A dynamic stiffness-based framework for harmonic input estimation and response reconstruction considering damage

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.