Reconstruction of vibration-deformation-induced pointing error via optimized acceleration measurement points for large reflector antennas

As large reflector antennas have a low natural frequency and primarily operate in open air without a radome, factors such as the stochastic wind disturbance and the moving platform obviously increase the vibration-deformation pointing error. Moreover, in the actual working operation of large reflector antennas, the traditional measurement method can only sense the pointing error at the hinge via encoders and cannot sense the vibration-deformation-induced pointing error of the main reflector. This paper presents a reconstruction method of the vibration-deformation-induced pointing error for the main reflector via optimized acceleration measurement points. First, an entire working condition model of the main reflector for vibration-deformation-induced pointing error observation is established to provide the general relations among the acceleration, location, number of measurement points, and vibration-deformation-induced pointing error. In this model, the vibration-deformation-induced pointing error is reconstructed based on the best-fitting paraboloid theory and the frequency-domain integration approach. Furthermore, a Tikhonov regularization scheme is adopted to mitigate the ill-posedness due to random noise in the measured accelerations. Second, to obtain a well-reconstructed vibration-deformation-induced pointing error with certain accuracy, this study proposes a novel four-symmetric-point dynamic optimization algorithm for optimization of the sensor layout is proposed. Finally, a wind disturbance simulation of a 7.3 m antenna is undertaken. The results show that under the accuracy constraint of 5%, a well-reconstructed vibration-deformation-induced pointing error is obtained from the 20 optimized measurement points. Compared with the effective independence method, four-symmetric-point dynamic optimization algorithm has higher precision in observing the vibration-deformation-induced pointing error and is more convenient for arranging the sensors.