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.

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.

This paper focuses on the safety analysis of a nonlinear hydro-generating unit (HGU) running under different loads. For this purpose, a dynamic balance experiment implemented on an existing hydropower station in China is considered, to qualitatively investigate the stability of the system and to obtain the necessary indices for safety assessment. The experimental data are collected from four on-load units operating at different working heads including 431 m, 434 m, 437 m, and 440 m. A quantitative analysis on the safety performance of the four units was carried out by employing an integration of entropy weights method with grey correlation analysis. This assisted in obtaining the safety degree of each unit, providing the risk prompt to the operation of nonlinear hydro-generating units. The results confirm that unit 4 has the highest level of safety while unit 3 operates with the lowest safety condition. This provides the optimal operational schedule of HGUs to cope with the fluctuations of electricity demand in the studied station. The proposed methodology in this paper is not only applicable to the HGUs in the studied station but could also be adopted to assess the safety degree of any hydropower facility.