Effects of Noise on the Accurate Identification of a Vibrating System

Analytically derived solutions for a linear multivariable four degree of freedom system are derived using initial conditions allowing equal representation of all the modes. The mechanical system analyzed is a torsional system consisting of four discs mounted on a common shaft fixed at one end. The analytic solution for the displacement of the system is constructed from eigen values and eigen vectors obtained through the Holzer method. The noiseless digitized output displacement is analyzed by a system identification program using maximum likelihood methods. Comparison of the noiseless results are made when measurement and process noise are separately introduced into the known system. Results indicate system estimates degrade much faster under measurement noise than process noise. In addition, there are indications that accurate characterization of the system by the data record, depends on the bandwidth of the system.