Quadtree SBFEM and optimization based forward and inverse interval analysis for PCM-integrated walls

Interval model is employed to describe the uncertain behavior of phase change materials (PCM) integrated walls. A numerical model is developed for the forward interval analysis, by which the interval bounds of thermal response, such as the temperature on the inner wall and the degree of phase change of PCM, can be estimated when materials and environmental parameters are interval variables. This model integrates the advantages of the quadtree-scaled boundary finite element method (quadtree SBFEM), the Legendre polynomial surrogate (LPS), interval model, and optimization method, to gain a comprehensive benefit of convenient mesh regeneration, reliable bounds estimation, and the alleviation of heavy computational burden in the optimization process. On the other side, a numerical model is presented for the inverse interval analysis, by which the interval bounds of material parameters can be identified when the intervals of measurement of temperature and the degree of phase change of PCM are provided, and the impact of nosy data is taken into account. This model may be enlightening for a deeper investigation of inverse interval analysis of PCM-integrated walls since no attention seems to have been paid to this issue. In terms of computing accuracy, computational cost, and numerical examples are provided to elucidate the effectiveness of proposed approaches, and satisfactory results are achieved in both forward and inverse interval analysis.