Genetic fuzzy system for data-driven soft sensors design

This paper proposes a new method for soft sensors (SS) design for industrial applications based on a Takagi–Sugeno (T–S) fuzzy model. The learning of the T–S model is performed from input/output data to approximate unknown nonlinear processes by a coevolationary genetic algorithm (GA). The proposed method is an automatic tool for SS design since it does not require any prior knowledge concerning the structure (e.g. the number of rules) and the database (e.g. antecedent fuzzy sets) of the T–S fuzzy model, and concerning the selection of the adequate input variables and their respective time delays for the prediction setting. The GA approach is composed by five hierarchical levels and has the global goal of maximizing the prediction accuracy. The first level consists in the selection of the set of input variables and respective delays for the T–S fuzzy model. The second level considers the encoding of the membership functions. The individual rules are defined at the third level, the population of the set of rules is treated in fourth level, and a population of fuzzy systems is handled at the fifth level. To validate and demonstrate the performance and effectiveness of the proposed algorithm, it is applied on two prediction problems. The first is the Box–Jenkins benchmark problem, and the second is the estimation of the flour concentration in the effluent of a real-world wastewater treatment system. Simulation results are presented showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily with appropriate input variables and delay selection and a reasonable number of rules. The proposed methodology is able to design all the parts of the T–S fuzzy prediction model. Moreover, presented comparison results indicate that the proposed method outperforms other previously proposed methods for the design of prediction models, including methods previously proposed for the design of T–S models.