Shibendu Mahata

Optimal and accurate design of fractional-order digital differentiator – an evolutionary approach

This study deals with the implementation of highly accurate, stable, minimum phase, and wideband fractional-order digital differentiators (FODDs) in terms of infinite impulse response filters using an efficient evolutionary optimisation algorithm called adaptive Gbest-guided gravitational search algorithm (GGSA). Performance evaluation of GGSA as compared with real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) based designs are carried out in terms of different magnitude and phase response error metrics, solution quality reliability, and convergence speed. Simulation results clearly demonstrate that GGSA significantly outperforms RGA, PSO, and DE in consistently achieving the most accurate FODDs in a computationally efficient manner. The proposed FODDs also significantly outperform all state-of-the-art designs in terms of magnitude responses.

Optimal design of wideband digital integrators and differentiators using hybrid flower pollination algorithm

In this paper, a recently proposed metaheuristic optimization technique called hybrid flower pollination algorithm (HFPA) is applied to design wideband infinite impulse response digital differentiators (DDs) and digital integrators (DIs). In recent years, benchmark nature-inspired optimization algorithms such as particle swarm optimization (PSO), simulated annealing, and genetic algorithm have been employed for the design of wideband DDs and DIs. However, individually, these algorithms show major drawbacks such as premature convergence, thus leading to a sub-optimal solution. HFPA, however, is a hybrid approach which combines the efficient exploitation and exploration capabilities of two different metaheuristics, namely PSO and flower pollination algorithm (FPA), respectively. The HFPA-based designs have been compared with real-coded genetic algorithm, PSO, differential evolution, success-history-based adaptive differential evolution with linear population size reduction (L-SHADE), self-adaptive differential evolution (jDE), and FPA-based designs with respect to the solution quality, robustness, convergence, and optimization time. Simulation results demonstrate that among all the algorithms, the HFPA-based designs consistently achieve superior performances in the least number of function evaluations. Exhaustive experimentations are conducted to determine the best values of the control parameters of HFPA for the optimal design of DDs and DIs. The proposed designs also outperform the recently reported designs based on non-optimal, classical, and nature-inspired optimization approaches in terms of magnitude response. The lower orders of the proposed designs render them suitable for real-time applications.

Optimal design of wideband infinite impulse response fractional order digital integrators using colliding bodies optimisation algorithm

This study presents a novel approach to design wideband infinite impulse response fractional order digital integrators (FODIs) for the half and one-fourth order integrators based on a parameter independent metaheuristic algorithm called colliding bodies optimisation (CBO). The performance of CBO-based FODIs have been compared with the designs based on three well-known benchmark evolutionary optimisation algorithms namely, real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) in terms of robustness, consistency, parameter sensitivity, convergence speed, and computational time. Simulations results confirm that the proposed CBO-based designed FODIs achieve consistently superior magnitude responses in a computationally efficient manner as compared with the designs based on RGA, PSO, and DE. The proposed CBO-based FODIs also significantly outperform all state-of-the-art designs reported in literature in terms of two different magnitude response error metrics. This research work underlines the potential of CBO as an efficient optimisation tool for the design of accurate digital approximations to the fractional order integrators.

Optimal design of fractional order low pass Butterworth filter with accurate magnitude response

Abstract The design of ( 1 + α ) order, 0 α 1 , low pass Butterworth filter approximated in terms of an integer order continuous-time transfer function using a nature-inspired optimization technique called Gravitational Search Algorithm (GSA) is presented in this paper. While approximations of the non-integer order Laplacian operator s α in terms of second order rational function using the continued fraction expansion method for the design of fractional order low pass Butterworth filters (FOLBFs) is recently reported in literature, however, such a design technique is non-optimal. In this work, the metaheuristic global search process of GSA efficiently explores and intensely exploits the nonlinear, non-uniform, multidimensional, and multimodal FOLBF design problem error landscape. At the end of the iterative search routine of GSA, the optimal values of the coefficients in terms of the third order rational approximations are achieved which accurately approximate the magnitude response of the ideal FOLBF. The proposed GSA based FOLBFs consistently achieve the best solution quality with the fastest convergence rate as compared with the designs based on Real coded Genetic Algorithm (RGA) and Particle Swarm Optimization (PSO). Comparison with the recent literature also demonstrates the superiority of the proposed designs. SPICE simulations justify the design feasibility of the proposed FOLBF models.

Enhanced colliding bodies optimisation-based optimal design of wideband digital integrators and differentiators

This paper presents an efficient approach to determine the optimal set of coefficients for the design of wideband infinite impulse response (IIR) digital integrators (DIs) and digital differentiators (DDs) of first, second, third, and fourth order, meeting the accurate magnitude response specification, using a recently proposed evolutionary optimisation algorithm called enhanced colliding bodies optimisation (ECBO). To demonstrate the effectiveness of the proposed approach, the results of the ECBO-based designs have been compared with those of eight other nature-inspired metaheuristic optimisation algorithms. Parametric and non-parametric statistical hypothesis tests are conducted to validate the consistency of the performance of the ECBO-based DIs and DDs. Simulation results demonstrate that ECBO-based designs achieve the least absolute magnitude error and demonstrate a competitive group delay response of the designed DIs and DDs of different orders as compared with the designs based on the competing algorithms. The proposed DIs and DDs also outperform those of the design approaches published in literature and achieve the best responses in terms of the maximum absolute magnitude error over a wide frequency range.

Accurate design of Digital Fractional Order differentiators using Improved Particle Swarm Optimization

Design of accurate, wideband, and infinite impulse response (IIR) type Digital Fractional Order Differentiators (DFODs) based on a swarm intelligence based algorithm called Improved Particle Swarm Optimization (IPSO) is presented in this paper. As compared with DFODs based on three benchmark evolutionary optimization algorithms, namely Real Coded Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), and Differential Evolution (DE), the IPSO based designs achieve the most accurate approximation to the ideal fractional order differentiator. The proposed DFODs also significantly outperform all state-of-the-art designs in terms of different magnitude response error metrics.

Efficient design of IIR Fractional Order Digital Integrators using Craziness based Particle Swarm Optimization

An efficient approach to design stable, minimum phase, wideband, and accurate infinite impulse response (IIR) Fractional Order Digital Integrators (FODIs) of second and third order based on a swarm intelligence based optimization technique called Craziness based Particle Swarm Optimization (CRPSO) is presented in this paper. The CRPSO based designs demonstrate a superior solution quality as compared with the designs based on three benchmark nature-inspired optimization algorithms. The proposed CRPSO based FODIs also achieve the best magnitude response as compared with all state-of-the-art designs. The lower orders of the proposed FODIs make them attractive for real-time signal processing applications.

Optimal design of IIR digital FOI using IPSO

ABSTRACT This paper presents an efficient approach to design digital Fractional-Order Integrators (FOIs) exhibiting an accurate magnitude response by employing a metaheuristic algorithm called Improved Particle Swarm Optimisation (IPSO). The proposed infinite impulse response (IIR) filter type IPSO-based digital FOIs have been judged against the Real-coded Genetic Algorithm, Particle Swarm Optimisation (PSO), and Differential Evolution -based digital FOIs with respect to various performance metrics. The superior performance of the IPSO-based designs is also emphasised using different statistical indices. Parametric and non-parametric statistical hypothesis tests demonstrate the reliable performance of IPSO-based designs. MATLAB simulation results confirm the accurate magnitude response of the proposed digital FOIs as compared with the published literature.

Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

This paper presents an efficient approach to design wideband, accurate, stable, and minimum-phase fractional-order digital differentiators (FODDs) in terms of the infinite impulse response (IIR) filters using an evolutionary optimization technique called flower pollination algorithm (FPA). The efficiency comparisons of FPA with real-coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE)-based designs are conducted with respect to different magnitude and phase response error metrics, parametric and nonparametric statistical hypotheses tests, computational time, and fitness convergence. Exhaustive simulation results clearly demonstrate that FPA significantly outperforms RGA, PSO, and DE in attaining the best solution quality consistently. Extensive analysis is also conducted in order to determine the role of control parameters of FPA on the performance of the designed FODDs. The proposed FPA-based FODDs outperform all the designs published in the recent literature ...

Accurate design of digital rational approximations to the fractional order integrator using crow search algorithm

This paper presents an accurate design of stable, minimum phase, and wideband digital rational approximations to the Fractional Order Integrators (FOIs) based on a recently proposed nature-inspired metaheuristic optimization approach motivated by the intelligent manners of crows called Crow Search Algorithm (CSA). The proposed CSA based Digital Fractional Order Integrators (DFOIs) are compared with those of the designs based on four well-known nature-inspired optimization algorithms in terms of different frequency response performance indices and computational efficiency. The CSA based design of filter orders 5 and 6 achieves improvement of 5.9 dB and 10.3 dB, respectively, over state-of-the-art designs in terms of root mean square magnitude error metric, and also demonstrates a competitive performance with respect to the phase response. The proposed work demonstrates that CSA can be considered as an efficient optimizer for the design of DFOIs.