Stochastic Subspace-based Damage Detection with Uncertainty in the Reference Null Space

Abstract

This paper deals with uncertainty considerations in damage diagnosis using the stochastic subspace-based damage detection technique. With this method, a model is estimated from data in a (healthy) reference state and confronted to measurement data from the possibly damaged state in a hypothesis test. Previously, only the uncertainty related to the measurement data was considered in this test, whereas the uncertainty in the estimation of the reference model has not been considered. We derive a new test framework, which takes into account both the uncertainties in the estimation of the reference model as well as the uncertainties related to the measurement data. Perturbation theory is applied to obtain the relevant covariances. In a numerical study the effect of the new computation is shown, when the reference model is estimated with different accuracies, and the performance of the hypothesis tests is evaluated for small damages. Using the derived covariance scheme increases the probability of detection when the reference model estimate is subject to high uncertainty, leading to a more reliable test.

Nonlinear Detection in Wave Loaded Structures

“…Finally, we will consider the SSI damage detection technique formulated 10-15 years ago, see [9][10]. This technique is based on the principle of defining the physical subspace as the modal subspace, and everything that falls out of the physical subspace as the socalled null-space defining components indicating damage.…”

“…T y (10) where + T is the pseudo inverse of T. Since we are assuming that sensors are mounted only on the topside of the structure, the physical part of the null space response will be rigid body motion, and since the magnitude of the translation does not matter but only the shape, the null space movement will be dominated by rotation only. We will divide the rotational response into two components, the principal rotational movement, and the compression of the neutral axis.…”