Finite Element Model Updating using Hamiltonian Monte Carlo Techniques
I Boulkaibet, L Mthembu, T Marwala (University of Johannesburg, South Africa), MI Friswell & S Adhikari (Swansea University)
Inverse Problems in Science & Engineering, Vol. 25, No. 7, 2017, pp. 1042-1070
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.
This material has been published in the Inverse Problems in Science & Engineering, Vol. 25, No. 7, 2017, pp. 1042-1070, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Taylor & Francis.
Link to paper using doi: 10.1080/17415977.2016.1215446
Inverse Problems in Science & Engineering