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Table 4: Annual sea state occurrence in the open North Atlantic ocean [20]. Geometry modification of the parent hull are based on the morphing aproach presented by Serani et al. [10]. This is based on modified designs, used as a basis function for the geometry modification space, as given by a combined geometry and physics based dimensionality reduc- tion method based on the KLE [9, 10]. The original design space was defined by 27 coefficients of orthogonal basis functions spanning a tridimensional domain embedding the hull [6]. The design space was reduced in dimensionality to 14 variables by the KLE method. Hereafter, only the first KLE function (and therefore only one design variable x) is used, corresponding

Table 4 Annual sea state occurrence in the open North Atlantic ocean [20]. Geometry modification of the parent hull are based on the morphing aproach presented by Serani et al. [10]. This is based on modified designs, used as a basis function for the geometry modification space, as given by a combined geometry and physics based dimensionality reduc- tion method based on the KLE [9, 10]. The original design space was defined by 27 coefficients of orthogonal basis functions spanning a tridimensional domain embedding the hull [6]. The design space was reduced in dimensionality to 14 variables by the KLE method. Hereafter, only the first KLE function (and therefore only one design variable x) is used, corresponding

Related Figures (9)

Figure 1: DDG-51 overview with bridge and flight deck location (images from the-blueprints.com and ship- bucket.com).
Figure 1: DDG-51 overview with bridge and flight deck location (images from the-blueprints.com and ship- bucket.com).
Table 1: DTMB 5415 main particulars. 2.2 Mathematical formulation of the simplified problem A simplified version of problem 1 is formulated. The expected value of the mean total resistance in waves is substituted by the total resistance evaluated in calm water, considering variable speed only. The resistance is divided by the ship displacement V in order to consider displacement variations in the optimization process. The OE considers a limited set of four constraints (NV, = 4), addressing roll (£4) and pitch (€;) motions, vertical velocity of the flying deck (vp), and vertical acceleration of the bridge (ag). Maximum allowable values for twice the RMS are summarized in Tab. 2. EY ie a cece, Oe OE ee: eee eee
Table 1: DTMB 5415 main particulars. 2.2 Mathematical formulation of the simplified problem A simplified version of problem 1 is formulated. The expected value of the mean total resistance in waves is substituted by the total resistance evaluated in calm water, considering variable speed only. The resistance is divided by the ship displacement V in order to consider displacement variations in the optimization process. The OE considers a limited set of four constraints (NV, = 4), addressing roll (£4) and pitch (€;) motions, vertical velocity of the flying deck (vp), and vertical acceleration of the bridge (ag). Maximum allowable values for twice the RMS are summarized in Tab. 2. EY ie a cece, Oe OE ee: eee eee
Table 2: Subsystem seakeeping performance criteria: maximum values for 2 RMS [16]. 3 Numerical methods, implementation, and setup
Table 2: Subsystem seakeeping performance criteria: maximum values for 2 RMS [16]. 3 Numerical methods, implementation, and setup
Figure 2: DDG-51 transit (a) and total speed-time (b) profiles using kernel density estimation of 2013 data from [19]. considers tne transit speed-tume prome of he VDUG-)1 [17] (See F1g. 2a). The OE is calculated using the RAOs provided by SMP combined with the Bretschneider spectrum with significant wave height (4, /3) and modal period (7;,) shown in in Tab. 4. The OE is evaluated using the full scale and a full factorial combination of sea state (2 < S' < 7), heading (Odeg < 6 < 180deg), and speed (Okn < U < 30kn). The PDF for S, 3, and U are based on the North Atlantic sea state occurrence [20] (see Tab. 4), an homogeneous distribution, and the total speed-time profile [19] (see Fig. 2b), respectively.
Figure 2: DDG-51 transit (a) and total speed-time (b) profiles using kernel density estimation of 2013 data from [19]. considers tne transit speed-tume prome of he VDUG-)1 [17] (See F1g. 2a). The OE is calculated using the RAOs provided by SMP combined with the Bretschneider spectrum with significant wave height (4, /3) and modal period (7;,) shown in in Tab. 4. The OE is evaluated using the full scale and a full factorial combination of sea state (2 < S' < 7), heading (Odeg < 6 < 180deg), and speed (Okn < U < 30kn). The PDF for S, 3, and U are based on the North Atlantic sea state occurrence [20] (see Tab. 4), an homogeneous distribution, and the total speed-time profile [19] (see Fig. 2b), respectively.
Table 3: Simulated conditions to build the SRBF training set. [18]. The steady 2DOF (sinkage and trim) equilibrium is achieved by iteration of the flow solver and the body equation of motion. The computational domain for the free surface is defined within 1 L,,, upstream, 3, downstream, and 1.5L, sideways. A total of 15.6k panels are used considering both hull and free-surface domain. The model scale is used for resistance (Lpp = 5.720 m) with speeds within the range 0.25 < Fr < 0.41 (corresponding to 18kn < U < 30kn at full scale). The latter values give the most probable range of speeds if one considers the transit speed-time profile of the DDG-5 I [19] (see Fig. 2a). ML. FVD 22. nanlniwlretnsy]] eam mem tn TIN ALN orem rtndnt h+~: ANAN 2.2... a ae a: ¢, a a ee: ae
Table 3: Simulated conditions to build the SRBF training set. [18]. The steady 2DOF (sinkage and trim) equilibrium is achieved by iteration of the flow solver and the body equation of motion. The computational domain for the free surface is defined within 1 L,,, upstream, 3, downstream, and 1.5L, sideways. A total of 15.6k panels are used considering both hull and free-surface domain. The model scale is used for resistance (Lpp = 5.720 m) with speeds within the range 0.25 < Fr < 0.41 (corresponding to 18kn < U < 30kn at full scale). The latter values give the most probable range of speeds if one considers the transit speed-time profile of the DDG-5 I [19] (see Fig. 2a). ML. FVD 22. nanlniwlretnsy]] eam mem tn TIN ALN orem rtndnt h+~: ANAN 2.2... a ae a: ¢, a a ee: ae
Figure 3: KLE eigenfunction for the shape modification of the simplified problem. X is the KLE eigenvalue. to the shape modification retaining the largest design variability (see Fig. 3). The modification function is normalized such as -—1 < x4 < 1.
Figure 3: KLE eigenfunction for the shape modification of the simplified problem. X is the KLE eigenvalue. to the shape modification retaining the largest design variability (see Fig. 3). The modification function is normalized such as -—1 < x4 < 1.
Figure 4: Total resistance over displacement (a) and operational effectiveness (b) sensitivity. The circles are the potential flow samples (SRBF training point).
Figure 4: Total resistance over displacement (a) and operational effectiveness (b) sensitivity. The circles are the potential flow samples (SRBF training point).
5 Conclusions and future work
5 Conclusions and future work
Figure 5: Non-dominated solution set with extrema optimal hull stations compared to the original. Table 5: Numerical results for the extrema of the non-dominated solution set.
Figure 5: Non-dominated solution set with extrema optimal hull stations compared to the original. Table 5: Numerical results for the extrema of the non-dominated solution set.
Related topics:
Multiobjective OptimizationStochastic Optimization
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