Inverse problem method application in building physics numerical optimization: new insight into ideal envelope properties determination

Building thermal design optimization is pivotal for energy efficiency and built environment improvement. The optimal thermophysical properties for building walls remain ambiguous. This ambiguity stems from the constraints of traditional building physics, which: (1) disjoins the enhancement of wall thermal performance from the building service system management; and (2) relies on the forward method that fails to identify the ideal variable thermophysical property, the solution to which is inherently a function. This study elucidates the optimal temperature-dependent volumetric specific heat (ρcp(t)) and thermal conductivity (k(t)) through the inverse problem and variation method. Illustrative example indicates that the optimal ρcp(t) closely resembles a combination of two 'δ' functions, while the optimal k(t) mirrors a square wave function. Utilizing these ideal thermophysical properties, the building energy consumption can be significantly reduced by 77.1% with the optimized ρcp(t) and 79.9% with the optimized k(t). The ideal thermophysical properties for active buildings differ significantly from those recommended for passive buildings, underscoring that minimal energy consumption does not necessarily imply minimal discomfort. Therefore, the thermophysical properties of active and passive buildings should be optimized distinctly. This research offers valuable insights for defining ideal thermophysical properties of active building walls and construction materials.