Collision detection for a flexible cantilever-beam subject to random disturbance based on innovation process

In this paper, an algorithm for detection of collisions for a flexible cantilever-beam subject to random disturbance based on a model-based fault diagnosis method is presented. The mathematical model of the flexible cantilever-beam is described by an Euler-Bernoulli type partial differential equation. The collision detection filter is constructed based on the Kalman filter for the finite-dimensional system corresponding to the mathematical model of the flexible beam. If collisions of the flexible beam and environmental obstacles occur, the statistics of the residual signal (innovation process) change. To detect such a statistical change of the residual signal due to the collision, a chi-squared like test is introduced. Several numerical results are presented.