Estimating Structural Reliability Under Hurricane Wind Hazard : Applications to Wood Structures

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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
• Probabilistic Mechanics Conference
• Albuquerque, NM July 26-28

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Acknowledgments

• Funding for this work was provided by NSF grant
  SGER (CMS-0335530)
• Discussions with Prof. Ellingwood, Dr. Simiu and
  Dr. McGuire are thankfully acknowledged

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Motivation

• 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

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Property Loss due to Hurricanes in the US
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Motivation (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.

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Hurricane Tracks - 1997
1997 was strongest El Nino year ? Fewer hurricanes
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Hurricane Tracks - 2000
2000 was a strong La Nina year ? more hurricanes
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- 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
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An 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
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Global Impacts of ENSO
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ENSO phenomena impacts climate over the US by
modulating The winter time jet stream
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Notice 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
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Motivation (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.

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Proposed Framework
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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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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)

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Nonparametric 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/

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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

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Basic 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

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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

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k-nearest neighborhoods A and B for xtxA and
xB respectively
Logistic Map Example
4-state Markov Chain discretization
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K-NN Local Polynomial
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ENSO 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

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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
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Joint PDF of Max. Wind Speed and ENSO index
Notice non-Gaussian features
Wind Speed
ENSO index
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Conditional 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
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All 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)

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CDFs 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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Failure Due to Panel Uplift
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Failure due to Roof-to-wall Separation
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Gust Effect - Failure due to Panel Uplift
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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)

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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