Sensor fusion based vibration estimation using inertial sensors for a complex lightweight structure

Flexible structures with spatially distributed accelerometers are a central feature of the “experimental modal analysis” serving to characterize the vibration properties of elastic mechanical systems. In contrast to this frequency based offline procedure, real-time tasks like motion control or health monitoring of such structures typically rely little on correspondingly spread inertial sensors. However, to improve approaches for motion control or health monitoring, a sophisticated measurement of the structural movement using distributed accelerometers and additionally gyros offers itself. On the other hand, the aspect of providing a good motion estimate by using only a limited number of sensor signals should also not be disregarded. It is well known that combining different types of sensors in order to take advantage of the complimentary characteristics of each sensing element is the basis of integrated navigation systems. It is called sensor fusion. Such a system can be established in general as a state observer design; and in navigation it determines the spatial motion of just a rigid body. However, extending such integrated systems to flexible structures using distributed structural sensors is possible, which was already proven for one dimensional continuums, i.e. a flexible beam. For more complicated structures, the theory needs to be extended to three dimensions. All such systems can be generalized as an integrated motion measurement. As a typical example, this paper presents an integrated motion measurement approach for the realtime estimation of the critical telescope vibrations of the Stratospheric Observatory for Infrared Astronomy (SOFIA). This application is important as the optical performance of SOFIA is affected by telescope oscillations being induced by aero acoustic disturbances. Distributed inertial sensors are used to obtain motion signals, which are additionally aided by strain gauges. The sensor fusion approach being developed here consists of a continuous-discrete extended Kalman filter. Besides the sensor signals to be fused, the filter requires a suitable kinematical model, which in turn determines the mechanical meaning of all measurements. The kinematic model is based on a reduced modal approach, i.e. a description of the telescope by vibration modes having high contribution to the optical quality at the focal plane of the astronomical instruments. To realize such an integrated measurement system, there are no mass and stiffness properties of the structure required. However, the approximate knowledge of the modal properties of the structure is necessary for the implementation of this method. Therefore, a finite element model of the telescope was chosen as a basis to extract such modal properties. In addition, the finite element model was employed to determine the appropriate number, position and orientation of the gyros, accelerometers and strain gages. Simulation results demonstrate the potential of the approach and its feasibility for complex lightweight structures.