A Differential Evaluation Markov Chain Monte Carlo algorithm for Bayesian Model Updating

The use of the Bayesian tools in system identification and model updating paradigms has been increased in the last 10 years. Usually, the Bayesian techniques can be implemented to incorporate the uncertainties associated with measurements as well as the prediction made by the finite element model (FEM) into the FEM updating procedure. In this case, the posterior distribution function describes the uncertainty in the FE model prediction and the experimental data. Due to the complexity of the modeled systems, the analytical solution for the posterior distribution function may not exist. This leads to the use of numerical methods, such as Markov Chain Monte Carlo techniques, to obtain approximate solutions for the posterior distribution function. In this paper, a Differential Evolution Markov Chain Monte Carlo (DE-MC) method is used to approximate the posterior function and update FEMs. The main idea of the DE-MC approach is to combine the Differential Evolution, which is an effective global optimization algorithm over real parameter space, with Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distribution function. In this paper, the DE-MC method is discussed in detail while the performance and the accuracy of this algorithm are investigated by updating two structural examples.

[1]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

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

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

[4]  Tshilidzi Marwala,et al.  Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to Aeronautical and Mechanical Engineering , 2016 .

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

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

[7]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

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

[10]  M. Friswell,et al.  Finite element model updating using Hamiltonian Monte Carlo techniques , 2017 .

[11]  Tshilidzi Marwala,et al.  Sampling Techniques in Bayesian Finite Element Model Updating , 2011, ArXiv.

[12]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using the Shadow Hybrid Monte Carlo Technique , 2015 .

[13]  Cajo J. F. ter Braak,et al.  A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces , 2006, Stat. Comput..

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

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

[16]  Ilyes Boulkaibet.  Finite element model updating using Markov Chain Monte Carlo techniques , 2015 .

[17]  David V. Hutton,et al.  Fundamentals of Finite Element Analysis , 2003 .

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

[19]  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..

[20]  Cajo J. F. ter Braak,et al.  Differential Evolution Markov Chain with snooker updater and fewer chains , 2008, Stat. Comput..

[21]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[22]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using an Evolutionary Markov Chain Monte Carlo Algorithm , 2015 .