Unified model modal expansion method for full field reconstruction and inversion under mechanical and thermal loading

In this paper, a novel method termed UMM-T&S (Unified Model Modal reconstruction and inversion method for Temperature field and Structural field under limited sensors) is proposed. This method aims to enhance highprecision structural performance inversion and reconstruction under mechanical and thermal loading conditions, particularly in the context of structural health monitoring within the aviation and aerospace sectors. The approach begins by deriving the "temperature modal" solution of the heat conduction equation, drawing upon the modal expansion techniques used in multi -degree -of -freedom systems. This is followed by constructing a parameter mapping relationship within the unified model, enabling the solution of both the structural field (encompassing strain and displacement) and the temperature field through a single structural model modal expansion. Furthermore, the paper details a numerical validation using two different temperature fields and a thermal loading experimental verification on a stiffened plate under five distinct working conditions. The proposed UMM-T&S method yields lower errors (ranging between 10%-40%) and more stable performance across various complex working conditions, in comparison to existing methods. The analysis also delves into the sources of errors and their cumulative impacts. In conclusion, the innovative UMM-T&S method offers a swift, precise, and robust solution for the intricate task of reconstructing and inverting structural performance under combined mechanical and thermal stresses. The method's efficacy and potential are substantiated through experimental validation and comparative analysis against an established methodology, underscoring its capability to effectively tackle the challenges faced in structural monitoring under such demanding conditions.