Development of Genetically tuned Fuzzy dynamic model for nonlinear dynamical systems: Application on reaction section of Tennessee Eastman process

Abstract

This work presents a new GA-fuzzy method to model dynamic behavior of a process, based on recurrent fuzzy modeling through Mamdani approach, whose inference system is optimized by genetic algorithms. By using the Mamdani approach, the proposed method surmounts the need to solve various types of mathematical equations governing the dynamic behavior of the process. The proposed method consists of two steps: i) constructing a startup version of the model and ii) optimizing the shape of membership functions of the fuzzy sets corresponding to the variables existing in the fuzzy model along with the production rules constituting the inference such that the obtained fuzzy model can predict the dynamic behavior of the process fairly accurately. The proposed method is used to predict the dynamic behavior of the reaction section of the Tennessee Eastman (TE) benchmark. The overall accuracy of the obtained results is shown in comparison with their corresponding counterparts in TE benchmark. The Mean Absolute Percentage Error (MAPE) of the key process variables, which are temperature, pressure, and level of the reactor, and the reactor cooling water outlet temperature are calculated 1.17%, 0.38%, 1.5%, and 1.57%, respectively, showing high prediction capability of the proposed method.

Optimization techniques on fuzzy inference systems to detect Xanthomonas campestris disease

“…The Mamdani type fuzzy inference system problem to identify a sick leave is modeled after the RGB value indicators, each one having 3 input sets (R,G,B color components) and the pixel status output set [23]: the first model has nine rules set representing the equivalence of a sane or ill pixel correlating it to the system's input and output, there are three triangular membership functions in the input sets established to depict low, medium, and high intensities for each RGB component as shown in Figure 3(a), the second system is defined by 17 rules and six membership functions in the input sets corresponding to the value intensity in the RGB scale (low, low-mid, mid-mid. Mid-high, high) as shown in Figure 3 As a general rule, fuzzy inference systems are characterized by their high interpretability and low accuracy, hence, it was necessary to implement genetic [24] and Quasi-Newton BFGS [25] optimization algorithms to every model to adjust the membership functions for input and output sets so an effective logical correlation with the system rules and inference system could be established among all four models developed. This led to a closer identification of the pixel status: being classified as ill when the value tends to 0.3884 and sane if the value sits around 0.62.…”