This paper develops a smooth model identifica-10 tion and self-learning strategy for dynamic systems taking 11 into account possible parameter variations and uncertain-12 ties. We have tried to solve the problem such that the 13 model follows the changes and variations in the system on 14 a continuous and smooth surface. Running the model to 15 adaptively gain the optimum values of the parameters on a 16 smooth surface would facilitate further improvements in 17 the application of other derivative based optimization 18 control algorithms such as MPC or robust control algo-19 rithms to achieve a combined modeling-control scheme. 20 Compared to the earlier works on the smooth fuzzy mod-21 eling structures, we could reach a desired trade-off between 22 the model optimality and the computational load. The 23 proposed method has been evaluated on a test problem as 24 well as the non-linear dynamic of a chemical process. 25 26 Keywords Fuzzy control Á Fuzzy IF-THEN systems 27 (TSK) Á Smooth compositions 28 1 Introduction 29 Soft computing methods are being used for identification of 30 non-linear and complex systems based on the input-output 31 data collected from the original system [1]. There are many
The aim of this work is to conduct numerical study of fluid flow and natural convection heat transfer by utilizing the nanofluid in a two-dimensional horizontal channel consisting of a sinusoidal obstacle by lattice Boltzmann method (LBM). The fluid in the channel is a water-based nanofluid containing Cuo nanoparticles. Thermal conductivity and nanofluid’s viscosity are calculated by Patel and Brinkman models, respectively. A wide range of parameters such as the Reynolds number ([Formula: see text]–400) and the solid volume fraction ranging ([Formula: see text]–0.05) at different non-dimensional amplitude of the wavy wall of the sinusoidal obstacle ([Formula: see text]–20) on the streamlines and temperature contours are investigated in the present study. In addition, the local and average Nusselt numbers are illustrated on lower wall of the channel. The sensitivity to the resolution and representation of the sinusoidal obstacle’s shape on flow field and heat transfer by LBM simulations are the main interest and innovation of this study. The results showed that increasing the solid volume fraction [Formula: see text] and Reynolds number Re leads to increase the average Nusselt numbers. The maximum average Nusselt number occurs when the Reynolds number and solid volume fraction are maximum and amplitude of the wavy wall is minimum. Also, by decreasing the [Formula: see text], the vortex shedding forms up at higher Reynolds number in the wake region downstream of the obstacle.
In this paper, a constrained optimal control problem is considered where constraint is elliptic partial differential equations of second order together with the boundary condition of Dirichlet type. The main purpose is detecting an appropriate solution for control and state function by using boundary element method in order to discretized PDEs. In this way, first a quadratic objective, linear constraints optimization problem rewritten respected to main problem, next it can be solved numerically with the help of appropriate solution algorithms, which should exploit the structure of the problem, we solved it by generalized Newton's method. Some numerical experiments obtained by using boundary element method (BEM) and finite element method (FEM) are given in the final section of this paper.
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