Double-Level Locally Weighted Extreme Learning Machine for Soft Sensor Modeling of Complex Nonlinear Industrial Processes

In order to provide the stable and reliable prediction of key quality variables for industrial processes with complicated nonlinear characteristic, this paper proposes a Double-level Locally Weighted Extreme Learning Machine (DLWELM) based soft sensor modeling method. Firstly, a just-in-time learning based extreme learning machine framework (JITELM) is designed for adaptive nonlinear soft sensor modeling. Then, one double-level similarity measure methodology is presented with considering both the variable importance and the sample distance. At the first level, the mutual information between different input variables and output variable is computed for evaluating the importance of the input variables, which results in the variable weight coefficients. Furthermore, the variable-weighted sample distances are obtained at the second level, which are utilized to build the similarity measure for the relevant samples searching. Lastly, with the relevant samples as the modeling dataset, the locally weighted ELM (LWELM) model is developed, which assigns different weights to the training samples according to their double-level similarity values. Three cases including one numerical system, the industrial debutanizer column plant and the industrial polypropylene production process, are used to test the methods and the results demonstrate that the proposed DLWELM method has higher prediction precision compared to the basic ELM methods.