Model Uncertainty in Finite-Element Analysis: Bayesian Finite Elements

In this paper, probabilistic models for structural analysis are put forward, with particular emphasis on model uncertainty. Context is provided by the finite-element method and the need for probabilistic prediction of structural performance in contemporary engineering. Sources of model uncertainty are identified and modeled. A Bayesian approach is suggested for the assessment of new model parameters within the element formulations. The expressions are formulated by means of numerical “sensors” that influence the model uncertainty, such as element distortion and degree of nonlinearity. An assessment procedure is proposed to identify the sensors that are most suitable to capture model uncertainty. This paper presents the general methodology and specific implementations for a general-purpose structural element. Two numerical examples are presented to demonstrate the methodology and its implications for probabilistic prediction of structural response.

[1]  Kathryn B. Laskey.  Model uncertainty: theory and practical implications , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[2]  David Draper,et al.  Assessment and Propagation of Model Uncertainty , 2011 .

[3]  Armen Der Kiureghian,et al.  Comparison of finite element reliability methods , 2002 .

[4]  Gail M. Atkinson,et al.  Development of seismic hazard maps for the proposed 2005 edition of the National Building Code of Canada , 2003 .

[5]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[6]  Kevin R. Mackie,et al.  Fourway: Graphical Tool for Performance-Based Earthquake Engineering , 2006 .

[7]  Gutierrez,et al.  Finite element reliability methods using DIANA , 1994 .

[8]  J. Beck,et al.  Model Selection using Response Measurements: Bayesian Probabilistic Approach , 2004 .

[9]  Michael Havbro Faber,et al.  On the Treatment of Uncertainties and Probabilities in Engineering Decision Analysis , 2005 .

[10]  Kathleen V. Diegert,et al.  Error and uncertainty in modeling and simulation , 2002, Reliab. Eng. Syst. Saf..

[11]  Keith Porter,et al.  An Overview of PEER's Performance-Based Earthquake Engineering Methodology , 2003 .

[12]  Enrique López Droguett,et al.  Bayesian Methodology for Model Uncertainty Using Model Performance Data , 2008, Risk analysis : an official publication of the Society for Risk Analysis.

[13]  Jack W. Baker,et al.  Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings , 2009 .

[14]  George E. Apostolakis,et al.  Including model uncertainty in risk-informed decision making , 2006 .

[15]  Ove Ditlevsen,et al.  Model uncertainty in structural reliability , 1982 .

[16]  Brendon A. Bradley,et al.  Efficient evaluation of performance-based earthquake engineering equations , 2009 .

[17]  Terje Haukaas,et al.  Unified reliability and design optimization for earthquake engineering , 2008 .

[18]  A. Kiureghian,et al.  Aleatory or epistemic? Does it matter? , 2009 .

[19]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[20]  Armen Der Kiureghian,et al.  PROBABILISTIC SEISMIC DEMAND MODELS AND FRAGILITY ESTIMATES FOR RC BRIDGES , 2003 .

[21]  Armen Der Kiureghian,et al.  MEASURES OF STRUCTURAL SAFETY UNDER IMPERFECT STATES OF KNOWLEDGE , 1989 .

[22]  R. Lebrun,et al.  An innovating analysis of the Nataf transformation from the copula viewpoint , 2009 .

[23]  A. Kiureghian.  Non‐ergodicity and PEER's framework formula , 2005 .

[24]  C. Frier,et al.  Finite element reliability analysis of chloride ingress into reinforced concrete structures , 2007 .

[25]  A. Kiureghian,et al.  Multivariate distribution models with prescribed marginals and covariances , 1986 .

[26]  Armen Der Kiureghian,et al.  Methods and Object-Oriented Software for FE Reliability and Sensitivity Analysis with Application to a Bridge Structure , 2007 .

[27]  Armen Der Kiureghian,et al.  A stochastic ground motion model with separable temporal and spectral nonstationarities , 2008 .

[28]  Armen Der Kiureghian,et al.  Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns based on Experimental Observations , 2002 .

[29]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[30]  Ian Hacking,et al.  The Emergence of Probability. A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference , 1979 .

[31]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[32]  Bruce R. Ellingwood,et al.  Earthquake risk assessment of building structures , 2001, Reliab. Eng. Syst. Saf..

[33]  Steven G. Vick.  Degrees of Belief: Subjective Probability and Engineering Judgment , 2002 .

[34]  George E. P. Box,et al.  Bayesian Inference in Statistical Analysis: Box/Bayesian , 1992 .

[35]  Jack P. Moehle,et al.  Seismic Performance Evaluation of Facilities: Methodology and Implementation , 2009 .

[36]  Armen Der Kiureghian,et al.  Space-variant finite element reliability analysis , 1999 .

[37]  Gregory L. Fenves,et al.  Software framework for distributed experimental–computational simulation of structural systems , 2006 .

[38]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[39]  Jacques Devooght,et al.  Model uncertainty and model inaccuracy , 1998 .