The optimization of the kind and parameters of kernel function in KPCA for process monitoring

Kernel principal component analysis (KPCA) has been widely used in chemical processes monitoring due to its simple principle. However, how to select the kind and parameters of kernel function still limits the application of the method until now. In this paper, an optimization method based on genetic algorithm is developed to choose proper kind and parameters of kernel function. In this method, kernel kind and parameters are seen as decision variables of optimization, using correct monitoring rate, number of principal components, and statistical control limit of square prediction error (SPE) as multi-objective. For this specific problem, the fitness function, the algorithm of genetic selection, crossover and mutation are designed to ensure the diversity of kernel function and more selected chances of optimal individual in evolution process. A simple example and penicillin fermentation process are used to investigate the potential application of the proposed method; simulation results show that the proposed method is effective. (C) 2012 Elsevier Ltd. All rights reserved.