Sensitivity of Building Loss Estimates to Major Uncertain Variables

This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa

Simplified Estimation of Seismic Life-Cycle Costs

Most seismic risk assessments for economic decision-making of commercial buildings are based on a risk metric called probable maximum loss (PML) that is associated with losses from an earthquake shaking severity with a 500-year return period. For various reasons, PML is a poor metric for economic performance assessment. This paper introduces an analogous measure, the probable frequent loss (PFL), defined as the mean loss resulting from shaking with 10% exceedance probability in 5 years (an approximately 50-year event). It overcomes many of the problems of PML, and offers the advantage that expected seismic life-cycle costs and expected annualized loss are approximately proportional to PFL through a seismic hazard coefficient that depends on site characteristics, fundamental period, and damage shaking threshold, and can be tabulated for ready use. A brief review is given of a building-specific seismic vulnerability method that may be used to calculate PFL

Bayesian Updating of Nonlinear Model Predictions using Markov Chain Monte Carlo Simulation

The usual practice in system identification is to use system data to identify one model from a set of possible models and then to use this model for predicting system behavior. In contrast, the present robust predictive approach rigorously combines the predictions of all the possible models, appropriately weighted by their updated probabilities based on the data. This Bayesian system identification approach is applied to update the robust reliability of a dynamical system based on its measured response time histories. A Markov chain simulation method based on the Metropolis-Hastings algorithm and an adaptive scheme is proposed to evaluate the robust reliability integrals. An example for updating the reliability of a Duffing oscillator is given to illustrate the proposed method

Impact of Seismic Risk on Lifetime Property Values

This report presents a methodology for establishing the uncertain net asset value, NAV, of a real-estate investment opportunity considering both market risk and seismic risk for the property. It also presents a decision-making procedure to assist in making real-estate investment choices under conditions of uncertainty and risk-aversion. It is shown that that market risk, as measured by the coefficient of variation of NAV, is at least 0.2 and may exceed 1.0. In a situation of such high uncertainty, where potential gains and losses are large relative to a decision-maker's risk tolerance, it is appropriate to adopt a decision-analysis approach to real-estate investment decision-making. A simple equation for doing so is presented. The decision-analysis approach uses the certainty equivalent, CE, as opposed to NAV as the basis for investment decision-making. That is, when faced with multiple investment alternatives, one should choose the alternative that maximizes CE. It is shown that CE is less than the expected value of NAV by an amount proportional to the variance of NAV and the inverse of the decision-maker's risk tolerance, [rho]. The procedure for establishing NAV and CE is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era hotel building in Van Nuys, California. The building, a 7-story non-ductile reinforced-concrete moment-frame building, is analyzed using the assembly-based vulnerability (ABV) method, developed in Phase III of the CUREE-Kajima Joint Research Program. The building is analyzed three ways: in its condition prior to the 1994 Northridge Earthquake, with a hypothetical shearwall upgrade, and with earthquake insurance. This is the first application of ABV to a real building, and the first time ABV has incorporated stochastic structural analyses that consider uncertainties in the mass, damping, and force-deformation behavior of the structure, along with uncertainties in ground motion, component damageability, and repair costs. New fragility functions are developed for the reinforced concrete flexural members using published laboratory test data, and new unit repair costs for these components are developed by a professional construction cost estimator. Four investment alternatives are considered: do not buy; buy; buy and retrofit; and buy and insure. It is found that the best alternative for most reasonable values of discount rate, risk tolerance, and market risk is to buy and leave the building as-is. However, risk tolerance and market risk (variability of income) both materially affect the decision. That is, for certain ranges of each parameter, the best investment alternative changes. This indicates that expected-value decision-making is inappropriate for some decision-makers and investment opportunities. It is also found that the majority of the economic seismic risk results from shaking of S[subscript a] < 0.3g, i.e., shaking with return periods on the order of 50 to 100 yr that cause primarily architectural damage, rather than from the strong, rare events of which common probable maximum loss (PML) measurements are indicative. The Kajima demonstration is performed using three Tokyo buildings. A nine-story, steel-reinforced-concrete building built in 1961 is analyzed as two designs: as-is, and with a steel-braced-frame structural upgrade. The third building is 29-story, 1999 steel-frame structure. The three buildings are intended to meet collapse-prevention, life-safety, and operational performance levels, respectively, in shaking with 10%exceedance probability in 50 years. The buildings are assessed using levels 2 and 3 of Kajima's three-level analysis methodology. These are semi-assembly based approaches, which subdivide a building into categories of components, estimate the loss of these component categories for given ground motions, and combine the losses for the entire building. The two methods are used to estimate annualized losses and to create curves that relate loss to exceedance probability. The results are incorporated in the input to a sophisticated program developed by the Kajima Corporation, called Kajima D, which forecasts cash flows for office, retail, and residential projects for purposes of property screening, due diligence, negotiation, financial structuring, and strategic planning. The result is an estimate of NAV for each building. A parametric study of CE for each building is presented, along with a simplified model for calculating CE as a function of mean NAV and coefficient of variation of NAV. The equation agrees with that developed in parallel by the CUREE team. Both the CUREE and Kajima teams collaborated with a number of real-estate investors to understand their seismic risk-management practices, and to formulate and to assess the viability of the proposed decision-making methodologies. Investors were interviewed to elicit their risk-tolerance, r, using scripts developed and presented here in English and Japanese. Results of 10 such interviews are presented, which show that a strong relationship exists between a decision-maker's annual revenue, R, and his or her risk tolerance, [rho is approximately equal to] 0.0075R[superscript 1.34]. The interviews show that earthquake risk is a marginal consideration in current investment practice. Probable maximum loss (PML) is the only earthquake risk parameter these investors consider, and they typically do not use seismic risk at all in their financial analysis of an investment opportunity. For competitive reasons, a public investor interviewed here would not wish to account for seismic risk in his financial analysis unless rating agencies required him to do so or such consideration otherwise became standard practice. However, in cases where seismic risk is high enough to significantly reduce return, a private investor expressed the desire to account for seismic risk via expected annualized loss (EAL) if it were inexpensive to do so, i.e., if the cost of calculating the EAL were not substantially greater than that of PML alone. The study results point to a number of interesting opportunities for future research, namely: improve the market-risk stochastic model, including comparison of actual long-term income with initial income projections; improve the risk-attitude interview; account for uncertainties in repair method and in the relationship between repair cost and loss; relate the damage state of structural elements with points on the force-deformation relationship; examine simpler dynamic analysis as a means to estimate vulnerability; examine the relationship between simplified engineering demand parameters and performance; enhance category-based vulnerability functions by compiling a library of building-specific ones; and work with lenders and real-estate industry analysts to determine the conditions under which seismic risk should be reflected in investors' financial analyses

Conduction in rectangular plates with boundary temperatures specified

Steady-state components of heat conduction solutions may have very slowly convergent series for temperatures and non-convergent heat fluxes for temperature boundary conditions. Previous papers have proposed methods to remove these convergence problems. However, even more effective procedures based on insights of Morse and Feshbach are given herein. In some cases it is possible to replace poorly-convergent or non-convergent series by closed-form algebraic solutions. Examples are given

Solving two-dimensional Cartesian unsteady heat conduction problems for small values of the time

a b s t r a c t This paper is intended to provide very accurate analytical solutions modeling transient heat conduction processes in 2D Cartesian finite bodies for small values of the time. Analysis of diffusion of thermal deviation effects indicates that, when the space and time coordinates satisfy a criterion developed in the paper, the simple transient 1D semi-infinite solutions may be &quot;used&quot; for generating extremely accurate values for temperature and heat flux at any point of a finite rectangle. Also, they may be &quot;used&quot; with excellent accuracy as short-time solutions when the time-partitioning method is applied (so avoiding the usually difficult integration of the short-cotime Green&apos;s functions). A complex 2D semi-infinite problem is solved explicitly and evaluated numerically as part of the analysis. The proposed criterion is based on an accuracy of one part in 10 n (n ¼ 1,2,...,10,...), where n ¼ 2 is for engineering insight and visual comparison while n ¼ 10 is for verification purposes of large numerical codes

Impact of an integrated disease management program in reducing exacerbations in patients with severe asthma and COPD

SummaryBackgroundConflicting data exists on the effectiveness of integrated programs in reducing recurrent exacerbations and hospitalizations in patients with Asthma and chronic obstructive lung disease (COPD). We developed a Pulmonologist-led Chronic Lung Disease Program (CLDP) for patients with severe asthma and COPD and analyzed its impact on healthcare utilization and predictors of its effectiveness.MethodsCLDP elements included clinical evaluation, onsite pulmonary function testing, health education, and self-management action plan along with close scheduled and on-demand follow-up. Patients with ≥2 asthma or COPD exacerbations requiring emergency room visit or hospitalization within the prior year were enrolled, and followed for respiratory related ER visits (RER) and hospitalizations (RHA) over the year (357 ± 43 days) after CLDP interventions.ResultsA total of 106 patients were enrolled, and 104 patients were subject to analyses. During the year of follow-up after CLDP enrollment, there was a significant decrease in mean RER (0.56 ± 1.48 versus 2.62 ± 2.81, p < 0.0001), mean RHA (0.39 ± 0.08 versus 1.1 ± 1.62, p < 0.0001), and 30 day rehospitalizations (0.05 ± 0.02 versus 0.28 ± 0.07, p < 0.0001). Reduction of healthcare utilization was strongly associated with GERD and sinusitis therapy, and was independent of pulmonary rehabilitation. Direct variable cost analyses estimated annual savings at $1.17 million. Multivariate logistic regression analysis revealed lack of spirometry utilization as an independent risk factor for severe exacerbations.ConclusionsA Pulmonologist-led disease management program integrating key elements of care is cost effective and significantly decreases severe exacerbations. Integrated programs should be encouraged for care of frequent exacerbators of asthma and COPD

A Model for the Analysis of Caries Occurrence in Primary Molar Tooth Surfaces

Recently methods of caries quantification in the primary dentition have moved away from summary ‘whole mouth’ measures at the individual level to methods based on generalised linear modelling (GLM) approaches or survival analysis approaches. However, GLM approaches based on logistic transformation fail to take into account the time-dependent process of tooth/surface survival to caries. There may also be practical difficulties associated with casting parametric survival-based approaches in a complex multilevel hierarchy and the selection of an optimal survival distribution, while non-parametric survival methods are not generally suitable for the assessment of supplementary information recorded on study participants. In the current investigation, a hybrid semi-parametric approach comprising elements of survival-based and GLM methodologies suitable for modelling of caries occurrence within fixed time periods is assessed, using an illustrative multilevel data set of caries occurrence in primary molars from a cohort study, with clustering of data assumed to occur at surface and tooth levels. Inferences of parameter significance were found to be consistent with previous parametric survival-based analyses of the same data set, with gender, socio-economic status, fluoridation status, tooth location, surface type and fluoridation status-surface type interaction significantly associated with caries occurrence. The appropriateness of the hierarchical structure facilitated by the hybrid approach was also confirmed. Hence the hybrid approach is proposed as a more appropriate alternative to primary caries modelling than non-parametric survival methods or other GLM-based models, and as a practical alternative to more rigorous survival-based methods unlikely to be fully accessible to most researchers

Genetic susceptibility, evolution and the kuru epidemic

The acquired prion disease kuru was restricted to the Fore and neighbouring linguistic groups of the Papua New Guinea highlands and largely affected children and adult women. Oral history documents the onset of the epidemic in the early twentieth century, followed by a peak in the mid-twentieth century and subsequently a well-documented decline in frequency. In the context of these strong associations (gender, region and time), we have considered the genetic factors associated with susceptibility and resistance to kuru. Heterozygosity at codon 129 of the human prion protein gene (PRNP) is known to confer relative resistance to both sporadic and acquired prion diseases. In kuru, heterozygosity is associated with older patients and longer incubation times. Elderly survivors of the kuru epidemic, who had multiple exposures at mortuary feasts, are predominantly PRNP codon 129 heterozygotes and this group show marked Hardy–Weinberg disequilibrium. The deviation from Hardy–Weinberg equilibrium is most marked in elderly women, but is also significant in a slightly younger cohort of men, consistent with their exposure to kuru as boys. Young Fore and the elderly from populations with no history of kuru show Hardy–Weinberg equilibrium. An increasing cline in 129V allele frequency centres on the kuru region, consistent with the effect of selection in elevating the frequency of resistant genotypes in the exposed population. The genetic data are thus strikingly correlated with exposure. Considering the strong coding sequence conservation of primate prion protein genes, the number of global coding polymorphisms in man is surprising. By intronic resequencing in a European population, we have shown that haplotype diversity at PRNP comprises two major and divergent clades associated with 129M and 129V. Kuru may have imposed the strongest episode of recent human balancing selection, which may not have been an isolated episode in human history