Nonlinear Inferential Sensor Development Based on GMM–ELM

In order to model nonlinear industrial processes for on-line estimating those quality-related but difficult-to-measure variables, this paper proposes an inferential sensing approach based on Gaussian mixture model and extreme learning machine which is referred to as the `GMM-ELM'. In the GMM-ELM, mixture of ELMs is developed under the framework of GMM to deal with nonlinear and non-Gaussian characteristics, where localization and localized ELMs are completed unifiedly instead of separately. In addition, Bayesian regularization is exerted for the weight vector that connects the hidden and output nodes for each ELM to handle overfitting. We also develop an efficient learning algorithm to train the GMM-ELM. Experiments are carried out on a real-world industrial process to evaluate the performance of the GMM- ELM, which demonstrate the effectiveness of the proposed approach as well as its promising foreground in monitoring or automatic control of the quality-related variables.