Application of an adaptive MCMC method for the heat flux estimation

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.

KEYWORDS:

• Inverse heat conduction problems
• Bayesian inference
• Markov chain Monte Carlo method
• adaptive method
• ill-posed

2010 MSC MATHEMATICS SUBJECT CLASSIFICATIONS:

• 80A20
• 80A23
• 65C05
• 65C40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [Grant Number 11372338]; Foundation of the State Key Laboratory of Aerodynamics: [Grant Number JBKY11030903].