The present research focuses on developing certain proposed machine learning neural network architectures along with certain mathematical criterion and stochastic population based swarm intelligence technique particle swarm optimization inspired by nature behavior to carry out wind speed prediction in renewable energy systems with real time wind farm datasets. In the developed machine learning model, the work concentrated on developing emotional neural network architecture models that are optimized employing the particle swarm optimization approach and the optimized emotional models are employed to carry out effective wind speed prediction for the given real time wind farm data. Four neural network models are proposed – PSO – EBPN (Emotional Back Propagation Neural Network) model, PSO – ERBFNN (Emotional Radial Basis Function Neural Network) model, PSO – EBPN model with hidden neuron criterion and PSO – ERBFNN model with hidden neuron criterion and as well all these four network models are employed to compute the predicted wind speed output. The developed models for wind speed prediction has performed in a better manner avoiding local and global minima problem and as well had a reasonable better convergence rate.
Dr. V. Ranganayaki Department of Electrical and Electronics Engineering, Dr. N.G.P. Institute of Technology, Coimbatore, Tamil Nadu, India.
S. N. Deepa Department of Electrical and Electronics Engineering, Anna University, Regional Campus, Coimbatore, Tamil Nadu, India.
Domar has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later Rippon pointed out that a modification of Domar’s argument gives in fact a better result. Using our previous, rather general and flexible modifications of Domar’s original argument, we extend their results both to the subharmonic and to the quasinearly subharmonic settings.
Juhani Riihentaus Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FI-90014 Oulun Yliopisto, Finland and Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland.
The aim of this chapter is to present the existence result for solution of nonlinear Volterra-Hammerstein-Fredholm integral equation (in short VHFIE) under some conditions. The main tools are Darbo’s fixed point theorem involving measure of noncompactness for investigating the existence of solution of nonlinear Volterra-Hammerstein-Fredholm integral equation. An application and illustrative example of Volterra-Hammerstein-Fredholm integral equation are also present in this chapter.
Mrs. Kavita Sakure Department of Mathematics, Govt. Digvijay Auto. P.G. College, Rajnandgaon, 491441, India.
It is known that the Euler and Navier-Stokes equations, which describe flows of ideal and viscid gases, are the set of equations of the conservation laws for energy, linear momentum and mass. As it will be shown, the integrability and properties of the solutions to the Euler and Navier-Stokes equations depend, firstly, on the consistency of equations of the conservation laws and, secondly, on the properties of conservation laws.
It was found that the Euler and Navier-Stokes equations have solutions of two types, namely, the solutions that are not functions (depend not only on coordinates) and generalized solutions that are functions but realized discretely and hence, functions or their derivatives have discontinuities. A transition from the solutions of first type to generalized solutions describes the process of transition of gas-dynamic medium from non-equilibrium state to the locally-equilibrium one. Such a process is accompanied by the emergence of any observable formations (such as waves, vortices, turbulent pulsations and soon). This discloses the mechanism of such processes as emergence vorticity and turbulence.
Such results were obtained when studying the equations the conservation laws for energy and linear momentum, which turned out to be inconsistent, due to the non-commutativity of the conservation laws.
In this chapter, we establish some common fixed point theorems for a pair of self mappings in fuzzy cone metric spaces under the generalize fuzzy cone contraction conditions. we extend and improve some recent results given in the literature.
Dr. Saif Ur Rehman Department of Mathematics, Gomal University, Dera Ismail Khan 29050, Pakistan.
This paper analyses wind speed characteristics and wind power potential of Naganur site using statistical probability parameters. A measured 10-minute time series average wind speed over a period of 4 years (2006- 2009) was obtained from Site. The results of mean wind speed data is the first step of prediction of wind speed data of the site under consideration and a PROLOG program was designed and developed to calculate the Annual mean wind speed data of the site and to assess the wind power potentials, MATLAB programming is used. The Weibull two parameters (k and c) were computed in the analysis of wind speed data. The data used were real time site data and calculated by using the MATLAB programming to determine and generate the Weibull and Rayleigh distribution functions. The monthly values of k range from 2.21 to 8.64 and the values of c ranged from 2.28 to 6.80. The most probable wind speed and corresponding maximum energy are in the range of 2.45 to 6.52 and 3.10 to 6.26 respectively. The Weibull and Rayleigh distributions also revealed estimated wind power densities ranging between 7.30 W/m2 to 116.51 W/m2 and 9.71 W/m2 to 266.00 W/m2 respectively at 10 m height for the location under study. This paper is relevant to a decision-making process on significant investment in a wind power project and use of PROLOG programming to calculate the Annual mean wind speed data of the site.
Dr. K. Mahesh Department of Electrical and Electronics Engineering, Sir M Visvesvaraya Institute of Technology, Bengaluru, India.
J. Lithesh Department of Electrical and Electronics Engineering, New Horizon College of Engineering, Bengaluru, India.