Approximate solution of non-linear dynamic energy model for multiple effect evaporator using fourier series and metaheuristics

Abstract

This article presents the approximate solution of non-linear dynamic energy model of multiple effect evaporator (MEE) using Fourier series and metaheuristics. The dynamic model of MEE involves first-order simultaneous ordinary differential equations (SODEs). Prior to solving the dynamic model, the non-linear steady-state model is solved to obtain the optimum steady-state process parameters. These process parameters serve as the initial conditions (constraints) for the SODEs. The SODEs are exemplified as an optimization problem by the weighted residual function to produce their approximate solutions. The optimization task is to find the best estimates of unknown coefficients in the Fourier series expansion using two preeminent metaheuristic approaches: Particle swarm optimization and harmony search. Besides, the influence of the number of approximation terms in Fourier series expansion on the accuracy of the approximate solutions has been investigated. The solution of the dynamic model assists in the investigation of open-loop dynamics of the MEE. Moreover, the acquired results may assist in designing suitable controllers to ensure energy-efficient performance of MEE and to monitor the product quality. The optimization results reveal that both the metaheuristic approaches offer minimum violation of the constraints and, therefore, validate their efficiency in solving such complex non-linear energy models.