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Due to the discreteness of material variables and nonlinearity of material plastic segment, the material-structure matching design efficiency of multiple parts is very low, and it is even difficult to achieve a feasible solution. To solve these problems, a performance-driven lightweight optimization method that combines multi-material selection method and multi-objective optimization is proposed. First, a lightweight multi-material selection method for the cab is proposed, which integrates static stiffness constraint, equivalent crashworthiness, and evaluation method for material selection. Subsequently, the multi-material selection designs for the skeleton beam of cab are carried out. The results show that the material selection scheme achieved a mass reduction of 12.41 kg and material cost reduction of 0.861 yuan. Finally, a multi-objective optimization method incorporating TOPSIS method is used to solve material-structure coupling design. The results show that the mass of cab is reduced by 47.4 kg. The performance of cab are slightly changed, indicating the rationality of the lightweight design method. [ABSTRACT FROM AUTHOR]

To improve the lightweight of the automotive body, the structure–connection–performance integration optimisation design was conducted for the multi-material body skeleton. The equivalent simplified joint model was established for dissimilar material self-piercing riveting (SPR) joints to address the problem that the finite element model of multi-material body skeleton was difficult to calculate due to the excessive number of elements of SPR joints. The rivet set coding technique was proposed to overcome the technical bottleneck that the SPR joint connection parameters cannot be integrated into the body structure–performance collaborative optimisation. The integrated optimisation parametric model of the structure–connection–performance of the multi-material body skeleton was established by combining structural parameterisation and mesh deformation techniques. The multi-objective automatic iterative optimisation of the body skeleton was achieved by using the RBFNN-Kriging hybrid surrogate model and NSGA-II, and the Pareto front was mined using AHP-TOPSIS method. The results show that the performance of the optimised body structure is significantly improved and fully meets the design requirements. The mass of the body skeleton is 116.88 kg, which is 28.62 kg lighter than the same size benchmark body skeleton, and the weight reduction ratio is 19.67%. A front-end structure of the body skeleton was developed and subjected to high-speed impact test, which validates the accuracy of the simulation analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a modified preference selection index (MPSI) to improve the efficiency and reliability of the multi-criteria decision-making process. MPSI absorbs the high efficiency of the preference selection index (PSI) and enhances the anti-interference ability of some performance indicators. Moreover, a lightweight optimization method based on multi-performance is proposed, combining Hammersley, the radial basis function neural networks-response surface method (RBFNN-RSM), and the non-dominated sorting genetic algorithm-II (NSGA-II) and MPSI. First, the finite element model and rigid-flexible coupled virtual prototype model are established and verified and the fatigue life of the original frame is calculated. Second, the size and shape of the frame were taken as variables, and the mass, root mean square stress, and life were taken as objectives. The experimental scheme is determined, and the RBFNN-RSM hybrid surrogate model and NSGA-II are used to find the optimal solution set. Finally, the optimal solution is determined using the PSI, principal component analysis-gray relational analysis (P-GRA), and MPSI. The results show that MPSI has higher reliability than PSI; the MPSI has higher efficiency than P-GRA. [ABSTRACT FROM AUTHOR]

To improve the computational cost and accuracy of approximate-based multi-objective optimization problems in engineering, an adaptive RBF neural network (ARBFNN) method integrating RBF neural network model, fuzzy subtractive clustering (FSC) sequence sampling method and non-dominated sorting genetic algorithm (NSGA-II) is proposed. To solve the problem that the number of new sample points is difficult to determine, FSC sequence sampling is proposed to select the clustering center points as newly added sample points. First, the ARBFNN method is verified by the five test functions. The results show that the ARBFNN method is significantly better than static RBFNN model based on multi-objective optimization (SRBFNN) in terms of global convergence and efficiency performance, and the other two adaptive approximate optimization methods in terms of overall efficiency. Based on the above, the accuracy and efficiency of ARBFNN method are very high. Finally, the method is applied to an engineering example: the lightweight and crashworthiness design of floor rails. The cab model coupled with implicit parameterized floor rails model is built using the SFE-CONCEPT software to achieve collaborative optimization design of shape-size-material. The optimization results show that the ARBFNN method can guarantee the error of the approximate optimal solution and the finite element solution (expensive solution) within 2%, so the accuracy of highly nonlinear (finite element analysis of collision conditions) approximate optimization is improved. Hence, the proposed ARBFNN method is feasible and effective in solving complex and expensive engineering optimization problems. [ABSTRACT FROM AUTHOR]

This study proposes a multi-objective lightweight and crashworthiness optimization design of complex cross-sectional shape and size of S-rail employing a hybrid multi-criteria decision-making (HMCDM) method. Several S-rails with special cross-sectional shapes of the reinforcement plate are established and compared. Response surface models with different orders are established considering the complex cross-sectional shapes and sizes. The objective function chosen for the two objectives is the specific energy absorption (SEA) and the peak force (PF). Meanwhile, the metrics for the three-objective are the PF, the total mass (M), and the energy absorption (EA). Two-objective Pareto fronts are obtained by the three-objective optimization confronting. Different multi-criteria decision-making methods are used to find the trade-off optimum points from the Pareto fronts. Results indicate that the proposed HMCDM method, including the technique for order preferences by similarity to ideal solution, gray relational analysis, and entropy weight, demonstrates a good trade-off frontier solution. In the case of a slight increase in M, the EA and SEA performances of the optimal model are greatly improved compared with the S-rail without a stiffener. Compared with the initial optimization model, the M of the optimal model is reduced by 25.62%, and the performance is improved. Therefore, the design of the cross-sectional shape and size of the S-rail and hybrid method can improve the crashworthiness. [ABSTRACT FROM AUTHOR]

This paper demonstrates a conjoint method integrating the proposed Hybrid Contribution Analysis (HCA) method, the Artificial Neutral Network (ANN) meta-model, the modified Non-dominated Soring Genetic Algorithm II (MNSGAII) and the Ideal Point Method (IPM), used for multi-objective lightweight and crashworthiness optimization of the side structure of an automobile body. First of all, the static-dynamic stiffness models of the automobile body and the vehicle side crashworthiness model are separately established and validated against corresponding actual experiments. Next, the initially selected parts for optimization are screened using the proposed HCA method to determine the final parts for optimization, thicknesses of which are taken as design variables. After that, design of experiment (DoE) coupled with ANN-based meta-models are utilized to approximate the output performance indicators of the automobile body, based on which the modified NSGA-II (MNSGAII) with ε-elimination technique is then employed to solve the multi-objective optimization process, considering the total mass and the torsional stiffness of the automobile body, the maximum intrusion deformation of the measuring point P1 on the inner panel of B-pillar and the measuring point D1 on the inner panel of front door as four optimization objectives. Finally, the IPM method identifies the optimal trade-off solution from the obtained Pareto set, and a comprehensive comparison between the optimized design and the baseline design further confirms the validity of the proposed conjoint method. Specially, the four-objective Pareto set approximately embodies that of each pair of separately run two-objective optimization, thus providing more optimization schemes for designers. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid method combining the Contribution Analysis Method, the Radial Basis Function Neutral Network (RBFNN)-Response Surface Method (RSM) hybrid surrogate modeling method, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), used for structure-material integrated multi-objective lightweight design of the front end structure of an automobile body. First, Contribution Analysis Method provides an effective approach to determine the final parts for lightweight design, and fourteen thickness variables and thirteen material variables are finally selected. Second, RBFNN-RSM hybrid surrogate modeling method successfully constructs the mapping between the input thickness-material variables and the output lightweight controlling quotas of the automobile body. Third, the MOPSO solves the multi-objective lightweight design process, considering the total mass and the torsional stiffness of the automobile body, the maximum impact acceleration at lower end of the B-pillar and the total material cost of the selected design parts as four conflicting objective functions. Accordingly, a set of Pareto-optimal solutions are obtained. Finally, a decision-making procedure based on TOPSIS method ranks all these Pareto-optimal solutions from the best to the worst for determining the best compromise solution. In addition, the proposed lightweight design method is demonstrated by the comparison among the baseline design, the actual experiment and the optimal design. The results show that the automobile body is lightweight designed with a mass reduction of 4.12 kg while other mechanical performance are well guaranteed. Hence, the proposed lightweight design method could be well applied to the lightweight design of the automobile body. [ABSTRACT FROM AUTHOR]

In this paper, the side structure of the automobile body, as the main assembly to withstand the impact force in side collision, is taken as the research object for multi-objective lightweight optimization. First, finite element analysis (FEA) models of the basic NVH (Noise, Vibration and Harshness) performance of the automobile body and the crashworthiness performance of the vehicle are respectively constructed and validated by actual experiments, through which lightweight controlling quotas are extracted. Second, contribution analysis is employed to determine the final parts for lightweight optimization considering both discrete material variables and continuous thickness variables. Third, design of experiment (DoE) based on Optimal Latin Hypercube Sampling (OLHS) method is performed, considering the total mass, the bending stiffness and the torsional stiffness of the automobile body, the maximum impact acceleration at lower end of the B-pillar and the total material cost of the selected optimization parts as five objective functions. On this basis, the combination of thickness-material parameters of the optimization parts is optimized based on Grey Relational Analysis (GRA), and the Principal Component Analysis (PCA) is applied to evaluate the weighting values corresponding to various objective functions. Meanwhile, a comparison between GRA and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is conducted to illustrate the unique merits of GRA in multi-objective lightweight optimization of the side structure of the automobile body. Finally, the effectiveness of the lightweight optimization is demonstrated by the comparison between the initial design and the optimal design. The results indicate that the total mass of the automobile body is reduced by 4.54 Kg while other mechanical performance of the automobile body are basically well guaranteed. Hence, the combined grey relational and principal component analysis is a very powerful method used for multi-objective lightweight optimization of the automobile body. [ABSTRACT FROM AUTHOR]

The optimization of the crashworthiness and lightweight design of S-rail extracted from the frontal body in white was studied in this paper. A physical test was conducted to verify the validity of S-rail model and then an implicit parameterization model was built based on the S-rail model using the software SFE-CONCEPT. Based on the implicit parameterization modeling, a steel-aluminum S-rail was designed to reduce the peak collision force (PCF) and increase the specific energy absorption (SEA) under the condition that the total weight (M) of S-rail does not increase. L (4) Taguchi array was used to collect sample points which will be prepared for the optimization design. The experimental results were analyzed through grey relational analysis (GRA) coupled with grey entropy measurement method. The multi-objective optimization was then converted into a single objective optimization problem based on the grey relational grade. The optimal combination of design parameters for S-rail was obtained using the proposed method. Meanwhile, a comparison was presented between the proposed method and other extensively used methods (i.e. NSGA-II, MOPSO, and ASA), and the proposed method reduces the PCF and M to 26.81% and 46.01% respectively, and increases the corresponding SEA by 176.06%. Moreover the computational cost can be reduced by 143.5% at least when compared with other extensively used methods. Therefore, the hybrid method can efficiently improve the crashworthiness and reduce the computational cost during the design process of S-rail. [ABSTRACT FROM AUTHOR]