基于数据融合的系列卡尔曼滤波新方法及结构动位移实时估计和多尺度识别结构局部损伤

After in-depth analyses of some conventional Kalman filter methods and the latest improved approaches, this proposed project aims at solving the existing problems in related approaches and providing the key methodologies for the real-time estimation of dynamic displacement from measured acceleration/velocity, structural local damage identification, especially local damage in nonlinear structural damage identification, and structural damage probability analysis. Some novel methods including Kalman filter with unknown inputs (KF-UI), extended Kalman filter with unknown inputs (EKF-UI), unscented Kalman filter with unknown inputs (UKF-UI), interval Kalman filter with unknown inputs (IKF-UI), and interval extended Kalman filter with unknown inputs (IEKF-UI) are proposed and combined with the studies on (1) real-time estimation of dynamic displacement by data fusing and multi-rate Kalman filter, in which bias in accelerations/velocities are treated as “unknown inputs”; (2) multi-scale detection of structural local damage, in which the inter-actions between the target substructure and the other part of a whole structure are treated as “unknown inputs” and structural local damage detection in the linear/nonlinear substructure is conducted with refine structural model; (3) interval analysis of structural state and dynamics parameters and probability analysis of structural damage under “unknown inputs” etc. Based on the conventional and latest improved methods, a series of novel methodologies are developed step by step, followed by numerical and experimental validations. The new methods established in the proposed project are expected to theoretically overcome the defects in previous works and provides novel methodologies and theoretical foundation for data analysis, structural identification and damage detection I structural health monitoring.

本项目在深入分析现有几种卡尔曼滤波及最新改进方法基础上，针对方法的不足，以及以加速度/速度数据实时估计位移，结构局部损伤尤其是非线性结构损伤识别及概率分析所需的关键方法，建立基于数据融合的未知输入下的卡尔曼滤波、扩展卡尔曼滤波、无迹卡尔曼滤波、区间卡尔曼滤波、区间扩展卡尔曼滤波新方法，并结合于：1）多速率数据融合实时识别结构动位移，将传感偏差作为“未知输入”；2）多尺度识别多传感进行局部损伤，将含局部损伤的子结构从整体中分离，其他部分结构的作用为“未知输入”，对线性尤其是非线性子结构局部损伤进行识别；3）考虑“未知输入”及不确定因素的区间，识别结构状态区间及局部损伤概率分析等研究。研究以已有方法为基础，逐步深入且互相关联，采用理论方法推导、数值及试验验证，从机理上解决已有卡尔曼滤波及改进方法的问题。提出的系列方法，有显著的创新与应用前景，为监测数据分析、结构状态与损伤识别等奠定理论基础。

本项目研究以传统卡尔曼滤波方法及理论推导为基础，针对传统卡尔曼滤波方法的不足，及已有相关改进方法的机理问题，通过方法的创新，由简入繁，提出了基于数据融合的系列卡尔曼滤波创新方法，包括：1）基于观测数据融合的未知输入下卡尔曼滤波（KF-UI）方法，广义未知输入下卡尔曼滤波（GKF-UI）方法，实时识别结构与未知输入；2）基于观测数据融合的未知输入扩展卡尔曼滤波（EKF-UI）方法，广义未知输入下扩展卡尔曼滤波（GKF-UI）方法，同时实时对线性结构状态、参数与未知输入进行识别；3）基于观测数据融合的未知输入无迹卡尔曼滤波（UKF-UI）方法，同时实时对强非线性结构状态、参数与未知输入进行识别；4）未知输入下区间卡尔曼滤波（IKF-UI）与区间扩展卡尔曼滤波（IEKF-UI）方法；5）基于GEKF-UI的线性结构以及非线性结构及未知地震作用的识别；6）基于GEKF-UI同时识别质量未知的链状系统结构和未知地震激励的方法；7）考虑大型结构其他部分对目标子结构作用，对子结构损伤进行识别的方法。项目研究成果不仅在理论上具有学术创新，而且具有实际应用价值与前景。..项目研究取得了较多成果，已在国内外学术杂志和学术会议文集上发表论文20篇，其中在SCI收录的国际学术期刊论文10篇；国际/国内学术会议论文9篇，另有2篇论文已分别为SCI收录的国际期刊和EI收录的国内期刊录用待发表，超出了申报书预期发表论文的数量。