Application of frequency domain ARX models and extreme value statistics to damage detection

Abstract

In this study, the applicability of an auto-regressive model with exogenous inputs (ARX) in the frequency domain to structural health monitoring (SHM) is explored. Damage sensitive features that explicitly consider the nonlinear system input/output relationships produced by damage are extracted from the ARX model. Furthermore, because of the non-Gaussian nature of the extracted features, Extreme Value Statistics (EVS) is employed to develop a robust damage classifier. EVS is useful in this case because the data of interest are in the tails (extremes) of the damage sensitive feature distribution. The suitability of the ARX model, combined with EVS, to nonlinear damage detection is demonstrated using vibration data obtained from a laboratory experiment of a three-story building model. It is found that the current method, while able to discern when damage is present in the structure, is unable to localize the damage to a particular joint. An impedance-based method using piezoelectric (PZT) material as both an actuator and a sensor is then proposed as a possible solution to the problem of damage localization.

Active sensing using impedance‐based ARX models and extreme value statistics for damage detection

“…The upper and lower conÿdence limits corresponding to a 99.5% conÿdence interval ( = 0:005) are then calculated from the known parameters using Equation (14), or an equivalent equation for minima. Previous work has shown that the application of the EVS-based statistical model shows excellent results when applied to a joint in the structure that is known to be damaged [15]. Table II compares the e ectiveness of the limits found using EVS with those calculated based on the normality assumption of the data.…”

“…E xx (15) where Z p is the electrical impedance of the PZT, Z a and Z s are the mechanical impedances of the PZT material and structure, respectively, Y E xx is the complex Young's modulus of the PZT with zero electric ÿeld, d 3x is a PZT coupling constant in the arbitrary x-direction at zero stress, T 33 is a dielectric constant at zero stress, is the dielectric loss tangent of the PZT, and a is a geometric constant of the PZT. When a structure becomes damaged, the mechanical impedance is altered by changes in the structural sti ness and=or damping.…”

Learning methods for structural damage detection via entropy‐based sensors selection

“…First, PCA is performed by calculating the EVD of the data: hence, the complexity of the algorithm increases as the number of sensors increases. In particular, the algorithm complexity of eigenvalue computation for an n × n matrix is O(n 3 ) with standard SVD algorithms. 21 As a consequence, even PCA can be computationally intractable or inefficient when the number of sensors is very large.…”

“…In Section 4 we define the PE modeling and its integration with Entropy‐based sensor selection methodology. In Sections 5.1–5.3 we validate the techniques derived in this article on 3 accelerometric datasets 3,43,45 provided by various institutions and accessible via the data repository of the LANL In particular, we compare our novel methodology with existing PCA‐based methods both in terms of prediction accuracy and damage detection sensitivity.…”

A new open‐database benchmark structure for vibration‐based Structural Health Monitoring

“…In the sense of open research, data sets of laboratory campaigns have been published and exploited for several SHM problems. Good examples are vibration test campaigns of bookshelf structures 6,7 that feature different damages and undergo several controlled variations. The research conducted with these data sets reaches from system identification 8 to detection, localization, 9 and quantification 10 of damage, to name but a few applications.…”