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

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

Voltage Stability Assessment and Enhancement in Power Systems

Voltage stability is a long standing issue in power systems and also is critical in the power system. This thesis aims to address the voltage stability problems. When wind generators reach maximum reactive power output, the bus voltage will operate near its steady-state stability limit. In order to avoid voltage instability, a dynamic L-index minimization approach is proposed by incorporating both wind generators and other reactive power resources. It then verifies the proposed voltage stability enhancement method using real data from load and wind generation in the IEEE 14 bus system. Additionally, power system is not necessary to always operate at the most voltage stable point as it requires high control efforts. Thus, we propose a novel L-index sensitivity based control algorithm using full Phasor measurement unit measurements for voltage stability enhancement. The proposed method uses both outputs of wind generators and additional reactive power compensators as control variables. The L-index sensitivity with respect to control variables is introduced. Based on these sensitivities, the control algorithm can minimise all the control efforts, while satisfying the predetermined L-index value. Additionally, a subsection control scheme is applied where both normal condition and weak condition are taken into account. It consists of the proposed L-index sensitivities based control algorithm and an overall L-index minimisation method. Threshold selection for the subsection control scheme is discussed and extreme learning machine is introduced for status fast classification to choose the method which has less power cost on the transmission line. Due to the high cost of PMUs, a voltage stability assessment method using partial Phasor measurement unit (PMU) measurements is proposed. Firstly, a new optimisation formulation is proposed that minimizes the number of PMUs considering the most sensitive buses. Then, extreme learning machine (ELM) is used for fast voltage estimation. In this way, the voltages at buses without PMUs can be rapidly obtained based on the PMUs measurements. Finally, voltage stability can be assessed by using L-index