Abstract
Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence.
Highlights
System identification or parameter estimation involves the approximation of unknown variables of the system, and this concept provides the foundation for solving different engineering, science and technology problems [1]
ADEA is operators developedofby introducing the concept of adaptiveness in the mutation and the standard Differential Evolution Algorithm (DEA)
Due to its usefulness and efficiency, this algorithm is applied to various problems, such as the parameter estimation of Hammerstein algorithm is applied to various problems, such as the parameter estimation of Hammercontrol autoregressive systems [38], deep belief network [42], effective long short-term stein control autoregressive systems [38], deep belief network [42], effective long shortmemory for electricity price prediction [43], parameter estimation of solar cells [44], efterm memory for electricity price prediction [43], parameter estimation of solar cells [44], fective electricity energy consumption forecasting using an echo state network [45]
Summary
System identification or parameter estimation involves the approximation of unknown variables of the system, and this concept provides the foundation for solving different engineering, science and technology problems [1]. Most real-time systems are nonlinear and complex in nature. There are many applications for nonlinear systems in science and engineering, such as the inverted pendulum system [2], motion control of a motor driven robot [3], average dwell-time switching [4], tail-control missile system [5], and weather station systems [6]
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