MAR模型模态参数识别的虚假模态判定方法

MAR (Multivariate Auto Regression) is a multivariate time series model, which can be applied to structural responses modeling and modal parameter identification. Like any other time-domain methods, MAR model based modal parameter identification method has to deal with the false modes problem. In this paper, a new method to discriminate false modes for the modal analysis is proposed for the MAR model. The basic idea is first to solve the auto-regression coefficients for the MAR model constructed from the multi-channel measurements of structures, and then to construct MAR models for each mode with error terms by the auto-regression coefficients and the modal parameters based on MAR model, and finally to determine the modes with large error terms as the false modes. The MAR models for structural responses and modal responses are discussed in the first place. Based on the principal of Duhamel's integral, the MAR model with an error term for the structural responses under ambient vibration is derived, and its discrete form is obtained by discretization in time. The discrete MAR model can be constructed by multi-channel measurements of structure responses, and the auto regression coefficients can be obtained by the least square fitting technique. Then the MAR model for each mode is constructed with an error term. A criterion is put forward to discriminate the false modes by quantitatively evaluating the errors associated with each mode using its Euclidean norm, and modes with larger error terms are determined as false modes. Numerical and experimental examples are provided to show the effectiveness of the proposed method. The results show that the stability diagram after eliminating the false modes is much clearer than the conventional stability diagram, which leads to more reliable identifications of real modes of the structures.