Recognition of Damage Degree of Tooth Root Crack based on PCA and Grey Relational

Jie Liu; Huanyu Li; Weiqiang Zhao

doi:10.16578/j.issn.1004.2539.2020.09.021

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Recognition of Damage Degree of Tooth Root Crack based on PCA and Grey Relational

Test·Analysis | 更新时间：2022-11-02

- Recognition of Damage Degree of Tooth Root Crack based on PCA and Grey Relational
- Journal of Mechanical Transmission Vol. 44, Issue 9, Pages: 133-139(2020)
- 作者机构：
  
  1.沈阳工业大学机械工程学院，辽宁沈阳 110870
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.09.021
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刘杰,李环宇,赵伟强.基于PCA和灰色关联的齿根裂纹损伤程度识别[J].机械传动,2020,44(09):133-139.

Liu Jie,Li Huanyu,Zhao Weiqiang.Recognition of Damage Degree of Tooth Root Crack based on PCA and Grey Relational[J].Journal of Mechanical Transmission,2020,44(09):133-139.
刘杰,李环宇,赵伟强.基于PCA和灰色关联的齿根裂纹损伤程度识别[J].机械传动,2020,44(09):133-139. DOI： 10.16578/j.issn.1004.2539.2020.09.021.

Liu Jie,Li Huanyu,Zhao Weiqiang.Recognition of Damage Degree of Tooth Root Crack based on PCA and Grey Relational[J].Journal of Mechanical Transmission,2020,44(09):133-139. DOI： 10.16578/j.issn.1004.2539.2020.09.021.

摘要

在齿轮齿根裂纹故障检测方面，利用倒频谱分析可以比较损伤程度的轻重，但很难具体量化损伤程度范围。为实现损伤程度的量化检测，提出采用主成分分析（Principal Component Analysis，PCA）与灰色关联分析（Grey Relational Analysis，GRA）相结合的方法。首先，利用能量法计算含不同齿根裂纹的齿轮副时变啮合刚度，分析不同损伤程度的响应，并结合损伤检测统计指标进行量化检测，通过PCA算法，对多维损伤检测统计指标进行降维优化后，计算待检目标序列与各个比较状态序列的关联度，用关联度表征裂纹损伤程度。在理论仿真的基础上，进行实验验证。结果表明，倒谱分析可有效地识别出齿根裂纹故障，损伤程度越大，倒谱的尖峰幅值越大。PCA与GRA结合算法与GRA算法计算的关联度相比更大，区分度也更加明显。并可以有效地量化待检目标的损伤程度，为齿根裂纹的定量识别提供理论依据。

Abstract

In the aspect of root crack fault detection， the severity of damage can be compared by cepstrum analysis， but it is impossible to quantify the extent of damage. In order to realize quantitative detection of damage degree， the method of Principal Component Analysis （PCA） and Grey Relational Analysis （GRA） are combined to use. Firstly， the energy method is used to calculate the time-varying meshing stiffness of gear pairs with different root cracks and analyze the response of different damage degrees. Then， statistical indicators of damage detection are also combined to carry out quantitative detection. Through PCA algorithm， the dimensional reduction of the multidimensional statistical indicators of damage detection is optimized. The relational degree between the target sequence to be examined and each comparison state sequence is calculated. The degree of crack damage is characterized by relational degree. On the basis of theoretical simulation， experimental verification is carried out. The results show that cepstrum analysis can effectively identify the root crack fault. The higher the damage degree， the higher the peak amplitude of cepstrum. The relational degree of PCA and GRA combined algorithm is larger and the discrimination degree is more obvious than that of direct GRA calculation. The damage degree of the target will can be effectively quantified， the theoretical basis for quantitative identification of tooth root crack is provided.

关键词

齿根裂纹主成分分析灰色关联分析故障识别损伤检测

Keywords

Tooth root crackPCAGRAFailure identificationDamage detection

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