One of the advanced Monte Carlo techniques employed to perform Bayesian model updating on the epistemic model parameter(s) is the Transitional Markov Chain Monte Carlo sampler. A key characteristic in its sampling approach involves the use of "transitional" distributions to allow samples to converge iteratively from the prior to the final posterior. Hence, the selection of the transition step size becomes of critical importance. Currently, the selection criterion is such that the optimal transition step size is one that realizes a 100% Coefficient of Variation in the statistical weights of the samples in a given iteration. The work presented here considers an alternative selection criterion on the transition step size involving the use of the Effective Sample Size as a metric. The optimal step size considered in this work is one which achieves an effective sample size equal to half the total sample size. To provide a comparative study, the standard Transitional Markov Chain Monte Carlo sampler, along with the modified Transitional Markov Chain Monte Carlo sampler imbued with the alternative selection criterion, are implemented to infer the friction force and the natural frequency of a single-storey frame structure with a metal-to-metal contact, whose dynamics is described by a non-linear differential equation. From there, the sampling performance is compared on the basis of the evolution of the tempering parameter, and the standard error of the estimates. @en

Several on-line identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected but might vary across different sequences of datasets. The proposed approach involves the implementation of the affine-invariant Ensemble sampler in place of the Metropolis–Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step-size of the affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the off-line and on-line identification of the most probable models under uncertainty. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a nonlinear dynamical system using experimental data.@en

Bayesian inference is a popular approach towards parameter identification in engineering problems. Such technique would involve iterative sampling methods which are often robust. However, these sampling methods often require significant computational resources and also the tuning of a large number of parameters. This motivates the development of a sampler called the Transitional Ensemble Markov Chain Monte Carlo. The proposed approach implements the Affine-invariant Ensemble sampler in place of the classical Metropolis–Hastings sampler as the Markov chain Monte Carlo move kernel. In doing so, it allows for the sampling of badly-scaled and highly-anisotropic distributions without requiring extra computational costs. This makes the proposed sampler computationally efficient as a result of having less auxiliary parameters to compute per iteration compared to the standard single particle Transitional Markov Chain Monte Carlo. In addition to such change, an adaptive tuning algorithm is also proposed within the new sampler. This algorithm allows for automatic tuning of the step-size of the Affine-invariant Ensemble sampler. Hence, such proposals not only ensure that the new sampler is “tune-free” for the users, but also improves its robustness by ensuring that the acceptance rate of samples is well-controlled within acceptable bounds. As a result, this approach could be significantly faster compared to standard Transitional Markov Chain Monte Carlo methods on badly scaled and highly skewed distributions, which can be encountered when dealing with complex engineering problems. The proposed sampler will be implemented on 2 benchmark numerical examples of varying complexities to demonstrate its strengths and advantages. In addition, the sampler is validated by investigating its parameter identification capability on an Aluminium Frame using experimental data.

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This work presents an application of the recently-developed Sequential Ensemble Monte Carlo sampler in performing on-line Bayesian model updating for the Prognostics Health Management of a passive component of an Advanced Reactor. The passive component involves a stainless-steel material subjected to a thermal creep deformation whose growth rate is modelled by a continuous piece-wise model consisting of 3 models, each representing a creep-growth stage.

There are 2 investigations done in this research. For the first investigation, the model identification capability of the Sequential Monte Carlo sampler is evaluated in identifying the most probable model for each creep-growth stage. For the second investigation, the on-line Bayesian model updating procedure via the aforementioned sampler is then undertaken. In addition, a method is proposed where the model updating approach will be done for each model sequentially across the different creep-growth stage. This process involves utilising information of the boundary conditions obtained from the model output interval at the transition times to determine the prior bounds for each model parameter to be updated. This method seeks to minimise the discontinuity in the updated piece-wise model at the transition times. From there, the Remaining Useful Life analysis on the component is performed.@en

This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the context of Bayesian model updating for engineering applications. Markov Chain Monte Carlo, Transitional Markov Chain Monte Carlo, and Sequential Monte Carlo methods are introduced, applied to different case studies and finally their performance is compared. For each of these methods, numerical implementations and their settings are provided. Three case studies with increased complexity and challenges are presented showing the advantages and limitations of each of the sampling techniques under review. The first case study presents the parameter identification for a spring-mass system under a static load. The second case study presents a 2-dimensional bi-modal posterior distribution and the aim is to observe the performance of each of these sampling techniques in sampling from such distribution. Finally, the last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data. The case studies presented in this paper consider the recorded data set as a single piece of information which is used to make inferences and estimations on time-invariant model parameters.

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