Flutter Derivatives Identification And Uncertainty Quantification For Bridge Decks

With the increasing of bridge span,the problems of wind-induced vibration of long-span bridges have become more and more serious.Flutter is a kind of divergent vibration that may lead to the collapse of the bridge.Flutter derivatives are important parameters to characterize the aerodynamic self-excited force of bridges,and the precise identification of flutter derivatives is the prerequisite for flutter analysis.Due to various uncertainties in engineering,it is necessary to quantify the uncertainties of flutter identification.This thesis mainly consists of four parts.Firstly,a swarm intelligence algorithm termed as Artificial Bee Colony algorithm is used to optimize the least square objective function of the free vibration signal of the two-degree-of-freedom sectional model including vertical and torsional motions,so as to identify flutter derivatives.The swarm intelligence optimization algorithm is used to directly search for the optimal parameters of the objective function to avoid the influence of initial values on the identification results,which is also the basis of the optimization solution of the objective functions in the follow-up research.Secondly,in order to quantify the uncertainties of the flutter derivatives with the traditional methods,a large number of time-consuming and labor-intensive repetitive wind tunnel tests are required.This thesis proposes to use Bootstrap resampling technique to generate a large number of samples from a small number of samples,and then identify the flutter derivatives accordingly,so as to obtain the statistical characteristics of the flutter derivatives in the sense of the frequency school in statistics(such as mean value and variance).On the other hand,in view of the general practice of preset weights related to vertical bending and torsional motion in the objective function based on experience,this thesis proposes to obtain the optimal solution of weights through iteration.In order to improve the accuracy and speed of parameter optimization for a large number of samples,the standard Artificial Bee Colony algorithm is improved in this thesis,and it is combined with the Powell local optimization algorithm,and an improved algorithm termed as MABC-Powell is proposed.Thirdly,based on Bayesian inference,the deterministic model is embedded into the probabilistic model by considering the model error and measurement error to obtain the Bayesian posterior probability distribution of flutter derivatives.Based on the Laplacian Gaussian approximation principle and the MABC-Powell optimization algorithm proposed above,the optimal value of flutter derivatives in the sense of maximum posterior probability is obtained,and its covariance matrix is also obtained to quantitatively describe the uncertainties of the identification results.Compared with the methods based on the frequency school,the Bayesian method can give the uncertainties of the identification results when there is only one set of data.Fourthly,aiming at solving the problem that the likelihood function is difficult to construct and the posterior distribution is difficult to solve in classical Bayesian inference,a flutter derivatives identification method based on Approximate Bayesian Computation theory is proposed.The subset simulation technique is used to sample the posterior probability distribution of flutter derivatives.The optimal value and statistical characteristics of flutter derivatives in the sense of maximum posterior probability can be obtained,and the uncertainties of flutter derivatives can be quantified.For the above four methods,an ideal plate numerical model and a real bridge sectional model are used to verify the effectiveness of each method.The contribution of this thesis lies in three fronts: a swarm intelligence algorithm termed as Artificial Bee Colony is applied to the identification of flutter derivatives to avoid the influence of initial value problems;the Bootstrap method is used to extract a large number of samples from a small number of samples,and the improved Artificial Bee Colony algorithm is used to solve the problem,then the uncertainties in the sense of frequency is obtained;Bayesian method and Approximate Bayesian Computation are used to identify flutter derivatives and quantify their uncertainties.The study on the uncertainties of flutter derivatives in this thesis can be further applied to the reliability-based aerodynamic shape optimization,flutter reliability analysis and probabilistic flutter control design,which is valuable in theory and engineering applications.