The work in this paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The extended system’s chaotic properties were validated through bifurcation analysis and spectral entropy. The presented system was employed in the substitution stage of an image encryption algorithm, including a generalized Arnold map for the permutation. The encryption scheme demonstrated its efficiency through statistical tests, key sensitivity analysis and resistance to brute force and differential attacks. The fractional-order memristive system includes a reconfigurable coordinate rotation digital computer (CORDIC) and Grünwald–Letnikov (GL) architectures, which are essential for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. The proposed system was implemented on the Artix-7 FPGA board, achieving a throughput of 0.396 Gbit/s. © 2023 by the authors.
Arithmetic optimization approach for parameters identification of different PV diode models with FOPI-MPPT
The Maximum Power Point Tracker (MPPT) provides the most efficient use of a Photo-voltaic system independent of irradiance or temperature fluctuations. This paper introduces the modeling and control of a photo-voltaic system operating at MPPT using the arithmetic optimization algorithm (AOA). The single and double Photo-voltaic models are investigated. Their optimal unknown parameters are extracted using AOA based on commercial Photo-voltaic datasheets. A comparison is performed between these optimal parameters extracted by AOA and other optimization techniques presented in the literature. These parameters generate the P – V and I – V curves for the studied models considering the temperature factor. A good match is achieved relative to the manufacturer data. A DC-DC boost converter is used as a link between the PV modules and the load. The converter duty cycle is adjusted, varying the climatic conditions using three cases: without a controller, using PI controller, and using the fractional-order PI controller (FOPI). The AOA is employed to set the optimum controllers parameters to maintain the impedance matching between the PV modules and the load. The FOPI shows a significant improvement in controlling the system performance. © 2021 THE AUTHORS
Discrete fractional-order Caputo method to overcome trapping in local optima: Manta Ray Foraging Optimizer as a case study
Enhancing the exploration and exploitation phases of the metaheuristic (MH) optimization algorithms is the key to avoiding local optima. The Manta ray foraging optimizer is a recently proposed MH optimizer. The MRFO showed a good performance in the simple optimization problems. However, it is trapped into the local optimum in the more elaborated ones due to the original algorithm’s low capability in exploiting the optimal solutions and its convergence. From this principle, in this work, a novel variant of the Manta ray foraging optimizer has been proposed for global optimization problems, engineering design optimization problems, and multi-threshold segmentation. In the proposed approach, the fractional calculus (FC) using Caputo fractional differ-sum operator has been adopted to enhance the manta rays movement in the exploitation phase via utilizing history dependency of FC to boost exploiting the optimal solutions via sharing the past knowledge over the optimization process. Moreover, to avoid premature convergence, the somersault factor has been adaptively tuned. The fractional-order Caputo Manta-Ray Foraging Optimizer (FCMRFO) has been proposed. The proposed algorithm’s sensitivity for the FC coefficients has been tested with ten-dimensional CEC2017 benchmarks. The scalability test of the proposed algorithm has been performed with 30, 50 and 100-dimensional CEC2017. Moreover, CEC2020 benchmarks with dimensions 5 and 20 have been applied for providing an extensive investigation, and the FCMRFO has been compared with recent state-of-the-art algorithms. Through utilizing the non-parametric statistical analysis and ranking test, the FCMRFO confirms its superiority and ability to avoid the local optimum in several cases. For the second part of the study, three constrained engineering design problems have been investigated; then, numerous natural images are applied to appraise the FCMRFO for multilevel threshold image segmentation. By performing several metrics, the FCMRFO proves its quality and efficiency compared to recent well-regarded algorithms in engineering applications and image segmentation. © 2021
Parameter Identification of Li-ion Batteries: A Comparative Study
Lithium-ion batteries are crucial building stones in many applications. Therefore, modeling their behavior has become necessary in numerous fields, including heavyweight ones such as electric vehicles and plug-in hybrid electric vehicles, as well as lightweight ones like sensors and actuators. Generic models are in great demand for modeling the current change over time in real-time applications. This paper proposes seven dynamic models to simulate the behavior of lithium-ion batteries discharging. This was achieved using NASA room temperature random walk discharging datasets. The efficacy of these models in fitting different time-domain responses was tested through parameter identification with the Marine Predator Algorithm (MPA). In addition, each model’s term’s impact was analyzed to understand its effect on the fitted curve. The proposed models show an average absolute normalized error as low as (Formula presented.). © 2023 by the authors.
Modified fractional-order model for biomass degradation in an up-flow anaerobic sludge blanket reactor at Zenein Wastewater Treatment Plant
This paper presents a modified fractional-order model (FOM) for microorganism stimulation in an up-flow anaerobic sludge blanket (UASB) reactor treating low-strength wastewater. This study aimed to examine the famine period of methanogens due to biomass accumulation in the UASB reactor over long time periods at a constant organic loading rate (OLR). This modified model can investigate the substrate biodegradation in a UASB reactor while considering substrate diffusion into biological granules during the feast and famine periods of methanogens. The Grünwald-Letnikov numerical technique was used to indicate the effect of biomass degradation on the biogas production rate and substrate biodegradation in a UASB reactor installed at Zenein Wastewater Treatment Plant (WWTP) in Giza, Egypt. Several fractional orders were applied in the dynamic model at biomass concentrations of 20 and 4 kg/ m3 in the reactor bed and blanket zones, respectively. An OLR of 0.9 kgCOD/ m3/ day using the calibrated kinetic parameters at 11 ?C was applied to comply with the experimental outcomes. The simulation results indicate that the removal efficiency of chemical oxygen demand (COD) was maintained at approximately 55 – 65 % , whereas the biogas production rate declined from 0.35 to 0.05 m3CH4/ kgCODr in the reactor bed zone due to a decline in food to microorganism (F/M) ratio from 0.04 to 0.018 d- 1 during the sludge retention time (SRT) in the UASB reactor. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Active and passive sensitivity analysis for the second-order active RC filter families using operational amplifier: a review
This work is a review article that sheds light on the active and passive sensitivities of the active RC filters based on opamp. This work provides a detailed analysis through different filters realization criteria and sensitivity summary tables and quantitative insight by discussing the most significant. However, some are almost forgotten, filters families in the literature over decades. A detailed mathematical analysis for the passive sensitivity to compare the filters’ realizations is presented. The concept of dealing between filter design theory and filter design circuit realization is highlighted. Some filters families are chosen from the literature for the analysis. Some detailed specifications tables for each filter family are given. Monte Carlo simulation is carried out on some filters to compare their passive sensitivity. Furthermore, the effect of the active sensitivity of some filters is verified through simulation by adjusting the input common-mode voltage to lower the DC gain of the amplifier. The results of the simulation match with the theoretical analysis and the summary provided in the specifications tables. © 2022, The Author(s).
High-performance fractional anisotropic diffusion filter for portable applications
Anisotropic diffusion is one of the most effective methods used in image processing. It can be used to eliminate the small textures of an image while preserving its significant edges. In this paper, a new anisotropic diffusion filter is proposed based on a fractional calculus kernel rather than integer kernel to improve the overall performance of the filter. Integer and fractional anisotropic filters are implemented using the Genesys-2 FPGA kit to utilize the efficiency of parallelism in FPGAs. Integer and fractional anisotropic filters are tested against the achievable PSNR value vs the number of iterations. The proposed fractional anisotropic filter has a better PSNR value using a smaller number of iterations, reducing the power and area compared to integer anisotropic filter. The proposed filter can be used in image smoothing, edge detection, image segmentation, image denoising, and cartooning. In addition, the proposed filter reduces the power consumption by 58.2% compared to integer-order filters, which makes the proposed filter suitable for battery-based applications. © 2023, The Author(s).
On the Design Flow of the Fractional-Order Analog Filters Between FPAA Implementation and Circuit Realization
This work explicitly states the design flows of the fractional-order analog filters used by researchers throughout the literature. Two main flows are studied: the FPAA implementation and the circuit realization. Partial-fraction expansion representation is used to prepare the approximated fractional-order response for implementation on FPAA. The generalization of the second-order active RC analog filters based on opamp from the integer-order domain to the fractional-order domain is presented. The generalization is studied from both mathematical and circuit realization points of view. It is found that the great benefit of the fractional-order domain is that it adds more degrees of freedom to the filter design process. Simulation and experimental results match the expected theoretical analysis. © 2013 IEEE.
A Unified FPGA Realization for Fractional-Order Integrator and Differentiator
This paper proposes a generic FPGA realization of an IP core for fractional-order integration and differentiation based on the Grünwald–Letnikov approximation. All fractional-order dependent terms are approximated to simpler relations using curve fitting to enable an efficient hardware realization. Compared to previous works, the proposed design introduces enhancements in the fractional-order range covering both integration and differentiation. An error analysis between software and hardware results is presented for sine, triangle and sawtooth signals. The proposed generic design is realized on XC7A100T FPGA achieving frequency of 9.328 MHz and validated experimentally for a sine input signal on the oscilloscope. The proposed unified generic design is suitable for biomedical signal processing applications. In addition, it can be employed as a laboratory tool for fractional calculus education. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
CORDIC-Based FPGA Realization of a Spatially Rotating Translational Fractional-Order Multi-Scroll Grid Chaotic System
This paper proposes an algorithm and hardware realization of generalized chaotic systems using fractional calculus and rotation algorithms. Enhanced chaotic properties, flexibility, and controllability are achieved using fractional orders, a multi-scroll grid, a dynamic rotation angle(s) in two- and three-dimensional space, and translational parameters. The rotated system is successfully utilized as a Pseudo-Random Number Generator (PRNG) in an image encryption scheme. It preserves the chaotic dynamics and exhibits continuous chaotic behavior for all values of the rotation angle. The Coordinate Rotation Digital Computer (CORDIC) algorithm is used to implement rotation and the Grünwald–Letnikov (GL) technique is used for solving the fractional-order system. CORDIC enables complete control and dynamic spatial rotation by providing real-time computation of the sine and cosine functions. The proposed hardware architectures are realized on a Field-Programmable Gate Array (FPGA) using the Xilinx ISE 14.7 on Artix 7 XC7A100T kit. The Intellectual-Property (IP)-core-based implementation generates sine and cosine functions with a one-clock-cycle latency and provides a generic framework for rotating any chaotic system given its system of differential equations. The achieved throughputs are (Formula presented.) Mbits/s and (Formula presented.) Mbits/s for two- and three-dimensional rotating chaotic systems, respectively. Because it is amenable to digital realization, the proposed spatially rotating translational fractional-order multi-scroll grid chaotic system can fit various secure communication and motion control applications. © 2022 by the authors.