Localization of dynamic forces on structures with an interior point method using group sparsity

This paper presents an algorithm for the localization of forces applied to a structure. The force estimation is performed in the frequency domain based on a limited number of sensors and a linear dynamic system model and it involves minimizing an objective function penalized with a group sparsity term. The minimization of this objective function is formulated as a second order cone program, which is solved using an interior point method. This allows for a reduction of the calculation time when compared to other algorithms that are currently available to enforce group sparsity on the forces, especially for large scale problems. The presented algorithm is first verified using numerical simulations. Next, a validation is performed using data obtained from a field test on a footbridge, where two locations on the bridge deck are excited using hammer impacts and the force localization is performed assuming a total of 108 possible force locations.