外文翻译--针对真空树脂灌注机镜头设备建立在自动诊断系统上的模糊数学

1 A Fuzzy Mathematics Based Fault Auto-diagnosis System for Vacuum Resin Shot Dosing Equipment HE Zheng-wen , XU yu , WU Jun School of Management, Xian Jiaotong univervsity, Xian 710049, P.R. China Abstract: On the basic of the analysis of faults and their causes of vacuum resin shot dosing equipment, the fuzzy model of fault diagnosis for the equipment is constructed, and the fuzzy relationship matrix, the symptom fuzzy vector, the fuzzy compound arithmetic operator, and the diagnosis principle of the model are determined. Then the fault auto-diagnosis system for the equipment is designed, and the functions for real-time monitoring its operation condition and for fault auto-diagnosis are realized. Finally, the experiments of fault auto-diagnosis are conducted in practical production and the veracity of the system is verified. Key words: fuzzy model, fault auto-diagnosis system, vacuum resin shot dosing equipment 1 Introduction Vacuum Resin Shot Dosing Equipment (VRSDE) is a key special equipment used to perfuse various kinds of electrical components, such as striking windings of vehicles and motorcycles, transformers, sensors, capacitors and so on (hereafter referred to as “workpieces” ) with epoxy resin. Its function is to purify and to mix epoxy resin (liquid A) with solidifying catalyst (liquid B) under a vacuum condition firstly, and then to perfuse them into workpieces in accurate proportion and quantum, thus finishing epoxy resin perfusion. Similar to most complicated equipment, the fault information environment of VRSDE is a fuzzy one, basically. Beginning with analyzing the relationship of faults and their causes, we construct the mathematical model of faults and their causes, we construct the mathematical model of fault diagnosis for the VRSDE based on fuzzy theory. On 2 the basis of this model we build a fault auto-diagnosis system for the equipment that fulfills the functions of real-time monitoring on the operation condition and fault auto-diagnosis of the equipment. The veracity of the system is verified in practical productions. 2 The main faults and their causes According to the impacts on the quality and the process of perfusion, the main faults of the VRSDE can be classified as the following kinds: proportion fluctuation, insufficient mixture, inadequate purification, leaking from shot mouth, quantum fluctuation, quantum reduction and no liquid shooting out from shot mouth. Our research on the formation mechanism of faults shows that these faults have relations on the following reasons to different extents: uni-direction valve being in malfunction state ,shutting-valve being in malfunction state, the pipe out of the perfusion chamber seeping, the pipe within the perfusion chamber seeping, liquid level in purifying canister being too low, vacuum degree of purifying canister being too low, liquid temperature fluctuation, moving down speed of the cylinder being too low, air pressure being too low, measuring pump wearing and tearing seriously, machining precision of measuring system being too low, proportion being too big or too small and resin containing arenaceous quartz. The correlative degree of faults and their causes can be described by Table 1 qualitatively. Table 1 The correlative degree of main faults and their causes of VRSDE Proportion fluctuation Insufficient mixture Inadequate purification Leakage From shot mouth Quantum fluctuation Quantum reduction No liquid shooting out from the shoot mouth Uni-direction valve being in malfunction state / / / / Shutting-valve being in malfunction state / / / The pipe out of perfusion chamber / 3 seeping The pipe out within perfusion chamber seeping / / / / Liquid level in purifying canister being too low / Vacuum degree of purifying canister being too low / Liquid temperature fluctuation / / Moving down speed of the cylinder being too low / / / / / Air pressure being too low / / / / Measuring pump wearing and tearing seriously / / / Machining precision of measuring system being too low / / / / / Proportion being too big or too small / / / / / Resin containing arenaceous quartz / Note: The number of “ “ indicates the correlative degree of causes and faults. 3 construction of fuzzy model for fault diagnosis We define that the operation condition set of the VRSDE consists of all kinds of faults 4 and is expressed by V: V1 Proportion fluctuation V2 Insufficient mixture V3 Inadequate purification V = V4 = Leakage from shot mouth V5 Quantum fluctuation V6 Quantum reduction V7 No liquid shooting out from shot mouth The symptom set of VRSED is composed of all reasons of faults and defined as U U1 Uni-direction valve being in malfunction state U2 Shutting-valve being in malfunction state U3 The pipe out of the perfusion chamber seeping U4 The pipe within the perfusion chamber seeping U5 Liquid level in purifying canister being too low U6 Vacuum degree of purifying canister being too low U = u7 = Liquid temperature fluctuation U8 Moving down speed of the cylinder being too low U9 Air pressure being too low U10 Measuring pump wearing and tearing seriously U11 Machining precision of measuring system being too low U12 proportion being too big or too small U13 Resin containing arenaceous quartz The fuzzy relationship matrix of operating condition set V and symptom set U is defined as R: r11 r12 . r17 R = r21 r22 . r27 . . . . r13.1 r13.2 r13.4 where rij=uji, 0 rij 1, 1 i 13 , 1 j 7 , rij denotes the correlative degree of operating condition j and symptom i of the VRSDE. Through dealing with the data gathered by sensors , we can obtain symptom fuzzy vector A:A=a1/u1+a2/u2+.+a13/u13=(a1,a2,.,a13) 0 ai 1 i=1,2,.,13 Vector A is the subset of symptom set U and its element ai represents the membership of ui to vector a. Element ai indicates the effect degree of symptom ui on the total symptom of the equipment, or in a common term, signifies whether cause i is serious or not to a certain extent. After symptom fuzzy vector A and fuzzy relationship matrix r are obtained, condition 5 fuzzy vector B can be calculated using the following formula: B= A . R Where “.” Represent fuzzy compound arithmetic operation. Vector B is the subset of symptom set V and can be written as follows: B=b1/v1+b2/v2+.+b7/v7=(b1,b2,.b7) Where 0 =bj a4 Membership of the Pipe within the Perfusion chamber Seeping to the Vector A Absolute difference Between the liquid pressure At the pipe joints and the Vacuum degree within The perfusion chamber(p) Down-Half-T membership function: 1 P a4= 1-e-k(P-) Pi a6 Membership of Vacuum degree of Purifying canisters Being too low to the Vector A Vacuum degree of purifying canisters(Pi) Up-Half-Gauss membership function a6=max(a6i) 0 Pi a6i= 1-e-k(Pi-100)2 Pi a8 Membership of moving down speed of the cylinder being too low to the vector A Moving down speed of the cylinder(x) Down-Half-Trapezia membership function: 1 0 x a8= (r2-x)/(r2-r1) 12 a9 Membership of air Pressure being too Low to the vector A Air pressure (P) Down-Half-Gauss membership function: 1 P a9= e-k(P-5)2 P Table3 Membership determination rules of symptom fuzzy vector As elements whose definition fields are not real number field Element Explanation Determination rules of membership a1 Membership of uni-direction valve being in malfunction state to the vector A Motion precision of uni-direction Valve &0.05mm & 0.05mm a1=0.98 a1=0.00 Motion Synchronization of two uni-direction valves t0.5s 0.1s0.05mm a2=0.96 & 0.05mm a2=0.00 Shutting pressure of shutting-valve P4.8c a7=0.95 2.6c3.6c a7=0.93 1.9cTb4.6c a7=0.98 2.1cTmix 4.6c a7=0.65 Tmix 2.1c a7=0.00 a10 Membership of measuring Pump wearing and tearing Seriously to the vector A Resin containing arenaceous quartz a10=0.15 Resin not containing arenaceous quartz a10=0.00 a11 Membership of machining Precision of measuring system Being too low to the vector A Operation duration of VRSDE being within 2 years a11=0.08 Operation duration of VRSDE being within 2-4 years a11=0.13 Operation duration of VRSDE exceeding 4 years a11=0.25 a12 Membership of the proportion Being too big or too small to the A:B=100:100 a12=0.08 A:B=100:80 a12=0.09 9 Vector A A:B=100:34 a12=0.34 a13 Membership of resin containing Arenaceous quartz to the vector Resin containing arenaceous quartz a13=0.80 Resin not containing arenaceous quartz a13=0.00 3.4 Determination of fault diagnosis principle In order to identify the operation conditions of the VRSDE accurately and to offer sufficient information related to the faults, we define two threshold valves, 1 and2 (12), and classify its operation states as the following three kinds: Normal state , pre-warning state and malfunction state. The principle of fault fuzzy diagnosis can be described as follows: When max (bj) 1 ,VRSDE is in pre-warning state； When1 2,VRSDE is in malfunction state. When the equipment is in a pre-warning or malfunction state ,the signals of pre-warning or warning are sent out to warn the operators and the fault kinds and their relative information are provided by the system at the same time. The valve of1 and2 can determination by iterative experiments and are given ultimately as follows: 1=0.50, 2=0.80 4 Fault auto-diagnosis experiments After constructing the mathematical model of fault diagnosis, we establish the fault auto-diagnosis system for the VRSDE by utilizing hardware such as sensors, data gathering circuits, computer, warning circuits and corresponding software, thus realizing the function of monitoring on the equipments operation condition, fault diagnosis, giving alarms, showing the relative information, etc. The mathematical model of the fault auto-diagnosis system for the VRSDE is constructed on the basis of experiences accumulates by a great number of experiments, so we have to carry out experiments to verify its correctness. The method of the experiments can be described as follows: during the practical operation of the equipment, if the system gives an alarm and indicates that there is a certain fault, we may carry out a special test to check whether the fault exists or not, thus the veracity of the system is proved. In addition , we may examine the working parameters of the VRSDE periodically so as to ascertain whether there exists problems of failing to report faults or not. 10 During half a year from May 2000 to November 2000, we carried out a series of experiments of fault diagnosis with a VCD-M3 VRSDE in Northwestern Forest Machine Limited Company and obtained the data shown in Table 4.From these data, we can see that the correct percentage of that diagnosis has reached 93.3% and the design requirements of the system have been met, basically. Then the correctness of the mathematical model of fault diagnosis can be validated indirectly by this result too. Within the table, there is a wrong diagnosis happening on July 31st, 2000. The reason for this mistake is that the lock nut of the shutting-valves piston was vibrated off and it choked up the piston and made it unable to move. The occurrence probability of this phenomenon was very little and it could be regard as a contingency. Besides the facts above, we still tested all working parameters of the VRSDE once a week and did not find any problems of failing to report faults during this period. Table 4 The data of fault auto-diagnosis experiments Warning date Information of operation condition Information of causes(ai) Correctness of diagnosis Condition fuzzy vector B Faults information May 11th (0.90 0.46 0.18 0.31 0.85 0.25 0.34) Proportion fluctuation, Quantum fluctuation The steel ball within uni-direction valve A being underlain up by the deposits of liquid A(a1 =0.98) Correct May 26th 0.93 0.42 0.96 0.68 0.92 0.95 0.36 Inadequate purification, Quantum reduction, Proportion fluctuation, Quantum fluctuation The liquid level in purifying canister A being too low (a5=1.00) Correct June 10th 0.81 0.41 0.18 0.33 0.72 0.29 0.36 Proportion fluctuation There being a time difference of the motion between two uni-direction valves(a1=0.85) Correct June 15th 0.23 0.42 0.20 0.81 0.73 0.34 0.36 Leakage from shot mouth The pipe within the perfusion chamber seeping (a4=0.91) Correct June 27th 0.32 0.46 0.90 0.65 0.66 0.44 0.37 Inadequate purification The vacuum degree of purifying canister A being too low (a6=0,94) Correct July 6th 0.23 0.42 0.20 0.91 0.91 0.94 0.78 0.56 Leakage from shot mouth Quantum fluctuation There existing a motion error of shutting-valve (a2=0.96) Correct July 13th 0.24 0.86 0.18 0.32 0.36 0.28 0.37 Insufficient mixture The pressing down speed of the cylinder being too slow (a8=0.93) Correct July 28th 0.42 0.41 0.91 0.63 0.65 0.45 0.33 Inadequate purification The vacuum degree of purifying canister B being too low (a6=0.94) Correct 11 July 31st 0.21 0.40 0.18 0.87 0.95 0.78 0.76 No liquid shooting out from shot mouth Shutting-valve not moving (a2=1.00) Wrong August 9th 0.93 0.43 0.22 0.30 0.87 0.32 0.27 Proportion fluctuation, Quantum fluctuation There existing a motion error of uni-direction valves A(a1=0.85) Correct August 21st 0.25 0.46 0.22 0.87 0.81 0.33 0.35 Leakage from shot mouth Quantum fluctuation The pipe within the perfusion chamber seeping (a4=0.94) Correct August 30th 0.91 0.50 0.93 0.72 0.94 0.91 0.33 Inadequate purification, Quantum reduction, Proportion fluctuation, Quantum fluctuation The liquid level in purifying canister B being too low (a5=1.00) Correct September 6th 0.80 0.30 0.94 0.68 0.88 0.45 0.36 Proportion fluctuation, Inadequate purification, Quantum fluctuation The pipe out of perfusion chamber seeping (a3=0.95) Correct October 5th 0.26 0.43 0.22 0.61 0.81 0.67 0.46 Quantum fluctuation The pressure of shutting-valve being too low (a2=0.75) Correct November 14th 0.27 0.47 0.20 0.80 0.72 0.35 0.38 Quantum fluctuation The pipe within the perfusion chamber seeping (a4=0.89) Correct 5 Conclusion The fault auto-diagnosis model for the VRSDE is constructed based on fuzzy mathematics, and the function of real-time monitoring on operation condition and auto-diagnosis faults of the equipment are realized by using the fault auto-diagnosis system for the VRSDE which is formed on the basis of the mathematical model. The application effects of the system show that the system attains the design purposed and meets customers expectations satisfactorily. The mathematical model of fault diagnosis is involved with a great deal of subjectivity for its many parameters； threshold valves and membership functions are all determined by experiences. As a result, it has to be verified and adjusted through repetitious experiments so as to coincide with the realities of the VRSDE. References 1 A.H. Zhang, Technologies of monitoring on operation condition and fault diagnosis for mechatronic equipment. Northwestern Poly technical University Press, 1995 (In Chinese) 2. Z.W. He, Primary research on the fault auto-diagnosis system for VRSDE: (Mastership Dissertation). Xian University of Technology, 2001(In Chinese) 3. A.P. Chen and C.C. Lin, Fuzzy approaches for fault diagnosis of trans formers. 12 Fuzzy Sets and Systems, Vol.118, pp.139-151, 2001 Brief Biographies HE Zheng-wen is now a Ph. D candidate in the school of Management of Xian Jiaotong University, his research interests include industry engineering and ERP. XU Yu is now a professor in the School of Management of Xian Jiaotong University, her research interests include integrated management and optimization of enterprises, and optimal collocation of science and technology resources. WU Jun is now a Ph. D candidate in the School of Management of Xian Jiantong University, his research interests include integrated management optimization of enterprises, and financial engineering. 针对真空树脂灌注机镜头 设备建立在自动诊断系统上的模糊数学 何政文 许钰 吴俊 西安交通大学管理学院，中国西安 710049 摘要 ：在分析真空树脂镜头药设备的基础之上，模糊数学模型已经建立起来，并且 模糊关系矩阵，症状模糊向量，模糊复合运算操作，模型的诊断原则已经确定。接着，设备的错误自动诊断系统也被设计完成，实时监控状态的功能和故障自动诊断可以得以实现。最后，故障自动诊断在实际生产下完成实验并且系统的真实性得到验证。 关键词 ：模糊模型，故障自动检测系统，真空树脂灌注机设备 1 引言 真空树脂灌注机设备（ VRSDE）特别主 要是用于各种电器元件的灌注，比如汽车、摩托车的打绕组，变压器，传感器，电容器等配有环氧树脂的器件（一下简称“工件”）。它的作用首先是净化和把环氧树脂（液态甲）和固态催化剂（液态乙）在真空下合成，接着把他们按照精确的比例和量注射到工件中，这样就完成了环形树脂的注射。 基本上，和大多数复杂的设备一样， VRSDE 的错误信息环境是模糊的。从分析错误和他们起因的关系开始，我们可以建立错误和起因之间的数学模型，同样我们可以在模糊原理的基础上对 VRSDE 建立数学模型 。在这个模型基础上我们建立了设备的故障自动检测系统已达 到实时监控运行状态和设备故障诊断的功能 .系统的真实性在实际操作中得到验证 . 2 主要的错误和他们的起因 13 根据注射质量和过程的影响 ,VRSDE 的主要错误可以归结成以下几种 :比列的浮动 ,不充分混合 ,不够净化 ,注射口的泄露 ,量子的不稳定 ,量子的减少和没有液体从射击口出来 .我们在对错误形成机理的研究表明在不同程度上错误的发生和以下的原因有关 : 单方向阀处于故障状态中，关阀处于故障状态中，注射器喷洒时液体的泄露，注射器内的液体渗漏，用于净化的容器内的液位或真空过低，液体温度的不稳定，缸向下移动的速度过低，气压过低，计量 泵 磨损严重，测量系统的机器精度过低，比例过大或过小并且树脂含有石英。错误及其原因的相关程度可以定性的描述成表 1。 表 1 VRSDE 的主要错误及其原因的相对程度 比例 浮动 不充分混 合 不精确净 化 喷射嘴的 泄露 量子的波 动 量子减少 喷射嘴中没有液体喷出 单方向阀处于故障状态中 / / / / 关阀处于故障状态中 / / / 喷射厅中的液体泄露 / 注射器内的液体渗漏 / / / / 用于净化的容器内的液位过低 / 14 用于净化的容器内的真空过低 / 液体温度的不稳定 / / 缸向下运动的速度太低 / / / / / 气体压力太低 / / / / 计量 泵磨损严重 / / / 测量系统的机器精度过低 / / / / / 比例过大或过小 / / / / / 树脂含有石英 / 说明：“ ”的数量表示错误及其原因的相对度 3 错误诊断的模糊模型的结构 我们确定 了 VRSDE 运行状态中的 各种故障 ，用 V 来 发表 ： 15 V1 比例浮动 V2 不充分混合 V3 不够净化 V = V4 = 喷射嘴泄露 V5 量子浮动 V6 量子减少 V7 没有液体从喷射嘴喷出 而引起各种错误症状的原 因，我们用 U 表示： U1 单方向阀故障状态 U2 闭阀故障状态 U3 喷射厅的液体泄露 U4 注射器内的液体泄露 U5 用于净化的容器内的液位过低 U6 用于净化的容器内的真空过低 U = u7 = 液体温度不稳定 U8 缸向下运动 的速度太低 U9 气体压力太低 U10 计量 泵磨损严重 U11 测量系统的机器精度过低 U12 比例过大或过小 U13 树脂含有石英 运行状态 U和症状 V 之间的模糊关系可以用矩阵 R 来表示 : r11 r12 . r17 R = r21 r22 . r27 . . . . r13.1 r13.2 r13.4 当 rij=uji, 0 rij 1, 1 i 13 , 1 j 7 时 , rij 定义为 VRSDE 的运行状态 j和症状 i 的相对度 . 通过对传感器数据的处理 ,我们可以得到症状模糊矩阵 : A:A=a1/u1+a2/u2+.+a13/u13=(a1,a2,.,a13) 0 ai 1 i=1,2,.,13 A是症状 U的一个子集 ,并且它的元素 ai代表 u到集合 a的映射 .元素 ai表示症状 16 ui在总的症状中的有效程度 ,或者从某种意义上讲代表原因 i严重与否 . 在模糊矩阵 A 和模糊关系矩阵 r 得到之后 ,状态模糊矩阵 B 可以从下面的公式算得 . B=A*R “ *”代表模糊复合运算 .矩阵 B 是症状 V 的一个子集 ,可由下列公式运算得到 : B=b1/v1+b2/v2+.+b7/v7=(b1,b2,.b7) 公式中 0 =bj a4 矩阵 A 中 ,表示在注射厅内泄露的元素 在注射厅内的真空度和和管子接头处液体压力相差太大 (p) Down-Half-T 元素数值 1 P a4= 1-e-k( P- ) Pi a6 矩阵 A 中 , 表示用于净化的容器内的真空度太低的元素 用于净化的容器内的真 空度 (Pi) Up-Half-Gauss 元素数值 a6=max(a6i) 0 Pi a6i= 1-e-k(Pi-100)2 Pi 18 a8 矩阵 A 中 , 表示缸向下运动的速度太低的元素 缸向下运动的速度 (x) Down-Half-Trapezia 元素数值 1 0 x a8= (r2-x)/(r2-r1) 1 2 a9 矩阵 A 中 , 表示气体压力过低的元素 气体压力 (P) Down-Half-Gauss 元素数值 1 P a9= e-k(P-5)2 P 表 3 症状模糊矩阵 A 中定义域不是在实数范围的元素的确定 元素 解释 元素的确定法则 a1 矩阵 A 中 ,表示单方向阀处于故障状态的元素 单方向阀的运动精度 &0.05mm & 0.05mm a1=0.98 a1=0.00 两个单方向罚的运动情况 t0.5s 0.1s0.05mm a2=0.96 & 0.05mm a2=0.00 闭阀关闭时的压力 P4.8 c a7=0.95 2.6 c3.6 c a7=0.93 19 不稳定时 1.9 cTb4.6 c a7=0.98 2.1 cTmix4.6 c a7=0.65 Tmix 2.1 c a7=0.00 a10 矩阵 A 中 ,表示计量泵磨损严重的元素 树脂含有石英 a10=0.15 树脂不含有石英 a10=0.00 a11 矩阵 A 中 ,表示测量系统的机器精度过低的元素 在 2 年内 VRSDE 的操作状态 a11=0.08 在 2-4 年 VRSDE 的操作状态 a11=0.13 超过 4 年 VRSDE 的操作状态 a11=0.25 a12 矩阵 A 中 ,表示比例过大或过小的元素 A:B=100:100 a12=0.08 A:B=100:80 a12=0.09 A:B=100:34 a12=0.34 a13 矩阵 A 中 ,表示树脂中含有石英的元素 树脂含有石英 a13=0.80 树脂不含有石英 a13=0.00 3 4 错误诊断原则的确定 为了准确的鉴定的 VRSDE 操作状态并且提供和错误有关的足够多的信 息 ,我们定义了两个值 1 和 2 ( 1 2),并把它的工作状态归结为以下三类 :正常状态 ,提前警告状态和故障状态 .错误模糊诊断的原则可以描述成 : 当 max (bj) 1时 , VRSDE 处于正常状态 20 当 1 2时 .VRSDE 处于故障状态 当设备处于提前警告状态或故障状态时 ,会发出预警信号或警告信号来警告操作同时系统会提供错误及其相关信息 .实验表明 1 和 2的最大值如下 : 1 =0.50 2 =0.80 4 错误自动诊断实验 在建立错误诊断的数学模型之后 ,我们利用诸如像传感器这样的硬件 ,数据采集器 ,电脑 ,报警线路和相关的软件建立了 VRSDE 的错误自动诊断系统 ,这样就实现了对设备操作条件 ,错误诊断 ,相关错误的监控并且显示出相关的信息等 . 错误自动诊断系统的数学模型建立在无数次实验得来的经验的基础上 ,因此我们必须进行实验来证实其准确性 .实验的方法可以描述成如下 :通过对设备实际操作 ,如果系统给出一个警告并且暗示设备存在错误 ,我们 可以进行特殊的试验来检测错误存在与否 ,这样可以保证系统准确无误 .此外 ,