Seismic Performance Uncertainty Estimation via IDA with Progressive Accelerogram-Wise Latin Hypercube Sampling

This research investigates the collapse responses of a concrete moment frame considering modeling uncertainties. These modeling uncertainties are considered for evaluating a collapse response related to the modified Ibarra-Krawinkler moment-rotation parameters for beam and column elements of a given structure. To analyze these uncertainties, the correlations between the model parameters in one component and between two structural components were considered. Latin Hypercube Sampling (LHS) method was employed to produce independent random variables. Moreover, Cholesky decomposition was adopted to produce correlated random variables. Performing 281 simulations for the uncertainties involved considering their inter-correlations, incremental dynamic analysis (IDA) was done using 44 far-field accelerograms to determine structural collapse responses. Collapse responses of each simulation, including mean collapse capacity, mean collapse drift, and mean annual frequency, were obtained. Then, the collapse responses were predicted using the response surface method and artificial neural network. The results show that the Correlation coefficients (R) between the target data resulted from incremental dynamic analysis (IDA), output data resulted from response surface method (RSM), and artificial neural network (ANN) were obtained for the collapse responses above 0.98. The maximum prediction errors for mean collapse capacity and mean collapse drift are less than 5% and for mean annual frequency less than 10% under response surface method (RSM), and artificial neural network (ANN).

Incremental dynamic analysis (IDA) has been extended by introducing a set of structural models in addition to the set of ground motion records which is employed in IDA analysis in order to capture record‐to‐record variability. The set of structural models reflects epistemic (modeling) uncertainties, and is determined by utilizing the latin hypercube sampling (LHS) method. The effects of both aleatory and epistemic uncertainty on seismic response parameters are therefore considered in extended IDA analysis. The proposed method has been applied to an example of the four‐storey‐reinforced concrete frame, for which pseudo‐dynamic tests were performed at the ELSA Laboratory, Ispra. The influence of epistemic uncertainty on the seismic response parameters is presented in terms of summarized IDA curves and dispersion measures. The results of extended IDA analysis are compared with the results of IDA analysis, and the sensitivity of the seismic response parameters to the input random variable using the LHS method is discussed. It is shown that epistemic uncertainty does not have significant influence on the seismic response parameters in the range far from collapse, but could have a significant influence on collapse capacity. Copyright © 2008 John Wiley & Sons, Ltd.

This report presents guidelines for evaluating uncertainty in mathematical equations and computer models applied to assess human health and environmental risk. Uncertainty analyses involve the propagation of uncertainty in model parameters and model structure to obtain confidence statements for the estimate of risk and identify the model components of dominant importance. Uncertainty analyses are required when there is no a priori knowledge about uncertainty in the risk estimate and when there is a chance that the failure to assess uncertainty may affect the selection of wrong options for risk reduction. Uncertainty analyses are effective when they are conducted in an iterative mode. When the uncertainty in the risk estimate is intolerable for decision-making, additional data are acquired for the dominant model components that contribute most to uncertainty. This process is repeated until the level of residual uncertainty can be tolerated. A analytical and numerical methods for error propagation are presented along with methods for identifying the most important contributors to uncertainty. Monte Carlo simulation with either Simple Random Sampling (SRS) or Latin Hypercube Sampling (LHS) is proposed as the most robust method for propagating uncertainty through either simple or complex models. A distinction is made between simulating a stochastically varying assessment endpoint (i.e., the distribution of individual risks in an exposed population) and quantifying uncertainty due to lack of knowledge about a fixed but unknown quantity (e.g., a specific individual, the maximally exposed individual, or the mean, median, or 95%-tile of the distribution of exposed individuals). Emphasis is placed on the need for subjective judgement to quantify uncertainty when relevant data are absent or incomplete.

This paper studies the effects of spatial correlation between the structural components on probabilistic seismic performance of steel moment resisting frames, using extended incremental dynamic analysis (IDA) method to consider the effects of aleatoric uncertainties caused by ground motion records. In this probabilistic assessment, a combination of Latin hypercube sampling (LHS) and Cholesky decomposition (CD) methods are utilized to take the epistemic uncertainties of the numerical model into account. In case the target correlation matrix is not positive definite, two powerful optimization algorithms are employed to find the closest positive definite correlation matrix.

Incremental Dynamic Analysis (IDA) is a technique to determine the overall seismic performance of structures under varied intensities of earthquakes. In this paper, the seismic performance of four-story steel braced frames equipped with superelastic Shape Memory Alloy (SMA) braces is assessed by performing IDA. The seismic response of SMA-braced frames was compared to that of corresponding Buckling-Restrained Braced Frames (BRBFs). Based on the results of this comparative study, the SMA-braced frames were generally effective in reducing maximum interstory drifts and permanent roof deformations. In addition, the SMA-braced frames demonstrated more uniform drift distribution over the height of the building. As the intensity of earthquake excitation increases, a higher response reduction can be expected for SMA-braced frames.

Latin Hypercube Sampling (LHS), unlike other simulation methods such as Monte Carlo Simulation (MCS), has not enjoyed wide applications in determination of reserve despite its capability to realize same accuracy as with the latter even with much fewer simulation trials. The parameters used in these distributions are extracted using software ‘digitizer’ from different plot of values derived from measurements of reservoir and fluid properties. This work dwells on analysis of two depleted gas fields for which the ultimate recovery is known. The distribution of porosity, water saturation, reservoir thickness and reserve size are input to crystalbal software to generate cumulative distribution function (CDF) and Probability density function (PDF) of original gas in place (OGIP) for each of the fields. The accuracy of Latin Hypercube Sampling is analysed by comparing the actual ultimate recovery and the OGIP predicted by LHS. The calculated recovery factors of 68.7% and 93.3%, for water driven and depletion driven gas reservoirs respectively, compare favourably with those of known gas reservoirs. Therefore, LHS is a good estimator of gas reserve. It is recommended that similar study should be carried out on condensate and oil reservoir, particularly on Niger Delta fields.

Seismic response and collapse analysis of a transmission tower-line system considering uncertainty factors

On Latin Hypercube sampling for efficient uncertainty estimation of satellite rainfall observations in flood prediction

Measurement uncertainty evaluation in whiplash test model via neural network and support vector machine-based Monte Carlo method

Risk analysis using stochastic reliability methods applied to two cases of deterministic water quality models

Take a typical cross-section of rockfill embankment slope in Yaan-Luku highway as the research object, reliability analysis is studied under the condition of water table of 840.85m, 851.50m, and loading condition of natural state and horizontal seismic acceleration of 0.2g, respectively. Raw data use Kolmogorov-Smirnov test (K-S test) to determine the distribution type of parametric variation. And the parameters were sampling with Latin hypercube sampling (LHS) method and Monte Carlo (MC) method, respectively, to obtain state function and determine safety factors and reliability indexes. A conclusion is drawn that the times of simulation based on LHS method were less than Monte Carlo method. Also the convergence of failure probability is better than the Monte Carlo method. The safety factor is greater than one and the failure probability has reached to 35.45% in condition of earthquake, which indicating that the instability of rockfill embankment slope is still possible.

It is effective to apply damage-sensitive features from vibration response for structural damage assessment. Fewer damage identification algorithms have been taken into account the material variation. The material variation could be caused by many reasons in engineering practice, these variations may affect the features used for structure monitoring and lead to an inaccurate damage assessment. In this research the authors proposed a model to assess statistical structural damage of free-free beam structure. The modal curvature-base feature was used to identify crack location. The statistical damage database was build by applying the Monte Carlo simulation with Latin hypercube sampling. The damage probability distribution among various crack depths were estimated by mapping measured frequencies to the statistical damage database, and its statistical significance of damage level were examined by t-test. The experimental modal analysis data from hardware samples and simulated beams were used to demonstrate the crack assessment procedures. From the assessment results, the authors concluded the proposed algorithm was robust and capable of identifying the multiple cracks in free-free beam with uniform mass density and stiffness variations.

Probabilistic seismic performance assessment of aqueduct structures considering different sources of uncertainty

Although the U.S. Congress established the Total Maximum Daily Load (TMDL) program in the original Clean Water Act of 1972, Section 303(d), it did not receive attention until the 1990s. Currently, two methods are available for tracking pollution in the environment and assessing the effectiveness of the TMDL process on improving the quality of impaired water bodies: field monitoring and mathematical/computer modeling. Field monitoring may be the most appropriate method, but its use is limited due to high costs and extreme spatial and temporal ecosystem variability. Mathematical models provide an alternative to field monitoring that can potentially save time, reduce cost, and minimize the need for testing management alternatives. However, the uncertainty of the model results is a major concern. Uncertainty is defined as the estimated amount by which an observed or calculated value may depart from the true value, and it has important policy, regulatory, and management implications. The source and magnitude of uncertainty and its impact on TMDL assessment has not been studied in depth. This article describes the collective experience of scientists and engineers in the assessment of uncertainty associated with TMDL models. It reviews sources of uncertainty (e.g., input variability, model algorithms, model calibration data, and scale), methods of uncertainty evaluation (e.g., first-order approximation, mean value first-order reliability method, Monte Carlo, Latin hypercube sampling with constrained Monte Carlo, and generalized likelihood uncertainty estimation), and strategies for communicating uncertainty in TMDL models to users. Four case studies are presented to highlight uncertainty quantification in TMDL models. Results indicate that uncertainty in TMDL models is a real issue and should be taken into consideration not only during the TMDL assessment phase, but also in the design of BMPs during the TMDL implementation phase. First-order error (FOE) analysis and Monte Carlo simulation (MCS) or any modified versions of these two basic methods may be used to assess uncertainty. This collective study concludes that a more scientific method to account for uncertainty would be to develop uncertainty probability distribution functions and transfer such uncertainties to TMDL load allocation through the margin of safety component, which is selected arbitrarily at the present time. It is proposed that explicit quantification of uncertainty be made an integral part of the TMDL process. This will benefit private industry, the scientific community, regulatory agencies, and action agencies involved with TMDL development and implementation.

To avoid global collapse of high-rise building structures caused by the damage of weak stories, a multi-objective optimization method based on damage control function of story group and failure probability was proposed. Through incremental dynamic analysis, the peak acceleration corresponding to the structural failure probability of 50% was selected as the objective earthquake intensity, and two performance indices:the damage control function of story group and failure probability, were defined and the section dimension of components was used as the variables to conduct the structural optimization analysis. A 30-story reinforced concrete frame-core structure was optimized, and the seismic performance of structure before and after optimization was assessed based on PACT (Performance Assessment Calculation Tool). Results indicate that the inter-story drift angle distribution of the optimized structure is more uniform than that of the original structure, and the damage is gradually decreased from the top to the bottom. The Collapse Margin Ratio (CMR) is increased by 29.8, and the repair cost is reduced for both the frame and core tube. The working coordination between the wall and the frame is strengthened, and the seismic perfomance of the structure after optimization has been significantly improved.