Operational modal analysis of three-dimensional structures by second-order blind identification and least square generalized inverse

Most complex engineering structures are three-dimensional in practice. The process of one-dimensional extending to three-dimensional is a challenge that must be conquered by Operational Modal Analysis (OMA) methods when these methods are applied to complex engineering applications supported by scientific researches. This study put forward a new three-dimensional structure OMA method based on Second-Order Blind Identification (SOBI) and general reversion of least square. Firstly, modal coordinates decomposition of one-dimensional structural vibration response signal with SOBI. Secondly, the reasons that modal parameters identified by SOBI including energy uncertainty, order uncertainty and modal missing are explained in theory. Thirdly, the SOBI algorithm is used to decompose the response signals of displacement of a direction whose vibration response is the largest, then the other two directions are calculated by using the least square generalized inverse algorithm, and the modal parameters of three-dimensional structures are identified by the matrix assembly method. Numerical simulation results in a cylindrical shell demonstrated that this novel method is practical and effective by applied to practice in OMA of three-dimensional structures, and robustness to Gauss measurement noise disturbances.