本文選題：數(shù)控機(jī)床 + 貝葉斯�。� 參考：《吉林大學(xué)》2015年博士論文

【摘要】：近年來,國產(chǎn)數(shù)控機(jī)床產(chǎn)品呈現(xiàn)出小批量生產(chǎn)、產(chǎn)品更新?lián)Q代節(jié)奏加快以及可靠性水平逐年升高的趨勢。對于國產(chǎn)高檔數(shù)控機(jī)床產(chǎn)品來說,這種趨勢尤為明顯,從而導(dǎo)致新型數(shù)控機(jī)床可靠性現(xiàn)場試驗(yàn)不能像傳統(tǒng)的試驗(yàn)?zāi)菢泳邆浯罅康耐吞?hào)被測產(chǎn)品和較長的試驗(yàn)時(shí)間,也不能像傳統(tǒng)的試驗(yàn)?zāi)菢宇l繁地觀測到故障。以上事實(shí)表明:數(shù)控機(jī)床在其可靠性現(xiàn)場試驗(yàn)中故障發(fā)生次數(shù)減少,從而故障數(shù)據(jù)樣本容量減小是不可避免的趨勢。在工程實(shí)踐中已經(jīng)出現(xiàn)了以下問題,即:國家科技重大專項(xiàng)支持研發(fā)的某些數(shù)控機(jī)床在可靠性現(xiàn)場試驗(yàn)中產(chǎn)生的數(shù)據(jù)樣本容量過小,以至于在進(jìn)行可靠性建模與評(píng)估時(shí),依賴于大樣本數(shù)據(jù)的經(jīng)典統(tǒng)計(jì)學(xué)方法因偏差過大而無法使用。此即為數(shù)控機(jī)床的小樣本問題。相比于航空航天等行業(yè),數(shù)控機(jī)床的小樣本問題出現(xiàn)較晚,相應(yīng)的解決方法也不成熟。近年來,數(shù)控機(jī)床行業(yè)的一些學(xué)者開始借鑒航空航天、核電和武器裝備領(lǐng)域的經(jīng)驗(yàn),采用貝葉斯可靠性建模與評(píng)估方法解決數(shù)控機(jī)床的小樣本問題。由于數(shù)控機(jī)床是復(fù)雜的可修復(fù)系統(tǒng),其可靠性模型與數(shù)據(jù)形式均與火箭、導(dǎo)彈等成/敗型系統(tǒng)不同。因此,機(jī)床行業(yè)專家在自主探索數(shù)控機(jī)床貝葉斯可靠性建模與評(píng)估技術(shù)的過程中:(a)一些已有問題的解決方法尚需完善;(b)針對一些已經(jīng)出現(xiàn)的新現(xiàn)象,需要提出新問題、以數(shù)學(xué)模型描述新問題并提出相應(yīng)的解決方案。以上討論即為本文的研究內(nèi)容與目標(biāo)。具體介紹如下:(1)貝葉斯可靠性建模與評(píng)估方法的第一個(gè)環(huán)節(jié)為建立可靠性模型參數(shù)的先驗(yàn)分布。而已有的相關(guān)文獻(xiàn)在先驗(yàn)分布的建立方面,大多數(shù)一筆帶過,僅簡要說明先驗(yàn)分布是由專家根據(jù)其經(jīng)驗(yàn)并結(jié)合類似產(chǎn)品的信息給出的。盡管在航天產(chǎn)品貝葉斯可靠性評(píng)估領(lǐng)域,該做法無可厚非,但數(shù)控機(jī)床可靠性模型參數(shù)不像火箭發(fā)射成功率那樣有明顯的物理意義,因而,由專家直接給出參數(shù)的先驗(yàn)分布無法避免較大的主觀偏差。實(shí)際上,專家判斷的提取技術(shù)是一個(gè)專門的研究領(lǐng)域,許多學(xué)者已經(jīng)提出了系統(tǒng)、結(jié)構(gòu)化的專家判斷提取流程。本文針對以上問題提出了小樣本數(shù)據(jù)下威布爾參數(shù)先驗(yàn)分布的間接建立方法,包含兩個(gè)階段:(a)定義了數(shù)控機(jī)床的多源先驗(yàn)信息等概念,設(shè)計(jì)了小樣本數(shù)據(jù)下適合數(shù)控機(jī)床的專家判斷提取流程,得到了量化的專家判斷結(jié)果;(b)提出了將專家判斷結(jié)果轉(zhuǎn)換為威布爾參數(shù)先驗(yàn)分布的數(shù)學(xué)方法。結(jié)合實(shí)例,應(yīng)用了所提出的威布爾參數(shù)先驗(yàn)分布的建立方法,實(shí)現(xiàn)了多源先驗(yàn)信息與專家經(jīng)驗(yàn)的融合,減少了因?qū)＜抑苯咏o出先ii驗(yàn)分布而帶來的主觀偏差。(2)貝葉斯可靠性建模與評(píng)估方法的第二個(gè)環(huán)節(jié)為計(jì)算可靠性模型參數(shù)的后驗(yàn)分布。對于兩參數(shù)威布爾分布來說,該環(huán)節(jié)的計(jì)算會(huì)遇到無解析解的高維積分問題,計(jì)算尤為困難。目前有許多文獻(xiàn)采用馬爾科夫鏈蒙特卡羅(mcmc,markovchainmontecarlo)算法來解決這一問題。然而,大多數(shù)已有的文獻(xiàn)盡管提及采用了mcmc算法,卻并未說明具體采用的是哪一種算法,因?yàn)閙cmc算法是一類算法的統(tǒng)稱,并非所有的mcmc算法都有能力解決數(shù)控機(jī)床可靠性模型參數(shù)后驗(yàn)分布的計(jì)算問題。針對以上問題,本文自主開發(fā)了用于計(jì)算威布爾參數(shù)后驗(yàn)分布的二元metropolis算法:mcmc算法族中的一員。給出了算法的各項(xiàng)參數(shù)如建議分布、接受概率等;給出了算法的迭代流程;給出了算法的matlab程序代碼。結(jié)合實(shí)例計(jì)算了參數(shù)估計(jì)值和機(jī)床的平均故障間隔時(shí)間:mtbf(meantimebetweenfailures)。(3)一些文獻(xiàn)采用winbugs軟件來解決復(fù)雜的可靠性模型參數(shù)后驗(yàn)分布的計(jì)算,但少有文章詳細(xì)介紹winbugs軟件的使用。實(shí)際上,用winbugs軟件解決數(shù)控機(jī)床的小樣本問題,使用者需要具備一定的貝葉斯統(tǒng)計(jì)學(xué)背景、學(xué)習(xí)一些bugs編程語言、掌握winbugs軟件特有的描述非標(biāo)準(zhǔn)分布的編程技巧。針對以上問題,本文詳細(xì)介紹了winbugs軟件操作的各個(gè)步驟;用bugs語言描述了數(shù)控機(jī)床貝葉斯可靠性模型;介紹并證明了描述非標(biāo)準(zhǔn)分布的“零技巧”。結(jié)合實(shí)例給出了bugs代碼,描述了軟件操作過程。最后得到了參數(shù)估計(jì)值和機(jī)床的mtbf,并指出winbugs軟件在計(jì)算后驗(yàn)分布時(shí)采用的是mcmc算法族中的slice抽樣。(4)無論是自主開發(fā)還是在winbugs軟件中運(yùn)行的mcmc算法,都存在共同的問題:(a)mcmc算法雖然在計(jì)算上精度高,但非標(biāo)準(zhǔn)分布會(huì)導(dǎo)致算法在隨機(jī)抽樣過程產(chǎn)生不穩(wěn)定和不確定的因素,甚至崩潰;(b)mcmc算法的原理較為復(fù)雜,自主開發(fā)或使用軟件均比較麻煩。因此,mcmc算法族并不利于貝葉斯方法在數(shù)控機(jī)床工程領(lǐng)域的普及應(yīng)用。針對以上問題,本文采用網(wǎng)格近似法,定義了參數(shù)的概率質(zhì)量函數(shù),將連續(xù)的先驗(yàn)分布離散化,推導(dǎo)了參數(shù)的離散形式的后驗(yàn)分布以及參數(shù)估計(jì)值的計(jì)算公式,解決了高維積分的計(jì)算困難。結(jié)合實(shí)例得到了參數(shù)估計(jì)值和機(jī)床的mtbf。將網(wǎng)格近似法、metropolis算法和winbugs軟件三者進(jìn)行對比,結(jié)果表明三者的mtbf估計(jì)值誤差小于0.03小時(shí)。證明自主提出的網(wǎng)格計(jì)算方法計(jì)算精度不輸于mcmc算法,且原理簡單,編程容易實(shí)現(xiàn),有利于貝葉斯可靠性建模與評(píng)估方法在數(shù)控機(jī)床可靠性工程領(lǐng)域的廣泛應(yīng)用。(5)數(shù)控機(jī)床在可靠性試驗(yàn)中發(fā)生故障的次數(shù)有可能為零,在零故障下的可靠性建模與評(píng)估是一個(gè)新問題,且尚未發(fā)現(xiàn)有文獻(xiàn)描述并解決這個(gè)問題。產(chǎn)品的零故障問題在其他行業(yè)由來已久,且相應(yīng)的解決方法幾乎都是貝葉斯方法,這些方法為解決數(shù)控機(jī)床的零故障問題提供了借鑒。針對以上問題,本文提出了數(shù)控機(jī)床零故障問題的數(shù)據(jù)形式,建立了相應(yīng)的貝葉斯統(tǒng)計(jì)學(xué)模型,提出了零故障數(shù)據(jù)下的專家判斷提取流程及威布爾參數(shù)先驗(yàn)分布的建立方法。結(jié)合實(shí)例,分別利用WinBUGS軟件和自主開發(fā)的網(wǎng)格近似法進(jìn)行了參數(shù)估計(jì)和MTBF計(jì)算。結(jié)果表明:由WinBUGS軟件和網(wǎng)格近似法得到的MTBF估計(jì)值的誤差小于1小時(shí)。再次證明網(wǎng)格近似法簡明易行且計(jì)算精度不降低的特點(diǎn),適合工程應(yīng)用。(6)為了回答一些針對貝葉斯方法的“主觀性”的質(zhì)疑,本文提出貝葉斯方法的驗(yàn)證策略,結(jié)合實(shí)例,對比貝葉斯方法與經(jīng)典方法,證明在樣本容量n≤10的條件下,貝葉斯方法比經(jīng)典方法更“客觀、準(zhǔn)確”,更接近實(shí)際。(7)將小樣本數(shù)據(jù)下專家判斷提取流程及威布爾參數(shù)先驗(yàn)分布建立方法與計(jì)算后驗(yàn)分布的網(wǎng)格近似方法打包,制作成B/S架構(gòu)的軟件:數(shù)控機(jī)床貝葉斯可靠性建模與評(píng)估系統(tǒng)。
[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.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TG659

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