`Evaluation of the Penalized Least Squares Method for Strain Computation

This work proposes an alternative procedure to smooth and differentiate experimental full-field displacement measurements to get strain fields. This one, the penalized least squares method, relies on the balance between the fidelity to original raw data and the smoothness of the reconstructed ones. To characterize its performance, a comparative study between this algorithm and two other commonly implemented strategies (the 'diffuse approximation' and the Savitzky-Golay filter) is achieved. The results obtained by the penalized least squares method are comparable in terms of quality of the reconstruction to those produced by the two other algorithms, while the proposed technique is the fastest as its computation time is totally independent from the asked amount of smoothing. Moreover, unlike both other considered methods, it is possible with this technique to perform the derivation to obtain strain maps before smoothing them (while the smoothing is normally applied to displacement maps before the differentiation) which can lead in some cases to a more effective reconstruction of the strain fields.