Atomic decomposition and sparse representation for complex signal analysis in machinery fault diagnosis: A review with examples

Abstract Complex signal analysis is a key topic in machinery fault diagnosis. For complex multi-component signals of various morphological contents, the commonly used basis expansion based signal processing method lacks adaptability and flexibility, thus being ineffective to extract the embedded meaningful information. Sparse signal representation has excellent adaptability and high flexibility in describing arbitrary complex signals based on atomic decomposition over redundant and over-complete dictionary, thus being free from the limitations imposed by orthogonal basis, and providing an effective approach to feature extraction from intricate signals for machinery fault diagnosis. This paper presents a systematic review on sparse signal representation, especially on two key topics, i.e. atomic decomposition algorithms (such as greedy pursuit, l p norm regularization and iterative shrinkage/thresholding) and dictionary design methods (including analytic dictionary design and dictionary learning) reported in more than 70 representative articles published since 1990. Their fundamental principles, advantages and disadvantages, and applications to machinery fault diagnosis, are examined. Some examples are provided to illustrate their performance.