Estimation of modes of vibration of a structure by Kalman filter

In this work, a novel technique is suggested to estimate transient response of individual modes of vibration ofstructure. A two degree of freedom spring-mass-damper is taken as test structure. Equations of motion of the teststructure are derived from free-body diagrams of the individual masses. The system of two second-order ordinarydifferential equations is converted into a first order state-space model. Discrete Kalman filter is then used to estimatemodal displacement in the time domain. A good match is observed between numerically calculated modaldisplacements and numerically estimated modal displacements. Kalman filter can be effectively explained to estimateindividual modes of vibration for usage in traditional fields of vibrations like condition monitoring, fault diagnosis etc.

Keywords:

Kalman filter , estimation , state observer , two degrees of freedom system