Structural Damage Classification Using Extreme Value Statistics

2005 ◽  
Vol 127 (1) ◽  
pp. 125-132 ◽  
Author(s):  
Hoon Sohn ◽  
David W. Allen ◽  
Keith Worden ◽  
Charles R. Farrar
Keyword(s):  
Extreme Values ◽  
Novelty Detection ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Series Data ◽  
Identification Algorithm ◽  
Damage Classification ◽  
Mass System ◽  
Damage Diagnosis ◽  
Normality Assumption

The first and most important objective of any damage identification algorithm is to ascertain with confidence if damage is present or not. Many methods have been proposed for damage detection based on ideas of novelty detection founded in pattern recognition and multivariate statistics. The philosophy of novelty detection is simple. Features are first extracted from a baseline system to be monitored, and subsequent data are then compared to see if the new features are outliers, which significantly depart from the rest of population. In damage diagnosis problems, the assumption is that outliers are generated from a damaged condition of the monitored system. This damage classification necessitates the establishment of a decision boundary. Choosing this threshold value is often based on the assumption that the parent distribution of data is Gaussian in nature. While the problem of novelty detection focuses attention on the outlier or extreme values of the data, i.e., those points in the tails of the distribution, the threshold selection using the normality assumption weights the central population of data. Therefore, this normality assumption might impose potentially misleading behavior on damage classification, and is likely to lead the damage diagnosis astray. In this paper, extreme value statistics is integrated with the novelty detection to specifically model the tails of the distribution of interest. Finally, the proposed technique is demonstrated on simulated numerical data and time series data measured from an eight degree-of-freedom spring-mass system.

scholarly journals Statistics of the largest geomagnetic storms per solar cycle (1844-1993)

1997 ◽  
Vol 15 (6) ◽  
pp. 719-728 ◽  
Author(s):  
D. M. Willis ◽  
P. R. Stevens ◽  
S. R. Crothers
Keyword(s):  
Statistical Analysis ◽  
Solar Cycle ◽  
Geomagnetic Storm ◽  
Extreme Values ◽  
Geomagnetic Storms ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Relative Dispersion ◽  
Solar Cycles ◽  
Aa Index

Abstract. A previous application of extreme-value statistics to the first, second and third largest geomagnetic storms per solar cycle for nine solar cycles is extended to fourteen solar cycles (1844–1993). The intensity of a geomagnetic storm is measured by the magnitude of the daily aa index, rather than the half-daily aa index used previously. Values of the conventional aa index (1868–1993), supplemented by the Helsinki Ak index (1844–1880), provide an almost continuous, and largely homogeneous, daily measure of geomagnetic activity over an interval of 150 years. As in the earlier investigation, analytic expressions giving the probabilities of the three greatest storms (extreme values) per solar cycle, as continuous functions of storm magnitude (aa), are obtained by least-squares fitting of the observations to the appropriate theoretical extreme-value probability functions. These expressions are used to obtain the statistical characteristics of the extreme values; namely, the mode, median, mean, standard deviation and relative dispersion. Since the Ak index may not provide an entirely homogeneous extension of the aa index, the statistical analysis is performed separately for twelve solar cycles (1868–1993), as well as nine solar cycles (1868–1967). The results are utilized to determine the expected ranges of the extreme values as a function of the number of solar cycles. For fourteen solar cycles, the expected ranges of the daily aa index for the first, second and third largest geomagnetic storms per solar cycle decrease monotonically in magnitude, contrary to the situation for the half-daily aa index over nine solar cycles. The observed range of the first extreme daily aa index for fourteen solar cycles is 159–352 nT and for twelve solar cycles is 215–352 nT. In a group of 100 solar cycles the expected ranges are expanded to 137–539 and 177–511 nT, which represent increases of 108% and 144% in the respective ranges. Thus there is at least a 99% probability that the daily aa index will satisfy the condition aa < 550 for the largest geomagnetic storm in the next 100 solar cycles. The statistical analysis is used to infer that remarkable conjugate auroral observations on the night of 16 September 1770, which were recorded during the first voyage of Captain Cook to Australia, occurred during an intense geomagnetic storm.

Bayesian Extreme Value Statistics for Novelty Detection in Gas-Turbine Engines

2008 ◽  
Author(s):  
David A. Clifton ◽  
Lionel Tarassenko ◽  
Nicholas McGrogan ◽  
Dennis King ◽  
Steve King ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Novelty Detection ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Turbine Engines ◽  
Gas Turbine Engines

scholarly journals Freezing transitions and extreme values: random matrix theory, and disordered landscapes

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120503 ◽  
Author(s):  
Yan V. Fyodorov ◽  
Jonathan P. Keating
Keyword(s):  
Matrix Theory ◽  
Extreme Values ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Constant Length ◽  
Energy Models ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Transition Scenario ◽  
Unitary Ensemble

We argue that the freezing transition scenario , previously conjectured to occur in the statistical mechanics of 1/ f -noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials p N ( θ ) of large N × N random unitary (circular unitary ensemble) matrices U N ; i.e. the extreme value statistics of p N ( θ ) when . In addition, we argue that it leads to multi-fractal-like behaviour in the total length μ N ( x ) of the intervals in which | p N ( θ )|> N x , x >0, in the same limit. We speculate that our results extend to the large values taken by the Riemann zeta function ζ ( s ) over stretches of the critical line of given constant length and present the results of numerical computations of the large values of ). Our main purpose is to draw attention to the unexpected connections between these different extreme value problems.

Electro-Mechanical Admittance-Based Damage Detection Using Extreme Value Statistics

2008 ◽  
Vol 385-387 ◽  
pp. 561-564 ◽  
Author(s):  
Costas P. Providakis
Keyword(s):  
Health Monitoring ◽  
Extreme Values ◽  
Simulated Data ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Engineering Structures ◽  
Value Analysis ◽  
Electromechanical Impedance ◽  
Tail Distribution

This paper presents the use of statistically rigorous algorithms combined with electromechanical (E/M) impedance approach for health monitoring of engineering structures. In particular, a statistical pattern recognition procedure is developed, based on frequency domain data of electromechanical impedance, to establish a decision boundary for damage identification. In order to diagnose damage with statistical confidence, health monitoring is cast in the context of outlier detection framework. Inappropriate modeling of tail distribution of outliers imposes potentially misleading behavior associated with damage. The present paper attempts to address the problem of establishing decision boundaries based on extreme value statistics so that the extreme values of outliers associated with tail distribution can be properly modeled. The validity of the proposed method is demonstrated using finite element method (FEM) simulated data while a comparison is performed for the extreme value analysis results contrasted with the standard approach where it is assumed that the damage-sensitive features are normally distributed.

Novelty Detection with Multivariate Extreme Value Statistics

2010 ◽  
Vol 65 (3) ◽  
pp. 371-389 ◽  
Author(s):  
David Andrew Clifton ◽  
Samuel Hugueny ◽  
Lionel Tarassenko
Keyword(s):  
Novelty Detection ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Multivariate Extreme Value

Extreme value statistics: potential benefits in water quality management

1997 ◽  
Vol 36 (5) ◽  
pp. 133-140 ◽  
Author(s):  
O. Thas ◽  
P. Vanrolleghem ◽  
B. Kops ◽  
L. Van Vooren ◽  
J. P. Ottoy
Keyword(s):  
Water Quality ◽  
Quality Management ◽  
Extreme Values ◽  
Water Quality Management ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Design Stage ◽  
Sea Levels ◽  
Wind Speeds ◽  
Potential Benefits

Recently extreme value statistics have proven useful in environmental applications like the assessment of sea-levels, wind speeds and ozone concentrations. In this paper, after a brief overview of the statistical theory of extreme values, modelling issues are discussed with stress on applications in water quality management. Risk analysis procedures are presented that consider the extremal behaviour of water quality in the design stage of environmental constructions.

scholarly journals Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part II: Trend Detection and Assessment

2007 ◽  
Vol 64 (7) ◽  
pp. 2159-2175 ◽  
Author(s):  
Mara Felici ◽  
Valerio Lucarini ◽  
Antonio Speranza ◽  
Renato Vitolo
Keyword(s):  
Time Series ◽  
Total Energy ◽  
Extreme Values ◽  
Linear Time ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Trend Detection ◽  
Ratio Test ◽  
Scale Parameters ◽  
Baroclinic Model

Abstract A baroclinic model for the atmospheric jet at middle latitudes is used as a stochastic generator of nonstationary time series of the total energy of the system. A linear time trend is imposed on the parameter TE, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent generalized extreme value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location μ and scale parameters σ depend quadratically and linearly on time, respectively, while the shape parameter ξ is kept constant. From this family, a GEV model is selected with Akaike’s information criterion, complemented by the likelihood ratio test and by assessment through standard graphical diagnostics. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on TE. In particular, power-law dependences of μ and σ on TE are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of TE spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

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