PSI - Issue 54

Wojciech Skarka et al. / Procedia Structural Integrity 54 (2024) 498–505 Bartosz Rodak/ Structural Integrity Procedia 00 (2019) 000 – 000

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5. Profile optimization by Gradient optimization method The CAD model, FEM mesh, boundary conditions, solver settings of the tested geometry is the same as in the case of optimization by the DoE method described in Chapter 4 [2]. The Adaptive Single-Objective method is a gradient-based algorithm [3], [4] that provides an improved global optimization result. It supports a single objective, multiple constraints and aims to find the global optimum. It is limited to continuous and producible input parameters. In practice, this means that the program generates twenty initial experiments, solves them, and then, based on the principles of gradient optimization, creates successive points according to the direction (ⅈ) and step ℎ (ⅈ) . A total of one hundred and forty experiments are set. An identical simulation was performed for each experiment. Table 3 below presents the dimensions giving the lowest aerodynamic drag found using gradient optimization.

Table 3. Coordinates of spline nodes, forming the optimal geometry.

Direction

Nominal dimension

After optimization dimension

Point

0 0 2

X Y X Y X Y X Y

0 0

0 0

40mm

43,6mm 11,8mm 125,5mm 4,4mm 186,7mm 0 1,2mm

2 3 3 4 4 Edge round

13mm 130mm 4mm 200mm 0 1mm

The new geometry achieved an aerodynamic drag of 0.06038N. That is, 2.88% less than the geometry obtained using DoE optimization. 6. Comparison of optimization methods Optimization using the DoE method reduced aerodynamic drag by 9.39%, while optimization using the gradient method reduced aerodynamic drag by 12.27%. The DoE method has the advantage of giving extensive information about what input parameter has what effect on the output parameter, so you can estimate how a change in the input parameter will affect the result. In Table 4 below, you can see what parameters the two methods have chosen. Figure 5 you can see the differences in how the two methods searched the range of input parameter values. The DoE method uniformly searched the entire range of parameters, while the gradient algorithm compacted the search closer to the optimum over time.

Table 4. Comparison of the coordinates of the spline nodes, created using the DoE and the gradient method.

Direction

After optimization dimension by DoE method

After optimization dimension by gradient method

Point

0 0 2 2 3 3

X Y X Y X Y

0 0

0 0

43,7mm 11,8mm 140,5mm 3,7mm

43,6mm 11,8mm 125,5mm 4,4mm