Influence Of Epistemic Uncertainties Research Articles

Seismic Risk Analysis of Subway Station Structures Combining the Epistemic Uncertainties from Both Seismic Hazard and Numerical Simulation

ABSTRACT To consider the influence of epistemic uncertainties in both seismic hazard and numerical simulation on seismic risk of subway station structures, the uncertainties mentioned above are uniformly characterized as the epistemic uncertainty of seismic demand of subway station structures from the perspective of uncertainty propagation in this paper. On this basis, the analytical formulations of seismic risk considering simultaneous aleatory and epistemic uncertainties are derived. The validity of the derived analytical formulations is verified by the Monte Carlo simulation and the influences of epistemic uncertainty on the seismic risk of subway station structure are further discussed.

A Monte Carlo framework for probabilistic analysis and variance decomposition with distribution parameter uncertainty

Probabilistic methods are used with modeling and simulation to predict variation in system performance and assess risk due to randomness in model inputs such as material properties, loads, and boundary conditions. It is common practice to assume that the input distributions are known. However, this discounts the epistemic uncertainty in the values of the distribution parameters, which can be attributed to the availability of limited data to define the input distributions. This paper proposes a Monte Carlo framework for unified treatment of both aleatory and epistemic uncertainty types when assessing system performance and risk. A Bayesian philosophy is adopted, whereby epistemic uncertainty is characterized using probability theory. Several computational approaches are outlined for propagation and sensitivity analysis with distribution parameter uncertainty. As a result of the outlined framework, the overall influence of epistemic uncertainties can be quantified in terms of confidence bounds on statistical quantities such as failure probability, and the relative influence of each source of epistemic uncertainty is quantified using variance decomposition. The proposed methods are demonstrated using both an analytical example and a fatigue crack growth analysis.

Comparison of methodologies for seismic fragility analysis of unreinforced masonry buildings considering epistemic uncertainty

The first-order second-moment (FOSM), Latin hypercube sampling (LHS), and Monte Carlo simulation (MC) methods were applied to perform seismic fragility analyses of unreinforced masonry (URM) buildings, incorporating incremental dynamic analysis (IDA). The epistemic uncertainty caused by parameter uncertainty was also considered by all three methods, which therefore obtained more accurate results compared with the conventional IDA analysis that only considers the aleatory uncertainty caused by the record-to-record variability. Nine structural parameters were selected as the epistemic uncertainty inputs, and the URM buildings were modeled by the equivalent frame models in OpenSees. The analysis results indicated that the epistemic uncertainty was non-negligible because of the high dispersion of the structural parameters and high nonlinearity of the seismic responses of the URM buildings. At the same time, the epistemic uncertainty values derived by LHS-IDA and MC-IDA were slightly larger than that derived by FOSM-IDA as a result of the consideration of the nonlinear response. In the final comparison, the LHS-IDA was proven to be the most efficient and accurate way to consider the influence of epistemic uncertainty.

Estimation of wind-induced extreme responses with various mean recurrence intervals considering model uncertainty due to limited data

The wind-induced extreme responses with various mean recurrence intervals (MRIs) can be estimated by accounting for the aleatory uncertainties in wind speed and extreme response coefficient in terms of their probability distributions. These distribution models when determined from limited samples of data also have uncertainties, referred to as epistemic uncertainties. This study addresses the epistemic uncertainties in probability distributions of wind speed and extreme response coefficient, and their influence on the estimated extreme responses with various MRIs. Closed-form expressions for quantifying the epistemic uncertainties in terms of coefficients of variation of the distribution model parameters are presented as functions of sample size. The influence of epistemic uncertainties on the predicted extreme responses with various MRIs is also estimated using closed-form expression in terms of confidence intervals. Based on the proposed formulations, a parametric study is carried out to shed light on the importance of consideration of various epistemic uncertainties. The results show that the epistemic uncertainty of wind speed generally predominates the predicted extreme response, while the epistemic uncertainty in the extreme response coefficient can also have considerable effect when the aleatory uncertainty in wind speed is low and that in extreme response coefficient is high. The proposed method is then applied to a long-span roof structure using wind loads determined from a wind tunnel test.

Improved Modelling and Assessment of the Performance of Firefighting Means in the Frame of a Fire PSA

An integrated deterministic and probabilistic safety analysis (IDPSA) was carried out to assess the performances of the firefighting means to be applied in a nuclear power plant. The tools used in the analysis are the code FDS (Fire Dynamics Simulator) for fire simulation and the tool MCDET (Monte Carlo Dynamic Event Tree) for handling epistemic and aleatory uncertainties. The combination of both tools allowed for an improved modelling of a fire interacting with firefighting means while epistemic uncertainties because lack of knowledge and aleatory uncertainties due to the stochastic aspects of the performances of the firefighting means are simultaneously taken into account. The MCDET-FDS simulations provided a huge spectrum of fire sequences each associated with a conditional occurrence probability at each point in time. These results were used to derive probabilities of damage states based on failure criteria considering high temperatures of safety related targets and critical exposure times. The influence of epistemic uncertainties on the resulting probabilities was quantified. The paper describes the steps of the IDPSA and presents a selection of results. Focus is laid on the consideration of epistemic and aleatory uncertainties. Insights and lessons learned from the analysis are discussed.

Assessment of earthquake-induced damage in Quebec city, Canada

A methodology is developed for first-order assessment of the seismic risk involving seismic hazard, local building inventory, and evaluation of respective vulnerability. Central to the vulnerability analysis is the concept of fragility functions used to determine the probability of exceedance of a specified damage state, where the nonlinear structural behaviour is defined by capacity curves. A new set of continuous hazard-compatible fragility functions is proposed for rapid risk assessment on urban and regional scales in interactive spreadsheet application. To demonstrate the method, it was applied in a dense urban environment of downtown Quebec City, Canada, for damage assessment of low-rise wood light frame and unreinforced brick masonry buildings. Earthquake scenario with M6.2 and distance 10km from the centroid of the study area was developed from deaggregation of the seismic hazard defined by the current National Building Code of Canada-NBCC 2010. The ground shaking was represented with a simplified site-specific response spectrum, fully defined with spectral accelerations at 0.3 and 1.0s. The results show that as much as 61% of the considered buildings would sustain certain degree of damage. The influence of epistemic uncertainties in the ground motion prediction and the site-class on damage estimation is evaluated.

Partially Observable Markov Decision Processes incorporatingepistemicuncertainties

The use of Markov Decision Processes for Inspection Maintenance and Rehabilitation of civil engineering structures relies on the use of several transition matrices related to the stochastic degradation process, maintenance actions and imperfect inspections. Point estimators for these matrices are usually used and they are evaluated using statistical inference methods and/or expert evaluation methods. Thus, considerable epistemic uncertainty often veils the true values of these matrices. Our contribution through this paper is threefold. First, we present a methodology for incorporating epistemic uncertainties in dynamic programming algorithms used to solve finite horizon Markov Decision Processes (which may be partially observable). Second, we propose a methodology based on the use of Dirichlet distributions which answers, in our sense, much of the controversy found in the literature about estimating Markov transition matrices. Third, we show how the complexity resulting from the use of Monte-Carlo simulations for the transition matrices can be greatly overcome in the framework of dynamic programming. The proposed model is applied to concrete bridge under degradation, in order to provide the optimal strategy for inspection and maintenance. The influence of epistemic uncertainties on the optimal solution is underlined through sensitivity analysis regarding the input data.

Seismogenic zonation and seismic hazard estimates in a Southern Italy area (Northern Apulia) characterised by moderate seismicity rates

Abstract. The northernmost part of Apulia, in Southern Italy, is an emerged portion of the Adriatic plate, which in past centuries was hit by at least three disastrous earthquakes and at present is occasionally affected by seismic events of moderate energy. In the latest seismic hazard assessment carried out in Italy at national scale, the adopted seismogenic zonation (named ZS9) has defined for this area a single zone including parts of different structural units (chain, foredeep, foreland). However significant seismic behaviour differences were revealed among them by our recent studies and, therefore, we re-evaluated local seismic hazard by adopting a zonation, named ZNA, modifying the ZS9 to separate areas of Northern Apulia belonging to different structural domains. To overcome the problem of the limited datasets of historical events available for small zones having a relatively low rate of earthquake recurrence, an approach was adopted that integrates historical and instrumental event data. The latter were declustered with a procedure specifically devised to process datasets of low to moderate magnitude shocks. Seismicity rates were then calculated following alternative procedural choices, according to a "logic tree" approach, to explore the influence of epistemic uncertainties on the final results and to evaluate, among these, the importance of the uncertainty in seismogenic zonation. The comparison between the results obtained using zonations ZNA and ZS9 confirms the well known "spreading effect" that the use of larger seismogenic zones has on hazard estimates. This effect can locally determine underestimates or overestimates by amounts that make necessary a careful reconsideration of seismic classification and building code application.

Incremental dynamic analysis with consideration of modeling uncertainties

AbstractIncremental 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.

Seismic Fragility Curves for Un-Anchored On-Grade Steel Storage Tanks: Bayesian Approach

In this article, Bayesian approach is used for estimation of seismic fragility of un-anchored on‐grade steel storage tanks based on historical data and American Lifeline Alliance tanks database. The approach properly accounts for epistemic as well as aleatory uncertainties. The point and interval estimates of the fragility are formulated based on structural reliability method that implicitly or explicitly reflects the influence of epistemic uncertainty. The fragility curves developed herein are compared to corresponding relations currently available in the technical literature, the comparison suggest that actual tank performance is better than that predicted in the literature. Finally, application of fragilities in loss estimation methodology is investigated and showing a considerable scatter in the results corresponding to different fragilities.