Effects of Noise on Sensor Placement for On-Orbit Modal Identification of Large Space Structures

A method of sensor placement for the purpose on-orbit modal identification and test-analysis correlation is presented. The method is an extension of the Effective Independence method presented in past work to include the effects of a general representation of measurement noise. Sensor noise can be distributed nonuniformly throughout the structure as well as correlated between sensors. The only restriction is that the corresponding noise covariance intensity matrix is positive definite. The technique presented offers a fast and efficient approach for reducing a relatively large initial candidate sensor location set to a much smaller optimum set which retains the linear independence of the target modes and maintains the determinant of the Fisher Information Matrix resulting in improved modal response estimates. The noise covariance intensity matrix which has been introduced into the method can be thought of as a sensor weighting matrix which modifies the shape of the target modes. The mode shape coefficients are modified based upon the noise levels at the sensor locations. Inclusion of the noise model results in higher ranking of sensor locations with low noise levels and suppression of sensor locations with high noise levels. A criterion is also presented which can be used during the course of the sensor placement analysis to determine how many sensors are required to maintain a desired level of signal-to-noise ratio over all the target modes. Simple numerical examples are presented which clearly demonstrate the ideas and trends presented in the paper.