
Analytical and Experimental Studies of Nonlinear Structural Models The proposed research is motivated by the need to develop a "toolkit" of methods, instrumentation, and data fusion approaches for monitoring the "health" of civil infrastructure systems subjected to arbitrary dynamic environments, through the use of advanced sensor and signal processing technologies. The research is focused on developing methods suitable for use with structural response measurements from flexible structural components and assemblages that may incorporate elements undergoing significant nonlinear (i.e., notnecessarilylinear) deformations. The project includes experimental studies of certain generic types of nonlinearities encountered in aerospace structures, civil structures, and other systems of interest such as computer disk drives. These studies will help us to better understand the physics of the underlying phenomena, and to develop suitable reducedorder mathematical models to characterize the essential features of the structural behavior. Such models can serve a dual purpose: as an efficient tool for analysts who need to predict the behavior of similar structures under dynamic loads for structural control applications, and as a useful tool for realtime condition assessment and damage detection. The research will be planned to develop innovative approaches and strategies for coping with the broad spectrum of situations arising in the applied mechanics field, by formulating a general approach for using structural vibration measurements to analyze and quantify the extent and location of relatively small changes in the structural parameters, which may be precursors of serious damage to the structure being monitored. Previous work by other authors has resulted in the development of estimation and modeling techniques for nonlinear structural systems, including systems with hysteretic behavior. These techniques provide realtime, robust tracking of the system response, as well as the ability to track timevarying properties of the structural system, such as structural deterioration. Figures 2(a) and 2(b) are typical of the type of problems that are being addressed by these techniques. The system of Figure2(b) is a discrete lumped mass representation of the general system of Figure 2, which is subjected to support motion and excitation and control forces, as well as nonlinear restoring forces. The methodologies developed by the authors are divided into two main categories: (a) Parametric and (b) Nonparametric. In the parametric case, a suitable model of the system is employed, based on physical modeling usually from first principles, and the parameters of the model are estimated online based on structural response measurements. In many cases this is a desirable approach, since the identified parameters have physical meaning, which can be traced back to structural characteristics, such as damping and stiffness. As has been shown, while this is a desirable approach, it has a drawback: in order to identify the parameters that have physical meaning, the corresponding restoring force signal must be measurable, and an appropriate model, specific to the system under study, must be selected. By contrast, the nonparametric approach employs generic models whose parameters have no physical meaning. Depending on their complexity, such models are able to model response behavior very accurately, and with considerable flexibility. Nonparametric techniques developed by the authors include techniques based on Volterra/Wiener neural networks (Figure 2(c)). This methodology requires very little a priori knowledge about the system, and fewer measured signals as compared to the parametric methods. The tradeoff is higher complexity, and a higher number of parameters for the underlying neural network. Both parametric and nonparametric techniques will be applied to the systems to be studied in the proposed project. For this activity, the Investigators will conduct analytical, numerical and experimental studies on structural models, including structural elements/components and structural assemblages.
X0j = Support displacement X1j = Displacement at points of measurement fj, uj = Excitation and control forces respectively Fig 2(a): General Continuous MDOF System
X0j = Support displacement X1j = Displacement at points of measurement fj, uj = Excitation and control forces respectively rj = General (nonlinear) restoring forces
Figure 2(b): Discrete ReducedOrder Representation of the General System Figure 2(c): Block Diagram of the VolterraWiener Neural Network

