Modal identification of building structures under unknown input conditions using extended Kalman filter and long-short term memory

Various system identification (SI) techniques have been developed to ensure the sufficient structural performance of buildings. Recently, attempts have been made to solve the problem of the excessive computational time required for operational modal analysis (OMA), which is involved in SI, by using the deep learning (DL) algorithm and to overcome the limited applicability to structural problems of extended Kalman filter (EKF)-based SI technology through the development of a method enabling SI under unknown input conditions by adding a term for the input load to the algorithm. Although DL-based OMA methods and EKF-based SI techniques under unknown input conditions are being developed in various forms, they still produce incomplete identification processes when extracting the identification parameters. The neural network of the developed DL-based OMA method fails to extract all modal parameters perfectly, and EKF-based SI techniques has the limitations of a heavy algorithm and an increased computational burden with an input load term added to the algorithm. Therefore, this study proposes an EKF-based long short-term memory (EKF-LSTM) method that can identify modal parameters. The proposed EKF-LSTM method applies modal-expanded dynamic governing equations to the EKF to identify the modal parameters, where the input load used in the EKF algorithm is estimated using the LSTM method. The EKF-LSTM method can identify all modal parameters using the EKF, which is highly applicable to structural problems. Because the proposed method estimates the input load through an already trained LSTM network, there is no problem with computational burden when estimating the input load. The proposed EKF-LSTM method was verified using a numerical model with three degrees of freedom, and its effectiveness was confirmed by utilizing a steel frame structure model with three floors.