Novelty Detection in a Cantilever Beam using Extreme Function Theory

Damage detection and localisation in beam-like structures using mode shape features is well-established in the research community. It is known that by inserting a localised anomaly in a cantilever beam, such as a crack, its mode shapes diverge from the usual deflection path. These novelties can hence be detected by a machine-learner trained exclusively on the modal data taken from the pristine beam. Nevertheless, a major issue in current practices regards discerning between damage-related outliers and simple noise in observations, avoiding false alarms. Extreme functions are here introduced as a viable mean of comparison. By combining Extreme Value Theory (EVT) and Gaussian Process (GP) Regression, one can investigate functions as a whole rather than focusing on their constituent data points. Indeed, n discrete observations of a mode shape sampled at D points can be assumed as 1-dimensional sets of n randomly distributed observations. From any given point it is then possible to define its Probability Density Function (PDF) and the Cumulative Density Function (CDF), whose minima, according to the EVT, belong to one of three feasible extreme distributions - Weibull, Frechet or Gumbel. Thus, these functions - intended as vectors of sampled data - can be compared and classified. Anomalous displacement values that could indicate the presence of a crack are therefore identified and related to damage. In this paper, the effectiveness of the proposed methodology is verified on numerically-simulated noisy data, considering several crack locations, levels of damage severity (i.e., depths of the crack) and signal-to-noise ratios.