The impact of epistemic uncertainty on an earthquake loss model

Models capable of estimating losses in future earthquakes are of fundamental importance for emergency planners, for the insurance and reinsurance industries, and for code drafters. Constructing a loss model for a city, region or country involves compiling databases of earthquake activity, ground conditions, attenuation equations, building stock and infrastructure exposure, and vulnerability characteristics of the exposed inventory, all of which have large associated uncertainties. Many of these uncertainties can be classified as epistemic, implying—at least in theory—that they can be reduced by acquiring additional data or improved understanding of the physical processes. The effort and cost involved in refining the definition of each component of a loss model can be very large, for which reason it is useful to identify the relative impact on the calculated losses due to variations in these components. A mechanically sound displacement‐based approach to loss estimation is applied to a test case of buildings along the northern side of the Sea of Marmara in Turkey. Systematic variations of the parameters defining the demand (ground motion) and the capacity (vulnerability) are used to identify the relative impacts on the resulting losses, from which it is found that the influence of the epistemic uncertainty in the capacity is larger than that of the demand for a single earthquake scenario. Thus, the importance of earthquake loss models which allow the capacity parameters to be customized to the study area under consideration is highlighted. Copyright © 2005 John Wiley & Sons, Ltd.     

Quantifying uncertainty of the semivariogram of transmissivity of an existing groundwater monitoring network

A method is presented for quantifying the uncertainty of the semivariogram of transmissivity and determining the required number of measurements. In this method, the estimated semivariogram and its 95% confidence limits are first determined from a finite number of measurements. The uncertainty of the estimated semivariogram is then quantified using the random field simulation technique. For a given value of the quantitative index of uncertainty, the required number of measured data can finally be obtained. Actual transmissivity data of an existing groundwater monitoring network are used in the application of the proposed method. The required numbers of measurements of transmissivity for four different values of the quantitative index of uncertainty are provided, from which reliable semivariograms of the transmissivity can be obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Weighing the importance of model uncertainty against parameter uncertainty in earthquake loss assessments

Epistemic uncertainties can be classified into two major categories: parameter and model. While the first one stems from the difficulties in estimating the values of input model parameters, the second comes from the difficulties in selecting the appropriate type of model. Investigating their combined effects and ranking each of them in terms of their influence on the predicted losses can be useful in guiding future investigations. In this context, we propose a strategy relying on variance-based global sensitivity analysis, which is demonstrated using an earthquake loss assessment for Pointe-à-Pitre (Guadeloupe, France). For the considered assumptions, we show: that uncertainty of losses would be greatly reduced if all the models could be unambiguously selected; and that the most influential source of uncertainty (whether of parameter or model type) corresponds to the seismic activity group. Finally, a sampling strategy was proposed to test the influence of the experts’ weights on models and on the assumed coefficients of variation of parameter uncertainty. The former influenced the sensitivity measures of the model uncertainties, whereas the latter could completely change the importance rank of the uncertainties associated to the vulnerability assessment step.     

矿产资源潜力预测不确定性评价

矿产潜力预测不确定性评价是矿产定量预测的重要环节,其主要研究内容包括未发现矿床数的不确定性、未发现矿床品位、吨位及资源量的不确定性等.本文简要介绍了矿产预测不确定性的主要来源与评价不确定性的途径与方法,并利用模糊集评价了未发现矿床数、品位、吨位及资源量的不确定性.     

Multisource hydrologic modeling uncertainty analysis using the IBUNE framework in a humid catchment

Hydrologic cycle is a complex system associated with both certain and uncertain constituents. The propagation of confidence bounds from different uncertainty sources to model output is of great significance for hydrologic modeling. In this paper, we applied the integrated bayesian uncertainty estimator to quantify the effects of parameter, input and model structure uncertainty on hydrologic modeling progressively. Two hydrologic models (Xinanjiang model and TOPMODEL) were applied to a humid catchment under three scenarios. Case I: the shuffled complex evolution metropolis (SCEM-UA) algorithm was conducted to determine the posterior parameter distribution of hydrologic models and analyze the corresponding forecast uncertainty. Case II: input uncertainty was also considered by assuming rain depth bias follows a normal distribution, and integrated with SCEM-UA. Case III: Simulations from two models were combined by the Bayesian model averaging to fully quantify multisource uncertainty effects. Results suggested that, from Case I to II, the containing ratio (percentage of observed streamflow enveloped by 95% confidence interval) obviously increased by an average magnitude of 10% for the study period 2000–2006. Besides, it also found that the width of 95% confidence interval became wider and narrower for Xinanjiang model and TOPMODEL, respectively, from Case I to II. This may indicate that the uncertainty of TOPMODEL results was more remarkable than Xinanjiang model in Case I. By combining results from two models, model structure uncertainty was also considered in Case III. The accuracy of uncertainty bounds further improved with the containing ratio of 95% confidence interval >95%. In addition, the optimized deterministic results from the uncertainty analysis showed that the average Nash–Sutcliffe coefficient increased continually from Case I to II and III (0.82, 0.84 and 0.90, respectively) for the study period. The analysis demonstrated the improvement of modeling accuracy when extra uncertainty sources were also quantified, and this finding also proved the applicability of IBUNE framework in hydrologic modeling.     

Three-dimensional liquefaction potential analysis using geostatistical interpolation

We applied three-dimensional geostatistical interpolation to evaluate the extent of liquefiable materials at two sites that liquefied during the 1994 Northridge Earthquake. The sites were the Balboa Blvd site and the Wynne Ave. site located in the alluvial San Fernando Valley. The estimated peak ground accelerations at the sites are 0.84 g (Balboa Blvd) and 0.51 g (Wynne Ave.). These sites were chosen because surface effects due to liquefaction were not predicted using available techniques based on thickness and depth of liquefiable layers (Ishihara [Ishihara K. Stability of natural deposits during earthquakes. Proceedings of the 11th international conference on soil mechanics and foundation engineering, vol. 1. Rotterdam, The Netherlands: A.A. Balkema; 1985. p. 321–76.]) and the Liquefaction Potential Index (Iwasaki et al. [Iwasaki T, Tatsuoka F, Tokida K, Yasuda S. A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: Proceedings of the second international conference on microzonation, San Francisco; 1978. p. 885–96.]). During the earthquake, both sites experienced surface effects including ground cracking and extension as a result of liquefaction. Foundations and buried utilities were damaged at both sites. The sites were investigated after the event by researchers with the United States Geologic Survey using standard penetration tests (SPT) and cone penetration tests. In this paper, liquefaction potential was estimated for each soil sample using results from SPTs according to the updated Seed and Idriss simplified procedure. The probability of liquefaction was estimated by applying an indicator transform to the results of the liquefaction potential calculation. We compared our results to detailed geologic mapping of the sites performed by other researchers. Using geostatistical interpolation to estimate the probability of liquefaction is a useful supplement to geologic evaluation of liquefaction potential. The geostatistical analysis provides an estimate of the continuous volume of liquefiable soil along with an assessment of confidence in an interpolation. The probability of liquefaction volumes compare well with those predicted using geologic interpretations.     

Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method

This study employs the Bayesian Markov Chain Monte Carlo (MCMC) method with the Metropolis–Hastings algorithm and maximum likelihood estimation (MLE) using a quadratic approximation of the likelihood function for the evaluation of uncertainties in low flow frequency analysis using a two‐parameter Weibull distribution. The two types of prior distributions, a non‐data‐based distribution and a data‐based distribution using regional information collected from neighbouring stations, are used to establish a posterior distribution. Eight case studies using the synthetic data with a sample size of 100, generated from two‐parameter Weibull distribution, are performed to compare with results of analysis using MLE and Bayesian MCMC. Also, Bayesian MCMC and MLE are applied to 36 years of gauged data to validate the efficiency of the developed scheme. These examples illustrate the advantages of Bayesian MCMC and the limitations of MLE based on a quadratic approximation. From the point of view of uncertainty analysis, Bayesian MCMC is more effective than MLE using a quadratic approximation when the sample size is small. In particular, Bayesian MCMC method is more attractive than MLE based on a quadratic approximation because the sample size of low flow at the site of interest is mostly not enough to perform the low flow frequency analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Calibration and uncertainty analysis of the SWAT model using Genetic Algorithms and Bayesian Model Averaging

In this paper, the Genetic Algorithms (GA) and Bayesian Model Averaging (BMA) were used to simultaneously conduct calibration and uncertainty analysis for the Soil and Water Assessment Tool (SWAT). In this combined method, several SWAT models with different structures are first selected; next GA is used to calibrate each model using observed streamflow data; finally, BMA is applied to combine the ensemble predictions and provide uncertainty interval estimation. This method was tested in two contrasting basins, the Little River Experimental Basin in Georgia, USA, and the Yellow River Headwater Basin in China. The results obtained in the two case studies show that this combined method can provide deterministic predictions better than or comparable to the best calibrated model using GA. The 66.7% and 90% uncertainty intervals estimated by this method were analyzed. The differences between the percentage of coverage of observations and the corresponding expected coverage percentage are within 10% for both calibration and validation periods in these two test basins. This combined methodology provides a practical and flexible tool to attain reliable deterministic simulation and uncertainty analysis of SWAT.     

Seismic health monitoring of an instrumented multistory building using the interpolation method

In this paper, a new approach to structural damage localization is presented using as damage feature the interpolation error related to the use of a spline function in modeling the operational deformed shapes of the structure. Statistically significant variations of the interpolation error between the undamaged and the inspection phase indicate the onset of damage. A threshold value of the damage feature is defined in terms of the tolerable probability of false alarm to select variations of the interpolation error because of damage from those due to random sources. The method is successfully applied to a calibrated model of the factor building a real densely instrumented building at the University of California, Los Angeles. Results show that the method is effective for damage localization for both single and multiple locations of damage also in case of responses corrupted by noise. Copyright © 2014 John Wiley & Sons, Ltd.     

Detecting the effects of spatial variability of rainfall on hydrological modelling within an uncertainty analysis framework

Spatial patterns of rainfall are known to cause differences in observed flow. In this paper, the effects of perturbations in rainfall patterns on changes in parameter sets as well as model output are explored using the hydrological model Dynamic TOPMODEL for the Brue catchment (135 km²) in southwest England. Overall rainfall amount remains the same at each time step so the perturbations act as effectively treated errors in the spatial pattern. The errors were analysed with particular emphasis on when they could be detected under an uncertainty framework. Higher rainfall perturbations (multipliers of × 4 and greater) in the low lying and high areas of the catchment resulted in changes to event peaks and accompanying compensation in the baseflow. More significantly, changes in the effective model parameter values required by the best models to take account of the more extreme patterns were able to be detected by noting when distributions of parameters change under uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Travel-time based model of bioremediation using circulation wells

Vertical circulation wells can efficiently provide microorganisms with substrates needed for enhanced bioremediation. We present a travel-time based approach for modeling bioreactive transport in a flow field caused by a series of circulation wells. Mixing within the aquifer is due to the differences in sorption behavior of the reactants. Neglecting local dispersion, transport simplifies to a single one-dimensional problem with constant coefficients for each well. Recirculation is characterized by the discharge densities over travel time. We apply the model to the stimulation of cometabolic dechlorination of trichloroethene (TCE) by alternate injection of oxygen and toluene into the circulation wells. Mixing within the wells can be minimized by interposing sufficiently long breaks between the oxygen and toluene pulses. In our simulation, the proposed injection scheme stimulates biomass growth without risking biofouling of the aquifer.     

Assessing the potential of reservoir outflow management to reduce sedimentation using continuous turbidity monitoring and reservoir modelling

In‐stream sensors are increasingly deployed as part of ambient water quality‐monitoring networks. Temporally dense data from these networks can be used to better understand the transport of constituents through streams, lakes or reservoirs. Data from existing, continuously recording in‐stream flow and water quality monitoring stations were coupled with the two‐dimensional hydrodynamic CE‐QUAL‐W2 model to assess the potential of altered reservoir outflow management to reduce sediment trapping in John Redmond Reservoir, located in east‐central Kansas. Monitoring stations upstream and downstream from the reservoir were used to estimate 5.6 million metric tons of sediment transported to John Redmond Reservoir from 2007 through 2010, 88% of which was trapped within the reservoir. The two‐dimensional model was used to estimate the residence time of 55 equal‐volume releases from the reservoir; sediment trapping for these releases varied from 48% to 97%. Smaller trapping efficiencies were observed when the reservoir was maintained near the normal operating capacity (relative to higher flood pool levels) and when average residence times were relatively short. An idealized, alternative outflow management scenario was constructed, which minimized reservoir elevations and the length of time water was in the reservoir, while continuing to meet downstream flood control end points identified in the reservoir water control manual. The alternative scenario is projected to reduce sediment trapping in the reservoir by approximately 3%, preventing approximately 45 000 metric tons of sediment from being deposited within the reservoir annually. This article presents an approach to quantify the potential of reservoir management using existing in‐stream data; actual management decisions need to consider the effects on other reservoir benefits, such as downstream flood control and aquatic life. Copyright © 2012 John Wiley & Sons, Ltd.     

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.     

深井电极交叉供电对自然电位的影响

通过实验论证平凉地震台深井电阻率观测自然电位畸变由电极交叉供电造成,讨论分析不同电极供电对自然电位的影响。结果表明:对测量极供电,会影响自然电位,不会影响电阻率测值;单极供电对自然电位的影响表现为阶跃突跳,并以指数形态恢复,恢复时间约10 h,干扰峰值与供电电流、供电时间等有关;对观测数据进行校正,取得较好效果。     

Identifying effects of local and nonlocal factors of soil water storage using cyclical correlation analysis

There are various factors governing the spatial and temporal variability of soil water storage including soil properties, topography and vegetation. Some factors act locally, whereas others act nonlocally, which means that a factor measured at one location has effect on soil water storage at another location. The objective of this study was to examine the effects of local and nonlocal controls of soil water storage in a hummocky landscape using cyclical correlation analysis. Soil water storage, soil properties and terrain indices were measured along a 128‐point transect of 576 m long from the semiarid, hummocky, prairie pothole region of North America. There are large coefficients of determination (r²) between soil water storage and sand content (r² = 0.32–0.53), organic carbon content (r² = 0.22–0.56), depth to carbonate layer (r² = 0.13–0.63), wetness index (r² = 0.25–0.45) and other variables at the measurement scale at different times, indicating strong local effects from these variables. The correlation coefficients were also calculated by physically shifting the spatial series of soil water storage with respect to that of controlling factors. The shifting improves the correlation between the spatial series, and the length of shifting indicated the difference in the response of soil water to its controlling factors. For example, the value of r² increased more than eightfold (r² = 0.47–0.64) after shifting the spatial series of soil water storage by 54 m, almost equal to the average length of existing slope, compared with the very weak correlation (r² = 0.02–0.08) at the measurement scale. This indicated the nonlocal effect from the relative elevation. The identification of nonlocal effects from factors improves the prediction of soil water storage. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of the uncertainty of the Robertson and Wride model for liquefaction potential evaluation

As the profession moves toward the performance-based earthquake engineering design, it becomes more important and pressing to examine the uncertainty of the limit state model used for liquefaction potential evaluation. In this paper, the uncertainty of the Robertson and Wride model, a simplified model for liquefaction resistance and potential evaluation based on cone penetration test, is investigated in detail for its model uncertainty in the framework of first-order reliability analysis. The uncertainties of the parameters used in the Robertson and Wride model are also examined. The model uncertainty is estimated by calibration with a fairly large set of case histories. The results show that the uncertainty of the Robertson and Wride model may be characterized with a mean-to-nominal of 0.94 and a coefficient of variation of 0.15 based on the case histories examined.     

Seismic hazard and uncertainty analysis of the Taiwan area

The objectives of this paper are (1) to obtain estimates on the effect of uncertainties of the hazard model, and (2) to evaluate the seismic hazard in Taiwan for structural analysis and design purposes. The seismic hazard in the Taiwan area is presented in terms of an iso-acceleration map. Such a map is developed for return periods of peak ground acceleration of 225 years and 475 years. The contour map of b-values and mean occurence rates for this region is also presented. Uncertainty analyses of model parameters in hazard analysis are concentrated on the analysis of dispersion of PGA values and the probabilistic modeling of stationary and nonstationary Poisson models of occurrences. Th e overall results are considered to be conservative since for most uncertainty analyses the more conservative values are used.     

Early detection of brine and CO2 leakage through abandoned wells using pressure and surface-deformation monitoring data: Concept and demonstration

In this paper, we develop a methodology for early detection of potential CO₂ leakage from geological storage formations using pressure and surface-deformation anomalies. The basic idea is based on the fact that leakage-induced pressure signals travel much faster than the migrating CO₂; thus such anomalies may be detected early enough for risk management measures taking effect in avoiding substantial CO₂ leaks. The early detection methodology involves automatic inversion of anomalous brine leakage signals with efficient forward pressure and surface-deformation modeling tools to estimate the location and permeability of leaky features in the caprock. We conduct a global sensitivity analysis to better understand under which conditions pressure anomalies can be clearly identified as leakage signals, and evaluate signal detectability for a broad parameter range considering different detection limits and levels of data noise. The inverse methodology is then applied to two synthetic examples of idealized two-aquifer-and-one aquitard storage systems, with an injection well and a leaky well, for different monitoring scenarios. In Example 1, only pressure data at the monitoring and injection wells are used for leakage detection. Our results show that the accuracy of leakage detection greatly depends on the level of pressure data noise. In Example 2, joint inversion of pressure and surface-deformation measurements significantly improves the speed of convergence toward the true solution of the leakage parameters and enables early leakage detection. In both examples, successful detection is achieved when two monitoring wells are appropriately placed within up to 4 km from the leaky well.     

Estimation of design flood using EWT and ENE metrics and uncertainty analysis under non-stationary conditions

Concepts of Expected Waiting Time (EWT) and Expected Number of Exceedances (ENE) have been presented in much literature for estimating the Design Flood (DF) under non-stationary conditions. The parameters of the EWT and ENE are generally no less than four, which inevitably leads to the uncertainty of the DF estimation. In this paper, the Bayesian method is proposed to analyze the impact of parameter estimation uncertainty on the EWT- and ENE-based estimation of the DF and Corresponding Design Reliability (CDR). In addition, a comparison analysis between the EWT and ENE is conducted in terms of the DF and CDR with or without a consideration being given to the impact of parameter uncertainty. In the case of giving no consideration to the impact of parameter uncertainty, the experiment results indicate that the EWT-based estimations are less than that of ENE in terms of DF and CDR in the case of a decreasing trend. While in the case of an increasing trend, the EWT-based estimations are bigger than that of ENE. In the case of considering the impact of parameter uncertainty, results in the case study show that the distribution of the EWT-based estimations of DF and CDR are left shifted compared to that of the ENE. Overall, the EWT-based estimations are significantly different from that of ENE in terms of DF and CDR. Therefore, it is necessary and open for further discussions about which metric will be optimal between the EWT and ENE for estimating the DF under non-stationarity.