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A PROBABILISTIC MODEL OF DAMAGE TO RESIDENTIAL STRUCTURES FROM HURRICANE WINDS A. Cope, and K. Gurley, M. ASCE University of Florida, Gainesville, FL 32611 [email protected], [email protected] J-P Pinelli, M. ASCE, J. Murphree Florida Institute of Technology, Melbourne, FL 32901 [email protected], [email protected] S. Gulati, and S. Hamid Florida International University, Miami, FL 33199 Abstract The paper presents a methodology to predict hurricane wind induced insurance losses for the State of Florida on an annualized basis and for predefined scenarios. Although several loss prediction commercial products exist in the market, this is one of the first public models entirely accessible for scrutiny to the scientific community. The model incorporates a probabilistic description of residential structural vulnerability and wind loading based on engineering criteria. Damage to the building exterior is related to non-structural damage to the building interior, and the overall damage in ratio with replacement cost is estimated. An actuarial model is then utilized to project insured loss. Although the model was developed for Florida, it is applicable to any hurricane prone region. The methodology can also be extended to other types of hazards. Introduction Over half of the hurricane-related damage in the United States to date has occurred in the state of Florida, which has $1.5 trillion in existing structures currently exposed to potential hurricane devastation. It is therefore critical for the state of Florida to be able to estimate future expected insurable losses due to hurricanes and their measure of dispersion. The Florida Department of Financial Services (FDFS) contracted a group of researchers to develop a public hurricane loss projection model that is fully transparent. The focus of this paper is the development of a probabilistic model for the projection of annualized insurable losses to residential structures due to hurricane damage by zip code in the state of Florida. The components of the model are the wind field, residential damage estimation, and the insured loss models. This paper presents an overview of the methodologies used in the damage estimation and insured loss projection components. Methodology The approach in this model requires the development of damage matrices whose entries are probabilities of occurrence of various types and levels of damage conditioned upon a specified 3-second gust wind speed. The probabilities that occupy the cells in the damage matrix are obtained from the result of a component-based Monte Carlo simulation engine that employs a detailed wind and structural engineering analysis to relate estimated probabilistic failure capacities of building components to wind speeds. The probabilistic structural models represent those residential structures most common in Florida based on a building classification study (Pinelli et al., 2003). The exterior damage from the MonteCarlo model is then related to interior non-structural and content damage. The damage data is then transformed into insurance losses subject to financial constraints such as deductible and insurance limits. Exterior Damage Model The physical damage to single-family homes is estimated with a component-based Monte Carlo (MC) simulation engine (Cope et al., 2003), conceptually similar to the HAZUSMH model developed through FEMA (Lavelle et al., 2003). The simulation relates estimated probabilistic capacities of building components to deterministic 3 sec peak gust wind speeds through a detailed wind and structural engineering analysis that includes effects of wind-borne missiles. This component approach explicitly accounts for both the uncertain resistance capacity of the various building components and the load effects produced by wind to predict damage at various wind speeds and directions. The resistance capacity of a building is broken down into the resistance capacity of its components and the connections between them. The components include roof cover, roof sheathing, roof to wall connections, walls, windows, doors, and garage doors (Fig. 1 left). Damage to the structure occurs when the load effects from wind or flying debris are greater than the component’s capacity to resist them. The probable damage to a particular building class at a given wind speed is estimated through thousands of simulations of the structure at that wind speed, randomly sampling component capacities and pressure coefficients between each simulation. Load redistribution as a result of component failure or internal pressurization due to envelope breach is also accounted for. Simulations are run over a wide range of prescribed, deterministic 3-second gust wind speeds. The end result is a database with probabilities of damage combinations conditioned upon peak 3second wind speeds (Fig. 1 right). This exterior damage estimation procedure is conducted for each of the building classifications under consideration (concrete block and timber walls, hip and gable roofs). The next steps in the model are to convert physical exterior damage to interior damage, and then to monetary loss. Cost Estimate Model The MC simulation does not model non-structural components such as: kitchen cabinets, carpeting, interior walls, interior doors, ceilings, plumbing supply lines, waste lines, finish fixtures, mechanical, or electrical assemblies. Replacing part or all of these components represents a significant portion of overall cost. Table 1 lists the approximate repair cost ratios for a masonry home in central Florida with a shingle roof and hurricane shutters, and shows that un-modeled non-structural, plumbing, mechanical, and electrical, make up a significant portion of repair costs for a home (59%). Therefore, the relationship between damage to modeled components and damage to un-modeled components must be determined. Roof Sheathing Roof Cover Roof to Wall Connections Walls Openings Figure 1: Left- Components modeled in the hurricane damage prediction simulation. Right- mean damage to components as a function of peak wind speed For each building type, the process includes: 1) estimate the physical damage to nonstructural elements and contents, based on the exterior and structural damage prediction, 2) estimate the replacement cost ratios of each component of the different types of residential homes of interest using cost estimation resources (e.g., Russel, 2004), engineering judgment, Florida Building Code requirements (2001), and expert input, 3) assign damage cost ratios to the combinations of exterior and associated non structural damage. The result will be a vulnerability matrix describing the probability of different damage cost ratio, conditional upon the occurrence of 3-sec peak gust speeds, 4) apply the vulnerability matrices together with a costing algorithm to predict monetary damage to insurance portfolios, for a given hurricane scenario or on an annual average basis. Repair Ratios Roof Sheathing 5% Roof Cover 7% Trusses 9% Exterior Walls 22% Windows 4% Shutters Entrance Door and Sliding Back Door 2% Garage Un-modeled NonStructural 1% 35% Plumbing 10% Mechanical 7% 1% Electrical 7% Total 110% Table 1: Repair costs ratios for subassemblies of masonry homes in Central Florida The repair ratios in Table 1 represent the approximate repair costs divided by the average cost of construction of a new home of this type in this region. Because the cost of repair includes removal of damage and replacement, it is greater than the cost of new construction. For this reason the sum of the repair ratios is greater than 100 percent. We are currently defining equations based on roof cover, roof sheathing, and opening damage to predict interior non-structural damage as well as damage to plumbing, mechanical, or electric subassemblies. These equations will be validated with hurricane claims data. Similar equations will also relate contents, appurtenant structure, and additional living expense losses to exterior and structural damage. Figure 2 presents preliminary results comparing the damage content ratio with the building exterior damage, where the line represents claims data and the scatter are the result of simulations. Figure 2: Building exterior damage vs. content ratios The total building damage cost can be computed based on the direct output of the MC damage simulation, its relationship to non-modeled damage, and the replacement cost ratios as shown in Table 1. The MC simulation damage output may be expressed as the percentage of a particular assembly. For example, if 3 of 15 windows are damaged this equates to 20% window loss. This value is then multiplied by the replacement ratio of the assembly. This is repeated for each assembly and the results are summed up to yield a total replacement ratio for that particular damage state. The procedure is repeated for each of the thousands of model simulations for 5 mph interval wind speeds, from 50 to 250 mph. The result for each building type will be a vulnerability matrix of damage ratios vs. wind speeds, where each cell of the vulnerability matrix gives the probability of occurrence of a damage ratio conditional upon a certain wind speed. Since each column of the matrix is a discretization of the probability distribution function of damage conditional upon a particular wind speed, the vulnerability of each building type m for a given wind speed V is defined as: Vulnerability(type m | V)= P(DR | V ,type i i m )* DR i (1) where the summation is performed over all the damage ratios DRi in a column of the matrix. An expression similar to Equation 1 applies to each of the wind speeds. The plot of the vulnerabilities vs. wind speed for each structural type m, will be a vulnerability curve for that particular type m. Insured Loss Model Assume that, within a particular zip code area, the probability of occurrence of a storm with a peak 3-second gust wind speed within the interval {v- v/2, v + v/2} mph is P(v)=p(v)v, where p(v) is the probability density function of the largest yearly wind speed, to be provided by the probabilistic wind field development team (Powell et al., 2003). The mean annual damage equation for a particular structure type m is Annual_Mean_Damage typem= Vulnerability(typem|Vi)*P(Vi-v/2<v<Vi+v/2) (2) windspeedi A statistical exposure study (Pinelli et al., 2003) provides the probability of occurrence of different building types for each region of Florida. For each home in a portfolio, these probabilities can be adjusted based on the fire resistance classification typically given in insurance portfolio files. The mean annual damage for a given portfolio home becomes: Annual_Mean_Damage = Annual_Mean_Damagetypei*P(typei) (3) Bldgtypei Multiplication of this latter result by the value of the home yields the mean annual monetary damage. The process is repeated for each home in the portfolio, and the results for each portfolio in Florida are added to obtain the expected hurricane-induced annual damage to buildings for the entire State. To derive the estimates of insured losses two major features of the insurance policies, deductibles and limits, must be modeled. The distribution of losses is truncated from below by the deductibles, and limited above by the policy limit. The insured loss function depends critically on the distribution of the damage ratios (DR) derived primarily by the engineering team and on the interpolation between the discrete estimates, as well as on data on the policy characteristics provided by the end users. Specifically, for the discrete case, the following equations are estimated. P(DRl ) Vj (P(DRl | type k ,V j )* P (V j )* P(type k )) (4) ty pesk Mean Loss Ratio is (with deductible and limit expressed as % of the home value): MLR= dedDRi(limitded) (DRi – ded) P(DRi) + limit * DRi(limitded) P(DRi) (5) Typically the policies on residential structures pay up to the limit if the losses exceed the limit + deductibles. The probabilities of individual loss ratios can be also derived from the P(DRi). The loss model is tested and recalibrated by using the individual claims data for a number of hurricanes provided by several insurance companies. Conclusions This paper provides an overview of the strategies employed to complete the Public Loss Hurricane Projection Model, developed for the Florida Department of Financial Services and coordinated by the International Hurricane Research Center. Physical damage is calculated within a probabilistic framework as function of a series of peak 3-second wind speeds using engineering analysis of wind loads and component capacities. The physical damage to exterior and structural components is compounded by damage to nonstructural systems, and translated to repair cost ratios using expert opinion and prescriptive documentation. Work is near completion on the development of this loss computation model for the various types of residential structures most common in Florida, including masonry and wood wall structures, various roof types, and manufactured homes. The resulting loss predictions will be validated against actual claim data provided by insurance companies. The model is scheduled for release in 2005. Acknowledgements The authors wish to acknowledge with thanks valuable advice from Emil Simiu at the National Institute of Standards and Technology. This work was done with the financial support of the Florida Department of Financial Services. Portions of this work were also supported in part by NSF grant CMS-9984663. References Cope, A., Gurley, K., Pinelli, J., Hamid, S., “Simulation model for wind damage predictions in Florida,” Proc. 11th ICWE, Texas Tech Lubbock TX, 2003. Florida Building Code, Tallahassee, FL, 2001 Lavelle, F., Vickery, P. J., Schauer, B., Twisdale, L. A., Laatsch, E.. “HAZUS-MH Hurricane Model,” Proc., 11th ICWE, Texas Tech, Lubbock, TX, 2003. Pinelli, J.P., Zhang, L., Subramanian, C., Cope, A., Gurley, K., Gulati, S. and Hamid, S. “Classification of Structural Models for Wind Damage Predictions in Florida”, 11th International Conference on Wind Engineering, Lubbock, TX, June 2-5, 2003. Powell,M., Soukup,G., Morisseau,N.,et al., “Florida Hurricane Loss Projection Model: Atmospheric Science Component,” Proc.,11thICWE, Lubbock, TX, 2003. Russel, J., 2004 National Renovation & Insurance Repair Estimator, Craftsman Book Company, Carlsbad CA.