A novel dynamical response reconstruction method using spatiotemporal transformation matrix and single sensor data

Response reconstruction offers significant advantages in enhancing the quality of monitoring data and plays a crucial role in advancing structural health monitoring (SHM). However, achieving high-accuracy response reconstruction using limited sensor data remains challenging. This paper presents a novel analytical time-domain method for reconstructing structural responses using measurements from a single sensor. The approach is based on a derived spatiotemporal transformation matrix that leverages amplitude-phase decoupling of dynamic responses. It is noteworthy that the proposed method is applicable to free vibration and forced resonance scenarios, and is not suited for stochastic or non-resonant forced vibrations. Within its scope of application, this formulation enables effective and precise reconstruction of structural responses, even in the presence of closely spaced modes. Two numerical examples, including well-separated modes and closely spaced modes, are provided to illustrate the overall reconstruction procedure. The effects of sensor locations, noise levels, damping ratios, sampling rates, and sampling time are investigated in detail. Furthermore, the method is validated through an experimental study on a realistic turbine blade structure, demonstrating its effectiveness and accuracy in practical applications. Results show that the proposed method achieves relative errors below 7 % in the turbine blade case. The proposed method overcomes the obstacle of requiring numerous sensors in response reconstruction, offering a robust and efficient analytical solution without compromising reconstruction accuracy.