Modal identification using Blind Source Separation techniques

Recent developments in Blind Source Separation (BSS) have prompted researchers in structural dynamics to utilize BSS techniques for modal analysis. Endeavors involving the use of BSS to perform modal identification have thus far involved straightforward application of various BSS algorithms without much concern about the relationship between the identified sources and modal responses.; This work provides connections between the source components of two BSS algorithms and modal responses of diagonally-damped structures. Modifications of the existing algorithms are proposed when necessary. The first technique involves gradient descent minimization of an objective function embodying information about higher order statistics of measures signals. The second technique is a second-order statistical method that involves joint approximate diagonalization of several covariance matrices of time shifted signals. The technique is known as Second-Order Blind Identification (SOBI). Use of each technique is illustrated on prototype examples. The two algorithms are evaluated for the purpose of extension to the general case of modal parameter estimation for arbitrary damping.; The SOBI method is adapted for the general case. Modal responses and mode shapes are estimated by the use of SOBI on an expanded and pretreated data set. Frequency and damping can be obtained from the modal responses by simple single degree of freedom methods. Using this approach, a class of new nonparametric, output-only modal identification algorithms is proposed and examples of its use are provided. The technique is dubbed Blind Modal IDendification (BMID). A modal contribution indicator is developed in order to aid in discrimination of structural modes from spurious noise modes. It is demonstrated that the proposed methodology provides a novel and robust approach to modal identification. For linear systems, it is shown that quality of the modal parameters produced by the method is competitive with the state-of-the-art methods. Furthermore, the technique is used to characterize mild structural nonlinearities when combined with the FREEVIB method. Application of BSS techniques to decompose vibration data greatly simplifies the modal identification task. As a result, many of the shortcomings of traditional parametric modal extraction techniques are eliminated with this method.