基于Bootstrap理论的小子样寿命评估模型

赵远; 杨琳

doi:10.13700/j.bh.1001-5965.2020.0536

基于Bootstrap理论的小子样寿命评估模型

doi: 10.13700/j.bh.1001-5965.2020.0536

赵远^1, ,,
杨琳²

1.
西安导航技术研究所, 西安 710068
2.
兰州理工大学理学院, 兰州 730050

详细信息

通讯作者:
赵远, E-mail: happy_life03@163.com

中图分类号: TB114.3
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- 被引次数: 0
出版历程
- 收稿日期: 2020-09-21
- 录用日期: 2021-01-03
- 网络出版日期: 2022-01-20

Lifetime evaluation model of small sample based on Bootstrap theory

ZHAO Yuan^{1
, ,},
YANG Lin²

1.
Xi'an Research Institute of Navigation Technology, Xi'an 710068, China
2.
School of Science, Lanzhou University of Technology, Lanzhou 730050, China

More Information

Corresponding author: ZHAO Yuan, E-mail: happy_life03@163.com

摘要

摘要:
针对航天产品小子样、长寿命的特点，提出了基于Bootstrap理论的小子样寿命评估模型。采用B-样条函数构造Bootstrap样本经验分布函数，进行放回抽样。在此基础上，分别采用非参数Bootstrap方法和参数Bootstrap方法建立了寿命评估模型。采用提出的模型对空心阴极循环点火寿命试验数据进行评估，得到多个寿命特征结果，与传统的参数极大似然估计方法的计算结果进行了对比分析，其评估精度满足工程的应用需求，验证了该模型的工程实用性和有效性。
- 小子样 /
- 寿命评估 /
- Bootstrap /
- B-样条函数 /
- 经验分布函数
Abstract:
This paper proposes a small sample lifetime evaluation model based on Bootstrap method for aerospace products which have the characteristics of small sample and long service life. Using B-spline function as the Bootstrap sample empirical distribution function, a random case sample with replacement is obtained. And on this basis, the lifetime evaluation model is established by using non-parametric Bootstrap method and parametric Bootstrap method respectively. Hollow cathode ignition test data are evaluated based on the proposed method, and multiple lifetime characteristic results are acquired. The results are contrastively analyzed with those concluded by conventional maximum likelihood estimation method of parameters, and it meets the need of the engineering precision, which demonstrates the engineering practicability and effectiveness of the method.
- small sample /
- lifetime evaluation /
- Bootstrap /
- B-spline function /
- empirical distribution function

HTML全文

图 1 基于Bootstrap理论的小子样寿命评估原理

Figure 1. Lifetime evaluation principle of small sample based on Bootstrap theory

下载: 全尺寸图片幻灯片

图 2 给定寿命的可靠度置信区域

Figure 2. Confidence region of reliability for a given lifetime

下载: 全尺寸图片幻灯片

图 3 给定可靠度的寿命置信区域

Figure 3. Confidence region of lifetime for a given reliability

下载: 全尺寸图片幻灯片

表 1 空心阴极点火寿命试验数据

Table 1. Hollow cathode ignition lifetime test data

点火循环模式	点火失效次数
点火成功后工作1 min，关闭冷却20 min	13 957
点火成功后工作1 min，关闭冷却20 min	14 255
点火成功后工作2 h，关闭冷却30 min	13 780
点火成功后工作2 h，关闭冷却30 min	14 576
点火成功后工作2 h，关闭冷却30 min	14 632

下载: 导出CSV

表 2 划分点数值和函数值

Table 2. Divide point value and function value

编号	数值	函数F₅值
a₀	13 780	0
a₁	13 822.6	0.096 3
a₂	13 865.2	0.192 5
a₃	13 907.8	0.233 1
a₄	13 950.4	0.269
a₅	13 993	0.304 8
a₆	14 035.6	0.340 7
a₇	14 078.2	0.376 6
a₈	14 120.8	0.409 6
a₉	14 163.4	0.437 1
a₁₀	14 206	0.464 6
a₁₁	14 248.6	0.492 1
a₁₂	14 291.2	0.519 7
a₁₃	14 333.8	0.547 2
a₁₄	14 376.4	0.574 7
a₁₅	14 419	0.603 7
a₁₆	14 461.6	0.648 9
a₁₇	14 504.2	0.694 1
a₁₈	14 546.8	0.739 3
a₁₉	14 589.4	0.784 5
a₂₀	14 632	1
a₂₁	14 674.6	1

下载: 导出CSV

表 3 寿命结果的相对误差

Table 3. Relative error of lifetime results

序号	计算方法	寿命结果	与T相对误差
1	近似的平均寿命	14 240	0
2	传统参数估计	14 242	0.000 14
3	非参数评估模型	14 245	0.000 35
4	参数寿命评估模型	14 260	0.001 3
5	非参数评估模型	(14 006，14 459)	(-0.016，0.015)

下载: 导出CSV

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