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Gearboxes have developed rapidly, and studies on gearbox degradation assessment are of great significance. In the interest of obtaining an effective gearbox degradation feature, a new methodology based on sparse representation and compressive sensing theory is proposed. The wavelet packet transform is an excellent time-frequency analysis method, and the subbands with the largest energy are selected for training the sparse dictionaries. Furthermore, the overcomplete dictionaries of each degradation state can well reflect the signal structure by calculating the compressive sensing reconstruction residuals. Based on the sparse representation feature, a Euclidean distance technique is performed to calculate the assessment rate for each degradation state. The validity and superiority of the proposed assessment method are validated by crack failure data and broken tooth failure data under three kinds of work loads. A comparison of the sparse representation feature with the features of wavelet packet energy, kurtosis, and Renyi entropy is also performed.

Gearbox degradation assessment based on a sparse representation feature and Euclidean distance technique