Raza Samar

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.

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.

Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem

In this paper, a stochastic technique is developed to solve 2-dimensional Bratu equations using feed-forward artificial neural networks, optimized with genetic and interior-point algorithms. The 2-dimensional equations are first transformed into a 1-dimensional boundary value problem, and a mathematical model of the transformed equation is then formulated with neural networks using an unsupervised error. Network weights are optimized to minimize the error. Evolutionary computing based on genetic algorithms is used as a tool for global search, integrated with an interior-point method for rapid local convergence. The methodology is applied to solve three cases of boundary value problems for the Bratu equations. The accuracy, convergence and effectiveness of the scheme is validated for a large number of simulations. Comparison of results is made with the exact solution derived using MATHEMATICA, and is found to be in good agreement.

Comparison of three unsupervised neural network models for first Painlevé Transcendent

Abstract In this paper, a reliable soft computing framework is presented for the approximate solution of initial value problem (IVP) of first Painlevé equation using three unsupervised neural network models optimized with sequential quadratic programming (SQP). These mathematical models are constructed in the form of feed-forward architecture including log-sigmoid, radial base and tan-sigmoid activation functions in the hidden layers. The optimization of designed parameters for each model is performed with SQP, an efficient constraint optimization problem-solving algorithm. The designed methodology is tested on the IVP, and comparative study is carried out with standard solution based on numerical and analytical solvers. The accuracy, convergence and effectiveness of the schemes are validated on the given benchmark problem by large number of simulations and their comprehensive analysis.

Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems

Abstract In this paper a Mexican Hat Wavelet based neural network is designed and applied for solving the nonlinear Bratu type equation. This equation is widely used in fuel ignition models, electrically conducting solids and heat transfer studies. The Mexican Hat Wavelet Differential equation artificial neural networks (MHW-DEANN) are used for the first time to construct an energy function of the system in an unsupervised manner. The tunable parameters of MHW-DEANN are trained with a hybrid evolutionary computing approach: we exploit the strength of Genetic Algorithms (GA) and Sequential Quadratic Programming (SQP) to find the best weights. Monte-Carlo simulations are performed for the proposed scheme with statistical analysis to validate the effectiveness and convergence of the proposed method for Bratu-type equations. It is observed that the proposed method converges in all cases and can solve the equation with high accuracy and reliability.

Solution of the 2-dimensional Bratu problem using neural network, swarm intelligence and sequential quadratic programming

Abstract In this paper, stochastic techniques have been developed to solve the 2-dimensional Bratu equations with the help of feed-forward artificial neural networks, optimized with particle swarm optimization (PSO) and sequential quadratic programming (SQP) algorithms. A hybrid of the above two algorithms, referred to as the PSO-SQP method is also studied. The original 2-dimensional equations are solved by first transforming them into equivalent one-dimensional boundary value problems (BVPs). These are then modeled using neural networks. The optimization problem for training the weights of the network has been addressed using particle swarm techniques for global search, integrated with an SQP method for rapid local convergence. The methodology is evaluated by applying on three different test cases of BVPs for the Bratu equations. Monte Carlo simulations and extensive analyses are carried out to validate the accuracy, convergence and effectiveness of the schemes. A comparative study of proposed results is made with available exact solution, as well as, reported numerical results.

Guidance of Air Vehicles: A Sliding Mode Approach

This paper presents a novel nonlinear guidance scheme for ground track control of aerial vehicles. The proposed guidance logic is derived using the sliding mode control technique, and is particularly suited for unmanned aerial vehicle (UAV) applications. The main objective of the guidance algorithm is to control the lateral track error of the vehicle during flight, and to keep it as small as possible. This is achieved by banking the vehicle, that is, by executing roll maneuvers. The guidance scheme must perform well both for small and large lateral track errors, without saturating the roll angle of the vehicle, which serves as the control input for the guidance algorithm. The limitations of a linear sliding surface for lateral guidance are indicated; a nonlinear sliding surface is thereafter proposed which overcomes these limitations, and also meets the criterion of a good helmsman. Stability of the nonlinear surface is proved using Lyapunov theory; control boundedness is also proved to ensure that the controls are not saturated even for large track errors. The proposed guidance law is implemented on the flight control computer of a scaled YAK-54 UAV and flight results for different scenarios (consisting of both small and large errors) are presented and discussed. The flight test results confirm the effectiveness and robustness of the proposed guidance scheme.

Application of three unsupervised neural network models to singular nonlinear BVP of transformed 2D Bratu equation

In this paper, numerical techniques are developed for solving two-dimensional Bratu equations using different neural network models optimized with the sequential quadratic programming technique. The original two-dimensional problem is transformed into an equivalent singular, nonlinear boundary value problem of ordinary differential equations. Three neural network models are developed for the transformed problem based on unsupervised error using log-sigmoid, radial basis and tan-sigmoid functions. Optimal weights for each model are trained with the help of the sequential quadratic programming algorithm. Three test cases of the equation are solved using the proposed schemes. Statistical analysis based on a large number of independent runs is carried out to validate the models in terms of accuracy, convergence and computational complexity.

Lateral Control for UAVs using Sliding Mode Technique

Abstract This paper presents sliding mode based lateral control for UAVs using a nonlinear sliding approach. The control is shown to perform well in different flight conditions including straight and turning flight and can recover gracefully from large track errors. Saturation constraints on the control input are met through the nonlinear sliding surface, while maintaining high performance for small track errors. Stability of the nonlinear sliding surface is proved using an appropriate Lyapunov function. The main contribution of this work is to develop a robust lateral control scheme that uses readily available sensor information and keeps the track error as small as possible without violating control constraints. In the proposed scheme the only information used in the control law is the lateral track error and the heading error angle. No information is required about the desired path/mission, which therefore can be changed online during run-time. This scheme is implemented on a high fidelity nonlinear 6-degrees-of-freedom (6-dof) simulation and different scenarios are simulated with large and small track errors in windy and calm conditions. Simulation results illustrate the robustness of the proposed scheme for straight and turning flight, in the presence of disturbances, both for large and small track errors. Furthermore it is shown that the saturation limits of the control input are not exceeded in all cases.

A genetic algorithm optimized Morlet wavelet artificial neural network to study the dynamics of nonlinear Troeschs system

Display Omitted Novel Design of Morlet Wavelets Neural Networks Models for differential equations.Bio-inspired Heuristics integrated with SQP for training of weights of the networks.The design scheme is viable to solve Troeschs problem arising in Plasma Physics.The results of the proposed algorithm are in good agreement with Adams methods.Accuracy and convergence are validated through results of the statistical Analyses. In this work, a new stochastic computing technique is developed to study the nonlinear dynamics of Troeschs problem by designing the mathematical models of Morlet Wavelets Artificial Neural Networks (MW-ANNs) optimized with Genetic Algorithm (GA) integrated with Sequential Quadratic Programming (SQP). The differential equation mathematical model for MW-ANNs are designed for Troeschs system by incorporating a windowing kernel based on Morlet Wavelets as an activation function and these networks are constructed to define a fitness function of Troeschs system in the mean squared sense. The unknown adjustable parameters of MW-ANNs are trained initially by an effective global search using GAs hybridized with SQP for rapid local refinement of the results. The proposed scheme is evaluated to solve the Troeschs problems for small and large values of the critical parameter in the system. Comparison of the proposed results with standard reference solutions of Adams method shows good agreement. Validation of accuracy and convergence of the proposed scheme is made using statistical analysis based on a sufficiently large number of independent runs, this is done in terms of performance measures of mean absolute deviation and root mean squared error.