A novel approach to solve inverse heat conduction problems: coupling scaled boundary finite element method to a hybrid optimization algorithm. (English) Zbl 1403.80006
Summary: Scaled boundary finite element method (SBFEM) has proved its abilities in problems with singularities successfully. In this work, the coupling of SBFEM and a hybrid optimization algorithm is employed to determine unknown heat flux in the transient heat conduction problems. The genetic algorithm (GA) is a stochastic method which solves problems considering a large number of generations, while the deterministic methods such as sequential quadratic programming (SQP), which are sensitive to the initial points, can solve problems faster. Combining GA, as the main optimizer, and SQP can lead to lower computational time. Herein, a square plate is considered as the case study. The inverse analysis is accomplished by utilizing the transient temperature data from direct solution. The difference between the calculated and the known values of temperature at four points within the plate is considered as the objective function, and the heat fluxes on the upper side of the plate are considered as the design variables. As a result, the exact value of the heat fluxes is obtained using this method. This new approach, in which the SBFEM as a meshless solver is combined with the hybrid GA-SQP as the optimizer, highlights its potentials in solving inverse problems.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 80M15 | Boundary element methods applied to problems in thermodynamics and heat transfer |
| 80M10 | Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65K05 | Numerical mathematical programming methods |
| 90C20 | Quadratic programming |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
scaled boundary finite element method (SBFEM); inverse heat conduction; hybrid optimization; GA-SQPReferences:
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