Results in Control and Optimization (Dec 2021)
Selection of ψ-Caputo derivatives’ functional parameters in generalized water transport equation by genetic programming technique
Abstract
The paper considers the usage of genetic programming technique to select an analytic form of functional parameter of the ψ-Caputo fractional derivative. We study one-dimensional space–time fractional water transport equation with such derivatives with respect to both time and space variables that generalizes the classical Richards equation. Having water head values measured by Watermark sensors as inputs, the statement of parameters identification problem is performed. The forms of functional parameters are represented as trees and found using a genetic programming algorithm. We compare the accuracy of field data description by the model with fixed and variable forms of derivatives’ functional parameters and obtained up to 30% increase in accuracy for the training dataset and up to 15% increase for the testing dataset when the considered method was used to select parameters’ forms.
