The Reference State Validation window allow you to inspect the performance of the Reference State Model used for a specific damage detection method. This diagram resembles the information also available in the Stochastic Subspace Identification techniques.
The Reference State Model is constructed from an average of Hankel matrices of covariance information of a series of reference measurements (sessions). The averaged Hankel matrix is decomposed using Singular Value Decomposition into left and right singular vectors and corresponding singular values. It is the singular values that below are presented as yellow horizontal bars.
From the most significant (largest) singular values the Observability matrix of the Reference State Model can be constructed. The most significant singular values are the ones below the green bar, that indicated the applied system order. These singular values are also referred to as the Dynamic Subspace. and indicated with the light-gray color.
The insignificant (smallest) singular values above the system order are the ones that relate to the left Null-space. The left Null-space is simply the corresponding left singular vectors. The dark gray color indicate this region, which is also called the Null Space.
Validation
The important validation to do is the following:
- Make sure that the Singular Values (yellow bars) become insignificant as the Hankel Matrix Dimension is increasing. If this is not the case re-run the estimation of the Reference State Model with larger Hankel size.
- Make sure that the selected System Order (green bar) divides the singular values into very significant ones (largest) below and very insignificant ones (smallest) above the green bar. The relative value called Ref. Singular Value ahould not be more than approx 1-5%. If it is higher, then the Null-space is "poluted" by the system dynamics. Below Ref. Singular Value value is 2.22% and the selected System Order is 10.
- Make sure that there are a proper number of singular values forming the Null-space. If the green bar is very close to the maximum Hankel Matrix Dimension, then re-run the estimation of the Reference State Model with larger Hankel size.
