A Fast Complexity Pursuit-Based Blind Source Separation Method for Structural Modal Identification

Complexity pursuit (CP) is an effective method for solving blind source separation (BSS) problems. Combined with the gradient descent algorithm, the complexity pursuit-gradient descent (CP-GD) algorithm can extract the structural modal contributions from vibration responses without measuring the inputs. However, the computational efficiency of CP-GD algorithm is very low since all data should be used in each iteration step of the gradient descent. This paper introduces the fast complexity pursuit-gradient descent (FCP-GD) algorithm, optimizing the traditional complexity calculation formula and using the subspace search method for calculating the de-mixing vectors, which significantly saves computation time. Furthermore, a comparative study between the FCP-GD and temporal predictability-generalized eigenvalue decomposition (TP-GED) algorithms was conducted using two-degree-of-freedom and three-degree-of-freedom systems and revealed an equivalence of these two algorithms. Finally, numerical simulations and experiments on multi-degree-of-freedom free vibration systems confirmed the effectiveness, efficiency, and robustness of the FCP-GD algorithm.