Abstract
Computational modeling plays an important role in prediction and optimization of real systems and processes. Models usually have some parameters which should be set up to the proper value. Therefore, parameter estimation is known as an important part of the modeling and system identification. It usually refers to the process of using sampled data to estimate the optimum values of parameters. The accuracy of model can be increased by adjusting its parameters to the optimum value which need a richer dataset. One simple solution for having a richer dataset is increasing the amount of data, but that can be costly and time consuming. When using data from animals or people, it is especially important to have a proper plan. There are several available methods for parameter estimation in dynamical systems; however there are some basic differences in chaotic systems due to their sensitivity to initial condition (butterfly effect). Accordingly, in this paper, a new cost function which is proper for chaotic systems is applied to the chaotic one-dimensional map. Then the efficiency of a newly introduced intelligent method experimental design in extracting proper data is investigated. The results show the success of the proposed method.
Highlights
Computational modeling plays an important role in the advancement of science by helping us to predict, optimize, simulate, and study the behavior of complex systems
The only difference is that when the queen is selected and the best neighbor of queen is calculated, a little perturbation is added to the queen in the direction of the best neighbor to achieve new data. We have applied both Twilight Method Experimental Design (TMED) and MTMED on system (1), in order to find the optimum values of the parameters
We have investigated the efficiency of a newly proposed experimental design method on gathering proper data for parameter estimation of a chaotic one-dimensional map
Summary
Computational modeling plays an important role in the advancement of science by helping us to predict, optimize, simulate, and study the behavior of complex systems. Two widely used structures which have shown good performance in real world applications are neural networks [4] and neurofuzzy models [5]. While the former is more efficient in extrapolation and more robust against high dimensional problems, the latter is very good for interpolation and providing better interpretation [1]. It is important to find a way to generate datasets that are as rich as possible using experimental design (ED) methods [6,7,8]. Experimental design methods are not directly involved in the modeling procedure, they are important
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