疲劳统计学智能化中的高镇同法

徐家进

doi:10.13700/j.bh.1001-5965.2020.0373

疲劳统计学智能化中的高镇同法

doi: 10.13700/j.bh.1001-5965.2020.0373

徐家进^,

力中国际融资租赁有限公司, 广州 510620

详细信息

通讯作者:
徐家进, E-mail: xujiajin666@163.com

中图分类号: O212.1
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出版历程
- 收稿日期: 2020-07-30
- 录用日期: 2020-11-27
- 网络出版日期: 2021-10-20

Gao Zhentong method in intelligentization of statistics in fatigue

XU Jiajin^,

L & Z International Leasing Co. Ltd., Guangzhou 510620, China

More Information

Corresponding author: XU Jiajin, E-mail: xujiajin666@163.com

摘要

摘要:
在疲劳统计学中威布尔分布起着非常重要的作用，但3个参数的威布尔分布在数学形式上比较复杂。通过样本数据估计这3个参数，可通过威布尔概率坐标纸，但其使用不便，且误差较大；也可通过解析法，求解3个联立的超越方程组，但存在不自冾的问题。为此，提出了智能化解决方案——高镇同法，高镇同法充分利用了Python的特点，能够方便地同时给出威布尔分布的3个参数，为威布尔分布的理论研究、实际应用和疲劳统计学的智能化奠定了坚实的基础。
- 三参数威布尔分布 /
- 安全寿命 /
- Python /
- 高镇同法 /
- 智能疲劳统计学
Abstract:
The Weibull distribution plays a very important role in statistics in fatigue, but the Weibull distribution of the three parameters is more complicated in mathematical form. The three parameters can be estimated through sample data. One is the "Weibull probability paper", but this method is inconvenient to use and the error is relatively large. The other is the "analytical method". To solve the three simultaneous transcendental equations, although it can be solved by a computer, there is still the problem of "incompatibility". To this end, an intelligent solution-Gao Zhentong method is proposed, which makes full use of the characteristics of Python and can conveniently give the three parameters of Weibull distribution at the same time. This lays a solid foundation for the theoretical research, practical application and intelligentization of statistics in fatigue of Weibull distribution.
- three-parameter Weibull distribution /
- safe life /
- Python /
- Gao Zhentong method /
- intelligent fatigue statistics

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图 1 标准威布尔分布概率密度函数

Figure 1. Standard Weibull distribution probability density function

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图 2 正态和威布尔分布可靠度比较(例1)

Figure 2. Comparison of normal and Weibull distribution reliability (Example 1)

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图 3 正态和威布尔分布可靠度比较(例2)

Figure 3. Comparison of reliability between Normal and Weibull distribution (Example 2)

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图 4 安全寿命与相关系数的关系(例3)

Figure 4. Safety life versus correlation coefficient (Example 3)

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图 5 安全寿命与相关系数的关系(例4)

Figure 5. Safety life versus correlation coefficient (Example 4)

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图 6 安全寿命与相关系数的关系(文献[11]中的表 3)

Figure 6. Safety life versus correlation coefficient (Table 3 of Ref.[11])

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图 7 S-N拟合曲线

Figure 7. S-N curve fiting

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图 8 a-N拟合曲线

Figure 8. a-N curve fitting

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表 1 一组疲劳寿命数据^[1]

Table 1. A set of fatigue life data^[1]

疲劳寿命/(10³ cycle)
350	380	400	430	450
470	480	500	520	540
550	570	600	610	630
650	670	730	770	840
均值N_av=557 标准差s=132.15 中值N_m=545

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表 2 100个试件在同一应力条件下疲劳寿命数据

Table 2. Fatigue life data of 100 specimens under the same stress condition

疲劳寿命/(10⁵cycle)
3.08	3.26	3.32	3.48	3.49	3.56	3.69	3.7	3.78	3.79
3.8	3.87	3.95	4.07	4.08	4.1	4.12	4.2	4.24	4.25
4.28	4.31	4.31	4.36	4.54	4.58	4.6	4.62	4.63	4.65
4.67	4.67	4.72	4.73	4.75	4.77	4.8	4.82	4.84	4.9
4.92	4.93	4.95	4.96	4.98	4.99	5.02	5.03	5.06	5.08
5.06	5.1	5.12	5.15	5.18	5.2	5.22	5.38	5.41	5.46
5.47	5.53	5.56	5.6	5.61	5.63	5.64	5.65	5.68	5.69
5.73	5.82	5.86	5.91	5.94	5.95	5.99	6.04	6.08	6.13
6.16	6.19	6.21	6.26	6.32	6.33	6.36	6.41	6.46	6.81
77.35	7.82	7.88	7.96	8.31	8.45	8.47	8.79	9.87
均值=5.315 标准差s=1.289 中值N_m=5.07

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表 3 例6的一组数据

Table 3. Example 6 a set of data

组号	S_max/MPa	lg N
1	380	2.593 3
2	353.6	2.897 6
3	326.4	3.220 1
4	299.2	3.867 1

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表 4 例7的一组数据

Table 4. Example 7 a set of data

组号	a/mm	N/h
1	0.497 8	4 800
2	0.642	5 200
3	0.665 5	5 600
4	0.797 6	6 000
5	0.932 2	6 400
6	1.099 8	6 800
7	1.292 9	7 200

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参考文献(15)

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