Identification of dynamic forces using group-sparsity in frequency domain

• Ill-conditioned inverse problems in the frequency domain are considered.
• Based on the structural model and the vibration data, point forces (e.g. impacts) on the structure are localized and reconstructed.
• A new approach is proposed for load identification based on mixed and penalized cost function optimization.
• The new cost function takes advantage of grouped sparsity using ℓp-norm properties.
• The numerical and experimental studies show that the proposed technique has better accuracy in force reconstruction comparing to classical methods.

The knowledge of acting dynamic forces is required for the design of structures. Given the structural model, inverse techniques offer the possibility to reconstruct the system’s input forces from vibration data. The inverse problem is highly sensitive to measurement noise, and the classical pseudo-inverse method generally fails to find the correct loads. In this paper we propose a new penalty function that combines the advantages of the ℓp-norm properties, together with a modified iterative optimization technique. The new algorithm (G-FISTA) is used to localize and reconstruct dynamic point-forces on a beam structure, with no prior knowledge on the force locations. The algorithm is validated by means of several simulations and experiments. The strain data is measured using Fiber Bragg Gratings (FBG) attached to the beam. The obtained results show that the location and time history of point forces are better estimated using the proposed technique.