ABSTRACT Based on Bayesian inference, an adaptive single component Metropolis–Hastings (SCMH) sampling algorithm is presented to estimate the surface heat flux which is a typical inverse heat conduction problem. The surface heat flux is expressed by two different basis functions, the piecewise linear function and the Fourier series, and for speeding up convergence process, the parameters of the Fourier series are arbitrarily decoupled in the burn-in period. For validating and analysing the performance of the sampling algorithm, several cases are discussed. The results show that the adaptive SCMH sampling algorithm is feasible and has accuracy comparable to the conjugate gradient method (CGM), and decoupling method can successively shorten the burn-in period. It also can be found that ‘adaptive’ algorithm can obviously accelerate the convergence process. Furthermore, the performances of the two basis functions are also analysed. Because of the correlation, the paths of Markov Chain of the Fourier coefficients seem more ‘random’, which indicated that the algorithm with Fourier series is more efficient than that with piecewise linear function. The influence of the number of parameters is also studied, which is similar as the regularization of the CGM, the fewer the parameters is, the smoother the estimated heat flux becomes.

中文翻译：

---

自适应 MCMC 方法在热通量估算中的应用

摘要 基于贝叶斯推理，提出了一种自适应单分量 Metropolis-Hastings (SCMH) 采样算法来估计表面热通量，这是一个典型的逆热传导问题。表面热通量用分段线性函数和傅立叶级数这两个不同的基函数表示，为了加快收敛过程，在老化阶段对傅立叶级数的参数进行了任意解耦。为了验证和分析采样算法的性能，讨论了几种情况。结果表明，自适应SCMH采样算法是可行的，精度可与共轭梯度法（CGM）相媲美，解耦方法可以逐步缩短老化时间。还可以发现，“自适应”算法可以明显加快收敛过程。此外，还分析了两个基函数的性能。由于相关性，傅里叶系数的马尔可夫链的路径看起来更“随机”，这表明傅里叶级数的算法比分段线性函数的算法效率更高。还研究了参数数量的影响，类似于CGM的正则化，参数越少，估计的热通量就越平滑。这表明傅里叶级数的算法比分段线性函数的算法效率更高。还研究了参数数量的影响，类似于CGM的正则化，参数越少，估计的热通量就越平滑。这表明傅里叶级数的算法比分段线性函数的算法效率更高。还研究了参数数量的影响，类似于CGM的正则化，参数越少，估计的热通量就越平滑。