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

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

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 (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”

Property Loss due to Hurricanes in the US

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.

Hurricane Tracks - 1997

1997 was strongest El Nino year Fewer hurricanes

Hurricane Tracks - 2000

2000 was a strong La Nina year more hurricanes

- 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

An index of ENSO(based on Sea Surface Temperatures and Sea Level Pressures in the tropical Pacific Ocean)

Notice theEvolution of Different El Nino andLa Nina events

Global Impacts of ENSO

ENSO phenomenaimpacts climate overthe US by modulatingThe winter time jet stream

Notice more Hurricanes during La Nina yearsand vice-versa

Notice negativecorrelations between #of AtlanticHurricanes and SSTsOver Eastern TropsicalPacific La Ninapattern

Motivation (contd..)(i) Clearly, large scale climate phenomenon (e.g.,

ENSO) has a significant impact the frequency and strength of hurricanes.

(ii) Incorporating this information is key to realistic estimation of structural reliability

(iii) Thus, need to develop a framework that will facilitate this.

Proposed Framework

Structural Failure Model

Structural failure states and their occurrence

probabilities based on combined loads – for a few structures (wood, concrete,

etc.,)

Hurricane Wind Scenarios Generation

1. Simulate hurricane wind scenarios from the historical probability density function. 2. Simulate hurricane winds conditioned upon large-scale climate features (e.g., ENSO). This will be used in the estimation of time-varying risk and in estimating risk in any given year (i.e., in a predictive mode).

Loss Estimation

Structural Reliability Estimation

Steps:1. Generate scenarios of maximum wind speeds

conditioned on large-scale climate information. - i.e. simulate from conditional PDF

f(wind speed | climate)“Load Scenarios”

2. 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

Walls - W

Roof Cover - T

Openings - O

Roof Sheathing - S

Roof to Wall Connections - C

Data for wind scenario

1. Historical Hurricane track data from http://www.nhc.noaa.gov

2. Get the historical track for the region of interest

(2deg X 2deg box over N. Carolina)

3. Estimate the annual maximum hurricane wind speed for the grid box (wind speed)

4. Climate information (e.g., El Nino index) is obtained from http://www.cdc.noaa.gov (climate index)

5. Simulate scenarios from the conditional PDF f(wind speed | climate)

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/

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

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 polynomialto 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

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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0 25 50 75 100 125

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A time series from the model

xt+1 = 1 - 4(xt - 0.5)2

Logistic Map Example

State

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k-nearest neighborhoods A and B for xt=x*A and x*B respectively

4-state Markov Chain discretization

K-NN Local Polynomial

ENSO characterization

• Tropical Pacific Ocean Sea Surface Temperature based index called (NINO3 index) is used to characterize ENSO

index value > 0.5 indicates El Nino years

values < -0.5 are La Nina years

ENSO index

Joint PDF of Max. Wind Speed and ENSO index

La Nina Years

El Nino YearsAll Years

Neutral Years

Histogram of #of Hurricane Occurrences over N. Carolina –With Respect to Large-scale Climate

ENSO index

WindSpeed

Joint PDF of Max. Wind Speed and ENSO indexNoticenon-Gaussianfeatures

ENSO index

Joint PDF of Max. Wind Speed and ENSO index

Conditioned onENSO index Value of –1 (solid line) (La Nina)

1 (dashed line)(El Nino)

Notice non-Gaussianfeatures

Conditional PDF of Max. wind speed

Joint PDF of Max. Wind Speed and ENSO indexAll Year SimulationsCDFs from unconditional simulations

CDF of

- Historical data in (purple)

-El Nino years in (red)

-La Nina years in (blue)

Joint PDF of Max. Wind Speed and ENSO indexCDFs of Wind Speeds conditioned on ENSO

Red line is thehistorical CDFof El Nino years

Blue line is the historical CDFof La Nina years

Notice the differences atLower speeds

Failure Due to Panel Uplift

Failure due to Roof-to-wall Separation

Gust Effect - Failure due to Panel Uplift

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)

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