A virtual force-based method for time-domain force identification with unknown initial conditions

This study proposes a virtual force-based Green's kernel function method (VFB-GKFM) for identifying time-domain force under unknown initial conditions. The key concept is to reinterpret the free vibration caused by unknown initial conditions as the response induced by virtual forces acting before the start of sampling. This method transforms the challenge of dealing with unknown initial conditions into the task of identifying virtual forces. This allows both the actual and virtual forces to be identified within the unified framework of conventional GKFM, requiring only impulse response functions that can be readily obtained through experiments. Numerical simulations demonstrate the effectiveness of the method for both single-force and multiple-force scenarios. Parameter sensitivity analysis shows that the required virtual force duration for stable identification is insensitive to structural damping, loading patterns, and pre-sampling motion duration. Further investigation reveals that the fundamental natural period of the structure may be useful for determining appropriate virtual force duration. The method is validated through experimental tests conducted entirely using experimental data without relying on finite element models, making it particularly well-suited for practical engineering applications where accurate structural models are difficult to obtain.