layer neurons. Especially, the original input variables are regarded as enhanced inputs; then the enhanced inputs and the nonlinear transformed variables are tied together as the whole independent variables. In this way, the PLSR can be carried out to identify the PLS components not only from the nonlinear transformed variables but also from the original input variables, which can remove the correlation among the whole independent variables and the expected outputs. Finally, the optimal relationship model of the whole independent variables with the expected outputs can be achieved by using PLSR. Thus, the PLSR-EIELM model is developed. Then the PLSR-EIELM model served as an intelligent measurement tool for the key variables of the Purified Terephthalic Acid (PTA) process and the High Density Polyethylene (HDPE) process. The experimental results show that the predictive accuracy of PLSR-EIELM is stable, which indicate that PLSR-EIELM has good robust character. Moreover, compared with ELM, PLSR, hierarchical ELM (HELM), and PLSR-ELM, PLSR-EIELM can achieve much smaller predicted relative errors in these two applications.