减速箱侧面8×M8钻孔专用机床设计含8张CAD图
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Journal of Intelligent Manufacturing 12, 3142, 2001# 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.A multi-agent approach to fixture designV. SUBRAMANIAM,* A. SENTHIL KUMAR and K.C. SEOWDepartment of Mechanical and Production Engineering, National University of Singapore,10 Kent Ridge Cresent, Singapore 119260, Republic of SingaporeReceived August 1999 and accepted March 2000The design of fixtures is a highly complex process that requires the human designer to draw from hisrich experience. In addition, for a given workpiece, multiple solutions may exist. By exploiting therecent advances in CAD/CAM and Artificial Intelligence techniques, one may constrain the multiplesolutions such that only good designs (measured through performance measures) are considered.In this paper, a multi-agent fixture design system is proposed that harnesses the advantages ofgenetic algorithms and neural networks. This system attempts to capture the relevant domainknowledge and uses it to produce acceptable solutions efficiently. The system is applied to a caseproblem and the suggested fixturing solution is compared to one offered by a human designer. Theagreement between the two solutions is very close.Keywords: Fixture design, neural networks, back propagation, genetic algorithms, multiple agents1. IntroductionFixtures are workholding devices that are used inmanufacturingoperationssuchasmachining,assembly, inspection, etc. (David and Reid, 1991;Nee et al., 1995). For a given workpiece, the fixturedesign is not unique since numerous designs arepossible. Traditionally, the design of a fixture reliesheavily on the designers expertise and experience.Performance evaluation of a fixture design solution isalso very difficult due to the highly non-linearrelationship of the design parameters. Consequently,for a given workpiece, it is not immediately apparentif a fixture design solution is optimal or near optimal.This paper attempts to replace the human expertdesigner with artificial intelligence agents (Dini,1997; Nelson and Illington, 1991; Senthil Kumar etal., 1998) such as neural networks (NN) and geneticalgorithms (GA). A hybrid combination (Goonatilakeand Khebbal, 1995; Kandel and Langholz, 1992) ofGA and NN is proposed to form the basic structure ofa multi-agent fixture design System (MAFDS). GAhas been reported to be an effective search mechanismfor locating optimal or near optimal solutions in largeand complex solution spaces (Arena et al., 1993;Montana, 1995; Goldberg, 1989) similar to the fixturedesign problem.The proposed MAFDS consists of two maincomponents, namely, the fixture designer and thefixture evaluator (Fig. 1). For a given fixture designproblem, the workpiece and process information canbe easily determined. The fixture designer and fixtureevaluator will use this problem-dependent informa-tion in the design process.The proposed MAFDS will be illustrated withprismatic workpieces consisting of simple featuressuch as holes and steps (Fig. 2). For such workpieces,the workpiece and process information required forthe fixture design process can be categorized asfollows:*Workpiece information1. Workpiece weight2. Part size3. Premachined features.*Process information1. Batch size*Corresponding author.2. Spindle speed3. Operation type4. Base support surface5. Primary locating surface6. Secondary locating surface.In addition, the basic skeletal configuration of afixturefortheseprismaticworkpiecescanbedescribed by the following seven components:1. Base locators2. Side locators3. End locators4. Clamping directions5. Type of clamp6. Type of clamp actuation7. Fixture body.The combinations of the variants of these sevencomponents constitute the design space of fixtures(Table 1). The fixture designer uses GA to searchthrough this space for an optimal or near optimalfixture design. Each fixturing design is represented asa chromosome (concatenated string) of the sevencomponents listed above and each individual compo-nent is referred to as a gene. The fixture designerselects chromosomes for reproduction based on theirrespective fitness values. New fixture designs of betterfitness values are evolved through genetic operatorssuch as crossover and mutation. This cycle ofoperations are repeated for several generationsuntil a fixture of good fitness is obtained.The fixture evaluator uses a neural network toevaluate the fitness values of individual chromo-somes. Each chromosome (fixturedesign) is evaluatedusing the workpiece and process information, thefixture configuration and the following performancecriteria:*Ease of loading and unloading*Cost*Rate of production.The evaluated fitness value is used by the fixturedesigner for the selection and reproduction of thechromosomes.Fig. 1. Basic framework for the MAFDS.Fig. 2. A prismatic workpiece (locating finger).32Subramaniam, Kumar and SeowTable 1. Performance matrixNo.Input typeVariantsCodeEase of loadingand unloadingProduction rateCostEffectScoreEffectScoreEffectScore1Base locatorsFlat with slot2Easy90Fast80High80Flat1Easy90Fast80Medium603 points0Medium60Medium40Low302Side locatorsFlat2Easy60Fast80High502 points1Medium30Medium40Low101 point & flat0Medium30Medium60Medium203End locatorsFlat1Easy60Fast80High401 point0Medium30Medium40Low104Clamping direction2 sides & top3Difficult10Slow102 sides2Easy70Fast901 side & top1Medium50Medium60NATop0Medium30Medium405Type of clampToggle2Easy70Fast80Medium40Cam1Easy70Fast80High50Flat0Difficult30Slow30Low206Type of clamp actuationHydraulic2Easy70Fast80High90Manual1Difficult40Slow30Low10Pneumatic0Easy70Fast80Medium507Fixture bodyWelded2Low10Casted1NANAHigh70Built-up0Low308Batch sizeLarge2Low30Medium1NANAMedium50Small0High709Spindle speedFast1NAFast90Low80Medium0Medium40Medium5010Workpiece weightHeavy2Difficult20Slow20Medium1Medium40Medium40NALight0Easy60Fast6011Part sizeLarge2Difficult20High90Medium1Medium60NALow50Small0Medium50Medium6012Premachined featuresHole1Medium50Medium50NAStep0Easy70Fast7013Base support surfacePlane1Easy80Fast80Low30Inclined0Difficult20Slow20High7014Primary locating surfacePlane1Easy70Fast80Low20Inclined0Difficult30Slow20High8015Secondary locating surfacePlane1Easy60Fast80Low10Inclined0Difficult40Slow20High9016Operation typeDrilling1Easy70Fast90Low40Milling0Difficult40Slow10High70NA: Choice of variant of the corresponding component was not considered in evaluating the performance criteria.A multi-agent approach to fixture design332. Fixture evaluatorThe basic structure of the fixture evaluator is as shownin Fig. 3. The fixture evaluator is a neural network thathas three outputs, ease of loading/unloading, cost andrate of production. These outputs are the performancecriteria by which a suggested fixture is evaluated, andlike most neural networks, the fixture evaluator needsto be trained before it can be used.For the training of the fixture evaluator, trainingexamples comprising of the workpiece and processinformation, the proposed fixtures and their perfor-mance measures (in terms of ease of loading/unloading, cost and rate of production) are required.However, sufficient industrial examples would benear impossible to collect. To overcome this lack ofreal industrial data, the authors have created aperformance matrix to relate the inputs and outputsof the fixture evaluator (Table 1), and this matrix willprovide the necessary training examples.The effects of each input on the three outputs(performance measures) are described by the fol-lowing linguistic variables (Table 1):PerformancemeasureEffectsEase of loadingand unloadingEasy, Medium and DifficultProduction rateFast, Medium and SlowCostHigh, Medium and LowTypical fixture evaluations by human experts ofteninvolve linguistic variables such as those used above.For the purposes of fitness evaluation, an appropriatenumerical score is assigned to each individuallinguistic variable. The fitness evaluation is illustratedfor a prismatic workpiece as shown in Fig. 2 in Table2. Initially, the scores of each input with respect to the3 performance criteria arc extracted and the totalscores for each performance criteria are then summedand the fitness value is calculated as follows:Fitness ? total score ?ease of loading and unloading? total score ?production rate? total score ?cost?:?1?The authors acknowledge that this approach ignoresFig. 3. Basic structure of a feedforward neural network.34Subramaniam, Kumar and Seowthe coupling effects of the inputs on the outputs, asTable 1 presupposes that the effects of the individualinputs on the performance measures are completelyindependent. Although the performance matrix isunrealistic, the authors believe that it is acceptable asa source for generating training examples to verify thefeasibility of the proposed multi-agent approach tofixture design. In future, the training examplesgenerated by the performance matrix can be replacedwith sufficient real industrial data.For the training, testing and verification of thefixture evaluator, 4000 examples are used and theseare randomly generated from the 16 inputs (namely,three workpiece information, six process informationandsevenfixturecomponents).Toensureanacceptable sampling of the entire search space, theexample selection process was constrained such thatbetween any two examples, there will be at least fourdifferent inputs. Of the 4000 examples, 2500 wereused for training, 1000 for testing and 500 forverification.The fixture evaluator was initially trained using thestandard back-propagation training algorithm. Usingthis approach, the fixture evaluator rapidly convergedto a local minimum. The back-propagation trainingalgorithm is based on gradient descent and usuallygets trapped in a local minimum (Montana, 1995;Dirk et al., 1993; Munro, 1993). There have beenrecent attempts to replace the back-propagationtraining algorithm with a GA training algorithm(Arena et al., 1993; Montana, 1995; Dirk et al.,1993). This training algorithm has the potential oflocating regions of very high performance, but due tothe stochastic behavior of GA, one can only expectquasi-optimum (frequently good) training (Alba et al.,1993). Ithas also been reportedin the literature that byTable 2. Sample fitness calculationSample input combination for locating finger (Fig. 2) is as follows:f2 1 1 2 2 1 2 1 1 0 0 1 1 1 1 1gScores assigned to selected input variants are tabulated as follows:Information typeInput typeSelected input variantScores assignedTypeCodeEase of loadingand unloadingProductionrateiCostiFixturing componentsBase locatorsFlat with slot2908080Side locators2 points1304010End locatorsflat1608040Clamping direction2 sides27090NAType of clampToggle2708040Type of clamp actuationManual140?3010Fixture bodyWelded2NANA10Process informationBatch sizeMedium1NANA50Spindle speedFast1NA9080Operation typeMilling0401070Workpiece informationWorkpiece weightLight06060NAPart sizeMedium160NA50Premachined featuresHole15050NASupport surfacePlane1808030Primary locating surfacePlane1708020Secondary locating surfacePlane1608010Total780850500Fitness?780?850?500?1130NA: Choice of variant of the corresponding component was not considered in evaluating the performance criteria.A multi-agent approach to fixture design35employing local optimization, one can substantiallyimprove the performance of genetic algorithms (Ulderet al., 1990).Therefore, a hybrid training approach based onGenetic Algorithms that uses back-propagation as aform of local optimization is proposed. The localoptimization was used for a small number of epochs,as experience has shown that the marginal improve-ment in increasing the number of epochs is relativelyinsignificant.Thepseudocodeforthistrainingalgorithm is as follows:Randomly generate a population of neural net-works (chromosomes in GA)Locally optimize the populationEvaluate fitness of chromosomesRepeat until termination criteriaMutate all chromosomesSelectionCrossoverLocal optimization of offspring chromosomesEvaluate fitness of offspring chromosomesReinsertionLocal optimization of new generationEvaluate fitness of new generationThis hybrid training approach is advantageous as itexploits the strengths of the GA training algorithmand addresses its weakness with the strengths of thebackpropagation training algorithm and vice versa.The details of the implementation of the hybridapproach are summarized in Table 3. The neuralnetwork to be trained is coded as a chromosome andeach gene represents either a bias or a weight in theneural network. The coding is designed such that thebias and weights belonging to the same node in theneural network are grouped together. This codingsystemintegratesthealreadyavailabledomainknowledge into the training approach. It also allowsTable 3. Summary of the GA-BP hybrid NN training algorithmSelection method? Standard roulette wheel selection.Ranking and scaling of fitness values are adjusted according to the rate of convergence.ReproductionCrossover? Nodal crossoveroperatorWeights and bias belonging to each node are grouped into nodal groups in thechromosome string. This modified version of the binary masking approach ensures thatcrossover is done without destroying the integrity of each nodal group.? Proportional crossoverThis operator caters to the continuous nature of the weights and bias. It allowsinterpolation of genetic material from the initial pool of chromosomes, hence improvingthe convergence rate.Mutation? Fitness-based mutation rate for individual chromosomeThis individualistic assignment of mutation rate allows more mutation on weakerchromosome and vise versa. With this approach, it would be less likely to lose goodgenetic material via mutation.Fitness evaluation? Back propagationOffspring created are locally optimized with BP. The application of BP to the offspringserves two purposes:1. To local optimized the offspring. This improves their fitness reasonably, henceprevent offspring of good potential from being discarded.2. To provide the fitness value of the offspring.Reinsertion method? Elitist reinsertionAfter the offspring are evaluation for fitness, they are combined with chromosomes fromtheir parent generation to form a chromosome pool. Members from this chromosome poolare selected (fitness-based) to forms the next generation.This approach is adopted to overcome excessive fluctuation at the later stage of theoptimization process.Local minimization? Back propagationThis increases the rate of convergence.36Subramaniam, Kumar and Seowfor a more effective nodal crossover operation in thereproduction process. In addition, a proportionalcrossover was created to cater to the continuousnature of the weights and biases.Numerous neural networks were trained using thetwo training algorithms, viz,*Back-propagation.*Genetic algorithms with back-propagation forlocal optimization.Populationswith160chromosomes each,wererandomly generated. Each chromosome is a neuralnetwork and its effectiveness is measured through theSSE (sum of squared errors). Each population is thentrained with the 2500 training examples using the twotraining algorithms for approximately the sameamount of CPU time. These trained population ofneural networks are then used on the testing (1000examples) and verification (500 examples) sets. Basedon the average performance, we identified the best andworst population for each training algorithm. Thechromosomes of these best and worst populationsare then ranked and sorted in ascending order (i.e.chromosomes #1 and #160 are the best and worstchromosomes of a population respectively). Ourresults for the testing set (Fig. 4) and the verificationset (Fig. 5) both indicate that the hybrid trainingapproach is much more effective than the standardback-propagation training algorithm alone.3. Fixture designerThe fixture designer is at the heart of the proposedMAFDS and is responsible for the formulation ofgood fixturing solutions to any prismatic workpiece.The fixture designer uses genetic algorithms to searchthe fixture design space for an appropriate fixture.The algorithm (pseudocode) used in the fixturedesigner is as follows: (Note, that this pseudocodepresupposes that the fixture evaluator has alreadybeen trained and is capable of generalizing thefixturing domain knowledge extracted from thetraining examples).Fig. 4. Performance of the training algorithms using the testing set.A multi-agent approach to fixture design37Fig. 5. Performance of the training algorithms using the verification set.Table 4. Summary of the fixture designerSelection method? Standard roulette wheel selection.Ranking and scaling of fitness values are fixed for the entire search.ReproductionoperatorCrossover? Multiple-points crossoverStandard multiple-points crossover available is used.Mutation? Fitness-based mutation rate for individual chromosomeThis individualistic assignment of mutation rate allows more mutation on weakerchromosome and vise versa. With this approach, it would be less likely to lose goodgenetic material via mutation.Fitness evaluation? Fixture evaluator (NN)NN is used to cater to the highly non-linear nature of the relationships between theinputs.Reinsertion method? Elitist reinsertionAfter the offspring are evaluation for fitness, they are combined with chromosomes fromtheir parent generation to form a chromosome pool. Members from this chromosomepool are selected (fitness-based) to forms the next generation.This approach is adopted to overcome excessive fluctuation at the later stage of theoptimization process.38Subramaniam, Kumar and SeowRandomly generate a population of fixture designsolutions (chromosomes in GA)Evaluate fitness of chromosomes using fixtureevaluatorRepeat until termination criteriaSelectionCrossoverMutationEvaluate fitness of offspring chromosomesusing Fixture EvaluatorReinsertionThe details of the fixture designer are presented inTable 4. Some of the characteristics of the MAFDSare:*Design knowledge is captured into the fixtureevaluator, and this enables faster evaluation ofthe fixture design. The fixture evaluator is easilytrained to adapt to additional examples, as thetraining and design phases of the MAFDS areindependent of one another.*The system has the ability to give not just oneoptimal solution, but also a group of sub-optimalsolutions. This will help the designer to explorealternate design schemes if needed. This facilityis not available in conventional optimizationtechniques such as linear programming.To test the effectiveness of the MAFDS, 330 sampleproblems were created. Each sample problem repre-sents the inputs to the MAFDS, and consists of thethree workpiece and six process information. Theoutputsofthe system arethesevenfixturinginformation. To ensure that the sample problems arewell distributed in the problem space, the problemselection procedures were constrained such thatbetween two sample problems, there are at least twoinputs that are different.For each sample problem, ten different initialpopulations were randomly generated and opti-mized using the MAFDS. The results of these testproblems are summarized in Table 5. The results showthat the average number of generations required forthe system to locate the global minimum is 14.3generations and 99.9% of all the sample problems hadtheir global minima located within 50 generations.Only four out of 3300 sample trials (*0.1%) did notresult in the location of the global minima. Thus,based on these results, the fixture designer is veryeffective in locating the best fixturing solution fordifferent sample problems.4. Case studyTo demonstrate the feasibility of the MAFDS, avibrator arm as shown in Fig. 6, is used as a casestudy. The fixture configurations suggested by theMAFDS and a human fixture designer are comparedand analyzed.The input information, for machining hole #1(Fig. 6), to the proposed MAFDS is presented inTable 6. For the purposes of a fair comparison, thehuman designer is constrained to design the fixtureTable 5. Rate of convergence to global minimumNo. ofNo. of test groups converging to global minimum of search spacegenerationsExperiment no.Averagerequired12345678910(%)Less than 1010487799283797486878786 (26.0)Less than 20259255239250265254248267249248253 (76.8)Less than 30320321319320319315318318313319318 (96.5)Less than 40326325319320326326326326326325325 (98.4)Less than 50330329 *330330330329 *329 *330329 *330330 (99.9)Average13.61414.714.713.914.314.314.3*In these experiments, 1 out of the 330 test groups did not locate the global minimum defined by the fixture evaluatorafter 50 generations of reproduction.A multi-agent approach to fixture design39configuration using the variants of the seven fixturecomponents described in Table 1.Using the information in Table 6, the suggestedfixture configurations obtained using the MAFDS andthe human fixture designer are summarized in Table 7.The two solutions are exact for five out of the sevenfixture components. The differ only with respect to thechoice of base locator and fixture body types.On careful inspection of the vibrator arm (Fig. 6and Table 6), we observe that a drilling operation isrequired and that the base of the workpiece has astep premachined feature. For drilling operations, asuitable fixture configuration may use either a 3-pin or a flat with slot base locator. The humandesigner rightfully chose the 3-pin configurationbecause the premachined step at the base is notnegligible and the flat with slot base locator typewould have been less suitable for this workpiece. TheMAFDS is incapable of determining if sufficientlocating area is available for flat locators. In theabsence of such information, the systems choice offlat with slot base locator is a reasonable one.If the batch size for producing a workpiece is small,Table 6. Workpiece and process information for vibratorarmInput typeInput variantCodeBatch sizeMedium1Spindle speedFast1Operation typeDrilling1Part weightLight0Part sizeMedium1Premachined featureStep0Base support surfacePlane1Primary locating surfacePlane1Secondary locating surfacePlane1Fig. 6. Avibrator arm.40Subramaniam, Kumar and Seowthen the built-up fixture body type would havebeen most appropriate. This fixture body type isreusable and its unit cost is high. On the other hand, ifthe batch size is large, the welded fixture body typewould have been the better choice. This fixture bodytype cannot be reused, but its unit cost is very low andit results in a very consistent fixture. In our case study,the batch size is medium and either fixture body typeswould have been reasonable choices.5. ConclusionsTo reduce the dependency and ambiguity in thedesigns of human expert designers, a MAFDSconsisting of a fixture evaluator based on neuralnetworks and a fixture designer based on geneticalgorithms is proposed. The authors have shown thatthe fixture evaluator is best trained using a hybrid GA-back propagation training scheme.Based on the results obtained, this multi-agentapproach to fixture design is capable of generatingoptimal or near-optimal solutions for the sampleproblems considered. In addition, the system isdynamic, as it is capable of learning. When moredesign examples become available for training, thesystems reliability and accuracy in providing goodperformance evaluation of fixturing solutions can beimproved. This will consequently lead to better designoptimization.The developed MAFDS system is capable ofcapturing the extensive knowledge of an experthuman designer consistently and unambiguously.Human designers can offer different solutions to thesame problem on different occasions or differenthuman designers provide different solutions to thesame problem.As highlighted by the case study, the disadvantageof the MAFDS is that the information that it currentlystores is quite limited. For example, it is unable todistinguish the available area on the base of aworkpiece for locating purposes. The solution to thisproblem will require the refinement of the inputinformation to include more details about the work-piece and process involved. The authors are currentlylooking into this
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