Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints

Chaotic Wind Driven Optimization with Fitness Distance Balance Strategy

Wind driven optimization (WDO) is a meta-heuristic algorithm based on swarm intelligence. The original selection method makes it easy to converge prematurely and trap in local optima. Maintaining population diversity can solve this problem well. Therefore, we introduce a new fitness-distance balance-based selection strategy to replace the original selection method, and add chaotic local search with selecting chaotic map based on memory to further improve the search performance of the algorithm. A chaotic wind driven optimization with fitness-distance balance strategy is proposed, called CFDBWDO. In the experimental section, we find the optimal parameter settings for the proposed algorithm. To verify the effect of the algorithm, we conduct comparative experiments on the CEC 2017 benchmark functions. The experimental results denote that the proposed algorithm has superior performance. Compared with WDO, CFDBWDO can gradually converge in function optimization. We further verify the practicality of the proposed algorithm with six real-world optimization problems, and the obtained results are all better than other algorithms.

Desert soil clay content estimation using reflectance spectroscopy preprocessed by fractional derivative

Effective pretreatment of spectral reflectance is vital to model accuracy in soil parameter estimation. However, the classic integer derivative has some disadvantages, including spectral information loss and the introduction of high-frequency noise. In this paper, the fractional order derivative algorithm was applied to the pretreatment and partial least squares regression (PLSR) was used to assess the clay content of desert soils. Overall, 103 soil samples were collected from the Ebinur Lake basin in the Xinjiang Uighur Autonomous Region of China, and used as data sets for calibration and validation. Following laboratory measurements of spectral reflectance and clay content, the raw spectral reflectance and absorbance data were treated using the fractional derivative order from the 0.0 to the 2.0 order (order interval: 0.2). The ratio of performance to deviation (RPD), determinant coefficients of calibration ([Formula: see text]), root mean square errors of calibration (RMSEC), determinant coefficients of prediction ([Formula: see text]), and root mean square errors of prediction (RMSEP) were applied to assess the performance of predicting models. The results showed that models built on the fractional derivative order performed better than when using the classic integer derivative. Comparison of the predictive effects of 22 models for estimating clay content, calibrated by PLSR, showed that those models based on the fractional derivative 1.8 order of spectral reflectance ([Formula: see text] = 0.907, RMSEC = 0.425%, [Formula: see text] = 0.916, RMSEP = 0.364%, and RPD = 2.484 ≥ 2.000) and absorbance ([Formula: see text] = 0.888, RMSEC = 0.446%, [Formula: see text] = 0.918, RMSEP = 0.383% and RPD = 2.511 ≥ 2.000) were most effective. Furthermore, they performed well in quantitative estimations of the clay content of soils in the study area.

A new computing approach for power signal modeling using fractional adaptive algorithms

Estimating the harmonic parameters is fundamental requirement for signal modelling in a power supply system. In this study, exploration and exploitation in fractional adaptive signal processing (FrASP) is carried out for identification of parameters in power signals. We design FrASP algorithms based on recently introduced variants of generalized least mean square (LMS) adaptive strategies for parameter estimation of the model. The performance of the proposed fractional adaptive schemes is evaluated for number of scenarios based on step size and noise variations. Results of the simulated system for sufficient large number of independent runs validated the reliability and effectiveness of the given methods through different performance measures in terms of mean square error, variance account for, and Nash Sutcliffe efficiency.

Design of minimum multiplier fractional order differentiator based on lattice wave digital filter

In this paper, a novel design of fractional order differentiator (FOD) based on lattice wave digital filter (LWDF) is proposed which requires minimum number of multiplier for its structural realization. Firstly, the FOD design problem is formulated as an optimization problem using the transfer function of lattice wave digital filter. Then, three optimization algorithms, namely, genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimal LWDF coefficients. The realization of FOD using LWD structure increases the design accuracy, as only N number of coefficients are to be optimized for Nth order FOD. Finally, two design examples of 3rd and 5th order lattice wave digital fractional order differentiator (LWDFOD) are demonstrated to justify the design accuracy. The performance analysis of the proposed design is carried out based on magnitude response, absolute magnitude error (dB), root mean square (RMS) magnitude error, arithmetic complexity, convergence profile and computation time. Simulation results are attained to show the comparison of the proposed LWDFOD with the published works and it is observed that an improvement of 29% is obtained in the proposed design. The proposed LWDFOD approximates the ideal FOD and surpasses the existing ones reasonably well in mid and high frequency range, thereby making the proposed LWDFOD a promising technique for the design of digital FODs.

State of charge estimation of lithium-ion batteries using fractional order sliding mode observer

This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov's stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estimation method is effective, and the designed observers have good performance.

An efficient closed-form design method for nearly perfect reconstruction of non-uniform filter bank

In this paper, an efficient closed form method for the design of multi-channel nearly perfect reconstruction of non-uniform filter bank with the prescribed stopband attenuation and channel overlapping is presented. In this method, the design problem of multi-channel non-uniform filter bank (NUFB) is considered as the design of a prototype filter whose magnitude response at quadrature frequency is 0.707, which is exploited for finding the optimum passband edge frequency through empirical formula instead of using single or multivariable optimization technique. Two main attributes used in assessing the performance of filter bank are peak reconstruction error (PRE) and computational time (CPU time). As compared to existing methods, this method is very simple and easy to implement for NUFBs. To implement this algorithm, a Matlab program has been developed, and several examples are presented to illustrate the performance of proposed method.

Optimal fractional delay-IIR filter design using cuckoo search algorithm

This paper applied a novel global meta-heuristic optimization algorithm, cuckoo search algorithm (CSA) to determine optimal coefficients of a fractional delay-infinite impulse response (FD-IIR) filter and trying to meet the ideal frequency response characteristics. Since fractional delay-IIR filter design is a multi-modal optimization problem, it cannot be computed efficiently using conventional gradient based optimization techniques. A weighted least square (WLS) based fitness function is used to improve the performance to a great extent. FD-IIR filters of different orders have been designed using the CSA. The simulation results of the proposed CSA based approach have been compared to those of well accepted evolutionary algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The performance of the CSA based FD-IIR filter is superior to those obtained by GA and PSO. The simulation and statistical results affirm that the proposed approach using CSA outperforms GA and PSO, not only in the convergence rate but also in optimal performance of the designed FD-IIR filter (i.e., smaller magnitude error, smaller phase error, higher percentage improvement in magnitude and phase error, fast convergence rate). The absolute magnitude and phase error obtained for the designed 5th order FD-IIR filter are as low as 0.0037 and 0.0046, respectively. The percentage improvement in magnitude error for CSA based 5th order FD-IIR design with respect to GA and PSO are 80.93% and 74.83% respectively, and phase error are 76.04% and 71.25%, respectively.