Korean Journal of Chemical Engineering ( IF 2.7 ) Pub Date : 2021-05-06 , DOI: 10.1007/s11814-021-0787-3 Drishti Yadav , Saurav Kumar , Om Prakash Verma , Nikhil Pachauri , Varun Sharma
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.
中文翻译:
多效蒸发器非线性动态能量模型的傅里叶级数和元启发式近似解
本文利用傅里叶级数和元启发式方法,给出了多效蒸发器(MEE)非线性动态能量模型的近似解。MEE的动力学模型涉及一阶联立常微分方程(SODE)。在求解动态模型之前,先对非线性稳态模型进行求解,以获得最佳的稳态过程参数。这些过程参数充当SODE的初始条件(约束)。通过加权残差函数将SODE例示为优化问题,以产生其近似解。优化任务是使用两种卓越的元启发式方法在傅立叶级数展开中找到未知系数的最佳估计:粒子群优化和和声搜索。除了,研究了傅立叶级数展开中逼近项数对逼近解精度的影响。动力学模型的解决方案有助于研究MEE的开环动力学。此外,获得的结果可能有助于设计合适的控制器,以确保MEE的节能性能并监视产品质量。优化结果表明,两种元启发式方法都提供了对约束的最小违反,因此验证了它们在求解这种复杂的非线性能量模型中的效率。获得的结果可能有助于设计合适的控制器,以确保MEE的节能性能并监控产品质量。优化结果表明,两种元启发式方法都提供了对约束的最小违反,因此验证了它们在求解这种复杂的非线性能量模型中的效率。获得的结果可能有助于设计合适的控制器,以确保MEE的节能性能并监控产品质量。优化结果表明,两种元启发式方法都提供了对约束的最小违反,因此验证了它们在求解这种复杂的非线性能量模型中的效率。