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Conclusion to Crashworthiness Optimization


  • The solution of the optimization problem presented in the example for detemining the optimal thickness of the bumper and the hood has been obtained with the three methodologies viz. Single Stage, SRSM continuous and Discrete method.
  • The choice of the optimum design parameters ( tbumper, thood ) is based on the objective of reducing the Head Injury Criteria (HIC).
  • The given constraint for the optimization problem is the permissible intrusion, measured as the distance between the nodes 167 and 432.
  • A discrete variable has been incoporated to illustrate a more practical approach for structural optimization due to the limitations in manufacturing processes.
  • A tabulated comparision of the results obtained by the three approaches has been produced below.
 Single StageContinuous (SRSM)Discrete (SRSM)
 RMS Error (HIC)27.7%3.43%4.61%
 SPRESS (HIC)91.4%11%13.7%
 R-sq (HIC)0.9220.8370.994
 Table: Comparision of results with three methods of optimization



  • The discrete method presented using the SRSM metamodel presents comparable results to the SRSM continuous variables.
  • The RMS error using the Single Stage yields relatively higher values, but the computation cost is less. Hence it is useful for a raw estimate of various parameter studies in the initial execution.
  • The SPRESS value of the SRSM presents better validation compared to the Single Stage method. Hence the prediction for the SRSM method builds more confidence in the metamodel.
  • Note that for the sequential approaches, the metamodel only represents the subregion of the design space of the respective iteration, it's not a global approximation.