The probability density function based neuro-fuzzy model and its application in batch processes

Motivated by the concept of probability density function (PDF) control, a new probability density function (PDF) based neuro-fuzzy model for batch processes is proposed in this paper. The probability density function (PDF) of modeling error is introduced as a criterion to measure the performance of the neuro-fuzzy model of batch processes. More specifically, the neuro-fuzzy model parameter updating approach is transformed into the shape control of the probability density function (PDF) of the modeling error. That is to say, the PDF shape control idea is used to tune neuro-fuzzy model parameters so that the modeling error PDF is controlled to follow a targeted PDF, which is Gaussian or uniform distribution. As a result, the mean square error and the distribution of modeling error are both considered. Moreover, it alternatively uses the method of minimum-entropy to acquire the parameters of the neuro-fuzzy model if the targeted probability density function (PDF) is unknown. An example is applied to illustrate the applicability of the proposed method and the simulation results show that the proposed approach is more effective.