Kernel Optimization-Based Kernel Principal Component Analysis Algorithm And Their Applications In Fermentation Process

In the penicillin fermentation process, many control parameters of the fermentation process produces a very significant impact, taking a good on-line monitoring on the changes of these parameters can make us keep abreast of the status of the fermentation process. So that we can make adjustments in time to ensure the normal operation of the fermentation process. PCA has been widely used in on-line monitoring. But PCA is a linear method, and it often can not obtain good result when dealing with nonlinear problems. Because of penicillin fermentation process has highly nonlinear, we choose kernel principle component analysis (KPCA) algorithm.Kernel function plays a most important part in KPCA, and it decides the degree of nonlinear features extracted from system. But how to select the kind and parameters of kernel function still limits the application of this method until now. In this paper, an optimization method is developed to decide the proper kernel function and kernel parameters. In this method, kernel kind and kernel parameters are seen as decision variables of optimization, using maximum correct monitoring rate(CMR), minimum number of principal components, the minimum prediction residual error sum of squares (PRESS) as a multi-objective. Access to literature, the parameter c of Gaussian kernel function is between0.1and50, the parameter d of polynomial kernel function is positive integer from1to8, the parameters β0and β1of sigmoid kernel function are both between-10and10.In this paper optimal model variables are kind of kernel function and its parameters which have discontinuity. And optimization index is classification index, and it also has discontinuity. Target value is a complex variable nonlinear implicit function, it is difficult to resolve and expression. And there may exist local minima. Based on this, in this paper we choose genetic algorithm to slove. The kind of kernel function is encoded in binary code, and the kernel parameters are encoded in hybrid code. Using enumeration method to generate every kinds of kernel function, and the kernel parameters of the individuals of initial population are generated by random. A weighted fitness function is constructed to ensure kind’s diversity of kernel function in the initial stages, and to highlight the role of fitness with the increase in the generation of evolution. Genetic operation is designed based on hybrid coding strategy. Using this method into a nonlinear system, and simulation results prove that the proposed method can find out the optimal kernel kind and kernel parameters and it isstability and consistency.Based on this, the optimal-based KPCA algorithm is applied to penicillin fermentation process monitoring. Though analyzing the important factors penicillin fermentation process,10variables are selected as monitoring variables, they are aeration rate, agitator power, temperature and so on. Through simulation software Pensim produce penicillin fermentation process data, joined step interference into aeration rate, agitator power and substrate feed rate. At last, this optimization method is applied to penicillin fermentation process, and we get the desired results.