The Extreme Function Theory for Damage Detection: An Application to Civil and Aerospace Structures

Abstract

Any damaged condition is a rare occurrence for mechanical systems, as it is very unlikely to be observed. Thus, it represents an extreme deviation from the median of its probability distribution. It is, therefore, necessary to apply proper statistical solutions, i.e., Rare Event Modelling (REM). The classic tool for this aim is the Extreme Value Theory (EVT), which deals with uni- or multivariate scalar values. The Extreme Function Theory (EFT), on the other hand, is defined by enlarging the fundamental EVT concepts to whole functions. When combined with Gaussian Process Regression (GPR), the EFT is perfectly suited for mode shape-based outlier detection. In fact, it is possible to investigate the structure’s normal modes as a whole rather than focusing on their constituent data points, with quantifiable advantages. This provides a useful tool for Structural Health Monitoring, especially to reduce false alarms. This recently proposed methodology is here tested and validated both numerically and experimentally for different examples coming from Civil and Aerospace Engineering applications. One-dimensional beamlike elements with several boundary conditions are considered, as well as a two-dimensional plate-like spar and a frame structure.

Detection and Localization of Multiple Damages through Entropy in Information Theory

“…This is relatively inconvenient for masonry or concrete structures, where the material inhomogeneity and variability may cause damage-unrelated fluctuations. In turn, these cause a higher risk of false-positive identifications [10], which are a common threat to vibration-based SHM [18]. On the other hand, for more homogeneous building materials, this greater accuracy can instead be exploited to detect small cracks in their earlier extension phases.…”

Bayesian Updates for an Extreme Value Distribution Model of Bridge Traffic Load Effect Based on SHM Data

“…As mentioned in Section 2.1, the probability model of peak-over-threshold traffic load effect, F * s (s * ), follows a GPD. With Equations ( 5) and ( 9), the CDF of the traffic load effect that exceeds a high threshold EV distribution for an FPP during the service period T is Equation (11), which obviously follows the GEV distribution:…”

“…The actual loads on trucks are often illegally overloaded, which has led to higher risks [7]. There is an increasing demand for a systematic and efficient safety assessment of bridges to prevent possible disasters [8][9][10][11].…”

“…Many approaches have been put forward for predicting the probability model of extreme traffic load effect based on limited site-specific data, such as the normal probability paper method and the Monte Carlo method [28]. To deal with the statistics of extremes, the extreme value theory (EVT) [29] represents an ideal framework, which has already been used for the purpose of structural dynamics [11]. The EVT has also been used for modeling extreme traffic load effect for several years.…”

“…Yiming Gu et al [14] proposed a novel Bayesian approach for estimating the extreme traffic. Most of the above research does not pay attention to the stochastic process, while some is under the framework of Gaussian processes [11,40]. According to the Unified Standard for Reliability Design of Highway Engineering Structures (GB/T 50283-1999), the traffic loading process conforms to a filtered Poisson process (FPP).…”