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On the treatment of non-optimal regularization parameter influence on temperature distribution reconstruction accuracy in participating medium

机译:非最优正则化参数的处理对参与介质温度分布重构精度的影响

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The choice of the regularization parameter plays a very important role in the inverse radiation problem of temperature distribution in participating medium and in practice the regularization parameter is not easy to determine accurately, which can directly affect the reconstruction accuracy and introduce errors into reconstruction results. This paper presents the alleviation of non-optimal regularization parameter influence on the temperature distribution reconstruction accuracy in participating medium using coupled methods, i.e., two kinds of regularization method (least square QR decomposition (LSQR) method and truncated singular value decomposition (TSVD) method) coupled with genetic algorithm (GA). The radiative heat transfer was described by the backward Monte Carlo method for its efficiency. Two kinds of temperature distributions with one peak and two peaks are considered. The results show that GA can still improve the accuracy of solutions even though the optimal regularization parameters are used in the coupled methods (LSQR-GA and TSVD-GA). GA can also reduce the temperature reconstruction errors due to the non-optimal choice of the regularization parameter and improve the accuracy of the reconstruction results in the coupled methods. Moreover, the coupled methods can even reach the same or better solutions accuracy for some samples with non-optimal regularization parameter, compared with the accuracy of solutions obtained by the single LSQR method or TSVD method with the optimal regularization parameter. This study demonstrates that the coupled method can alleviate non-optimal regularization parameter influence and obtain more accurate results for the inverse radiation problem of temperature distribution in participating medium.
机译:正则化参数的选择在参与介质中温度分布的反辐射问题中起着非常重要的作用,在实践中,不容易准确地确定正则化参数,这会直接影响重建的准确性并将误差引入重建结果。提出了两种正则化方法(最小二乘QR分解(LSQR)和截断奇异值分解(TSVD))耦合方法,缓解了非最优正则化参数对参比介质温度分布重构精度的影响。 ),再加上遗传算法(GA)。辐射热传递通过反向蒙特卡洛方法进行了描述,以提高其效率。考虑具有一个峰和两个峰的两种温度分布。结果表明,即使在耦合方法(LSQR-GA和TSVD-GA)中使用了最佳的正则化参数,GA仍可以提高解的精度。遗传算法还可以减少由于非最优选择正则化参数而引起的温度重建误差,并提高耦合方法中重建结果的准确性。此外,与通过单一LSQR方法或具有最佳正则化参数的TSVD方法获得的解的精度相比,对于具有非最佳正则化参数的某些样本,耦合方法甚至可以达到相同或更好的解精度。这项研究表明,耦合方法可以减轻非最优正则化参数的影响,并获得更准确的结果,解决参与介质中温度分布的反辐射问题。

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