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In recent years, the fault detection and diagnosis of gear transmission systems have received considerable attention, as it can reduce mechanical downtime and secondary damage caused by faults. Compared to simple planetary gear systems, compound planetary gear systems achieve more ideal transmission ratios in the same or smaller volume and are widely used in aviation, aerospace, wind power and other machinery. Therefore, it is significant to diagnose faults in compound planetary gear systems. Currently, vibration signal-based fault diagnosis technology is the most widely used technique for detecting and diagnosing rotating machinery faults. In practical applications, however, faulty information signals are often obscured by healthy component vibration signals and background noise; thus there is a need to study new signal processing methods for fault diagnosis based on vibration signals. This research focuses on the vibration signal fault diagnosis problem of compound planetary gear systems as follows: