Data

The “Mesh independence verification.xlsx” file was the trend of the maximum temperature within the computational domain changing with the number of grids, as seen Figure 2A.The parameter sensitivity analysis(seen Figure 3B-G) was constructed as following:Firstly, 27 orthogonal experiments were constructed with COMSOL 6.0 software, and TC1, TC2, and TC3 were extracted by Matlab 2022b software，seen in the "TC1, TC2, and TC3 of 27 orthogonal experiments.xlsx".Then, Minitab 19 software was used to construct the main effect map and analysis of variance for parameter sensitivity analysis, seen in the "Parameter sensitivity analysis.mpx".The COMSOL Livelink with MATLAB interface was used to establish a connection between COMSOL and MATLAB. The MATLAB code controls COMSOL to perform parametric sweep calculations and extract results,seen "Single parameterized sweep.xlsx" file.Evolution of error S(P) , k₂ , σ₁ and σ₂ versus the number of iterations using the non-noise TC1 transient temperature,as seen "GN_iteration.xlsx" file.Temperature mearsurment at different niose level,seen in file "Noise Level.xlsx".Inversion results under different temperature measurement noise levels using LM algorithm,seen in file "LM_iterations.xlsx".The temperature distribution at different moments (10s, 20s, 40s, 60s, 80s, and 100s respectively) on truncated line were extracted by MATLAB code,seen in file "Temperature of the truncated line.xlsx".The differences between estimated and the exact temperatures at TC1, TC2, and TC3 were extracted respectively,seen in file "Temperature Difference.xlsx".