introduction to artificial neural network by zurada pdf to word

Akbari, Ganji, Majidian, and Ahmadi ( 2014) solved Van derpol, Rayleigh, and Duffing equations using an algebraic method. In this regard, a linearization method has been employed by Motsa and Sibanda ( 2012) for solving the Duffing and Van der Pol equations. In recent years, various types of numerical and perturbation techniques such as Euler, Runge-Kutta, homotopy perturbation, linearization, and variational iteration methods have been used to solve the nonlinear equation. The results reveal that this method is reliable and can be applied to other nonlinear problems too. Thus, the proposed HeNN method is efficient. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Computed results are depicted in term of graphs. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Three mathematical example problems and two real-life application problems of Van der Pol–Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method.

Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. The Van der Pol–Duffing and Duffing oscillator equations may not be solved exactly. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials.

Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol–Duffing oscillator equation.

Introduction to artificial neural network by zurada pdf to word