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Also, no changes to the hullshapewere permitted along the keel line up to thebulb. This wasmostly a consideration for ease offabrication. Figure 5 shows the region that wasallowed to bemodified. Additional design con-straints included that therewould be no change inthe total displacement of the ship, and that therewould be no change in the LCB. Further con-straintswere added to provide smooth transitionsin the hull shape definition fromthe unperturbedhull portion to the bow section. Finally themaximumperturbation was limited to 10.0 ft(3.048m), which corresponds to approximately1.0%of the length between perpendiculars.The results of the single objective function opti-mization for Fr50.193 are given in Figure 6.Here the perturbation is given in ship-scale feet.The figure shows the hull form and computa- tional mesh used in three views, from the bowlooking aft, from the port side, and an isometricview. The graphic on the left shows the baselinehull form, which in this case was the originalbaseline bulbModel 5653 variant that wastested, but represented at ship scale. The graphicon the right shows the resulting hull shape afterminimizing the total resistance at a forwardspeed of 20 knots, corresponding to Fr50.193.Owing to the constraints applied to the optimi-zation procedure, the only changes are in theforward section of the bow and the bow bulb. Ascan be seen in the right graphic, the predictedoptimum geometry includes some added volumeto the forward end and top of the bow bulb,along with some small contraction of the lowerbow section toward the keel and aft of the bulb.When reevaluating the final result from the op-timizer, the total resistance was reduced by3.5%. A similar comparison of the baseline andoptimized hull shape for Fr50.290 is given inFigure 7. As shown in the graphic on the right,the optimization procedure at this speedattempts to alter the bow dome shape to includea lower protrusion. Because of the designconstraint to maintain the total displacement,the optimizer also pulls in the hull shape movingaft from the bow bulb. In this case, the totalresistance was reduced by approximately 2.0%.Finally, the baseline and optimized hull shape forFr50.386 is given in Figure 8. As shown in the graphic on the right, there is a continuation ofthe trend toward adding volume to the forwardend and top portion of the bulb. In this case,when the optimized hull shape was reevaluatedusing TSD in the fast mode, the total resistanceincreased just slightly by approximately10.02%.What this means is that the improvedhull shape determined by the optimizer turnedout to not be an improved design whenreevaluated by the solver. This is why the re-evaluation step is so important when evaluatinthe designs that are generated. It is also likelythat the constraint on the LCB is overlyconstraining the optimization process, as it isdifficult to optimize a small bow region withouallowing this to change.At this point, some comments regarding thenumber of basis functions used are warranted.Recall that in the previous total ship optimiza-tion example, a total of 35 basis functions werused. In many cases, this is found to be a suffi-cient number to examine the changes to thedesign. Generally speaking, one expects to findthat the improvements to the baseline designshould increase with increasing degrees of free-dom, assuming the same constraints are used. Imany cases, diminishing returns are observedfrom going to higher numbers of basis functiondue to decreasing impacts from shorter lengthscales. In the present bow shape optimizationexample, however, it was found that muchbetter behavior was found by increasing thenumber of degrees of freedom. In this case, the number of basis functions used forFr5 0.193 was 8 (longitudinal) and 6 (trans-verse) for a total of 48 degrees of freedom. TheFr50.29 optimization used 8 7 (total of 56)and the Fr50.386 optimization used 8 4 (totalof 32).Without additional testing of the resulting opti-mized shapes, we cannot make any definitivejudgment as to the magnitude of the reduction inresistance. But all of this has proved to be a use-ful demonstration of this type of capability andthe potential to incorporate shape optimizationtools within the IHDE.MultispeedOptimizationAnother caution in performing design optimiza-tions for ships is that there can be significantdependence on the speed for which the design isoptimized. In other words, a hull that is opti-mized for a single objective function at a givenspeed may perform much worse when at speedsother than the design speed. This is illustrated inFigure 9 that shows the predicted total resistancenormalized by the total resistance of the baselinehull shape for each of the single speed optimizedhull forms as a function of Froude number. Inthis example, the global constraints related tochanges in the displacement and changes in theLCB have been removed.As shown in Figure 9, the performance of thehull shapes that are optimized based on a singlespeed, perform very well at the speed at whichthey were optimized. Moving away from thosespeeds, however, can cause a significant degra-dation in the performance. This is particularlytrue when examining the hulls optimized atFr50.29 and Fr50.386 at the lower speedrange (Fro0.2). Also shown in Figure 9 are thepredicted normalized total resistance evalua-tions for a hull shape that was determined byusing multiple speeds in evaluating the objectivefunction. In this example, the three speeds weregiven weights of 0.5, 0.25, and 0.25 for theFr50.193, 0.290, and 0.386 conditions,respectively. As indicated in the figure, this mul-tispeed optimized hull shape performs quite well across much of the speed range. In a real designapplication, it would be more appropriate toapply a weighting based on the ships intendedspeed or mission profile, but this serves as asimple example to demonstrate the capability forperforming multispeed optimization using theSHAPE framework.Multi¢delity OptimizationAs discussed, it is intended to implement theshape optimization process within the CREATEIHDE for early stage design studies. In order toprovide improved accuracy, but still maintainefficient solutions, it is planned to incorporatea multifidelity approach to the solution of theobjective function. This would involve responsesurface modeling for the potential flow methods,to be corrected through the use of nonlinearresistance prediction tools. The current limitationis in regard to how to modify the volume meshneeded by the RANS code to predict the changesin the objective function for all of the hull shapeperturbations that result from applying the basisfunction pairs. This work is ongoing.SummaryThis project is aimed at assessing the use ofdifferent hydrodynamic tools in hull shape opti-mization and in a larger ship design process.Current efforts have focused on validation, inorder to provide confidence in the use of thetools, as well as automated processes that couldbe used within a ship design environment. Vali-dation work has been performed for URANSand potential flow analysis codes that areplanned for use in the CREATE IHDE.