Signpost the Future: Simultaneous Robust and                  Design Optimization of a Knee Bolster                       ...
www.altairproductdesign.comAbstractThe future of engineering design optimization is robust design optimization whereby a d...
www.altairproductdesign.com                                        DEFINE                                                 ...
www.altairproductdesign.com        Key parameter identification: identifies the parameters which have the most        sign...
www.altairproductdesign.comStage 1: Assessment & Optimization of the baseline design performance under ideal         condi...
www.altairproductdesign.combeam, on which the methodology was developed and the second is an industrial example: thedesign...
www.altairproductdesign.com2.2     CharacterizeThe key parameters for the beam and their variations are as given in the p-...
www.altairproductdesign.com                                                                                      Optimum  ...
www.altairproductdesign.comanalysis it can be reasonably assumed that the resulting statistics (using a RLH) will bepracti...
www.altairproductdesign.com2.3.3   Stage 3: Simultaneous Robustness Optimization Under Real ConditionsIn order for a desig...
www.altairproductdesign.com                                                                         Baseline Deterministic...
www.altairproductdesign.com                  Knee                 Bolster           (a) Sub-System Model                  ...
www.altairproductdesign.comare that the normalized force and displacement values are less than 1. The normalization isdone...
www.altairproductdesign.com              DEFINE        CHARACTERIZE            OPTIMIZE                                  T...
www.altairproductdesign.com3.3     CharacterizeThe next stage was to identify the key parameters which have the greatest e...
www.altairproductdesign.com         DEFINE      CHARACTERIZE                                                 Typical Respo...
www.altairproductdesign.comThe optimization is carried out using the gradient-based optimizer in Altair HyperStudy. Theres...
www.altairproductdesign.com3.4.2   Stage 2: Design Assessment - Under Real ConditionsIn order to assess real life performa...
www.altairproductdesign.com           DEFINE                             5th Left                        5th Right        ...
www.altairproductdesign.com           DEFINE                              5th Left                          5th Right     ...
www.altairproductdesign.com4.0     ConclusionsThe future of engineering design optimization is robust design optimization ...
www.altairproductdesign.com[3]     LS-DYNA Version 970’, Livermore Software Technologies Corporation, LSTC        Technica...
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Jaguar Land Rover - Robust Design Optimization of a Knee Bolster

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Robust Design Optimization of a Knee Bolster - an engineering technical paper from Jaguar Land Rover and Altair ProductDesign.

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Jaguar Land Rover - Robust Design Optimization of a Knee Bolster

  1. 1. Signpost the Future: Simultaneous Robust and Design Optimization of a Knee Bolster Tayeb Zeguer Jaguar Land Rover W/1/012, Engineering Centre, Abbey Road, Coventry, Warwickshire, CV3 4LF tzeguer@Jaguar.com Stuart Bates Altair ProductDesign Imperial House, Holly Walk, Royal Leamington Spa, CV32 4JG Andy.burke@uk.altair.comwww.altairproductdesign.comcopyright Altair Engineering, Inc. 2011
  2. 2. www.altairproductdesign.comAbstractThe future of engineering design optimization is robust design optimization whereby a designis optimized for real world conditions and not just for one particular set of ideal conditions (i.e.nominal). There is no practical point trying to get to the peak of a mountain to get the bestview when a slight gust of wind can blow you off, what is practical is to find the highest plateauwhere the view is unaffected. The same is true for engineering design, there is no point incoming up with a design which is optimized for a set of ideal conditions when in reality thereexists uncertainty in the materials, manufacturing and operating conditions.This paper introduces a practical process to simultaneously optimize the robustness of adesign and its performance i.e. finds the plateau rather than the peak. The process is appliedto two examples, firstly to a composite cantilever beam and then to the design of anautomotive knee bolster system whereby the design is optimized to account for different sizedoccupants, impact locations, material variation and manufacturing variation.Keywords: Optimization, HyperStudy, Stochastic, Uncertainty, LS-DYNA1.0 IntroductionThe competitive nature of the automotive industry demands continual innovation to enablesignificant reductions in the design cycle time while satisfying ever increasing designfunctionality requirements (e.g. minimising mass, maximising stiffness etc). The challengesfor computer-aided engineering (CAE) to overcome are: Development cycle must be reduced. Failure modes have to be found and resolved earlier.The enablers for CAE are: Faster model creation, CPU, Automation, Material propertyIdentification, Robustness Optimisation and Validation. The aim of this work is to show thatAltair HyperStudy [1] can be used as powerful CAE enabler to facilitate robust design.Over the last decade industry has been indoctrinated into the philosophy of manufacturingquality to six sigma. This paper presents increasing applications of designing systems tosigma levels of quality. Thus ensuring that designs or numerical models perform withinspecified limits of statistical variation.Copyright Altair Engineering, Inc., 2011 2
  3. 3. www.altairproductdesign.com DEFINE CHARACTERIZE OPTIMIZE Robust VERIFY Optimized Design Figure 1: Design for Six-Sigma ProcessAn overview of each stage of the Design for Six Sigma (DFSS) process is given below.1.1 DefineThe first step is to carry out brainstorming to define the system inputs, outputs, controllableand uncontrollable factors. The Parameter Diagram or p-diagram (Figure 2) is a useful tool forsuch a purpose. DEFINE CHARACTERIZE Uncontrollable OPTIMIZE Factors VERIFY INPUT OUTPUT Performance DESIGN Performance Targets Controllable Factors Figure 2: Define – P-Diagram1.2 CharacterizeThe characterization phase involves the following :-Copyright Altair Engineering, Inc., 2011 3
  4. 4. www.altairproductdesign.com Key parameter identification: identifies the parameters which have the most significant effect on the performance (output) of the design. This is done typically through the use of design of experiments (DoE) and statistics (e.g. analysis of variance ANOVA). Surrogate Model generation: Typically, in CAE the analysis of a non-linear design will require simulation times ranging from one hour to a day, making the use of full analyses for iterative design optimisation computationally expensive and a robustness assessment requiring hundreds or thousands of Monte Carlo simulations impractical. To overcome these problems a response surface approximation or surrogate model is required. This is done using the information generated by the DoE together with advanced surface-fitting algorithms. The surrogate model gives the value of a key output variable in the design space, e.g. peak deceleration, as a function of the design variables. Thousands of simulations of the surrogate model can be run in a few minutes.1.3 OptimizeFigure 3 shows a typical design space (response surface) for two design variables. If youassume there is no variation in the operating and manufacturing conditions then point A is theoptimum solution. However, in reality there are variations in the manufacturing and operatingconditions such that it is very easy to fall off this optimum point (A). A “better” or robustoptimum is point B since the design space is flatter in that region i.e. the performance of thedesign is less sensitive to real life variations.The aim of this optimization phase is to identify the most robust solution in the design space. • SIMPLE OPTIMUM POINT • Absolute highest peak ignored due to sharp gradients surrounding it, reflecting the non-robust nature of the solution • A small change in input (X or Y) will result in a rapid change in output (Z) • ROBUST OPTIMUM CLOUD • Peak B has value lower than Peak A • The flatter landscape in the region of the peak results in more robust solutions in that area • The output (Z) will not be highly sensitive to small changes X or Y Figure 3: Robust Optimum IdentificationThe process developed here is shown in Figure 4 and consists of the following three stages:Copyright Altair Engineering, Inc., 2011 4
  5. 5. www.altairproductdesign.comStage 1: Assessment & Optimization of the baseline design performance under ideal conditions (i.e. deterministic optimization). This enables a rapid judgment as to whether an improved/feasible design exists within the bounds of the design i.e. for the initial structural layout within the allowable thickness ranges.Stage 2: Robustness assessment: assessment of the mean and variation in the performance of a design when subjected to real conditions.Stage 3: Optimization under real conditions (robustness optimization) – simultaneously optimize the mean and variation of performance when subjected to real life variations.Previous studies have performed deterministic optimization followed by robustnessassessments [2]. However, this study presents the first HyperStudy applications ofsimultaneous robust optimization. Baseline Stage 1 Design Design Assessment & Optimization – Under Ideal Suitable Conditions Design ? Yes No Stage 2 Design Assessment – Under Real Conditions Stage 3 Robustness Optimization: Robust Design Optimization – Under Optimized Real Conditions Design Figure 4: Simultaneous Robust and Design Optimization Process1.4 VerifyThe staged optimization process (section 1.3) provides invaluable sensitivity data in order tounderstand which variables are driving the robustness or optimization of the system. Thisinevitably will produce better design. In addition, since a consistent virtual environment isused for all three stages of this optimization process, a high degree of self checking isautomatically performed.However, the true verification of the process is the production of the physical design whichexhibits a robust performance in any experimental testing programme and ultimately reducedwarranty claims from the field.The methodology for generating optimal robust designs that has been developed in this workis primarily focused on the “optimize” phase of the DFSS loop (Figure 1). It is describedthrough use of two examples described in Sections 2 & 3. The first is a composite cantileverCopyright Altair Engineering, Inc., 2011 5
  6. 6. www.altairproductdesign.combeam, on which the methodology was developed and the second is an industrial example: thedesign of a knee bolster system.2.0 Composite Beam DesignThis example is concerned with the minimization of the weight of a cantilevered compositebeam (Figure 5) subjected to a parabolic distributed load (q) with uncontrollable andcontrollable factors such as manufacturing or material variation. The DFSS process has beenapplied to the problem and is described below. Figure 5: Composite Beam Subjected to a Parabolic Distributed Load2.1 DefineFigure 6 shows the p-diagram for the composite beam.The performance targets for the beam are as follows: Deflection at the free end of the beam < 1 (normalized). Maximum bending stress in the beam < 1 (normalized). Height < 10 times the width (to avoid torsional lateral buckling). DEFINE NOISE CHARACTERIZE •fiber volume fraction ± 0.03 •Young’s modulus of the fiber ± 2% OPTIMIZE •Young’s modulus of the resin ± 2% •Density of the fiber ± 2% VERIFY •Density of the resin ± 2% •Width ± 0.3mm •Height ± 0.3mm INPUT OUTPUT Deflection & Stress COMPOSITE Max Deflection, Max Targets BEAM Bending Stress, Height to width ratio PARAMETERS •Beam Height •Beam Width •Fibre Volume Fraction Figure 6: P-Diagram for the Composite BeamCopyright Altair Engineering, Inc., 2011 6
  7. 7. www.altairproductdesign.com2.2 CharacterizeThe key parameters for the beam and their variations are as given in the p-diagram in Figure6. The analysis of the beam is via an analytical expression, as such there is not a requirementto replace the analysis with a surrogate model as is the case for the knee bolster analysis inSection 3.2.3 Optimize2.3.1 Stage 1: Design Assessment & Optimization – Under Ideal ConditionsTypically, during an engineering design process once a baseline design has been generated(e.g. from a topology optimization) it is assessed to determine whether or not it meets theperformance criteria.The baseline design performance is given in Table 2, it can be seen that the design meets thetargets and has a weight of 4.8N. The next stage is to determine the minimum weight designwhich meets the targets.In order to reduce complexity, ideal conditions are assumed at this stage and optimization iscarried out on perturbations of the initial structural layout and thicknesses. This stage rapidlyprovides information as to whether or not an improved/feasible design exists within thesedesign bounds. The engineer can then make a judgment as to whether or not the design issuitable for further development and can be taken forward to stage 3 or if a modified baselinedesign is required.The optimization of the beam is set up is as follows: Objective: o Minimize Weight Constraints: o Maximum deflection at the free end of the beam (normalized) < 1 o Maximum bending stress in the beam (normalized) < 1 o Height to 10 x Width ratio (normalized) < 1 (to avoid torsional lateral buckling) Design Variables: o 4mm ≤ Beam Width ≤ 20mm o 20mm ≤ Beam Height ≤ 50mm o 0.4 ≤ Fibre Volume Fraction ≤ 0.91Altair HyperStudy is used for the optimization and the results are shown in Table 1. It can beseen that, the optimum design (for ideal conditions) meets the targets and represents a 39%weight reduction over the baseline design.Copyright Altair Engineering, Inc., 2011 7
  8. 8. www.altairproductdesign.com Optimum Baseline Under Ideal Design variables Min Max design Conditions width [mm] 4 20 10.0 4.5 height [mm] 20 50 30.0 44.8 Fibre volume fraction 0.4 0.91 0.79 0.52 Objective (min): weight [N] - - 4.82 2.95 Constraints Normalized stress constraint <=1 - - 1 1 Normalized displacement constraint <=1 - - 1 1 Normalized Height to 10 x width ratio <=1 - - 0.3 1 Table 1: Performance of the Baseline and Optimum Designs Under Ideal Conditions2.3.2 Stage 2: Design Assessment - Under Real ConditionsAt this stage, the design is subjected to variations in the uncontrollable/controllable factorspresent in a real system. The mean and variation of the performance is assessed via a“stochastic study” in HyperStudy. For the beam example the variations imposed on the designare material and manufacturing tolerances. Note, the variations are assumed to be normallydistributed and ±3σ covers the interval of the tolerance where σ is the standard deviation ofthe distribution. Table 2 identifies the tolerances and their assumed variations. Material related tolerances Variation fiber volume fraction ± 0.03 Young’s modulus of the fiber ± 2% Young’s modulus of the resin ± 2% Density of the fiber ± 2% Density of the resin ± 2% Geometric related tolerances Width ± 0.3mm Height ± 0.3mm Table 2: Variations on Manufacturing and Material TolerancesThe mean and variation (σ) in the performance of a design is determined by executing a10,000 Monte Carlo (MC) simulation run using a random Latin Hypercube DoE (RLH) (Figure7(a)) on the design with the imposed variations listed in Table 1. Note, a 500 MC simulationrun (Figure 7(b)) was also carried out and the resulting statistics were similar to the 10,000MC simulation as can be seen in Table 3, therefore for a more computationally expensiveCopyright Altair Engineering, Inc., 2011 8
  9. 9. www.altairproductdesign.comanalysis it can be reasonably assumed that the resulting statistics (using a RLH) will bepractically the same with a reduced number of runs. (a) 10,000 runs (b) 500 runs Figure 7: Comparison of Monte Carlo Simulation Run Plots for the Baseline Design Stochastic Assessment Mean Standard Deviation 500 runs 10000 runs 500 runs 10000 runs weight [N] 4.8240 4.8240 0.07300 0.07430 Normalized stress 1.0000 1.0000 0.01200 0.01200 Normalized displacement 1.0000 1.0000 0.04070 0.04060 Normalized height to width ratio 0.3000 0.3000 0.00316 0.00317 Table 3: Comparison of Statistics for the Monte Carlo Simulations on the Baseline DesignThe results of the stochastic studies carried out on the baseline and deterministic optimumdesigns are given in Figure 8 and Table 4. Each point on the plots represents a run in the MCsimulation and the resulting “cloud” of points gives the resulting mean and variation inperformance of a particular design. The green circle (Figure 8) represents the boundary of 3σ i.e. 3-sigma design. Hence, if an engineer is aiming for a 3-sigma performance (99.73 %reliability) then this circle must lie in the feasible region.It can be seen, that the clouds for both the baseline and deterministic optimum designs arecentred on the point where the stress and displacement = 1 i.e. the mean performance is thetarget value of 1, however it can also be seen that approximately 75% of the runs for bothdesigns are infeasible since their values >1 i.e. the 3σ boundary lies in the infeasible zone.Note also, that the cloud for the deterministic optimum has a greater scatter than the baselinei.e. it is less robust since it’s variation in performance is greater. As a result neither design canbe considered as “robust”.Copyright Altair Engineering, Inc., 2011 9
  10. 10. www.altairproductdesign.com2.3.3 Stage 3: Simultaneous Robustness Optimization Under Real ConditionsIn order for a design to be simultaneously robust and optimized the centre of the performancecloud (i.e. mean performance) must be as close to the constraint boundaries as possiblewhilst ensuring that, for 3-sigma performance, the 3-sigma boundary remains in the feasibleregion i.e. 99.73% of the points in the cloud are in the feasible region. Similarly, for 6-sigmadesigns the 6-sigma boundary remains in the feasible region.The robustness optimization of the beam for 3-sigma performance is set up is as follows (notethe mean and σ are calculated as in Stage 2) and carried out using HyperStudy. Objective: o Minimize Mean Weight Constraints: o σweight ≤ 3σ (assume σweight = 0.1) o Mean Normalized Stress + 3σ ≤1 (assume σstress= 0.1) o Mean Normalized Displacement + 3σ ≤ 1 (assume σdisp= 0.1) o Mean Normalized height to width ratio + 3σ ≤ 1 (assume σh2w= 0.1) Design Variables: o 4mm ≤ Beam Width ≤ 20mm o 20mm ≤ Beam Height ≤ 50mm o 0.4 ≤ Fibre Volume Fraction ≤ 0.91where σ is the standard deviation.The results of the robustness optimization are given in Figure 8 and Table 4. The robustoptimum represents a 29% weight reduction over the baseline design. It can be seen, that thecloud for the robust optimum design is centred within the feasible stress-displacement regionand the 3σ boundary lies in the feasible zone. Baseline Deterministic Robust Optimum Optimum Indicates 3 sigma boundary Figure 8: Results of the Stochastic StudiesCopyright Altair Engineering, Inc., 2011 10
  11. 11. www.altairproductdesign.com Baseline Deterministic Robust Design variables Min Max design Optimum OptimumMean width [mm] 4.0 20.0 10.0 4.5 4.8Mean height [mm] 20.0 50.0 30.0 44.8 44.8Mean Fiber volume fraction v f 0.40 0.91 0.79 0.52 0.57Objective (min): Mean Weight [N] - - 4.8246 2.9535 3.4474 ConstraintsMean Normalized stress constraint + 3 sigma <=1 - - 1.0361 1.0736 0.9965Mean Normalized displacement constraint + 3 sigma <=1 - - 1.1234 1.1885 0.9959Mean Normalized Height to 10 x width ratio + 3 sigma <=1 - - 0.3095 1.0674 0.9952 meets targets fails targets Table 4: Performance of Baseline, Deterministic Optimum and Robust Optimum2.4 VerifySince all of the performance calculations are carried out using the full analysis of the beam i.e.an analytical equation, the verification phase is completed at the optimization stage.3.0 Knee Bolster Study3.1 IntroductionThe aim of this study was to apply the same process as in Section 2 to determine a robustand optimized design of a knee bolster.The study has been carried out on a sub-system model of the knee bolster (Figure 9a). Thedynamic finite element analysis code LS-DYNA [3] was used to compute the response of thesystem to various design inputs. The objective of the study was to automatically vary variousdesign variables to optimize the energy absorbing characteristics of the system whilstsatisfying various force and displacement limiting constraints based on federal requirements:FMVSS 208 [4]; final verification was carried out using full occupant / interior modelsimulations using LS-DYNA (Figure 9b).Copyright Altair Engineering, Inc., 2011 11
  12. 12. www.altairproductdesign.com Knee Bolster (a) Sub-System Model (b) Full Model Figure 9: LS-DYNA Analysis of the Knee Bolster DesignThe Design for Six-Sigma (DFSS) process (Section 1) has been applied to the knee bolsterdesign as is described in this section.3.2 DefineThe knee bolster system is defined through the p-diagram shown in Figure 10. DEFINE NOISE CHARACTERIZE •Material Yield Stress •Manufactured Thickness OPTIMIZE •Manufactured Shape •Impactor type (5th%, 50th%) VERIFY •Impactor position variation INPUT OUTPUT FMVSS208 Knee Force-displacement USNCAP Bolster Pulse EURONCAP PARAMETERS •Thickness •Shape •Material Properties •Impactor position P-Diagram Figure 10: P-Diagram for the Knee Bolster SystemIt can be seen, that the inputs are the legislative targets for the system which are based on theforce-displacement and energy absorption of the knee bolster. Hence the output is the force-displacement pulse measured from the LS-DYNA simulation. The targets for the knee bolsterCopyright Altair Engineering, Inc., 2011 12
  13. 13. www.altairproductdesign.comare that the normalized force and displacement values are less than 1. The normalization isdone according to FMVSS 208 [4]. A set of typical force-displacement pulses for the 5thLeft/Right & 50th Left/Right impactors is shown in Figure 11. It can be seen, that this solutionis feasible since the corresponding normalized force and displacement values are less thanone i.e. in the feasible region. DEFINE CHARACTERIZE OPTIMIZE VERIFY Feasible Region Figure 11: Typical Force-Displacement OutputThe thickness and shape parameters are identified in Figure 12. The thickness ranges areassumed to vary between 1 and 10mm. The shape factor varies between -1 and 1. Figure 13shows the assumed variation of ±25mm in the centre point of the 5th and 50th impactors.Copyright Altair Engineering, Inc., 2011 13
  14. 14. www.altairproductdesign.com DEFINE CHARACTERIZE OPTIMIZE Thickness 1 VERIFY Thickness 2 PARAMETERS •Thickness Thickness 3 •Shape •Material Properties •Impactor position Thickness 4 Shape Variable Note: the thickness and shape variables are the same for each knee bolster Figure 12: Thickness and Shape Parameters for the Knee Bolster DEFINE CHARACTERIZE OPTIMIZE VERIFY PARAMETERS •Thickness •Shape •Material Properties •Impactor position (a) 5th Percentile Impactors (b) 50th Percentile Impactors Figure 13: Impactor Position VariationCopyright Altair Engineering, Inc., 2011 14
  15. 15. www.altairproductdesign.com3.3 CharacterizeThe next stage was to identify the key parameters which have the greatest effect on the kneebolster performance. This was done using Altair HyperStudy using the following process:1 Run a DoE with all the parameters2 Create an approximation of the responses3 Carry out a statistical analysis of the approximation using Analysis of Variance (ANOVA)Figure 14 shows the results of the ANOVA study for the displacement of the 5th left Impactor.This is typical of the results for the other responses. It can be seen, that the position of theimpactors, the shape and thickness variables and the yield stress contribute the most to theresponse. It is assumed that changes to these parameters are sufficient to characterize theknee bolster system. DEFINE CHARACTERIZE 20 ANOVA plot OPTIMIZE % Contributions of the Parameters Contributing % Impactor position Horizontal VERIFY to Displacement of 5th Left Impactor Impactor position vertical Thickness 1 Thickness 2 Thickness 3 Thickness 4 Yield Stress Shape Other less significant parameters 0 Contributing Source Figure 14: Key Parameter Identification – Typical ANOVA PlotFollowing on from this, a response surface of the LS-DYNA analysis was generated for use inthe optimization phase. There are a number of possibilities available in HyperStudy for doingthis. However, the recommended approach (used here) is to carry out a DoE study using theoptimal design filling algorithm – Optimal Latin Hypercube, and then use this data to create asurrogate model via the moving least squares method. Figure 15 shows a typical responsesurface generated for the force response in the 50th left impactor.Copyright Altair Engineering, Inc., 2011 15
  16. 16. www.altairproductdesign.com DEFINE CHARACTERIZE Typical Response Surface OPTIMIZE VERIFY Force 50th Left Im pa l cto ica rP ert os nV it ion s itio Ho r Po rizo cto nta pa l Im Figure 15: Typical Response SurfaceWith the knee bolster system define and characterized the next step is then to optimize thedesign.3.4 OptimizeAs described earlier the optimize phase has 3 stages which are shown in Figure 4, these aredescribed in this section.3.4.1 Stage 1: Design Assessment & Optimization– Under Ideal ConditionsThe first stage is to assess and optimize the design under ideal conditions i.e. no noise isimposed on the system. Therefore, the only parameters under consideration are the thicknessand shape variables (Figure 12). The response surface generated in the characterizationphase is used for the analysis. The setup is as follows: Objective: o Maximize Sum Normalized Energies Constraints: o Normalized Force: 1.0 o Normalized Displacement: 1.0 Design Variables (Figure 12): o 1mm ≤ 4 Thicknesses ≤ 10mm o -1 ≤ Shape variable Scale Factor ≤ 1Copyright Altair Engineering, Inc., 2011 16
  17. 17. www.altairproductdesign.comThe optimization is carried out using the gradient-based optimizer in Altair HyperStudy. Theresults are given in Table 5 and Figure 16, it can be seen that for ideal conditions the solutionmeets the performance targets. The question arises at this point: how does this solutionbehave in reality? This is addressed in the next section. Design Optimized for IDEAL Design variables Min. Max conditions Shape Variable -1.0 1.0 0.2 Thickness 1 [mm] 1.0 10.0 3.4 Thickness 2 [mm] 1.0 10.0 4.5 Thickness 3 [mm] 1.0 10.0 5.0 Thickness 4 [mm] 1.0 10.0 5.7 Objective (max): Sum of Normalized Energy - - 0.983 Constraints 5th 50th left right left right Normalized displacement constraint <=1 - - 0.70 0.84 0.78 0.77 Normalized force <=1 - - 1.00 0.97 0.91 0.89 Table 5: Assessment of the Design Optimized for Ideal Conditions DEFINE 5th Left 5th Right CHARACTERIZE OPTIMIZE VERIFY 50th Left 50th Right Figure 16: Assessment of the Design Optimized for Ideal ConditionsCopyright Altair Engineering, Inc., 2011 17
  18. 18. www.altairproductdesign.com3.4.2 Stage 2: Design Assessment - Under Real ConditionsIn order to assess real life performance a robustness assessment (stochastic study) of thedesign “optimized for ideal conditions” is carried out. This is done with a Monte Carlosimulation carried out on the response surface, here a 500 run random Latin Hypercube isused. The parameters and assumed real life variations imposed on the system are identifiedin Table 6. Note, the following assumptions have been made: the variations are normallydistributed and ±3σ covers the interval of the tolerance where σ is the standard deviation ofthe distribution. Material related tolerances Variation Yield Stress ± 10% Geometric related tolerances Thickness ± 0.1mm Shape Scale Factor ± 0.01 Impactor position variation Position ± 25mm Table 6: Knee Bolster Noise Parameters and VariationsThe results of the robustness assessment performed on the design optimized under idealconditions are shown in Figure 17. It can be seen from the resulting “performance clouds” thatthere are a large number of solutions which fail the force performance targets and the designis considered non-robust.Copyright Altair Engineering, Inc., 2011 18
  19. 19. www.altairproductdesign.com DEFINE 5th Left 5th Right CHARACTERIZE OPTIMIZE VERIFY 50th Left 50th Right Figure 17: Design Optimized for Ideal Conditions - Robustness Assessment3.4.3 Stage 3: Robustness Optimization: Design Optimization – Under Real ConditionsAt this stage the robustness assessment is incorporated in the optimization loop. The outputfrom the robustness assessment used in the optimization loop is the mean and standarddeviation of the responses. The optimization is set up as follows: Objective: o Maximize Mean of the Summed Normalized Energies Constraints: o Normalized Displacement: Mean + 3σ 1.0 o Normalized Force: Mean + 3σ 1.0 Design Variables (Figure 12): o 1mm ≤ 4 Thicknesses ≤ 10mm o -1 ≤ Shape variable Scale Factor ≤ 1The results of the simultaneous robustness and design optimization are shown in Figure 18. Itcan be seen the “performance clouds” have been shifted into the feasible region, Althoughthere are a small number of solutions which fail the performance targets, the design isconsidered as robust as possible for the current knee bolster structural layout.Copyright Altair Engineering, Inc., 2011 19
  20. 20. www.altairproductdesign.com DEFINE 5th Left 5th Right CHARACTERIZE OPTIMIZE VERIFY 50th Left 50th Right Figure 18: Design Optimized for Real Conditions - Robustness Assessment3.5 VerifyAt this stage of the DFSS process significant information about the performance of the kneebolster has been generated. The next step is then to “plug” the design back into the fullvehicle model which has been concurrently updated with other optimized components of thecar.It is a design challenge to produce a virtual design that can achieve the constraint targetswithin ±3σ due to the conservative nature of this numerical test environment (e.g. totally rigidbacking structure, conservative impact velocity etc.). This technology can be efficiently usedto determine the most efficient design for the specified design variations.The design determined by this process is similar to a production component used on a recentvehicle. However, this design was achieved in a fraction of the design time with an increasedunderstanding of the performance drivers.Copyright Altair Engineering, Inc., 2011 20
  21. 21. www.altairproductdesign.com4.0 ConclusionsThe future of engineering design optimization is robust design optimization whereby a designis optimized for real world conditions and not just for one particular set of ideal conditions.There is no point in coming up with a design which is optimized for a set of ideal conditionswhen in reality there exists uncertainty in the materials, manufacturing and operatingconditions.Altair HyperStudy has been used to simultaneously optimize the robustness and performanceof a real world component (i.e. automotive knee bolster). The resulting design was similar toan existing production component. However, this design was achieved in a fraction of thedesign time with an increased understanding of the performance drivers. A unique processhas been developed which is computationally efficient for complex non-linear systems. Thisprocess can be further enhanced and automated. The study has shown that Altair HyperStudycan be used as a key CAE enabler.Achieving robust design is inherent in the quality philosophy of many companies. It willbecome an increasing requirement to demonstrate that digital designs achieve the requiredquality levels. This will initially be achieved on a component level and gradually migrate tocomplex systems. The initial requirement will be to understand the probabilistic variation ofvarious parameters. This will require an increasing amount of measurement and an increasedunderstanding of the physical drives of the component / system. Robustness can only beachieved by understanding the variation of the various factors.Adding noise factors during optimisation is the best way in obtaining a robust solution the useof DFSS principle helps identify failure modes and eliminate them earlier in the designprocess.For certain parameters, suppliers are already instructed to deliver product within specificsigma quality levels. This technology can identify parameters which drive the quality and helpdevelop guidelines to control the variation of these quantities. This control will beaccompanied by an associated cost penalty.Increased availability of inexpensive powerful computing and improvements to softwareintegration and the predictive algorithms heralds the new development of producing digitaldesigns to sigma levels of quality.5.0 References[1] ‘Altair HyperStudy 8.0’ Altair Engineering Inc. (2006).[2] ‘Design Optimization and Probabilistic Assessment of a Vented Airbag Landing System for the ExoMars Space Mission’, Richard Slade and Andrew Kiley, 5th Altair UK Technology Conf., April 2007.Copyright Altair Engineering, Inc., 2011 21
  22. 22. www.altairproductdesign.com[3] LS-DYNA Version 970’, Livermore Software Technologies Corporation, LSTC Technical Support, 2006.[4] ‘FMVSS 208 – Occupant Crash Protection’, Federal Motor Vehicle Safety Standards and Regulations.Copyright Altair Engineering, Inc., 2011 22

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