{'fraction_non_alphanumeric': 0.02072538860103627, 'fraction_numerical': 0.0, 'mean_word_length': 5.438095238095238, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An equivalent cyclic energy indicator for bearing performance degradation assessment

Bearing performance degradation assessment has attracted much attention in recent years because it is a key step to estimating the remaining useful life of bearings. Because cyclic spectral analysis has superior ability to characterize some kinds of non-stationary signals, such as non-stationary bearing fault signals, many efforts have been made to use cyclic spectral analysis for bearing fault diagnosis. However, the application of cyclic spectral analysis to bearing prognosis, especially bearing performance degradation assessment, is rarely reported. Recently, based on the integration of spectral correlation over spectral frequency, a novel bearing heath indicator, the cyclic energy indicator (CEI), was proposed by some scholars. In this paper, an equivalent cyclic energy indicator (ECEI) is introduced. It is mathematically proofed that the ECEI is equal to the CEI. Additionally, because the calculations of the ECEI do not involve spectral correlation, which is a two-dimensional power density function and requires searching an amount of cyclic frequencies to discover the cyclic evolution in signals, the time complexity of the ECEI is simpler than that of the CEI. This can prove to hold mathematically for the estimators of the ECEI and the CEI.