Bootstrapped Artificial Neural Networks for the seismic analysis of structural systems

Abstract We look at the behavior of structural systems under the occurrence of seismic events with the aim of identifying the fragility curves. Artificial Neural Network (ANN) empirical regression models are employed as fast-running surrogates of the (long-running) Finite Element Models (FEMs) that are typically adopted for the simulation of the system structural response. However, the use of regression models in safety critical applications raises concerns with regards to accuracy and precision. For this reason, we use the bootstrap method to quantify the uncertainty introduced by the ANN metamodel. An application is provided with respect to the evaluation of the structural damage (in this case, the maximal top displacement) of a masonry building subject to seismic risk. A family of structure fragility curves is identified, that accounts for both the (epistemic) uncertainty due to the use of ANN metamodels and the (epistemic) uncertainty due to the paucity of data available to infer the fragility parameters.

[1]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[2]  S. Roberts,et al.  Confidence Intervals and Prediction Intervals for Feed-Forward Neural Networks , 2001 .

[3]  Fabio Nobile,et al.  A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2007, SIAM Rev..

[4]  João Cardoso,et al.  Review and application of Artificial Neural Networks models in reliability analysis of steel structures , 2015 .

[5]  Enrico Zio,et al.  How to effectively compute the reliability of a thermal–hydraulic nuclear passive system , 2011 .

[6]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[7]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[8]  Pol D. Spanos,et al.  A neural network approach for simulating stationary stochastic processes , 2009 .

[9]  Bruno Sudret,et al.  Computing derivative-based global sensitivity measures using polynomial chaos expansions , 2014, Reliab. Eng. Syst. Saf..

[10]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[11]  Bruce R. Ellingwood,et al.  Quantifying and communicating uncertainty in seismic risk assessment , 2009 .

[12]  Enrico Zio,et al.  Polynomial chaos expansion for global sensitivity analysis applied to a model of radionuclide migration in a randomly heterogeneous aquifer , 2013, Stochastic Environmental Research and Risk Assessment.

[13]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[14]  Mary Drouin,et al.  Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making (NUREG-1855) , 2009 .

[15]  Terje Aven,et al.  On the Need for Restricting the Probabilistic Analysis in Risk Assessments to Variability , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  G. Lewicki,et al.  Approximation by Superpositions of a Sigmoidal Function , 2003 .

[17]  Ling Li,et al.  Sequential design of computer experiments for the estimation of a probability of failure , 2010, Statistics and Computing.

[18]  Dan M. Frangopol,et al.  Time-Variant Robustness of Aging Structures , 2014 .

[19]  Edoardo Patelli,et al.  Emerging Concepts and Approaches for Efficient and Realistic Uncertainty Quantification , 2013, Maintenance and Safety of Aging Infrastructure.

[20]  Fabio Nobile,et al.  A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..

[21]  Keith Porter,et al.  A Beginner’s Guide to Fragility, Vulnerability, and Risk , 2016 .

[22]  Fernando Lopez-Caballero,et al.  EFFECT OF THE INELASTIC DYNAMIC SOIL–STRUCTURE INTERACTION ON THE SEISMIC VULNERABILITY ASSESSMENT , 2011 .

[23]  Enrico Zio,et al.  Comparison of bootstrapped artificial neural networks and quadratic response surfaces for the estimation of the functional failure probability of a thermal-hydraulic passive system , 2010, Reliab. Eng. Syst. Saf..

[24]  G. Apostolakis The concept of probability in safety assessments of technological systems. , 1990, Science.

[25]  Fabio Nobile,et al.  A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2010, SIAM Rev..

[26]  E. Zio,et al.  A study of the bootstrap method for estimating the accuracy of artificial neural networks in predicting nuclear transient processes , 2006, IEEE Transactions on Nuclear Science.

[27]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[28]  S. Ferson,et al.  Different methods are needed to propagate ignorance and variability , 1996 .

[29]  Eric Walter,et al.  An informational approach to the global optimization of expensive-to-evaluate functions , 2006, J. Glob. Optim..

[30]  Jorge E. Hurtado,et al.  Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis , 2007 .

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

[32]  Bruno Sudret,et al.  Meta-model-based importance sampling for reliability sensitivity analysis , 2014 .

[33]  Enrico Zio,et al.  Application of metamodel-based techniques for the efficient seismic analysis of structural systems , 2015 .

[34]  Pan Wang,et al.  Efficient structural reliability analysis method based on advanced Kriging model , 2015 .

[35]  Léon Personnaz,et al.  CONSTRUCTION OF CONFIDENCE INTERVALS IN NEURAL MODELING USING A LINEAR TAYLOR EXPANSION , 1998 .

[36]  Enrico Zio,et al.  Some considerations on the treatment of uncertainties in risk assessment for practical decision making , 2011, Reliab. Eng. Syst. Saf..

[37]  H Y Kim,et al.  STATISTICAL ANALYSIS OF FRAGILITY CURVES , 2000 .

[38]  Thomas Most,et al.  A comparison of approximate response functions in structural reliability analysis , 2008 .

[39]  Enrico Zio,et al.  NSGA-II-trained neural network approach to the estimation of prediction intervals of scale deposition rate in oil & gas equipment , 2013, Expert Syst. Appl..

[40]  Pedro G. Coelho,et al.  Structural reliability analysis using Monte Carlo simulation and neural networks , 2008, Adv. Eng. Softw..

[41]  Thomas Ulrich,et al.  Fragility curves for risk-targeted seismic design maps , 2014, Bulletin of Earthquake Engineering.