Sage Journals: Discover world-class research

Abstract

A multi-objective optimization method is presented in this paper, aiming at improving the fatigue life of the engine hood while achieving light weight. By analyzing the factors affecting the fatigue life of the engine hood, a multi-objective optimization model was established that considered five design variables including the thickness of the inner plate, the thickness of the outer plate, the stiffness of the hook, the stiffness of the sealing strip, and the height of the buffer block. Then, the multi-objective particle swarm method was used for optimization, and the optimal solution was obtained in the form of a Pareto set. The ideal compromise solution was determined from the Pareto set by using fuzzy membership functions. On this basis, the optimal solution was determined from the Pareto set by comprehensively considering the steel plate material specification, mold and cost constraints. The torsional deformation test and switch fatigue test show that for the optimized engine hood, the fatigue life is increased by 117%, the mass is reduced by 0.51 kg, and the torsional deformation of the engine hood does not increase significantly. The proposed multi-objective optimization method is proved to be feasible and effective in improving engine hood fatigue life and lightweight design.

Keywords

Multi-objective optimization fuzzy membership functions best compromise solution finite element model stiffness

Introduction

The main solutions for lightweight hood include material replacement and structural design.^1–5 The engine hood is subjected to dynamic impact loads when opened and closed. Therefore, the fatigue life of engine hood must be considered and verified in the development process.^6–8 In the process of structural design of engine hood, the thickness of the sheet metal parts is used as the design variable to perform the single-objective optimization of the minimum mass. Munroe et al.⁹ implemented anisotropic multi-material topology optimization with four configurations of continuous carbon fiber reinforced epoxy. The mass of an engine hood panel was reduced by up to 44.5%. To solve the conflicting design requirements on the mass and pedestrian head impact, Vyas et al.¹⁰ presented an innovative automotive hood design concept, which integrates active stiffness control composites in order to achieve improved design performance trade-offs in terms of structural weight reduction and pedestrian head impact. By combining XGBoost and LightGBM algorithms with the bagging method, Chen et al.¹¹ proposed a hybrid model with hyperparameters optimized by the grey wolf algorithm to predict the torsional stiffness of engine hood. Bere et al.¹² proposed new CFRP materials and stacking sequence for manufacturing the CFRP engine hood, and analyzed in terms of static stiffness and strain monitoring in three different points for lateral, longitudinal, and torsional loading cases. While the optimization reduces the weight significantly or head impact mitigation, the fatigue life of engine hood is not discussed further. There are few studies on the fatigue life of engine hood. It is necessary to verify the reliability of the optimized design through fatigue strength test, which leads to a longer development cycle. Therefore, the lightweight design of the engine hood needs to consider the influence of the mass and stiffness of the engine hood assembly on the fatigue life, and carry out multi-objective optimization.

Classical multi-objective optimization techniques and meta-heuristic (modern) multi-objective optimization techniques can be used to solve multi-objective optimization problems (MOP).¹³ Traditional multi-objective optimization techniques such as the weighted sum method are often difficult to determine the appropriate weighting scheme to meet the designer’s optimization goal.^14,15 Inappropriate design of constraints in the $ε$ -constraint method can lead to non-optimal solutions being mistaken for optimal solutions.¹⁶ Meta-heuristic (modern) multi-objective optimization techniques include multi-objective genetic algorithm (MOGA), multi-objective quantum evolutionary algorithm(MOQEA), archived multi-object simulated annealing (AMOSA), multi-objective tabu search (MOTS), and multi-objective particle swarm optimization algorithm (MOPSO).^17–22 The random search in the MOGA may lead to slow convergence, long calculation time and loss of global optimization. The MOQEA is optimized under the assumption that multi-objective problems can be decomposed into multiple single-objective problems, and cannot be used for all MOP. The ability of the AMOSA to converge to the global optimum is inversely proportional to the convergence speed and time-consuming. The MOTS is difficult to execute efficiently on the parallel computing architecture and highly depends on the initial variables. The MOPSO can solve continuous optimization problems and discrete optimization problems. It has fast convergence speed and does not fall into local optimization. Therefore, MOPSO is widely used in automobile optimization design. The MOPSO in Qiu et al.²³ was carried out to optimize the fatigue and mass of truck cab. The improved particle swarm optimization algorithm with the constraints of frequency and stiffness was proposed in Li et al.²⁴ to realize the multi-objective optimization of hood lightweight involving and reducing pedestrian injury.

The Pareto front provides a set of non-dominated solutions. In engineering applications, a compromise solution that weighs multiple objectives needs to be selected as the best compromise solution (BCS). BCS can be determined by fuzzy theory, technique for order preference by similarity to ideal solution (TOPSIS), Nash equilibrium based decision making, VIKOR (Serbian: Vlsekriterijumska Optimizacija I Kompromisno Resenje), and gray correlation degree.^25–27 The fuzzy decision maker (FDM) and min-max method were presented by Shojaei et al.²⁸ to determine the BCS. Li et al.²⁹ presented fuzzy C-means (FCM) to cluster the Pareto front set, and calculated the advantages of each decision plan by grey relational projection (GRP) to determine the BCS reflecting the different preferences of decision makers. Wang and Li³⁰ suggested entropy weight gray correlation analysis to calculate the gray correlation degree of the non-dominated Pareto solution obtained according to NSGA-II. However, before solving the BCS, GRP needs to determine the design target value. The BCS is extracted from the Pareto front using a hierarchical clustering and an equilibria-based multicriteria decision-making scheme by Zhou et al.³¹ Using Euclidean normalization, the BCS is determined by TOPSIS from the non-dominated Pareto solution.^32,33 However, the BCS is determined by VIKOR used linear normalization. TOPSIS and VIKOR are mainly applied to the Pareto frontier obtained by NSGA-II.^34,35 In this paper, the Pareto front was obtained by MOPSO, and the fuzzy membership function is used to determine the BCS.

However, the studies on multi-objective optimization of engine hood are relatively limited, especially in terms of lightweighting and fatigue life. MOPSO is a popular optimization approach because it is relatively simple compared to other evolutionary algorithms and shows a better performance compared to other evolutionary multi-objective optimization algorithms.³⁶ Hence, MOPSO was used to study the multi-objective optimization of the lightweight and fatigue life of a certain engine hood in this paper. Considering the limitation of steel plate material specification, mold and cost, the final best solution was selected from the Pareto set according to the best compromise solution.

The rest of this article is organized as follows: In section 2, the finite element model of engine hood assembly is established and verified by switch fatigue test and stiffness test. The influence of the main parameters of the engine hood assembly on its fatigue life is studied in section 3. Further, multi-objective optimization of lightweight and fatigue life of engine hood is presented in section 4. The multi-objective optimization of engine hood is carried out by MOPSO, and the BCS is obtained by fuzzy theory and engineering practice. Test verification and discussion are conducted in Section 5. Finally, the concluding remarks are presented in Section 6.

Establishment and verification of finite element model

Establishment and verification of finite element model of engine hood torsional stiffness

According to the design, a 3D model of the engine hood assembly was established, the geometric model was simplified and cleaned up by HyperMesh, the shell element was selected to divide the mesh, and the 4-node quadrilateral (QUAD4) was used, and the local accuracy was achieved through mesh refinement. A small amount of triangular element (TRIA3) was used to meet the needs of the mass of the transition grid. Block element and the short beam were used to connect the solder joints, and the point-surface contact method was used to simulate the adhesive part. The finite element model of the engine hood is shown in Figure 1, which contains 168098 elements.

Figure 1.

Finite element model of engine hood.

The calculation accuracy of the finite element model is an important factor affecting the fatigue life analysis. To verify the accuracy of the model, the torsional stiffness of the trial-produced prototype of engine hood assembly was tested, as shown in Figure 2. The comparison between torsional stiffness simulation and torsional stiffness test is shown in Table 1, which shows the simulation results of the engine hood are basically consistent with the test, and the error is within an acceptable range. Therefore, the accuracy of the finite element model of engine hood assembly meets the requirements.

Figure 2.

Torsional stiffness test of engine hood.

Table 1.

Comparison of simulation deformation and test deformation under static load 80 N.

Measuring point	Simulation (mm)	Test (mm)	Error (mm)
MP1	0.065	0.07	7.14%
MP21(2)	−0.424	−0.44	3.63%
MP3	−0.952	−0.96	0.83%
MP4	−1.467	−1.53	4.12%
MP5	−1.923	−1.99	3.37%
MP22(6)	−2.468	−2.49	0.88%
MP7	−2.568	−2.58	0.47%

Finite element model and fatigue test verification of engine hood assembly

The finite element model of engine hood system including engine hood sealing strip, buffer block, engine hood hinge, engine hood lock, lock hook, and front longitudinal beam of vehicle body was established, as shown in Figure 3, including 203857 elements. The OGDEN material model was used for the model of the engine hood sealing strip, and the sealing force curve of the model was consistent with the measured value by adjusting the model parameters.

Figure 3.

Finite element model of engine hood system: (a) view from the bottom and (b) bird’s eye view.

The finite element model was adjusted according to the internal engine hood test standard setting, so that the closing speed and energy of the engine hood were consistent with the fatigue test of the engine hood. The RADIOSS solver of Hyperworks software was used to calculate the force curve at the lock hook during the closing process of the engine hood, as shown in Figure 4. The S-N curve of the inner plate material of the engine hood is shown in Figure 5. The fatigue life at the lock hook of the engine hood was the lowest according to Femfat for life calculation, as shown in Figure 6. The simulation shows that fatigue damage will occur when the engine hood is opened and closed about 4000 times, which is lower than the design and user’s requirements of 5000 times. There is a high risk of fatigue durability, which does not meet the design and test requirements.

Figure 4.

Force curve of lock hook when engine hood is closed.

Figure 5.

The S-N curve of inner plate material of engine hood.

Figure 6.

Fatigue life simulation of engine hood.

The prototype of the engine hood was installed on the same platform body, and the switch fatigue test was carried out. After the engine hood was turned on and off 3466 times, the metal plate of the engine hood lock hook strengthening plate cracked, as shown in Figure 7. The fatigue life simulation of the engine hood assembly was 4000 times. Therefore, the results of the simulation and the test are within the allowable range, and the accuracy of the simulation model meets the calculation requirements.

Figure 7.

Fatigue test of engine hood: (a) prototype vehicle and (b) engine hood crack.

According to the fatigue life simulation and experimental verification, the reason for the crack at the lock hook strengthening plate of the engine hood was that the structural strengthening part is not covered to the crack area, and other structural designs fail to give appropriate life compensation. When the engine hood was turned on and off, the lock hook is subjected to the impact load of the lock, resulting in cracks in the inner plate sheet metal. Since the internal plate sheet metal material and material properties have been determined, the focus of improvement is to ameliorate the stress concentration of the engine hood assembly structure.

Analysis of influence factors on fatigue life of engine hood

According to the above analysis, the influence of the hook reinforcement plate structure, the height of the buffer block, the thickness of the inner plate, the thickness of the outer plate, the stiffness of the locking plate and the stiffness of the sealing strip on the fatigue life of the engine hood were studied respectively.

Lock hook reinforcement plate structure

According to the analysis of the section 2.2, the structure of the improved lock hook reinforcing plate is shown in Figure 8. The von Mises stress curve of dangerous element was extracted and the fatigue life was simulated by FEMFAT based on fatigue damage theory. Fatigue simulation of the improved engine hood is shown in Figure 9. The simulation displayed that fatigue damage will occur when the engine hood was turned on and off about 6800 times, which was about 1.7 times of the original design. The fatigue life of the upper end of the improved lock hook reinforcement plate was about 7100 times. Although the position of the original lock hook reinforcement plate was no longer the weakest position of fatigue, there was still a risk of failure. The maximum von Mises stress of the most dangerous element was 213.5 MP, and there are many dangerous points of stress concentration at the inner plate stiffener. Therefore, the scheme of improving the structure of the lock hook reinforcing plate has the risk of failure.

Figure 8.

Look hook strengthening plate: (a) original structure and (b) optimized structure.

Figure 9.

Fatigue life of improved engine hood.

Buffer block height

When the engine hood is closed, the height of the buffer block will directly affect the distribution of the impact load on the engine hood, thereby affecting the fatigue life of the engine hood. The simulation results are shown in Figure 10. As the height of the buffer block increases, the life of the engine hood fluctuates, and the maximum stress is mainly concentrated in the stiffeners of the inner plate. When adjusting the position of the buffer block, the fatigue life of adjusting 1 mm is similar to the fatigue life of the initial position, which is the best solution.

Figure 10.

The relation curve between the displacement of buffer block and fatigue life.

Inner plate thickness and outer plate thickness

The effect of inner plate thickness on fatigue life of engine hood was simulated, and the simulation results are shown in Figure 11. With the increasing thickness of the inner plate, the fatigue life of the engine hood increases first and then decreases. When the inner plate thickness is 0.55 mm, the fatigue life of the engine hood is the largest. When the inner plate thickness is between 0.53 and 0.57 mm, the fatigue life of the engine hood is sensitive to the change of the inner plate thickness. Therefore, the inner plate thickness can maximize the fatigue life of the engine hood, which needs to be comprehensively considered in the actual design.

Figure 11.

Relationship curve between inner plate thickness and fatigue life.

The fatigue life of the engine hood is simulated by changing the thickness of the outer plate, as shown in Figure 12. With the increase of outer plate thickness, the fatigue life of the engine hood increases first and then decreases. When the thickness of the outer plate is between 0.6 and 0.68 mm, the fatigue life of the engine hood is basically unchanged with the increase of the thickness of the outer plate. When the outer plate thickness is greater than 0.68 mm, the life of the engine hood increases rapidly, and reaches the maximum when the outer plate thickness is 0.72 mm. When the outer plate thickness is greater than 0.72 mm, the fatigue life of the engine hood decreases with the increase of the outer plate thickness. Therefore, the thickness of the outer plate can minimize the fatigue life of the engine hood, which needs comprehensively consideration in the actual design.

Figure 12.

The relation curve between outer plate thickness and fatigue life.

Look hook stiffness and sealing strip stiffness

The stiffness of the lock hook directly affects the stress of the engine hood at the moment of closing. The simulation of the fatigue life of the engine hood by changing the lock hook stiffness is shown in Figure 13. With the increase of lock hook stiffness, the fatigue life of engine hood increases first and then decreases. The fatigue life of the engine hood reaches the maximum at the original design of the lock hook stiffness. Therefore, the lock hook stiffness can maximize the fatigue life of the engine hood, which needs to be considered comprehensively in the actual design.

Figure 13.

Relationship curve between lock hook stiffness and fatigue life.

The main function of the sealing strip is to seal, with a certain stiffness, and play a supporting role in the process of closing the engine hood. Figure 14 shows that the fatigue life of the engine hood decreases slightly and then increases with the increase of the sealing strip stiffness. When the sealing strip stiffness is greater than 6.5 N/mm, the fatigue life of the engine hood decreases gradually. Therefore, the stiffness of the sealing strip can make the fatigue life of the engine hood reach the maximum, which needs to be comprehensively considered in the actual design.

Figure 14.

Relationship curve between sealing strip stiffness and fatigue life.

Multi-objective optimization

Model formulation of engine hood

The lightweight and fatigue life of engine hood was formulated as a multi-objective optimization problem based on a series of optimization parameters and constraints. The mathematical model of objective optimization is described as:

{\begin{matrix} Minimize F (x) = (M (x), - L (x))^{T} \\ Subject to : | M P_{1} (x) - M P_{10} | < d \times M P_{10} \\ x_{L} \leq x \leq x_{U} \end{matrix}

(1)

Where $M P_{1} (x)$ and $M P_{10}$ are respectively deformation value and initial deformation value of $M P_{1} (x)$ point of engine hood. The $M P_{10}$ is −2.575. d is the constraint coefficient of $M P_{1} (x)$ point of engine hood. According to the value of $M P_{10}$ , d is 10%. In order to ensure that the deformation of the engine hood is qualified after optimization, the deformation range of the engine hood is between −10% and +10% of the thickness. Five engine hood parameters, such as the thickness of the inner plate, the thickness of the outer plate, the stiffness of the hook, the stiffness of the sealing strip, and the height of the buffer block, were the design variables according to the above analysis of factors affecting engine hood fatigue life. $x_{L}$ and $x_{U}$ are the minimum and maximum of each design variable, respectively.

According to the analysis of the five parameters variable characteristic curve ranges and the designer’s suggestion, the range of variability of each parameter shown in Table 2, was determined. The initial value is the value before engine hood optimization. The maximum and minimum values are the constraint values for the optimization calculation of each parameter variable.

Table 2.

Initial, minimum and maximum values of design variables.

Design variable	Initial	Minimum	Maximum
Thickness of inner plate $X_{1}$ /mm	0.6	0.45	0.65
Thickness of outer plate $X_{2}$ /mm	0.7	0.6	0.8
Stiffness of hook $X_{3}$ /%	0	−10	10
Stiffness of sealing strip $X_{4}$ /N/mm	5	4	14
Height of buffer block $X_{5}$ /mm	0	0	2

Multi-objective particle swarm optimization algorithm

MOPSO is an extension of the standard particle swarm optimization algorithm (PSO) applied to single objective optimization problems.^37,38 PSO is originated from research on the foraging behavior of birds. The position and velocity of $j$ th dimension $i$ th particle at the $t$ th iteration are expressed as $x_{i, j} (x)$ and $v_{i, j} (x)$ , respectively. $x_{i, j} (x)$ and $v_{i, j} (x)$ are initialized randomly and are updated at the next step according to the following equations:

\begin{matrix} v_{i, j} (t + 1) = ω (t) v_{i, j} (t) + c_{1} r_{1} (pbes t_{i, j} (t) - x_{i, j} (t)) + \\ c_{2} r_{2} (gbes t_{i, j} (t) - x_{i, j} (t)) \end{matrix}

(2)

\begin{matrix} x_{i, j} (t + 1) = x_{i, j} (t) + v_{i, j} (t) \end{matrix}

(3)

Where $v_{i, j} (t + 1)$ indicates the velocity of $j$ th dimension $i$ th particle at the $t + 1$ th iteration, $x_{i, j} (t + 1)$ represents the position of $j$ th dimension $i$ th particle at the $t + 1$ th iteration, $ω (t)$ denotes the inertia weight factor, $c_{1}$ and $c_{2}$ are the maximum increments caused by particle optimization and global optimization respectively, which is learning rate or learning factor. $r_{1}$ and $r_{2}$ denotes random number between 0 and 1. $pbes t_{i, j} (t)$ represents $j$ th dimension of historical best position of $i$ th particle, and $gbes t_{i, j} (t)$ indicates the global best particle.

When solving multi-objective optimization problems, standard PSO has the characteristics of low particle swarm diversity, easy premature and weak particle exploration ability in a wider range. Therefore, the standard PSO cannot directly apply the multi-objective optimization problem, and must be improved and extended on its own basis to form MOPSO:

Anyone in the Pareto set has a chance to be selected as a leader. The leader of each particle is randomly selected from the Pareto set according to the crowding distance;

At each iteration, Turbulence operator is used to perturb the speed of a small number of particles, which makes the potential flight directions of the particles more diverse, expands the optimization space of the particles, increases the probability of finding the global optimum, and expands the coverage of the design space;

External archiving technology that allows storage of non-dominant particles can spread and maintain the Pareto front.

The algorithm can be implemented by the following five steps and its flowchart is given in Figure 15.

Figure 15.

Flowchart of the MOPSO.

Then, the engine hood will be computed to show the process of the method step by step.

Step 1: Randomly initialize the position and velocity of each particle in the population.

Step 2: Evaluate the fitness of each particle, store the current position and fitness of each particles in the pbest, select all the individuals with the optimal fitness of pbest, and then store those individuals’ fitness and location in gbest.

Step 3: Use formula (2) and (3) to update the particle velocity and position.

Step 4: Compare the fitness of each particle with the best position it has experienced. If it is better, it will be the best location at the moment; compare all current pbest and gbest and update gbest.

Step 5: If the stop condition is satisfied, stop the search and output the result, otherwise return to step 3 to continue the search.

The particle swarm scale of the multi-objective particle swarm algorithm is 50. Number of iterations is 100. The Pareto front can be easily obtained by adopting MOPSO, as shown in Figure 16.

Figure 16.

Pareto front.

Selected solution

In order to obtain an optimization that is ultimately applied to engineering, a compromise between the weight and the fatigue life of the hood needs to be selected from the Pareto set, that is, the BCS for engine hood. Fuzzy theory can help decision makers effectively select the BCS from Pareto set based on fuzzy mechanism. The membership function in fuzzy theory is expressed as:

δ_{n} = {\begin{matrix} 0 g_{n} \geq g_{n, \max} \\ \frac{g_{n, \max} - g_{n}}{g_{n, \max} - g_{n, \min}} g_{n, \min} < g_{n} < g_{n, \max} \\ 1 g_{n} \leq g_{n, \min} \end{matrix}

(4)

Where $g_{n, \max}$ , $g_{n, \min}$ , and $g_{n}$ are the maximum, minimum and current values of the $n$ th optimization objective, respectively. The standardized dominating function of the kth non-dominated solution in the Pareto set is represented as:

φ_{n} = \frac{\sum_{k = 1}^{N_{obj}} δ_{n}^{k}}{\sum_{m = 1}^{M_{par}} \sum_{n = 1}^{N_{obj}} δ_{n}^{m}}

(5)

Where $M_{par}$ is the number of non-dominated solutions in the Pareto front. $N_{obj}$ denotes the number of optimization objectives.

According to the equation (5) of the dominance function, the dominance value of each non-dominated solution in the Pareto set can be obtained, and the results of the dominance value are shown in Figure 17. The dominance value reflects the comprehensive performance of the non-dominated solutions, and the solution with the largest dominance value is the BCS. The fatigue life of the engine hood corresponding to the maximum dominating function No. 9 is about 8400 times, and the mass is about 13.57 kg, as shown in Figure 16.

Figure 17.

Dominance function.

Considering the limitation of steel plate material specifications, molds and cost,the No. 13 hood with the same fatigue life as the No. 9 hood was trial-produced. The design variables are shown in Table 3. The mass of No. 13 engine hood is about 13.98 kg, which is 0.41 kg more than that of No. 9 engine hood. However, considering the model calculation error of 15.4% in the section 2.2, No. 13 is selected to ensure that the engine hood can simultaneously meet the requirements of design fatigue life of 5000 times and lightweight.

Table 3.

Design variable of engine hood.

Design variable	Initial	Optimization
Thickness of inner plate $X_{1}$ /mm	0.6	0.55
Thickness of outer plate $X_{2}$ /mm	0.7	0.7
Stiffness of hook $X_{3}$ /%	0	−3.25
Stiffness of sealing strip $X_{4}$ /N/mm	5	6.5
Height of buffer block $X_{5}$ /mm	0	1

The optimized engine hood simulation shows that the dangerous point of the inner plate is in the area of the locking hook reinforcing plate, and the maximum von Mises stress of the dangerous unit is 208.9 MPa, as shown in Figure 18. The stress of the dangerous point after the optimization of the engine hood is reduced compared with that before the optimization. The fatigue life is about 2.1 times that before optimization, and the stress of other parts of the engine hood has also been improved. The mass of engine hood assembly is reduced by 0.51 kg compared with that before optimization.

Figure 18.

Von Mises stress at original danger point after optimization.

Experimental verification and discussion

According to the optimized compromise scheme, No. 13 was selected for the trial production of engine hood prototype. The torsional deformation test of engine hood was carried out, and the comparison of simulation and test results before and after optimization is shown in Table 4. Although the torsional deformation of the optimized engine hood was slightly increased, it also met the design requirements for engine hood deformation and the optimization requirements for constant stiffness.

Table 4.

Deformation comparison under static load of 80 N.

Measuring point	Simulation deformationbefore optimization (mm)	Simulation deformation after optimization (mm)	Test beforeoptimization (mm)	Test afteroptimization (mm)
MP1	0.065	0.071	0.07	0.08
MP2	−0.424	−0.443	−0.44	−0.53
MP3	−0.952	−0.962	−0.96	−1.04
MP4	−1.467	−1.513	−1.53	−1.62
MP5	−1.923	−1.974	−1.99	−2.07
MP6	−2.468	−2.492	−2.49	−2.61
MP7	−2.568	−2.591	−2.58	−2.71

The engine hood prototype was installed on the vehicle for the engine hood switch fatigue test. After the engine hood was turned on and off 5000 times, there is no crack at the reinforcing plate of the engine hood, as shown in Figure 19. The engine hood was dismantled and inspected, and there was no fatigue durability damage, which verified the correctness of the optimized improvement plan.

Figure 19.

Fatigue test of optimized engine hood.

In order to verify the accuracy of the calculation results, the fatigue test of engine hood continues until fatigue failure occurs. After the engine hood was turned on and off 7534 times, the sheet metal crack at the position of the locking hook reinforcing plate, and no fatigue damage was found at other parts after the disassembly and inspection of the engine hood, as shown in Figure 20. The fatigue life error between the multi-objective optimization calculation and experiment is 11.49%, which proves the correctness of the optimized method.

Figure 20.

Crack of optimized engine hood.

Conclusions

A multi-objective structural optimization of the engine hood is carried out in this paper, considering both lightweight and fatigue life, with the overall goal of minimizing the overall weight and maximizing the fatigue life. The factors affecting the fatigue life of the engine hood are analyzed, and five engine hood parameters, such as the thickness of the inner plate, the thickness of the outer plate, the stiffness of the hook, the stiffness of the sealing strip, and the height of the buffer block, were selected as design variables. The deformations of engine hood were imposed as the constraints.

The optimization process was performed by the MOPSO and Pareto front were achieved. The fuzzy membership function fully mines the information contained in the Pareto frontier distribution, and combines the steel plate material specifications, molds and cost constraints to achieve a scientific compromise plan selection;

Switch fatigue test verification was performed according to the optimized parameters. The test results show that compared with the original engine hood, the fatigue life is increased by 117%, the mass is reduced by 0.51 kg, and the torsional deformation of the engine hood does not increase significantly. The combination of Multi-objective structural optimization and optimization algorithm can quickly and effectively find the structural parameters and the performance parameters that meets high fatigue life and lightweight, saving the cycle and cost of calibration.

Footnotes

Handling Editor: Chenhui Liang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is supported by the National Key Research and Development Program of China (Grant no. 2018YFB0106200).

ORCID iD

Henghai Zhang

References

Cecchel

Materials and technologies for lightweighting of structural parts for automotive applications: a review. SAE Int J Mater Manf 2020; 14: 81–97.

Zhu

Meng

, et al. Lightweight design and formability analysis of saloon car aluminum-alloy engine hood. China J Highw Transp 2011; 24: 113–120.

Sathaye

Bhattacharyya

Lightweighting of automobile hood using multistep optimization for composite material. SAE Int J Adv Curr Prac Mobility 2019; 1: 113–119.

Liu

Yan

KK.

Application of fiber reinforced composite in auto-body panel. J Jilin Univ (Eng Technol Ed) 2020; 50: 417–425.

Resende

Silveira

Resende

Topologycal optimization applied to design of an automotive hood. SAE technical paper 2016-36-0210, 2016.

Swamy

Noorsumar

Chidanandappa

Mass optimized hood design for conflicting performances. SAE technical paper 2019-28-2546, 2019.

Unadkat

Kangde

Burkul

, et al. Development of virtual hood slam test. SAE technical paper 2016-01-1365, 2016.

Kim

Seo

Jung

, et al. Two-step hood opening system development for easier hood opening operation. SAE technical paper 2014-01-0363, 2014.

Munroe

Roper

Bohrer

, et al. Automotive hood panel design utilizing anisotropic multi-material topology optimization. SAE Int J Adv Curr Prac Mobility 2021; 3: 2658–2665.

10.

Vyas

André

Sala

Toward lightweight smart automotive hood structures for head impact mitigation: integration of active stiffness control composites. J Intell Mater Syst Struct 2020; 31: 71–83.

11.

Chen

Cheng

Zhang

, et al. Rapid mechanical evaluation of the engine hood based on machine learning. J Braz Soc Mech Sci Eng 2021; 43: 1678–5878.

12.

Bere

Dudescu

Neamàu

, et al. Design, manufacturing and test of CFRP front hood concepts for a light-weight vehicle. Polymers 2021; 13: 1374.

13.

Stewart

Palmer

DuPont

A survey of multi-objective optimization methods and their applications for nuclear scientists and engineers. Prog Nucl Energy 2021; 138: 103830.

14.

Zadeh

Optimality and non-scalar-valued performance criteria. IEEE T Automat Contr 1963; 8: 59–60.

15.

Andersson

A survey of multi-objective optimization in engineering design, lith-IKP-R-1097. Linköping, Sweden: Department of Mechanical Engineering Linköping University, 2000.

16.

Chiandussi

Codegone

Ferrero

, et al. Comparison of multi-objective optimization methodologies for engineering applications. Comput Math Appl 2012; 63: 912–942.

17.

Jiang

Sun

Liu

, et al. Multi-objective reliability-based optimization of control arm using MCS and NSGA-II coupled with entropy weighted GRA. Appl Sci 2021; 11: 5825.

18.

Lin

, et al. A research on multi-disciplinary optimization of the vehicle hood at early design phase. SAE technical paper 2020-01-0625, 2020.

19.

Wei

Fujimura

Multi-objective quantum evolutionary algorithm for discrete multi-objective combinational problem. In: 2010 international conference on technologies and applications of artificial intelligence, Hsinchu, Taiwan, 18–20 November 2010. New York: IEEE.

20.

Sengupta

Saha

Reference point based archived many objective simulated annealing. Inf Sci 2018; 467: 725–749.

21.

Hansen

MP.

Tabu search for multiobjective optimization: MOTS. In: Proceedings of the 13th international conference on multiple criteria decision making (MCDM 1997) (ed J

Climaco

), pp.574–586. Springer.

22.

Wang

Duan

, et al. A multi-energy scheduling strategy for orderly charging and discharging of electric vehicles based on multi-objective particle swarm optimization. Sustain Energy Technol Assess 2021; 44: 101037.

23.

Qiu

Jin

Liu

, et al. Hybrid multi-objective robust design optimization of a truck cab considering fatigue life. Thin Wall Struct 2021; 162: 107545.

24.

Liu

Zhu

An improved multi-objective optimization algorithm with mixed variables for automobile engine hood lightweight design. J Mech Sci Technol 2021; 35: 2073–2082.

25.

Long

Lai

Liu

, et al. Pressure retarded osmosis: operating in a compromise between power density and energy efficiency. Energy 2019; 172: 592–598.

26.

Myerson

RB.

Game Theory Analysis of Conflict. Cambridge, MA: Harvard Univ. Press, 1991.

27.

Wang

Zhang

, et al. Pareto tribe evolution with equilibrium-based decision for multi-objective optimization of multiple home energy management systems. Energy Build 2018; 159: 11–23.

28.

Shojaei

Ghadimi

Miveh

, et al. Multiobjective reactive power planning considering the uncertainties of wind farms and loads using information gap decision theory. Renew Energy 2021; 163: 1427–1443.

29.

and Li

GQ.

Optimal Power Flow for AC/DC system based on cooperative multi-objective particle swarm optimization. Electr Power Syst 2019; 43: 1427–1443.

30.

Wang

SH.

Lightweight optimization design of side collision safety parts for BIW based on Pareto mining. China Mech Eng 2021; 32: 1584–1590.

31.

Zhou

Chan

, et al. Strength Pareto multigroup search optimizer for multiobjective optimal reactive power dispatch. IEEE Trans Ind Inform 2014; 10: 1012–1022.

32.

Jafaryeganeh

Ventura

Guedes Soares

Effect of normalization techniques in multi-criteria decision making methods for the design of ship internal layout from a Pareto optimal set. Struct Multidiscipl Optim 2020; 62: 1849–1863.

33.

Mojaver

Khalilarya

Chitsaz

, et al. Multi-objective optimization of a power generation system based SOFC using Taguchi/ahp/topsis triple method triple methoundefined. Sustain Energy Technol Assess 2020; 38: 100674.

34.

Opricovic

Tzeng

GH.

Compromise solution by mcdm methods: a comparative analysis of vikor and topsis. Eur J Oper Res 2004; 156: 445–455.

35.

Chen

Liu

Jiang

Optimal design of multichannel fiber Bragg grating filters using Pareto multi-objective optimization algorithm. Opt Commun 2016; 358: 59–64.

36.

Coello

Pulido

Lechuga

MS.

Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 2004; 8: 256–279.

37.

Kennedy

Particle Swarm optimization. In: Sammut

Webb

(eds.) Encyclopedia of Machine Learning. Boston, MA: Springer, 2011, pp. 760–766.

38.

Spano

Anselma

Misul

, et al. Exploitation of a particle swarm optimization algorithm for designing a lightweight parallel hybrid electric vehicle. Appl Sci 2021; 11: 6833.

Research on lightweight and fatigue life of engine hood based on multi-objective particle swarm optimization

Abstract

Keywords

Introduction

Establishment and verification of finite element model

Establishment and verification of finite element model of engine hood torsional stiffness

Finite element model and fatigue test verification of engine hood assembly

Analysis of influence factors on fatigue life of engine hood

Lock hook reinforcement plate structure

Buffer block height

Inner plate thickness and outer plate thickness

Look hook stiffness and sealing strip stiffness

Multi-objective optimization

Model formulation of engine hood

Multi-objective particle swarm optimization algorithm

Selected solution

Experimental verification and discussion

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References