Various parametric skewed distributions are widely used to model the time-to-failure (TTF) in the reliability analysis of mechatronic systems, where many items are unobservable due to the high cost of testing. Estimating the parameters of those distributions becomes a challenge. Previous research has failed to consider this problem due to the difficulty of dependency modeling. Recently the methodology of Bayesian networks (BNs) has greatly contributed to the reliability analysis of complex systems. In this paper, the problem of system reliability assessment (SRA) is formulated as a BN considering the parameter uncertainty. As the quantitative specification of BN, a normal distribution representing the stochastic nature of TTF distribution is learned to capture the interactions between the basic items and their output items. The approximation inference of our continuous BN model is performed by a modified version of nonparametric belief propagation (NBP) which can avoid using a junction tree that is inefficient for the mechatronic case because of the large treewidth. After reasoning, we obtain the marginal posterior density of each TTF model parameter. Other information from diverse sources and expert priors can be easily incorporated in this SRA model to achieve more accurate results. Simulation in simple and complex cases of mechatronic systems demonstrates that the posterior of the parameter network fits the data well and the uncertainty passes effectively through our BN based SRA model by using the modified NBP.
Uncertainty quantification has always been an important topic in model reduction and simulation of complex systems.In this aspect, Global Sensitivity Analysis (GSA) methods such as Fourier Amplitude Sensitivity Test (FAST) are well recognized as effective algorithms. Recently, some data-based meta-modeller such as Random Forest (RF) also developed their own variable importance selection solutions for parameters with perturbations. This paper proposes a visual comparison of these two uncertainty quantification methods, using datasets retrieved from vibroacoustic models. Their results have a lot in common and are capable to explain many results. The remarkable agreement between methods under fundamentally different definitions can potentially improve their compatibility in various occasions.
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