Study on Multi-objective Optimization of Airbag Landing Attenuation System for Heavy Airdrop

Study on Multi-objective Optimization of Airbag Landing Attenuation System for Heavy Airdrop

A f i nite element model of vehicle and its airbag landing attenuation system is established and verif i ed experimentally.Two design cases are selected to constrain the airbag design for extreme landing conditions,while the height and width of airbag and the area of vent hole are chosen as design variables.The optimization is forced to compromise the design variables between the conf l icting requirements of the two extremes.In order to optimize the parameters of airbag,the multi-dimensional response surfaces based on extended Latin hypercube design and radial basis function are employed instead of the complex f i nite element model.Pareto optimal solution sets based on response surfaces are then obtained by multi-objective genetic algorithm.The results show the optimization method presented in this paper is a practical tool for the optimization of airbag landing attenuation system for heavy airdrop.

Copyright?2013,China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.

Airbag;Multi-objective optimization;Finite element analysis;Response surface

1.Introduction

The airbag landing attenuation system is one of the most important technologies for the landing impact attenuation for heavy airdrop.There are many landing cushion technologies, suchashoneycombandretro,whichnormallyhavecomplicated structures and thus are very expensive.Airbag landing attenuation system is comparatively simple,convenient,eff i cient and cheap.Itcanabsorbmostoflandingimpactenergytoreducethe impact force by exhausting the inf l ation gas through vents.

Droptestsare credible toresearchairbag landing attenuation system but too expensive.The safety and time are the other two key problems.Thus it is practically impossible to optimize the parameters of airbag landing attenuation system for heavy airdrop only by experimental methods.Development of simulation technology makes the problems overcome.Several simulation models of airbag were established[1-3].It’s feasible to optimize the parameters of airbag landing attenuation system for heavy airdrop using simulation technology.

In this paper,a f i nite element model of vehicle with airbag landing attenuation system was established based on control volumemodelandf i niteelementmethod.Theestablishedmodel was validated by drop test.Furthermore,the multi-dimensional response surfaces were employed instead of the complex f i nite element model.Pareto optimal solution sets based on response surfaceswerethenobtainedbymulti-objectivegeneticalgorithm.

2.Modeling and verif i cation

2.1.FE Model of airbags

Airbag landing attenuation system consists of eight independent and identical airbags,as shown in Fig.1.It’s connected to the bottom of vehicle.Each airbag has a mainchamber and an assistant chamber connected with main chamber through communication holes.The injection holes are located in the bottom of the main chamber in order to implement air inf l ation when vehicle descends.When the bottoms of airbags are in contact with the ground,the injection holes are closed.The vent holes are located at the sides of airbags for exhaust.These holes are closed initially and are opened when the pressure difference between the inside and outside airbags exceeds venting pressure Fig.1.

The model of airbag landing attenuation system can be modeled on the basis of the following assumptions[4]:

1)Perfect gas law and adiabatic condition are valid for the gas in airbag during landing process.

2)The aerodynamic resistance is negligible in the process of landing cushion.

3)The air in airbag is exhausted only through the vent holes.

4)The pressure in airbag is uniform.

The equations of the air in airbag are

Fig.1.Airbag landing attenuation system.

where P is the gas pressure in airbag;Vis the gas volume;m is the gas mass;T is the gas temperature;R is the gas constant;ρ is the gas density;E is the energy in airbag;and γ is the ratio of specif i c heat.

Airbag is regarded as expanding control volume[5].For each time step,the gas pressure in airbag is calculated based on the thermodynamics equations.When the gas pressure acts on the elements of airbags,the shape of airbags can be then obtained.Control volume is given as

where xiis the mean value of x coordinate values of element I; nixis the direction cosine between normal of element and x direction;and Aiis the surface area of element i.

The mass fl ow rate in control volume is given by the mass fl ow of gas injected into airbag and the mass fl ow of gas expulsed out of airbag.

where˙minis the mass f l ow of gas injected into airbag;and˙moutis the mass f l ow of gas expulsed out of airbag.

2.2.Contact model between vehicle,airbag and ground

The transformations of shape and position of airbags are very complex in the process of landing cushion.The airbags may contact with each other because of large compression deformation.Here,penalty method is adopted to describe selfcontact of airbags[6].Every side of airbags is slave surface as well as master surface.For each time step,it’s checked whether the slave nodes penetrate the master surfaces f i rst.If a slave node does not penetrate through master surface,no treatment is required.Otherwise,an interface force vector is introduced at the position between slave node and master surface.It can be modeled as a normal spring between the slave node and the master surface.The absolute magnitude of force is proportional to penetration l and master surface stiffness ki.

where fsis the contact force vector between slave node and master node;and niis the normal unit vector in contact point of master surface Si.

The contact between airbag landing attenuation system and vehicle is described by tied contact model.The bottom of simplif i ed vehicle model is def i ned as master surface,while the top of airbag landing attenuation system is def i ned as slave surface.With a tied contact model,it is possible to connect rigidly the slave surface nodes with a master surface.This kinetic constraint is applied on all slave nodes.They remain at the same position on their master surfaces.The acceleration and velocity of each master node are calculated from the force and mass applied by the slave nodes.

Fig.2.Finite element model.

The ground is modeled as an inf i nite plane.The contact between airbags and ground is described and solved by penalty method,too.The FE model of vehicle and airbags cushion system is shown in Fig.2.

2.3.Result verif i cation

The FE model was established based on the simplif i cations and assumptions.Thus,the model should be validated by experiment because of unexpected errors.The test data is obtained from the drop test which was thoroughly discussed in Ref.[7].The initial vertical velocity is 7.0 m/s,the initial horizontal velocity is 0 m/s,and the ground is f l at.The accuracy of the model was validated by the comparison of acceleration results,as shown in Fig.3.

As shown in Fig.3,the curves of simulation and experiment match well with each other.The error of maximal acceleration is 8.1%.Thus,the established model can be used for further research.

Fig.3.Result comparison.

3.Response surfaces

3.1.Response surface method

Airbaglanding attenuation system offers anattractivemeans of impact attenuation for heavy airdrop.Design optimization of airbag landing attenuation system relies on explicit f i nite element analysis because of the non-linear behavior of cushion characteristics and the diff i culty of adequate airdrop test. However,the simulation of an impact typically requires tens of hours.As a result,it is diff i cult to use the traditional iterative approach to optimize the design based on a nonlinear model. The response surface method presents a methodology for overcoming these problems with design optimization of airbag landing attenuation system for heavy airdrop.

A response surface[8]gives the value of a key output variable in the design space as a function of design variables. In response surface modeling approach,the response surfaces are approximated from a relatively small number of FE analysis runs by using surface-f i tting algorithms.The response surface method can be used to solve optimization problem with minimal computational effort.

The success of the response surface modeling approach depends on the quality of the response surface approximations. These must reproduce highly non-linear response functions over a large parameter space from only a limited number of analyzed points.The quality of the response surface approximations is determined by selecting the sampling points in the parameter space and the surface-f i tting algorithm through the sample points.

Fig.4.Extended Latin hypercube design.

3.2.Extended Latin hypercube design

The choice of the sampling points is important for generating response surface.There are different methods to select the locations of the sampling points.As one of these methods, the eff i ciency of Latin hypercube design was proven for wide range of applications.Latin hypercube design developed by McKay et al.[9]is an alternative approach which can yield precise estimates of output statistics with a lesser number of samples.The Latin hypercube samples are random but are guaranteed to be relatively uniformly distributed over each dimension.

In practice,Latin hypercube design can be obtained as follows.The range of each design variable is divided into n non-overlapping intervals on the basis of equal probability. One value from each interval is selected at random with respect to the probability density in the interval.The n values thus obtained for x1are paired in a random manner with the n values of x2.These n pairs are combined in a random manner with the n values of x3to form n triplets and so on.A similar procedure is followed for x4,...,xn,which exhausts all observations and results in n LHD points.In this design,the points are generated randomly.But The Latin hypercube samples can be iteratively generated to f i nd the best one according to careful design criterion.

Extended Latin hypercube design is a Latin hypercube design with the addition of the corner points in the parameter space.This ensures that the extreme parameter combinations are included in the analyzed set and give a uniform f i lling ofthe design space.For the design optimization of airbag landing attenuation system,3 variables were considered and 28 combinations of these parameters obtained by extended Latin hypercube design were sought as sampling points for the FE analysis runs,as shown in Fig.4.

3.3.Response surface f i tting

The response values are obtained according to the simulation of FE analysis runs.Most literature about airbag design optimization just considered vertical landing case.However, the landing environment is commonly complex.Two design cases were selected to constrain the airbag design.In Case 1, the contact area with the ground is maximized in the case of vertical impact.Relatively tall prof i le is required to reduce the impact force,but it makes vehicle stability worse.In Case 2, high lateral landing velocity component,pitch-down angle and upper slope landing site are added.This case tends to push the airbag design towards a larger plane area.Relatively short prof i le is better for stability.

28 FE analysis runs are performed for each landing case (i.e.,a total of 56 runs)for the design parameter combinations. The response values listed were then extracted from the FE analyses.The response surfaces are f i tted to the analysis results using radial basis function.The response surfaces at a vent area of 38,000 mm2are shown in Figs.5 and 6.

Fig.5.Acceleration response surface.

Fig.6.Attitude angle response surface.

4.Multi-objective optimization

4.1.Optimization analysis

Here the height and width of airbag and the area of vent hole are chosen as design variables,while the objective of the optimization is to minimize the maximum acceleration and the maximum attitude angle.It’s a multi-objective optimization problem.There is no unique solution to this problem.Instead, the concept of non-inferiority(also called Pareto optimality) must be used to characterize the objectives.A non-inferior solution is one in which an improvement in one objective requires a degradation of another.The mission of multiobjective optimization is to work out a set of non-inferior solutions.

Multi-objective genetic algorithm can solve the type of problem eff i ciently.NSGA-II(fast elitist non-dominated sorting genetic algorithm)is one of better elitist multiobjective genetic algorithms[10].It reduces the computational complexity,assures the preservation of previously found best solutions,and makes the algorithm independent of users. Thus,considering both cushion performance and stability,a set of non-inferior solutions and the Pareto front are obtained by NSGA-II based on response surfaces,as shown in Fig.7 and Table 1.The Pareto front PF*is def i ned as PF*=｛f→（x→） x→∈P*｝,where P is a set of all non-inferior solutions.

The Pareto plot displays two competing objectives.The horizontal axis is the maximum acceleration,while the vertical axis is the maximum attitude angle.In Fig.7,there are 14 points on the Pareto front.A set of Pareto solutions include the 14 points.The f i nal design parameters can be chosen from the 14 points.The 3 non-inferior solutions in left lower part of Fig.7 have smaller acceleration and attitude angle.For other solutions,an improvement in one objective requires a relatively large degradation of another objective.The 3 noninferior solutions are the 1st solution,the 3rd solution and the 14th solution listed in Table 1.Compared with the other two solutions,the cushion performance of the 1st solution is obviously improved,while the stability is not worse.Thus the 1st solution is chosen as optimized solution.

Fig.7.Pareto front.

Table 1A set of Pareto solutions.

4.2.Comparison of airbags cushion characteristics

In order to estimate the improvement of airbags cushion performance and stability,the optimized velocity,acceleration,pressure inside airbags,residual energy and attitude angle are compared with the original results,as listed in Table 2.

As listed in Table 2,the landing velocity is decreased from 2.20 m/s to 0.73 m/s,and the maximum acceleration of airborne vehicle is decreased by 16%.The maximum pressure inside airbags is slightly increased.Because the energy absorption performance of airbags is improved,the residual energy of the system is decreased by 23%.The maximum attitude angle is decreased in Case 2.Overall,the cushion performance of airbags cushion system is obviously improved after optimization,while the stability is slightly improved.It indicates that the optimization method presented in the paper is feasible to such complex nonlinear problem.

5.Conclusions

1)A FE model of vehicle and its airbag landing attenuation system was established on the basis of volume control model in this paper.The established model was validated by drop test.The simulation results agree very well with the experimental results.

2)In order to optimize the parameters of airbags,the multidimensional response surfaces based on extended Latin hypercubemethodandradialbasisfunctionwere employed instead of the complex f i nite element model. The method overcomes the diff i culties in traditional iterative optimization method.

3)The cushion performance of airbags cushion system is obviously improved after optimization,while the stability is slightly improved.It indicates the optimization method presented in the paper is feasible to such complex nonlinear problem.

Table 2Comparison of simulation results and original values.

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Hong-yan WANG*,Huang-jie HONG,Jian-yang LI,Qiang RUI
Academy of Armored Force Engineering,Beijing 100072,China

8 November 2013;revised 29 November 2013;accepted 6 December 2013 Available online 17 December 2013

*Corresponding author.Tel.:+86 13811431852.

E-mail address:why_cvt@263.net(H.-Y.WANG).

Peer review under responsibility of China Ordnance Society.

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2214-9147/$-see front matter Copyright?2013,China Ordnance Society.Production and hosting by Elsevier B.V.All rights reserved.

http://dx.doi.org/10.1016/j.dt.2013.12.004