Soft-sensing development using adaptive PSO optimization based multi-kernel ELM with error feedback

It is very hard to measure some process variables directly in actual industrial processes, so a soft senor model using adaptive particle swarm optimization (PSO) optimization based multi-kernel ELM with error feedback is proposed in this paper. Firstly, multi-kernel ELM is constructed by adding Gaussian and polynomial kernel function to ameliorate the overfitting problem in traditional ELM. Secondly, we propose an adaptive PSO (APSO) for ameliorating the low efficiency problem in the later period of PSO method by adding mutation operator. When given parameter reaches a threshold, the mutation operator adaptively adjusts the position of the particle. Also, the proportion of two kernel functions and the kernel parameters in training process are obtained by APSO. In each iteration, the training error is back propagated to the hidden layer as the co-outputs of hidden layer for further improving the accuracy and stability of the model. Finally, a simulation experiment on the purified terephthalic acid (PTA) solvent system is made to verify the modeling accuracy and optimized performances. The evaluation result demonstrates that the proposed method can provide higher accuracy and a more reliable soft senor model compared with other method.