Probabilistic Inverse Analysis Of The Structural States And Performance-based Assessment Based On The Deflection Of Prestressed Concrete Bridge

Deflection is not only a crucial serviceability metric of prestressed concrete(PC)bridges,but it is also a dependent variable that corresponds to multiple unobservable structural state variables.Taking full advantage of the evident information in the deflection measurements to calibrate and update the state variable provides a practical path to performance-based assessment.In this paper,the on-site deflection measurements of PC bridges are utilized to update the state variables under a probabilistic inverse analysis frame,which considers the uncertainties of the state variables and their time-dependency.The updated state variables are used in performance-based structural assessment,and the utility of test information is quantified by the value of information,based on which the optimal test scheme is proposed.The main contents of this paper are summarized as follows1.A probabilistic inverse analysis frame is established conditioned on the on-site deflection measurements of PC bridges,in which the forward physical model considered the major contributors to the deflection of PC bridge,and the frame makes use of both the prior knowledge of the forward model and the evident information to make inference of the relevant state variables.In light of the complicated forward model,as well as the non-standard posterior distributions caused by the high stochastic creep and shrinkage behavior,the Markov chain Monte Carlo(MCMC)algorithm is applied to draw samples that are used to approximate the statistics of the posterior distribution.The results of the illustrative application suggest the uncertainties associated with the state variables are reduced significantly after the inverse analysis,and the expected predicted deflection can better fit the measurements and characterize significantly lower scatterness.2.Considering the spatial-temporal uncertainties of the state variables,the creep is modeled as a stochastic process following the Karhunen-Loeve decomposition,and the structural rigidity is modeled as stochastic field.The stochastic process/fields are considered in the stochastic FEM in the computation of the long-term deflection of PC bridges using the local average method,and the spatiotemporal details of the state variables are inferred conditioned on the test information.In light of the high-dimensional posterior distribution of the state variables,the HMCMC algorithm is utilized to draw samples to approximate the statistics of the posterior distribution.The results of the inverse analysis on the case bridge suggest the time-dependency of creep development,while the updated stochastic field of structural rigidity is able to indicate the distribution of structural damage.3.Considering the stochastic time-dependency associated with the prior knowledge of state variables,a state space model is established to inference the state variables and their time-dependency,in which the state transition equation is modeled by the Wiener process.The parameter space is augmented by introducing the hyperparameters that control the time-dependencies of the state variables.Short-term variation in deflection is removed by use of wavelet analysis,while the low-pass component is used as the target information to make inference of the state variables and their time-dependency.Using the cyclic MCMC sampler,samples are alternatively drawn from the state variables and their time-dependencies by taking advantage of their conditional densities.4.Performance-based assessment is conducted based on the posterior distributions of the state variables and their time-dependencies.In light of the non-standard profiles of the failure zone in the high-dimensional parameter space,the MCMC algorithm is utilized to draw samples in the vicinity of the failure frontier,which are served as the design of experiments for the Kriging model that approximates the optimal importance sampling density.Targeting on the failure criterion defined by excessive deflection,cracking and effective structural stiffness,the time-dependent failure probabilities of each performance metric are quantified based on the posterior distribution of the state variables.5.The utility of test information on the bridge management of PC bridges is quantified based on the value of information metric.Conditional value of information of certain test data is quantified by the decision optimizations before and after the inverse analysis.The deflection development of PC bridges is modeled by a Gauss process that uses a Dirichlet basis,and value of information is calculated as the expected conditional value of information in each time step.The illustrative case study shows that properly increase the test interval can enhance the value of test information.While smaller standard deviation in the likelihood function leads to higher value of information,excessively low standard deviation can underestimate the uncertainties of the state variables and overestimate the value of information.