Aircraft Wing Design Against Bird Strike Using Metaheuristics

Abstract

Bird strikes pose a significant threat to aviation safety, particularly affecting the wing structures of aircraft. This research aims to design and analyze the impact of bird strikes on wing structures using response surface method and metaheuristics (MHs), which are used to explore various risk minimization and damage mitigation techniques. The optimization problem is the minimization of the maximum von Mises stress of aircraft wing structure against bird strike that is subject to displacement and stress constraints. The design variables include skin and rib thickness, as well as sweep angle. Difficulty due to embedded bird strike simulation and optimization design can be alleviated using a response surface method (RSM). The regression technique in the RSM of the data can reach our goal of model fitting with a higher R² until 0.9951 and 0.9919 are obtained for the displacement and von Mises stress model, respectively. The response surface function of the displacement and von Mises stress are related to skin thickness, while sweep angles rather than rib thickness have a greater impact on both design variables. The optimized design of the design variables is performed using MHs, which are TLBO, JADE, and PBIL. The comparative result of MHs can conclude that the PBIL outperformed others in all descriptive statistics. The optimized design results revealed that the optimum solution can release better energy due to bird strike with the highest limit of skin thickness, moderate rib thickness, and less than half of the sweep angle. The results are in accordance with the response surface function analysis. In conclusion, the optimized design of the aircraft wing structure against bird strike can be accomplished with our proposed technique.

1. Introduction

Our interest in this research topic stemmed from a series of recent aviation incidents, including the tragic Jeju Air 2216 that crashed on 29 December 2024, which, like many others, was attributed to bird collisions. Within just a few weeks, several high-profile bird strike-related accidents raised significant concerns about the safety of aircraft operations. These events left us wondering how these collisions impact aircraft structures and whether there are ways to minimize the risks and damage caused by bird strikes. Given the increasing frequency of these incidents, we decided to focus on understanding the mechanics of bird strikes, their effects on aircraft, and exploring methods to mitigate the resulting damage.

Bird strikes occur when birds collide with aircraft during takeoff or landing, or in flight. These events involve high-speed impacts, transferring a significant amount of kinetic energy to the aircraft structure. Bird strikes are often considered soft-body impacts, as birds deform and behave like fluids upon collision. This fluid-like deformation of bird tissues has been a subject of study for several decades [1]. This work introduced the concept of soft-body impact mechanics, noting the extensive deformation that birds undergo when struck at high velocities. The accuracy of how bird tissue deforms in a fluid-like manner when subjected to high-velocity impacts with aircraft surfaces was further confirmed by Dede (2015) [2], who compared various simulation methods, including smoothed particle hydrodynamics (SPH), arbitrary Lagrangian–Eulerian (ALE), and Eulerian methods. His research showed that SPH was more effective at simulating bird deformation and pressure distribution during collisions.

The key parameters that influence the severity of bird strike damage are the impact velocity, bird mass and density, and the angle of impact. Research has shown that higher velocities result in greater deformation and more damage, while larger birds cause more forceful impacts. The angle at which the bird strikes the aircraft also determines how the impact force is distributed across the aircraft structure, influencing the failure mode of the materials. Hedayati and Ziaei-Rad [3] found that oblique bird strikes produce different stress distributions compared to direct frontal strikes, which further emphasizes the importance of understanding these impact dynamics.

Given the difficulty and high cost of conducting physical bird strike tests, finite element analysis (FEA) has become an invaluable tool for simulating these impacts. The explicit finite element method is particularly useful for simulating the nonlinear, high-speed deformations that occur during bird strikes. FEA allows researchers to model and predict the behavior of materials under impact, which is crucial for designing more resilient aircraft structures. Dede (2015) [2] highlighted the accuracy of FEA simulations in predicting the interaction between bird tissues and aircraft components. However, when it comes to simulating the deformation of soft-body impacts, the smoothed particle hydrodynamics (SPH) method was identified as the most effective approach. Several studies have demonstrated the reliability of SPH in bird strike simulations. Guida et al. (2014) [4] showed that SPH simulations closely aligned with experimental bird strike tests, validating the method’s effectiveness. Lavoie et al. (2015) [5] compared SPH results with real-world bird strike incidents and found that SPH provided the accurate predictions of stress propagation and material failure, confirming its use as a reliable tool in bird strike research.

Aircraft structures, particularly the materials used in their wings, play a vital role in determining how well an aircraft can withstand the impact of a bird strike. Materials such as aluminum alloys and carbon-fiber-reinforced polymer (CFRP) [6] composites are commonly used in aircraft design, but they respond to impacts in very different ways and different anti-bird strike design components have also been studied [7]. The impact resistance of honeycomb material and different leading-edge structures has been studied to face the bird strike [8]. In addition, it was found that composite sandwich panels with energy-absorbing cores significantly improved the impact resistance of aircraft structures, using topology optimization design [9].

From the literature review, it was found that some recent works of aircraft wing structure design still lack an optimized design against bird strike, especially for the application using MHs to design the aircraft wing structure to alleviate bird strike damage, as it is difficult to embed the optimization technique in this field of study. The response surface technique is an alternative to connect both techniques and working together.

2. Methodologies

This part will conduct numerical simulation techniques, using necessary data for aircraft wings and bird properties for bird strike analysis. The methodology consists of the following:

Data collection: Reviewing literature for preparing theory background for past bird strike simulation.

Simulation setup: Preparing simulation technique background, aircraft wing model, material properties, including validation.

Optimum design: In this study, the optimum design of aircraft wing structure is a combination of bird strike simulation technique and optimum design in a group of metaheuristics (MHs) with the use of response surface method (RSM).

The flow diagram of the proposed methodology for aircraft wing design against bird strike is provided in Figure 1. This flow diagram shows the difference between the present technique and the past one. The present technique combines optimization design and bird strike simulation. The task, due to non-continuous run of the bird strike simulation, can be accomplished with a response surface methodology. The details of each section are presented as follows.

2.1. Aircraft Wing Structure Model and Bird Parameters

In this paragraph, aircraft wing model and bird parameters are prepared. The aircraft wing models with a section of straight wing composed of four ribs and skin, as shown in Figure 2. The simple model of the aircraft wing is chosen for this design demonstration due to its composition of ribs and skin, as used for validation in previous work [4,5,10,11]. The model validation is presented in the next section. The difference between the previous validation model and present wing structure is that the current one is added with ribs at the side, as shown in Figure 1. The present model of the aircraft wing made it close to an actual wing. The design parameters are skin thickness (t_s), rib thickness (t_r), and sweep angle (Λ). The main parameters of this model section are 1000 mm in chord, 1500 mm in span, and 100 m/s of aircraft speed for a low-speed aircraft. The overall parameters of the aircraft wing and bird are presented in

Table 1. Wing and bird parameters.

No.	Parameters	Values/Shape
1	A section-span length, L(mm)	1500
2	Root chord length, RC (mm)	1000
3	Tip chord length, TC (mm)	1000
4	Sweep angle Λ, (degree)	0–40°
5	Number of ribs	4
6	NACA	0012
7	Number of skin	1
8	Skin thickness (ts) (mm)	0.5–2
9	Ribs thickness (tr) (mm)	0.5–5
10	Aircraft speed (m/s)	100
11	Bird shape	ellipsoid

, while its’ material properties are presented in

Table 2. Wing and bird material properties.

Aluminum (AL5083H116) Properties	Value	Unit
Young’s modulus (E)	70 × 109	Pa
Yield stress (σy)	167 × 106	Pa
Poisson’s ratio (ν)	0.3	-
Density (ρ)	2700	kg/m3
Bird (Water 2) Properties	Value	Unit
Mass	1.81	kg
Poisson’s ratio (ν)	-	-
Density (ρ)	1000	kg/m3

.

2.2. SPH and Validation of Wing Model

In the past, there were three models used for modeling bird strikes, such as arbitrary Lagrangian–Eulerian (ALE)approaches, arbitrary Eulerian method (AE), and smoothed particle hydrodynamics (SPH) [3]. The first technique is used to handle large deformations in simulations while maintaining accuracy. It is commonly applied in bird strike analysis to model both the bird and aircraft structures. The second technique is a variation of the Eulerian method. It is useful for simulating fluids or highly deformable materials, such as bird issues in impact studies. Sometimes, AE is used interchangeably with ALE. The last one technique is called a mesh-free, particle-based method, which is well suited for modeling soft-body impacts, like bird strikes, as it accurately captures deformation and pressure distribution. It is often preferred over ALE for bird strike simulations due to better accuracy [3]. SPH was developed in 1983 to avoid limitation of mesh grid in finite element method. The response surface function is constructed from multiple simulation runs following the design of the experiment (DoE), as the accuracy of the model is needed. To validate the wing model and the simulation technique, the necessary parameter in the setting is from the review of the literature [4,5,6,7,8,10,11]. Bird speed is tested at 129 m/s [4,11]. The mass of birds is 3.66 kg (its density of 1000 kg/m³). In the validation, the bird strike is a case of direct frontal strikes, of which the model is an ellipsoid in shape [12], as shown in Figure 2. Wing and bird are meshing with 5858 elements. For the first start, the wing and bird are modeled in explicit dynamics (ANSYS v.2023), which are then transferred to AUTODYN to be solved with the SPH solver. The SPH model of the bird is replaced with 3097 particles. From the previous work, the following parameters are recommended [8]. Bulk viscosity control (the quadratic viscosity coefficient) uses parameters Q1 = 2 and (the linear viscosity coefficient) Q2 = 0.25. For setting hourglass energy control (Flanagan–Belytschko viscous form), the parameters used are IHQ = 2 and the hourglass coefficient QH = 0.14. Finally, the contact type is the contact node to the surface. The analysis time of the bird strike simulation is set up for 5 × 10⁻³ sec. In this study, the aluminum alloy is chosen as a tool for validation, which has material properties as shown in Table 2. The aluminum alloy type has been used for validation testing in the work [10,13]. The present study, its thickness was simplified to 1.8 mm (considering only aluminum face thickness without considering a honeycomb core). In this study, von Mises stress and the leading-edge deformation of the wing are examined due to its objective function and constraint, respectively. Postprocessing deformations of the skin and ribs are presented in Figure 3. The deformation shape of the wing and ribs obtained in this study are consistent with the results by [8,11]. Especially for the von Mises stress result of Figure 4a, the validation result is more conservative than the reference data [11]. The present stress is 322.4 MPa, while the reference is 350 MPa. The reason for the difference is from reinforcement by an addition of a rib besides the original double ribs. Furthermore, buckling occurred at the upper and lower skin of the leading edge, as shown in Figure 4b due to the deformed shape during collision, which is caused by compressive load. This behavior is consistent with the results by [8,11]. Furthermore, the collision effect tries to pull both the leading edge of middle ribs together, as shown in Figure 4, which is similar to the previous work for both the simulation and experiment [8,11]. From validation, the construction of the RSM function with DoE is ready, as presented in the next section.

2.3. Response Surface Method

2.3.1. Regression Model

The task in modeling with the SPH method for the bird strike simulation and optimization of design can be accomplished using the regression technique and design of experiment (DoE). The lack of capability in the continuous simulation of SPH with an optimizer can be alleviated with the RSM. The design variable of an aircraft wing structure can be modeled in the form of regression function, which is developed from the DoE results. The general form of first-order and second-order regression can be expressed as follows. The first order only considers the first three terms.

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_{11}{x}_1^2+{\beta }_{122}{x}_2^2+{\beta }_{12}{x}_1{x}_2+\epsilon$$

(1)

where y is the output, and β_j, j = 0, 1, …, k are the regression coefficients. The x_i is a k independent variable. The regression coefficients are approximated using DoE results y_i, i = 1, …, n and n > k. The use of least square technique system equation of (1) can change to matrix form:

$$y=X\beta +\epsilon$$

(2)

where the output y is a vector n × 1, X is matrix n × p (p = k + 1), β is vector of regression coefficient p × 1, and ε is vector of residual error n × 1. In general, we expect to minimize the least square error with using partial differentiation, and then the regression coefficient can be calculated as follows:

$$b={(X^{\prime }X)}^{-1}{X}^{\prime }y$$

(3)

More details of the RSM with the regression technique can found in [14].

2.3.2. Design of Experiment

The simplest of the DoE depends on k variables and level. For example, two or three levels of k variable can be represented by 2^k! and 3^k!. The example of the graphical representation of three factors is presented in Figure 5. Variables that are greater than 3 need a judgment tool in the form of a highly influential variable, which is called the Plackett–Burman design. This tool provides information on important variables, which is expected to reduce computation time in experiments.

2.3.3. Statistical Analysis

The quality fitting of the model from DoE and response surface method needs statistical analysis, which affects the optimum design in the final stage. In this study, the fitting of model is considered the fitting quality of the model in the form of the determination coefficient (R²) and the adjust determination coefficient (R²_adj). The quality of each data to the model fitting from DoE can be tested with studentized residuals (r_i) and R-student (t_i). The value of R² is in range [0, 1] where it is higher 0.8, representing a good fitting quality [15]. In general, the value R²_adj is less than R² but it should be greater than 0.7 for a good-quality fitting model. For measuring the quality of each datum by statistical parameters, r_i and t_i are used to point to some data that need a repeated experiment if its value is higher than 2.0 [14]. The RSM is coded in MATLAB software R2024a.

2.4. Optimization Problem

From the fitting model by DoE and the RSM technique of the maximum von Mises stress (VMS) and displacement of aircraft wing, the optimization design problem can be performed as shown in the following section. Against bird strike, the optimum of skin thickness, ribs thickness, and sweep angle are needed in this study.

2.4.1. Optimization Design Problem

The design optimization problem is to minimize the maximum von Mises stress that is subject to the maximum displacement constraint and limit of design variables:

$$\mathrm{Min}\mathit{f}\left(\mathit{x}\right)=\max \left(\sigma \right)$$

(4)

Subject to

δ ≤ 10 mm

(5)

$$\sigma \le {\sigma }_y\mathrm{MPa}$$

(6)

x_l ≤ x ≤ x_u.

(7)

where x = {x₁, x₂, x₃, }^T, and x_l and x_u are the lower and upper limits of design variables.

2.4.2. Metaheuristics

In this design, to mitigate the bird strike damage, the optimum aircraft wing structure is our research aim. The optimization function and constraints make the optimization process more challenging. At present, researchers have increasingly turned to metaheuristic algorithms due to the fact they are free of gradient function. These techniques—such as genetic algorithms (GAs), differential evolution (DE), teaching–learning-based optimization (TLBO), and population-based incremental learning (PBIL) are well known in solving engineering problems because they do not rely on gradients and can handle diverse constraints [16,17]. In this research, the comparative optimization of aircraft wing structure against bird strike is studied by comparing three optimizers: JADE, PBIL and TLBO. All codes in comparative study are coded in MATLAB.

3. Experimental Design

In this study, the process of the experiment will start from DoE under different conditions (x₁ = aircraft skin thickness (t_s), and x₂ = ribs thickness (t_r), x₃ = impact angles due to swept back angle (Λ)), using ANSYS to model and simulate bird strikes as shown in Figure 6. The DoE experiment setup is presented in

Table 3. Three factor 3³! with one central point.

Run	x1 = ts (mm)	x2 = tr (mm)	x3 = Λ (degree)	y1 (mm)	y2 (MPa)
1	0.5	5.0	40	98.35	259.6
2	2.0	0.5	40	5.33	106.8
3	2.0	5.0	40	5.325	49.51
4	0.5	5.0	40	98.35	259.6
5	0.5	5.0	20	150.6	271.2
6	2.0	0.5	20	6.453	95.58
7	2.0	5.0	20	5.315	39.41
8	0.5	5.0	20	150.6	271.2
9	0.5	5.0	0	170	345.9
10	2.0	0.5	0	6.485	87.79
11	2.0	5.0	0	5.417	39.33
12	0.5	5.0	0	170	345.9
13	1.25	2.75	20	10.18	94.62

(column 1–4). Following the standards [18], the speed of the aircraft is tested at 100 m/s for a low-speed aircraft and the mass of the birds is 1.81 kg (it has a density of 1000 kg/m³), as presented in Table 1 and Table 2. In this study, the bird strike is in the case of direct frontal strikes. The bird shape is ellipsoid as modeled in the past by the work [12], as shown in Figure 2. Its volume can easily be calculated with a simple formular of ellipsoid geometry. Wing and bird are auto meshing with moderate element size, the explicit dynamics of which are modeled (ANSYS) with 5858 elements overall. Then, it transfers to AUTODYN to solve with the SPH solver. The SPH model of bird involves 3097 particles. The assigned number of particles is in range of medium-density mesh, which proves its performance in studying bird strike [19]. Although the higher particles of the SPH simulation can be more accurately receive than the lower particles [20], its time consumption is important in DoE testing. Then, the accurate and time consumption is needed to compromise. The medium-density mesh of SPH is used in this study. In this study, the bulk viscosity control (the quadratic viscosity coefficient) is used for parameters Q1 = 2 and (the linear viscosity coefficient) Q2 = 0.25. For the setting hourglass energy, the control is used (Flanagan–Belytschko viscous form with parameters IHQ =2 and the hourglass coefficient QH = 0.14. Finally, the contact type is the contact node to the surface. All the parameters of SPH bird model are used following recommendations in the validation part and additional references [19,20,21]. The analysis time of the bird strike simulation is setup for 5 × 10⁻³ s. An example of bird strike simulation for case 1 in Table 3 is presented in Figure 7 for both von Mises stress and deformation. The objective function and constraint are modeled with the regression technique. The regression model needs to be checked by statistical analysis, and if the R² is lower than 0.8, the model needs to add some results, as shown in Figure 6. An analysis of mitigation techniques can explore passive methods for reducing the risks of bird strike and post-impact damage from the results’ discussion. The optimum design of the optimization problem in (4)–(7) is performed with three optimizers. The setup parameters of each optimizer [22] are as follows:

(1)

Teaching–learning-based optimization (TLBO): Parameter settings are not required.

(2)

Adaptive differential evolution with optional external archive (JADE): The parameters are self-adapted during an optimization process.

(3)

Population-based incremental learning (PBIL). The learning rate, mutation shift, and mutation rate are set at 0.5, 0.7, and 0.2, respectively.

The validation step serves to compare the optimum result and the repeated simulation of the bird strike at the same design variable. If the optimum result from the optimization design becomes worse than a DoE experimental result, the process will return to filling samples, constructing RSM function, and starting the optimization loop again, as presented in Figure 1.

For solving the optimum design of aircraft wing structure for mitigating bird strike damage, the population size n_P = 100 is used for all algorithms. The maximum number of function evaluations has a termination criterion set to 200,000, while the number of optimization runs is 10 due to statistical analysis.

4. Design Results and Discussions

The DoE results are presented in Table 3 (column 5–6). The lowest R² of the displacement and von Mises stress for DoE 3³! is not calculated and some result needs to be added. The present study chose to add lower layer points, as shown in Figure 5, and additional testing in

Table 4. Lower-addition layer points of three factor 3³! with one central point in Table 3.

Run	x1 = ts (mm)	x2 = tr (mm)	x3 = Λ (degree)	y1 (mm)	y2 (MPa)
14	1.25	0.5	0	14.52	120.9
15	2.0	2.75	0	5.917	43.93
16	0.5	2.75	0	177.4	298.6
17	1.25	5.0	0	11.63	129.7

.

Table 5. DoE raw testing results of displacement and von Mises Stress.

Run	y1 (mm)	Results	y2 (MPa)	Results
1	98.35		259.6
2	5.33		106.8
3	5.325		49.51
4	98.35		259.6
5	150.6		271.2
6	6.453		95.58
7	5.315		39.41
8	150.6		271.2
9	170		345.9
10	6.485		87.79
11	5.417		39.33
12	170		345.9
13	10.18		94.62

shows the DoE raw testing results without additional results. The selected result from experiment 8 is enlarged and presented in Figure 8. The thickness of the skin and mass of bird are less than the validation model, but von Mises stress results in higher yield stress. The model does not withstand the bird strike. Focusing on the buckling deformation shape during collision by compressive load causes buckling at the upper and lower skin of the leading edge, as shown in Figure 8b. The behavior is consistent with the validation results (Figure 3) and work by [8,11]. The aircraft wing dimensions in experiments 8 and 9 (Table 3) are similar but the sweep angle is different. Increasing sweeping causes stress to be alleviated. It has similar trends for displacement, as shown in Figure 8a. The lowest R² of displacement and von Mises stress for DoE 3³! with additional layer points are 0.9951 and 0.9919, respectively. The quality of each datum of DoE can be confirmed with the acceptance of studentized residuals (r_i) and R-student (t_i) values. The statistical test can confirm the proportional variability of the data that can be explained by the mathematical model. The regression model of the displacement and von Mises stress can be expressed as follows.

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_{12}{x}_1{x}_2+{\beta }_{13}{x}_1{x}_3+{\beta }_{23}{x}_2{x}_3+{\beta }_{11}{x}_1^2+{\beta }_{22}{x}_2^2+{\beta }_{33}{x}_3^2+\epsilon$$

(8)

and

b₁ = {362.906, −445331.421, 3792.478, −1.505, 234746.164, 1194.399, 4.729, 1.323 × 10⁸, −827274.239, −0.022}

b₂ = {4.406 × 10⁸, −3.765 × 10¹¹, 8.764 × 10⁹, −4003952.747, −1.598 × 10¹³, 1.644 × 10⁹, −7.278 × 10⁷, 1.025 × 10¹⁴, 2.313 × 10¹², 35431.705}

where b₁ is a vector of the regression coefficient for maximum displacement, and b₂ is a vector of the regression coefficient for a maximum of von Mises stress. The response surface and contour plot of the maximum displacement and maximum von Mises stress of independent variables x₁, x₂, and x₃ are represented in Figure 9 and Figure 10, respectively. From Figure 9a, the skin thickness rather than rib thickness largely affects displacement in such a way that having more skin thickness leads to less deformation [7]. The second most important factor in maximum displacement is the sweep angle, as shown in Figure 9b,c. Figure 9b presents an increasing sweep angle, which can decrease deformation [3,12]. For maximum von Mises stress, skin thickness still has a greater effect on the stress than rib thickness, just like the maximum displacement. However, rib thickness has a greater impact on stress rather than displacement, as mentioned previously. Furthermore, Figure 10b,c clearly show the impact of the sweep angle: the more sweep there is, the less the stress is studied in [3].

If the model passes the statistical test with an acceptable R², it is ready as an optimum design of the aircraft wing structure to mitigate bird strike (Figure 1). The optimum results with three optimizers are presented in

Table 6. Optimum design results.

Run	TLBO	JADE	PBIL	Actual
ts (mm)	1.8	1.7	1.8	1.8
tr (mm)	2.0	2.0	2.0	2.0
Λ (degree)	16.439	18.456	17.610	17.610
Max VMS (MPa)	54.775	59.334	54.177	39.09
Disp. (mm)	−0.3343	−4.5968	−0.4595	6.669
Mean	59.483	60.372	56.562
Min	54.775	55.934	54.177
Max	64.921	66.694	61.178
Std	3.692	3.488	2.115

. The results reveal the best optimizer is PBIL, due to the fact it reaches the lowest von Mises Stress and meets the constraints. The winner is not surprising when considering the comparative results in the past, where the performance of the algorithm has been demonstrated [23]. Descriptive statistics (mean, min, max and std) in Table 6 (last four rows) show that PBIL outperforms other algorithms. Furthermore, the results show that the optimum design variables of all MHs are quite similar for the rib thickness, and different in the remaining design variables. The results confirm properly defined initial setup parameters and the termination criterion of all algorithms.

Studying the impact of bird strike on the aircraft wing structure must consider the optimum results and compare them with an arbitrary point of the design. The results are shown in the form of von Mises stress, deformation, and total energy, as shown in Figure 11, Figure 12, Figure 13 and Figure 14, respectively.

From the validation optimum design result and DoE data in the form of stress, the optimum wins. Comparing the optimum design and the arbitrary point in the form of stress and displacement, it can be confirmed that the optimum point becomes better in both results. Looking deeper into energy release from all parts can confirm that the optimum design can release and distribute more energy when compared with the arbitrary design, as shown in Figure 13. The energy absorbed by the optimum design is lower than the arbitrary point, which is mainly absorbed by the skin of the optimum design and the arbitrary points around 133.628 J and 754.709 J (Figure 14), respectively. According to reference [7], it is stated that the more energy absorption there is, the more serious the damage. The main total energy absorbed due to bird strike from both designs is from the skin [7], as shown in Figure 14, which is why the skin is the main serious damage. From this study, the proposed design scheme can be used for designing aircraft wing structure and mitigate the effect of bird strike by compromising between the skin and rib thickness as well as the sweep angle. This is especially the case as skin thickness and sweep angle can alleviate the damage that may occur due to bird strike.

5. Conclusions

In this study, N aircraft wing structure design against bird strike is proposed. The bird strike aircraft wing structure design needs a special technique to model the design variables such as skin thickness, rib thickness, and sweep angle. The 3³! DoE design with the additional sampling points was used to study the independent variables and the dependent variables, namely the von Mises stress and displacement. The response surface model of the data can reach our goal of model fitting with a higher R² until 0.9951 and 0.9919 are obtained for the displacement and von Mises stress model, respectively. The response surface function of the displacement and von Mises stress are related to skin thickness, while sweep angles have a greater impact on dependent variables than rib thickness. The optimized design of the independent variables is performed using TLBO, JADE, and PBIL. The optimized design results revealed that the optimum solution can release better energy due to bird strike, with the highest limit of skin thickness, moderate rib thickness, and less than half a sweep angle. The results are in accordance with the response surface function analysis. Furthermore, the comparative results of the optimum result and arbitrary design point revealed that the optimum solution was outperformed. The comparative result of MHs can conclude that the PBIL outperformed others in all descriptive statistics. In conclusion, the optimized design of aircraft wing structure against bird strike can be accomplished with our proposed technique. The impact of birds on wings can lead to material deformation, structural damage, and, in extreme cases, catastrophic failure.

For future work, the knowledge from this study can be applied to the design of leading-edge structures to protect the front spar from damage from bird strikes.