###### Abstract  
The rolling bearing is an important part of mechanical equipment, and its performance significantly affects the quality and life of the mechanical equipment. This article uses the integrated fiber Bragg grating resonant structure sensor excited by periodic micro-shocks caused by micro faults to realize the extraction of information relating to potential faults. Because the fault signal is weak and can easily be interfered with by ambient noise, in order to extract the effective signal, this article determines the autoregressive model of bearing vibration by the final prediction error criterion and the recursive least squares estimation algorithm. The augmented state space model is established based on the autoregressive model. A Kalman filter is used to reduce the noise interference, and then the reduction noisy signal is analyzed by power spectrum and improved autocorrelation envelope spectrum to realize the detection of bearing faults. Through data analysis and method comparison, the proposed improved autocorrelation envelope spectrum analysis can directly extract the bearing fault frequency, which is superior to other methods such as cepstral analysis. bearing fault; fiber Bragg grating resonance monitoring; autoregressive model; Kalman filter; spectrum analysis +
Footnote †: journal: Applied  
0000-0001-4000-3390-3  
and reliable method for extracting weak fault features has always been a prominent and difficult point in engineering application research. At the same time, it has important practical significance for the monitoring and forecasting of the equipment's status and for later equipment maintenance [6; 7]. At present, the research on fault detection and diagnosis of rolling bearings has made certain progress. [PERSON] et al. directly used discrete wavelet transform to identify early bearing faults, and successfully extracted weak feature information after signal decomposition and reconstruction, but the wavelet transform needs to select a suitable wavelet threshold and a suitable number of wavelet decomposition layers [8]. [PERSON] et al. studied the method of extracting the weak feature of the bearing, which combined the adjustable quality factor wavelet transform and the aggregate empirical mode decomposition, and successfully applied it to the actual signal analysis, but the empirical mode decomposition has problems of mode aliasing and end effects, and it is necessary to select a sufficient number of eigenmode functions [9]. [PERSON] et al. used the minimum direct deconvolution to filter the early fault signals of the bearing, and used the full-period signal of the bearing to verify that the characteristics of the fault signal after noise reduction can be more obvious, but the minimum direct deconvolution is a non-globally-optimal filter, which has poor robustness and is susceptible to interference from a few abnormal spikes during signal processing [10]. [PERSON] et al. used enhanced sparse representation algorithm based on an adaptive period matching to extract the initial fault features of the bearing [11]. [PERSON] et al. combined the signal processing with ensemble bagged-trees-based machine learning and used the decomposition and reconstruction methods in the stochastic resonance to diagnose early bearing fault, but the time efficiency of mechanical fault detection of this method needs to be improved [12]. As an intelligent fault diagnosis method, machine learning has been applied to rotating systems fault diagnosis [13]. [PERSON] et al. proposed a method to identify shallow cracks in rotor systems by using convolutional neural networks and persistent spectra during steady state operation [14]. Then, based on supervised learning and convolutional neural network methods, intelligent methods for automatic detection of imbalance, crack and parallel dislocation in rotating machinery are compared [15]. Using machine learning requires a substantial amount of time and computing power. In recent years, some researchers have used models to analyze bearing faults. [PERSON] et al.