An accelerated sequential function specification method based on LM gradient for transient inverse heat conduction problem

Abstract

The sequential function specification method (SFSM) and the Levenberg-Marquardt method (LM) are two typical methods for inverse heat conduction problems (IHCP). However, these two methods have poor convergence and low convergence speed. Therefore, the combination of LM with SFSM is depended on to propose a modified Sequential Levenberg-Marquardt gradient method (SLM). The computation results of three shapes of heat fluxes with noise show the SLM is averagely improved over 16.3% more than SFSM in computation accuracy, but equally reduced over 39.9% less than in computation time. On other hand, when the emphasis is on the effect of the Aitken acceleration method, Tikhonov regularization and polynomial order on SLM, a neural network prediction model of the root mean square error is trained by regularization factor, polynomial order and the number of future time steps. Subsequently, the genetic algorithm optimization method is proposed for the minimum root mean square error so that it can improve the computation accuracy and efficiency of IHCP to the maximum extent. Finally, Second-order polynomial order and small order-of-magnitude regularization factor are highly recommended for parameter selection with multiple choices. The ASLM only needs to determine the optimal number of future time steps.