1. Estimating Structural Reliability Under Hurricane Wind Hazard : Applications to Wood Structures
Balaji Rajagopalan, Edward Ou, Ross Corotis and Dan Frangopol
Department of Civil, Environmental and Architectural Engg.
University of Colorado
Boulder, CO
COALESCE – Spring 2004

2. Acknowledgements
Funding for this work is provided by NSF grant SGER (CMS )
Results from this work are being written up as a paper for Probabilistic Mechanics Conference – 04 (Albuquerque, NM, July 2004)

3. Motivation
Insured losses in the US from “natural hazards” reached $22 billion in 1999
Second largest loss during 1990’s - $26 billion in 1992 due to Hurricane Andrew (in Florida and Louisiana) Topics ( Munich)
The U.S. House of Representatives, is working on bill H.R Hurricane, Tornado and Related Hazards Research Act, to promote :
inter-disciplinary research in understanding and mitigating windstorm related hazard impacts
new methodologies for improved loss estimation and risk assessment

4. Property Loss due to Hurricanes in the US

5. Hurricane Tracks

6. ENSO as a “free” mode of the coupled ocean-atmosphere dynamics in the Tropical Pacific Ocean

9. Significant Differences in Atlantic Hurricane attributes relative to NINO3 phases
Rajagopalan et al., 2000

11. Motivation
(i) Often, structural reliability is estimated in isolation of realistic likelihood estimates of hurricane frequencies and magnitudes.
(ii) Knowledge of year-to-year variability in occurrence and steering of hurricanes in the Atlantic basin is not incorporated in structural reliability estimation.
(iii) The estimation of losses is purely empirical, based on the wind speed and no consideration of structural information. (For example, a new structure and a 25 year old structure are assumed to have the same probability of failure for a given wind speed.)
(iv) The life cycle cost of structures is also not considered  substantial misrepresentation of losses and consequently sub-optimal decision making.

12. Proposed Framework

13. Structural Reliability Estimation
Steps:
Generate scenarios of maximum wind speeds
conditioned on large-scale climate information.
- i.e. simulate from conditional PDF
f(wind speed | climate)
“Load Scenarios”
Scenarios generated for different large-scale climate states (El Nino, La Nina)
3. Convert the maximum wind speed to 3-second gust (gust correction factor, Simiu, 1996)
4. “convolute” with fragility curves to estimate the failure probability – consequently the reliability
5. Considered 25 year time horizon, wooden structures

15. Data for wind scenario
Historical Hurricane track data from
Get the historical track for the region of interest
(2deg X 2deg box over N. Carolina)
Estimate the annual maximum hurricane wind speed for the grid box (wind speed)
Climate information (e.g., El Nino index) is obtained from (climate index)
Simulate scenarios from the conditional PDF f(wind speed | climate)

16. Nonparametric Methods
Kernel Estimators
(properties well studied)
Splines
Multivariate Adaptive Regression Splines (MARS)
K-Nearest Neighbor Bootstrap estimators
Locally Weighted Polynomials

17. k-nearest neighborhoods A and B for xt=x*A and x*B respectively
Logistic Map Example
4-state Markov Chain discretization

18. K-NN Local Polynomial
Alpha = 0.2
N= 100
K= 20

19. Nonparametric Methods
A functional (probability density, regression etc.) estimator is nonparametric if:
It is “local” – estimate at a point depends only on a few neighbors around it.
(effect of outliers is removed)
No prior assumption of the underlying functional form – data driven

20. Classical Bootstrap (Efron):
Given x1, x2, …... xn are i.i.d. random variables with a cdf F(x)
Construct the empirical cdf
Draw a random sample with replacement of size n from
Moving Block Bootstrap (Kunsch, Hall, Liu & Singh) :
Resample independent blocks of length b<n, and paste them together to form a series of length n
k-Nearest Neighbor Conditional Bootstrap (Lall and Sharma)
Construct the Conditional Empirical Distribution Function:
Draw a random sample with replacement from

21. Define the composition of the "feature vector" Dt of dimension d.
(1) Dependence on two prior values of the same time series.
Dt : (xt-1, xt-2) ; d=2
(2) Dependence on multiple time scales (e.g., monthly+annual)
Dt: (xt-t1, xt-2t1, xt-M1t1; xt-t2, xt-2t2, xt-M2t2) ; d=M1+M2
(3) Dependence on multiple variables and time scales
Dt: (x1t-t1, x1t-M1t1; x2t, x2t-t2, x2t-M2t2); d=M1+M2+1
Identify the k nearest neighbors of Dt in the data D1 ... Dn
Define the kernel function ( derived by taking expected values of distances to each of k nearest neighbors, assuming the number of observations of D in a neighborhood Br(D*) of D*; r0, as n , is locally Poisson, with rate (D*))
for the jth nearest neighbor
Selection of k: GCV, FPE, Mutual Information, or rule of thumb (k=n0.5)

22. Applications to date…. Monthly Streamflow Simulation
Multivariate, Daily Weather Simulation
Space and time disaggregation of monthly to daily streamflow
Monte Carlo Sampling of Spatial Random Fields
Probabilistic Sampling of Soil Stratigraphy from Cores
Ensemble Forecasting of Hydroclimatic Time Series
Downscaling of Climate Models
Biological and Economic Time Series
Exploration of Properties of Dynamical Systems
Extension to Nearest Neighbor Block Bootstrapping -Yao and Tong

23. Histogram of #of Hurricane Occurrences over N. Carolina –
With Respect to Large-scale Climate
Joint PDF of Max. Wind Speed and ENSO index
El Nino Years
All Years
Neutral Years
La Nina Years
ENSO index

24. Joint PDF of Max. Wind Speed and ENSO index

25. All Year Simulations
Joint PDF of Max. Wind Speed and ENSO index
Wind
Speed

26. El Nino Year
Simulations
Joint PDF of Max. Wind Speed and ENSO index
Wind
Speed
Historical CDF
ENSO index

30. Failure Due to Panel Uplift

31. Failure due to Roof-to-wall Separation

32. Gust Effect - Failure due to Panel Uplift

33. Summary
Integrated (Interdisciplinary) framework to estimate infrastructure risk due to hurricane hazard is presented
Nonparametric method is used to generate hurricane wind scenarios conditioned on large-scale climate state (El Nino, La Nina etc.)
Large-scale climate state appears to impact the number of hurricanes, maximum wind speed and consequently, infrastructure risk (over N. Carolina)

34. Further Extensions Extension to other types of structures
(concrete, bridges etc.)
Investigate gust correction factors for hurricane winds
Study the impact of time-varying infrastructure risk estimation on the loss estimates
Incorporate other relevant climate information for Hurricane occurrence and steering (such as, North Atlantic Ocean and Atmospheric conditions)
Integrating life-cycle cost for optimal decision making on maintenance and replacement