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Electro-hydraulic actuator system (EHAS) has imposed a challenge in the research community for accurate mathematical modeling and identification due to non-linearities. In this paper, autoregressive exogenous (ARX) structure is used for EHAS modeling and identification is performed by exploiting the competency of atomic physics-based chaotic atom search optimization (CASO) that adapts ten chaotic maps (Chebyshev, Circle, Gauss, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal and Tent) in position update of atom search optimization (ASO). The fitness/merit function of the EHAS model is developed in mean-square error (MSE) sense between desired and approximated values. Simulations and analysis show that ASO with a chaotic logistic map (CASO5) performs better than the ASO and its other chaotic variants, as well as other recently introduced metaheuristics for diverse variations in the system model. Statistics based on MSE, learning plots, results of autonomous trials and average fitness analyses verify the consistency and reliability of the CASO5 for the identification of the EHAS model. [ABSTRACT FROM AUTHOR]

In this article, a chaotic computing paradigm is investigated for the parameter estimation of the autoregressive exogenous (ARX) model by exploiting the optimization knacks of an improved chaotic grey wolf optimizer (ICGWO). The identification problem is formulated by defining a mean square error-based fitness function between true and estimated responses of the ARX system. The decision parameters of the ARX model are calculated by ICGWO for various populations, generations, and noise levels. The comparative performance analyses with standard counterparts indicate the worth of the ICGWO for ARX model identification, while the statistical analyses endorse the efficacy of the proposed chaotic scheme in terms of accuracy, robustness, and reliability. [ABSTRACT FROM AUTHOR]

Swarm-based metaheuristics have shown significant progress in solving different complex optimization problems, including the parameter identification of linear, as well as nonlinear, systems. Nonlinear systems are inherently stiff and difficult to optimize and, thus, require special attention to effectively estimate their parameters. This study investigates the parameter identification of an input nonlinear autoregressive exogenous (IN-ARX) model through swarm intelligence knacks of the nonlinear marine predators' algorithm (NMPA). A detailed comparative analysis of the NMPA with other recently introduced metaheuristics, such as Aquila optimizer, prairie dog optimization, reptile search algorithm, sine cosine algorithm, and whale optimization algorithm, established the superiority of the proposed scheme in terms of accurate, robust, and convergent performances for different noise and generation variations. The statistics generated through multiple autonomous executions represent box and whisker plots, along with the Wilcoxon rank-sum test, further confirming the reliability and stability of the NMPA for parameter estimation of IN-ARX systems. [ABSTRACT FROM AUTHOR]

Fractional calculus tools have been exploited to effectively model variety of engineering, physics and applied sciences problems. The concept of fractional derivative has been incorporated in the optimization process of least mean square (LMS) iterative adaptive method. This study exploits the recently introduced enhanced fractional derivative based LMS (EFDLMS) for parameter estimation of power signal formed by the combination of different sinusoids. The EFDLMS addresses the issue of fractional extreme points and provides faster convergence speed. The performance of EFDLMS is evaluated in detail by taking different levels of noise in the composite sinusoidal signal as well as considering various fractional orders in the EFDLMS. Simulation results reveal that the EDFLMS is faster in convergence speed than the conventional LMS (i.e., EFDLMS for unity fractional order). [ABSTRACT FROM AUTHOR]

A recommender system not only "gains users' confidence" but also helps them in other ways, such as reducing their time spent and effort. To gain users' confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the users' interest by tracking the users' transactional behavior to provide a fast and highly related set of top recommendations out of thousands of products. The standard ranking-based models, i.e., the denoising auto-encoder (DAE) and collaborative denoising auto-encoder (CDAE), exploit positive-only feedback without utilizing the ratings' ranks for the full set of observed ratings. To confirm the rank of observed ratings (either low or high), a confidence value for each rating is required. Hence, an improved, confidence-integrated DAE is proposed to enhance the performance of the standard DAE for solving recommender systems problems. The correctness of the proposed method is authenticated using two standard MovieLens datasets such as ML-1M and ML-100K. The proposed study acts as a vital contribution for the design of an efficient, robust, and accurate algorithm by learning prominent latent features used for fast and accurate recommendations. The proposed model outperforms the state-of-the-art methods by achieving improved P@10, R@10, NDCG@10, and MAP scores. [ABSTRACT FROM AUTHOR]

The mathematical modelling and optimization of nonlinear problems arising in diversified engineering applications is an area of great interest. The Hammerstein structure is widely used in the modelling of various nonlinear processes found in a range of applications. This study investigates the parameter optimization of the nonlinear Hammerstein model using the abilities of the marine predator algorithm (MPA) and the key term separation technique. MPA is a population-based metaheuristic inspired by the behavior of predators for catching prey, and utilizes Brownian/Levy movement for predicting the optimal interaction between predator and prey. A detailed analysis of MPA is conducted to verify the accurate and robust behavior of the optimization scheme for nonlinear Hammerstein model identification. [ABSTRACT FROM AUTHOR]

Nature-inspired metaheuristic algorithms have gained great attention over the last decade due to their potential for finding optimal solutions to different optimization problems. In this study, a metaheuristic based on the dwarf mongoose optimization algorithm (DMOA) is presented for the parameter estimation of an autoregressive exogenous (ARX) model. In the DMOA, the set of candidate solutions were stochastically created and improved using only one tuning parameter. The performance of the DMOA for ARX identification was deeply investigated in terms of its convergence speed, estimation accuracy, robustness and reliability. Furthermore, comparative analyses with other recent state-of-the-art metaheuristics based on Aquila Optimizer, the Sine Cosine Algorithm, the Arithmetic Optimization Algorithm and the Reptile Search algorithm—using a nonparametric Kruskal–Wallis test—endorsed the consistent, accurate performance of the proposed metaheuristic for ARX identification. [ABSTRACT FROM AUTHOR]

Swarm intelligence-based metaheuristic algorithms have attracted the attention of the research community and have been exploited for effectively solving different optimization problems of engineering, science, and technology. This paper considers the parameter estimation of the control autoregressive (CAR) model by applying a novel swarm intelligence-based optimization algorithm called the Aquila optimizer (AO). The parameter tuning of AO is performed statistically on different generations and population sizes. The performance of the AO is investigated statistically in various noise levels for the parameters with the best tuning. The robustness and reliability of the AO are carefully examined under various scenarios for CAR identification. The experimental results indicate that the AO is accurate, convergent, and robust for parameter estimation of CAR systems. The comparison of the AO heuristics with recent state of the art counterparts through nonparametric statistical tests established the efficacy of the proposed scheme for CAR estimation. [ABSTRACT FROM AUTHOR]

• This study presents a novel fractional order adaptive algorithm, called MIFLMS. • The MIFLMS extends the scalar innovation into a vector innovation. • It reveals a faster convergence speed than the FLMS with no noticeable increase in the computational burden. • The proposed algorithm effectively estimates the parameters of nonlinear systems. • The MIFLMS is more robust than the FLMS and provide consistent accurate and convergent performance. The development of procedures based on fractional calculus is an emerging research area. This paper presents a new perspective regarding the fractional least mean square (FLMS) adaptive algorithm, called multi innovation FLMS (MIFLMS). We verify that the iterative parameter adaptation mechanism of the FLMS uses merely the current error value (scalar innovation). The MIFLMS expands the scalar innovation into a vector innovation (error vector) by considering data over a fixed window at each iteration. Therefore, the MIFLMS yields better convergence speed than the standard FLMS by increasing the length of innovation vector. The superior performance of the MIFLMS is verified through parameter identification problem of input nonlinear systems. The statistical performance indices based on multiple independent trials confirm the consistent accuracy and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

In contemporary power systems, harmonics as undesired electrical phenomena, have drawn considerable attention of the research community investigating in design and development of optimal electrical networks. Harmonics affect the power electronics devices with a number of negative impacts, including higher power losses, worse power quality, and interference with other delicate grid connected equipment. An objective function of inter- and sub-harmonics is constructed for joint estimation of amplitude and phase with known frequency. Accurate estimation of the harmonics model is carried out with stupendous knacks of raptor-inspired Harris Hawks optimization algorithm (HHOA), a revolutionary population-based, nature-motivated optimization approach. The primary sources of inspiration for HHOA are Harris Hawks cooperative demeanor and surprise pounce chasing style in nature. The HHOA’s performance is assessed for harmonics parameter estimation with several noise conditions, differing particle sizes and iterations. The proposed HHOA-based estimation technique provides accurate, convergent and robust performance for harmonics estimation. The reliable level of fitness is achieved consistently in the range of 10−3 to 10−10, an evidence of valuable precision, stability and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This study presents an astrophysics-inspired transit search optimization (TSO) algorithm based on exoplanet search divided into five phases: galaxy phase, star phase, transit phase, neighbor phase and exploitation phase for effective parameter estimation of fractional Hammerstein control autoregressive (Fr-HCAR) systems. Various physical phenomena and real processes can be modeled with Fr-HCAR systems and estimating the Fr-HCAR parameters becomes a vital task. The mean-square error (MSE)-based criterion function is developed, and efficacy of the TSO for Fr-HCAR identification is deeply analyzed for different fractional orders, disturbance levels and degrees of freedom. The TSO remained accurate, convergent, robust and stable for all variations in Fr-HCAR but the accuracy level degrades a little bit for high disturbance and increased degrees of freedom. The reliability and trustworthiness of the TSO for Fr-HCAR identification are endorsed through statistical analyses conducted on sufficient autonomous executions of the scheme. [ABSTRACT FROM AUTHOR]

• The fractional gradient based innovative fractional order LMS (I-FOLMS) algorithm is presented for power signal estimation. • The I-FOLMS is fast in terms of convergence for high fractional orders and good at steady state for low fractional orders. • The effectiveness of the I-FOLMS is verified through comparison with the standard FOLMS for different fractional orders. Parameter estimation is an important issue for the quality monitoring and reliability assessment of power systems. In this study, an innovative fractional order least mean square (I-FOLMS) adaptive algorithm is presented for an effective parameter estimation. The I-FOLMS algorithm exploits the fractional gradient in its recursive parameter update mechanism, because its performance can be tuned by means of the fractional order. High values of the fractional order are good for fast convergence, but lead to steady state mis-adjustments. While, low values provide a smooth steady state behavior, but require a compromise in the convergence rate. The effective performance of I-FOLMS is verified and validated through two numerical examples of power signals estimation for different levels of noise variance and values of the fractional orders. [ABSTRACT FROM AUTHOR]

Fractional calculus plays a fundamental role in understanding the physics of nonlinear systems due to its heritage of uncertainty, nonlocality and complexity. In this study, novel sign fractional least mean square (F-LMS) algorithms are designed for ease in hardware implementation by applying sign function to input data and estimation error corresponding to first and fractional-order derivative terms in weight update mechanism of the standard F-LMS method. Theoretical expressions are derived for proposed sign F-LMS and its variants; strength of methods for different fractional orders is evaluated numerically through computer simulations for parameter estimation problem based on nonlinear Hammerstein system for low and high signal–noise variations. Comparison of the results from true parameters of the model illustrates the worth of the scheme in terms of accuracy, convergence and robustness. The stability and viability of design methodologies are examined through statistical observations on sufficiently large number of independent runs through mean square deviation and Nash–Sutcliffe efficiency performance indices. [ABSTRACT FROM AUTHOR]

The strength of evolutionary computational heuristic paradigms is exploited for parameter estimation of power signal modeling problems by incorporating differential evolution (DE), genetic algorithms (GAs) and pattern search (PS) methodologies. The objective function of power signal harmonics is constructed by utilizing the power of approximation theory in mean squared error sense. The stiff optimization task of signal harmonics is performed with heuristic solvers DE, GAs and PS that provide efficacy, fast convergence rate and avoid getting trapped in local minima. Statistics reveal that DE outperforms its counterparts in terms of accuracy, robustness and complexity measures. [ABSTRACT FROM AUTHOR]

In this study, adaptive filtering paradigm-based kernel least mean square (KLMS) algorithm is developed for feed-forwarded active noise control (ANC) systems by exploiting the strength of activation functions of neural network (NN) as kernels. The transfer functions NN based on logistic, tan-sigmoid and inverse-tan kernels are introduced as a variant of KLMS, normalized KLMS and affine projection KLMS algorithms. All three proposed adaptive filtering strategies are implemented for optimization of design parameters of ANC system of a headset with nonlinear noise interference under several scenarios based on tonal, narrowband, broadband and varying acoustic path. Comparison studies on the basis of detailed numerical experimentation are conducted to establish the worth of the proposed methodologies. [ABSTRACT FROM AUTHOR]

In the present study, strength of fractional-order adaptive signal processing through fractional Volterra least mean square (FV-LMS) algorithm is exploited for Hammerstein nonlinear control autoregressive model (HN-CAR) identification. The FV-LMS method is a generalization of standard V-LMS by taking usual gradient as well as fractional derivative of cost function in the optimization process. The adaptive scheme FV-LMS is applied to HN-CAR systems for different variations of step size parameter, noise and fractional order. Comparative study of the optimized design variables by FV-LMS from true values of HN-CAR model is carried out using performance metrics of fitness and mean square error, to establish its effectiveness. The performance of the proposed scheme is validated through comparison with standard V-LMS based on multiple independent runs of the scheme. [ABSTRACT FROM AUTHOR]

Highlights • Novel normalized fractional methods for automatic adjustment of the learning rate. • Better adaptation performance than standard fractional order gradient methods. • Reliabilty is proven through MSE, NSE and VAF evaluation metrics. • Application of proposed methods to nonlinear system identification. • Validation through accurate estimation of electrically stimulated muscle model. Abstract The trend of applying mathematical foundations of fractional calculus to solve problems arising in nonlinear sciences, is an emerging area of research with growing interest especially in communication, signal analysis and control. In the present study, normalized fractional adaptive strategies are exploited for automatic tuning of the step size parameter in nonlinear system identification based on Hammerstein model. The brilliance of the methodology is verified by mean of viable estimation of electrically stimulated muscle model used in rehabilitation of paralyzed muscles. The dominance of the schemes is established by comparing the results with standard counterparts in case of different noise levels and fractional order variations. The results of the statistical analyses for sufficient independent runs in terms of Nash-Sutcliffe efficiency, variance account for and mean square error metrics validated the consistent accuracy and reliability of the proposed methods. The proposed exploitation of fractional calculus concepts makes a firm branch of nonlinear investigation in arbitrary order gradient-based optimization schemes. [ABSTRACT FROM AUTHOR]

In the present work, strength of momentum least mean square (MLMS) algorithm is exploited for nonlinear system identification problems represented with Hammerstein model. The MLMS algorithm uses the previous gradient information to estimate the current weights instead of using only current value of gradient; thus, it is faster in the convergence and less probable to trap in local minima. The perfection of the design scheme is certified through effective parameter estimation of nonlinear Hammerstein control autoregressive models. The robustness of the scheme is established by examining the performance for different levels of noise variance. The performance comparison through mean square error and Nash-Sutcliffe efficiency parameters, calculated for sufficiently large number of multiple runs, proves the intrinsic worth of MLMS algorithm in system identification. [ABSTRACT FROM AUTHOR]

In the present study, a novel generalization of Volterra least mean square (V-LMS) algorithm to fractional order is presented by exploiting the renowned strength of fractional adaptive signal processing. The fractional derivative term is introduced in weight adaptation mechanism of standard V-LMS to derive the recursive relations for modified V-LMS (MV-LMS) algorithm. The design scheme of MV-LMS algorithm is applied to parameter identification of Box-Jenkins system by taking different values of fractional orders, step-size variations and small to high signal-to-noise ratios. The proposed adaptive variables of MV-LMS are compared from true parameters of Box-Jenkins systems as well as with the results of the V-LMS for each case. The correctness and reliability of the given scheme MV-LMS are also validated from the results of statistical performance measures calculated on large dataset based on multiple independent runs. [ABSTRACT FROM AUTHOR]

In this paper, strength of fractional adaptive signal processing is exploited for parameter identification of control autoregressive autoregressive (CARAR) systems using normalized version of fractional least mean square (FLMS) and its recently introduced modification of type 1 and 2. The adaptation performance of the proposed normalized FLMS methods is compared with standard counterparts for CARAR identification model by taking different noise levels as well as fractional orders. The results of the statistical analyses are used to validate the consistency of the proposed normalized fractional adaptive methodologies in terms of convergence, accuracy and robustness. The reliability and effectiveness of the design schemes is further validated through consistently approaching the desired identification parameters based on performance metrics of mean square error, variance account for and Nash–Sutcliffe efficiency. [ABSTRACT FROM AUTHOR]

Fractional adaptive algorithms have given rise to new dimensions in parameter estimation of control and signal processing systems. In this paper, we present novel fractional calculus based LMS algorithm with fast convergence properties and potential ability to avoid being trapped into local minima. We test our proposed algorithm for parameter estimation of power signals and compare it with other state-of-the-art fractional and standard LMS algorithms under different noisy conditions. Our proposed algorithm outperforms other LMS algorithms in terms of convergence rate and accuracy. [ABSTRACT FROM AUTHOR]

In this study, the strength of fractional signal processing is exploited in designing fractional adaptive algorithms for parameter estimation of input nonlinear Box–Jenkins (INBJ) systems. The idea is to develop fractional least mean square (F-LMS) and auxiliary model F-LMS (AM-FLMS) algorithms with three values of fractional order to adopt the variables of INBJ system for different scenarios based on noise and step size variations. The comparative study of the proposed results is made with true values of the system, as well as, with the results of Volterra and Kernel LMS adaptive algorithms in order to establish the correctness of the design scheme. The accuracy and convergence of the proposed scheme is analyzed on large data set generated through statistical analysis based on sufficient number of independent runs of the algorithm and result in term of performance measures established the worth of the scheme. [ABSTRACT FROM AUTHOR]

In the present study, single and two-stage least mean square (LMS) adaptive strategies based on fractional signal processing are developed for parameter estimation of controlled autoregressive moving average (CARMA) systems. The main idea is to use fractional LMS identification (FLMSI) and two-stage FLMSI (TS-FLMSI) algorithms for CARMA model that is decomposed into a system and noise models. The performance analyses for both proposed FLMSI and TS-FLMSI schemes are conducted based on adapting the prior known design parameters of the system and comparing the results with standard adaptive algorithms. The accuracy and convergence of the design schemes are verified and validated through the results of statistical analyses based on sufficient number of independent runs to adapt CARMA system. Comparative studies established the dominance of single and two-stage fractional adaptive algorithms over other counterpart in term of model accuracy and reliability in case of different scenarios based on variant signal to noise ratios and step size parameters. [ABSTRACT FROM AUTHOR]

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness. [ABSTRACT FROM AUTHOR]

Most real-time systems are nonlinear in nature, and their optimization is very difficult due to inherit stiffness and complex system representation. The computational intelligent algorithms of evolutionary computing paradigm (ECP) effectively solve various complex, nonlinear optimization problems. The differential evolution algorithm (DEA) is one of the most important approaches in ECP, which outperforms other standard approaches in terms of accuracy and convergence performance. In this study, a novel application of a recently proposed variant of DEA, the so-called, maximum-likelihood-based, adaptive, differential evolution algorithm (ADEA), is investigated for the identification of nonlinear Hammerstein output error (HOE) systems that are widely used to model different nonlinear processes of engineering and applied sciences. The performance of the ADEA is evaluated by taking polynomial- and sigmoidal-type nonlinearities in two case studies of HOE systems. Moreover, the robustness of the proposed scheme is examined for different noise levels. Reliability and consistent accuracy are assessed through multiple independent trials of the scheme. The convergence, accuracy, robustness and reliability of the ADEA are carefully examined for HOE identification in comparison with the standard counterpart of the DEA. The ADEA achieves the fitness values of 1.43 × 10−8 and 3.46 × 10−9 for a population size of 80 and 100, respectively, in the HOE system identification problem of case study 1 for a 0.01 nose level, while the respective fitness values in the case of DEA are 1.43 × 10−6 and 3.46 × 10−7. The ADEA is more statistically consistent but less complex when compared to the DEA due to the extra operations involved in introducing the adaptiveness during the mutation and crossover. The current study may consider the approach of effective nonlinear system identification as a step further in developing ECP-based computational intelligence. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The efficient parameter estimation of harmonics is required to effectively design filters to mitigate their adverse effects on the power quality of electrical systems. In this study, a fractional order swarming optimization technique is proposed for the parameter estimation of harmonics normally present in industrial loads. The proposed fractional order particle swarm optimization (FOPSO) effectively estimates the amplitude and phase parameters corresponding to the first, third, fifth, seventh and eleventh harmonics. The performance of the FOPSO was evaluated for ten fractional orders with noiseless and noisy scenarios. The robustness efficiency of the proposed FOPSO was analyzed by considering different levels of additive white Gaussian noise in the harmonic signal. Monte Carlo simulations confirmed the reliability of the FOPSO for a lower fractional order (λ = 0.1) with a faster convergence rate and no divergent run compared to other fractional orders as well as to standard PSO (λ = 1). [ABSTRACT FROM AUTHOR]

The knacks of evolutionary and swarm computing paradigms have been exploited to solve complex engineering and applied science problems, including parameter estimation for nonlinear systems. The population-based computational heuristics applied for parameter identification of nonlinear systems estimate the redundant parameters due to an overparameterization problem. The aim of this study was to exploit the key term separation (KTS) principle-based identification model with adaptive evolutionary computing to overcome the overparameterization issue. The parameter estimation of Hammerstein control autoregressive (HC-AR) systems was conducted through integration of the KTS idea with the global optimization efficacy of genetic algorithms (GAs). The proposed approach effectively estimated the actual parameters of the HC-AR system for noiseless as well as noisy scenarios. The simulation results verified the accuracy, convergence, and robustness of the proposed scheme. While consistent accuracy and reliability of the designed approach was validated through statistical assessments on multiple independent trials. [ABSTRACT FROM AUTHOR]

In this study, a novel application of differential evolution (DE)-based computational heuristics is proposed for the identification of Hammerstein structures representing the electrically stimulated muscle (ESM) models as a part of rehabilitation interventions for the stock patient to prevent the post-spinal cord injury atrophy. The strength of approximation theory is incorporated for defining the fitness function for ESM system based on mean square deviation between actual and estimated responses. DE, genetic algorithms (GAs), particle swarm optimization (PSO), pattern search (PS), and simulated annealing (SA) are used as optimization mechanisms to identify the ESM models with input nonlinearities of sigmoidal, polynomial, and spline kernels for noiseless and noisy environments. Comparative studies based on detailed statistics establish the worth of DE-based heuristics over its counterparts GAs, PSO, PS, and SA in terms of accuracy, convergence, robustness, and efficiency for the identification of ESM models arising in rehabilitation of the stock patients. [ABSTRACT FROM AUTHOR]

Fast and effective recommender systems are fundamental to fulfill the growing requirements of the e-commerce industry. The strength of matrix factorization procedure based on stochastic gradient descent (SGD) algorithm is exploited widely to solve the recommender system problem. Modern computing paradigms are designed by utilizing the concept of fractional gradient in standard SGD and outperform the standard counterpart. The performance of fractional SGD improves considerably by adaptively tuning the learning rate parameter. A nonlinear computing paradigm based on normalized version of fractional SGD is developed in this paper to investigate the adaptive behavior of learning rate with novel application to recommender systems. The accuracy of the proposed approach is verified through root mean square error metric by using different latent features, learning rates, fractional orders and datasets. The superiority of the designed method is validated through comparison with the state-of-the-art counterparts. [ABSTRACT FROM AUTHOR]

In this study, nature-inspired computational intelligence is exploited for active noise control (ANC) systems using variants of particle swarm optimization (PSO) algorithm and its memetic combination with efficient local search technique based on active-set (AS), interior-point (IP), Nelder–Mead (NM) and sequential quadratic programming (SQP) algorithms. In ANC, filtered extended least mean square algorithm is normally used for finding the optimal parameters of the linear finite-impulse response filter, which is more likely to trap in local minima (LM). The issue of LM problem is effectively handled with competence of nature-inspired heuristics by developing four variants of memetic computing approaches based on PSO-NM, PSO-AS, PSO-IP, and PSO-SQP in order to adapt the design variables of ANC with linear and nonlinear primary and secondary paths by taking input noise interferences of pure sinusoidal, random and complex random types. The comparative studies of proposed schemes through statistical performance indices have established the worth of the schemes in terms of accuracy, convergence and complexity parameters. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a novel design of intelligent neuro-supervised networks (INSNs) in order to study the dynamics of a mathematical model for Parkinson's disease illness (PDI), governed with three differential classes to represent the rhythms of brain electrical activity measurements at different locations in the cerebral cortex. The proposed INSNs are constructed by exploiting the knacks of multilayer structure neural networks back-propagated with the Levenberg–Marquardt (LM) and Bayesian regularization (BR) optimization approaches. The reference data for the grids of input and the target samples of INSNs were formulated with a reliable numerical solver via the Adams method for sundry scenarios of PDI models by way of variation of sensor locations in order to measure the impact of the rhythms of brain electrical activity. The designed INSNs for both backpropagation procedures were implemented on created datasets segmented arbitrarily into training, testing, and validation samples by optimization of mean squared error based fitness function. Comparison of outcomes on the basis of exhaustive simulations of proposed INSNs via both LM and BR methodologies was conducted with reference solutions of PDI models by means of learning curves on MSE, adaptive control parameters of algorithms, absolute error, histogram error plots, and regression index. The outcomes endorse the efficacy of both INSNs solvers for different scenarios in PDI models, but the accuracy of the BR-based method is relatively superior, albeit at the cost of slightly more computations. [ABSTRACT FROM AUTHOR]

In this paper, a defused decision boundary which renders misclassification issues due to the presence of cross-pairs is investigated. Cross-pairs retain cumulative attributes of both classes and misguide the classifier due to the defused data samples' nature. To tackle the problem of the defused data, a Tomek Links technique targets the cross-pair majority class and is removed, which results in an affine-segregated decision boundary. In order to cope with a Theft Case scenario, theft data is ascertained and synthesized randomly by using six theft data variants. Theft data variants are benign class appertaining data samples which are modified and manipulated to synthesize malicious samples. Furthermore, a K-means minority oversampling technique is used to tackle the class imbalance issue. In addition, to enhance the detection of the classifier, abstract features are engineered using a stochastic feature engineering mechanism. Moreover, to carry out affine training of the model, balanced data are inputted in order to mitigate class imbalance issues. An integrated hybrid model consisting of Bi-Directional Gated Recurrent Units and Bi-Directional Long-Term Short-Term Memory classifies the consumers, efficiently. Afterwards, robustness performance of the model is verified using an attack vector which is subjected to intervene in the model's efficiency and integrity. However, the proposed model performs efficiently on such unseen attack vectors. [ABSTRACT FROM AUTHOR]

In this paper, weighted differential evolution (WDE)-based evolutionary heuristic computing is presented for parameter estimation of nonlinear dynamics of the electrically stimulated muscle system based on a Hammerstein model structure as an element of rehabilitation program for the stroke patient. The approximation theory is defined on the basis of mean square error of actual and estimated responses for the system's fitness function. Optimization technique based on WDE is employed to find the optimal parameters of ESM model with sigmoidal, polynomial and spline as input nonlinear functions. Statistical analysis verified the worth of WDE as computational heuristic technique for identification of electrically stimulated muscle system. [ABSTRACT FROM AUTHOR]

In this presented communication, a novel design of intelligent Bayesian regularization backpropagation networks (IBRBNs) based on stochastic numerical computing is presented. The dynamics of peristaltic motion of a third-grade fluid in a planar channel is examined by IBRBNs using multilayer structure modeling competency of neural networks trained with efficient optimization ability of Bayesian regularization method. The reference dataset used as inputs and targets parameters of IBRBN has been obtained via the state-of-the-art Adams numerical method. The data of solution dynamics is created for multiple scenarios of the peristaltic transport model by varying the volume flow rate, material parametric of a third-grade fluid model, wave amplitude, and inclination angles. The designed integrated IBRBNs are constructed by exploiting training, testing, and validation operations at each epoch via optimization of a figure of merit on mean square error sense. Exhaustive simulation of IBRBNs with comparison on mean square error, histograms, and regression index substantiated the precision, stability, and reliability to solve the peristaltic transport model. [ABSTRACT FROM AUTHOR]

Estimation of the effectiveness of Au nanoparticles concentration in peristaltic flow through a curved channel by using a data driven stochastic numerical paradigm based on artificial neural network is presented in this study. In the modelling, nano composite is considered involving multi-walled carbon nanotubes coated with gold nanoparticles with different slip conditions. Modeled differential system of the physical problem is numerically analyzed for different scenarios to predict numerical data for velocity and temperature by Adams Bashforth method and these solutions are used as a reference dataset of the networks. Data is processed by segmentation into three categories i.e., training, validation and testing while Levenberg–Marquart training algorithm is adopted for optimization of networks results in terms of performance on mean square errors, train state plots, error histograms, regression analysis, time series responses, and auto-correlation, which establish the accurate and efficient recognition of trends of the system. [ABSTRACT FROM AUTHOR]

The designed fractional order Stuxnet, the virus model, is analyzed to investigate the spread of the virus in the regime of isolated industrial networks environment by bridging the air-gap between the traditional and the critical control network infrastructures. Removable storage devices are commonly used to exploit the vulnerability of individual nodes, as well as the associated networks, by transferring data and viruses in the isolated industrial control system. A mathematical model of an arbitrary order system is constructed and analyzed numerically to depict the control mechanism. A local and global stability analysis of the system is performed on the equilibrium points derived for the value of α = 1. To understand the depth of fractional model behavior, numerical simulations are carried out for the distinct order of the fractional derivative system, and the results show that fractional order models provide rich dynamics by means of fast transient and super-slow evolution of the model's steady-state behavior, which are seldom perceived in integer-order counterparts. [ABSTRACT FROM AUTHOR]

In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts. [ABSTRACT FROM AUTHOR]

This study presents a novel implementation of evolutionary heuristics through backtracking search optimization algorithm (BSA) for accurate, efficient and robust parameter estimation of power signal models. The mathematical formulation of fitness function is accomplished by exploiting the approximation theory in mean squared errors between actual and estimated responses, as well as, true and approximated decision variables. Variants of BSA-based meta-heuristics are applied for parameter estimation problem of power signals for identification of amplitude, frequency and phase parameters for different scenarios of noise variation. Analysis of performance evaluation for BSAs is conducted through exhaustive statistical observations in terms of mean weight deviation, root mean square error and Thiel inequality coefficient-based assessment metrics, as well as, ANOVA tests for statistical significance. [ABSTRACT FROM AUTHOR]

• Novel application of BSAs for effective estimation of amplitude and DOA parameters. • Performance verification of BSA variants for 2, 3 and 4 far field sources based model. • Viability of proposed BSA variants for both noiseless and noisy cases of the models. • Validation of the performance of BSA on Monte-Carlo simulations and their statistics. In this study, the strength of nature inspired computing (NIC) paradigm through backtracking search algorithms (BSA) is exploited for measurement of amplitude and direction of arrival (DOA) parameters of sources impinging on uniform linear array from Fraunhofer zone. The NIC techniques based on variant of BSAs are designed through varying the backtracking history and individual of the populations for effective optimization of the fitness evaluation function based on mean squared error between true and measured responses. Optimization mechanism of BSAs is applied for different degrees of freedom models of DOA from far field sources for noisy and noiseless environment. Comparative studies are conducted through outcomes of statistics based on multiple executions of each solver by means of different gauges of accuracy and complexity. [ABSTRACT FROM AUTHOR]

Aim of this research is to explore the strength of evolutionary and swarm intelligence techniques for parameter identification of control autoregressive moving average (CARMA) systems. The fitness function for CARMA system identification problem is formulated through error function created in mean square sense, and learning of unknown parameters of the system model is carried out with an effective global search techniques based on genetic algorithms and particle swarm optimization algorithm. Comparative study of the design methodology is conducted from actual parameters of the systems for different values of noise variance and degree of freedom in CARMA identification model. The correctness of the proposed scheme is validated through the results of various performance measures based on mean absolute error, mean weight deviation, variance account for and Theil's inequality coefficient, and their global variants for sufficiently large number of independent runs. [ABSTRACT FROM AUTHOR]

Abstract In this paper, strength of recently introduced nature inspired heuristic computing technique named fireworks algorithms (FWA) and its variants are exploited in the field of system identification based on active noise control (ANC) systems. Residual error based fitness function is constructed for ANC system and optimization of parameter is carried out with the help of fireworks, enhance fireworks and adaptive fireworks algorithms. The design scheme is applied to number of scenarios of ANC system for different primary and secondary paths. The designed methodology is evaluated for three different noise interferences based on sinusoidal and random signals. The scheme validated by means of accuracy and convergence operators through the results of statistics based on ample number of independent trails. The comparative study of results is also made for three variants of FWA to establish their worth in terms of precision, stability and complexity measures. [ABSTRACT FROM AUTHOR]