A Modal Superposition Based Method for Real-Time Structural Displacement and Force Reconstruction Using Sparse Sensor Data

Reliable estimation of full-field structural displacements and internal forces from limited sensor data remains a key challenge in Structural Health Monitoring (SHM), particularly during strong dynamic events. This study proposes the Modal Structural Stress Mapping (MSSM) method, a real-time reconstruction technique for structural displacements and internal forces using sparse sensor measurements and modal superposition. Unlike traditional SHM approaches that detect damage through modal parameter shifts, MSSM provides direct physical response estimations that can support rapid damage localization and performance evaluation. The method has been implemented in a structural analysis software platform, integrated with an IoT-based SHM workflow, and validated through both numerical simulations and the instrumented Van Nuys hotel testbed. The results demonstrate that MSSM can reconstruct structural response with high accuracy, showing displacement errors below 0.12% compared to full time history analyses. The method extends beyond seismic applications and is suitable for various structural typologies, including fatigue assessment under wind and vehicular loads. It provides a robust framework for evaluating long-term structural integrity and identifying potential damage in both structural and non-structural elements based on observed deformation patterns.