Estimation of unknown heat source function in inverse heat conduction problems using quantum-behaved particle swarm optimization

The estimation of temporal dependent heat source in transient heat conduction problem is investigated. A stochastic method known as quantum-behaved particle swarm optimization (QPSO) is used to estimate the heat source without a priori information on its functional form, which is classified as the function estimation by inverse calculation. Because of the ill-posedness of this kind of inverse problems, Tikhonov regularization method is applied in this paper to stabilize the solution. Numerical experiments indicate the validity and stability of the QPSO method. Comparison with the conjugate gradient method (CGM) is also presented in this paper.     

Robustness in the volume-to-point heat conduction optimization problem

This paper deals with the systematic and quantitative robustness analysis of solutions to the volume-to-point (VP) heat conduction optimization problem, including solutions by constructal theory (CT), bionic optimization (BO), simulated annealing (SA) as well as random solutions. The impacts of both load-induced and random failures are examined. All the solutions behave similarly during a failure. A tiny high-heat-flux-induced failure causes huge performance loss, which is the worst possible case. While the best case is a failure at positions of low heat flux, a large amount of which only causes a small performance loss. Random failure generally results in a loss roughly linear with failure amount, but sudden loss increase happens. Both intuitive and practical definitions of robustness are considered. Intuitively, a performance-robustness trade-off is seen for all the solutions, with poorer solutions being robuster. Practically things are different, with SA solutions both the best in performance and the robustest during a failure in the worst case. However, CT and BO solutions turn out to be robuster than SA solution in the best case, and CT solution may be more preferable in practice due to its regular geometry. With robustness taken into consideration, different solutions could be evaluated more comprehensively, the critical aspects concerning the practical realization of the solutions are also revealed, and furthermore the significance of robustness analysis in general VP problems is accentuated.     

Particle Swarm Optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux

An inverse analysis of estimating a time-dependent surface heat flux for a three-dimensional heat conduction problem is presented. A global optimization method known as Particle Swarm Optimization (PSO) is employed to estimate the unknown heat flux at the inner surface of a crystal tube from the knowledge of temperature measurements obtained at the external surface. Three modifications of the PSO-based algorithm, PSO with constriction factor, PSO with time-varying acceleration of the cognitive and social coefficients, and PSO with mutation are carried out to implement the optimization process of the inverse analysis. The results show that the PSO with mutation algorithm is significantly better than other PSO-based algorithms because it can overcome the drawback of trapping in the local optimum points and obtain better inverse solutions. The effects of measurement errors, number of dimensionalities, and number of generations on the inverse solutions are also investigated.     

Wind turbines type and number choice using combinatorial optimization

The paper addresses the problem associated with the optimal wind park design. A combinatorial optimization model for wind turbines type and number choice and placement considering the given wind conditions and wind park area is developed. The wind park investment costs and the total power relation as function of wind turbines number and type are used as optimization criteria. The optimization problem is formulated as a single criterion mixed-integer nonlinear discrete combinatorial task. The different wind park conditions are introduced into optimization tasks formulation as variables relations and restrictions. Two basic wind directions cases are taken into consideration – uniform and predominant wind directions for two wind park area shapes – square and rectangular. The developed wind park design approach was tested numerically by solving of different optimization tasks formulations based on wind turbines real parameters data. The numerical testing shows the applicability of the developed optimization approach. Using it will help to find mathematically reasoned wind turbines choice as contradiction to the heuristic approaches.     

Iterative algorithms for solving inverse problems of heat conduction in multiply connected domains

The presented paper displays a method of solving the inverse problems of heat transfer in multi-connected regions, consisting in iterative solving of convergent series of the direct problems. For known temperature and flux values at the outer boundary of the region the temperature and flux values at the inner boundaries are sought (the cauchy problem for the Laplace equation). In case of such a formulation of the problem, the solution does not always exist, one of the conditions is met in the mean-square sense, providing the optimization criterion. The idea of the process consists in solving the direct problem in which the boundary condition is subject to iterative changes so as to attain minimum of the optimization criterion (the square functional). Two algorithms have been formulated. In the first of them the heat flux at the inner boundaries of the region, while in the other the temperature were subject to changes. Convergence of both the algorithms have been compared.The numerical calculation has been made for selected examples, for which an analytical solution is known. The effect of random disturbance of the boundary conditions on the solution obtained with iterative algorithms has been checked. Moreover, a function was defined, serving as convergence measure of the solution of the inverse problem solved with the algorithms proposed in the paper. The properties of the function give evidence that it tends to the value exceeding unity.     

Inverse heat conduction problems by using particular solutions

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two‐dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least‐square and singular value decomposition (SVD) techniques are adopted to solve the ill‐conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20335     

Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique

Shell-and-tube heat exchangers (STHEs) are the most common type of heat exchangers that find widespread use in numerous industrial applications. Cost minimization of these heat exchangers is a key objective for both designer and users. Heat exchanger design involves complex processes, including selection of geometrical parameters and operating parameters. The traditional design approach for shell-and-tube heat exchangers involves rating a large number of different exchanger geometries to identify those that satisfy a given heat duty and a set of geometric and operational constraints. However, this approach is time-consuming and does not assure an optimal solution. Hence the present study explores the use of a non-traditional optimization technique; called particle swarm optimization (PSO), for design optimization of shell-and-tube heat exchangers from economic view point. Minimization of total annual cost is considered as an objective function. Three design variables such as shell internal diameter, outer tube diameter and baffle spacing are considered for optimization. Two tube layouts viz. triangle and square are also considered for optimization. Four different case studies are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO technique are compared with those obtained by using genetic algorithm (GA).     

Solution of inverse heat conduction problems using maximum entropy method

A solution scheme based on the maximum entropy method (MEM) for the solution of one-dimensional inverse heat conduction problem is proposed. The present work introduces MEM in order to build a robust formulation of the inverse problem. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. In order to seek the most likely inverse solution, the present method converts the inverse problem to a non-linear constrained optimization problem. The constraint of the problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the maximum entropy estimation. The characteristic feature of the method is discussed with the sample numerical results. The presented results show considerable enhancement in the resolution of the inverse problem and bias reduction in comparison with the conventional methods.     

Relativistic heat conduction

The hyperbolic heat conduction equation (HHCE), which acknowledges the finite speed of heat propagation, is based on microscopic evidence from the kinetic theory and statistical mechanics. However, it was argued that the HHCE could violate the second law of thermodynamics. This paper shows that a HHCE-like equation (RHCE) can be derived directly from the theory of relativity, as a direct consequence of space-time duality, without any consideration of the microstructure of the heat-conducting medium. This approach results in an alternative expression for the heat flux vector that is more compatible with the second law. Therefore, the RHCE brings the classical field theory of heat conduction into agreement with other branches of modern physics.     

Horizontal axis wind turbine systems: optimization using genetic algorithms

A method for the optimization of a grid‐connected wind turbine system is presented. The behaviour of the system components is coupled in a non‐linear way, and optimization must take into account technical and economical aspects of the complete system design. The annual electrical energy cost is estimated using a cost model for the wind turbine rotor, nacelle and tower and an energy output model based on the performance envelopes of the power coefficient of the rotor, C_P, on the Weibull parameters k and c and on the power law coefficient α of the wind profile. In this study the site is defined with these three parameters and the extreme wind speed V_max. The model parameters vary within a range of possible values. Other elements of the project (foundation, grid connection, financing cost, etc.) are taken into account through coefficients. The optimal values of the parameters are determined using genetic algorithms, which appear to be efficient for such a problem. These optimal values were found to be very different for a Mediterranean site and a northern European site using our numerical model. Optimal wind turbines at the Mediterranean sites considered in this article have an excellent profitability compared with reference northern European wind turbines. Most of the existing wind turbines appear to be well designed for northern European sites but not for Mediterranean sites. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimization of network planning by the novel hybrid algorithms of intelligent optimization techniques

This paper proposes a new hybrid algorithm Meta-heuristic for the problem of network planning systems. The main goal of this paper is, to develop an efficient optimization tool which will minimise the cost functions of the stated optimization problems in network planning systems. The following are the objectives of the research: to investigate the capabilities of genetic algorithm, simulated annealing and tabu search for the defined optimization tasks; to develop a hybrid optimization algorithm which will produce improved iterations compared to those found by GA, SA, and TS algorithms. The performance of the hybrid algorithm is illustrated and six hybrid algorithms are developed, to improve the iterations obtained. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. It is advantageous to use exact DC load flow constraint equations based on the modified form of Kirchhoff's Second Law because the iterative process for line addition is not required. Hence, the computation time is decreased. Finally, the hybrid VI shows to be a very good option for network planning systems given that it obtains much accentuated reductions of iteration, which is very important for network planning.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

Solution of inverse heat conduction problem using the Tikhonov regularization method

It is hard to solve ill-posed problems, as calculated temperatures are very sensitive to errors made while calculating “measured” temperatures or performing real-time measurements. The errors can create temperature oscillation, which can be the cause of an unstable solution. In order to overcome such difficulties, a variety of techniques have been proposed in literature, including regularization, future time steps and smoothing digital filters. In this paper, the Tikhonov regularization is applied to stabilize the solution of the inverse heat conduction problem. The impact on the inverse solution stability and accuracy is demonstrated.     

Optimization of solar systems using artificial neural-networks and genetic algorithms

The objective of this work is to use artificial intelligence methods, like artificial neural-networks and genetic algorithms, to optimize a solar-energy system in order to maximize its economic benefits. The system is modeled using a TRNSYS computer program and the climatic conditions of Cyprus, included in a typical meteorological year (TMY) file. An artificial neural-network is trained using the results of a small number of TRNSYS simulations, to learn the correlation of collector area and storage-tank size on the auxiliary energy required by the system from which the life-cycle savings can be estimated. Subsequently, a genetic algorithm is employed to estimate the optimum size of these two parameters, for maximizing life-cycle savings: thus the design time is reduced substantially. As an example, the optimization of an industrial process heat-system employing flat-plate collectors is presented. The optimum solutions obtained from the present methodology give increased life-cycle savings of 4.9 and 3.1% when subsidized and non-subsidized fuel prices are used respectively, as compared to solutions obtained by the traditional trial-and-error method. The present method greatly reduces the time required by design engineers to find the optimum solution and in many cases reaches a solution that could not be easily obtained from simple modeling programs or by trial-and-error, which in most cases depends on the intuition of the engineer.     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.     

Thermodynamic optimization of cross flow plate-fin heat exchanger using a particle swarm optimization algorithm

This study explores the use of particle swarm optimization (PSO) algorithm for thermodynamic optimization of a cross flow plate-fin heat exchanger. Minimization of total number of entropy generation units for specific heat duty requirement under given space restrictions, minimization of total volume, and minimization of total annual cost are considered as objective functions and are treated individually. Based on the applications, heat exchanger length, fin frequency, numbers of fin layers, lance length of fin, fin height and fin thickness or different flow length of the heat exchanger are considered for optimization. Heat duty requirement constraint is included in the procedure. Two application examples are also presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO are validated by comparing with those obtained by using genetic algorithm (GA). Parametric analysis is also carried out to demonstrate the effect of heat exchanger dimensions on the optimum solution. The effect of variation of PSO parameters on convergence and optimum value of the objective has also been presented.     

Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction

This work presents an improved apparatus and a numerical approach to obtain the estimate of thermal diffusivity of complex materials. Transient thermal response at the axis of cylindrical sample is measured when boundary temperature is suddenly changed. Instead of assuming an ideal step temperature excitement, a measured temperature of a material boundary was employed. An iterative procedure, based on minimizing a sum of squares function with the Levenberg–Marquardt method, is used to solve the inverse problem. A graphical user interface is built to enable easy use of the inverse thermal diffusivity estimation method. The reference materials used to evaluate the method are Agar water gel, glycerol and Ottawa quartz sand.     

Fundamental approach to anisotropic heat conduction using the element-based finite volume method

This work describes the fundamentals of the element-based finite volume method for anisotropic heat conduction within the framework of the finite element space. Patch tests indicate no element inconsistencies or deficiencies when facing mesh distortion and poor aspect ratio. Convergence and accuracy assessments show that the method presents asymptomatic rate of convergence with discretization errors approaching a second-order scheme. Anisotropic heat conduction in a periodical solid lattice illustrates the application of the method. Application of an optimization technique demonstrates that the choice of a proper material orientation when manufacturing the solid lattice can increase the global heat transfer coefficient.     

An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform

An analytical method has been developed for two-dimensional inverse heat conduction problems by using the Laplace transform technique. The inverse solutions are obtained under two simple boundary conditions in a finite rectangular body, with one and two unknowns, respectively. The method first approximates the temperature changes measured in the body with a half polynomial power series of time and Fourier series of eigenfunction. The expressions for the surface temperature and heat flux are explicitly obtained in a form of power series of time and Fourier series. The verifications for two representative testing cases have shown that the predicted surface temperature distribution is in good agreement with the prescribed surface condition, as well as the surface heat flux.     

Levenberg-Marquardt算法求解三维圆管稳态导热反问题

应用Levenberg-Marquardt算法求解三维水平圆管导热反问题,以反演圆管内壁未知的温度分布。使用有限单元法求解三维导热正问题。在周向及轴向上引入插值函数,把内壁温度场的反演转化为内壁有限点温度的反演。分析了圆管内壁两种不同温度分布的反问题,并通过引入随机测量误差,探讨了测量误差对反演结果的影响。数值计算结果表明:所构算法能精确地反演出圆管内壁的温度分布。