Kalman Filter Nonlinear Identification

Application of Kalman Filter Nonlinear Identification in Civil Engineering Health Monitoring

As a classic state estimation algorithm, the Kalman filter plays a vital role in structural health monitoring for engineering applications. While traditional Kalman filters are designed for linear systems, actual engineering structures often exhibit nonlinear behaviors such as stiffness degradation caused by seismic actions, material deterioration, or local damage. Therefore, the identification capability of nonlinear Kalman filters has become one of the key technologies in structural health monitoring.

In civil engineering, nonlinear Kalman filters are primarily used for structural damage identification. By collecting real-time vibration response data (e.g., acceleration, displacement) and integrating them with nonlinear dynamic system models, Kalman filters can iteratively correct state estimation errors to identify parameter variations in structures. For example, when cracks develop in bridges or buildings, or connections become loose, stiffness or damping characteristics change. The nonlinear Kalman filter can detect these changes by comparing observed data with model predictions, locating damage positions and quantifying damage severity.

Common variants of nonlinear Kalman filters include the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). The EKF handles nonlinearity through local linearization, offering higher computational efficiency but potentially reduced accuracy for strongly nonlinear systems. The UKF uses unscented transformation, making it more suitable for highly nonlinear systems though computationally more intensive. In practice, algorithm selection depends on structural characteristics and monitoring requirements.

The advantage of nonlinear Kalman filters lies in their ability to handle time-varying systems under noise interference while enabling real-time monitoring. However, their performance heavily relies on model accuracy - significant initial model deviations may lead to false identification. Therefore, combining machine learning or data-driven methods to optimize model parameters represents a key research focus.