Bayesian uncertainty analysis for complex physical systems modelled by computer simulators with applications to tipping points

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn this paper we present and illustrate basic Bayesian techniques for the uncertainty analysis of complex physical systems modelled by computer simulators. We focus on emulation and history matching and also discuss the treatment of observational errors and structural discrepancies in time series. We exemplify such methods using a four-box model for the termohaline circulation. We show how these methods may be applied to systems containing tipping points and how to treat possible discontinuities using multiple emulators.

Uncertainty analysis of depth predictions from seismic reflection data using Bayesian statistics

“…In this paper we will use the Gaussian Process emulators. An emulator is defined as a stochastic belief specification, which expresses probabilistic judgements for a deterministic function f (a) [Craig et al, 1997;O'Hagan, 2006;Vernon et al, 2010;Caiado & Goldstein, 2015]. Commonly, they are expressed in the following form:…”

“…In order to perform model calibration and reduce the parameter input space we use the approach known as Bayesian History Matching [Craig et al, 1997;Vernon et al, 2010]. Bayesian History Matching (BHM) is an established method and combined with emulation techniques has been tested successfully in a variety of different scientific disciplines such as reservoir modelling [Craig et al, 1997;Cumming & Goldstein, 2009] climate modelling [Caiado & Goldstein, 2015] and galaxy formation modelling [Vernon et al, 2010]. BHM should not be confused with the term History Matching widely used in the oil industry, as in the latter case, we are trying to match empirical data, such as production rates and observed pressure from well logs, with a complex model (normally called simulator) that is assumed to represent part of the subsurface (reservoir), where the parameters that govern the model don't include any uncertainty estimation.…”

Identifying the stiffness and damping of a nonlinear system using its free response perturbed with Gaussian white noise

“…In the process of identifying parameters, uncertainty is a key point that should be taken into consideration (Adhikari, 2007; Fonseca et al, 2005; Ibrahim, 1987). To account for this, Bayesian methods have been widely applied in model updating and parameter identification (Caiado and Goldstein, 2015; Link and Barker, 2010). Beck and Katafygiotis applied Bayesian methods to structural dynamics problems in the 1990s and established a Bayesian framework, in which a Laplace approximation is used to resolve high-dimensional integrals (Beck and Katafygiotis, 1998; Katafygiotis and Beck, 1998).…”

تنظیم و کالیبراسیون مدل‌های پیچیده‌ی رایانه‌یی با رویکرد مهندسی - آماری مطالعه‌ی موردی: ماشین کاری به کمک لیزر

“…|Q=t; \=@vDU= [11]15 xrwB=w}U w 14 =vU [12]16 TwUwQ &|}=tv CUQO u} QDW}@ [13]17 CvQ@ uw}UQoQ &wrQ=m Cvwt wrQ=m Cvwt [14]18 w} R [15] u= Q=mty w 19 wy u} R}@ OQm}wQ [16]21 u=o=yw= w 20 |Ovm [17] Cwmrt w 22 uWwQ [18]24 |Ov= Qo w 23 lQ=B [19]26 u}DUOro w 25 =O=}=m [20]28 u=wO=y=t w 27 u=t= Q= Qmv=U [21]30 uUwD w 29 TwQB [22] u= Q=mty w 31 |r=B=D=Q} [23]33 |DJvwQ w 32 uwOQ=vwr \=@vDU= [24]34 O} Q |}=tvCUQO [25] u= Q=mty w 35 |Dvwt} R;…”

“…=(0=010; 2 719;0=132; 0=010) 0 ; 2 =10=0560; 2 =1=5907 (19) |Q}oQ=m x@ =@ = Q CQ}=et`@=D u=wD|t xOW OQw; Q@ |=yQDt= Q=B uDW=O =@ 'p=L "OQm x@U=Lt 5 |x]@= Q OwW|t xOy=Wt "s}R=OQB|t ( (x)) CQ}=et |rY= C= QF= |UQQ@ x@ 'uwvm= |rY= C= QF= 'u}vJty "4 pmW OQ=O |O=}R |Q=PoQ}F -=D x2 pt=a R}v VN@ u}= QO "OvwW|t xO}O 5 pmW QO 'lD x@ lD CQwY x@ 'f(x) + (x) w f(x)`@=wD "CU= Qo}O pt=wa R= QDQ=PoQ}F -=D w syt Q=}U@ x2 pt=a Kw[w x@ pOt x@ =D s} R=OQB|t |UOvyt pOt s}_vD x@ 'G}=Dv x@ xHwD =@ '=Hu}= QO =@ xOW xO=O |UOvyt pOt QO '=DU= Q u}= QO "s}@=} CUO Q_v OQwt |Q=t; -|UOvyt xOW s}_vD |Q=t; -|UOvyt pOt x@ 'x2 Q}eDt QO 0 0803 ?} Q[ l} ?Q[ V}B = (1; 0=0803;1; 1) %CW=O s}y=wN`k=w QO " (19 |x]@= Q) s}UQ|t…”