Application of Automatic Nesting to Ship Hulls Using the FINEST Algorithm

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1 Application of Automatic Nesting to Ship Hulls Using the FINEST Algorithm NAHIMA Tomoki : NIWA Futoshi : HIRANO Hikaru : OKADA Tetsuo : Engineering Department, IHI Engineering Marine Co., Ltd. Ship & Offshore Design Department, IHI Marine United Inc. Advanced Technology Integration Department, IHI Marine United Inc. Manager, Ship & Offshore Design Department, IHI Marine United Inc. Nesting is the process used to arrange many complicated hull structure pieces from rectangular steel plates. Automation of this process has been studied for many years, but full application to the hull of ships was difficult. A newly developed method, called the FINEST algorithm, has two important developments. The first is to calculate repulsive forces based on lapping area calculation of the pieces. The second is to search for the optimum arrangement using stochastic moves and rotations, introducing temperature, or a parameter to express randomness. In this paper, the algorithm is summarized, and the usefulness of this method explained through application to an actual ship hull structure. 1. Introduction The hull structure is built by assembling its component members, one by one, cut out from rectangular steel plates. At that time, the members are arranged on the steel plates in a way that minimizes scraps after cutting (to improve yield) and to efficiently operate the plasma cutting machine. This work is called nesting. Heretofore this work has been done manually requiring a lot of work time. Recently, computerized automatic nesting has been observed. The method consists of programming empirical rules, developing a genetic algorithm, (1)-(3) and simulating annealing. (4) But the shapes of the members of the hull structure are complicated, making it very difficult to develop an automatic nesting method that will simultaneously realize a small scrap ratio and NC cutting conditions that do not require repairing after nesting. Therefore, no complete automation has been realized. Under such circumstances, the authors developed an automatic nesting algorithm by a completely new method described below. Normally natural work approaches the state of energy level minimum when disturbance is properly given. When an earthquake occurs, gaps in soil are compacted and water contained in the gaps gushes out causing a liquefaction phenomenon. If the temperature of steel is properly controlled, its structure is made uniform and internal stress is relieved. Taking a hint from these phenomena, we defined the state of lapping and scattering of members as the state of a high energy level and devised an algorithm to arrange the members without gaps by properly controlling the temperature or the range and amount of stochastic motion and rotation, and named this the FINEST algorithm. In this paper, we outline the FINEST algorithm and system development in applying it for nesting on an actual ship and explain the usefulness of this method referring to its application on actual blocks of the ship. 2. FINEST algorithm Normally a ship is built one portion or block at a time, and nesting is done for each block. In the nesting process, hundreds of members to form a block are allocated in accordance with thickness and material for several to tens of rectangular steel plates and arranged for efficient cutting-out at a small scrap ratio. The hull structure members vary in shape and especially many of the hull s internal structural members have complicated shapes, making it difficult to realize automatic nesting with a satisfactory scrap ratio. In nesting, a method of cutting efficiently must also be considered. To satisfy such various requirements of nesting, we have developed a versatile nesting algorithm described below and realized a practical automatic nesting system. 2.1 Outline of FINEST algorithm Members are randomly arranged on steel plates, a proper repulsive force is virtually generated on the lapping between the members, and the members are moved so as to eliminate the lapping. On portions protruded from the steel plate as well, a proper repulsive force is generated and the members are moved to eliminate the protrusion. The members are repeatedly moved by such 38

2 repulsive force, making it possible to simulate a member arrangement that minimizes the lapping and protrusion from the first random member arrangement. If the initial combination of initial member arrangements is proper and the steel plate size is sufficient, member arrangements without lapping between members or protrusion can be obtained. But if the initial member arrangements are improper or the members are closely arranged, the members will hit one another and the lapping among members and protrusion from the steel plate may remain. For this reason, the repulsive factor with the member temperature as a parameter to be described later is increased to make the member arrangement state unstable, and the members with high temperature are moved or replaced with one another to cause transition to a new member arrangement state, thus repeating the simulation. Figure 1 shows the flowchart of the FINEST algorithm. 2.2 Member shape for simulation For the member shape to be used for simulation, a cutting margin range is added in accordance with the joint geometry in order to consider the cutting margin. To simplify the simulation of the member motion on a computer, arcs and spline curves included in the member shape are linearly approximated so that they will remain within the allowable error range, and a counterclockwise loop is formed. Figure 2 shows the member shapes for simulation for the arcs. For the steel plate shape, however, it is necessary to recognize portions of the members protruded from the steel plate, and so a clockwise loop is formed opposed to that for the member shape, and lapping with the area outside the steel plate is recognized. 2.3 Member motion simulation Lapping among members and protrusion area from the steel plate (hereinafter called lap) are recognized. Virtual repulsive force is generated on the lap and the members are moved so as to eliminate the lap. Such member movement is repeated on all the members until the lap Member input Arrangement of input members Fig. 2 d (Note) : Cutting margin : Simulated shape side d : Simulated shape error Piece contour shape expression for simulation amount and decreases in member temperature described later are no more recognized Lap recognition and member movement by repulsive force It is judged if the intersection of component sides between members and the apex are internal points including in the other member. The shape of the lap area can be obtained by connecting these intersections and internal points. For the protrusion area from the steel plate as well, the lap is recognized. Then, repulsive force is generated at the center of gravity of the lap to move the member. Figure 3 shows an example of member movement due to lap Member temperature and repulsive factor The repulsive force generated in mutually counteracting directions in one member is taken as internal energy accumulated in the member and defined as member temperature parameter. The member temperature is reflected as the repulsive factor between members (Fig. 4) on the member movement. Figure 4 shows the effects of introducing the member temperature parameter assuming that 3 members A, B, and C are arranged in a lapped way. Member B at the center hardly moves because it receives repulsive force from members A and C on both sides (-(a)). Members A and C on both sides move about half the lap amount but the half of the lap remains (-(b)). In the next member movement, since the member temperature at the center is high, the amount d Input member arrangement completed Simulation of member movement due to repulsive force Yes Lap elimination Searching for member arrangement Control of randomness, moving/replacing Crowded-out members No Cannot be eliminated Repetitive simulation of some arrangement states Yes Lap elimination No Cannot be eliminated Repetitive simulation of different input member arrangements Simulation of member movement due to repulsive force b3 c1 b1 b2 a1 c2 c1, c2 : Intersection a1 : Internal point of member A b1, b2, b3 : Internal point of member B Member A : Repulsive force : Repulsive force working point (lap gravitational point) : Lap shape component side Member B Member movement due to repulsive force Fig. 1 Flowchart of the FINEST algorithm Fig. 3 Movement and rotation of pieces based on lapped area 39

3 (b) Step 1 Member temperature increased due to repulsive force from right and left Member temperature at the center is high and so repulsive factor increases Lap amount eliminated much Repulsive force from right/left decreases and member temperature decreases Fig. 4 (a) Step 0 (initial state) Member A Member B Member C Repulsive force to center member canceled (Note) (c) Step 2 : Repulsive force to members on both sides : Repulsive force to center member : Member temperature Piece temperature and repulsive factor of movement of the members A and C on both sides whose temperature is relatively low increases. As a result, the lap amounts of members A, B, and C greatly decrease (-(c)). 2.4 Member arrangement Priority of nesting The nesting is done in the descending order of area from steel plates low in grade and thin in thickness. In accordance with the conditions such as grade and thickness of steel plates, members subject to nesting are selected and the nesting is tried, one member at a time, in the following order of priority. As to members whose grade and thickness are specified lower within the allowable range, the nesting is tried by lowering the order of priority. Members to be nested on a particular steel plate are selected in the following order of priority. q Steel plate explicitly is specified. w Less difference in thickness from the steel plate e Less difference in material grade r Large in area Pairing In manual nesting, 2 to 4 members similar in shape may be combined and arranged, which is called pairing. Pairing makes it possible to reduce the number of holes, called piercing points, for starting member cutting. Another merit of the pairing is to facilitate the nesting because the peripheral shape of the paired members becomes almost rectangular. This automatic system can also pair 2 members to facilitate the member arrangement Arranging input members In the order of priority, the nesting is tried for each member or members paired if effective pairing is possible. The input members are arranged as follows. At random from the left end of the steel plate, members are input, searching for empty places where no other members are arranged. Members are input in other empty places repeatedly until the lap disappears through member motion simulation. Figure 5 shows an application example in which this method is effective. In this example, the slender members indicated as FB in Fig. 5 are arranged in the longitudinal direction of the steel plate. This acts as a restraint to prevent dropping from the surface plate during NC cutting. The FINEST algorithm seeks stochastic arrangement purely from member shape and material shape, and the possibility of simply giving such restraint condition as member arrangement instructions is one of its advantages Searching for member arrangement In the aforementioned arrangement of input members, members are input and the nesting is tried in empty places when some members are already arranged. In some cases, however, the nesting may not be possible, depending on the combination of member arrangements before members are input. In such a state, the aforementioned temperature greatly increases because the lap is not eliminated. In such a case, members high in temperature are largely moved or rotated in a stochastic way and replaced in arrangement with other members, and the member arrangement simulation is tried several times by combining new member arrangements. This method is effective when the combination of member arrangements is important. Figure 6 shows an application example. 3. Peripheral system for applying to actual ship Figure 7 shows the outline of the FINEST system for application to an actual ship. The FINEST data creation system takes out members subject to nesting from steel data and parts list data and creates the data for the Member Steel plate SL32 5N10 KAM size : piece No. : 48 r (Note) FB : Longitudinal arrangement of slender members against steel plate Member FB Fig. 5 Application example (1) Steel plate SL32 5N02 KAS size : piece No. : 9 r Fig. 6 Application example (2) 40

4 Parts list data Piece CAD data FINEST data creation system Block, mid-assembly priority file Material list file Member list file FINEST system P-NEST conversion file P-NEST conversion system P-NEST file P-NEST conversion system Fig. 7 Steel plate data Outline of FINEST system flow Nesting list List of crowded-out members Log file FINEST system. It has additional functions to efficiently apply to the actual ship such as a function to forcefully allocate the specified members to a particular steel plate (arrangement for nomination). Figure 8 shows the data creation menu screen in the FINEST data creation system. The P-NEST conversion system converts the data created above to the format for P-NEST. P-NEST is an interactive program for nesting developed by IHI Marine United Inc. With P-NEST, it is possible to manually correct the nesting arrangement, and a cutter path is defined and NC data are created. 4. Example of application to actual ship 4.1 Block applied to actual ship We describe an example where the automatic nesting by means of the FINEST system (hereinafter called FINEST) was done with a 4D32 block, a block of the Fig. 8 FINEST data preparation menu engine room of a large TEU container ship. The members were limited to internal structural members and the number of material steel plates was 20. Table 1 shows the yield rate comparison results in the ascending order of plate thickness between FINEST and manual nesting. A comparison of both results shows that FINEST has more allocated members and better yield than manual nesting. The number of crowded-out members (members not contained within the steel plates) was 11 out of 410 members in total for the manual nesting against 3 members for FINEST, which used many stored plates. As a result, the application of FINEST increased the yield by 1.5%. Depending on the block, the number of material plates is several to tens of plates, and the more material plates handled at a time, the more the yield tends to improve. 4.2 Results of FINEST Figure 9 shows the results of FINEST of all the 20 places of 4D32. As to the members of mm or more in length, FINEST was carried out by subjecting particular material members to the arrangement for nomination. As a result of FINEST, the rectangular members are regularly nested in Fig. 9-(a). In -(b), 3 members (A, B, C) subjected to the arrangement for nomination are nested fully to the material width. As to the other material plates, we confirmed that the members subjected to the arrangement for nomination were not crowded out. In FINEST, the material plates were allocated in the Code Plate No. 9G17 9G06 9G07 9G26 9G15 9G05 9G25 9G16 9G23 9G04 9G24 9G21 9G14 9G22 9G03 9G02 9G01 9G13 9G12 9G11 Table 1 Material G2A G2A G2A Yield rate comparison results (4D32) Thickness (mm) Width (mm) Length (mm) FINEST Yield (%) Manual nesting

5 (a) Result 1 (g) Result 7 4D32 9G17 size : piece No. : 14 r D32 9G25 size : piece No. : 15 r (b) Result 2 (h) Result 8 A B C 4D32 9G06 size : piece No. : 18 r (c) Result 3 4D32 9G16 G2A size : piece No. : 19 r (i) Result 9 4D32 9G07 size : piece No. : 12 r (d) Result 4 D 4D32 9G23 size : piece No. : 21 r (j) Result 10 4D32 9G26 size : piece No. : 23 r (e) Result 5 4D32 9G04 size : piece No. : 47 r (k) Result 11 4D32 9G15 size : piece No. : 60 r (f) Result 6 4D32 9G24 size : piece No. : 1 r D32 9G05 size : piece No. : 26 r Fig. 9 Results of FINEST application -1 (4D32) 42

6 ( ) Result 12 (q) Result 17 4D32 9G01 size : piece No. : 38 r D32 9G21 size : piece No. : 4 r (m) Result 13 (r) Result 18 4D32 9G14 size : piece No. : 14 r D32 9G13 size : piece No. : 18 r (n) Result 14 (s) Result 19 4D32 9G22 size : piece No. : 6 r D32 9G12 G2A size : piece No. : 3 r (o) Result 15 (t) Result 20 4D32 9G03 size : piece No. : 54 r (p) Result 16 4D32 9G11 size : piece No. : 4 r D32 9G02 G2A size : piece No. : 10 r Fig. 9 Results of FINEST application -2 (4D32) ascending order of plate thickness, and the 5th material plate (-(e)) decreased in yield compared with manual nesting. This is because the performance of FINEST was good, and the members of 11.0 mm in thickness allocated for the material plates of -(e) in the manual work were nested with the material plates of -(b) to -(d), and the number of members left for -(e) decreased. In the manual nesting, 5 small brackets of 11.0 mm in thickness were not contained in the plates up to -(e) and they were allocated for the material plates of 12.0 mm in thickness. In FINEST, however, they were all nested up to -(e). In -(f), -(g), and -(h), members of 12.0 mm in thickness were sufficiently prepared, and the yield rate increased again, showing the tendency of better results than with manual nesting. For the arch-type member D of -(i), normally a bridge is provided for the opening. This time, however, no bridge was provided in the prior production of piece data, and members were nested in the opening as well. In the FINEST of -(j), large and small members including those subjected to the arrangement for nomination were randomly nested and the yield rate is higher than with manual nesting. In comparison with the results of the manual nesting shown in Fig. 10, the results of FINEST show that the nesting was fully done. In manual work, regular nesting was emphasized, and 43

7 Fig. 10 Results of manual nesting (4D32 9G04) this means that the random arrangement without gaps tends to have a higher yield. With the 5 material plates of mm in thickness in Fig. 9-( ) to -(p), many members were nested without gaps in the beginning 3 plates, leaving fewer members to be allocated in -(o) and -(p), thus decreasing the yield rate. In -(s) and -(t), while the minimum plate size to be ordered is mm in width and mm in length, the number of members to be allocated is small, thus decreasing the yield rate. For both FINEST and manual nesting, the same members were allocated, resulting in the same yield rate. In the result of -(t), the members were nested on the left side, and the surplus material plates on the right side can be effectively utilized as stored plates in the future. 4.3 Future subjects for study In connection with FINEST, future subjects for study include: (1) Presently, as to finished products such as flat bar, cutting-out from plates is not taken into consideration for the purchase order of the material. In FINEST, members are packed as much as possible as described in Section 4.2, and as a result, a gap tends to occur with the last material plate of the same thickness. Utilizing this good performance and by inserting the finished products during FINEST, the yield rate can be expected to further increase. (2) In manual nesting, consideration is given to various conditions to improve the cutting efficiency. With FINEST, for example, large and small members are randomly nested without gaps. In manual nesting, on the other hand, small members are arranged on the origin side (lower left) and large members are cut last, in consideration of the cutting sequence. Also in manual nesting, the members may be regularly arranged so that single-stroke cutting can be done for many members. Future subjects in operation are how to reduce the nesting correction after P-NEST converting and optimization of the cutter path. (3) There are detailed rules to be considered for the cutter path such as arch-type bridge and cutter-stop treatment. It is indispensable, for example, to improve operation rules through FINEST such as including the bridge in the production of piece data prior to FINEST. 5. Conclusion In this paper, we have outlined the FINEST algorithm devised anew as an automatic nesting method through the stochastic method and explained its usefulness referring to cases in which it was applied for blocks of an actual ship. As to the yield, we realized arrangements unlikely to be imagined by human, and generally it tends to be better than with the manual method. By this method, the nesting time can be greatly reduced. We have successfully developed an automatic nesting system that can be practically applied. In the future, we intend to promote our investigation toward realizing more efficient automatic nesting systems of good quality while accumulating experience in applying them to actual ships. REFERENCES (1) Berthold Kroeger, Peter Schwenderling and Oliver Vomberger : Parallel Genetic Packing of Rectangles, Proc. of Parallel Problem Solving from Nature 1st Workshop (1991) pp (2) K. Fujita, S. Akagi and N. Hirokawa : An Approach for Optimal Nesting Using Genetic Algorithm and Local Minimization Algorithm, The Japan Society of Mechanical Engineers, The Second Conference on Design Engineering, System Section No Dec pp (3) S. Yamauchi and K. Tezuka : Automatic Nesting System by Use of Genetic Algorithm, Journal of The Society of Naval Architects of Japan Vol. 178 Nov pp (4) P. Jain, P. Fenyes and R. Richter : Optimal Blank Nesting Using Simulated Annealing, Advances in Design Automation DE-Vol.23-2, ASME (1990) pp