Inverse Methods Project

Inverse Methods Project – Thermal Diffusivity Estimation (Flash Method, ENSAM)

Conducted within an ENSAM “Inverse Methods” project, this work focused on estimating key thermal parameters (mainly thermal diffusivity) from Flash/LFA thermograms. The objective was to compare analytical estimation techniques with inverse and probabilistic methods, and to evaluate their robustness to measurement noise for both single-layer (monolayer) and two-layer (bilayer) thin-film cases.

Starting from the physics of 1D heat conduction (Parker / Carslaw & Jaeger background) and practical non-idealities (losses and finite pulse duration), the project implemented a full workflow: initial parameter guessing, signal smoothing, nonlinear least-squares identification (Gauss–Newton), and a Bayesian approach using MCMC (Metropolis–Hastings) to quantify uncertainty and parameter correlations.

Key Outcomes

• Flash method modeling: Built a consistent forward model for thermograms and discussed ideal vs non-ideal conditions (losses, pulse effects), with clear physical interpretation of parameters.
• Initial-guess strategies: Compared Parker half-rise time, partial times, and temporal moments to build a reliable starting vector for iterative inversion.
• Noise & filtering: Implemented polynomial smoothing (polyfit) with a Monte-Carlo framework to assess the impact of noise and improve stability of analytical estimators.
• Gauss–Newton inversion: Performed nonlinear least-squares fitting on the full thermogram, and analyzed the critical role of initialization (convergence vs local minima / divergence).
• MCMC uncertainty quantification: Used Metropolis–Hastings to estimate posterior distributions, highlight parameter correlations, and provide credible intervals (particularly informative on the rear-face configuration).
• Monolayer vs bilayer insights: Extended the approach to a thin-film + substrate model, showing how effusivity ratios can make identification easier or ill-posed depending on the measurement face.

This project strengthened my skills in heat-transfer modeling, parameter identification, and uncertainty analysis. It provided a complete, engineering-oriented view of inverse problems: from physics-based modeling to robust estimation under noisy experimental conditions, and from deterministic optimization to probabilistic inference.

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