UNEQUAL INTERVAL STRESS SPECTRUM COMPILATION METHOD BASED ON CLUSTER ANALYSIS AND SUPPORT VECTOR MACHINE
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摘要: 为保证根据实测应力-时间历程数据编制的应力谱最大程度反映载荷实际作用特性，提出了一种基于疲劳损伤的非等间隔应力谱编制方法。通过引入非等间隔自适应比值系数，根据损伤等效原则，建立应力谱分级数与疲劳损伤关系数学模型；考虑每个应力循环的属性特征，采用聚类分析对所有应力循环进行分类，结合支持向量机多分类进行判别，得到不同分级数下的准确率和预测图；综合考虑数学模型得到的损伤相对误差和支持向量机分类准确率，选取应力谱最佳分级数，编制了相应的非等间隔应力谱，并与目前常用的等间隔和非等间隔8级谱进行比较。分析结果表明：基于损伤等效原则，采用聚类分析和支持向量机进行应力谱分级，不仅考虑了所有应力循环的整体特征，很大程度保留了应力的局部信息和属性，且根据疲劳累积损伤理论得到的损伤与实际损伤结果差异明显降低，从而更能准确反映实测数据的应力特性和疲劳效应，可为其他实测载荷-时间历程数据进行非等间隔分级和载荷谱编制提供参考。Abstract: A method of unequal interval stress spectrum compilation based on fatigue damage was proposed to ensure the stress spectrum compilation from the measured stress-time history to reflect the actual effect characteristics of the load. According to the damage equivalence principle, a mathematical model of the relationship between the stress spectrum classification numbers and fatigue damage were established by adding unequal interval adaptive ratio coefficients. Considering the attribute characteristics of each stress cycle, cluster analysis was used to classify all stress cycles, while the classification accuracy and prediction map under different classification numbers were obtained based on the support vector machine multi-classification. Considering the relative error of damage obtained from the mathematical model and the classification accuracy of support vector machine, the corresponding unequal interval stress spectrum were compiled by means of the optimal number of stress spectrum, which was compared with the equal interval spectrum and unequal interval spectrum of 8 levels. The results show that the stress spectrum of classification based on the damage equivalent principle, cluster analysis and support vector machine considers the overall characteristics of all stress cycle and the local information and properties of the stress, and the results of the fatigue cumulative damage theory are significantly lower than the actual damage, so that the measured data of stress characteristic and the effects of fatigue are accurately reflected. This method can be used for other measured load-time history to unequal interval classification and load spectrum compilation.
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Key words:
- stress spectrum /
- fatigue damage /
- unequal interval /
- cluster analysis /
- support vector machine
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图 1 应力-时间历程处理前后对比
Figure 1. Comparison of stress-time history before and after processing
图 2 分级数-准确率/相对误差关系
Figure 2. Classification numbers-accuracy/relative error relationship
表 1 聚类分析分为16类时各类样本数
Table 1. The number of samples of each type when cluster analysis is divided into 16 categories
类别 等效应力/MPa 样本数 类别 等效应力/MPa 样本数 1 0.53 20467 9 7.62 8 2 1.60 1635 10 8.53 4 3 2.42 373 11 9.55 2 4 3.11 286 12 10.77 1 5 3.97 139 13 11.92 3 6 4.74 37 14 13.07 1 7 5.43 27 15 13.91 0 8 6.42 21 16 14.75 2 
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表 2 不同分级方式下16级应力谱损伤比较
Table 2. Comparison of 16-level stress spectrum damage under different grading methods
应力谱分级方法 损伤相对误差/(%) 目前等间隔 9.65 本文非等间隔 2.22
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表 3 目前分级方法与本文编谱方法分析比较
Table 3. Comparison of the current grading method and the proposed compiling method
谱级数 目前分级方法 本文采用的方法 等间隔 非等间隔 非等间隔 应力/MPa 循环次数 比值系数 应力/MPa 循环次数 自适应比值系数 应力/MPa 循环次数 1级 2.78 879 0.125 1.91 722 0.175 2.67 961 2级 4.44 158 0.275 4.20 320 0.319 4.88 100 3级 6.11 39 0.425 6.50 36 0.429 6.56 17 4级 7.78 11 0.575 8.79 12 0.537 8.21 12 5级 9.45 4 0.725 11.08 5 0.687 10.50 2 6级 11.11 4 0.850 12.99 1 0.758 11.60 3 7级 12.78 1 0.950 14.52 1 0.897 13.71 2 8级 14.45 2 1.000 15.28 1 1.000 15.28 1 总循环数 1098 1098 1098 损伤相对误差/(%) 4.46 7.80 4.10
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