A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices i...A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices is generated using time-shifted, analytic data and assembled into several Hankel matrices. Dissimilar left and right matrices are found, which diagonalize the set of nonhermetian Hankel matrices. The complex-valued modal matrix is obtained from this decomposition. The modal responses, modal auto-correlation functions and discrete-time plant matrix (in state space modal form) are subsequently identified. System eigenvalues are computed from the plant matrix to obtain the natural frequencies and modal fractions of critical damping. Joint Approximate Diagonalization (JAD) of the Hankel matrices enables the under determined (more modes than sensors) problem to be effectively treated without restrictions on the number of sensors required. Because the analytic signal is used, the redundant complex conjugate pairs are eliminated, reducing the system order (number of modes) to be identified half. This enables smaller Hankel matrix sizes and reduced computational effort. The modal auto-correlation functions provide an expedient means of screening out spurious computational modes or modes corresponding to noise sources, eliminating the need for a consistency diagram. In addition, the reduction in the number of modes enables the modal responses to be identified when there are at least as many sensors as independent (not including conjugate pairs) modes. A further benefit of the algorithm is that identification of dissimilar left and right diagonalizers preclude the need for windowing of the analytic data. The effectiveness of the new modal identification method is demonstrated using vibration data from a 6 DOF simulation, 4-story building simulation and the Heritage court tower building.展开更多
Current methods of order tracking, such as synchronous resampling, Gabor filtering, and Vold-Kalman filtering have undesirable traits. Each method has two or more of the following deficiencies: requires measurement or...Current methods of order tracking, such as synchronous resampling, Gabor filtering, and Vold-Kalman filtering have undesirable traits. Each method has two or more of the following deficiencies: requires measurement or estimate of rotational speed over time, failure to isolate the contribution of crossing orders in the vicinity of the crossing time, large computational expense, end effects. In this work a new approach to the order tracking problem is taken. The Second Order Blind Identification (SOBI) algorithm is applied to synthesized data. The technique is shown to be very successful at isolating crossing orders and circumvents all of the above deficiencies. The method has its own restric-tions: multiple sensors are required and sensors must be mounted on a structure that responds quasi-statically to exci-tation of the rotational system.展开更多
文摘A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a set of correlation matrices is generated using time-shifted, analytic data and assembled into several Hankel matrices. Dissimilar left and right matrices are found, which diagonalize the set of nonhermetian Hankel matrices. The complex-valued modal matrix is obtained from this decomposition. The modal responses, modal auto-correlation functions and discrete-time plant matrix (in state space modal form) are subsequently identified. System eigenvalues are computed from the plant matrix to obtain the natural frequencies and modal fractions of critical damping. Joint Approximate Diagonalization (JAD) of the Hankel matrices enables the under determined (more modes than sensors) problem to be effectively treated without restrictions on the number of sensors required. Because the analytic signal is used, the redundant complex conjugate pairs are eliminated, reducing the system order (number of modes) to be identified half. This enables smaller Hankel matrix sizes and reduced computational effort. The modal auto-correlation functions provide an expedient means of screening out spurious computational modes or modes corresponding to noise sources, eliminating the need for a consistency diagram. In addition, the reduction in the number of modes enables the modal responses to be identified when there are at least as many sensors as independent (not including conjugate pairs) modes. A further benefit of the algorithm is that identification of dissimilar left and right diagonalizers preclude the need for windowing of the analytic data. The effectiveness of the new modal identification method is demonstrated using vibration data from a 6 DOF simulation, 4-story building simulation and the Heritage court tower building.
文摘Current methods of order tracking, such as synchronous resampling, Gabor filtering, and Vold-Kalman filtering have undesirable traits. Each method has two or more of the following deficiencies: requires measurement or estimate of rotational speed over time, failure to isolate the contribution of crossing orders in the vicinity of the crossing time, large computational expense, end effects. In this work a new approach to the order tracking problem is taken. The Second Order Blind Identification (SOBI) algorithm is applied to synthesized data. The technique is shown to be very successful at isolating crossing orders and circumvents all of the above deficiencies. The method has its own restric-tions: multiple sensors are required and sensors must be mounted on a structure that responds quasi-statically to exci-tation of the rotational system.
