Constrained adaptive lifting and the CAL4 metric for helicopter transmission diagnostics

This paper presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting (CAL) algorithm, an adaptive manifestation of the lifting scheme. Lifting is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Adaptivity is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation synchronous signal-averaging algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have approximately the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local waveform changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. A diagnostic metric based on the lifting prediction error vector termed CAL4 is developed. The CAL diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the CAL4 metric is compared with the classic metric FM4.