CN113361037B - 一种不确定性情况下的相邻齿轮间的失效相关性计算方法 - Google Patents

一种不确定性情况下的相邻齿轮间的失效相关性计算方法 Download PDF

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CN113361037B
CN113361037B CN202110651900.2A CN202110651900A CN113361037B CN 113361037 B CN113361037 B CN 113361037B CN 202110651900 A CN202110651900 A CN 202110651900A CN 113361037 B CN113361037 B CN 113361037B
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唐樟春
魏晨竹
植良蕊
夏艳君
穆帅
李凌云
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University of Electronic Science and Technology of China
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Abstract

该发明公开了一种不确定性情况下的相邻齿轮间的失效相关性计算方法，涉及可靠性信息融合领域。本发明首先将一个齿轮的可靠性范围转换为寿命分布函数，再对相邻的两个齿轮的寿命分布函数进行融合计算，可以达到在其中一个齿轮在不确定性情况下，计算两个相邻齿轮的失效相关性。

Description

一种不确定性情况下的相邻齿轮间的失效相关性计算方法
技术领域
本发明涉及可靠性信息融合领域，具体而言，涉及一种不确定性情况下的相邻齿轮间的失效相关性计算方法。
背景技术
信息融合是将各种类型的数据进行整合和组合的过程：例如，人类的大脑就是最佳的融合处理器。人类大脑对信息进行捕取、信息分析、信息，最终得到有效信息，而融合就是模拟人类大脑对信息处理的这一过程，即集成、关联、组合。多源信息融合得到的信息比单一信息源更加全面、可靠，并有较高的容错性，因而所做出的决策也就更加可信。信息融合是信息发展，科技智能化的极其重要的一部分，是现阶段全球研究热点之一。
如今，信息融合技术将多传感器中得到的各个信息进行归类分析，所得到的信息可能互补，亦可能冗余。因此，针对信息间的关系选择合适的方法进行融合，才能得到准确度和可信度较高的结果。随着系统越来越复杂，信息源越来越多，单个传感器和单一信息源已无法对系统进行准确的评估和决策。为提高结果精度得到准确的信息，人们对此领域进行了大量的研究并发展成多源信息融合技术。
实际工程机电装备系统极为复杂，由于共享变量的存在，各特征参数之间存在较强的相关性，收集到的可靠性数据信息同样存在较强的相关性；如若处理不当，则很有可能产生有偏估计，设置完全错误的估计，导致融合结果出现较大偏差，不利于工程实际可靠性评估，甚至导致完全错误的评估结论。工作中的齿轮之间也存在相关信息融合问题。啮合的齿轮之间，其中一个如果失效，另外的齿轮也会受到影响。
发明内容
本发明针对背景技术中的不足之处，提供的一种不确定性情况下的齿轮失效关系的信息融合方法。
本发明提供一种技术方案为：一种不确定性情况下的相邻齿轮间的失效相关性计算方法，该方法包括：
步骤1：齿轮1和齿轮2相邻，获取齿轮1的寿命分布函数u1，齿轮2的寿命分布函数不确定，但已知齿轮2的第j个时间点的可靠性范围
Figure BDA0003111861430000011
步骤2：采用如下公式将齿轮2的可靠性范围转换为寿命分布函数u2；
Figure BDA0003111861430000021
fYj(yj)表示寿命分布函数u2中第j个时间点对应的寿命；
步骤3：采用如下公式计算齿轮1和齿轮2之间的失效相关性C
Figure BDA0003111861430000022
其中，θ为采用下式根据极大似然估计法进行计算得到，c(u1,u2；θ)为Copula函数C((u1,u2；θ))的密度函数
Figure BDA0003111861430000023
本发明将一个齿轮的可靠性范围转换为寿命分布函数，再对寿命分布函数进行融合，可以达到在其中一个齿轮在不确定性情况下，计算两个相邻齿轮的失效相关性。
附图说明
图1为本发明具体实施方式中的齿轮结构图。
图2为本发明的随机与认知不确定共存失效关系图。
具体实施方式
下面以齿轮间失效关系为例对本发明的具体实施方式进行详细说明。
针对Copula函数的分布函数随机与认知不确定性共存情况，本发明提供以下方案：
步骤1：若齿轮间失效关系为随机与认知不确定性共存情况，三个齿轮的结构图如图2所示，三个传动齿轮，齿轮1和齿轮3的寿命分布函数为：
齿轮1：
Figure BDA0003111861430000024
齿轮3：
Figure BDA0003111861430000025
步骤2：齿轮2的寿命分布函数为：
Figure BDA0003111861430000026
f 2(t)分别表示取值的上下界，由于通过经验和计算确定的参数存在认知不确定性，若给定f2(t)的取值范围为：
Figure BDA0003111861430000031
通过最大熵可以得到f2(t)：
Figure BDA0003111861430000032
步骤3：可得齿轮1和齿轮2、齿轮2和齿轮3的Copula函数为：
Figure BDA0003111861430000033
Figure BDA0003111861430000034
Figure BDA0003111861430000035
则C1，2C2，3，C1，2，3的图形分别如图2所示。
图2可以看出，齿轮1和齿轮2的寿命失效关系随着工作时间的增加，失效关系关联性越强，齿轮2和齿轮3的寿命失效关系随着工作时间的增加，失效关系关联性越强，由齿轮1、齿轮2和齿轮3组成齿轮箱，随着工作时间的增加，齿轮箱失效关系关联性越强。
本发明提供的技术方案能够解决经典的Copula函数无法解决的随机与认知不确定性共存情况的信息融合。

Claims (1)

1.一种不确定性情况下的相邻齿轮间的失效相关性计算方法，该方法包括：
步骤1：齿轮1和齿轮2相邻，获取齿轮1的寿命分布函数u1，齿轮2的寿命分布函数不确定，但已知齿轮2的第j个时间点的可靠性范围
Figure FDA0003111861420000011
步骤2：采用如下公式将齿轮2的可靠性范围转换为寿命分布函数u2；
Figure FDA0003111861420000012
Figure FDA0003111861420000013
表示寿命分布函数u2中第j个时间点对应的寿命；
步骤3：采用如下公式计算齿轮1和齿轮2之间的失效相关性C
Figure FDA0003111861420000014
其中，θ为采用下式根据极大似然估计法进行计算得到，c(u1,u2；θ)为Copula函数C((u1,u2；θ))的密度函数：
Figure FDA0003111861420000015
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