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Rolling bearing is widely used in rotating machinery and, at the same time, it is easy to be damaged due to harsh operating environments and conditions. As a result, rolling bearing is critical to the safe operation of the machinery devices. Compound fault of rolling bearing is not a simple superimposition of multiple single faults, but the coupling of multiple fault features, making the vibration signal, becomes complicated. In our study, sparsity-oriented nonconvex nonseparable regularization (SONNR) method is proposed to rolling bearing compound fault diagnosis under noisy environment. Firstly, a theoretical model of rolling bearing compound fault is established, and the vibration characteristics of rolling bearing compound fault are analyzed. Secondly, four-layer structure of the SONNR method is proposed: input layer, nonconvex sparse regularization layer, signal reconstruction layer, and compound faults isolation layer. Finally, the validity of the method is verified by simulation data and actual data, and it is compared with the traditional time domain diagnostic methods and artificial intelligence methods.