Development of Data-Driven Reduced-Order Models for Complex Nonlinear Systems from Experimental Data

This paper presents an overview of a comprehensive experimental and computational study to develop and evaluate some promising testing procedures and processing approaches to obtain high fidelity, data-driven, model-free, reduced-order, representations of complex nonlinear systems in a format that is convenient for use in computational mechanics studies, control applications, and structural health monitoring investigations. A re-configurable test apparatus was designed and assembled so as to allow the incorporation of a wide class of realistic nonlinearities, both stationary as well as nonstationary, that had nonlinear features (such as polynomial-like, dead-space, saturation, dry friction, hysteresis, etc.) that are widely encountered in the applied mechanics field, at various scales spanning the range from large civil infrastructure systems to micro-electro-mechanical devices. Both parametric approaches (based on adaptive least-squares methods) and nonparametric identification methods (using polynomial-basis functions and artificial neural networks) were used in conjunction with data sets obtained from the nonlinear test apparatus when using deterministic as well as stochastic excitations. The application of the proposed analysis methods to several illustrative nonlinear examples is presented. It is shown that the variety of methods that were evaluated in this study provide a "toolkit" containing a useful collection of efficient methods that can handle a very broad class of problems and situations that are often encountered in the nonlinear structural dynamics field.