Muhammad Asif Zahoor Raja

Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems

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. Novel single and two stage Fractional LMS algorithms are designed for CARMA systems.Validation and verification of proposed schemes for step size and noise variations.The designed algorithms outperformed their counterpart in accuracy and convergence.The statistical analysis established the consistent accuracy of the designed scheme.The illustrative worth of the scheme is its wider applicability to nonlinear systems.

Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP

In this paper, an efficient procedure based on the neural networks methodology is presented for the solution of the fuel ignition model in one dimension. The neural networks were optimised with the particle swarm optimisation algorithm hybridised with sequential quadratic programming. The accuracy and convergence of the scheme are analysed by Monte Carlo simulations and their statistical analyses for three test cases of the problem represented by Bratu-type equations. It was found that the hybrid approach converges in all cases, and can solve the problem with higher accuracy and reliability than most of the methodologies used so far to solve this problem.

Design of stochastic solvers based on genetic algorithms for solving nonlinear equations

Abstract In the present study, a novel intelligent computing approach is developed for solving nonlinear equations using evolutionary computational technique mainly based on variants of genetic algorithms (GA). The mathematical model of the equation is formulated by defining an error function. Optimization of fitness function is carried out with the competency of GA used as a tool for viable global search methodology. Comprehensive numerical experimentation has been performed on number of benchmark nonlinear algebraic and transcendental equations to validate the accuracy, convergence and robustness of the designed scheme. Comparative studies have also been made with available standard solution to establish the correctness of the proposed scheme. Reliability and effectiveness of the design approaches are validated based on results of statistical parameters.

Numerical treatment for nonlinear MHD Jeffery-Hamel problem using neural networks optimized with interior point algorithm

In this paper new computational intelligence techniques have been developed for the nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel flow problem using three different feed-forward artificial neural networks trained with an interior point method. The governing equation for the two-dimensional MHD Jeffery-Hamel flow problem is transformed into an equivalent third order nonlinear ordinary differential equation. Three neural network models using log-sigmoid, radial basis and tan-sigmoid activation functions are developed for the transformed equation in an unsupervised manner. The training of weights of each neural network is carried out with an interior point method. The proposed models are evaluated on different variants of the Jeffery-Hamel problem by varying the Reynolds number, angles of the walls and the Hartmann number. The accuracy, convergence and effectiveness of the designed models are validated through statistical analyses based on a sufficiently large number of independent runs. Comparative studies of the proposed solutions with standard numerical results, as well as recently reported solutions of analytic solvers illustrate the worth of the proposed solvers.

Numerical treatment for boundary value problems of Pantograph functional differential equation using computational intelligence algorithms

For the first time, stochastic numerical treatment of Pantograph functional differential equations is presented.Development of neural networks mathematical modeling in an unsupervised manner.Obtain...

Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory

In this research, the well-known non-linear Lane–Emden–Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.

Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes

Novel design of unsupervised ANNs for solving nanofluidic problems in mechanics.Hybrid computing GA-IPA is exploited for finding design parameters of networks.Design scheme is tested effectively on variant fluid flow and heat transfer scenarios.Correctness of scheme is verified by closely matched results from standard solutions.Statistical performance indices validate consistent accuracy and convergence. In the present study, a new soft computing framework is developed for solving nanofluidic problems based on fluid flow and heat transfer of multi-walled carbon nanotube (MWCNT) along a flat plate with Navier slip boundary with the help of artificial neural networks (ANNs), Genetic Algorithms (GAs), Interior-Point Algorithm (IPA), and hybridized approach GA-IPA. Original PDEs associated with the problem are transformed into system of nonlinear ODEs using similarity transformation. Mathematical model of transformed system is constructed by exploiting the strength of universal function approximation ability of ANNs and an unsupervised error function is formulated for the system in a least mean square sense. Learning of the design variable of the networks is carried out with GAs supported with IPA for rapid local convergence. The design scheme is applied to solve number of variants by taking water, engine oil, and kerosene oil as a base fluids mixed with different concentrations of MWCNTs. The reliability and effectiveness of the design scheme is measured with the help of results of statistical analysis based on sufficient large number of independent runs of the algorithms rather than single successful run. The comparative studies of the proposed solution are made with standard numerical results in order to establish the correctness of the given scheme.

A new adaptive strategy to improve online secondary path modeling in active noise control systems using fractional signal processing approach

In this paper, a new adaptive strategy based on fractional signal processing is proposed using multi-directional step size fractional least mean square algorithm for online secondary path modeling, which is a fundamental problem in practical active noise control systems, as opposed to the generally-employed increasing step size strategy that compromises model accuracy for faster convergence. The design approach presents step size strategy in relation with disturbance signal in the desired response of modeling filter which is not available directly so an indirect approach is used to track its variations. Comparative results for narrowband and broadband noise signals show that the proposed technique outperforms other state-of-the-art methods in terms of model accuracy and convergence rate. A new scheme is designed for noise control as shown in Fig. 3.The fractional LMS method is employed the ANC system.The scheme uses variable step sizes to achieve fast convergence.The proposed method achieves better performance in terms of accuracy and convergence speed.

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

A new stochastic intelligence method is developed to solve first Painleve equation.Design of three unsupervised ANN models that satisfying exactly initial conditions.Optimization capability of SQP is exploited for training of design parameter of ANNs.Accuracy and convergence are validated in term of various performance criterions.Impact on effectiveness of the models is investigated by varying neurons in ANNs. In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painleve equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.

Reliable numerical treatment of nonlinear singular Flierl-Petviashivili equations for unbounded domain using ANN, GAs, and SQP

Detail flow diagram of processes for obtaining the proposed solution of FP equation using neural networks trained with hybrid approach GA-SQP.Novel stochastic solver for boundary value problems of Flierl-Petvishivile equations.Strength of model is to avoid singularity and satisfy the conditions for unbounded domain.The accuracy of the approach is validated on three variants of two nonlinear problems.Detail simulations are performed to evaluate the reliability and effectiveness. In this paper, a novel intelligent computational approach is developed for finding the solution of nonlinear singular system governed by boundary value problems of Flierl-Petviashivili equations using artificial neural networks optimized with genetic algorithms, sequential quadratic programming technique, and their combinations. The competency of artificial neural network for universal function approximation is exploited in formulation of mathematical modelling of the equation based on an unsupervised error with specialty of satisfying boundary conditions at infinity. The training of the weights of the networks is carried out with memetic computing based on genetic algorithm used as a tool for reliable global search method, hybridized with sequential quadratic programming technique used as a tool for rapid local convergence. The proposed scheme is evaluated on three variants of the two boundary problems by taking different values of nonlinearity operators and constant coefficients. The reliability and effectiveness of the design approaches are validated through the results of statistical analyses based on sufficient large number of independent runs in terms of accuracy, convergence, and computational complexity. Comparative studies of the proposed results are made with state of the art analytical solvers, which show a good agreement mostly and even better in few cases as well. The intrinsic worth of the schemes is simplicity in the concept, ease in implementation, to avoid singularity at origin, to deal with strong nonlinearity effectively, and their ability to handle exactly traditional initial conditions along with boundary condition at infinity.