机械毕业设计115英文翻译外文文献翻译201
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附录 附录 1 An Improved Rough Set Approach to Design of Gating Scheme for Injection Moulding F. Shi,1 Z. L. Lou,1 J. G. Lu2 and Y. Q. Zhang1 1Department of Plasticity Engineering, Shanghai Jiaotong University, P. R. China; and 2Center of CAD, Nanjing University of Chemical Technology, P. R. China The gate is one of the most important functional structures in an injection mould, as it has a direct influence on the quality of the injection products. The design of a gating scheme includes the selectionof the types of gate and calculation of the sizes and determination of the location, which depends heavily on prior experience and knowledge and involves a trial-and-error process. Due to the vagueness and uncertainty in the design of a gating scheme, classical rough set theory is not effective. In this paper, a fuzzy rough set model is proposed, which is not based on equivalent relationships but on fuzzy similarity relationships. An inductive learning algorithm based on the fuzzy rough set model (FRILA) is then presented. Compared to decision tree algorithms, the proposed algorithm can generate fewer classification rules; moreover, the generated rules are more concise. Finally, an intelligent prototype system for the design of a gating scheme based on an induced fuzzy knowledge base is developed. An illustrative example proves the effectiveness of the proposed method. Keywords: Fuzzy rough set; Gating scheme; Injection mold; Intelligent design; Knowledge acquisition 1. Introduction The manufacturing industry for plastic products has been growing rapidly in recent years, and plastics are used widely to substitute for metals. The injection moulding process is the most popular moulding process for making thermoplastic parts. The feeding system, which is one of the important functional structures, comprises a sprue, a primary runner, a secondary runner and a gate. The molten plastic flows from the machine nozzle through the sprue and runner system and into the cavities through the gate. Acting as the connection between the runner and the cavity, the gate can influence directly the mould venting, the occurrence of jetting, the location of weld lines, and warpage, shrinkage and residual stresses. Hence, the gate design is important for assuring the quality of the mould. The design of a gate includes the selection of the type of gate, calculation of the size and determination of the location. And the design of a gate is based on the experience and knowledge of the designers. The determinations of the location and sizes are made based on a ntstrial-and-error process. In recent years, a feature-modelling environment and intelligent technology have been introduced for gate design. Lee and Kim investigated gate locations using the evaluation criteria of warpage, weld lines and izod impact strength. A local search was used to determine the nodes of the location of the gate 1. Saxena and Irani proposed a frame for a non-manifoldtopology-based environment. A prototype system for gate location design was developed. The criteria for evaluation were based on geometry-related parameters 2. Lin selected the injection location and size of the gate as the major control parameters, and chose the product performance (deformation) as the optimising parameter. Combining the technologies of abductive networks and simulation annealing optimisation algorithms, the optimal model for the location and size of the gate was constructed 3,4. Zhou et al. established a rule set for determining the location of the gate based on analysis of the plastic parts. The location of the gate was determined through reasoning with rules 5. Pandelidis et al. developed a system which can optimise gate location based on the initial gating plans. The system used MOLDFLOW software for flow analysis, and controlled the temperature differential and the number of elements overpacked with an optimisation strategy 6. Deng used ID3 and its modified algorithms to generate the rule set for the selection of the gate types 7. However, there are many fuzzy or vague attributes in the selection of the types, such as the attribute of loss of pressure that has two fuzzy linguistic variables i.e. can be high and must be low. The ID3 algorithms cannot deal with fuzzy or “noise” information efficiently. It is also difficult to control the size of the decision tree extracted by the algorithms and sometimes very large trees are generated, making comprehensibility difficult 7,8. Rough set theory provides a new mathematical approach to vague and uncertain data analysis 9,10. This paper introduces the theory of rough sets for the design of a gating scheme. The selection of the type of gate is based on the theory of rough sets. Considering the limitations of rough sets, this paper proposes an improved approach based on rough set theory for the design of the gating scheme. The improved rough set approach to the scheme design will be given first. A fuzzy rough-set-based inductive learning algorithm (FRILA), which is applied in the improved approach, will then be presented. An example of the design of a gate will finally be given. Table 1. Classication criteria. Condition attributes Fuzzy linguistic variables Style of plastic parts (p) (Deep, Middle, Shallow) Shell, (Deep, Middle, Shallow) Tube, (Deep, Middle, Shallow) Ring ntsNumber of cavities (n) Single-cavity, Multi-cavity Loss of pressure (l) Can be high, Must be low Condition of separating gate from parts (q) Must be easy, Not request specially Machining performance (m) Must be easy, Not request specially 2. A Rough Set Approach to Gating Scheme Design 2.1 Design of the Gating Scheme The model of the gating scheme design can be described as follows. A decision table with 4-tuples can be represented as T = （ U, C, D, T） . where U is the universe. C = C1, C2, , Ck is the set of condition attributes, each of which measures some important feature of an object in the universe U. T(Ck) = Tk 1,T2k ,.,TkSk is the set of discrete linguistic terms. In other words, T(Ck)is the value set of the condition attributes. D = D1, D2, , Dl is the set of decision attributes, that is, each object in the universe is classified by the set D. Generally, the condition attributes can be classified as five sets, including style of plastic parts, number of cavities, loss of pressure, condition of separating gate from parts and machine performance. The details of the five condition attributes and corresponding variables of the fuzzy linguistic are shown in Table 1. From the table, it can be seen that most of the attributes are vague since they represent a human perception and desire. For instance, shell, tube and ring are selected for the classification of plastic parts and their fuzzy linguistic values are “deep”, “middle” and “shallow”, respectively. For the attribute loss of pressure, “can be high” and “must be low” are selected to approximate the fuzzy attribute. A fuzzy rule for gating scheme design can be written in the following form: IF (C1 is T1 i1) AND (Ck is Tik) THEN (DisDj) (1) where Tkik is the linguistic term of condition attribute Ck, and Dj is a class term of the decision attribute D. Fuzzy rules with the form of Eq. (1) are used to perform min-max fuzzy inference. Let ck be the membership value of an object in Tk and d be the forecast value of Dj, where d = ik min(ck) and min is the minimum operator. If two or more rules have the sameconclusion, the conclusion with the largest value of d, which is also named the certainty factor is chosen. For the problem of the gating schemedesign, a fuzzy design rule can be described as follows. IF (Type of plastic part = middle shell) AND (Number of cavities = single) AND (Condition of separating gate from part = not request especially)(2) ntsTHEN (Gating scheme = straight gate) CF = 0.825 From the above rule, the gating scheme of the straight gate will be selected is s with a certainty factor of 0.825, if the type of part is middle shell and the number of cavities is single and the condition of separating gate from part is not required. The above is just like human language and is easy to understand. 2.2 Basic Concepts of Rough Sets In recent years, the rough set (RS) theory, proposed by Pawlak, has been attracting the attention of the researchers. The basic idea of RS is to classify the objects of interest into similarity classes (equivalent classes) containing indiscernible objects via the analysis of attribute dependency and attribute reduction. The rule induction from the original data model is data-driven without any additional assumptions. Rough sets have been applied in medical diagnosis, pattern recognition, machine learning, and expert systems 10,11. A decision table with a 4-tuple can be represented as T = , where U is the universe, , C and D are the sets of condition and decision attributes, respectively, V is the value set of the attribute a in A, and f is an information function. Assuming a subset of the set of attributes, two objects x and y in U are indiscernible with respect to P if and only if , .The indiscernibility relation is written as IND(P). U/IND(P) is used to denote the partition of U given the indiscernibility relation IND(P). A rough set approximates traditional sets by a pair of sets, which are the lower and the upper approximations of the sets. The lower and upper approximations of a set Y . U given an equivalence relation IND(P) are defined as follows: The definition of the lower approximation of a set involves an inclusion relation whereby the objects in an equivalence class of the attributes are entirely contained in the equivalence class for the decision category. This is the case of a perfect or unambiguous classification. For the upper approximation, the objects are possibly classified using the information in attribute set P. Attribute reduction is important for rough set theory. Based on the above definitions, the concept of reduction, denoted by RED(P), is defined as follows: Q . P is a reduction of P if and only if IND(P)=IND(Q). 2.3 An Improved Rough Set Approach In the design of the gating scheme, it is crucial to acquire the fuzzy rules efficiently. ntsKnowledge acquisition is the bottleneck. A rough set is applied to solve the problem for the design of the gating scheme. The block diagram for the design of the gating scheme with the rough set is shown in Fig. 1. The case library is obtained from the experience and knowledge of experts and some reference books. A rough-set-based inductive learning algorithm is adopted to identify the hidden patterns and relationships in the case library and acquire knowledge. The knowledge is represented as a set of fuzzy “ifThen” rules. During the design stage, the system employs the fuzzy rules to perform fuzzy inference according to the design requirements. Then the appropriate gating scheme can be obtained. Although the rough set is efficient for knowledge acquisition, there are some limitations for the application of the original rough set in the selection of the gating scheme. 1. The original rough set is efficient for problems with discrete attributes, but it cannot deal with the fuzzy attributes efficiently. For fuzzy attributes, the traditional decision table is normally transformed into a binary table by obtaining Fig. 1. Block diagram of the gating scheme design with RS. the -cut set of the fuzzy set. Obviously, there is no crisp boundary between the fuzzy attributes. 2. The original rough set is based on the indiscernibility relation. The universe is classified into a set of equivalent classes with the indiscernibility relation. The lower and upper approximations are generated in terms of the equivalent classes. In practice, the original rough set classifies the knowledge too fussily, which leads to the complexity of the problem. The fuzzy set and rough set theories are generalisations of classical set theory for modelling vagueness and uncertainty. Pawlak and Dubois proposed that the two theories were not competitive but complementary 11,16. Both of the theories are usually applied to model different types of uncertainty. The rough set theory takes into consideration the indiscernibility between objects, whereas the fuzzy set theory deals with the ill-definition of the boundary of a class through the membership functions. The attributes can be presented by fuzzy variables, facilitating the modelling of the inherent uncertainty of the knowledge domain. It is possible to combine the two theories to solve the design problem of the gating scheme better. A fuzzy rough set model is presented based on the extension of the classical rough set theory. The continuous attributes are fuzzified with the proper fuzzy membership functions. The indiscernibility relation is generalised to the fuzzy similarity relation. An inductive learning algorithm based on fuzzy rough set model (FRILA) is then proposed. The fuzzy design rules are extracted by the proposed FRILA. The gate design scheme is then obtained after fuzzy inference. The detailed implementation will be discussed in the next section. nts Fig. 1. Block diagram of the gating scheme design with RS. 3. Implementation of FRILA A fuzzy rough-set-based inductive learning algorithm consists of three steps. These steps are the fuzzification of the attributes, attribute reduction based on the fuzzy similarity relation and fuzzy rule induction. 3.1 Fuzzifying the Attributes Generally, there are some fuzzy attributes in the decision table, such as loss of pressure. These attributes should be fuzzified into linguistic terms, such as high, average and low. In other words, each attribute a is fuzzified into k linguistic values Ti, i = 1, , k. The membership function of Ti can be subjectively assigned or transferred from numerical values by a membership function. A triangular membership function is shown in Fig. 2, where (x) is membership value and x is attribute value. For instance, a shell part can be described as 0.8/deep, 0.4/middle, 0/shallow. It should be mentioned that membership is not probability and the sum of the membership values may not equal 1. The concept of fuzzy distribution is given as follows. Assuming that attribute A has k linguistic terms whosemembership function is Ai(x), respectively, where x is the value of A and i = 1, 2, , k, the fuzzy distribution of A is ,Rough Set Approach to Gating Scheme for Injection Moulding 665 Step 1. Calculate normal similarity relation matrix R. in terms of de.nition 3. Step 2. Select ,and let and . Step 3. Step 4. If and , then X . X . xj, Y . Yxj.; Step 5. . Step 6. If j ， 其中 U是总值， D, C和 D是集的条件和决策属性， v是值集的属性 a在 A中， f是一个信息功能。 假设的一个子集的属性 ， p 包含于 A，在 U 中的两个物体 x 和 y 是 indiscernible 当且仅当 , . 不可分辨关系 被写作 IND（ P）。 U/IND(P)是用来分割 给出的不可分辨关系的 U。 粗糙集近似于传统的双组集，这是降低和逼近上面的集。定义如下： 组的较低的近似值的定义包括一个包含关系那里在一个同等中的物体属性的班级完全地被包含在同等为决定种类分类。这是一个完美或不含糊的情形分类。对于上面的近似值，物体可能被分类使用归于 P中。 属性减少，是重要的粗集理论。基于对上述定义，概念的减少，记红色（ P ）的定义如下： Q包含于 P， P是减少的，当且仅当 IND(P)=IND(Q) 2.3. 一种改进的粗糙集方法 在设计浇注计划，关键是要 有效率的掌握模糊规则。 知识的获取是瓶颈。 粗糙集适用于解决浇注计划的问题。 框图，为设计的浇注计划与粗糙集显示在图 1。可以从专家和一些参考书籍上获取经验和知识。 粗略设定为基础的感应式学习算法是通过找出隐藏模式和关系案 来 获取知识 。 知识是派一组模糊 如果 -那么 规则。在设计阶段，该系统采用了模糊规则，以履行模糊推理按照这个设计要求。 然后适当的浇注计划，可获得的。 虽然粗糙集是一种有效的获取知识 的途径 ， 但是还是有一些限制在选择原有的浇注计划上。 1原始粗糙集能够有效的处理离散属性，但它不能有效的处理模糊属性。作 为模糊属性，传统的决策表通常转化为一个二进制表所获取 -截集的模糊集。 显然， 在模糊属性之间不存在脆化边界。 nts2. 原始粗糙集是建立在不可分辨的关系上的。总值被分为相等的关系在不可分辨的关系中。高的和低的属性近似产生而言相当于同等关系。 在实践中，原来的粗糙集分类 知识太繁琐，从而导致了问题的复杂性。 模糊集和粗糙集理论是以偏概全 了古典集合论模型的模糊性和不确定性。 Pawlak 和Dubois 提出了这两个理论不互相排斥的，而是互补的【 11， 16】。这两个理论通常适用于不同类型模型的不确定性。粗糙集理论考虑了不同物体之间，而模糊理论处理了隶属函数边界的错误定义。 该属性可以由模糊变量 表现 ，有利 于 该造型的不确定性知识领域 。 为了将浇注计划问题设计的更好，有可能将两者合二为一。 这种模糊粗糙集模型是建立在经典的模糊粗糙集上的。 连续属性是模糊化具有适当的模糊隶属函数。该不可分辨关系，是以偏概全 了模糊的相似性关系。 一种归纳学习算法基于模糊粗糙 集模型（ frila ） 被提议。模糊规则的设计是在提取拟议 frila之后。浇道的设计计划是在得到了模糊推论之后。详细的实施将在下节讨论。 3. 实施 frila 基于 一种模糊粗糙集归纳学习算法构成 3 个步骤。 这些模糊属性的步骤是建立在模糊相似关系和模糊规则的建立上 的。 3.1 模糊属性 一般来说，在决策表中有一些模糊的属性，例如压力的亏损。这些属性应该模糊到语言的条件上来 ,如 :高 ,平均及低 .换言之 ,i = 1, , k. 调隶属函数的钛可以主观转让或转移，数值功能是由会员制定的 .三角形隶属函数显示如图 . 2. 在那里 ,(x)的会集值和 x 的属性值 .举例来说 ,一个客体的一部分 ,可以说是（ 0.8/deep ， 0.4/middle ， 0/shallow ） 。值得一提的是成员的概率是不确定的 ,总的价值也可能不等于 1.概率模糊化的分布如下 . 假设属性 A有 K的语言学而言 ,他的隶属函数就是 Ai(x),分别的 ,X是 A的价值 , i = 1, 2, , k, A的模糊分配是 ,其中 根据该定义，模糊分布情况壳体部分代表作为（ 0.67 ， 0.33 ， 0 ） 。 nts 3.2 属性基于模糊相似关系 经典的定义上 ,低的和高的属性引进参考的不确定关系 ,被假定为一种等价关系 (自反 ,对称 ,传递 ).在实践中 ,不可分辨关系可以延长到一个模糊相似关系 . 考虑到 U = u1, u2, , un 的总值 ,模糊相似关系 R _n_在总值中被称为模糊相似矩阵 ,如果每个 元素 rij有以下两个属性 : 自反 : 对称 : 为了构建模糊相似关系，应先测量该模糊相似关系 .一般情况下 ,采用极大极小方法，对关联系数法与 Minkowski基于距离贴近度法是用来计算因子 rij 。 考虑到 R是一个模糊相似矩阵 ,是水平值时 , 矩阵 R 就是所谓正常的相似关系矩阵 经过以下操作。 该矩阵 R 有特性的自反性和 symmetrivity 。 为了获得分割铀鉴于模糊相似关系 R ，给出了算法如下。 算法一 输入：模糊相似矩阵 R 和水平的价值。 输出： / ind （ ） ，这是一个分区铀给模糊相似关系 和水平的价值。 粗糙集改进注塑浇注成型计划 665. 第 1步。计算正常相似关系矩阵 而言定义 3 。 第 2步。选择的 ，和设 和 。 第 3步。 nts第 4步。如果 和 ，则 第 5步。 。 第 6步。如果 j N ，则转到第 4步，否则，直接到下一步骤。 第 7 步。如果卡（ y ）的 1 ，然后选择喜 跳至第 3步，否则，直接到下一步骤。 第八步。输出设置 X和设 。 第九步，如果 ，然后结束，否则，跳至第 2步。 在第七步，卡（ y ）的指基数集 . 根据该算法 , 就是分割计算鉴于属性 A和水平值 _i.U的部分给予属性集 A的水平集在以下被定义 . 其中 A和 _是属性集和水平价值集 ,分别的 ,管理定义如下 : 考虑的一个子集 xcu和模糊相似关系 R定义 U,下属性 X,被定义为 RA_(X),上属性的 X,被定义为 R(X),分别定义如下 : 假设 / ind （ c ）和 Y两种分割对 U ，那里 / ind （ c ） = （象 X1 ， x2 ， ，空间 XK ）和 Y = （ y1 ， Y2型， ， 54 ） ， 积极地区名次（ y ）的定义如下： 该数据量通常非常大，并有一大量的冗余信息。减少属性可以成功的移除多余的噪音信息 .属性的减少 ,属性集不是单独的 , 基数根据削减订定的维度问题，所以这是很重要的 ,最起码的减少 ,可以定义如下 : 假设一个子集 C_ C,C是属性集 ,C是最低限度的减少 ,当且仅当 C的特点有以下两个属性 : 假设条件属性集 C和决策属性定 d时， C对 D的依赖程度 ,定义如下 : 卡（ x ）的指基数的集 x和 0小于等于 Y, (C,D) _ 1666 F. Shi et al. nts根据该定义的依赖程度，每一个属性的
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