Operational Modal Analysis (OMA) identifies modal properties of mechanical structures from vibration data collected from a few sensors under operation conditions. These methods are widely used to monitor civil engineering structures that are modeled as time-invariant systems. However, when dealing with wind turbines and rotating machines, many dedicated OMA techniques were developed to deal with the time-periodic behavior. Existing methods pre-process the data to adapt them to classical identification techniques. Yet, these methods present limitations as either requiring a high number of measured rotation periods, assuming the assumption of an isotropic rotor (i.e. undamaged), or the knowledge of the rotational speed. This work proposes to lift these difficulties by proving that the application of the classical system identification methods can produce meaningful estimates for anisotropy monitoring. This observation is based on directly approximating the time-periodic dynamic behavior of the wind turbine as a properly defined time-invariant system under periodic inputs. It results in the possibility of using classical identification methods without modification to retrieve the system matrices of the approximated time-invariant system. This approach does not require knowing the rotor speed, requiring relatively fewer measurements and it is not restricted to isotropic rotors. The identified modes can be used reliably for the monitoring of operating wind turbines and more especially for fault detection, at the expense of losing a part of the complete description of the periodic system. The resulting anisotropy monitoring approach and its capacities are illustrated in two cases. Firstly, on an academic model of a wind turbine and then on an aero-servo-elastic numerical model of a rotating 10MW wind turbine to demonstrate the ability of the method to deal with realistic and representative data. It is shown for the latest case, from sensors located on the blades of the wind turbine, the approach is able to identify correctly the system properties (frequencies and mode shapes) and is also able to detect efficiently a fault on a blade.