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Nonlinear Modeling of Complex Structures

     The proposed research covers the development of high-fidelity, reduced-order, nonlinear (i.e., not-necessarily-linear) mathematical models for complex structures. These models will be essential for the implementation of the next generation of high-performance computational tools, which will be used for numerical simulation, control applications, condition assessment, and damage detection in aerospace systems as well as in a broad range of physical systems ranging from Micro Electrical Mechanical Systems (MEMS) to large civil infrastructure systems.

     The need for accurate mathematical models of a large space structure arises in several contexts. First, such a model is typically required for the design of a feedback control system used for spacecraft orientation, station-keeping, and vibration suppression. In addition, mathematical models are quite important for determining structural characteristics such as damping in structural joints, and the extent of nonlinearities such as hysteretic properties of active structural members, dead space in joints, buckling of imperfect struts, etc. Also, accurate mathematical models can be used to explore the differences in the behavior of structures in space as opposed to the 1-g environment, and eventually such models may be used to minimize the necessity for costly tests. Finally, accurate mathematical models are useful as a tool for "health monitoring" of precision space structures on the basis of system identification approaches. NASA's interest in the subject of modeling, identification, control, and fault detection is reflected in the major effort expended in developing testbeds such as the one in the SPACE laboratory at CSULA.

     The vast majority of system identification procedures available today are based on the assumption that the structure will behave in a linear fashion. The state of the art for linear system identification has advanced to a great extent, and commercial software packages are currently available for on-line identification of such linear properties as natural frequencies, mode shapes, and damping ratios. The scope of available approaches for identification of nonlinear structural behavior is much more limited. The common approach based on Volterra integrals is generally unsuitable for application since it requires excessive data storage and computation, as well as restrictions on the nature of the excitation and on the class of nonlinearities to be identified.

     The proposed research will investigate the range of validity of some novel and powerful nonlinear system identification approaches (both parametric as well as nonparametric) that have been developed by the USC-CSULB team members, in the context of applications involving aerospace structures such as the segmented space telescope at CSULA, as well as civil structures, in order to assess the utility of the approaches and to develop optimum strategies for their applications under realistic conditions.