Updating the singular value decomposition dating several people at the same time
This method, proposed by Hasselman et al (IMAC 1998), has been applied to both simulated and actual experimental data for low degree of freedom spring-mass systems with cubic nonlinearity and light damping.
The main results that will be presented are the following: (1) the SVD updating is robust in the presence of noise, (2) SVD based updating is effective for both linear and nonlinear systems,more » and (3) in some cases the nonlinear updating problem is actually easier to do than the linear problem because of the additional ''information'' contained in the harmonics produced by the nonlinearity.
The comparison criterion of interest is the theoretical computational complexity, it being understood that the dimension of the observation vectors is much larger than the number of observations.This work is a departure from most classical model updating work, which utilizes model data to update linear structural dynamics models.In the present application a singular value decomposition (SVD) of the measured data (e.g., m of the N coordinates are measured at n sampling times) is the basis of the updating. A possible limitation of the approach is the computing time needed to do the parameter optimization. Individual works may require securing other permissions from the original copyright holder.
The SVD produces a representation of the data as a linear combination of the so-called principal components, which are analogous to modal coordinate time histories in a linear system.