A truncated generalized singular value decomposition algorithm for moving force identification with ill-posed problems

This paper proposes a new methodology for moving force identification (MFI) from the responses of bridge deck. Based on the existing time domain method (TDM), the MFI problem eventually becomes solving the linear algebraic equation in the form Ax=b. The vector b is usually contaminated by an unknown error e generating from measurement error, which often called the vector e as ''noise''. With the ill-posed problems that exist in the inverse problem, the identification force would be sensitive to the noise e. The proposed truncated generalized singular value decomposition method (TGSVD) aims at obtaining an acceptable solution and making the noise to be less sensitive to perturbations with the ill-posed problems. The illustrated results show that the TGSVD has many advantages such as higher precision, better adaptability and noise immunity compared with TDM. In addition, choosing a proper regularization matrix L and a truncation parameter k are very useful to improve the identification accuracy and to solve ill-posed problems when it is used to identify the moving force on bridge.