Title: Estimating%20Structural%20Reliability%20Under%20Hurricane%20Wind%20Hazard%20:%20Applications%20to%20Wood%20Structures
1Estimating 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
- Probabilistic Mechanics Conference
- Albuquerque, NM July 26-28
2Acknowledgments
- Funding for this work was provided by NSF grant
SGER (CMS-0335530) - Discussions with Prof. Ellingwood, Dr. Simiu and
Dr. McGuire are thankfully acknowledged
3Motivation
- Insured losses in the US from natural hazards
reached 22 billion in 1999 - Second largest loss during 1990s - 26 billion
in 1992 due to Hurricane Andrew (in Florida and
Louisiana) Topics (2000 - Munich) - The U.S. House of Representatives, is working on
bill H.R. 2020 - 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
5Motivation (contd..)
- (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.
6Hurricane Tracks - 1997
1997 was strongest El Nino year ? Fewer hurricanes
7Hurricane Tracks - 2000
2000 was a strong La Nina year ? more hurricanes
8- La Nina conditions are almost a reverse of the
El Nino conditions. - The ENSO phenomenon is
irregular occurring every 3 8 years. - Impacts
global weather and climate
9An index of ENSO (based on Sea Surface
Temperatures and Sea Level Pressures in the
tropical Pacific Ocean) Notice the Evolution of
Different El Nino and La Nina events
10Global Impacts of ENSO
11ENSO phenomena impacts climate over the US by
modulating The winter time jet stream
12Notice more Hurricanes during La Nina years and
vice-versa
Notice negative correlations between of
Atlantic Hurricanes and SSTs Over Eastern
Tropsical Pacific ? La Nina pattern
13Motivation (contd..)
- Clearly, large scale climate phenomenon (e.g.,
ENSO) has a significant impact the frequency and
strength of hurricanes. - Incorporating this information is key to
realistic estimation of structural reliability - (iii) Thus, need to develop a framework that will
facilitate this.
14Proposed Framework
15 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
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17 Data for wind scenario
- Historical Hurricane track data from
http//www.nhc.noaa.gov - 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 http//www.cdc.noaa.gov (climate
index) - Simulate scenarios from the conditional PDF
f(wind speed climate)
18Nonparametric Methods
- Kernel Estimators
- (properties well studied)
- Splines
- Multivariate Adaptive Regression Splines (MARS)
- K-Nearest Neighbor Bootstrap estimators
- Locally Weighted Polynomials
- http//civil.colorado.edu/balajir/
19Nonparametric 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 -
20Basic Philosophy
- Find K-nearest neighbors to the desired point x
- Fit a polynomial (or weighted average) to the
neighbors ? recovers the underlying PDF
(nonparametric density estimation) - If the data is X and Y then fitting a polynomial
- to the neighbors ? recovers the underlying
relationship (nonparametric regression) - Number of neighbors K and the order of polynomial
p is obtained using GCV (Generalized Cross
Validation) K N and p 1 ? Linear modeling
framework. - Several variations to this are possible
21Applications 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
22k-nearest neighborhoods A and B for xtxA and
xB respectively
Logistic Map Example
4-state Markov Chain discretization
23K-NN Local Polynomial
24ENSO characterization
- Tropical Pacific Ocean Sea Surface Temperature
based index called (NINO3 index) is used to
characterize ENSO - index value gt 0.5 indicates El Nino years
- values lt -0.5 are La Nina years
25Histogram 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
26Joint PDF of Max. Wind Speed and ENSO index
Notice non-Gaussian features
Wind Speed
ENSO index
27Conditional PDF of Max. wind speed
Joint PDF of Max. Wind Speed and ENSO index
- Conditioned on
- ENSO index
- Value of
- 1 (solid line)
- (La Nina)
- (dashed line)
- (El Nino)
- Notice non-Gaussian
- features
-
ENSO index
28All Year Simulations
Joint PDF of Max. Wind Speed and ENSO index
CDFs from unconditional simulations
- CDF of
- - Historical
- data in
- (purple)
- El Nino
- years in
- (red)
- La Nina
- years in
- (blue)
29CDFs of Wind Speeds conditioned on ENSO
Joint PDF of Max. Wind Speed and ENSO index
Red line is the historical CDF of El Nino
years Blue line is the historical CDF of
La Nina years Notice the differences at Lower
speeds
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33Failure Due to Panel Uplift
34Failure due to Roof-to-wall Separation
35Gust Effect - Failure due to Panel Uplift
36Summary
- 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)
37Further 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