Optimization Design For Vehicle Crash Safety Considering Parametric Uncertainty

Opt imizat ion design for vehicle crash safet y is a very co mplicated and difficult system engineering.Due to manufacturing process,human cognit ive levels and external environmental factors,vehicle crash engineering problems invo lve various uncertaint ies such as material properties,geo metric characterist ics and loads in pract ice.Under the coupling effect o f various uncertain factors,t he tradit ional determinist ic opt imizat ion design for vehicle crash safet y may produce large analysis deviat ions,making it challenging to meet the design requirements well.Wit h the improvement o f people's cognit ive level and safet y awareness,the uncertain opt imizat ion design theory and method for vehicle crash safet y emerged.The uncertain optimizat ion design can obtain the opt imization so lut ions sat isfying the design requirements with the considerat ion of the effects of uncertaint ies on the feasibilit y do main o f constraints or variat ion range s o f object ives in the opt imizat ion.Alt hough the research on the uncertain opt imizat ion design for vehicle crash safet y has attracted wide attent ion fro m the scient ific and engineering circles for a long time,it is not yet mature and needs to be improved and perfected.Especially for the problems with co mplex parametric uncertainties and the so lut ion and efficiency o f opt imizat ion design,there are st ill a series o f technical difficult ies to be so lved urgent ly.Aiming at the uncertain opt imizat ion problem of large tolerance,mult i-parameter associat ion as well as the imprecise probabilit y in the opt imization design for vehicle crash safet y,the works o f this paper spread out fro m the change informat ion o f uncertain parameters,various correlat ion relatio ns and uncertaint y measurement.The research ideas are from the perspect ives of the bounded uncer taint y,mult i-source uncertaint y,mixed uncertaint y and co mplex nonlinear correlat ion o f design variables or design parameters,striving to give so me exploratory methods for parametric uncertain analysis modeling and opt imizat ion so lut ion and finally provi ding guidance and reference for the effect ive design and improvement o f vehicle crash safety.First ly,in order to reduce the sensit ivit y with respect to the fluctuation o f uncertaint y parameters in bounded ranges,the interval model is emplo yed to describe the uncertaint y o f parameters for the to lerance problem and a robust optimizat ion model considering to lerance design is established.Furthermore,considering the mult i-source correlation problem o f uncertain parameters,a robust opt imizat ion model for ve hicle crash safet y to deal with independence and correlat ion amo ng interval parameters is established,and an efficient algorithm is developed.Secondly,considering the non-single uncertaint y problem of the imprecise probabilit y distribut ion,a hybrid reliabilit y-based design optimizat ion model and an efficient design method for vehicle crash safet y are developed by integrat ing the interval uncertaint y into the probabilit y uncertaint y.In addit ion,considering the uncertaint y problem wit h co mplex parametric correlation,the reliabilit y analysis and an efficient design method for vehicle crash safet y are studied.In view o f the above ideas,this paper carries out and co mpletes the fo llowing research contents:1)Based on interval uncertaint y analysis,an optimizat ion design method for vehicle crash safet y considering parametric bounded uncertaint y is developed.For the uncertaint y problem of the dimensio nal and geo metrical to lerances of the crit ical design co mponents in vehicle crash opt imizat ion,the interval model is used to quant ify the uncertaint y o f design parameters through symmetric to lerance.According to the robustness theory,the radius o f the object ive funct ion is taken as the robustness evaluat ion index.By combining the parameter design with the t o lerance design,a robust optimizat ion model is established through introducing the to lerance evaluatio n index,which can realize opt imizat ion of the no minal values o f design variables and their to lerances in a simultaneous manner.The reliabilit y-based possibilit y degree o f interval(RPDI)is used to cope with the uncertain constraints in the model,then the robust opt imizat ion problem considering the tolerance can be converted into a nested determinist ic mult i-objective opt imizat ion problem,and the corre sponding opt imizat ion algorithm is developed.The applicat ion o f this method to the opt imizat ion designs for vehicle body crashworthiness shows that it can ensure the robustness o f passive safet y and realize the maximizat ion o f the to lerance range for improving the manufacturing process,avo iding abundant duplicat ion of design,and reducing product ion costs by synchronously adjust ing no minal values and to lerances of design variables.2)Based on interrelated relationships amo ng interval uncertaint ies,a n opt imizat ion design method for vehicle crash safet y considering parametric mult i-source uncertaint y is developed.For the uncertain problem with independent and correlated interval parameters in vehicle crash opt imizat ion,a mult idimensio nal parallelepiped convex model is emplo yed to describe the mult i-source uncertaint y fo r interval parameters.Thus all independent and correlated interval parameters can be reasonably quant ified wit hin a unified framework.Then a robust opt imizat ion desig n model considering t he mult i-source uncertaint y is established,which takes the midpo int and radius o f the object ive function as optimizat ion object ive s.Through an independence transforming procedure,the uncertain parameters are transformed into independent standard interval parameters,and the mult idimensional parallelepiped uncertain do main is transformed into a mult idimensio nal cube do main.As a result,the robust opt imizat ion model with mult i-source uncertaint y can be converted into an independent interval robust model,which great ly facilitates the subsequent robust analysis and optimizat ion design.The RPDI is used to cope with the uncertain constraints,and then the robust opt imizat ion problem can be converted into a nested determinist ic mult i-object ive opt imizat ion problem.An efficient robust opt imizat ion algorithm using the micro mult i-object ive genet ic algorithm as a framework is developed by coupling wit h the independence transformat ion and interval analysis based on first-order Taylor expansion,which can effect ively eliminate the inner opt imizat ion o f the nested problem.The applicat ion of this method to the opt imizat io n designs for the restraint systems considering occupant damage shows that it can ensure the robustness o f passive safet y and improve the accuracy o f opt imizat ion results.3)Based on non-single interval uncertaint y,an optimizat ion design method for vehicle crash safet y considering parametric hybrid uncertaint y is developed.For the uncertaint y problem wit h the imprecise probabilit y distribut ion in vehicle crash opt imizat ion,it is not easy to obtain an exact probabilit y distribut ion function,but it is possible to obtain the distribut ion t ype and the ranges o f distribut ion parameters.The parameterized Probabilit y box(P-box)is emplo yed to quant ify this kind o f probabilit y and interval mixed uncertaint y,and then a hybrid reliabilit y-based desig n opt imizat ion model for vehicle crash safet y taking the reliabilit y o f passive safet y as constraints is established.Due to the existence o f interval parame ters,the probabilist ic constraints in the reliabilit y assessment fo llow the conservat ive principle.Based on the classical SORA method,the MPP and the interval vector(the worst-case po int)in the worst case o f mixed reliabilit y are obtained by PMA-based,and then a shift ing vector is constructed according to the worst case.By an efficient decoupling algorithm considering the worst case,the nested opt imizat ion problem is converted into the sequent ial iterat ive process o f performing the determinist ic desig n opt imizat ion and hybrid reliabilit y analysis alt ernately,as a result avo iding the nested opt imizat ion and achieving fast convergence and high efficiency o f the hybrid reliabilit y-based design optimizat ion for vehicle crash safet y.The applicat ion of t his method to the opt imizat ion designs for vehicle body crashworthiness and the restraint system considering occupant damage shows that it can ensure the reliabilit y o f passive safet y and improve the accuracy o f opt imizat ion results.4)Based on various correlat ions,an opt imizat ion design method for vehicle crash safet y considering parametric co mplex correlat ion is developed.For the uncertaint y problem wit h various parametric correlations in vehicle crash opt imizat ion,Copula funct ions are integrated to q uant ify the weak nonlinear correlation,strong nonlinear correlat ion and tail dependence.Then a reliabilit y-based design opt imizat ion model for vehicle crash safet y considering parametric correlatio n is established,which takes the reliabilit y o f passive safet y as constraints.According to the number o f sample po ints,the Bayesian method or parameter est imat ion metho d is chosen to select the opt imal Copula functio n matching most closely the sample po ints o f correlated parameters to build the jo int distribu t ion funct ion,then parametric correlat ions are integrated into the reliabilit y analysis.Based on the classical SORA method,an efficient decoupling algorithm considering parametric correlation is adopted,which converts the nested opt imizat ion problem in to the sequent ial iterat ive process of carrying out the determinist ic design opt imizat ion and Copula function-based reliabilit y analysis alternately,achieving the reliabilit y desig n for vehicle crash safet y with the considerat ion o f co mplex correlat ion be tween parameters quickly.The applicat ion o f this method to the optimizat ion design s fo r vehicle body crashworthiness shows it can ensure the reliabilit y o f passive safet y and improve the accuracy of optimizat ion results.