桥梁时变系统的张量子空间识别方法研究及试验验证

Tensor subspace identification method for bridge time-varying system and its test verification

针对2维矩阵子空间系统识别方法在系统识别计算效率、抗噪性与识别能力不强的问题,基于张量平行因子分解理论,引入时间维度,提出一种新的张量子空间系统识别方法以追踪非线性桥梁系统的模态参数时变规律。将时间维度引入至2维Hankel矩阵,构建Hankel时变3维张量;基于结构振动的状态空间模型,推导建立张量子空间系统识别数学模型;运用张量因子分解理论,结合稳定图方法,平行求解系统矩阵,剔除虚假模态信息。基于两座斜拉模型桥试验,通过与滑窗子空间系统识别方法对比,验证了该方法在计算效率与结果精确性上的提升,其结果表明,所提方法可用于求解确定和随机非线性时变桥梁系统识别问题。

Here,aiming at problems of lower computing efficiency,anti-noise and system identification ability of the 2D matrix subspace system identification method,based on the theory of tensor parallel factor decomposition and introducing time dimension,a new tensor subspace system identification method was proposed to track time-varying laws of modal parameters of nonlinear bridge systems.Time dimension was introduced into the 2D Hankel matrix to construct Hankel time-varying 3D tensor.Based on the state space model of structural vibration,the mathematical model for tensor subspace system identification was derived.Adopting the tensor factor decomposition theory combined with the stability graph method,the system matrix was solved in parallel and the false modal information was eliminated.Based on two cable-stayed model bridge tests,compared with the sliding window subspace system identification method,the proposed method’s improvement of calculation efficiency and result accuracy was verified.The results showed that the proposed method can be used to solve system identification problems for deterministic and random nonlinear time-varying bridges.