Chaotic forecasting of time series of heat-transfer coefficient for an evaporator with a two-phase flow

Time Series Modeling of Two‐ and Three‐Phase Flow Boiling Systems with Genetic Programming

“…(1) formation of the initial population, (2) implementation of the genetic operations, (3) evaluation of the individual by a fitness function value, (4) judgment of algorithm termination criterion: if yes, go to step (5) and otherwise, go to step (2) after the number of genetic generations increases by one, (5) output of the results, i.e., the optimum individual in the population is decoded as the optimum solution to the problem. Fig.…”

“…Based on the chaos theory, the correlation dimension of the nonlinear signal measured from the dynamic system indicates the necessary original value of the minimum variable number to describe the systems dynamic evolution behavior. For the two-and three-phase flow boiling evaporation systems, correlation dimension values are between 1 and 2 [2][3]. Therefore, the equation containing two independent variables was adopted to conduct the modeling investigations.…”

“…The fluidized bed evaporator can be used in many industrial processes since it is able to solve severe fouling problems and enhance boiling evaporation due to the circulation of fluidized solid particles through the heated tubes of vertical shell and tube exchangers [1][2][3]. However, the quantitative description of the behavior in such a system is still a difficult task due to the system complexity.…”

“…However, the quantitative description of the behavior in such a system is still a difficult task due to the system complexity. Only a few semi-empirical correlations have been proposed to forecast the steady-state characteristics of flow and heat transfer, i.e., average pressure drop and heat transfer coefficients, and no explicit mathematical models that can describe the evolution or transient behavior of the system have been reported in the literature, even though the evolution behavior reveals significant information on the system process mechanism and accurate prediction of the transient behavior is also important for establishing the proper operation and control strategies of such an evaporator [2,3].…”

“…Recent investigations indicate that flow and heat transfer transient behavior in flow boiling systems, including a system with fluidized solid particles manifests nonlinear and nonequilibrium characteristics [2,3]. Thus, the linear dynamic models cannot describe the system characteristics irrespective of the model order value and therefore, it may be possible to develop some effective, simple but nonlinear dynamic models from the point of view of nonlinear dynamics.…”