Bayesian Optimization Algorithm And Its Application Study In Design Of Vehicle Body

Structural and multi-disciplinary optimization technologies have been developed rapidly in recent decades,and are widely used in automobiles,ships,aircrafts and other fields.Bayesian optimization algorithm based on surrogate models is the main mean to solve the structural optimization design in engineering,which can be significant improve the utilization rate of materials.However,with the complexity of engineering problems,it often contains many expensive constraints,and even multiple objectives need to be optimized at the same time,which takes a long time to obtain relatively excellent solutions,and brings challenges for the robustness and efficiency in optimization process.In order to solve the above-mentioned problems,based on the Constraint Expected Improvement(CEI)criterion in the traditional Bayesian optimization algorithm,this paper proposes a constraint criterion based on the Lower Confidence bound(LCB),referred to as CLCB criterion.Through a reasonable combination of the numerically normalized LCB function and the Probability of feasible(Po F),the constraint of single objective LCB criterion is realized.Subsequently,the CLCB and CEI criteria are tested on six global optimization mathematical examples.The numerical results showed that the proposed CLCB criterion has a faster convergence speed and can obtain a better approximate global optimal solution.Finally,the CLCB criterion was applied to the crashworthiness optimization design of the hat-shaped structures,and the effectiveness of the finite element model was verified by the axial impact experiment.The optimization results showed that under the constraint of maximum peak force,the specific energy absorption of the hat-shaped structure is increased by 34.73% during the axial impact process,showing a strong ability to optimize engineering problems and can effectively improve the crashworthiness of the hat-shaped structures.To deal with expensive multiobjective optimization problems,this paper develops a multiobjective LCB infill-criterion based on the LCB improvement matrix.By introducing a improvement function,the LCB improvement matrix is normalized to a single numerical value,namely LCBM criteria,which is then maximized for adding solution points sequentially in multiobjective Bayesian optimization algorithm.All these LCBM criteria have closed-form expressions and can maintain the monotonicity properties with low time complexity.Subsequently,the proposed LCBM criteria and traditional criteria were tested on different objectives and variables on ZDT and DTLZ benchmarkes,numerical results showed that the proposed LCBM criteria has a faster convergence speed than the traditional criteria and be able to generate excellent Pareto front at a relatively low computational cost.Finally,the LCBMhcriterion with excellent performance was applied to the optimal design of the crashworthiness of hat-shaped thin-walled structure.Compared with the initial design,the specific energy absorption increased by 21.43% and the peak force decreased by 12.12%.Furthermore,the LCBMh criterion was applied to the three-objective safety design of automobile B-pillar subject to side impact.The optimized mass,intrusion and maximum intrusion speed were reduced by20.90%,25.06% and 18.82%,respectively,demonstrating the powerful optimization performance of LCBMh,it can efficiently solve such nonlinear engineering problems.