Abstract
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.
Highlights
The need to design structures which can withstand environmental and man-made hazards arises in many areas of structural engineering
The probability of Di can be expressed in the form of a mean value: P(Di | AA) = ∫ P(Di | y) dFY ( y) = E(P(Di | Y )), (1) all y where AA is the random event of occurrence of an accidental action; Y is the random vector of action characteristics; y and FY(y) are the value of Y and its joint distribution function, respectively; P(Di | y) is the fragility function relating y to the probability of Di
An application of fragility functions to assessment of potential damage due to an accidental action has been considered. The result of this assessment was a probability of foreseeable damage event
Summary
The need to design structures which can withstand environmental and man-made hazards arises in many areas of structural engineering. An assessment of potential damage due to accidental action may require to handle aleatory and epistemic uncertainties related to both action and fragility function. These uncertainties can be quantified in line with the classical Bayesian approach to QRA (Aven, Pörn 1998; Vaidogas 2006, 2007b). The paper considers the case where the new data used for the updating of the prior distribution has the form of a small-size statistical sample Elements of this sample are observations of potential accidental action recorded in experiment. The estimation is expressed as a problem of Bayesian statistical inference about a mean value of a fictitious population consisting of fragility function values
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