Rapid Multi-Objective Optimization of Periodically Operated Processes Based on the Computer-Aided Nonlinear Frequency Response Method

Abstract

The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved to the computer-aided NFR method (cNFR) through a user-friendly software application for the automatic derivation of the functions necessary to estimate process improvement. By combining the cNFR method with standard multi-objective optimization (MOO) techniques, we developed a unique cNFR–MOO methodology for the optimization of periodic operations in the frequency domain. Since the objective functions are defined with entirely algebraic expressions, the dynamic optimization of forced periodic operations is extraordinarily fast. All optimization parameters, i.e., the steady-state point and the forcing parameters (frequency, amplitudes, and phase difference), are determined rapidly in one step. This gives the ability to find an optimal periodic operation around a sub-optimal steady-state point. The cNFR–MOO methodology was applied to two examples and is shown as an efficient and powerful tool for finding the best forced periodic operation. In both examples, the cNFR–MOO methodology gave conditions that could greatly enhance a process that is normally operated in a steady state.

Forced periodic operations of a chemical reactor for methanol synthesis – The search for the best scenario based on Nonlinear Frequency Response Method. Part II Simultaneous modulation of two inputs

“…Therefore, theoretical prediction and evaluation of possible process improvement, prior to any experimental investigation, is an important task (Petkovska and Seidel-Morgenstern, 2013). In our previous work we introduced the Nonlinear Frequency Response (NFR) method for evaluation of possible improvements owing to periodic operations, as well as for evaluation of optimal forcing parameters and conditions which should be satisfied in order to obtain the highest possible improvement (Currie et al, 2018;Marković et al 2008;Nikolić-Paunić and Petkovska, 2013;Nikolić et al, 2014aNikolić et al, , 2014bNikolić et al, , 2015Nikolić et al, , 2016aNikolić et al, , 2016bNikolić et al, , 2020Nikolić, 2016;Nikolić and Petkovska, 2016;Petkovska et al, 2010Petkovska and Seidel-Morgenstern, 2013Živković et al 2020a;2020b).…”

Forced periodic operations of a chemical reactor for methanol synthesis – The search for the best scenario based on Nonlinear Frequency Response Method. Part I Single input modulations

“…It is therefore of economic importance to carry out theoretical studies for assessing the effects of forced periodic operations of chemical processes, before any experimental studies (Chen et al, 1994). In our previous work (Marković et al, 2008;Nikolić, 2016;Petkovska and Seidel-Morgenstern, 2013;Petkovska et al, 2018) we introduced the Nonlinear Frequency Response (NFR) method as a reliable analytical tool for evaluating possible improvements and finding the best forcing parameters (Nikolić, 2016;Živković et al, 2020b).…”

Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity

“…Equation (36) forms the basis for the nonlinear FRF method for fast evaluation of periodic operations with single input modulations. The function G…”

“…The multi-objective optimisation (MOO) of the steady-state operation was performed in MATLAB 2019b by using a non-dominated sorting genetic algorithm II (NSGA-II) [36,62]. The upper limit of y A,in,s parameter was limited based on the vapour pressure to prevent the formation of liquid phase at 340 K [63].…”

“…More recently, the so-called computer-aided nonlinear frequency response (cNFR) method was introduced by developing a user-friendly software application for implementing the NFR method [27]. By combining the NFR method and multi-objective optimisation techniques, a new methodology for the optimisation of periodic operations was established [36], which is much faster than the classical methods based on numerical integrations.…”