Sensitivity or Bayesian model updating: a comparison of techniques using the DLR AIRMOD test data

Deterministic model updating is now a mature technology widely applied to large-scale industrial structures. It is concerned with the calibration of the parameters of a single model based on one set of test data. It is, of course, well known that different analysts produce different finite element models, make different physics-based assumptions, and parameterize their models differently. Also, tests carried out on the same structure, by different operatives, at different times, under different ambient conditions produce different results. There is no unique model and no unique data. Therefore, model updating needs to take account of modeling and test-data variability. Much emphasis is now placed on what has become known as stochastic model updating where data are available from multiple nominally identical test structures. In this paper two currently prominent stochastic model updating techniques (sensitivity-based updating and Bayesian model updating) are described and applied to the DLR AIRMOD structure.

[1]  John E. Mottershead,et al.  The sensitivity method in finite element model updating: A tutorial (vol 25, pg 2275, 2010) , 2011 .

[2]  James L. Beck,et al.  Bayesian Updating and Model Class Selection for Hysteretic Structural Models Using Stochastic Simulation , 2008 .

[3]  Edoardo Patelli,et al.  COSSAN: A Multidisciplinary Software Suite for Uncertainty Quantification and Risk Management , 2017 .

[4]  J. Mottershead,et al.  Interval model updating with irreducible uncertainty using the Kriging predictor , 2011 .

[5]  John E. Mottershead,et al.  Parameter selection and covariance updating , 2016 .

[6]  Gerhart I. Schuëller,et al.  A stochastic model updating technique for complex aerospace structures , 2011 .

[7]  John E. Mottershead,et al.  Stochastic model updating: Part 1—theory and simulated example , 2006 .

[8]  A. H,et al.  REGULARISATION METHODS FOR FINITE ELEMENT MODEL UPDATING , 1998 .

[9]  Tshilidzi Marwala,et al.  Model selection in finite element model updating using the Bayesian evidence statistic , 2011 .

[10]  Jm M. Ko,et al.  An improved perturbation method for stochastic finite element model updating , 2008 .

[11]  Michael Link,et al.  Stochastic model updating—Covariance matrix adjustment from uncertain experimental modal data , 2010 .

[12]  M. Degener,et al.  Ground Vibration Test and Finite Element Analysis of the GARTEUR SM-AG19 Testbed. , 1996 .

[13]  M. Friswell,et al.  Perturbation methods for the estimation of parameter variability in stochastic model updating , 2008 .

[14]  M. Böswald,et al.  Identification of Non-linear Joint Parameters by using Frequency Response Residuals , 2005 .

[15]  John E. Mottershead,et al.  A comparison of two stochastic model updating methods using the DLR AIRMOD test structure , 2015 .

[16]  Ricardo Perera,et al.  A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation , 2012 .

[17]  C Soize,et al.  Maximum entropy approach for modeling random uncertainties in transient elastodynamics. , 2001, The Journal of the Acoustical Society of America.

[18]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[19]  Jean-Claude Golinval,et al.  Cost Action f3 'structural Dynamics' (1997-2001)—AN European Co-Operation in the Field of Science and Technology , 2003 .

[20]  Jérôme Antoni,et al.  A comprehensive Bayesian approach for model updating and quantification of modeling errors , 2011 .

[21]  Patrick Paultre,et al.  Consistent regularization of nonlinear model updating for damage identification , 2009 .

[22]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[23]  John E. Mottershead,et al.  Model structure correction and updating of aeroengine casings using fictitious mass modifications , 2005 .

[24]  Michael Link,et al.  Using stochastic experimental modal data for identifying stochastic finite element parameters of the AIRMOD benchmark structure , 2012 .

[25]  J. Beck,et al.  UPDATING MODELS AND THEIR UNCERTAINTIES. II: MODEL IDENTIFIABILITY. TECHNICAL NOTE , 1998 .

[26]  John E. Mottershead,et al.  SELECTION AND UPDATING OF PARAMETERS FOR AN ALUMINIUM SPACE-FRAME MODEL , 2000 .

[27]  Hans Günther Natke,et al.  Einführung in Theorie und Praxis der Zeitreihen- und Modalanalyse , 1983 .

[28]  Ricardo Perera,et al.  Damage identification by response surface based model updating using D-optimal design , 2011 .

[29]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .

[30]  Vicente J. Romero,et al.  Calibration and Uncertainty Analysis for Computer Simulations with Multivariate Output , 2008 .

[31]  Michael Link,et al.  WORKING GROUP 1: GENERATION OF VALIDATED STRUCTURAL DYNAMIC MODELS—RESULTS OF A BENCHMARK STUDY UTILISING THE GARTEUR SM-AG19 TEST-BED , 2003 .

[32]  Jon D. Collins,et al.  Statistical Identification of Structures , 1973 .

[33]  John E. Mottershead,et al.  Model Updating In Structural Dynamics: A Survey , 1993 .

[34]  Bernd A. Berg Markov Chain Monte Carlo Simulations and Their Statistical Analysis , 2004 .

[35]  S. Au,et al.  Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm , 2015 .

[36]  D. J. Bartholomew,et al.  Scientific Inference, 3rd Ed. , 1976 .

[37]  J. Ching,et al.  Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging , 2007 .

[38]  J.E. Mottershead,et al.  Stochastic model updating: Part 2—application to a set of physical structures , 2006 .

[39]  Y. Govers,et al.  Stochastic model updating of an aircraft like structure byparameter covariance matrix adjustment , 2010 .

[40]  K. Yuen Bayesian Methods for Structural Dynamics and Civil Engineering , 2010 .

[41]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[42]  J. Beck,et al.  Bayesian Updating of Structural Models and Reliability using Markov Chain Monte Carlo Simulation , 2002 .

[43]  Guido De Roeck,et al.  Dealing with uncertainty in model updating for damage assessment: A review , 2015 .

[44]  C. Schedlinski,et al.  Experimental Modal Analysis and Computational Model Updating of a Car Body in , 2004 .

[45]  John E. Mottershead,et al.  Combining Subset Selection and Parameter Constraints in Model Updating , 1998 .