【作者】 吴志峰； 黄斌； 薛凯仪；

【Author】 Wu Zhifeng;Huang Bin;Xue Kaiyi;Huazhong University of Science and Technology;Wuhan University of Technology;

【机构】 华中科技大学土木与水利工程学院； 武汉理工大学土木工程与建筑学院；

【摘要】 基于同伦的概念,提出了一种新的静力随机有限元模型修正方法。将结构参数和测量误差假定为有界分布的随机变量,用单元修正因子表示单元刚度的改变量,建立了关于单元修正因子的随机模型修正方程。构造了随机模型修正方程的同伦形变方程,并求解得到了随机修正因子的同伦级数解。静力凝聚方法和正则化方法分别用来解决有限测量节点及随机模型修正方程不适定性的问题。最后,将得到的随机修正因子回代到结构的静力平衡方程中得到修正后结构的静力响应,以验证随机模型修正的效果。框架结构的数值算例结果表明,当测量误差的变异性增大时,所提出的方法比低阶摄动方法的修正精度更高。混凝土连续梁的试验结果表明,相比基于延缓拒绝自适应抽样的贝叶斯模型修正方法和快速贝叶斯模型修正方法,该方法在修正结果精度相当的情况下计算量更小。更多还原

【Abstract】 Based on the concept of the homotopy,a new static stochastic finite element model updating method is proposed.The structural parameters and the measurement errors are assumed to be random variables subjected to the bounded distributions,and the element update factor is used to represent the variation of the element stiffness.Then the stochastic model updating equations for element update factors are set up.To obtain the homotopy series solutions of stochastic model updating factors,the homotopy deformation equations corresponding to the stochastic model updating equations are established.The static condensation technique and the regularization method are used to solve the problem of the limited measurement points and the ill-posed problem of the stochastic model updating equations respectively.Finally,the structural static responses are obtained by substituting the stochastic updating factors into the static equilibrium equations.The numerical results of the frame structure show that different from the low-order perturbation method,this new method can produce better accuracy in cases with large stochastic measurement errors.The tested results of the concrete continuous beam show that compared with the Bayesian method with the Delayed Rejection Adaptive Metropolis sampling technique and even a fast Bayesian method,the proposed method utilizes much less computational time and provides an equivalent accuracy.更多还原