In this paper authors present hybrid algorithm to solve heat con- duction inverse problem. Considered heat conduction equation with Riemann- Liouville fractional derivative can be used to model heat conduction in porous materials. In order to effectively model the phenomenon of heat flow, all parameters of the model must be known. In considered inverse problem thermal conductivity coefficient, initial condition and heat transfer coefficient are unknown and must be identified having some information about output of the model (measurements of temperatures). In order to do that, function describing the error of approximate solution is constructed and then minimized. The hybrid algorithm, based on the probabilistic Ant Colony Optimization (ACO) algorithm and the deterministic Nelder-Mead method, is responsible for searching mini- mum of the objective function. Goal of this paper is reconstruction unknown parameters in heat conduction model with fractional derivative and show that hybrid algorithm is effective tool and works well in these type of problems.

### Parameter Identification of the Fractional Order Heat Conduction Model Using a Hybrid Algorithm

#### Abstract

In this paper authors present hybrid algorithm to solve heat con- duction inverse problem. Considered heat conduction equation with Riemann- Liouville fractional derivative can be used to model heat conduction in porous materials. In order to effectively model the phenomenon of heat flow, all parameters of the model must be known. In considered inverse problem thermal conductivity coefficient, initial condition and heat transfer coefficient are unknown and must be identified having some information about output of the model (measurements of temperatures). In order to do that, function describing the error of approximate solution is constructed and then minimized. The hybrid algorithm, based on the probabilistic Ant Colony Optimization (ACO) algorithm and the deterministic Nelder-Mead method, is responsible for searching mini- mum of the objective function. Goal of this paper is reconstruction unknown parameters in heat conduction model with fractional derivative and show that hybrid algorithm is effective tool and works well in these type of problems.
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/20.500.11769/371413`
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