Multi-axial flexible manipulators are structures typically employed in the maintenance of large hydropower equipment such as turbine runners. This kind of multi-process robot was specifically designed for repair jobs related to material removal via grinding or polishing. In general, the estimation of the contact forces between the grinding cup and the workpiece is crucial for improving the robot’s performance and minimizing unwanted vibration at the end effector. However, due to working in a harsh environment, the direct force measurements cannot be implemented. This paper introduces a new method using a Kalman filter based on a time series Auto-Regressive with eXogenous excitation (ARX) modelling to deal with the inverse problem, where ARX model is modified by employing ambient vibration data only. The recursive least squares algorithm is adopted to reduce the effect of high random noises, thus allowing to identify the excitation forces in multiple directions under grinding operations. The proposed method was illustrated via different examples with numerical simulations and experiments on a cantilever beam and on a flexible manipulator. The numerical simulations allow for investigating the robustness of the method against noise, while its ability to identify the forces and the modal properties of structures is also presented.