Uncertainty Quantification Of Dynamic Characteristics Of Bridge Structures Based On Polynomial Chaos Expansion

The traditional dynamic analyses of bridge structures often ignore the parameter uncertainty.However,the uncertainty inevitably exists in the parameters of actual bridge structures.The parameter uncertainty will inevitably lead to the structural dynamic characteristics uncertainty.In order to well characterize dynamic characteristics of the true bridge structures,it is very necessary to quantify the uncertainty of the dynamic characteristics propagated from the parameter uncertainty.Statistical moments(such as mean and variance)and probability density function(PDF)are important quantities that characterize the uncertainty of structural dynamic properties.Statistical moments reflect the statistical properties of structural dynamic properties,and the PDF comprehensively characterizes the distribution of structural dynamic properties.In this paper,the polynomial chaos expansion(PCE)method is used to efficiently calculate the statistical moments of structural dynamic characteristics,and then the analytical expression of the probability density function(PDF)of structural dynamic characteristics can be derived by the maximum entropy principle and the obtained statistical moments.The main contributions of this paper are summarized as follows:(1)The importance of uncertainty quantification(UQ)of dynamic characteristics of bridge structures is introduced briefly,and the sources of uncertainties in the actual bridge structures are comprehensively discussed.This paper reviews UQ methods in uncertainty in structural dynamics,such as Monte Carlo simulation(MCS)method,stochastic finite element perturbation method,interval analysis method,orthogonal polynomial method.And their advantages and disadvantages are discussed.(2)According to the PCE theory,the orthogonal polynomials related to the random variables with arbitrary probability distributions are derived.Then,the multivariate orthogonal polynomials,which are formulated by the orthogonal polynomials,are used to obtain the PCE.By combining the statistical moments of random variables and PCE coefficients,the high-order statistical moments of structural dynamic characteristics can be efficiently calculated.Thus,the high-dimensional complex integrals associated with the calculation of high-order statistical moment becomes easy.A flat aluminum plate is used for demonstration of the PCE method.Results of the PCE method are compared with the MCS method.The comparison results show the accuracy of the PCE method.(3)In order to well characterize the uncertainty of structural dynamic characteristics,the PDF of structure dynamic characteristics is needed.Herein,the maximum entropy principle(MEP)is proposed to infer the PDF.Specifically,based on the statistical moment information of the structural dynamic characteristics obtained by the polynomial chaotic expansion method,then the MEP is used to infer the analytical expression of the PDF of the structural dynamic characteristics,and the PDF is able to provide sufficient information about the uncertainty of dynamic characteristics.A steel truss bridge is used to verify the PCE-MEP method for estimating the PDF.Likewise,the MCS is adopted to verify the effectiveness of the PCE-MEP method.(4)Finally,the PCE method proposed in this paper is applied for UQ of an actual pedestrian bridge,that is,quantification of uncertainty in dynamic characteristics resulting from parameter uncertainty.In addition,the influence of coefficient of variation of parameters on the statistical moment and probability density function of structural dynamic characteristics is fully investigated.