Force reconstruction: analysis and regularization of a deconvolution problem

The reconstruction of force is considered by means of indirect measurements. This necessitates taking measurements from the impacted structure and then to deconvolve those signals from the impulse response function. More precisely, the purpose of the work described here is to analyze a deconvolution technique and to solve the problems which occur. Thus, it is highlighted that the associated deconvolution problem depends on the location of the measurement points: is it possible or not to reconstruct the impact force versus the location of this point. Numerical predictions are compared and validated with experiment. But, the deconvolution is a well-known ill-posed problem: the results are often unstable. This is why it is necessary to regularize the problem, which consists of adding a condition to the solution which does not appear in the initial problem. Some regularization methods are presented. Nevertheless, they necessitate the determination of a parameter; the difficulty is to calculate an appropriate value of this regularization parameter. The methods are successfully used to recover an experimental force.