A novel design of fractional Mayer wavelet neural networks with application to the nonlinear singular fractional Lane-Emden systems

In this study, a novel stochastic computational frameworks based on fractional Meyer wavelet artificial neural network (FMW-ANN) is designed for nonlinear-singular fractional Lane-Emden (NS-FLE) differential equation. The modeling strength of FMW-ANN is used to transformed the differential NS-FLE system to difference equations and approximate theory is implemented in mean squared error sense to develop a merit function for NS-FLE differential equations. Meta-heuristic strength of hybrid computing by exploiting global search efficacy of genetic algorithms (GA) supported with local refinements with efficient active-set (AS) algorithm is used for optimization of design variables FMW-ANN., i.e., FMW-ANN-GASA. The proposed FMW-ANN-GASA methodology is implemented on NS-FLM for six different scenarios in order to exam the accuracy, convergence, stability and robustness. The proposed numerical results of FMW-ANN-GASA are compared with exact solutions to verify the correctness, viability and efficacy. The statistical observations further validate the worth of FMW-ANN-GASA for the solution of singular nonlinear fractional order systems.This paper is partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-097198-BI00 and Fundación Séneca de la Región de Murcia grant number 20783/PI/18

Identification of Input Nonlinear Control Autoregressive Systems Using Fractional Signal Processing Approach

A novel algorithm is developed based on fractional signal processing approach for parameter estimation of input nonlinear control autoregressive (INCAR) models. The design scheme consists of parameterization of INCAR systems to obtain linear-in-parameter models and to use fractional least mean square algorithm (FLMS) for adaptation of unknown parameter vectors. The performance analyses of the proposed scheme are carried out with third-order Volterra least mean square (VLMS) and kernel least mean square (KLMS) algorithms based on convergence to the true values of INCAR systems. It is found that the proposed FLMS algorithm provides most accurate and convergent results than those of VLMS and KLMS under different scenarios and by taking the low-to-high signal-to-noise ratio

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley–Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This paper has been partially supported by Fundación Séneca de la Región de Murcia grant numbers 20783/PI/18, and Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-0971-B-100

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors have not disclosed any funding

Enhanced Fractional Adaptive Processing Paradigm for Power Signal Estimation

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)

Numerical treatment for mathematical model of farming awareness in crop pest management

The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios

A predictive neuro-computing approach for micro-polar nanofluid flow along rotating disk in the presence of magnetic field and partial slip

The present study aims to design a Levenberg-Marquardt backpropagation neural network (LMB-NN) integrated numerical computing to investigate the problem of fluid mechanics governing the flow of magnetohydrodynamics micro-polar nanofluid flow over a rotating disk (MHD-MNRD) model along with the partial slip condition. In terms of PDEs, the basic system model MHD-MNRD is transformed into a system of non-linear ODEs by applying the similarity of transformations. For MHD-MNRD scenarios, the comparative dataset of the built LMB-NN procedure is formulated with the technique of Adams numerical by variation of micro-polar parameters, Brownian motion, Lewis number, magnetic parameter, velocity slip parameter and thermophoresis parameter. To compute the approximate solution for MHD-MNRD for various scenarios, validation, testing and training procedures are carried out in accordance to adjust the networks under the backpropagation procedure in terms of the mean square error (MSE). The efficiency of the designed LMB-NN methodology is highlighted by comparative study and performance analysis based on error histograms, MSE analysis, regression and correlation

Soft computing paradigms to find the numerical solutions of a nonlinear influenza disease model

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system

Novel FDIs-based data manipulation and its detection in smart meters’ electricity theft scenarios

Non-technical loss is a serious issue around the globe. Consumers manipulate their smart meter (SM) data to under-report their readings for financial benefit. Various manipulation techniques are used. This paper highlights novel false data injection (FDIs) techniques, which are used to manipulate the smart meter data. These techniques are introduced in comparison to six theft cases. Furthermore, various features are engineered to analyze the variance, complexity, and distribution of the manipulated data. The variance and complexity are created in data distribution when FDIs and theft cases are used to poison SM data, which is investigated through skewness and kurtosis analysis. Furthermore, to tackle the data imbalance issue, the proximity weighted synthetic oversampling (ProWsyn) technique is used. Moreover, a hybrid attentionLSTMInception is introduced, which is an integration of attention layers, LSTM, and inception blocks to tackle data dimensionality, misclassification, and high false positive rate issues. The proposed hybrid model outperforms the traditional theft detectors and achieves an accuracy of 0.95%, precision 0.97%, recall 0.94%, F1 score 0.96%, and area under-the-curve (AUC) score 0.98%