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Updated: Jan 17, 2026

High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition
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High-precision Electromagnetic Flowmeter with Empty Pipe Detection via Complex Programmable Logic Device-based Waveform Recognition

Published on: June 27, 2025

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Design of efficient generalized digital fractional order differentiators using an improved whale optimization

Mohammed Ali Mohammed Moqbel1,2, Talal Ahmed Ali Ali1,2,3, Zhu Xiao1,2

  • 1College of Computer Science and Electronic Engineering, Hunan University, Changsha, China.

Peerj. Computer Science
|September 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces an improved whale optimization algorithm (IWOA) for designing generalized digital fractional-order differentiators (GFODs). The novel method achieves highly accurate GFOD approximations with reduced implementation complexity, suitable for digital signal processing.

Keywords:
Generalized fractional order differentiatorImproved whale optimization algorithmInfinite impulse response

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Area of Science:

  • Digital Signal Processing
  • Control Systems Engineering
  • Optimization Algorithms

Background:

  • Fractional-order calculus extends traditional calculus, offering advanced modeling capabilities.
  • Digital implementation of fractional-order operators, like generalized digital fractional-order differentiators (GFODs), is crucial for practical applications.
  • Existing methods for GFOD design face challenges in accuracy and computational complexity.

Purpose of the Study:

  • To propose a novel design and realization method for generalized digital fractional-order differentiators (GFODs).
  • To enhance the whale optimization algorithm (WOA) for computing optimal coefficients of infinite impulse response (IIR) subfilters.
  • To demonstrate the superiority of the proposed method in terms of accuracy and implementation complexity.

Main Methods:

  • A composite structure of infinite impulse response (IIR) subfilters is employed for GFOD realization.
  • An improved whale optimization algorithm (IWOA), incorporating piecewise linear chaotic mapping (PWLCM) and adaptive hyperbolic tangent inertia weight (AIWHT), is developed.
  • Simulation experiments compare IWOA against RCGA, PSO, and WOA for coefficient optimization.

Main Results:

  • The proposed IWOA demonstrates superior performance in achieving accurate GFOD approximations compared to other metaheuristics.
  • The IIR-based GFOD design achieves approximately 50% reduction in implementation complexity compared to state-of-the-art methods.
  • Simulation results validate the effectiveness and efficiency of the developed IWOA and GFOD design.

Conclusions:

  • The developed IWOA is highly effective for optimizing GFOD coefficients, outperforming existing algorithms.
  • The proposed IIR-based GFOD realization offers significant advantages in implementation complexity and accuracy.
  • This method presents a viable solution for real-world digital signal processing applications requiring fractional-order differentiation.