Real time detection of stiffness change using a radial basis function augmented observer formulation

Existing methods for structural health monitoring pose a formidable challenge to real time implementation due to the significantly large computational loads. The proposed algorithm is suitable for online applications because it maintains good pattern recognition capabilities while possessing a computationally compact network topology. This study employs the computational efficiency of single layer radial basis function (RBF) approximaters to create a subspace capable of isolating faults in multi-degree of freedom systems which involve coupled and uncoupled stiffness changes in real time. The RBF network transforms the displacement-time history of the varying plant into a decoupled output space which is then compared to a baseline healthy observer which undergoes the same decoupling transformation. The online comparison of the output of the time varying plant and the healthy observer in a decoupled subspace comprises the observer based error function. The error function is shown to not only detect the existence of faults, but also isolate these faults in real time in the presence of base excitation. The method is validated for systems that experience earthquake induced damage, as well as an experimental system using a semi-active independent variable stiffness device which is capable of varying system stiffness in real time. By simply observing the displacement-time history responses, the RBF augmented observer formulation is capable identifying changes in the stiffness at each degree of freedom.