Multi-amplitude Nonlinear Fatigue Reliability Evaluation Of Stayed Cable Based On Probability Density Evolution Method

The stayed cable is the main load-bearing component of the cable-stayed bridge and transfers the bridge deck load to the pylon.Under the action of wind,rain and vehicles,corrosion and fatigue are the main causes of the stayed cable damage.At present,the detection,monitoring and evaluation techniques of cable corrosion have been developed rapidly and applied in engineering.However,due to the limitation of analysis method,linear or linear equivalent methods are mainly used to evaluate cable fatigue damage.This analysis method ignores the nonlinear fatigue loads such as amplitude variation load sequence effect and load interaction effect,which makes it difficult for the accuracy of cable fatigue state assessment to meet the engineering requirements.Therefore,the regular cable replacement method is adopted to avoid sudden fatigue brittle failure.In recent years,the development of bridge health monitoring technology provides a new way to consider the non-linear fatigue evaluation of stayed cables under variable amplitude load.Therefore,based on the essential characteristics of non-linear fatigue damage of stayed cables,this paper studies the multi-amplitude nonlinear fatigue reliability evaluation method of stayed cables based on probability density evolution method.It provides new technical support for accelerating the fundamental transformation from preventive cable replacement to predictive cable replacement.The main research contents and results of this paper are as follows:(1)The accuracy of generalized density evolution equation(GDEE)is affected by initial condition discretization,a normalized initial condition discretization method is proposed.The initial condition should be discretized before solving GDEE with total variable reduction difference method.The commonly used impulse function discretization method only discretize the initial value in a very narrow area,which affects the accuracy of reliability solution.The Dirac function is discretized by using normal distribution to make the initial condition more smoothly discretized to the spatial coordinates.The KL divergence and gradient descent are used to optimize the parameter σ,and the obtained probability density function curve is more consistent with the actual situation.(2)To analyze the amplitude variation load of stay cables,it is necessary to generate high-dimensional point set.Therefore,the generating high-dimensional random variable point set method is proposed.This paper analyzes the mechanism of the point selection method of number theory to get the coordinates of point set from generating vector.The power function calculation of generated vector is converted to the linear function product calculation.The new method is proposed to generate high dimensional point set by linear recursion,which greatly reduces the calculation time and breaks through the limitation of dimension of point set.Based on the principle of minimum star discrepancy,the selection method of generating vector element root is analyzed.A fast optimization algorithm for element roots in odd-even partition is proposed.The total number of point sets and the corresponding optimal element roots of random variables up to 600 dimensions are given to simplify the selection process of element roots.Numerical results show that the efficiency of GDEE solution can be increased 2-3 times by the proposed method.(3)The sieving point radius of hypersphere sieving point method is affected by subjective experience,the equal volume hypersphere sieving method is proposed to obtain effective representative points.The hypercube space of random variables is transformed into an equal volume hypersphere.The radius of hypersphere is obtained by inverse calculation of volume equivalence,and the effective representative points are sieved by equal volume hypersphere to obtain enough representative points.The influence of hypersphere radius on the uniformity of effective representative points is studied.The equivalent hypersphere radius is optimized based on the minimum star dicrepancy principle to avoid the influence of subjective factors on the determination of sieving point radius.Numerical examples show that the proposed method can effectively improve the computational accuracy and efficiency of the probability density evolution method.(4)A nonlinear fatigue reliability analysis method based on modified Manson-Halford(M-H)model is proposed to solve the problem that the calculation accuracy of fatigue reliability of stay cables is insufficient due to ignoring the load history effect.The M-H damage curve model is constructed.A modified M-H model is proposed by multiplying the stress amplitude ratio and life ratio index as the characteristic index.The fatigue state equation is established based on the modified M-H model.The nonlinear fatigue reliability analysis method is proposed based on the probability density evolution method.The calculation results show that the proposed modified M-H model and the reliability analysis method can accurately consider the influence of multi-amplitude loads on stayed cable.(5)Based on the monitoring system of Yangtze River Bridge,the proposed nonlinear fatigue reliability analysis method is verified.According to the vehicle load monitoring data obtained from dynamic weighing system,random traffic flow is generated by cellular automata model,and the cable stress time history data is calculated by combining with the cable axial force impact surface.The rain-flow counting method is used to extract the fatigue load effect of the cable.The fatigue reliability of typical stayed cables is analyzed.The application of real bridge shows that long cables are more prone to fatigue failure during service time.The proposed method can successfully realize the fatigue assessment of stay cables.