An adaptive markov chain monte carlo method for bayesian finite element model updating

Abstract: In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure

Finite Element Model updating using Hamiltonian Monte Carlo techniques

Abstract: Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterise the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems this function is difficult to solve analytically. In such cases the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate (AR) of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics (MD) trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large-system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms

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