Structural identification and model updating based on active learning Kriging approach and Bayesian inference

Abstract

Structural health monitoring has been adopted for the structural assessment and maintenance of major bridge crossings over the past few decades. Various techniques are proposed to analyse and interpret the measured data, e.g. modal parameter identification and finite element model updating. Model updating is an essential step to calibrates the numerical models for response simulation, reliability analysis and damage assessment. The intensive computations can be alleviated by surrogate models, e.g. the Kriging approach. However, the performance of Kriging predictors depends on the number of samples obtained from the finite element analysis. Moreover, the uncertainties in measurement, surrogate modelling and numerical simulation should also be considered quantitatively. To overcome these difficulties, a novel active learning Kriging model updating framework is proposed such that those regions which might help improve the current Kriging predictor for model updating are refined and explored automatically. The Kriging model generated by this data-driven process with a limited sample size has satisfactory local accuracy, high efficiency and robust performance for model updating. A new learning function, i.e. the HP function, is derived using Bayesian inference and information entropy to select candidate samples by evaluating their potential contributions and uncertainties. The proposed framework is verified experimentally by a two-span continuous test beam and further applied to the model updating of Ting Kau Bridge, a cable-stayed bridge in Hong Kong. The Bayesian framework comprising modal identification and model updating can effectively estimate the structural parameters and quantify their uncertainties. The integration of the active learning Kriging approach and Bayesian framework is therefore investigated in the present study. The integrated framework comprises three major components: the fast Bayesian spectral density approach for modal identification, the active learning Kriging method for meta-modelling, and the Bayesian model updating. The uncertainties in measurements, Kriging regression and finite element simulation are considered quantitatively in building up the likelihood function adopted in the active learning and model updating. The integrated framework is validated by a two-span continuous test beam and applied to Jiu Zhou Bridge, a cable-stayed bridge in the Hong Kong-Zhuhai-Macao Bridge project, using the monitoring data. The results prove that the active learning method significantly reduces the uncertainties of the Kriging predictor with fewer samples compared with the ordinary Kriging approach. Apart from the common time-independent assumption in model updating, the implementation of the active learning Kriging algorithm in time-varying structural identification has been explored as well. Cable force monitoring is studied as an important task in the maintenance of cable-supported bridges. An online cable force monitoring system based on the active learning Kriging time-frequency ridge extraction algorithm and data fusion technique is established. The real-time cable forces under complex non-stationary excitations can be identified with efficient and robust performance. The active learning algorithm can extract the instantaneous frequencies by using a modified S-transform, and the potential outliers are detected by data fusion. The proposed algorithm and system are verified by numerical studies and test cases using the field data from Jiu Zhou Bridge in the regular operation and Super Typhoon Mangkhut scenarios.