Sampling Techniques in Bayesian Finite Element Model Updating

Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main problem in the development and updating of FEMs. This paper highlights the complexities and challenges of implementing any Bayesian method when the analysis involves a complicated structural dynamic model. In such systems an analytical Bayesian formulation might not be available in an analytic form; therefore this leads to the use of numerical methods, i.e. sampling methods. The main challenge then is to determine an efficient sampling of the model parameter space. In this paper, three sampling techniques, the Metropolis-Hastings (MH) algorithm, Slice Sampling and the Hybrid Monte Carlo (HMC) technique, are tested by updating a structural beam model. The efficiency and limitations of each technique is investigated when the FEM updating problem is implemented using the Bayesian Approach. Both MH and HMC techniques are found to perform better than the Slice sampling when Young’s modulus is chosen as the updating parameter. The HMC method gives better results than MH and Slice sampling techniques, when the area moment of inertias and section areas are updated.

[1]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[2]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[3]  Eugenio Oñate,et al.  Structural Analysis with the Finite Element Method , 2009 .

[4]  Eugenio Oñate,et al.  Structural Analysis with the Finite Element Method Linear Statics , 2013 .

[5]  J. Z. Zhu,et al.  The finite element method , 1977 .

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

[7]  J. Beck,et al.  Bayesian Model Updating Using Hybrid Monte Carlo Simulation with Application to Structural Dynamic Models with Many Uncertain Parameters , 2009 .

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

[9]  D. J. Ewins,et al.  Modal Testing: Theory and Practice , 1984 .

[10]  Radford M. Neal.  Slice Sampling , 2003, The Annals of Statistics.

[11]  C. S. Kraaij.  Model updating of a 'clamped'-free beam system using FEMtools , 2006 .

[12]  Sou-Sen Leu,et al.  Bayesian updating of reliability of civil infrastructure facilities based on condition-state data and fault-tree model , 2009, Reliab. Eng. Syst. Saf..

[13]  Kenneth M. Hanson,et al.  Markov chain Monte Carlo posterior sampling with the Hamiltonian method , 2001, SPIE Medical Imaging.

[14]  Singiresu S. Rao.  The finite element method in engineering , 1982 .

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

[16]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[17]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[18]  Tshilidzi Marwala,et al.  Finite-element-model Updating Using Computional Intelligence Techniques , 2010 .

[19]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using Bayesian Framework and Modal Properties , 2005 .

[20]  Linda Simo Mthembu,et al.  FINITE ELEMENT MODEL UPDATING , 2013 .

[21]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using Computational Intelligence Techniques: Applications to Structural Dynamics , 2010 .