Abstract
A shape identification scheme was developed to determine the geometric shape of the inaccessible parts of two-dimensional objects using the measured temperatures on their accessible surfaces. The finite volume method was used to calculate the measured point’s temperature in the forward problem. In the inversion problem, the decentralized fuzzy adaptive Proportion Integral Differential (PID) control (DFAC) algorithm was used to compensate for the inversion boundary by using the difference between the measurement temperature and the calculation temperature. More accurate inversion results were obtained by introducing the weighted and synthesized normal distribution. In the inversion problem, the effects of the initial guess, the number of measuring points, and the measurement error were studied. The experiment calculation and analysis showed that the methods adopted in this paper still maintain good validity and accuracy with different initial guesses and decrease the number of measuring points and the existence of measurement errors.
Highlights
In studies of heat conduction problems, the geometric shape of the studied object, thermal conductivity, initial conditions, boundary conditions, and inner heat source are all known
The finite volume method (FVM) was used to solve the forward problem, the Differential (PID) control (DFAC) algorithm was used to compensate for the initial guess of the estimate boundary in order to minimize the residual between the calculated and the measured values of the temperature, and the true geometry boundary was obtained
The results showed that when there were some measurement errors, the inversion results were still satisfactory
Summary
In studies of heat conduction problems (forward problems), the geometric shape of the studied object, thermal conductivity, initial conditions, boundary conditions, and inner heat source are all known. If the temperature values at specific points in the system are known but one or more of the initial conditions, boundary conditions, geometry, inner heat source, or thermal conductivity are unknown, these unknowns’ details can be estimated using inverse problem methods. There are few reports on the application of the decentralized fuzzy adaptive PID control (DFAC) to IGPs. In this study, the finite volume method (FVM) was used to solve the forward problem, the DFAC algorithm was used to compensate for the initial guess of the estimate boundary in order to minimize the residual between the calculated and the measured values of the temperature, and the true geometry boundary was obtained.
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