This paper proposes a multi-rate method to identify the propagation path of a persistent disturbance in an enlarged system envelope which includes the process plant and its electromechanical equipment. The need to integrate process and equipment diagnosis has been highlighted by industrial commentators.However, process and electromechanical measurements often have different sampling rates. The multi-rate method proposed extends a state-of-the-art propagation path method so that it combines fast-sampled electromechanical measurements and slow-sampled process measurements. The method is based on non-linear mutual prediction, which yields the directionality in the relationship between two time series. The method was demonstrated and validated, giving the expected outcome in an experimental case study, in which the root cause and propagation path of the disturbance were known.