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Reconfigurability analysis of manufacturing system based on rough sets Xie Xiaowen, Xue Wei, Zheng Beirong College of Mechanical performanceevaluation; manufacturing system; reconfigurability; rough sets I.INTRODUCTION Face to competitive market, how to enhance the ability to rapidly response to complex and changeable production needs of multiple species and variable batches, and how to reduce production cost and shorten the replace time of products have an important influence on survival and development of enterprise. Traditional manufacturing systems (such as DMS and FMS) have been difficult to satisfy the above needs. Reconfigurable manufacturing system (RMS)1 is a novel complexmanufacturingsystem.Atitsfirststageof scheduling and design, a specific product family is analyzed, and other related factors about manufacturing are considered, appropriate system redundancy are increased, and then a reasonable system design plan is constructed. Moreover, when the market and production task are changed, RMS can rapidly response, and reconfigure its own configurations. Thus, the comprehensive evaluation of configuration design, planning, reconfiguration scheme and optimization hasveryimportantimpactonsystemdesignand reconfiguration of RMS2. However, nowadays the researches of performance evaluation system of RMS are limited to some specific areas, and an comprehensive evaluation system from the whole aspect has not been constructed. In the paper, based on the analysis of key performance indicators, the reconfigurability analysis system architecture and technology scheme are presented using rough sets theory. The system performance evaluation is applied to various areas, and it is related to a large amount of knowledge hard to identify. The related knowledge is difficult to describe accurately, and information is continuously changing. Thus, in relation to non-precise knowledge, Rough sets theory (RST) can be used as a theory base of discussion of knowledge3,4. II.PERFORMANCEEVALUATIONSYSTEM AND INDICATORCONNOTATION Performance Evaluation System economy Capacity and functions reconfigurability Reliability Environmental friendliness Risks System productivity Running cost Reconfiguration cost Design cost System availability Mean time between failures diagnosability Ramp-up time Logistic reconfigurability Process reconfigurability Equipment reconfigurability balance Process capacity limits Equipment utilization Market risk Organize risk Technology risk Friendly interface security Optimal use of resource Figure 1. Performance evaluation indicator of RMS Inordertoconstructasystematical,normaland reasonableindicatorevaluationsystem,theevaluation indicator selection of RMS should follow the following principles: Comprehensive; ? _ 978-1-4244-4520-2/09/$25.00 2009 IEEE Unique; Scientific; Binding of qualitative and quantitative indicators; Operable. From the above principles, in accordance with the most essential features of RMS, the following system performance indicators are obtained5:, which is shown in Fig.3.2 A.Economy Design cost The design cost mainly consists of the cost of design, facilities, equipments, materials, human resources, and the cost at the initial stage of system, which can be obtained through prediction and computation. Reconfiguration cost The reconfiguration cost means the reconfiguration capital, production disruptions caused by reconfiguration in the new conditions, and the reconfiguration cost is the main indicator that decides the system reconfiguration strategy. Running cost The running cost includes: material consumption of production,energyconsumption,managementcosts, equipment and tooling costs. B.Capacity and functions System productivity Thesystemproductivitycanberepresentedby manufactured product quantity in unit time. Equipment utilization The equipment utilization means the degree of processing equipment being used, and its computation formula is nn m i ii n tk tk U = = 1 Where, n Uis the equipment utilization; i kis the use cost of ith equipment per hour; i tis the work time of ith equipment; n kis the cost of machining equipment per hour; n tis the running time of machining system;mis the number of machining equipments. Processing capacity limits The processing capacity limits means the ability that the system can satisfy different product processing needs. Production balance The production balance means the balance degree of various processes, which is closely related to their process time. C.Reconfigurability Equipment reconfigurability The equipment reconfigurability is mainly reflected in themodularextentofmachinetoolanddynamic reconfiguration capabilities of controllers. Process reconfigurability The process reconfigurability is the ability that different process modules form a new processing technology to apply to changing production needs. Logistic reconfigurability The logistics work status should be adjusted at any time to make it optimization in the public base, shortest transportation route and most inexpensive cost. D.System reliability Ramp-up time The ramp-up time means the time from starting running to the stage that achieves the design quality, which is an important evaluation indicator that determines whether it is feasible. Diagnosability The diagnosability means the failure analysis and identification ability of products quality and failure reasons. Mean time between failures (MTBE) MTBE means the mean time between two system failures. System availability The system availability is the probability that system is at status able to work or use, and it is the combination of unit availability, which can be calculated by the inherent availability. E.Environmental friendliness Optimal use of resource It means the system ability to optimal use natural resource. System security The system security means the extent of harm when the system fails. Friendly interface The friendly interface means that the extent of comfort for workers in the run-time. F.Risks Technology risk The technology risk means that the risks during the process of new technology implementation and integration. Organize risk The organize risk is the risk that during the process of system construction and implementation, organizational structure and management system can not meet the needed requirements. Market risk The market risk is the risk resulted from inadequate ability of dynamic response to market changes and customer customized needs. III.PERFORMANCEEVALUATIONMETHODSBASED ON RST Rough set theory (RST) as proposed by Pawlak(Pawlak., et al., 1995), provides a formal tool for data analysis and knowledgediscoveryfromimpreciseandincomplete information. Using the concepts of lower and upper approximations in RST, the knowledge hidden in the systems may be discovered and expressed in the form of decision ? rules. Due to its ability, it has been widely applied to many problems,includingdecisionanalysis,data-mining, intelligentcontrol,patternrecognitionandfault diagnosis(Shen and Jensen, 2007; Shen et al.,2000; Francis and Shen, 2003). The research object of RST is an informationsystem()fVAUS,= where N xxxU, 21 ?=is a finite set of objects, which in this case are states of the environment; A is a finite set of attribute; the attributes in A are further classified into two disjointsubsets,conditionattributesCanddecision attributesD, such thatDCA=and=DC; aAa VV =is a set of attribute values and a V is the domain of attribute a (the set of values of attributea); VAf: is an information function which assigns particular values from domains of attributes to objects such that () ai Vaxf, , for all Uxi and Aa . Every object that belongs to U is associated with a set of values corresponding to the condition attributes C and decision attributesD. In the paper, RST is applied to the performance evaluation system of RMS, and the performance evaluation knowledge acquisition module of RMS can be defined as ()fVAUS,= .The set of condition attributes A represents the performance evaluation indicators such as production system economy, reliability, reconfigurability; the set of decision attributes D is the set of results of performance evaluation. The characteristic samples are gathered according to the set of attributes A , and constituting the union of objects U . Because of the essence of continuity of performance indicators, its value should be discretized firstly before other treatments inRST. By the reduction of condition attribute and rule generation, the decision tables are then obtained, and eventually the performance evaluation knowledge are acquired6,7. The failure object set is partitioned according to attribute A,namely :/ AAA RxxRU= or :/ DDD RxxRU= ,where )()(:),( jaiajiA xfxfxxR= )(Aa ; )()(: ),( jdidjiD xfxfxxR= )(Dd arecalled indiscernibility relationship decided by A. For any AB , anequalvaluerelationcanbeobtained, )()(:),( jaiajiB xfxfxxR= )(Ba , and one partition isthenacquired B RU / ,namely ),( : BB Ryxyx= 6? The decision table is the set of group of decision knowledgewhichisthefaultdiagnosisknowledge represented by rules that is generated by reduct. Moreover, it is a process to identify decision knowledge class and complete knowledge acquisition of performance evaluation knowledge base. The process of automatic performance evaluation acquisition is described as Fig.3.3: Figure 2. Performance evaluation knowledge discovery based on RST The main steps are as follows: Data acquisition and analysis; FormationandDiscretizationofknowledge acquisition samples based RST; Reduct computation of decision table; Construction of Minimal decision rule table; Representationofperformanceevaluation knowledge; Knowledge reasoning. IV.CASESTUDY An enterprise carries out the design and planning of RMS, and intend to conduct its trial run in order to respond quickly to changes in dynamic market. A.Data Acquisition and Analysis Based on the performance evaluation indicator of manufacturing system, the data of manufacturing line is acquired and analyzed. For example, if the manufacturing line is designed and planned to have high flexibility and reconfigurability, but need a large amount of capital investment,havehighrisksandcapacity,lower environmental friendliness, then its performance would be evaluated to be general. Furthermore, it then can be a case of performance evaluation of RMS. B.Formation and Discretion of Samples of Knowledge Acquisition Based Rough Set After samples of knowledge acquisition based on rough set are obtained, their characteristics should be pickup and discretized. The condition attributes are 61 aa , namely economy,capacityandfunctions,reconfigurability, reliability, environmental friendliness, risks. The attribute value equals 1 means high, 2 means general and 0 means low. Z as the decision attribute is to decide the performance evaluation result. The value of 1 represents the performance is good; 2 represents the performance is general; 3 represents it is bad. After discretization, the condition and decision attributes compose a two-dimension table in which a row represents a practical object and each column represents one attribute. The table is shown in table.1. ? TABLE I.DECISIONTABLE OFPERFORMANCEEVALUATION Economy Capacity and Functions Reconfigurabilityreliability Environmental Friendliness Risks Results of evaluation 1generalhighlowhighlowgeneralgeneral 2lowlowhighhighlowhighlow 3generalgenerallowhighhighlowgeneral 4generalhighhighhighhighgeneralhigh 5highhighgeneralhighgenerallowhigh 6generalhighhighgeneralhighgenerallow 7generallowgenerallowlowgenerallow 8lowlowlowgenerallowlowlow C.Reduction Computation of Decision Table The purpose of reduction computation is to delete those attributes and attribute values that have little influence on faultdiagnosisdecision,mainlyincludingconditional attribute reduction (delete redundant column) and attribute value reduction ( delete redundant attribute value in decision table). By reduction, the minimal decision rule set is constructed in the end. (1) Conditional attribute reductionthe discernibility matrix method is adopted to reduce attributes8. The reduction steps are as follows: ?Compute the discernibility matrix M(S). The discernibility M(S) is a symmetric nn matrixwithentries , 1,)()(:njiUuuuauaAa jiji ?= ,each entry thus consists of the set of attributes upon which objects ui and uj differ. ?Compute the discerenibility function )(SM f . )(SM f isaBooleanfunctionof * 1 , m aa ? (corresponding to the attributes m aa, 1? ) defined as follows: ()= ijijmA cnijcaaf,1|, * 1 ? , where ijij caac=| * .Intheinformationsystem,the )()()()(),( 543643542432654321)( aaaaaaaaaaaaaaaaaaf SM = )( 654 aaa . ?Compute the minimal disjunctive normal form. The attributes ), 432 aaa is adopted, then the reduced decision table is shown in Table3.2. Each row can generate one decision rule. TABLE II.DECISIONTABLE AFTERREDUCTION a2a3a4Z 11312 23113 32312 41111 51211 61121 73233 83323 (2) Attribute value reductionAccording to the above attribute reduction table and core value table, to compute the attribute value reduction table. Take the computation of attribute value reduction of decision rule 1 for example. Let 1,1,1,1 5421aaaa F = , and in order to computer the reduction of F, all subset F should be computed. For example, Zaa 1 1 1 32 = , Za 1 6 , 5 , 4 , 1 1 2 = , Za 1 8 , 3 , 1 1 3 = and Za 1 6 , 5 , 4 , 3 , 2 , 1 1 4 = . Thus, the reduct of decision rule 1 are 132 Zaa or 143 Zaa . According to the above rule, the attribute value reduction table is shown in table 3.3. TABLE III.ATTRIBUTEVALUEREDUCTION Ua2a3a4Z 113*2 1*312 23*3 32*2 411*1 4*111 512*1 5?*211 611*1 6*121 6”1*21 7*33 833*3 (3) Formation of Minimal Decision Rule TableAfter combination and selecting decision rules, then one minimal decision rule table is shown as follows: TABLE IV.ONE MINIMALDECISIONRULE TABLE Ua2a3a4Z 1*322 211*1 312*1 433*3 (4)FormationofKnowledgeRepresentationof PerformanceEvaluationSystemAfterreduction, performance evaluation rules are input into knowledge base of RSFDS. By generation rule, the knowledge based RST are ? represented as “If?Then” form, namely, ),( 21m pppIF? , ),( 21n qqqTHEN? , where m ppp, 21 ? represents the conditionalattributesinthequickdiagnosisrules; n qqq, 21 ? represents the corresponding decision attributes. The decision rules based on table 3.4 are as follows: IF reconfigurability is low and reliability is low THEN the performance of system is general; IF capacity and function is high and reconfigurability is high, THEN the performance of s