基于网格近似法的数控机床贝叶斯可靠性评估研究

发布时间：2018-04-22 10:15

本文选题：数控机床 + 贝叶斯　；参考：《吉林大学》2015年博士论文

【摘要】：近年来,国产数控机床产品呈现出小批量生产、产品更新换代节奏加快以及可靠性水平逐年升高的趋势。对于国产高档数控机床产品来说,这种趋势尤为明显,从而导致新型数控机床可靠性现场试验不能像传统的试验那样具备大量的同型号被测产品和较长的试验时间,也不能像传统的试验那样频繁地观测到故障。以上事实表明:数控机床在其可靠性现场试验中故障发生次数减少,从而故障数据样本容量减小是不可避免的趋势。在工程实践中已经出现了以下问题,即:国家科技重大专项支持研发的某些数控机床在可靠性现场试验中产生的数据样本容量过小,以至于在进行可靠性建模与评估时,依赖于大样本数据的经典统计学方法因偏差过大而无法使用。此即为数控机床的小样本问题。相比于航空航天等行业,数控机床的小样本问题出现较晚,相应的解决方法也不成熟。近年来,数控机床行业的一些学者开始借鉴航空航天、核电和武器装备领域的经验,采用贝叶斯可靠性建模与评估方法解决数控机床的小样本问题。由于数控机床是复杂的可修复系统,其可靠性模型与数据形式均与火箭、导弹等成/败型系统不同。因此,机床行业专家在自主探索数控机床贝叶斯可靠性建模与评估技术的过程中:(a)一些已有问题的解决方法尚需完善;(b)针对一些已经出现的新现象,需要提出新问题、以数学模型描述新问题并提出相应的解决方案。以上讨论即为本文的研究内容与目标。具体介绍如下:(1)贝叶斯可靠性建模与评估方法的第一个环节为建立可靠性模型参数的先验分布。而已有的相关文献在先验分布的建立方面,大多数一笔带过,仅简要说明先验分布是由专家根据其经验并结合类似产品的信息给出的。尽管在航天产品贝叶斯可靠性评估领域,该做法无可厚非,但数控机床可靠性模型参数不像火箭发射成功率那样有明显的物理意义,因而,由专家直接给出参数的先验分布无法避免较大的主观偏差。实际上,专家判断的提取技术是一个专门的研究领域,许多学者已经提出了系统、结构化的专家判断提取流程。本文针对以上问题提出了小样本数据下威布尔参数先验分布的间接建立方法,包含两个阶段:(a)定义了数控机床的多源先验信息等概念,设计了小样本数据下适合数控机床的专家判断提取流程,得到了量化的专家判断结果;(b)提出了将专家判断结果转换为威布尔参数先验分布的数学方法。结合实例,应用了所提出的威布尔参数先验分布的建立方法,实现了多源先验信息与专家经验的融合,减少了因专家直接给出先ii验分布而带来的主观偏差。(2)贝叶斯可靠性建模与评估方法的第二个环节为计算可靠性模型参数的后验分布。对于两参数威布尔分布来说,该环节的计算会遇到无解析解的高维积分问题,计算尤为困难。目前有许多文献采用马尔科夫链蒙特卡罗(mcmc,markovchainmontecarlo)算法来解决这一问题。然而,大多数已有的文献尽管提及采用了mcmc算法,却并未说明具体采用的是哪一种算法,因为mcmc算法是一类算法的统称,并非所有的mcmc算法都有能力解决数控机床可靠性模型参数后验分布的计算问题。针对以上问题,本文自主开发了用于计算威布尔参数后验分布的二元metropolis算法:mcmc算法族中的一员。给出了算法的各项参数如建议分布、接受概率等;给出了算法的迭代流程;给出了算法的matlab程序代码。结合实例计算了参数估计值和机床的平均故障间隔时间:mtbf(meantimebetweenfailures)。(3)一些文献采用winbugs软件来解决复杂的可靠性模型参数后验分布的计算,但少有文章详细介绍winbugs软件的使用。实际上,用winbugs软件解决数控机床的小样本问题,使用者需要具备一定的贝叶斯统计学背景、学习一些bugs编程语言、掌握winbugs软件特有的描述非标准分布的编程技巧。针对以上问题,本文详细介绍了winbugs软件操作的各个步骤;用bugs语言描述了数控机床贝叶斯可靠性模型;介绍并证明了描述非标准分布的“零技巧”。结合实例给出了bugs代码,描述了软件操作过程。最后得到了参数估计值和机床的mtbf,并指出winbugs软件在计算后验分布时采用的是mcmc算法族中的slice抽样。(4)无论是自主开发还是在winbugs软件中运行的mcmc算法,都存在共同的问题:(a)mcmc算法虽然在计算上精度高,但非标准分布会导致算法在随机抽样过程产生不稳定和不确定的因素,甚至崩溃;(b)mcmc算法的原理较为复杂,自主开发或使用软件均比较麻烦。因此,mcmc算法族并不利于贝叶斯方法在数控机床工程领域的普及应用。针对以上问题,本文采用网格近似法,定义了参数的概率质量函数,将连续的先验分布离散化,推导了参数的离散形式的后验分布以及参数估计值的计算公式,解决了高维积分的计算困难。结合实例得到了参数估计值和机床的mtbf。将网格近似法、metropolis算法和winbugs软件三者进行对比,结果表明三者的mtbf估计值误差小于0.03小时。证明自主提出的网格计算方法计算精度不输于mcmc算法,且原理简单,编程容易实现,有利于贝叶斯可靠性建模与评估方法在数控机床可靠性工程领域的广泛应用。(5)数控机床在可靠性试验中发生故障的次数有可能为零,在零故障下的可靠性建模与评估是一个新问题,且尚未发现有文献描述并解决这个问题。产品的零故障问题在其他行业由来已久,且相应的解决方法几乎都是贝叶斯方法,这些方法为解决数控机床的零故障问题提供了借鉴。针对以上问题,本文提出了数控机床零故障问题的数据形式,建立了相应的贝叶斯统计学模型,提出了零故障数据下的专家判断提取流程及威布尔参数先验分布的建立方法。结合实例,分别利用WinBUGS软件和自主开发的网格近似法进行了参数估计和MTBF计算。结果表明:由WinBUGS软件和网格近似法得到的MTBF估计值的误差小于1小时。再次证明网格近似法简明易行且计算精度不降低的特点,适合工程应用。(6)为了回答一些针对贝叶斯方法的“主观性”的质疑,本文提出贝叶斯方法的验证策略,结合实例,对比贝叶斯方法与经典方法,证明在样本容量n≤10的条件下,贝叶斯方法比经典方法更“客观、准确”,更接近实际。(7)将小样本数据下专家判断提取流程及威布尔参数先验分布建立方法与计算后验分布的网格近似方法打包,制作成B/S架构的软件:数控机床贝叶斯可靠性建模与评估系统。
[Abstract]:In recent years, the domestic CNC machine tool products have shown a small batch production, the pace of product updating and replacement is accelerated and the level of reliability is increasing year by year. For domestic high-end CNC machine tools, this trend is particularly obvious, which leads to the reliability field test of the new CNC machine tools, which can not have a large number of similarities as traditional tests. The model test product and the longer test time can not observe the fault as frequently as the traditional test. The above facts show that the number of failures of the CNC machine tool in its reliability field test is reduced and the failure data sample size is inevitable. In the engineering practice, the following problems have appeared, namely: The data sample size produced by some CNC machine tools supported by national science and technology major projects is too small in reliability field test, so that classical statistical methods relying on large sample data can not be used because of too large deviation in reliability modeling and evaluation. This is a small sample problem of CNC machine tools. In the aerospace industry, the small sample problems of CNC machine tools appear late, and the corresponding solutions are not mature. In recent years, some scholars in the CNC machine tool industry have begun to learn from the experience of aerospace, nuclear power and weapon equipment, and use Bias reliability modeling and evaluation method to solve the small sample problem of CNC machine tools. It is a complex repairable system, its reliability model and data form are different from rocket, missile and other system. Therefore, in the process of autonomous exploration of Bayesian Reliability Modeling and evaluation technology by machine tool industry experts, (a) some existing problems need to be improved; (b) some new phenomena which have already appeared, New problems are needed to describe new problems with mathematical models and propose solutions. The above discussion is the content and goal of this paper. (1) the first link of Bias's reliability modeling and evaluation method is to establish the prior distribution of the reliability model parameters. In the field of establishment, most of them have been carried out only briefly to show that the priori distribution is given by the experts based on their experience and the information of similar products. Although this approach is not very good in the field of Bayesian reliability assessment of space products, the parameters of the reliability model of CNC machine tools are not as significant as the success rate of rocket launch. Therefore, the prior distribution of the parameters directly by the expert can not avoid the larger subjective deviation. In fact, the extraction technology of the expert judgment is a special research field. Many scholars have proposed the system and structured experts to judge the extraction process. In this paper, a priori score of Weibull parameters under the small sample data is put forward. The indirect method of establishing cloth consists of two stages: (a) the concept of multi source prior information of CNC machine tools is defined, and the expert judgment extraction process suitable for numerical control machine tools is designed under small sample data, and the quantitative expert judgment results are obtained. (b) a mathematical method of converting expert judgment results into a prior distribution of Weibull parameters is proposed. The method of establishing a priori distribution of Weibull parameters is applied to realize the fusion of multi source prior information and expert experience, and the subjective deviation caused by the direct II test distribution is reduced by experts. (2) the second links of the Bias reliability modeling and evaluation method are the posterior scores for the calculation of the parameters of the reliability model. For the two parameter Weibull distribution, the calculation of this link will encounter the problem of high dimensional integral without analytic solution. It is very difficult to calculate the problem. There are many documents using the Markov Monte Carlo (MCMC, markovchainmontecarlo) algorithm to solve this problem. However, most of the existing literature, despite the reference to the use of the MCMC algorithm, It does not explain which algorithm is used, because the MCMC algorithm is the general name of a class of algorithms, not all MCMC algorithms have the ability to solve the calculation problem of the posterior distribution of the parameters of the reliability model of CNC machine tools. In this paper, the two element Metropolis algorithm for calculating the posterior distribution of the Weibull parameter is independently developed in this paper: MCM A member of the C algorithm family. The parameters of the algorithm are given, such as the proposed distribution, the acceptance probability, etc. the iterative process of the algorithm is given. The matlab program code of the algorithm is given. The parameter estimation and the average fault interval time of the machine tool are calculated with an instance: MTBF (meantimebetweenfailures). (3) some documents are solved by WinBUGS software The calculation of the posterior distribution of the complex reliability model parameters, but few articles introduce the use of WinBUGS software in detail. In fact, using WinBUGS software to solve the small sample problem of CNC machine tools, users need to have a certain Bayesian statistical background, learn some bugs programming language, and master the special description of the non standard distribution of WinBUGS software. In view of the above problems, this paper introduces the steps of the WinBUGS software operation in detail, describes the Bayesian reliability model of CNC machine tools with bugs language, introduces and proves the "zero skill" in describing the non standard distribution. The bugs code is given with an example, and the software operation process is described. Finally, the parameter estimation value is obtained. And the MTBF of the machine tool, and points out that the WinBUGS software uses the slice sampling in the MCMC algorithm family when calculating the posterior distribution. (4) there are common problems in both autonomous development and MCMC algorithm running in WinBUGS software: (a) MCMC algorithm, although high in calculation, can cause the algorithm to produce in random sampling process. The factors of instability and uncertainty and even collapse; (b) the principle of the MCMC algorithm is more complex, and the independent development or use of software is more troublesome. Therefore, the MCMC algorithm family is not conducive to the popularization and application of Bayesian method in the field of numerical control machine tool engineering. The continuous distribution of a priori distribution is discretized, the discrete form of the posterior distribution of parameters and the calculation formula of parameter estimation are derived, and the difficulty in calculating the high dimensional integral is solved. A comparison is made between the estimated value of the parameters and the mtbf. of the machine tool with the grid approximation method, the Metropolis algorithm and the WinBUGS software three. The results show the MT of the three. The error of BF estimation is less than 0.03 hours. It is proved that the accuracy of the proposed grid computing method is not lost to the MCMC algorithm, and the principle is simple and the programming is easy to be realized. It is helpful for the Bayesian Reliability Modeling and evaluation method to be widely used in the reliability engineering field of CNC machine tools. (5) the number of failures of CNC machine tools in reliability test. The reliability modeling and evaluation under zero fault is a new problem, and there is no literature to describe and solve this problem. The problem of zero fault in the products has a long history in other industries, and the corresponding solutions are almost all Bayesian methods. These methods provide a reference for solving the problem of zero fault in CNC machine tools. In view of the above problems, this paper puts forward the data form of the zero fault problem of CNC machine tools, establishes the corresponding Bias statistical model, puts forward the method of establishing the expert judgment extraction process and the prior distribution of Weibull parameters under the zero fault data, and uses the WinBUGS software and the self developed grid approximation method respectively. The parameter estimation and MTBF calculation show that the error of the MTBF estimation obtained by the WinBUGS software and the mesh approximation is less than 1 hours. Again, it is proved that the grid approximation method is simple and easy and the calculation precision is not reduced. (6) in order to answer some questions about the "subjectivity" of Baines method, this paper puts forward shellfish. The validation strategy of leaf method, combining with examples, contrasts Bayes method and classical method, proves that the Bayesian method is more objective and accurate than the classic method under the condition of sample size n less than 10. (7) the method of establishing the extraction process and the prior distribution of Weibull parameters under the small sample data and the distribution of the posterior distribution The grid approximation method is packaged and made into B/S software: Bayesian Reliability Modeling and evaluation system for CNC machine tools.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TG659

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