Selection of optimal material and operating conditions in composite manufacturing. Part II: complexity, representation of characteristics and decision making

International Journal of Machine Tools & Manufacture 43 (2003) 175–184

Selection of optimal material and operating conditions incomposite manufacturing. Part II: complexity, representation of

characteristics and decision making

S.Y. Yanga, V. Girivasana, N.R. Singha, I.N. Tansela,∗, C.V. Kropas-Hughesb

a Center for Engineering and Applied Sciences, Department of Mechanical Engineering, Florida International University, 10555 West FlaglerStreet, Miami, FL 33174, USA

b Wright Patterson AFB, Air Force Research Laboratory, AFRL/MLLP, Building 655, R166, 2230 Tenth Street, Wright-Patterson AFB, OH45433-7746, USA

Received 16 July 2002; accepted 30 July 2002

Abstract

An automated procedure is proposed to select the optimum material and processing conditions for composite materials. Thecomplexity of the part is estimated from the STL files of the CAD/CAM programs by evaluating the angles between the triangles,which cover the surface. A correction algorithm identifies the holes and calculates the complexity without considering the trianglesat their surfaces if they will be drilled later. Using multiple neural networks represented the most important characteristics of thecomposite material manufacturing for the user. For each considered material one genetic algorithm is assigned to select the optimaloperating conditions. The optimal material is selected by comparing the good qualities of each material after the optimization. Theproposed procedure is very attractive for optimization of complex systems when multiple approaches and their several characteristicsare considered. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Neural networks; Genetic algorithm; Composite material; STL; Optimization; Complexity

1. Introduction

Composite materials have many desired character-istics including high strength, corrosion resistance, andlow weight. These characteristics have allowed them tofind many military and civilian applications and to be avery promising candidate for many other applications inthe future. During the design stage, engineers needextensive computational help to select proper materialand operating conditions, since changing design andmanufacturing parameters can control many character-istics of the composite end product. The objective of thispaper is to propose a human-like decision-making toolfor selection of the optimal material and operating con-ditions in the composite material manufacture. The pro-

∗ Corresponding author. Tel.:+1-305-348-1932; fax:+1-305-348-3304.

E-mail address: [email protected] (I.N. Tansel).

0890-6955/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0890-6955 (02)00133-5

posed procedure uses multiple neural networks and gen-etic algorithms for this purpose and can be easilyadopted for many other optimization problems.

Many methods have been developed for cost esti-mation in composite material manufacture [1–21]. Mostof these studies target only cost estimation for a part byusing the design parameters and an extensive databasefrom the manufacturer. In this study, additional charac-teristics such as strength and manufacturing time areconsidered. The proposed approach could easily handleother decision-making parameters such as surface rough-ness and tolerances. The main objective of the developedpackage is to find the optimal material and processingparameters according to the priorities of the user by con-sidering all the important decision-making parameters.

The proposed procedure performs the optimizationtask in three stages. First, multiple neural networks aretrained to estimate the most significant decision-makingparameters such as cost, strength, and manufacturingtime. The user can select the number and the design

176 S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175–184

parameters of interest according to his needs. In thesecond stage, the complexity of the part is evaluatedfrom the STL output files of the CAD/CAM automati-cally. In the last stage, the genetic algorithm selects theoptimum processing parameters for each material byusing neural networks. When multiple materials are con-sidered, the best one is selected by comparing the meritsof each according to the user’s selected criteria.

Most of the manufacturers save the CAD files of com-pleted parts. Precisely located, perfectly round holes ofthe parts are usually drilled after the composite parts aremanufactured. If the complexity of the part is estimatedby considering the surfaces of holes, the value drasticallyincreases with the number of holes. Similarly, cost andmanufacturing time estimates will artificially increase. Ifthe parts are large and contain many holes, the cost andmanufacturing time estimates are completely unrealistic.Instead of removing the holes from the CAD drawingmanually and preparing the STL files of the parts withoutholes, a correction algorithm is necessary to identify thetriangles at the surfaces of the holes and to ignore themduring the complexity estimation.

To evaluate the performance of the proposed pro-cedure, a graphic utility, neural network training, andan optimization program were developed using a VisualBasic program. This evaluation package was calledComposite Material Selection Advisor (CoMaSA).

2. Previous work

In this section the available cost and complexity esti-mation methods are outlined.

2.1. Cost estimation in composite materialmanufacturing

Hundreds of different operations are performed bythousands of people to manufacture complex militaryhardware such as airplanes. During the optimization ofdesign and material selection, engineers should know theactual cost of already produced similar parts but theyneed some computational tools to estimate the cost oftheir new designs.

Manufacturing cost [1–4] is calculated by using eitherthe traditional methods or activity-based costing (ABC).Traditional methods use volume-based measures includ-ing the labor hours, which normally becomes the mostinfluential part of the calculated cost. Since compositepart manufacture is labor intensive, costs are usually cal-culated unfairly compared to the cost estimates of mass-produced parts. ABC is preferred in composite materialmanufacturing to be able to evaluate the overhead costsmore accurately and to obtain the cost of compositeparts precisely.

Parametric cost models (PCM) or manufacturing pro-

cess cost models (MPCM) can be used for the estimationof the cost of the composite parts [4–6]. Developmentand procurement costs for aircraft (DAPCA IV) [7] is aPCM. Advanced composite cost estimating model(ACCEM) [8], manufacturing cost model for composites(MCMC) [9] and composite optimization software fortransport aircraft design evaluation (COSTADE) [10] areMPCM. DAPCA IV is primarily prepared from rela-tively old information, and validity of the estimationsis questionable for composites. Most of the MPCM areprepared by considering the operation and needs of spe-cific companies by using their database and are verycomplicated. The accuracy of the models could be lim-ited when used by other companies.[4,5].

A totally integrated manufacturing cost estimatingsystem (TIMCES) estimates the cost of parts from thedesign inputs [11] following a well-structured method-ology. This approach separately estimates the cost ofmaterial, labor, machinery, operations, and overheads. Atheoretical cost model [12] was developed for compositefabrication by using first-order models and consideringthe complexity of the part. Eaglesham [4] proposed adecision support system, which arranges the existingaccounting data and uses intelligent search methods toestimate the cost at the conceptual design stage.

NASA [13] has given links to many cost estimationresources including books, government reports, per-iodicals, references, software, and technical reports ontheir web page. However, most of these resources arenot directed to composite material manufacture.

2.2. Complexity estimation in composite materialmanufacturing

Complexity of a part represents the difficulty of cre-ating the required shape, achieving the expected charac-teristics and meeting the necessary tolerances. Com-plexity should be considered during the cost estimationof composite materials since the manufacturing time andnecessary support will be directly related to the projec-tions.

ACCEM [8] uses correction factors in cost estimationto make the necessary adjustments by considering thegeometric features of the part. For the theoretical costmodel [12] a series of features was used to estimate thecomplexity including bending of fibers in compositematerials [14], number of nonredundant dimensions ona part drawing [15], and shear and ply stacking [16]. Inaddition, the complexity of parts was also studied byconsidering other manufacturing applications includingassembly and mold making [17–20]. The level of dis-continuity [17], the number of dimensions in the drawing[18], and symmetry [19] were used to obtain the com-plexity. Parametric consultants evaluate the complexityby considering the known cost of similar equipment[13,20]. Li et al. [21] recently indicated the importance

177S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175–184

of the curvature angle(s) of the part on the complexityand proposed collection of the information from the out-puts of the commercial packages.

3. Selection of the optimum material and operatingconditions

In the following sections, automated evaluation of theCAD/CAM files to estimate the complexity of the part,correction of the estimation if there are vertical holes,structure of the optimization, and operation of the pro-posed system will be presented.

3.1. Estimation of complexity from CAD/CAM files

Almost all the sophisticated CAD/CAM programssave their data by using different formats. In this study,the use of STL files was selected to transfer the datafrom CAD/CAM program to CoMaSA since almost allthe commercial solid-modeling programs have theoption to save the data as a STL file. In addition, STLfiles are much easier to use to evaluate the geometriccharacteristics of the parts. The CoMaSA graphic utilityprogram was developed to read the STL file to calculatethe volume and complexity of a part automatically. Inthis study, all the CAD drawings of the parts were pre-pared by using the Parametric Corporation’s Pro-E pack-age. The calculated volume and estimated complexitywere written to the “FixedInput.txt” fi le, which containsthe value of all fixed inputs that are used in the generaloptimization program.

The complexity of a part is calculated according tothe following equation [22]:

� � �qiLi(Part) /�qkLk (1)

(Cube having the same surface area as the part)

where θi is the angle between the normal vectors of twoadjacent triangles of the STL file of the part, Li is thelength of their common side, and θk, Lk are the sameparameters defined for the cube. Fig. 1 demonstratesparameters used in the complexity calculation.

Fig. 1. Parameters used in complexity calculation.

Fig. 2. User interface of the graphics utility program of the CoMaSApackage.

According to the formula, if the normal of neighbor-ing triangles are parallel to each other or have very smallangles, complexity will be a small number. Larger angleswill increase the calculated complexity. Triangles make90-degree angles at the edges of the part. Normally,manufacturing of these edges is easier. The algorithmchecks the angles and reduces the calculated complexityfor that edge if the normals are perpendicular to eachother.

The user interface of the graphic utility program ispresented in Fig. 2. The demonstrated part had 556 tri-angles. The program calculated the volume and com-plexity as 61.87 in.3 and 3.77 respectively. Part rotation,imaging solid object, wire-frame model presentation,and hidden line removal capabilities are added to thegraphic utility program for convenience of the user.

3.2. Complexity correction algorithm for holes

After the program receives all the information fromthe STL file, the part is cut with a horizontal test planeat the middle (Fig. 3) to determine the triangles at thesurfaces of the holes.

Fig. 3. Part with a hole is cut with a horizontal test plane.


The program calculates all of the intersection pointsbetween the horizontal plane and the edges of the tri-angles that cover the part surface.The equation of thehorizontal plane is

z � C,-��x�+�,and-��y�+� (2)

where C is a constant and is equal to half the total heightof the part.The equation of a line in triangle is

x�x1x1�x2

�y�y1y2�y1

�z�z1

z2�z1. (3)

To determine if the edges of each triangle are cut by theplane, f(z) = z–C is used. Coordinates from the begin-ning (x1, y1, z1) and the end of the line (x2, y2, z2) aresubstituted in the f(z) expression. A sign change whenthe beginning and end-points are used indicates that theline had been cut by the test plane (Fig. 4). After thisinspection, the program calculates the exact coordinatesof the intersection by substituting Z = C into the lineequations (eq. (3)) so that:

x �c � y1

y2 � y1∗(x1 � x2) � x1Andy (4)

�c � y1y2 � y1

∗(y1 � y2) � y1.

This procedure is repeated until all intersections betweenthe horizontal plane and the edges of the triangles areidentified. Two intersections are obtained for each tri-angle if the plane intersects it. Since the triangles coverthe surface of the part completely, two neighboring tri-angles will always have identical intersections with thehorizontal test plane. The neighboring triangles aresorted by using this property. If no neighboring triangleis found, and there are extra intersections, one of themis randomly taken and the procedure is then followeduntil no points are left.

Inspection of the array starts from the second pointof the last triangle in the array. Algorithms follow thesequence until the coordinates of the starting point areencountered. For each hole and outer surface of the part,there will be one loop. The number of holes is equalto number of loops minus one. The largest loop is theintersection of the test plane with the outer surface ofthe part. The other loops are checked to determine if

Fig. 4. Determination of the intersection between the horizontal planeand each triangle.

they are round. If they are round, their radius and centerlocations are calculated.

For correction of the complexity estimation, the tri-angles which intersect with the horizontal plane do notbelong to the outer shell of the part and are not usedduring the complexity calculation.

3.3. Structure of the optimization program

The structure of the optimization program is presentedin Fig. 5 when m decision parameters of n different com-posites are considered to select the best material andoptimum operating conditions.

When a part is considered, the volume and complexityof the part are the fixed parameters. Depending on theapplication, surface finish, optical characteristics, andmany other properties may be added to the list. If thesecharacteristics affect the estimated decision parameters,neural networks should be selected to take these valuesas inputs. The operating conditions could be the fillerpercentage, process temperature, and other adjustableparameters. The allowable ranges of these parameterswould be given to the program.

One genetic algorithm is assigned for each compositematerial. The genetic algorithm gives the fixed para-meters of the part and various values for each operatingcondition parameter to the neural networks as input.Neural networks estimate the decision parameters suchas cost, manufacturing time, strength, and others. Eachgenetic algorithm tries to obtain the optimum operatingconditions for one composite material. After all the gen-etic algorithms reach the optimal solution, the process isstopped. The composite material that offers the lowestor highest value for the objective function according tothe problem is selected. The estimated optimumoperating conditions for that material will be used. Thedeveloped package does not have limitations on thenumber of n, and m could be a maximum of 6; however,very large n values require very long optimization times,while a large value of m will need very a extensive train-ing process. The package allows the user to select onedesign parameter to be maximized or minimized, and todetermine the acceptable range for all. In addition, it ispossible to give an optimization function that considersmultiple design parameters.

3.4. Operation of the proposed package

In addition to the graphic utility and optimization pro-grams, the CoMaSA package contains a neural networktrainer. All the neural networks are the back-propagationtype. All the constants and parameters of the operatingcondition are the inputs. To estimate each decision-mak-ing parameter one neural network with one output isassigned. Interaction of the CoMaSA with the user ispresented in Fig. 6.


Fig. 5. Structure of the optimization program of the CoMaSA.

4. Case study

To evaluate the performance of the CoMaSA, optim-ization was repeated with three different objectives. Inthe optimizations, three composite materials were con-sidered. For the composite materials the following nineequations were assumed to represent the manufacturingtime, cost, and strength of the prepared product:

material1:Time � 0.113f0.85v0.65c1.15(h.), (5)

Cost � 3.08f0.8v0.7c1.1($), (6)

Strength � 226f0.8(kPa), (7)



Strength � 332f0.82(kPa), (10)


Cost � 3.25f0.82v0.66c1.31($), (12)

Strength � 345f0.85(kPa) (13)

where v is volume of a part, c is the complexity of thepart, and f is the fiber volume to be used. The actualcharacteristics of the composite materials were not usedin this study since the material suppliers and manufac-turers did not want to distribute their priority infor-mation.

The volume and complexity of the part were constant.The optimization was repeated three times with the fol-lowing objectives: Minimum manufacturing time, lowest


Fig. 6. Proposed procedure for selection of optimal material andoperating conditions.

cost, and maximum strength. In each optimization theacceptable range of the two other design parameterswere selected. Fiber volume was the only parameter ofthe operating condition to be determined during the opti-mization. The allowable range of it was selected between0.1 and 0.9 in this study to see if it would be able touse the whole range. In the practical cases the volumepercentage of the filler is selected well below 90%.

5. Results and discussion

In this section the validity of the proposed complexityestimation procedure, correction of complexity byremoving the round holes, and performance of the opti-mization process will be discussed.

5.1. Validity of the proposed complexity estimationprocedure

To evaluate the validity of the proposed complexitycalculation procedure, the relationship between thecharacteristics of the parts and the calculated values arecompared. Ideally, the complexity should be constantwhen the part geometry is represented at different resol-utions; however, it should increase when the length andbend angle increase.

According to the desired part resolution, CAD/CAMpackages use different numbers of triangles to representthe parts. A valid procedure should estimate the same

Fig. 7. Part plotted with varying number of triangles (The surface ofthe half sphere on the left is represented by 2060 triangles while only106 triangles were used for the one on the right).

Fig. 8. Variation of complexity with number of triangles.

complexity for the same part with minimal deviation forthe number of triangles. A hemisphere is presented inFig. 7 when its surface is covered with 2060 and 106triangles. Both drawings were prepared using the Pro-Epackage. The variation of the complexity with the num-ber of triangles for the same part is presented in Fig. 8.The complexity changed very slightly when the numberof triangles changed twenty times.

Stringers are parts that are widely used in the struc-tures of aircraft, especially in the fuselage. Fig. 9 showsthe variation of the complexity parameter with the lengthfor various stringer shapes. The complexity of the partalso increases with the length. It is more expensive tobuild longer composite parts than the shorter ones. TheACCEM manual also indicates a similar relationship.

Fig. 9. Variation of complexity with length.


The proposed system correctly estimated the increase ofthe complexity with the length. In addition to the com-plexity, the volume of the part also increases with length.The cost of the longer parts will not only be the functionof the increasing complexity but also the increasing vol-ume.

Fig. 10 shows the variation of the complexity withthe bend angle. Bend angles increase the difficulty ofmanufacturing a part and its cost. Beams with rectangu-lar cross-sections and varying bend angle (angle betweenthe end planes) were modeled by using Pro-Engineerand analyzed using the complexity estimation system.The estimated complexity had an almost linear relation-ship with the bend angle of the part.

In this study decision-making parameters are calcu-lated by using neural networks. Since the neural net-works are capable of representing even very non-linearcharacteristics, identical trends between complexity anddecision-making parameters, such as cost, are not neces-sary.

5.2. Correction of complexity estimation with roundhole removal procedure

To evaluate the accuracy of the proposed complexitycorrection process by round hole removal, a cube wascreated with 5 in. edges. The STL file of the part wasprepared when the part had 1 to 12 holes with diametersof 0.50 in. and 1.00 in.. The complexity of the part wascalculated with holes. When the correction algorithmwas not used, part complexity changed between 1.69 and7.63 (Table 1 and Fig. 11). Complexity increased witheach extra hole. When the complexity was estimatedafter the round holes were removed, almost the samecomplexity values were obtained as the part with noholes. There was a small decrease in the complexitysince the number of holes used for the part were reduced.The complexity of the part without any holes was 1.00.The user interface of the program is presented in Fig.12. The correction algorithm also found the location ofthe holes and their diameter. The accuracy of both theestimated position and radius is satisfactory (Table 2) toestimate the drilling cost accurately.

Fig. 10. Variation of complexity with the bend angle.

Table 1Complexity of a part with holes and when the correction algorithmremoved the triangles at the surfaces of round holes

ComplexityNo. of holes Before holes removed After holes removed

1 1.69 0.99982 2.33 0.99663 2.93 0.99244 3.54 0.99445 4 0.98346 4.5 0.9789 6.22 0.984112 7.63 0.9788

Fig. 11. Complexity of the part increases with the number of holes.Proposed correction algorithm eliminates the error.

Fig. 12. The user interface of the complexity estimation programwith correction algorithm with round hole removal.


Table 2Hole locations and radiuses. Actual and calculated values are presented. Measurements are in inches

Hole no. Actual coordinates Calculated coordinates Hole no. Actual radius Calculated radius

1 X –1.500 –1.513 1 0.25 0.26Y 0.000 0.000 2 0.25 0.26Z 1.500 1.498 3 0.25 0.26

2 X –1.500 –1.513 4 0.25 0.26Y 0.000 0.000 5 0.25 0.26Z 0.000 –0.002 6 0.25 0.26

3 X –0.500 –0.513 7 0.25 0.26Y 0.000 0.000 8 0.25 0.26Z 1.500 1.498 9 0.25 0.26

4 X –0.500 –0.513 10 0.25 0.26Y 0.000 0.000 11 0.25 0.26Z 0.000 –0.002 12 0.25 0.3

5 X 0.500 0.487Y 0.000 0.000Z 1.500 1.498

6 X 0.500 0.487Y 0.000 0.000Z 0.000 –0.002

7 X 1.500 1.487Y 0.000 0.000Z 1.500 1.498

8 X 1.500 1.487Y 0.000 0.000Z 0.000 –0.002

9 X 1.500 1.487Y 0.000 0.000Z –1.500 –1.502

10 X 0.500 0.487Y 0.000 0.000Z –1.500 –1.502

11 X –0.500 –0.513Y 0.000 0.000Z –1.500 –1.502

12 X –1.500 –1.522Y 0.000 0.000Z –1.500 –1.456

Table 3Selected optimal material and operating conditions

Minimize Cost Minimize Time Maximize Strength

Ranges of output Time 2 to 8 (h.) Cost 100 to 200 ($) Cost 50 to 220 ($)Strength 150 to 350 (kPa) Strength 170 to 350 (kPa) Time 3 to 12 (h.)

Optimized values 118.3 ($) 5.037 (h.) 302.669 (kPa)Other outputs Time 5.631 (h.) Cost 143.912 ($) Cost 219.965 ($)

Strength 150.0 (kPa) Strength 170.0 (kPa) Time 11.702 (h.)Iterations 345 175 230Fiber volume 0.376 0.698 0.854Fittest material Material 2 Material 1 Material 3

5.3. Selection of the optimal material and operatingconditions

Nine back-propagation-type neural networks weretrained to represent the manufacturing time, cost, andstrength characteristics of three composite materials.

Each neural network had three inputs. The inputs werethe volume, complexity, and fiber volume percentage.The organization of the neural networks and geneticalgorithms is presented in Fig. 13. Optimization wasrepeated three times to obtain the minimum cost, theshortest manufacturing time, and maximum strength.


Fig. 13. Structure of the optimization composite material manufac-ture.

The user interface of the program after the completionof the optimization task is presented in Fig. 14. Theselected optimal material and operating conditions afterthe optimization process are presented in Table 3. Theaccuracy of the neural network training program andoptimization programs were demonstrated in the pre-vious paper [23].

6. Conclusion

In this paper, the representation of the characteristicsof the composite materials by using neural networks, andselection of the optimal material and operating con-ditions by using the genetic algorithms is proposed. Toevaluate the accuracy of the proposed automated pro-cedure, the Composite Material Selection Adviser(CoMaSA) package was developed. The package usesthree separate programs. These programs train the neuralnetworks to represent the characteristics of the parts,

Fig. 14. Selected optimum material and operating condition (fibervolume).

estimate complexity from the STL files, and optimummaterial and process parameters are selected by usingmultiple neural networks and genetic algorithms. Theprograms require minimum user input as almost all thecritical values are obtained automatically.

The proposed complexity estimation procedure auto-matically estimates the part complexity. If the part hasholes to be drilled after the manufacturing of the com-posite part is completed, correction algorithms estimatethe complexity of the part automatically after the roundholes are removed. This algorithm also reports the sizeand location of the holes. The complexity estimationprocedure was not sensitive to the number of the tri-angles, which cover the part surface. The estimated com-plexity increased proportionately when the length andthe bend angle changed. In all the studied cases, the opti-mal conditions were obtained without converging tolocal minimums.

The proposed multi-neural network system estimatedthree important decision-making parameters of com-posite material manufacturing very conveniently. It ispossible to increase the number of parameters. Once theparameters to be optimized were selected or an optimiz-ation function was determined, genetic algorithms foundthe optimal material and operating conditions within theselected boundaries. The proposed procedure is veryconvenient also to model and optimize other complexsystems.

Acknowledgements

This work was partially supported by the Air ForceResearch Laboratory (contract # F33615-99-C5703), andNational Research Council Summer Fellowship. Theauthors thank AFPL/MLLP, and NRC for the support.


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Documents

Selection of optimal material and operating conditions in composite manufacturing. Part II: complexity, representation of characteristics and decision making