Study On Reconstruction Algorithm Of The3-D Temperature Distributions In Combustion

Detection of the three-dimensional (3-D) temperature distributions based on radiationimage processing technology, whose theory is using inversion method of radiation inverseproblems to reconstruct3-D temperature distributions through the flame image capturedby Charge-Coupled Device (CCD). Radiation inverse problems always are ill-posed, as aresult, that make the solving of problems to be more difficult. Based on this background,following research was done in this paper:Parameters of the optical thickness of the media are important reasons of energyextinction. With optical thickness increasing, the mean free path of photons reduces. So,the fewer the number of photons reach the optical signal receiver arranged in the boundary,which greatly increases the ill-posedness of inverse radiation problem. Consequently,impact of the optical thickness on the ill-posedness of inverse radiation problems for a10m×10m×20m high-temperature thermal radiation furnace was analyzed in this paper.To solve ill-posed inverse radiation problem, Tikhonov Regularization (TR) methodis a classic method has been applied in various fields, and proved to be a reliable methodfor solving the inverse problem. Regularization parameter used in TR method plays animportant role in the solving process and is critical for reflection of the accurateinformation of3-D temperature distributions. L-Curve Criterion (LCC) methodcontaining cubic spline interpolation to select regularization parameter was established inthis paper, to improve accuracy and efficiency of the selection of regularization parameter.The results showed that the method can get ideal regularization parameter, and only20s isneeded when the interpolation points are equal to7, and the final results are satisfied withthe reconstruction of3-D temperature distributions.For a large-scale matrix (7200×1200), TR method greatly reduces its efficiencybecause of its inevitable inversion of matrix. Generalized Singular Value Decomposition(GSVD) technique can decompose matrix in advance, after, only a small part of calculation required can get the whole3-D temperature distributions. Therefore, TRcombined with GSVD (TR-GSVD) method was proposed in this paper, to increaseefficiency of reconstruction process and efficiency of selection of regularization parameter.The results show that TR-GSVD greatly reduces the CPU time of selection ofregularization parameter which only needs about2s, and the reconstruction CPU time isabout0.0312s, under the same condition of accuracy.CCD receives different values of radiation energy at different wavelengths because ofthe spectrum response. It is insufficient that radiation energy in the whole spectrumreceived by the CCD imaging. There are some deficiencies in monochromatic radiationimaging model that color filter were added to CCDs for obtaining radiation at a singlewavelength, because it is difficult to ensure that a single radiation was received by theoptical device. Therefore, this paper presented an imaging model with spectral response.The final results showed that accuracy of the reconstruction of3-D temperaturedistributions was improved.