Epistemic Uncertainties in Component Fragility Functions

2010 ◽  
Vol 26 (1) ◽  
pp. 41-62 ◽  
Author(s):  
Brendon A. Bradley
Keyword(s):  
Quality Assurance ◽  
Earthquake Engineering ◽  
Epistemic Uncertainty ◽  
Finite Size ◽  
Seismic Demand ◽  
Fragility Functions ◽  
Seismic Performance Assessment ◽  
Fragility Function ◽  
Documentation Quality ◽  
Performance Based Earthquake Engineering

This paper is concerned with the inclusion of epistemic uncertainties in component fragility functions used in performance-based earthquake engineering. Conventionally fragility functions, defining the probability of incurring at least a specified level of damage for a given level of seismic demand, are defined by a mean and standard deviation and assumed to have a lognormal distribution. However, there exist many uncertainties in the development of such fragility functions. The sources of epistemic uncertainty in fragility functions, their consideration, combination, and propagation are presented and discussed. Two empirical fragility functions presented in literature are used to illustrate the epistemic uncertainty in the fragility function parameters due to the finite size of the datasets. These examples and the associated discussions illustrate that the magnitude of epistemic uncertainties are significant and there are clear benefits of the consideration of epistemic uncertainties pertaining to the documentation, quality assurance, implementation, and updating of fragility functions. Epistemic uncertainties should therefore always be addressed in future fragility functions developed for use in seismic performance assessment.

scholarly journals Creating Fragility Functions for Performance-Based Earthquake Engineering

2007 ◽  
Vol 23 (2) ◽  
pp. 471-489 ◽  
Author(s):  
Keith Porter ◽  
Robert Kennedy ◽  
Robert Bachman
Keyword(s):  
Expert Opinion ◽  
Professional Practice ◽  
Earthquake Engineering ◽  
Damage Analysis ◽  
Fragility Functions ◽  
Fragility Function ◽  
Applied Technology ◽  
Engineering Demand Parameter ◽  
Performance Based Earthquake Engineering ◽  
First Time

The Applied Technology Council is adapting PEER's performance-based earthquake engineering methodology to professional practice. The methodology's damage-analysis stage uses fragility functions to calculate the probability of damage to facility components given the force, deformation, or other engineering demand parameter (EDP) to which each is subjected. This paper introduces a set of procedures for creating fragility functions from various kinds of data: (A) actual EDP at which each specimen failed; (B) bounding EDP, in which some specimens failed and one knows the EDP to which each specimen was subjected; (C) capable EDP, where specimen EDPs are known but no specimens failed; (D) derived, where fragility functions are produced analytically; (E) expert opinion; and (U) updating, in which one improves an existing fragility function using new observations. Methods C, E, and U are all introduced here for the first time. A companion document offers additional procedures and more examples.

Analysis of Seismic Fragility Functions of Highway Embankments

2020 ◽  
Author(s):  
Balázs Hübner ◽  
András Mahler
Keyword(s):  
Finite Element ◽  
Earthquake Engineering ◽  
Seismic Fragility ◽  
Response Analysis ◽  
Fragility Functions ◽  
Ground Response ◽  
Ground Response Analysis ◽  
Fragility Function ◽  
Damage States ◽  
Log Normal

Vulnerability assessment of structures is a vitally important topic among earthquake engineering researchers. Generally, their primary focus is on the seismic performance of buildings. Less attention is paid to geotechnical structures, even though information about the performance of these structures (e.g. road embankments, levees, cuts) during an earthquake is essential for planning remediation and rescue efforts after disasters. In this paper the seismic fragility functions of a highway embankment are defined following an analytical methodolgy. The technique is a displacement-based evaluation of seismic vulnerability. Displacements of an embankment during a seismic event are approximated by a 2-D nonlinear ground response analysis using the finite element method. The numerical model was calibrated based on the results of a 1-D nonlinear ground response analysis. The expected displacements were calculated for 3 different embankment heights and Peak Ground Acceleration (PGA) values between 0,05 and 0,35g. Based on the results of the 2-D finite element analysis, the relationship between displacements and different seismic intensity measures (PGA, Arias-intensity) was investigated. Different damage states were considered, and the probability of their exceedance was investigated. The seismic fragility functions of the embankments were developed based on probability of exceedance of these different damage states based on a log-normal fragility function. The legitimacy of using a log-normal fragility function is also examined.

scholarly journals ASSESSMENT OF STRUCTURES SUBJECTED TO ACCIDENTAL ACTIONS USING CRISP AND UNCERTAIN FRAGILITY FUNCTIONS

2009 ◽  
Vol 15 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Egidijus R. Vaidogas ◽  
Virmantas Juocevičius
Keyword(s):  
Prior Distribution ◽  
Epistemic Uncertainty ◽  
Mean Value ◽  
Fragility Functions ◽  
Sources Of Information ◽  
Industrial Facilities ◽  
Fragility Function ◽  
Damage Probability ◽  
Aleatory And Epistemic Uncertainty ◽  
Statistical Sample

An application of fragility functions to the assessment of potential damage due to an accidental action is analysed. The assessment is carried out as an estimation of the probability of a foreseeable damage event (damage probability). This probability is expressed as a mean value of a fragility function developed for the damage event under study. A Bayesian prior (posterior) distribution specified for this mean value is used as an estimate of the damage probability. The prior distribution is derived by transforming prior knowledge through the fragility function and “mapping” this knowledge on the scale of probability values. The technique of Bayesian bootstrap resampling is applied to update the prior distribution. The new information used for the updating consists of a relatively small number of experimental observations of the accidental action. To facilitate the updating, these observations are transformed into a fictitious statistical sample of fragility function values. The updating is first carried out with a fragility function which expresses aleatory uncertainty only. Then it is proposed how to perform the updating with the fragility function which quantifies both aleatory and epistemic uncertainty. This is done by discretising continuous distributions of the epistemic uncertainty related to values (parameters) of the fragility function. The proposed approach allows to utilise different sources of information for the damage assessment. A potential field of application of this approach is risk studies of hazardous industrial facilities. Santrauka Analizuojamas pažeidžiamumo funkcijų taikymas vertinant potencialius statybinių konstrukcijų pažeidimus avariniais poveikiais. Vertinimas atliekamas skaičiuojant galimos konstrukcijos pažaidos tikimybę. Ši tikimybė yra išreiškiama vidutine pažeidžiamumo funkcijos reikšme. Ta funkcija yra formuojama analizuojamam pažaidos įvykiui. Apriorinis ir aposteriorinis Bajeso skirstiniai yra taikomi pažaidos tikimybės reikšmei vertinti. Apriorinis skirstinys yra gaunamas pasinaudojant turima informacija apie avarinį poveikį ir transformuojant šią informaciją per pažeidžiamumo funkciją. Aposteriorinis skirstinys yra gaunamas pasitelkiant naują, eksperimentinę informaciją apie avarinį poveikį. Aposterioriniam skirstiniui gauti taikomas kartotinio statistinio ėmimo (būtstrapo) metodas. Naują informaciją sudaro eksperimentiniai avarinio poveikio charakteristikų matavimai, kurie tiksliai atitinka konstrukcijos ekspozicijos tiriamo poveikio situaciją. Apriorinis ir aposteriorinis skirstiniai išreiškia episteminį neapibrėžtumą vertinamos pažaidos tikimybės reikšmės atžvilgiu. Šie skirstiniai yra gaunami taikant tiek pažeidžiamumo funkciją, kuri išreiškia tik stochastinį neapibrėžtumą, tiek funkciją, kurios reikšmės yra neapibrėžtos epistemine prasme. Potenciali siūlomo metodo taikymo sritis yra pavojingų pramoninių objektų rizikos vertinimas.

Fragility Analysis Methods for Steel Storage Tanks in Seismic Prone Areas

2016 ◽  
Author(s):  
Hoang Nam Phan ◽  
Fabrizio Paolacci ◽  
Silvia Alessandri
Keyword(s):  
Seismic Vulnerability ◽  
Structural Response ◽  
Response Analysis ◽  
Seismic Demand ◽  
Fragility Functions ◽  
Storage Tanks ◽  
Demand Model ◽  
Limit States ◽  
Environmental Consequences ◽  
Fragility Function

Catastrophic failure of above ground storage tanks was observed due to past earthquakes causing serious economic and environmental consequences. Therefore, the evaluation of the seismic vulnerability of existing liquid storage tanks located in seismic prone areas is an important task. Seismic fragility functions are useful tools in order to quantify the seismic vulnerability of structures. These functions give a probability that a seismic demand on a structural component meets or exceeds its capacity, and are generally derived by a variety of approaches, e.g., field observations of damage, static structural analyses, judgment, or analytical fragility functions. Unlike the other methods, the analytical fragility functions are developed from a coupling of the structural response analysis and a probabilistic seismic demand model. The objective of this study is to investigate the seismic vulnerability of above ground steel storage tanks using different analytical methods of the fragility function. A comparison of the well-known cloud method and the incremental dynamic analysis is performed at different limit states for two existing cylindrical steel storage tanks. The first tank represents a slender geometry with a fixed-roof and the second one is a broad tank, unanchored, and provided with a floating roof.

Fragility of Mechanical, Electrical, and Plumbing Equipment

2010 ◽  
Vol 26 (2) ◽  
pp. 451-472 ◽  
Author(s):  
Keith Porter ◽  
Gayle Johnson ◽  
Robert Sheppard ◽  
Robert Bachman
Keyword(s):  
Professional Practice ◽  
Earthquake Engineering ◽  
Fragility Functions ◽  
Subsequent Work ◽  
Engineering Research ◽  
Modifying Factors ◽  
Industrial Buildings ◽  
Average Condition ◽  
Performance Based Earthquake Engineering ◽  
Level Performance

A study for the Multidisciplinary Center for Earthquake Engineering Research (MCEER) provides fragility functions for 52 varieties of mechanical, electrical, and plumbing (MEP) equipment commonly found in commercial and industrial buildings. For the majority of equipment categories, the MCEER study provides multiple fragility functions, reflecting important effects of bracing, anchorage, interaction, etc. The fragility functions express the probability that the component would be rendered inoperative as a function of floor acceleration. That work did not include the evidence underlying the fragility functions. As part of the ATC-58 effort to bring second-generation performance-based earthquake engineering to professional practice, we have compiled the original MCEER specimen-level performance data into a publicly accessible database and validate many of the original fragility functions. In some cases, new fragility functions derived by ATC-58 methods show somewhat closer agreement with the raw data. Average-condition fragility functions are developed here; we will address in subsequent work the effect of potentially important—arguably crucial—performance-modifying factors such as poor anchorage and interaction.

Demonstration of a Practical Method for Seismic Performance Assessment of Structural Systems

2012 ◽  
Vol 28 (2) ◽  
pp. 811-829 ◽  
Author(s):  
T. Y. Yang ◽  
Bozidar Stojadinovic ◽  
Jack Moehle
Keyword(s):  
Seismic Performance ◽  
Earthquake Engineering ◽  
Practical Method ◽  
Performance Comparison ◽  
Practical Implementation ◽  
Structural Systems ◽  
Earthquake Hazards ◽  
Seismic Performance Assessment ◽  
Braced Frame ◽  
Performance Based Earthquake Engineering

Performance-based earthquake engineering aims to describe the seismic performance of a structure using metrics that are of immediate use to both engineers and stakeholders. A rigorous yet practical implementation of performance-based earthquake engineering methodology is used to compare the seismic performance of two steel, concentrically braced structural systems, an inverted-V-braced frame and a suspended zipper-braced frame. The principal difference between these two structural systems is the design approach used to transfer the unbalanced forces when the braces buckle. A probabilistic seismic performance comparison for a three-story office building located in Berkeley, California designed using these two structural systems is presented. The results indicate the suspended zipper-braced frame has lower expected repair cost under different levels of earthquake hazards and is 25% lighter than the corresponding capacity-designed inverted-V-braced frame.

Fragility and Qualification of Components Using Censored Seismic Demand Data

2009 ◽  
Vol 25 (3) ◽  
pp. 719-727
Author(s):  
Avinash M. Nafday
Keyword(s):  
Earthquake Engineering ◽  
Survival Data ◽  
Technical Note ◽  
Statistical Characteristics ◽  
Seismic Demand ◽  
Random Component ◽  
Data Set ◽  
Critical Facilities ◽  
Using Data ◽  
Performance Based Earthquake Engineering

Fragility functions are vital for the risk assessment of critical facilities and to calculate component probability of damage in performance-based earthquake engineering. Seismic qualification is used to prove the adequacy of components in existing facilities or to satisfy their design criteria in new facilities. This technical note describes an approach for component fragility development and seismic qualification using data for seismic demand experienced by similar components and their resulting performance. Depending on the observed component failure or survival, the seismic demand values either exceed or fall short of the random component capacity. The concept of censoring, which captures this excess or shortfall, is introduced to model such data and account for the different statistical characteristics of failure and survival data. The censored data are analyzed by survival analysis, which provides a rigorous and efficient approach to extract information from the data set.

Multivariate Fragility Models for Earthquake Engineering

2016 ◽  
Vol 32 (1) ◽  
pp. 441-461 ◽  
Author(s):  
Abbas Javaherian Yazdi ◽  
Terje Haukaas ◽  
Tony Yang ◽  
Paolo Gardoni
Keyword(s):  
Logistic Regression ◽  
Earthquake Engineering ◽  
Shear Walls ◽  
Performance Assessments ◽  
Fragility Functions ◽  
Structural Components ◽  
Logistic Regression Models ◽  
Damage Models ◽  
Damage States ◽  
Performance Based Earthquake Engineering

This paper employs a logistic regression technique to develop multivariate damage models. The models are intended for performance assessments that require the probability that structural components are in one of several damage states. As such, the developments represent an extension of the univariate fragility functions that are omnipresent in contemporary performance-based earthquake engineering. The multivariate logistic regression models that are put forward here eliminate several of the limitations of univariate fragility functions. Furthermore, the new models are readily substituted for existing fragility functions without any modifications to the existing performance-based analysis methodologies. To demonstrate the proposed modeling approach, a large number of tests of reinforced concrete shear walls are employed to develop multivariate damage models. It is observed that the drift ratio and aspect ratio of concrete shear walls are among the parameters that are most influential on the damage probabilities.

scholarly journals Empirical fragility functions and loss curves for Italian business facilities based on the 2012 Emilia-Romagna earthquake official database

2019 ◽  
Vol 18 (4) ◽  
pp. 1693-1721 ◽  
Author(s):  
Leonardo Rossi ◽  
Marco Stupazzini ◽  
Davide Parisi ◽  
Britta Holtschoppen ◽  
Gabriella Ruggieri ◽  
...  
Keyword(s):  
Earthquake Engineering ◽  
Economic Losses ◽  
Seismic Events ◽  
Fragility Functions ◽  
Administrative Authority ◽  
Specific Data ◽  
Related Data ◽  
Long Span ◽  
Performance Based Earthquake Engineering ◽  
Source Of Information

AbstractThe 2012 Emilia-Romagna earthquake, that mainly struck the homonymous Italian region provoking 28 casualties and damage to thousands of structures and infrastructures, is an exceptional source of information to question, investigate, and challenge the validity of seismic fragility functions and loss curves from an empirical standpoint. Among the most recent seismic events taking place in Europe, that of Emilia-Romagna is quite likely one of the best documented, not only in terms of experienced damages, but also for what concerns occurred losses and necessary reconstruction costs. In fact, in order to manage the compensations in a fair way both to citizens and business owners, soon after the seismic sequence, the regional administrative authority started (1) collecting damage and consequence-related data, (2) evaluating information sources and (3) taking care of the cross-checking of various reports. A specific database—so-called Sistema Informativo Gestione Europa (SFINGE)—was devoted to damaged business activities. As a result, 7 years after the seismic events, scientists can rely on a one-of-a-kind, vast and consistent database, containing information about (among other things): (1) buildings’ location and dimensions, (2) occurred structural damages, (3) experienced direct economic losses and (4) related reconstruction costs. The present work is focused on a specific data subset of SFINGE, whose elements are Long-Span-Beam buildings (mostly precast) deployed for business activities in industry, trade or agriculture. With the available set of data, empirical fragility functions, cost and loss ratio curves are elaborated, that may be included within existing Performance Based Earthquake Engineering assessment toolkits.

scholarly journals Fragility of Hydraulic Elevators for Use in Performance-Based Earthquake Engineering

2007 ◽  
Vol 23 (2) ◽  
pp. 459-469 ◽  
Author(s):  
Keith Porter
Keyword(s):  
Earthquake Engineering ◽  
Cumulative Distribution ◽  
Nonstructural Components ◽  
Engineering Research ◽  
Fragility Function ◽  
The Pacific ◽  
Applied Technology ◽  
Binary Regression Analysis ◽  
Ground Motion Records ◽  
Performance Based Earthquake Engineering

New performance-based earthquake engineering methods developed by the Pacific Earthquake Engineering Research Center, the Applied Technology Council, and others include damage analysis at a highly detailed level, requiring the compilation of fragility functions for a large number of damageable generic structural and nonstructural components. This brief paper presents the development of a fragility function for hydraulic elevators. It uses post-earthquake survey data from 91 elevators in nine California locations after two earthquakes. Surveys were used to collect data on facilities and elevators. Ground-motion records from the California Integrated Seismic Network were used to estimate engineering demands at each site. Binary regression analysis was used to fit a fragility function, which takes the form of a lognormal cumulative distribution function with median value of PGA=0.42 g and logarithmic standard deviation of 0.3. The fragility function appears to be reasonable based on four criteria.

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