多源不确定性环境下动载荷识别的非侵入型非概率方法

Multi-source uncertainties are objectively ubiquitous and have significant influences on the identification of dynamic loads due to difficulties in the full control of dynamic characteristics of engineering structures and incomplete measurements of response signals. It is, therefore, necessary to develop methods for the quantification of uncertainty effects on the dynamic loads. In the case of uncertainties with small samples, there are obstacles for current researches including uncertainty modeling (few available models), transformation modes of the dynamic load identification problem with uncertainties (the portability of classical methods for the dynamic load identification to those involved with uncertainties), the accuracy and efficiency of the inverse calculation (especially for the nonlinear mappings under 'big' uncertainty inputs). Based on the classical methods for the dynamic load identification, nonintrusive non-probabilistic ones under uncertainties with small samples are developed in this project, where the non-probabilistic set theory, non-stochastic process theory, and hybrid-uncertainty modeling are adopted. It is worth mentioning that the focus of this research is the nonintrusive propagation of multi-source uncertainties rather than classical dynamic load identification methods. Main contents are as follows: nonintrusive transformation modes for the dynamic load identification with time-invariant uncertainties based on the novel non-probabilistic set and hybrid-uncertainty analysis methods; development of fuzzy process model based on the convex-model process and interval process; methods for the quantification of influences of time-varying uncertainties on the reconstruction of dynamic loads based on non-stochastic process models; numerical validation of key methods. This project will enrich the research of uncertain inverse problem in mechanics and serve the theoretical support for the refined management of structural systems.

由于结构动态特性难以实现完全控制及响应数据难以实现完备测量，多源不确定性在动载荷识别中广泛存在且影响显著，亟需发展动载荷不确定性效应的定量化方法。在不确定性信息为小样本条件下，目前研究面临在不确定性建模（单一）、确定性转化模式（动载荷识别可移植性）、反求精度与效率（非线性映射关系下大不确定性输入）等方面的困难。本项目以非概率集合理论、非随机过程理论及混合不确定性建模为工具，以多源不确定性非侵入型传播分析为重点，以经典动载荷识别为基础，发展小样本不确定性环境下动载荷识别的非侵入型非概率方法。研究内容包括：建立非概率与混合不确定性分析新方法，提出时不变不确定性环境下动载荷识别的非侵入型确定性转化模式；基于凸模型过程与区间过程理论发展模糊过程建模方法，建立时变不确定性对动载荷识别影响规律的定量化分析方法；完成关键方法的数值验证。本项目将深化不确定性力学反问题研究，为结构精细化管理提供理论基础。

动载荷是结构全生命周期管理的必要前提，间接识别有效克服了因技术、经济等因素限制而难以甚至不可能直接测量的困难。从数学原理看，不适定性是动载荷识别问题的本质属性；从客观现实看，不确定性是结构与测量的本质属性。因此，动载荷识别综合表现为不适定性与不确定性的耦合分析过程。为保证经典动载荷识别方法的可移植性，以非侵入型不确定性分析实现解耦是可行途径。本项目聚焦贫信息集值参数条件下动载荷识别问题，完成了非概率凸集与混合不确定性传播分析研究、动载荷识别非侵入型确定性转化模式研究、时变不确定性对动载荷识别影响规律研究。构建了一类适用于不同样本容量共存条件下的非侵入型不确定性传播分析方法，实现了大不确定性在强非线性映射中的高精度传播；建立了一种正则化框架下动载荷分散性评估方法，实现了低频集中动载荷的非侵入正则化反演；提出了一种具有时变可拓展性的基于“欲取先予”理念的顺序双阶段方法，实现了反问题的正向求解；修正了区间摄动方法，为现有侵入型识别提供了方法支持。本项目研究提供了一类多源不确定性环境下高精度动载荷识别方法，定量揭示了多源不确定性对动载荷识别的影响规律，进一步深化了不确定性力学反问题研究，为结构精细化管理提供了理论和方法基础，可应用于地面车辆、航空航天、海洋平台等领域的安全性设计、优化与控制。在执行周期内，项目团队已发表学术论文6篇（其中SCI收录中科院TOP期刊4篇）、申请发明专利5项（其中授权2项），团队成员3人晋升高级职称，培养本科生3人。基于已有研究成果，本项目后续拟在区间过程分析、面向大型变结构空间航天器的冲击载荷环境预示、结构健康监测与弹性波反演方向开展持续性研究。