Inversion of GIS Vibration Source Localization Based on Modal Space Method

To address the challenges of localizing internal vibration sources and quantifying force-time histories in Gas-Insulated Switchgear (GIS), this paper proposes a source inversion method based on modal space analysis. A two-step framework of “modal force reconstruction—source localization” is established. First, a Physics-Informed Gaussian Process (PIGP) combined with the system’s dynamic equations is employed to reconstruct modal forces from sparse external acceleration responses. Then, based on the collinearity principle between modal force vectors and modal shape vectors, a Genetic Algorithm (GA) is used for global optimization to determine the excitation source location, and the force-time history is obtained via orthogonal projection. To validate the method’s effectiveness, numerical simulations under two typical conditions—transient impact and steady-state harmonic excitation—were conducted. The results demonstrate that the method can effectively identify the source location with an error of less than 2.3%. The reconstructed force-time histories highly match the true excitations, with Pearson Correlation Coefficients (PCC) exceeding 0.995. This study confirms the potential of the proposed method for precise, quantitative vibration source inversion and fault diagnosis in complex equipment.