Research Projects

In resource-constrained vibration monitoring contexts, it is often the case that only RMS/peak response measurements can be logged. This enables the detection of anomalously high vibration levels as they arise, but precludes any prognostics. For instance, vibrations of helicopter rotors running at hundreds of rpm are only logged once every few minutes (in terms of peak/RMS values). Since the data is significantly undersampled, it is impossible to reconstruct the exact vibration waveform, rendering traditional predictive condition monitoring untenable. The waveform may be thought of as being composed of the "fast-varying" periodic vibration modulated by a "slowly varying" envelope. Since most of the diagnostic information is contained in the latter, classical envelope/modulation analysis techniques from signal processing are invoked for condition monitoring. This is, however, not possible in the data-starved context, and the envelope measurement needs to be considered in isolation from the waveform. While the theory of multiple time scale dynamics exists in the literature as an analytical framework capable of this, it has not found widespread adoption in the experimental/practical community. The most important reason for this is that these techniques require the exact form of the governing differential equations. In the above example, for instance, accurate physical modeling of the complex aero-elastic (flutter, vortex shedding effects, etc.) and nonlinear mechanical (composite blades undergoing large deformations) interactions makes equation-based investigations prohibitively challenging. The development of a fully data-driven time-scale decomposition approach that is integrated with the theory of multiple scales can fix this drawback, leading to potentially significant improvements in predictive condition monitoring. This proposal seeks to develop a fully data-driven approach for experimental time-scale decomposition that can be implemented in an adaptive setting (model learns in real time). A novel gray-box identification approach will be proposed for this and validated against experiments. A nonlinear beam-type system subject to large deflections and a rotating system (rotor/gear-train) subjected to run-up & run-down, Steady-state, and narrow-band random excitation tests (where applicable) will be chosen as experimental benchmarks. Being data-driven and adaptive, this will also enable control applications for output rate-limited contexts (buffered/serial control). As a control application, the secondary focus of the project will be on the development of adaptive controllers to drive (weakly) nonlinear systems to resonance. Termed Nonlinear Modal Testing (NMT), all current implementations involve expensive "hardware-timed" real-time controllers. This work, therefore, will lead to a novel low-cost platform for NMT. As NMT gains acceptance in critical industry, this work has the potential to inform future industry standards.