Inverse Analysis of Structure by Filter Theory of Stochastic Dynamic System

1.从计算力学的角度出发，提出了求解各种结构反问题的新方法。这些程序是将求解数值连续场的有限元法或边界元法与估计未知状态向量的基于维纳滤波或投影滤波的滤波算法相结合。特别是对于复杂的反问题，提出了两步求解的方法，具有较高的效率。执行第一步分析以猜测关于未知数的一些先验信息，随后使用获得的先验信息执行第二步分析以识别未知数。在各种反问题中的应用通过对以下问题的数值模拟，证明了该方法的适用性和有效性。(1)材料常数空间分布的不确定利用边界上测量的位移分量，求解过程可用于弹性体中弹性常数（杨氏模量和泊松比）空间分布的识别分析。(2)缺陷识别本程序可用于弹性场或热场中未知缺陷的识别。特别地，利用在多个边界点测量的瞬态温度作为附加信息，对二维物体中的圆形缺陷进行了数值模拟。采用有效的两步求解方法，可以从测量的位移分量中识别弹性体中未知的复数缺陷。(3)损伤检测本程序适用于结构损伤检测问题。单元连接浮式结构的损伤位置和损伤刚度可以用结构的固有频率来表示。

1.Novel Solution Procedure for Inverse ProblemsFrom view-point of computational mechanics, noval solution procedures to solve various inverse problems in structure are proposed. These procedures are a combination of the finite element method or the boundary element method to solve numerically continuous fild and the filtering algorithms based on the Wiener filter or the projection filter to estimate the unknown state vector.Especially, for complicated inverse problems, two step solution procedure to be expected more efficiency is also proposed. The first step analysis is performed to guess some apriori information on the unknowns and the second analysis to identify the unknowns is subsequently performed with use of the obtained apriori information.2.Application to Various Inverse ProbelmsApplicability and effectiveness of the procedures are demonstrated with numerical simulations on the following problems.(1)Indetification of Spatial Distribution of Material ConstantsThe solution procedure can be applied to identification analysis of spatial distribution of elastic constants (Young's modulus and Poisson's ratio) in elastic body with use of displacement components measured on the boundary.(2)Defect(s) IdentificationThe procedure can be applied to identification of unknown defect in elastic field or in thermal field. Especially, numerical simulation is carried out for identification of a circular defect in a two dimensional body by using transient temparature measured at several boundary points as additional information. The unknown plural defects in elastic body can be identification from the measured displacement components by using effectively two step solution procedure.(3)Damage DetectionThe procedure is applied to a structural damage detection problems. Both location and stiffness on damage in the unit-linked floating structure can be defected with natural frequencies of structure.