First principles versus artificial neural network modelling of a solar desalination system with experimental validation

ABSTRACT

The present study mainly focuses on enhancing the performance of solar still unit using solar energy through cylindrical parabolic collector and solar panels. A 300 W solar panel is used to heat saline water by thermal elements outside the solar still unit. Solar panels are cooled during the hot hours of the day; thus, reducing their temperature may lead to an increase in solar panel efficiency followed by an increase in the efficiency of the solar still unit. The maximum amount of freshwater used in the experiment was 2.132 kg/day. The experiments were modelled using ANNs. Based on neural network simulation results, there is a significant correlation between experimental data and neural network modelling. This paper compares experimental data with data obtained from mathematical modelling and ANNs. As a conclusion, the artificial neural network prediction has been more accurate than the simplified first principles model presented.     

Solitary waves for the perturbed nonlinear Klein–Gordon equation

In this work, we study the perturbed nonlinear Klein–Gordon equation. We shall use the sech-ansätze method to derive the solitary wave solutions of this equation.     

Short-Term Prediction of the Sea State Dynamics

Forecasting of the sea level plays a key role to control on- and offshore facilities. First, we start with a determinstic time series method based on the state space embedding to determine the vector field of the nonlinear dynamical system and deduce the solution of its corresponding high-order differential equation. Second, We assume that the sea state is a stochastic process governed by a deterministic part and by noise so that this dynamical system can be modelled by the Langevin equation. We extract the nonlinear dynamical system considering fluctuations directly from a measured time series by estimating the drift vector and the diffusion matrix of the Fokker-Planck equation. In order to determine the prediction accuracy, the numerical solutions of the deterministic model and the Langevin equation are compared to the data values at future time. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Soc-Injective Rings and Modules*

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple submodule K of N, any R-homomorphism f : K → M extends to N. In this article, we investigate the notion of soc-injectivity.     

A numerical solution of a two-dimensional IHCP

In this paper, we will first study the existence and uniqueness of the solution of a two-dimensional inverse heat conduction problem (IHCP) which is severely ill-posed, i.e., the solution does not depend continuously on the data. We propose a stable numerical approach based on the finite-difference method and the least-squares scheme to solve this problem in the presence of noisy data. We prove the convergence of the numerical solution, then to regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization 0th, 1st and 2nd method to obtain the stable numerical approximation to the solution. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method.     

A neural network to solve quadratic programming problems with fuzzy parameters

In this paper, a representation of a recurrent neural network to solve quadratic programming problems with fuzzy parameters (FQP) is given. The motivation of the paper is to design a new effective one-layer structure neural network model for solving the FQP. As far as we know, there is not a study for the neural network on the FQP. Here, we change the FQP to a bi-objective problem. Furthermore, the bi-objective problem is reduced to a weighting problem and then the Lagrangian dual is constructed. In addition, we consider a neural network model to solve the FQP. Finally, some illustrative examples are given to show the effectiveness of our proposed approach.     

Bi-criteria optimization problems for decision rules

We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems—minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion—we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria—we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.     

A generalization of Eagon–Reiner’s theorem and a characterization of bi-CMt bipartite and chordal graphs

We give a generalization of Eagon-Reiner’s theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CM_t property of its Alexander dual. Then we characterize bi-CM_t bipartite graphs and bi-CM_t chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.     

The recovery of the acoustic stiffness coefficient

We are concerned with the reconstruction of a non‐differentiable acoustic stiffness reactance coefficient of a one‐dimensional hyperbolic equation using the smallest possible number of boundary readings generated by classical initial conditions. To this end, a complete set of spectral data of a string is extracted from either a single or at most two readings of the trace of the solution on the boundary. The sought coefficient is then uniquely recovered by the Krein inverse spectral theory. Copyright © 2013 John Wiley & Sons, Ltd.