AI Method Tracks Hidden Forces in Real Time

Monitoring the health of large structures like bridges and buildings typically requires extensive sensor networks to track both external forces and internal responses—an expensive and often impractical approach. Researchers at Columbia University have developed a computational method that can identify unknown forces acting on a system while simultaneously estimating its properties and dynamic states using only output measurements from sensors. This joint input-parameter-state unscented Kalman filter (IPS-UKF) provides real-time monitoring capabilities that could make structural health assessment more accessible and reliable.

The key finding is that this method successfully estimates three critical elements simultaneously: the system's unknown external inputs (like wind or traffic loads), its parameters (such as stiffness and damping), and its dynamic states (displacement, velocity, and acceleration). This is achieved through a two-stage process within each time step: first predicting the input, then correcting it to provide the final estimation. The approach was validated on both linear and nonlinear multi-degree-of-freedom systems, demonstrating accurate tracking even when inputs were unknown beforehand.

Methodologically, the researchers built upon the standard unscented Kalman filter framework but modified it to handle joint estimation without requiring Jacobian derivatives, least squares introductions, or non-physical propagation processes. The algorithm operates in discrete time steps, using sigma points to capture the mean and covariance of the state distribution through nonlinear transformations. For a 3-degree-of-freedom linear system excited by a 100N pulse lasting 0.01 seconds, the method successfully identified all parameters and the unknown input force using displacement, velocity, and acceleration measurements contaminated with 5% Gaussian white noise.

Results analysis shows the method's robust performance across different scenarios. In the linear 3-DOF system, the estimated responses, stiffness parameters, damping parameters, and input forces closely matched the true values, with satisfactory convergence observed within the 30-second simulation period. For the nonlinear 2-DOF Duffing system with cubic stiffness terms, the algorithm similarly achieved accurate estimation of all unknown quantities. The researchers also investigated measurement requirements, finding that displacement and velocity measurements provided adequate results, while acceleration-only measurements led to unreliable estimates with continuous drift in input and response tracking.

The real-world implications are significant for structural health monitoring of civil infrastructure. This approach allows engineers to extract maximum information from limited sensor networks, potentially reducing instrumentation costs while improving damage detection and prognosis capabilities. By identifying unknown inputs in real-time, the method could help monitor structures under unpredictable loading conditions like earthquakes or severe weather without requiring direct measurement of those forces.

Limitations noted in the paper include the identifiability challenge for single-degree-of-freedom systems, where even with flawless knowledge of mass, the system remains unidentifiable in the time domain due to equivalent erroneous input combinations. Additionally, the method's performance depends on proper calibration of covariance matrices, though this aspect was outside the scope of the current work. The acceleration-only case proved particularly challenging, with results varying significantly between runs and often diverging from true values.