An Error-Pursuing Adaptive Uncertainty Analysis Method Based on Bayesian Support Vector Regression

The Bayesian support vector regression (BSVR) metamodel is widely used in various engineering fields to analyze the uncertainty arising from uncertain parameters. However, the accuracy of the BSVR metamodel based on the traditional one-shot sampling method fails to meet the requirements of the uncertainty analysis of complex systems. To this end, an error-pursing adaptive uncertainty analysis method based on the BSVR metamodel is presented by combining a new adaptive sampling scheme. This new sampling scheme was improved by a new error-pursuing active learning function that is named, herein, adjusted mean square error (AMSE), which guides the adaptive sampling of the BSVR metamodel's design of experiments (DoE). During the sampling process, AMSE combines mean square error and leave-one-out cross-validation error to estimate the prediction error of the metamodel in the entire design space. Stepwise refinement of the metamodel was achieved by placing the sampled regions at locations with large prediction errors. Six benchmark analytical functions featuring different dimensions were used to validate the proposed method. The effectiveness of the method was then further illustrated by a more realistic application of an overhung rotor system.

Automated summary

The accuracy of the BSVR metamodel is insufficient for analyzing uncertainty in complex systems using the traditional one-shot sampling method. To address this issue, this study presents an error-pursuing adaptive uncertainty analysis method based on the BSVR metamodel, incorporating a new adaptive sampling scheme. The new sampling scheme utilizes an adjusted mean square error (AMSE) function to guide the adaptive sampling process, estimating the prediction error of the metamodel. The proposed method was validated using benchmark analytical functions and demonstrated its effectiveness in a realistic application of an overhung rotor system.