基于copula的多参数结构有限元模型修正方法研究

当前结构健康监测技术研究当中，多参数识别问题一直是相当棘手的难题。多年来在模型修正方向上虽有着诸多突破，但一直受困于结构系统的复杂性或高不确定性,未对多参数模型修正方法取得突破性进展。特别是对于非线性相关的结构参数，其修正问题尤难解决。基于最近在copula联合分布模型精准性上的突破，本申请提出运用以copula为基础的多参数结构模型修正方法，着重阐明如何利用copula模型描述结构模型内多参数间的不确定性和相关性，以更高的精准性来修正结构有限元模型。通过理论推导以及试验验证来归纳多参数模型修正的处理方法、方案、准则。在此基础上，详细研究多参数修正方法中的结构模型参数过滤理论， copula模型的优化设置以及不确定性量化指标。结合典型的建筑结构模型，为结构健康监测中在处理多参数修正的问题上提供切实可行并且行之有效的理论依据。

In the development of structural health monitoring techniques, the model updating for multivariate parameters is still a difficult task. Although there are quite a number of studies contributed to this area, breakthrough works are quite limited because of the structural complexity and high uncertainty. Especially for nonlinear structural parameters, the model updating procedures are extremely difficult. The recent development of copula theory shows a possible solution to solve this problem. Therefore, this project aims to improve the traditional multivariate model parameter updating methodology by utilizing the copula theory. The project will focus on how to use copula model in modelling the uncertainties and dependences for improving the updating of finite element structural model. Through the theoretical development and experiment validation, this study will conclude the detailed methodology, principals and guidelines for copula based multivariate model updating. The investigation will be concentrated on three aspects, namely, parameter filtering, copula characterization and uncertainty quantification. By combining the research development with real practices, this project will provide a detailed engineering based rule which could offer instructive information for the structural health monitoring.