Abstract:The principal deficiency of the widely utilized Alfrey-Price (AP) scheme for computing reactivity ratios in the widely used free radical copolymerization is that it ignores important factors, such as the steric effects. This often leads to inaccurate reactivity ratio predictions by AP model. Accordingly, in this study, exclusively data-driven, Q-e parameter-based new models have been developed for the reactivity ratio prediction in free radical copolymerization. In the model development, a novel artificial int… Show more
“…Steps (ii) to (iv) are performed iteratively (see the flowchart in Figure 2) until a best-fitting candidate solution (expression) is secured. An in-depth treatment of the GPSR procedure can be found in several studies [24][25][26][27] .…”
The hydrodynamics of a gas-solid fluidized bed (FB) is affected by the bubble diameter, which in turn strongly influences the performance of a fluidized bed reactor (FBR). Thus, determining the bubble diameter accurately is of crucial importance in the design and operation of an FBR. Various equations are available for calculating the bubble diameter in an FBR. It has been found in this study that these models show a large variation while predicting the experimentally measured bubble diameters. Accordingly, the present study proposes a new equation for computing the bubble diameter in a fluidized bed. This equation has been developed using an efficient, yet infrequently employed computational intelligence (CI)-based datadriven modelling method termed genetic programming (GP). The prediction and generalization performance of the GP-based equation has been compared with that of a number of currently available equations for computing the bubble diameter in a fluidized bed and the results obtained show a good performance by the newly developed equation.
“…Steps (ii) to (iv) are performed iteratively (see the flowchart in Figure 2) until a best-fitting candidate solution (expression) is secured. An in-depth treatment of the GPSR procedure can be found in several studies [24][25][26][27] .…”
The hydrodynamics of a gas-solid fluidized bed (FB) is affected by the bubble diameter, which in turn strongly influences the performance of a fluidized bed reactor (FBR). Thus, determining the bubble diameter accurately is of crucial importance in the design and operation of an FBR. Various equations are available for calculating the bubble diameter in an FBR. It has been found in this study that these models show a large variation while predicting the experimentally measured bubble diameters. Accordingly, the present study proposes a new equation for computing the bubble diameter in a fluidized bed. This equation has been developed using an efficient, yet infrequently employed computational intelligence (CI)-based datadriven modelling method termed genetic programming (GP). The prediction and generalization performance of the GP-based equation has been compared with that of a number of currently available equations for computing the bubble diameter in a fluidized bed and the results obtained show a good performance by the newly developed equation.
“…analyzed the free base binary copolymerization reaction in 1944 and deduced the copolymer composition from the four chain growth reactions, a variety of methods for the determination of the monomer racemization rate have been derived [5][6] , and the estimation of the racemization rate of copolymerized monomers by Monte Carlo probability statistics is the most widely used and effective method of determination at present [7] .…”
Bio-based PA5T/56 was successfully prepared by a nover modulated polymerization on this condition when the relationship between temperature and pressure was strictly controlled during the process to render the reactivity ratio of each monomers basically the same. In this case, the obtained PA5T/56, with approximately alternating copolymerization structure, possesses better physical and chemical performance and melt flowing properties. Meanwhile, the real-time sampling and testing was operated during the process to get the experimental values of reactivity ratio. Furthermore, the chain growth process of the ternary polymerization reaction was also calculated and simulated by referring to the Mayo-Lewis formula as well as using the Monte Carlo method, and a probabilistic statistical treatment for estimating the reactivity ratio was given. Finally, by comparing the results, it can be found that the experimental values of the reactivity ratio were in general accord in the calculated values with reference to the Mayo-Lewis formula and the simulated values of the mathematical model, the values of \({r}_{12}\) and \({r}_{13}\) are basically the same, which confirmed the successful synthesis of the bio-based PA5T/56 with approximately alternating copolymerization structure, and that the established mathematical model for estimating the reactivity ratio is relatively accurate and is applicable to the ternary polymerization.
Availability of an accurate and robust dynamic model is essential for implementing the model dependent process control.When first principles based modeling becomes difficult, tedious and/or costly, a dynamic model in the black-box form is obtained (process identification) by using the measured input-output process data. Such a dynamic model frequently contains a number of time delayed inputs and outputs as predictor variables. The determination of the specific predictor variables is usually done via a trial and error approach that requires an extensive computational effort. The computational intelligence (CI) based data-driven modeling technique, namely, genetic programming (GP) can search and optimize both the structure and parameters of a linear/nonlinear dynamic process model.It is also capable of choosing those predictor variables that significantly influence the model output.Thus usage of GP for process identification helps in avoiding the extensive time and efforts involved in the selection of the time delayed input-output variables. This advantageous GP feature has been illustrated in this study by conducting process identification of two chemical engineering systems. The results of the GP-based identification when compared with those obtained using the transfer function based identification clearly indicates the outperformance by the former method.
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