Nassiopoulos, Alexandre (2008) Identification rapide de la température dans les structures du génie civil. PhD thesis, ENPC p.178.

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Abstract

Structural Health Monitoring techniques come up against dominant environmental effects due to ambient temperature variations. Real time temperature data assimilation is crucial for the elimination of these effects in ambient vibration monitoring algorithms. We develop algorithms for the estimation of the temperature field at a given moment, based on pointwise measurements over the time period preceding that moment. The approach is based upon the adjoint method in optimal control theory. The problem consists in minimizing in the least squares sense a regularized quadratic performance index measuring the gap between the data and a reconstructed temperature at sensor locations.

The well-known convergence difficulty of the adjoint technique near the final instant of the observation period is eliminated here by minimizing the performance index in a smooth enough functional space, thus enabling the reconstruction of the current temperature in the entire domain. High regularity spaces must be chosen so that we can define pointwise values of the temperature field. In order to use standard discretization methods, we propose special transposition-based techniques for the computation of the adjoint state.

A dual formulation enables precomputing strategies and constructs high-speed algorithms well suited for real-time applications.

The robustness of the algorithms with respect to modelling errors or measurement noise is tested both numerically and experimentally.

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