Further Studies On Fuzzy Inference Method For Inverse Heat Transfer Problems

The inverse heat transfer problems (IHTP) involves the estimation of the unknownparameters, such as the thermophysical properties, the geometrical shape, the boundaryconditions, based on the output information of the heat transfer systems. The IHTP iswidespread in the fields of aerospace, power engineering, mechanical engineering,constructional engineering and biomedical Engineering. It is of important scientific andengineering significance to further research the IHTP.IHTP is a typical uncertain reasoning subject, the traditional optimizationalgorithms are can be classed as certain methods. The deficiencies are unavoidablewhen these traditional optimization algorithms are applied to research the IHTP. Thedecentralized fuzzy inference (DFI) method is a typical uncertain reasoning methodbased on the fuzzy set theory. The DFI method owns strong capacity of resistingdisturbance to input information. It can effectively use the imprecise and incompleteinformation to perform the reasoning process and possesses better anti-ill-posedcharacter. In this paper, the DFI method for IHTP is further researched on the basis ofour prior research, and the main works of this paper are as follows:①Take the problem of determining the heat flux on the surface of a cylinder forexample. The sensitivity weighting decentralized fuzzy inference (SDFI) method isapplied to solve this IHTP. Numerical experiments are conducted, the influence of theinitial guesses of the unknown heat flux, the measurement errors, and the couplingeffects of measurement errors and measurement points number on the inversion resultsare discussed. Comparisons with the conjugate gradient method (CGM) and the geneticalgorithm (GA) are also conducted. Finally, the validity and superiority of SDFI aresummarized.②The determining of the universes of discourse of DFI is researched. For thelimitations of the DFI method based on the fixed universes of discourse scheme relyingon the expertise and the existing DFI method based on the variable universes ofdiscourse scheme, the converging character of the objective function is considered to setup the self-adaptive adjustment strategy for the universes of discourse, and a new DFImethod based variable universes of discourse, the VDFI method, is proposed. The VDFIis performed to image the temperature boundary of a two-dimensional flat. The effect ofdifferent universes of discourse on the inverse results are researched, comparisons with the DFI method based on the fixed and the existing variable universes of discourse areconducted. The results show the practicality of our VDFI method. The influence of themeasurement errors and measurement points number on the inversion results are studied,and the validity and superiority of our VDFI method are proved.③The synthetic issue of SDFI is studied, taking a three-dimensional IHTP forexample, the shortcoming that the inverse results are sensitive to the boundaryconditions of SDFI method is point out. For this problem, we propose the spatialnormal distribution weighting DFI (SND-DFI) method. The SND-DFI method isapplied to estimate the convective heat transfer coefficient of a three-dimensional flat.The effects of variance parameters on the SND-DFI method are detailed and the suitableranges of variance parameters are given. The influence of the measurement errors on theinversion results are studied, comparisons with the SDFI method are researched. Theresults show the validity and superiority of our SND-DFI method.④The DFI method based on the measured space decomposition (MSD-DFImethod) is presented relying on the local influence characteristic of heat transfer system.The MSD-DFI is proposed for the IHTP that the local effect characteristic is apparent,and the number of unknown parameters and measurement points are large. For this kindof heat transfer systems, the synthesizing matrix is large and often difficult to set up.The MSD-DFI method has no need of the synthesizing matrix. The basic ideas ofMSD-DFI method are: Firstly, the measured space (namely, the measured information)decomposition is conducted according to the local influence by analyzing the direct heattransfer problem, and the measured subspaces corresponding to every estimatedparameter is built; Then, the fuzzy inference are performed for each measuredsubspaces to obtain the fuzzy inference outputs; Finally, the fuzzy decoupling algorithmproposed in this paper are applied to the fuzzy inference outputs, and the inverseprocess is accomplished. The MSD-DFI method is applied to estimate the temperaturedistribution of furnace inner surface. The influences of the initial guesses of thetemperature distribution and the measurement errors on the inversion results areresearched. Comparisons with the SDFI method are researched. The results show thevalidity of MSD-DFI method.⑤The DFI method is applied to the unsteady IHTP. For the problems that theinverse results are depending on the number of future time steps, and the optimalnumber of future time steps is difficult to obtain, and the inverse results are sensitive tothe measurement errors when the Sequential Function Specification Method (SFSM) is used for solving the unsteady IHTP, the DFI method for the unsteady IHTP bydecomposing and synthesizing the measured information in the temporal domain basedon our previous study on the steady IHTP. The heat flux of one-dimensional flat isdetermined by the DFI method, the influence of the number of future time steps, theoptimal number of future time steps, measurement errors and measurement position onthe estimated results are discussed. Comparisons with the SFSM are discussed. Theresults show that the DFI can more effective use the measured infoemation in the futuretime to estimate the heat flux availabl, even without the optimal number of future timesteps, and significantly reduces the dependence of the estimated results on the numberof future time steps, and also weakens the effects of measurement errors. The DFIpossesses higher accuracy than the SFSM. The advantages that DFI can effectivelyutilize imprecise, uncertain and incomplete information to infer and make strategicdecisions are reflected, DFI possesses better anti-ill-posed character.