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Optimal Design Based on Rough Set and Implementation of Worm Gear in Valve Actuator [Sensors & Transducers (Canada)](Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: Rough set optimization method was applied to design the worm gear in valve actuator. The superfluous constraints are reduced based on the methodology of rough set at the model of optimization that was established. The importance of each constraint condition and the coordination of the objective function can be got. Through example it can be seen that the optimal scheme made worm gear accord with the practical situation. So the volume of valve actuator was reduced and the efficiency was increased. Copyright © 2013 IFSA. Keywords: Valve electric actuator, Worm gear, Rough set, Attribute reduct, Multi-objective optimization. (ProQuest: ... denotes formulae omitted.) 1. Introduction The valve is an important part of the pipeline control system. It is widely used in metallurgical, chemical, oil and other industries. Valve electric actuator is the essential implementation components of a valve centralized control, automatic control and remote control. A conventional valve electric actuator is constituted by reduction gears, mechanical stroke control mechanism, torque control mechanism, valve position indication institutions, valve position signal feedback mechanism and electrical control part. Because of its complex structure, low control accuracy, it can not meet the requirements of automatic control, not to meet the evolving needs of industrial automation control and computer intelligent control [2, 14]. Now, new valve electric actuator has used mechatronics technology [3]. Its asynchronous motor directly drives worm drive opening and closing of the valve. The flexible valve shutdown, accurate positioning is achieved by its built-in inverter and fuzzy control system. The mechanical transmission is simplified. In this actuator, as an important part of drive and power, worm drive's design reasonable or not directly related to the quality and efficiency. In the previous design, the uncertainty, vagueness of various factors affecting the worm drive were not taken into account, such as the level of manufacturing, material, component design parameters uncertainties and the importance of judgment on the fuzziness design. These make ordinary design method is often difficult to conform to the actual situation [5]. Rough Set optimal design method combines rough set theory and mechanical design methods, analyzes engineering uncertainties, and optimizes the processing. Optimization design of worm gear in valve actuator is actually a multi-objective programming problem. Each condition is different to the binding force of the each objective function. In this paper, based on the methodology of rough set, superfluous constraints are reduced. The importance of each constraint condition and the coordination of the objective function can be got. This result provides a more dependable basis for the optimization design. 2. Build Mathematical Model to Optimize Design 2.1. Initial Conditions We use the data of the literature [2] to the initial settings. Where, the worm speed ni =1380 r /min, and the transmission ratio i = 38, the input power P = 5.5 kW. Valve electric device transmission principle is shown in Fig. 1. 2.2. Determine the Design Variables According to the design requirements of electric devices, the main parameters of the worm drive are: total number of worm Z; modulus m; worm diameter factor q. The design variables: ... 2.3. Establish the Objective Functions 1) Volume objective function. To meet the requirements, electric device should be saving material, that is, the volume of the crown to a minimum, which also allows the smallest of the electric device. Shown in Fig. 2, the volume is: ... (1) where d\ is the worm gear tooth crown outside diameter (mm); ... d2 is the worm gear pitch diameter (mm) d2 = mZ2: Z2 is the worm gear teeth; e is the tooth crown smallest thickness (mm) e=2m; B is the worm wheel width (mm) B = 0.65da; da is the worm tooth crest circle diameter (mm) da = mq+ 2m; 2) Efficiency objective function. The transmission efficiency of electric apparatus is highest if the worm rotation efficiency is highest. That is, amount of wear and heat are the minimum. It should enable the tooth surface's relative sliding velocity minimum. There are: ... (2) This is a multi-objective optimization. With weighted coefficient method, a total objective functions: ... (3) where CO/, cc>2 are the weighting factors, and CO/+CO2 = 1. 3. Determine the Constraint Conditions The constraints are mainly two aspects: performance constraints and boundary constraints. There is a transition process from fully available to completely unavailable. Constraints and boundary constraints that affect the performance of the worm drive can be seen as a subset of the design space. The obtained constraint conditions are as follows: a) Worm gear tooth contact strength constraints ... (4) where oH is the worm gear calculation of contact stress (N/mm2); ZF is the material factor; K is the load factor; T2 is the worm gear suffered torque (N-mm); [<j\H is the fuzzy allowable contact strength (N /mm2) b) Worm gear bending strength constraints. ... (5) where oF is the worm wheel dedendum calculated bending stress; [o]H is the fuzzy allowable bending stress (N /mm2); YF is the worm gear tooth form factor; Yß is the helix angle factor; c) Worm stiffness constraints. The maximum deflection should not exceed m/50 when the worm work, that is ... (6) where [y] is the worm fuzzy permissible deflection, mm; FYi, Ft1 are the radial force, the circumferential force of the worm, respectively, N L is the worm span (mm); E is the worm material elastic modulus (N /mm2); J is the inertia torque of the worm at the dangerous ... dfX is the worm tooth root circle diameter (mm). d) Upper and lower constraints of design variables According to the specifications and experience, the design variables will be within an approximate range of values, namely: ... (7) ... (8) ... (9) From the above analysis, the design variables and the objective functions are determined; the only constraint is vague and uncertain. So, the worm drive optimization model of electric device is an ordinary uncertain constraints asymmetric optimization model. 4. Constraints and Application Based on Attribute Reduction Rough set theory is a new data analysis theory to deal with imprecise, uncertain data, proposed by Polish mathematician Z. Pawlak at 1982 [7].It has been widely used in the field of artificial intelligence, pattem recognition and intelligent information [9]. It can effectively analyze and deal with imprecise, inconsistent, incomplete information, and discover hidden knowledge, revealing potential mies [13]. The rough set method simulates the human abstract logical thinking. It is based on indiscemibility and knowledge reduction, and derived logic mies from data as a knowledge system model. The knowledge space can be reducted. Inference mies are obtained from the sample data. Next, we first described the concept of attribute reduction and core, and then provide the calculation method of attribute reduction. 4.1. Attribute Reduction and Core In an information system S=(U,A,V,f), a subset PczA can determine a binary indiscemibility relationship IND(P): IND(P)= {(x,y)e UxU\\fa eflx,a)=fiy,a)}. Obviously, IND(P) is an equivalence relation on the domain U, and ... ... Definition 1. Let S={U,A,V,f) be an information system. Attribute a is called unnecessary in A (redundant) if IND{A-{a))=IND{A). Otherwise, a is called a necessary in the A; If every attribute asA in A are necessary, then A is independent, otherwise known as the A dependence. Definition 2. Let S={U,A,V,f) be an information system, PçzA. P is a reduct of A if P Satisfies: 1) IND(P)=IND(A); 2) P is independent. Rough approximation is used to deal with imprecise and uncertain information. It has a strong ability of identification data. To this end, we constitute effective solution set U (finite) of a new model that removes some of the constraints which are not important, denoted U={xi, x2,..., xm}, called the domain. Efficient solution classification knowledge in U is expressed in the form of relational tables. Rows of relational tables are corresponding to the object (the effective solution of the simplified model). Columns are corresponding to the object's properties (including condition attribute and decision attribute). The information of an object is specified by each attribute's value of the object to express. Each constraint is seen as condition attributes, while the effective solution of the U is or not is the effective solution of the original problem as a decision attribute. Then, we can get a decision table. The relationship constituted by condition attributes and decision attributes is denoted by R. From the literature [14]: An attribute is corresponding to an equivalence relation. Table 1 can be seen as a family of equivalence relations, namely knowledge base. In the previous table, the attribute value v,y is 1 if xi satisfies the constraint condition of the original problem C,-. If it is not the case, vÿ is 0. Decision attribute value bk is taken as 1 if xi is the optimal solution of the objective function fk. Otherwise, tik is 0. This can get a decision information table. So for V_X<zTJ, define lower approximation and upper approximations of X are: ... So any effective solution set X of simplified model can be expressed as: (RX,RX). Lower approximation ofXis certainly part of the original problem solution set; upper approximation of X is the set of effective solutions that may belong to the original problem. RX = RX , when removing redundant constraints conditions, that is, effective solution of the simplified model is the original model of effective solutions. If indicates unacceptable solution, "0" is the solution may not be able to accept, "+" is perfectly acceptable solution, we can describe "against", "neutral" and "fully agreed" attitude of the objective function to a feasible solution. According to this view, there is a decision information table of relevant objective function with feasible solution, as shown in Table 2. There are the following relationships between the objective functions. Suppose that Fi, Fkis objective function. For any feasible solution xi: 1) Coordination R\,(Fi,Fk) = 1, if Fi and Fk holds the same attitude to xi, 2) Independence Rxi (F,,Fk) = 0, if at least a neutral attitude in Fi and Fk, 3) Competition R~'(F,,Fk) = -1, If Fi and Fkhave different attitude to xi. We know that Rlxi(F,,Fk) is an equivalence relation for solution xi by [7]. According to Table 2, Table 3-6 indicates the relationship between the objective functions and each candidate solutions, respectively. Table 3 shows that: the objective function F2, F3, F4 for candidate solution xi, x3, x4, is a coordinated relationship, but they compete with Fi, F5. Table 4 shows that: the objective function F2, F3, F5 with candidate solution x2 is a coordination relationship. Fi, F4 hold neutral stance to candidate solution x2. Similarly, other cases can be analyzed. Decision makers can determine a priority of noninferior solution based on the satisfaction of the objective function to the feasible solutions. ... (10) In (10), x2 is the best non-inferior solutions. It can be seen by the description: The objective function F2, F3, F5 show "fully agreed" support x2. Fi, F4 remain as neutral. By contrast, x3 is the worst non-inferior solutions. Therefore, taking satisfaction 0.80, we can get a really efficient solution x2. 4.2. Constraints Analysis Based Attribute Reduction Suppose that we denote the constraint condition that we are concerned with the condition attributes as Cj, c2,..., c4. The set of condition attributes is denoted as C= {ci, c2,..., c4}. Its attribute values are numeric data. The optimal solution of objective function and removing the constraint condition ci, c2,..., c4,respectively, can be obtained using Lindo linear programming software. Their related information is shown as Table 7. Here, we compare optimal values of Fi, F2, F3, F4 under the conditions C-{c/},C-{c2},C-{c3}, C-{c4}with the optimal value of the original constraints groups (6) at the last line, respectively. It is not difficult to fmd: the optimal values in C-{c4) and C={ci, c2,..., c4} are identical. This indicates that the conditions c4 is relatively redundant constraints, getting rid of them without changing the original problem. Thus, the original optimization problem (*) and removing redundant constraints optimization problem (**) have the same solution. It is easy to see from Table 7: All objective functions are constrained by constraint ci .To give up it may produce an unfeasible solution contrary to the original constraints. c2, c3 bound F2. c4 constrains F2. In summary, the importance of the four necessary constraint conditions: ci is the most important; c2, c3, followed; c4 is unimportant. According to the above analysis, it is noted that F, and F2 is coordination. It can take Fi weighting coefficient as 0.8, while F2 is a weight coefficient of 0.2. The original problem of conversion: ... ... We can get a non-inferior solution (3.0612,4.9547,10.0328)r. This solution can enable the two objective functions Fi, F2 to achieve optimum values. The fuzzy optimization result [2] is X=[3.0612,4.9547, 10.032 8]r. In this case, the number of worm head and the worm diameter coefficient is an integer, taking Z=3, «7=10. Modulus should be taken as the standard value, and the upper and lower approximation of the modulus calculated values are 5, 4.5. This takes m=5, i.e. X = [3,5,10] T .Crown volume: F0=285667. 83 mm3, efficiency Tjd= 0.8696. The results with the rough set method are X=[3,4,9]r, L0=278966. 23 mm3, ri0= 0.8966. After the comparison of the two results, we can see that crown volume is reduced by 2.34 % and its efficiency is improved by 3.1 %. 5. Conclusions After instance, analysis and comparison, we obtain the following conclusions :(a) Rough set optimal design method can not only make the minimum volume of the crown, and thus make electric devices the smallest. Also electric device can be the most efficient. Its performance can be improved, (b) This method for multi-objective programming problem has a certain practicality. It is more flexible, simple to use in large-scale multi-stage dynamic programming. Acknowledgment This work was supported in part by a grant from 2013 scientific research fund of Zhejiang province of China education department (Y201327861), Shaoxing, Zhejiang province science and technology projects of China (2013B7006). References [1] . A. M. Alfredo, A. C. Carlos, and M. M. Efrén. Evolutionary Algorithms Applied to Multi-Objective Aerodynamic Shape Optimization, Computational Optimization, Methods and Algorithms, 2011, pp. 211-240. [2] . X. M. Han, Z. S. Zhao, and Z. X. Tie, Fuzzy optimization design of worm gear in new type valve actuator, Modern Machinery, No. 6,2004, pp. 20-21, 33. [3] . S. Koji, Y. Shu, J. Shinkyu, O. Shigeru, and Y. Yasuyuki, Multi-Objective Design Optimization for a Steam Turbine Stator Blade Using LES and GA, Journal of Computational Science and Technology, Vol. 5, No. 3,2011, pp. 134-147. [4] . V. S. Luis, G. H. Alfredo, M. Julián, A. C. Carlos, C. Rafael, DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems, Computers & Operations Research, Vol. 37, No. 3, 2010, pp. 470-480. [5] . S. B. Liu, A. S. Shui, J. P. Chen, R. Zhou, and H. Long, Research and Simulation on Intelligent Velocity Controller of Valve Electric Actuator, Journal of Logistical Engineering University, Vol. 27, No. 2, 2011, pp. 75-80. [6] . S. Obayashi. (2011). Extraction of design rules from multi-objective design exploration (MODE) using rough set theory, Fluid Dynamics Research, Vol. 43, No. 3, p. 70-80. [7] . Z. Pawalak, An inquiry into anatomy of conflicts, Journal of Information Sciences, No. 14, 1998, pp.65-78. [8] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, Vol. 11, No. 5, 1982, pp. 341-356. [9] Z. Pawlak, A. Skowron, Rudiments of rough sets, Information Sciences, Vol. 177, No. 1,2007, pp. 3-27. [10] . L. Sen, T. S. Felix, and S. H., Chung, A study of distribution center location based on the rough sets and interactive multi-objective fuzzy decision theory, Robotics and Computer-Integrated Manufacturing, Vol. 27, No. 2,2011, pp. 426-433. [11] . O. Shigeru, J. Shinkyu, and S. Koji, Multi-Objective Design Exploration and its Applications, International Journal of Aeronautical and Space Science, Vol. 11, No. 4, 2010, pp. 247-265. [12] . J. P. Xu, L. H. Zhao, A multi-objective decisionmaking model with fuzzy rough coefficients and its application to the inventory problem, Information Sciences, Vol. 180, No. 5, 2010, pp. 679-696. [13] . W. X. Zhang, W. Z. Wu, J. Y. Liang, and D. Y. Li, Rough Sets Theory and Method, Science Press, Beijing, (In Chinese), 2005. [14] . R. R. Zhu, S. W. Zhang, G. H. Shu, The design of an intelligent controller for use with electric valveactuators, Industrial Instrumentation & Automation, No. 4, 2005, pp. 26-28. [15] . B. Cai, Y. Liu, A. Abulimiti, R. Ji, Y. Zhang, X. Dong, Y. Zhou, Optimal Design Based on Dynamic Characteristics and Experimental Implementation of Submersible Electromagnetic Actuators, Strojniski vestnik - Journal of Mechanical Engineering, Vol. 59, No. 7-8,2013, pp. 473-482. * Fan Chang Xing, Wu Qiang Department of Computer Center, Shao Xing University, Shaoxing, Zhejiang, 312000, China *Tel.:13345859960 * E-mail: [email protected] Received: 6 November 2013 /Accepted: 20 November 2013 /Published: 30 November 2013 (c) 2013 International Frequency Sensor Association |