Sequential Parameter Identification of Fractional‐Order Duffing System Based on Differential Evolution Algorithm

Li, Lai; Ji, Yuandong; Zhong, Shun; Zhang, Lu

doi:10.1155/2017/3572365

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…To estimate the orders and parameters in an incommensurate fractional-order chaotic system, Zhu et al [95] proposed a switching differential evolution scheme, where the switching population size is adjusted dynamically. Motivated by this proposal, Lai et al [96] employed a sequential parameter identification method for a fractional-order Duffing system based on a differential evolution scheme. These authors then demonstrated an improved convergence of the proposed algorithm via numerical implementation.…”

Section: System Identificationmentioning

confidence: 99%

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Zou

Zhang

et al. 2018

Journal of Power Sources

428

155

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Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15-30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.

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Section: System Identificationmentioning

confidence: 99%

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Zou

Zhang

et al. 2018

Journal of Power Sources

428

155

View full text Add to dashboard Cite

show abstract

“…Nguyen et al [6] investigated the subharmonic resonance of a Duffing oscillator with a fractional-order derivative and analyzed its stability. In reference [7,8], the fractional-order Duffing system was investigated by a numerical method. The bifurcation behavior of a fractional-order Duffing system was studied, and its rich nonlinear behavior was found [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation

Wang

Shen

2022

Fractal Fract

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The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order systems. The pitchfork bifurcation, Hopf bifurcation and limit cycle bifurcation are discussed in detail, and it was found that Hopf bifurcation only happens while the fractional order is bigger than 1. On the other hand, the influence of the amplitude of parametric excitation on cluster oscillation models is discussed. The results show that amplitude regulates cluster oscillation models with different bifurcation types. The point–point cluster oscillation only relates to pitchfork bifurcation. The point–cycle cluster oscillation includes pitchfork bifurcation and Hopf bifurcation. The point–cycle–cycle cluster oscillation involves three kinds of bifurcation, i.e., the pitchfork bifurcation, Hopf bifurcation and limit cycle bifurcation. The larger the amplitude, the more bifurcation types are involved. The research results of cluster oscillation and its generation mechanism will provide valuable theoretical basis for mechanical manufacturing and engineering practice.

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“…The modified quantum bacterial foraging algorithm is applied to identify the parameters of the fractional-order system, which has a faster convergence rate and higher accuracy [27]. Literature [28][29][30] proposed improved differential (DE) evolution (IDE) algorithm, respectively, and applied to identify fractional-order chaotic system parameters, which greatly improves the identification speed and accuracy.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order system identification based on an improved differential evolution algorithm

Liang

Chen

et al. 2021

Asian Journal of Control

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With the continuous increasing of system modeling accuracy and control performance requirements, the fractional‐order models are applied to describe the dynamic characteristics of the real systems more accurately over traditional integer‐order models. Traditional identification algorithms for fractional‐order system require stringent information on the derivatives of the objective function and initial values of the parameters, which is difficult in practical applications. The differential evolution (DE) algorithm has the advantage of simple implementation and superior performance for solving multi‐dimensional complex optimization problems which is suitable for the identification of fractional‐order systems. Aiming at improving the solution accuracy and convergence speed, an improved DE (IDE) algorithm for fractional‐order system identification is proposed. The movement strategy of the marine predator algorithm (MPA) and the mutation strategy of randomly selecting one from the optimal individual population as the basis vector are both adopted in this proposed IDE algorithm. The parameter information of the successfully mutated individual is archived during the iteration process. The scaling factor and crossover probability factor are adaptively adjusted according to the archived information to enhance the best solution accuracy obtained in the search process. By testing 13 sets of unimodal and multimodal functions with high‐performance optimization algorithms, the accuracy performance of the proposed IDE solution is verified. The IDE algorithm is applied to identify the parameters of the fractional‐order system of permanent magnet synchronous motor with simulation and experiment. The identification results clearly show the effectiveness of the proposed methodology.

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Sequential Parameter Identification of Fractional‐Order Duffing System Based on Differential Evolution Algorithm

Cited by 6 publications

References 25 publications

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation

Fractional‐order system identification based on an improved differential evolution algorithm

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