A quantification method for model parameter uncertainty based on an improved sequential Monte Carlo filter

Abstract

The quantification of model parameter uncertainty is of great importance for the safety of engineering structures. However, traditional particle filter methods face challenges in avoiding particle degradation and impoverishment when estimating and predicting model parameters. Thus, this paper uses three improved particle filters combined with a Gaussian mixture model to evaluate the uncertainty of the model parameters. Fatigue crack growth model is established based on the Paris equation, and the performance of the filter is validated through two numerical examples with engineering backgrounds. Numerical example 1 analyzes a pressure vessel with a central crack, comparing the performance of different filters in estimating crack length, stress intensity factor, and posterior parameter distribution. By comparing the performance of PFGM, IBIS, and SMC under 10⁷ loading cycles, it was found that SMC, compared to the other two methods, effectively reduces the estimation error of the posterior parameter distribution, with the error not exceeding 3%. Additionally, the time consumption of the resampling process was reduced by 12.7%. Numerical example 2 studied the central crack model of a Q235 steel plate, combining the K-L expansion method to quantify the material parameter random field. The results show that SMC outperforms the other filtering methods in terms of dynamic adaptability, prediction accuracy (RMSE reduced by 23.5%), and computational efficiency. In summary, SMC, through its adaptive resampling method, significantly reduces computation time and improves prediction accuracy in parameter estimation. It effectively quantifies the uncertainty of structural model parameters, enhancing the precision and stability of uncertainty assessments, thus providing a reliable tool for uncertainty quantification in large-scale structural health monitoring.