Inverse Geometry Problem Based On Boundary Element Method And Decentralized Fuzzy Inference Method

Inverse geometry problem of heat conduction is to estimate the unknown geometryboundary according to the information of temperature measurement and other boundaryconditions of the research object. Inverse geometry problem of heat conduction hasbroad application prospects in non-destructive testing, geometry optimization,biological lesion detection and other fields. Now, the main research methods of inversegeometry problem of heat conduction are Conjugate Gradient Method (CGM),Levenberg-Marquarat method (L-MM) and Steepest Descent Method (SDM), which arethe gradient-based optimization methods. On the one hand, the gradient-basedoptimization methods belong the local search algorithm, which are easy to fall into localminima, and the inversion results are sensitive to the initial guess for the geometry; Onthe other hand, due to the inverse problem of heat transfer is a typical ill-posed problem,the inversion results depend heavily on the completeness and accuracy of thetemperature measurement information when using the gradient-based optimizationmethod to study inverse heat transfer problem, if the temperature measurementinformation is incomplete or has errors, inversion results will deteriorate.Decentralized Fuzzy Inference (DFI) method is an inversion algorithm for theinverse heat transfer problem proposed in recent years, which has good robustness andfault tolerance and can enhance ability of anti-ill-posed for the algorithm. Thetwo-dimensional geometry boundary identification problem is studied based onboundary element method (BEM) and decentralized fuzzy inference (DFI) in this paper,the main contents contain the following four aspects:①The basic principles of BEM is introduced and a numerical model for solvingtwo dimensional heat conduction problems is established based on BEM. Thecorrectness and grid–independent of results of the thermal positive problem based onthe BEM are verified. The shortcomings that each iteration requires redrawing the gridof the entire region are overcome when using BEM solve the thermal positive problem,the difficulty and the amount of calculation are reduced.②The unknown boundary geometry are estimated based on BEM and CGM forthe two-dimensional flat and cylindrical thermal conduction problem. Then, the effectsof the initial guesses, the number of measurement points and measurement error on theinversion results are discussed, which show the main problems of CGM for the geometric inverse problems.③For the two-dimensional steady-state heat transfer system, a decentralizedfuzzy inference system for the inverse geometry problem is built and a set of fuzzyinference unit is constructed. A set of fuzzy inference component is obtained accordingto the temperature difference between the measuring temperature and the calculatedtemperature. The compensation of boundary geometry is obtained by weighting the setof fuzzy inference component. The guesses of boundary geometry are compensated andrefreshed. The process that using the decentralized fuzzy inference system identify thegeometry is introduced.④BEM and DFI are used to identify the boundary geometry of cylinder model andplate model, which verifies the effectiveness of the DFI. The influence of the initialguesses, the number of measuring points and measurement errors to the results arediscussed and comparisons with CGM are made.Numerical results show that BEM only need to discrete the inversion boundary ineach iteration, which reducing the difficulty and the amount of calculation of inversegeometry problem of heat conduction. For the two-dimensional heat transfer system,DFI can effectively identify boundary geometry, and compared with the CGM, DFI canreduce the dependence of the initial guess and the number of measuring points, whileenhance the temperature measurement error of anti-interference ability. The DFIeffectively improves the resistance of inversion results.