A method for operating a hydraulic system of an industrial machine, which hydraulic system comprises an actuator and a hydraulic pump which are connected fluidically via a hydraulic line which is assigned a pressure sensor. The hydraulic pump comprises an electric motor and a pump head driven by the latter. A pressure within the hydraulic line is measured via the pressure sensor, and a first pressure value is generated therefrom. A second pressure value is determined on the basis of operating data of the electric motor and a theoretical model. A fault is detected if the first pressure value differs from the second pressure value by more than a tolerance value. An industrial machine is also provided.