Multi-objective Optimization Method CBQNA And Its Application In Structures Under Dynamic Impact

In order to realize the significant strategic deployment of "made in China 2025",China manufacturing industry faces the challenge of moving from “great manufacturing nation" to "manufacturing power",which puts forward higher requirements for the design and production level of Chinese industrial products.The requirements of structural strength,lightweight and low cost need to be considered simultaneously to carry out the optimization design of mechanical products.And multi-objective optimization theories and methods have become the main means to solve such optimization design problems,improve product performance and accelerate product optimization and upgrading.Based on review of predecessor's study and mathematical optimization theory,this paper discusses the multi-objective methods,which are easy to implement in engineering application.Then an effective algorithm IBWSA is proposed for multi-objective optimization design and its convergence and computational efficiency are also analyzed and studied.And on this basis,the method CBQNA and the engineering optimization strategy are constructed for solving multi-objective problems with the inequality constraints.Furthermore,the proposed method and optimization strategy are used in optimization design of the mechanical structures under dynamic impact.Impulsive load will cause crumpling and bending deformation of mechanical structure,thus the influence of contact conditions,structural geometry and material nonlinearity on product performance should be considered in the optimization design of such mechanical structures.Therefore,there are various design variables affecting the performance indicators of such products,and mathematical models with multiple objects and constraints are often utilized in optimization design of such related mechanical products.This dissertation is supported by the 2017 National Natural Science Foundation Youth Project “Study on the Effective Simulation Method of Collision Energy Absorption of Thin Wall Beams”(No.11502092)and the cooperative development project between the research group of the author and a domestic automobile research institution-Tianjin intelligent manufacturing technology major projects?Research and development on key technologies of special robots for intelligent vehicle passive safety detection ?(No.16ZXZNGX00100).This doctoral thesis concentrates on the establishment of an effective multi-objective optimization method,which combined BFGS quasi-Newton's method and weighted sum technique,and its application in the safety design of the vehicle structure under impact collision.This principle research work in this paper focuses on the following aspects:(1).Based on the detailed analysis of the existing optimization theory,more attention is paid to quasi-Newton's algorithms,which have been widely applied to engineering application.A novel BFGS quasi-newton algorithm(abbreviated as IBWSA)combining BFGS and weighting and strategy is proposed to solve the unconstrained multi-objective optimization problems.The convergence and the convergence speed of the proposed algorithm are demonstrated through detailed and scientific theoretical analysis.The conventional mathematical test functions are used to compare the calculation results of IBWSA algorithm,multi-objective genetic algorithm and Newton weighted sum algorithm,and the distribution characteristics of Pareto optimal frontier are systematically analyzed.The calculation efficiency and convergence of the three algorithms are compared under the same calculation accuracy,and found that the IBWSA algorithm can not only obtain the Pareto optimal frontier with a wide distribution range and better uniformity,but also has the fastest convergence speed.In summary,the above process has shown the effectiveness and superiority of the proposed algorithm in this paper.(2).In consideration of the high non-linearity of the optimization design problem of mechanical structure under impact collision,surrogate models are adopted to approximate the mathematical model to reduce the complexity of optimization problems.In order to solve the multi-objective optimization problem with inequality constraint in practical engineering,Frisch penalty function method is applied to deal with the constraint conditions,and then the inequality constraint problem are transformed into unconstrained multi-objective optimization problem.The weighted sum technique is utilized to convert the multi-objective problem into a single-objective unconstrained problem.The cautious BFGS method is utilized to solve the above unconstrained single-objective problem and its Pareto optimal solutions and corresponding optimal frontier are obtained by adjusting the weighting factors,so that the designer can choose the optimal design of the original engineering problem.Based on the above processes,a cautious BFGS quasi-newton method for multi-objective optimization problem with inequality constraints is proposed,which is abbreviated as CBQNA method.And then a fast multi-objective optimization strategy for practical engineering problems is constructed in this study.(3).In order to verify the correctness and validity of the proposed CBQNA method and the optimization strategy,on the one hand,two numerical examples are applied to analyze the difference of CBQNA algorithm,multi-objective genetic algorithm(MOGA)and Newton weighted sum Frisch algorithm(NSWFA).The calculation results show that the proposed method CBQNA has the best performance in terms of the calculation efficiency and computing power.On other hand,the CBQNA based optimization strategy is applied to investigate the influences of the geometric parameters on the crashworthiness of the main front energy-absorbing components such as crash-box and front rail structures and the Pareto optimal fronts of the relevant multi-objective optimization problems are rapidly obtained.According to the evaluation parameters of crashworthiness,optimal design schemes are selected and the simulation results show that the peak value of collision force of the crash box and front rail structures reduce 14.87% and 3.0% respectively,and the specific energy-absorption increase 1.49% and 3.27% respectively,which demonstrates that the performance of the optimized crash-box and front rail are all better than the original models before optimization design.(4)The crashworthiness optimization and lightweight design of S-shaped thin-walled beam with square cross section are toughly investigated in this chapter.Firstly,to study the effects of the derivational groove and reinforcing rib design on the crashworthiness of the S-shaped thin-walled beam,eight different thin-walled beams are constructed according to the number,size and the location distribution of the feature structure.The optimum distribution of characteristic structures in S-shaped thin-walled beams is determined by comparing the performance indexes of collision force peak,energy absorption and the mass of the structure.And then,consider the parameters of the cross section and the geometric parameters of the feature structure as the design variable,the total mass of the structure as the constraints and the improvement of crashworthiness as optimal objective,a multi-objective optimization problem is established.The optimizing strategy for practical engineering problems is utilized to obtain the optimal design scheme of S-shaped thin-walled beam that satisfies the lightweight design and has better performance than the original model.Finally,the material of feature structure is modified to aluminum-magnesium alloy from traditional steel,the lightweight design and crashworthiness optimization of the S-shaped thin-walled beam model with square cross section is finally realized,and the optimization design process and optimal scheme of the S-shaped beam can provide new ideas for the anti-collision and lightweight design of other thin-walled structures.(5)For improving the analysis efficiency and the "anthropomorphic" precision of collision dummy equipment in vehicle safety design,a simplified finite model of the dummy chest is constructed by simplifying the components,elements,and nodes of the Hybrid III 50 th dummy chest structure.The simplified model is characterized with coarse and fine meshes and its validity is proved by using the experimental calibration according to several performance evaluation indicators such as the chest pendulum force,the chest displacement and the lag rate.To improve the “anthropomorphic” precision of the simplified dummy chest model,three main structural parameters are selected as design variables and the multi-objective problem is constructed for optimizing the dummy chest structure.And then the optimal design scheme of the dummy chest model is achieved by the CBQNA based multi-objective optimization strategy.Analysis based on objective criteria and subjective comparison demonstrate that the simplified model of dummy chest established in this paper not only meets the requirements of "anthropomorphic" precision,but also significantly improves the analysis efficiency of automobile collision,and can be used as a more efficient evaluation tool for automobile safety design.