In structural health monitoring (SHM), the measurement is point-wise but structures are continuous. Thus, input estimation has become a hot research subject with which the full-field structural response can be calculated with a finite element model (FEM). This paper proposes a framework based on the dynamic stiffness theory, to estimate harmonic input, reconstruct responses, and to localize damages from seriously deficient measurements. To begin, Fourier transform converts the dynamic equilibrium equation to an equivalent static one in the frequency domain, which is under-determined since the dimension of measurement vector is far less than the FEM-node number. The principal component analysis has been adopted to “compress” the under-determined equation, and formed an over-determined equation to estimate the unknown input. Then, inverse Fourier transform converts the estimated input in the frequency domain to the time domain. Applying this to the FEM can reconstruct the target responses. If a structure is damaged, the estimated nodal force can localize the damage. To improve the damage-detection accuracy, a multi-measurement-based indicator has been proposed. Numerical simulations have validated that the proposed framework can capably estimate input and reconstruct multi-types of full-field responses, and the damage indicator can localize minor damages even with the existence of noise.

在结构健康监测 (SHM) 中，测量是逐点的，但结构是连续的。因此，输入估计已成为一个热点研究课题，利用有限元模型（FEM）可以计算全场结构响应。本文提出了一个基于动态刚度理论的框架，用于估计谐波输入、重建响应并定位严重缺陷测量造成的损害。首先，傅里叶变换将动态平衡方程转换为频域中的等效静态方程，由于测量矢量的维数远小于 FEM 节点数，因此该方程是欠定的。采用主成分分析对欠定方程进行“压缩”，形成超定方程来估计未知输入。然后，傅里叶逆变换将频域中的估计输入转换为时域。将此应用于 FEM 可以重建目标响应。如果结构损坏，估计的节点力可以定位损坏。为了提高损伤检测的准确性，提出了一种基于多测量的指标。数值模拟验证了所提出的框架可以有效地估计输入并重建多种类型的全场响应，并且即使存在噪声，损伤指示器也可以定位轻微损伤。提出了一个基于多测量的指标。数值模拟验证了所提出的框架可以有效地估计输入并重建多种类型的全场响应，并且即使存在噪声，损伤指示器也可以定位轻微损伤。提出了一个基于多测量的指标。数值模拟验证了所提出的框架可以有效地估计输入并重建多种类型的全场响应，并且即使存在噪声，损伤指示器也可以定位轻微损伤。