Bayesian-based Uncertainty Quantification Of Parameter Of Bridge

Bridge structures always have various errors and uncertainties to varying degrees.These errors may cause large deviations or unpredictability in the dynamic characteristics of the structure,thereby affecting the assessment of the reliability and safety of the entire structure.Therefore,the uncertainty quantification of bridge structure parameters is very important.Environmental vibration testing is a method of structural health monitoring that has attracted much attention.Compared with traditional vibration testing and modal parameter identification methods,it is more efficient and convenient,and it can save costs for expensive equipment and human resources.And the test process will not cause damage to the structure and will not interrupt the normal use of the structure,and at the same time it is more in line with the actual operation of the structure.However,most of the existing modal parameter identification methods based on environmental vibration testing can only identify the basic modal parameters of the structure,and cannot obtain deep-level modal parameters and their uncertainty.In order to support the maintenance management and safety decision-making of the bridge structure,how to identify the deep-level modal parameters and uncertainties of the bridge structure is an urgent problem to be solved.This thesis focuses on the identification of deep-level parameters and quantification of the uncertainty,such as the vibration mode scaling factor,mass normalized mode shape,displacement flexible matrix,and deflection of the structure under static load based on environmental vibration test.The main research content and innovations of this paper are as follows:(1)Many of the modal parameter identification methods of structures is introduced,and the fast Bayesian FFT transform is derived in detail.After that,the method originally used for acceleration data is extended to displacement and speed data,so it can be applied to advanced monitoring systems,such as the use of microwave radar and optical measurement in the calculation and analysis of structural displacement data.(2)Based on fast Bayesian method FFT transform and the mass change strategy,the theoretical formula of the uncertainty of the deep-level modal parameters was strictly deduced.It solves the problem that the vibration test method that only uses the output response can only identify the basic dynamic characteristic parameters of the engineering structure and cannot effectively support the performance evaluation of the structure.The proposed method was verified through numerical experiments.(3)Based on the dynamic equations of the vehicle-bridge coupling model,according to the knowledge of probability statistics and matrix theory,the deep-level modal parameters of the bridge structure under the time-varying system are solved.The proposed method only uses the bridge response data of the vehicle passing the bridge stage to identify the deep-level modal parameters and their uncertainties of the system.It is verified by numerical a test case.(4)Based on the synchroextracting transform and the variational Bayesian theory,the method to solve the deep-level parameters of the bridge structure and quantify the uncertainty under the moving spring mass model is deduced in detail.The proposed method uses the bridge response data when the vehicle passing the bridge stage to identify the deep-level modal parameters and their uncertainties of the system.It is verified by numerical test cases.(5)The proposed method was verified by the on-site vibration test of the Sutong Yangtze River Bridge.It not only identified the basic modal parameters(natural frequency,mode shape,etc.),but also identified the in-depth modal parameters(flexibility,deflection,etc.),the recognition result is in line with expectations,the predicted deflection is consistent with the GPS measured value,and the GPS value is within the confidence interval of the predicted deflection,which proves the effectiveness and feasibility of the proposed method.In addition to the advantages of convenient operation,high efficiency and low cost,this method uses the Bayesian method with rigorous theory and can obtain the confidence interval of displacement flexibility and predicted deflection,so it can more effectively evaluate the safety state of the structure.According to the method proposed above,the basic dynamic parameters and in-depth parameters of the structure can be identified from the data of either the environmental vibration test or the driving vibration test,and the uncertainty of the above parameters can be quantified.The results obtained can be used to support structural performance evaluation,maintenance management and decision-making.Specifically,it can be applied to many aspects such as structural finite element model optimization,structural damage state assessment,and structural reliability assessment.