July 2014 

NASA/TM–2014-218290 

Preliminary Structural Sensitivity Study of 

Hypersonic Inflatable Aerodynamic Decelerator 

Using Probabilistic Methods 

Karen H. Lyle 

Langley Research Center, Hampton, Virginia 
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July 2014 

NASA/TM–2014-218290 

Preliminary Structural Sensitivity Study of 

Hypersonic Inflatable Aerodynamic Decelerator 

Using Probabilistic Methods 

Karen H. Lyle 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

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Abstract

Acceptance of new spacecraft structural architectures and concepts requires validated 

design methods to minimize the expense involved with technology validation via flighttesting. This paper explores the implementation of probabilistic methods in the sensitivity 

analysis of the structural response of a Hypersonic Inflatable Aerodynamic Decelerator 

(HIAD). HIAD architectures are attractive for spacecraft deceleration because they are 

lightweight, store compactly, and utilize the atmosphere to decelerate a spacecraft 

during re-entry. However, designers are hesitant to include these inflatable approaches 

for large payloads or spacecraft because of the lack of flight validation. In the example 

presented here, the structural parameters of an existing HIAD model have been varied 

to illustrate the design approach utilizing uncertainty-based methods. Surrogate models 

have been used to reduce computational expense several orders of magnitude. The 

suitability of the design is based on assessing variation in the resulting cone angle. The 

acceptable cone angle variation would rely on the aerodynamic requirements.

Introduction

High reliability entry, descent, and landing systems have been in demand for all classes 

of space applications. Specific applications include, ISS return mass, sample return, 

Mars exploration vehicles, and human-rated exploration vehicles. Architectures that 

incorporate Hypersonic Inflatable Aerodynamic Decelerators (HIADs) show promise for 

many of these applications, as discussed in Refs. [1-3]. Also various Inflatable 

Aerodynamic Decelerators (IADs) were proposed, studied, and reported in Refs. [4-6]. 

More recently, a series of small-scale test flights has demonstrated a basic functionality 

of a stacked torus configuration at the 3-m diameter scale, see Refs. [7 and 8]. HIAD 

diameters up to 81-m have been proposed, Ref. [1]. Traditionally, for such designs to 

gain acceptability, they need to be verified and validated through full-scale testing. 

Unfortunately, ground test demonstration of the structural reliability to aerodynamic 

loading is difficult due to limited test facility size and gravity effects. Therefore, such 

concepts will require certification through test-validated analysis. Fortunately, significant 

advances have occurred in the numerical simulation of the response of complex 

structural systems. For example, simulations can incorporate structural aspects such as 

geometrically accurate models and advanced material models to include nonlinear 

stress-strain behaviors, woven fabrics, and airbag inflation. This was demonstrated for 

the Orion Landing System – Advanced Development Project, where the space landing 

system effectively incorporated modeling of airbags (soft goods) in the early design 

process, see Refs. [9 and 10].

The HIAD structural analysis problem presents several design challenges. 1) Formal 

design approaches do not exist to address the various HIAD concepts. 2) HIAD 

structures exhibit complex structural responses to include soft goods and multiple load 

paths. 3) Designs of such systems require computationally efficient and robust modeling 

tools. Detailed computational tools to analyze the structural response of such systems 

are becoming sufficiently mature to accurately model the response of these complex 

structures. Computationally efficient models are also critical to enable completion of 

numerous simulations, where numerous executions of nonlinear, transient dynamics 

simulations are needed to verify the design. This study concentrates on extending 

preliminary modeling work by incorporating probabilistic methods in the design process. 

Concurrent with this analysis effort, experiments were conducted to acquire structural 
4

response data for 3-m and 6-m HIAD stacked-torus configurations to support model 

assessment of simulation adequacy. Refs. [11 and 12] contain additional information 

about this HIAD application.

Probabilistic analysis (PA) methods are often used to study parameter variability during 

the design process for the purposes of assessing reliability and robustness. In these 

cases parameter variations and their representation are selected based on expected 

parameter excursions from the as-built system. However, in this study PA tools are used 

to conduct parametric studies where the uncertainty model description represents a 

design space, as opposed to the uncertainty space. It is easy to lose sight of the fact that 

for many complex structures relying on inflated elements, that brute force approaches 

are often impractical. In addition more sophisticated methods may be required to 

optimally use the results from a relatively small number of simulations. For example, 

thousands of simulations using a Monte Carlo approach are typically not feasible. As the 

number of parameters, number of responses, and runtimes increase, a more 

streamlined and systematic approach may be required. One option is to incorporate 

surrogate models in the implementation of probabilistic methods to improve the 

computational efficiency. Refs. [13 and 14] provide examples for aeronautical 

applications, which focus on model adequacy. Ref. [15] provides an example for 

implementation in the spacecraft design process.

This paper begins with a brief overview of the finite element model (FEM) and the 

probabilistic analysis approach, followed by a discussion of the results. Within the 

discussion of the results, parameter sensitivity and variation in cone angle results are 

provided. Finally, concluding remarks provide general comments about the approach 

and findings.

Model Description

Figure 1a shows the FEM representation of the inflatable decelerator. In this FEM, eight 

stacked and inflated tori are constrained by a network of woven straps with loads 

reacted at the Center Body. A uniform 0.75-psi pressure load is applied to the thin, 

flexible cover, see Figure 1b, which is fully constrained at the inner and outer rims. The 

pressure load is transferred to the HIAD structure through specification of contact 

surfaces within the FEM. Most of the applied pressure is reacted by the HIAD, with 

approximately 10 percent reacted at the cover constraints. This cover and loading 

configuration was modeled to replicate the planned static loading tests, Ref. [11].

The numerical simulations were executed in LS-DynaTM, a commercial, general-purpose, 

nonlinear, transient-dynamics, finite element code, Ref. [16]. The finite element model 

(FEM) contained 252,809 nodes, with 219,736 4-noded, fully-integrated, shell elements

and 3752 2-noded seatbelt elements. The straps and tori were modeled with a shell 

element specially formulated for fabric materials undergoing large deformations. Torusto-torus and strap-to-torus interactions were modeled using contact features. Each 

simulation required approximately four hours using four processors to compute the 0.2-

second responses. Unlike many applications employing LS-Dyna, the end-state results 

and not the time varying responses were of primary interest. Additional simulations 

incorporating structural members with fabrics can be found in Refs. [17 and 18}.

For each torus, the nodal displacements along a radial line will be examined. Figure 2 

contains a schematic of the inflated tori with the nodal locations identified. The loading is

axisymmetric and the large number of straps make the structure nearly axisymmetric. 
After examination of numerous circumferential locations, the response was deemed 

sufficiently axisymmetric for the application to examine one node per torus. The resultant 

displacements for these eight nodes are considered as critical response quantities for 

the overall design process. The tori displacements provide a direct measurement of the 

deformed shape as a function of an applied aerodynamics load. Knowledge of the 

deformed shape is used to conduct predictions of the aerodynamic stability, heating 

loads, and control performance during re-entry. In this preliminary study, the nodal 

coordinates of Torus 1 and Torus 7 are used to approximate the global cone angle. 

Although not explicitly studied here, other design aspects, such as strap loads, could be 

evaluated with a similar process.

Sensitivity Analysis using Analysis of Variance

To study the global sensitivity of the critical response quantities due to parameter 

variations, five design parameters are assumed to be uncertain. The five design 

parameters used in this study are listed in Table 1 in terms of upper and lower bounds. 

Four of the parameters are related to material stiffness, namely - Tori fabric Young’s 

modulus (ETori); 4K strap Young’s modulus (E4K); 3K strap Young’s modulus (E3K); and 

multiplier for the axial cord load curve (MAxial cord). In addition, the torus fabric weave 

angle (αTori) was varied 10-degrees. Numerical values for each of the parameters 

identified in Table 1 are assumed to be equally likely (i.e., to have uniform distribution) 

within the ranges specified in the table. 

This study provides an example of incorporating probabilistic analysis for this type of 

application. Results reported here were focused on varying structural material 

parameters. The results and conclusions for a flight vehicle would vary as the design, 

design parameters, and parameter variances change. Prior to initiation of the 

probabilistic design process and to verify numerical stability, an extensive review of 

several simulation responses was performed. These responses include constraint 

forces, component energies, internal contact forces, tori pressures, displacements, strap 

loads, and visual inspection of deformed shapes.

Several approaches exist to conduct Analysis of Variance (ANOVA) for global parameter 

sensitivity estimates. In most cases, classical design of experiments (DOE) sampling of 

the parameter space is used where a parameter or set of parameters is held constant 

while other parameters are varied. This works well for most ANOVA applications. For 

computationally intensive problems, DOE sampling may not be appropriate when 

developing surrogate models is the ultimate goal. Although there are many techniques to 

create more adequate sampling of the parameter space, Halton-Leap deterministic 

sampling technique was chosen for this study, Ref. [19]. The Halton-Leap method 

creates multi-dimensional, uniformly distributed values between 0 and 1, which are then 

converted to engineering parameter values within the bounds specified in Table 1. 

Numerous executions of nonlinear, dynamic simulations are not typically feasible 

because of time constraints. To alleviate this problem, a surrogate model in conjunction 

with the Sobol computation, Ref. [21], has been used to compute contributions of the five 

input parameters to the time-varying variance of the resultant displacement. For this 

problem, 80 LS-Dyna simulations were conducted and used to create a time-varying 

surrogate model using the Extended Radial Basis Function (ERBF) approach developed 

by Mullur and Messac, Ref. [20]. Global sensitivity measures were computed using the 

Sobol method, with the resultant displacement as the response of interest for the 
6

parameter sensitivities. Sobol’s method is suitable for a nonlinear design space where a 

simple gradient computation at the parameter’s mean may not be sufficient. A drawback 

of variance-based global sensitivity measures is the need for a large number of 

response samples (i.e, thousands) to compute the variance. Even for this application, 

while 10,000 responses using the surrogate model are possible to compute in less than 

20 minutes, 10,000 FEM simulations could require orders of magnitude longer.

Results

The 80-simulation set containing displacement time histories was used to generate the 

surrogate models (i.e., ERBF response surfaces). A unique response surface is 

generated at each time step. For the resultants presented in this document, 2001 

response surfaces were generated for each torus displacement response location. 

Although the end-state results are of primary interest, the change in sensitivities over 

time provides insights into the model behavior and stability during loading. 

When working with surrogate models, users should always be concerned about their 

adequacy. Surrogate model adequacy was assessed by the removal of the ith LS-Dyna 

solution from the solution set and the comparison of it to the surrogate prediction. In 

other words, the surrogate model did not contain the ith solution being evaluated. This 

approach was implemented because nonlinear FEM simulations are often 

computationally expensive. The removal process, depicted in Figure 3, can be 

performed with all 80 LS-Dyna solutions. The comparison of end-state resultant 

displacement for the ERBF surrogate and the LS-Dyna simulation for Torus 1 and Torus 

7 are provided in Figures 4 and 5, respectively. The greater discrepancy between ERBF 

and LS-Dyna for Torus 7 when compared to that for Torus 1 is likely attributed to the 

greater distance from the Center Body. The farther the torus is from the Center Body the 

greater the number of structural elements that become involved in the response. Perfect 

agreement is not anticipated when approximating the detailed multi-hour simulation of 

the complete structure response with a surrogate response requiring less than a second 

to compute. The level of agreement, as evidenced by a correlation coefficient greater 

than 0.9, is considered sufficient to proceed with assessing parameter importance. If this 

level of agreement were deemed insufficient, new simulation results can be incorporated 

to improve the surrogate’s accuracy. Also, subsequently the surrogate model results can 

be used to compute the cone angle.

Sensitivity Results

Figures 6 and 7 show the time-dependent results of the Sobol variance computations for 

Torus 1 and Torus 7, respectively. The bars at each time slice provide an indication of 

the contribution of the parameter to the total variance. For example, in Figure 6, at the 

final time (0.2 s) nearly all of the variance of the resultant displacement for Torus 1 can 

be attributed to variation in E4K (indicated in mustard). For Torus 7, the variability is 

primarily split between the three Young’s modulus parameters. These results show that 

the parameter sensitivities of the displacements vary by torus. Drastic variations over 

time could results from insufficient number of FEM simulations or FEM numerical 

instabilities. Thus the smooth variations over time and nearly constant distributions after 

0.1 s provide additional encouragement about quality of the sensitivity results. It was 

anticipated that one of the parameters could have been eliminated. These results

indicate that variations in the Axial Strap Multiplier and the Torus Braid Angle do not 

significantly contribute the variability of the tori resultant displacements. Thus these 

parameters could be held constant or eliminated as uncertain variables.
In general, methods such as that proposed by Sobol, should be used to determine 

parameter importance for problems exhibiting significant non-linear behavior. However, 

for this problem, the correlation coefficient of the displacements for each torus as a 

function of uncertain parameter are also computed and provided in Figure 8. The results 

in Figure 8 show a shift in importance of the Young’s modulus parameters when 

progressing from inner to outer tori. More importantly, the parameter sensitivity of the 

displacements varies by torus. Thus the displacements of multiply tori must be 

incorporated when considering parameter importance on the deformed global structural 

shape.

The variance computations provide insight into parameter importance. However, care 

must be exercised when one uses variance information in the design process since the 

variance is implicitly dependent on the range of the input parameters. Thus, if the 

parameter maxima and minima in Table 1 were changed, then the corresponding 

parameter contribution to the variance will also change.

Cone Angle Variation Results

The end-state cone angle of the collective HIAD tori structure is derived from end-state 

coordinates of Torus 1 and Torus 7. The cone angle approximations using Torus 1 and 

Torus 7 results are shown in Figure 9. Statistics for 10,000 ERBF approximations are 

also provided. The re-entry heating, stability, and decelerations are strongly dependent 

on this cone angle. For example, a notional aeroheating requirement could limit the cone 

angle to vary no more than 0.5-degrees from the nominal. In that case, the design space 

is too broad with regard to the material properties. If, on the other hand, the aeroheating 

could accept 3-degree variations from the nominal, then the current design space is 

sufficient. 

Concluding Remarks

Acceptance of new spacecraft structures architectures and concepts requires validated 

design methods to minimize the expense involved with technology validation flighttesting. This paper discusses a global sensitivity approach for evaluation of the structural 

response of a Hypersonic Inflatable Aerodynamic Decelerator (HIAD). The simulation of 

the response of a HIAD structure with static external pressure loading was automated 

with a combination of Matlab scripts and LS-Dyna simulations. A surrogate model was 

generated to provide displacement responses, and a correlation coefficient metric was 

established to evaluate the surrogate adequacy. The global sensitivity of the resultant 

displacement results shows that parameter sensitivity is dependent on torus location. 

However, the displacement variations were most affected by the Young’s modulus of the 

straps and the tori. For this application, the axial strap multiplier and tori fabric angle 

could be held constant. Finally, the end-state cone angle was derived from two tori 

coordinates. The cone angle variation was compared to a notional cone angle 

requirement. Ultimately, an acceptable range in cone angles would be specified by 

project.

Acknowledgements

The author would like to acknowledge Mr. Benjamin Tutt (Airborne Systems North 

America) for generating the preliminary LS-Dyna HIAD model and Dr. Lucas Horta

(NASA Langley Research Center) for supplying many of the Matlab probabilistic analysis 

scripts.
8

References

1. Dwyer Cianciolo, A. M., et al: Entry, Descent and Landing Systems Analysis Study: 

Phase 1 Report. NASA TM 2010-216720, July 2010.

2. Smith, B. P., et al: A Historical Review of Inflatable Aerodynamic Decelerator 

Technology Development. Proceedings of the 2010 IEEE Aerospace Conference, 

IEEEAC Paper No. 1276, Big Sky MT, March 2010.

3. Bose, D. M., et al.: The Hypersonic Inflatable Aerodynamic Decelerator (HIAD) 

Mission Applications Study. Proceedings of the AIAA Aerodynamic Decelerator 

Systems Conference, AIAA Paper No. 2013-1389, Dayton Beach FL, March 25-28, 

2013.

4. Leonard, R. W.; Brooks, G. W.; McComb, H. G.: Structural Considerations of 

Inflatable Reentry Vehicles. NASA TND-457, September 1960.

5. Anderson, J. S.; Robinson, J. C.; Bush, H. G.; Fralich, R. W.: A Tension Shell 

Structure for Application to Entry Vehicles, NASA TN D-2675, March 1965.

6. Bohon, H. L.; and Miserentino, R.: Attached Inflatable Decelerator Performance 

Evaluation and Mission-Application Study. Proceedings of the AIAA Aerodynamic 

Deceleration Systems Conference, AIAA Paper No. 70-1163, Dayton OH,

September 14-16, 1970.

7. Lindell, M. C.; Hughes, S. J.; Dixon, M. and Willey, C. E.: Structural Analysis and 

Testing of the Inflatable Re-entry Vehicle Experiment (IRVE). Proceedings of the 47th 

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials 

Conference, AIAA Paper No. 2006-1699, Newport RI, May 1-4, 2006.

8. Hughes, S. J., et al.: Inflatable Re-entry Vehicle Experiment (IRVE) Design 

Overview. Proceedings of the 18th AIAA Aerodynamic Decelerator Systems 

Technology Conference and Seminar, AIAA Paper AIAA 2005-1636, Munich, 

Germany, May 23-26, 2005.

9. Timmers, R. B.; Hardy, R. C.; and Welch, J. V.: Modeling and Simulation of the 

Second-Generation Orion Crew Module Air Bag Landing System. Proceeding of the 

20th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, 

AIAA Paper No. 2009-2921, Seattle WA, May 4-7, 2009.

10. Tutt, B.; Johnson, R. K.; and Lyle, K.: Development of an Airbag Landing System for 

the Orion Crew Module. Proceedings of the 10th International LS-Dyna Users 

Conference, Dearborn MI, June 8-10, 2008. 

11. Cassell, A. M., et al: Overview of Hypersonic Inflatable Aerodynamics Decelerator 

Large Article Ground Test Campaign. Proceedings of the 21st AIAA Aerodynamic 

Decelerator Systems Technology Conference and Seminar. AIAA Paper No. 2011-

2569, Dublin, Ireland, May 23-26, 2011.

12. Swanson, G. T., et al: Structural Strap Tension Measurements of a 6 meter 

Hypersonic Inflatable Aerodynamic Decelerator under Static and Dynamic Loading. 

Proceedings of the AIAA Aerodynamic Decelerator Systems Conference, AIAA 

Paper No. 2013-1287, Dayton Beach FL, March 25-28, 2013. 

13. Annett, M.S. and Horta, L.G.: Comparison of Test and Finite Element Analysis for 

Two Full-Scale Helicopter Crash Tests. Proceeding of the 52nd

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials 

Conference, AIAA Paper No. 2011-1804, Denver CO, April 4-7, 2011.

14. Lyle, K. H.; Stockwell, A. E.; and Hardy, R. C.: Application of Probability Methods to 

Assess Airframe Crash Modeling Uncertainty. AIAA Journal of Aircraft. Vol. 44, No. 

5, 2007, pp. 1568-1573.

15. Lyle, K. H.; and Horta, L. G.: Deployment Analysis of a Simple Tape Spring Hinge 

Using Probabilistic Methods. Proceedings of the 53nd AIAA/ASME/ASCE/AHS/ASC 

Structures, Structural Dynamics, and Materials Conference, AIAA Paper No. 2012-

1915, Honolulu HI, April 23-26, 2012.
16. LS-Dyna Keyword User’s Manual, Version 971, July 27, 2012 (revision: 1617).

17. Tutt, B. A.; and Taylor, A. P.: Applications of LS-Dyna to Structural Problems Related 

to Recovery Systems and Other Fabric Structures. Proceedings of the 7th

International LS-Dyna Users Conference, Dearborn MI, May 19-21, 2002.

18. Tanner, C. L.; Cruz, J. R.; Braun, R. D.: Structural Verification and Modeling of a 

Tension Cone Inflatable Aerodynamic Decelerator. Proceedings of the 51st

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials 

Conference, AIAA Paper No. 2010-2830, Orlando FL, April 12-15, 2010.

19. Halton, J.H.: On the Efficiency of Certain Quasi-Random Sequences of Points in 

Evaluating Multi-Dimensional Integrals. Numerische Mathematik, Vol. 2, 1960, pp. 

84–90.

20. Sobol, I.M., et al: Estimating Approximation Error When Fixing Unessential Factors in 

Global Sensitivity Analysis. Reliability Engineering and System Safety, Vol. 92, 2007, 

pp. 957–960.

21. Mullur, A. A. and Messac, A.: Extended Radial Basis Functions: More Flexible and 

Effective Metamodeling. Proceedings of the 10th AIAA/ISSMO Multidisciplinary 

Analysis and Optimization Conference, AIAA Paper 2004–4573, Albany, NY, August

30 – September 1, 2004.

Table 1. Parameter uncertainty model.

Parameter Minimum Maximum

MAxial cord 0.1 1.0

αTori 60° 70°

ETori 1x105 psi 1x106 psi

E3K 4x105 psi 4x106 psi

E4K 2x105 psi 2x106 psi
10

Figure 1a. Finite element model without cover.

Figure 1b. Finite element model with cover.
Figure 2. Location of displacement responses on tori.

Figure 3. Schematic of simulation removal process
12

Figure 4. Comparison of LS-Dyna and ERBF end-time displacements for Torus 1 

(Correlation coefficient=0.97).

Figure 5. Comparison of LS-Dyna and ERBF end-time displacements for Torus 7 

(Correlation coefficient=0.95).
Figure 6. Time histories and variance for resultant displacement of Torus 1.

Figure 7. Time histories and variance for resultant displacement of Torus 7.

Figure 8. Correlation coefficients of tori end-time displacements as a function of design 

parameter.	
14

Figure 9. Cone angles for the 10,000 ERBF realizations.
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Preliminary Structural Sensitivity Study of Hypersonic Inflatable 

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14. ABSTRACT

Acceptance of new spacecraft structural architectures and concepts requires validated design methods to minimize the expense involved with 

technology validation via flight-testing. This paper explores the implementation of probabilistic methods in the sensitivity analysis of the 

structural response of a Hypersonic Inflatable Aerodynamic Decelerator (HIAD). HIAD architectures are attractive for spacecraft

deceleration because they are lightweight, store compactly, and utilize the atmosphere to decelerate a spacecraft during re-entry. However, 

designers are hesitant to include these inflatable approaches for large payloads or spacecraft because of the lack of flight validation. In the 

example presented here, the structural parameters of an existing HIAD model have been varied to illustrate the design approach utilizing 

uncertainty-based methods. Surrogate models have been used to reduce computational expense several orders of magnitude. The suitability 

of the design is based on assessing variation in the resulting cone angle. The acceptable cone angle variation would rely on the aerodynamic 

requirements. 

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