Kalman Filtering and Grey Theory for Deformation Monitoring Prediction and Forecasting

Application of Kalman Filtering and Grey Theory in Predictive Forecasting for Deformation Monitoring

In engineering fields, deformation monitoring is crucial for ensuring structural safety. Traditional monitoring methods often rely on extensive historical data, while the combination of Kalman filtering and Grey theory offers a more efficient predictive forecasting solution.

The advantage of Kalman filtering lies in its ability to process noisy observation data in real-time through recursive algorithms that continuously update state estimates. This characteristic makes it particularly suitable for dynamic deformation monitoring systems, especially when data contains uncertainties. Kalman filtering effectively reduces error interference through its prediction-correction cycle, typically implemented using state-space models and covariance matrices to optimize estimations.

Grey theory excels at handling "small sample, poor information" problems by generating accumulated sequences to reveal inherent data patterns. When deformation monitoring data is limited or partially missing, Grey models (such as GM(1,1)) can establish effective prediction models. The implementation involves data preprocessing through accumulating generation operations (AGO) to strengthen regularity, followed by solving differential equations to obtain prediction parameters.

The integration of both methods typically adopts series or parallel configurations: Grey models first provide preliminary trend predictions, which are then optimized and corrected by Kalman filtering. This hybrid model leverages Grey theory's trend-capturing capability while utilizing Kalman filtering to suppress noise interference, significantly improving long-term prediction stability. In code implementation, this often involves creating an interface where GM(1,1) output serves as the measurement input for the Kalman filter's update step.

In practical applications, this technology has been successfully used for deformation warning systems in bridges, dams, and other engineering projects. By real-time assimilation of monitoring data, the system can predict potential risk points hours or even days in advance, providing valuable time for maintenance decisions. With the development of edge computing, this algorithm is expected to be further embedded in intelligent monitoring terminals, enabling more agile response mechanisms through optimized computational efficiency and reduced latency.