Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator

Yin, Kaili; Pu, Yi-Fei; Lu, Lu

doi:10.1016/j.neucom.2020.02.022

Cited by 31 publications

(6 citation statements)

References 40 publications

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“…Consequently, the proposed fractional MWNN-GASQP algorithm is not famous for smooth operational/viable solutions, but one can extend and implement this technique easily. In future, one can exploit the fractional MWNN-GASQP-based FMNEICS scheme to solve the linear and nonlinear system represented with differential equation involving both integer and fractional-order terms (Yin et al 2020;Masood 2020).…”

Section: Conclusion and Further Related Workmentioning

confidence: 99%

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

et al. 2020

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In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane-Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNE-ICS for DSMF-LES is presented after derivation from standard Lane-Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the meansquared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver. Keywords Multi-fractional Lane-Emden model • Multi-singular systems • Artificial neural networks • Meyer wavelet neural networks • Sequential quadratic programming • Genetic algorithms Mathematics Subject Classification 34-XX • 34A08 • 34A34 • 82B31

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Section: Conclusion and Further Related Workmentioning

confidence: 99%

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

et al. 2020

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“…Fractional calculus operators are also exploited to design novel recursive/adaptive algorithms as well as evolutionary/swarm computation heuristics for different optimization tasks involved in engineering and science applications. For example, fractional gradient descent/fractional least mean square algorithm was proposed for various applications including recommender systems [10], channel estimation [11], automatic identification system [12], power system optimization [13], economics [14], radar signal processing [15], system identification [16,17], Hammerstein output error identification [18], wireless sensor network [19], neural network optimization [20][21][22][23][24], chaotic time-series prediction [25,26], oscillator [27], vibration rejection [28], nonlinear AR-MAX identification [29] and parameter estimation of input nonlinear control autoregressive (IN-CAR) systems [29,30].…”

Section: Introduction 1literature Reviewmentioning

confidence: 99%

Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems

et al. 2022

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In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification.

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“…At the same time, its efficiency in noise reduction is also verified (George and Gonzalez, 2013). Similar combination methods are also used to achieve fast convergence and low steady-state error of the noise reduction system (Yin KL et al, 2020; Zhao et al, 2016). In addition to the above work on nonlinear systems, Larbaoui et al (2021) and Belabbes and Larbaoui (2015) proposed the Lyapunov’s second method to obtain a robust controller and tracking the controlled system’s signal by the backstepping method which is often used in noise reduction systems.…”

Section: Introductionmentioning

confidence: 99%

An investigation of active enclosed-space noise control with a nonlinear loudspeaker

Liu

Zhu

et al. 2022

Journal of Vibration and Control

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Active control algorithms are widely used in enclosed-space noise control with the nonlinearities of secondary-source loudspeakers ignored. Inspired by nonlinear energy transfer resulting from nonlinear stiffness, this work concerns using a nonlinear loudspeaker to improve enclosed-space noise control. An enclosed-space active noise control system with a nonlinear loudspeaker is modeled. Based on the model, an approximate frequency response function of the noise control system is derived analytically via the harmonic balance method and verified using numerical methods. A globally consistent and bounded Lyapunov function is derived. The effects of the mass, nonlinear stiffness, volume, and area ratio on the noise reduction are also explored. Both analytical and numerical results demonstrate that the improved nonlinear loudspeaker is effective in improving the low-power characteristics of the loudspeaker, increasing noise reduction and improving fault-tolerant and robustness of the active noise control system.

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Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator

Cited by 31 publications

References 40 publications

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems

An investigation of active enclosed-space noise control with a nonlinear loudspeaker

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