Model-Based Processing

Appendix DOutput‐Only Subspace Identification

In this appendix, we address the subspace identification approach for the constrained “output‐only” realization problem where no input excitation data are available in contrast to the developments of Chapters 6 and 7. Output‐only problems occur frequently in practice, especially in structural dynamics, seismic analysis, medical diagnosis to name a few prominent problem areas. For instance, in structural dynamics, large buildings, bridges, or tunnels are excited by wind or daily traffic, while earthquakes provide the excitation for seismic monitoring where medical applications are driven by unknown sources.

Subspace methods have evolved primarily from the early work of Akaike 1,2 and Aoki 3 in stochastic realization and projection theory. The primary idea, when applied to the “output‐only” problem, is to perform an orthogonal projection in a Hilbert space occupied by random vectors. That is, if is a finite random vector of future outputs and a random vector of past outputs, then the orthogonal projection of the “future output data onto the past output data” is defined by . The concept of projecting a vector onto a subspace spanned by another ...