# A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection

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## Abstract

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## 1. Introduction

- A novel advancing signal processing method based on coupled multi-stable stochastic resonance is proposed to detect the faults of motor bearings;
- The output signal-to-noise ratio (SNR) for system parameters and coupling coefficients are analyzed in depth;
- The SOA is used to adaptively optimize and determine the system parameters of the SR by using the subsampling technique;
- The actual vibration data of induction motor bearings are used to prove the effectiveness of the proposed CMSR system.

## 2. Theoretical Background

#### 2.1. First-Order MSR System Model

#### 2.2. Mode of CMSR System

#### 2.3. System Measurement Index

#### 2.4. The Flow of the CMSR System

- Signal preprocessing. The envelope signal obtained after filtering and demodulating the collected bearing vibration signal is recorded as ${s}_{1}$, ${s}_{2}={s}_{1}-mean\left({s}_{1}\right)$, $s={s}_{2}/2\mathrm{max}\left(abs\left({s}_{2}\right)\right)$, S is the input signal;
- Parameter initialization. Number of iterations, population size, and range of parameters are determined;
- Calculate the target value of each position using the output SNR formula;
- Parameter optimization. The SNR is considered as the fitness function of the seeker optimization algorithm (SOA) to adaptively optimize and determine the system parameters of the SR by using the subsampling technique;
- If the set value is equal to the current number of iterations, output the best system parameters a, b, r, R and enter the next step; otherwise, return to the previous step;
- Signal detection. Import the pre-processed signal into the CMSR system with the determined parameters to get the output signal ${x}_{1}$ Scale recovery of signal frequency and amplitude $x={x}_{1}\times 2\mathrm{max}\left(abs\left({s}_{2}\right)\right)$;
- Fault detection. Fourier transform of x to complete fault detection.

## 3. System Parameter Analysis

## 4. Engineering Application

## 5. Conclusions

- The CMSR system can detect weak high-frequency signals by combining the variable-scale method;
- With the output SNR as the fitness function of the SOA the parameters of the CMSR system can be determined;
- The engineering data-processing results show that the CMSR system has better filtering performance, higher output SNR, and more effective detection results than traditional SR methods, which has broader prospects for weak signal processing.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Inner Diameter (mm) | Outer Ring Diameter (mm) | Pitch Diameter (mm) | Roller Diameter (mm) | Roller Number | Angular Contact Angle |
---|---|---|---|---|---|

25.001 | 51.999 | 39.04 | 7.94 | 9 | 0 |

Objects | Theoretical Value | Obtained Value | Error |
---|---|---|---|

Inner race | 162.2 Hz | 162.6 Hz | 0.4 Hz |

Rolling element | 141.1 Hz | 140.6 Hz | 0.5 Hz |

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**MDPI and ACS Style**

Cui, H.; Guan, Y.; Chen, H.; Deng, W.
A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection. *Appl. Sci.* **2021**, *11*, 5385.
https://doi.org/10.3390/app11125385

**AMA Style**

Cui H, Guan Y, Chen H, Deng W.
A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection. *Applied Sciences*. 2021; 11(12):5385.
https://doi.org/10.3390/app11125385

**Chicago/Turabian Style**

Cui, Hongjiang, Ying Guan, Huayue Chen, and Wu Deng.
2021. "A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection" *Applied Sciences* 11, no. 12: 5385.
https://doi.org/10.3390/app11125385