Propagation of hybrid uncertainties in transient heat conduction problems

In this paper, the propagation of hybrid uncertainties is studied in transient heat conduction problems. Based on the layer-by-layer analysis strategy, a novel mixed method using the stochastic theory and the convex model is presented. Two types of models for the uncertainties are considered: random parameters and uncertain-but-bounded parameters. Firstly, the matrix perturbation theory is utilized to deal with random parameters, obtaining the temperature response expectation and variance. Then using the Taylor series expansion and the Lagrange multiplier method to analyze the convex model, we derive the intervals of the temperature response probabilistic characters. Four numerical examples are presented to address transient heat conduction problems with random and uncertain-but-bounded parameters or pure uncertainties. The results are compared with those of the Monte Carlo method to verify the feasibility and practicality of the proposed method. In addition, the proposed method is also applicable to the steady-state problems.