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This paper presents a multi-objective topology optimization process for the body structure of the suspension mounting point to determine the optimum configuration that reduces the acceleration under external dynamic loads. As it is difficult to avoid the excitation force that occurs inside or outside the vehicle while driving, it is important to install a reinforcing structure in the vehicle to decrease the vibration that can directly affect the ride comfort of occupants. However, when a dynamic load is considered in the topology optimization problem, it is difficult to determine the optimum reinforcing bracket configurations because the material distribution is not always continuous, and the design variables converge to intermediate values that make the optimum design representation ambiguous. Discontinuous and unclear design tends to occurs more in dynamic load problems since the distribution of material in a design domain mostly affects the dynamic performance. Moreover, the objective function results would be worsened or enhanced depending on how the design space is defined. Therefore, it is necessary to develop a systematic process to derive an optimized design that not only enhances performance but is also suitable for manufacturability. Accordingly, an optimum reinforcing bracket configuration was obtained via a systematic approach. The area connected to nearby components is determined via sequential optimization, and both dynamic and static loads are simultaneously considered in the multi-objective optimization to derive a continuous design. The material distribution trend in the design space is investigated from the obtained designs, and the final design is modeled using shell elements considering manufacturability. It was confirmed that within a limited amount of material, the overall vehicle acceleration could be reduced. [ABSTRACT FROM AUTHOR]

In this article, the design sensitivity is examined using the material derivative concept of the shape sensitivity analysis to use a gradient-based algorithm for the multi-objective benchmark testing electromagnetic analysis methods (TEAMs) problem. To calculate the shape sensitivity, the original objective functions are replaced with the definite integral form of the functionals, and the p-norm expression is used to handle the minimax problem. The computed sensitivities are validated using the finite-difference numerical sensitivities. The validity of the modified objectives is demonstrated using the results of the single-objective optimization. The results show that the analytical sensitivities agree well with the numerical ones, and the modified objective functions are valid for the benchmark optimization problem. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-objective optimization method using an adaptive weight determination scheme and tunneling method. To find the optimum designs that are evenly distributed on the Pareto front, the weights of different objective functions are adaptively determined by using the concept of a hyperplane so that new solutions can be gradually found in the objective space. In addition, to avoid locally optimized solutions that are dominated by other Pareto optimum designs, a tunneling method is employed in the optimization process. To confirm the effectiveness of the proposed method, topology optimization of the magnetic actuator is performed. The magnetic force and volume of the actuator are considered as two conflicting objective functions in the optimization problem, and Pareto optimum solutions that are evenly distributed in the objective space could be obtained. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective topology optimization method for a magnetic actuator design considering both magnetic force and actuator volume. We use a gradient-based optimization algorithm and the multi-objective optimization problem is formulated using a weighted sum of the objective functions. An adaptive weight determination scheme is iteratively employed to update the weighting coefficients of the objective functions to obtain non-dominated solutions. To ensure that the optimal solutions are evenly distributed in the objective domain, $\varepsilon $ -equality constraints are applied in the empty regions of the non-dominated solutions. The values of the constraints are determined by considering the distance ratios of the objective functions. The optimization problem is formulated to maximize the magnetic force and minimize the volume of the actuator. A level set function is used as a topological design variable to obtain optimal designs that have clear structural boundaries. [ABSTRACT FROM AUTHOR]

A novel multi-objective topology optimization method is developed by simultaneously considering the diversity and uniformity of the optimum solutions in the objective and design variable spaces. To guarantee the diversity of the solutions, a configuration-based clustering scheme is developed and applied to avoid similar designs. By clustering Pareto optimal designs during the optimization process, the searching region in the objective space is gradually reduced, and the time cost required for optimization can be decreased. Additionally, the uniformity of the solutions in the objective space is considered using an adaptive weight determination scheme. The results of the benchmark problems confirm that using the proposed method could reduce the time cost. Furthermore, the overall Pareto front and configuration of different designs are also explored. • Weights are systematically determined to obtain evenly distributed optimum solutions. • Reference point-based compromise programming is employed in the non-convex region of the Pareto front. • Clustering scheme is proposed to distinguish the Pareto optimal designs. • Adaptive weighted-sum and configuration-based clustering are incorporated in the optimization process. • The Pareto front can be explored while reducing the optimization process time cost. [ABSTRACT FROM AUTHOR]

• Developing a complex vehicle model including tire, suspension, and firing system. • Uncertainty definition for significant parameters selected by analysis of variance. • Constructing the surrogate models using an effective adaptive sampling method. • Prediction of uncertainty propagation by using surrogate model-based Monte Carlo simulation. • Obtaining a joint probability of correctness for integrated vehicle performance. The design uncertainties of vehicles cause variation of the vehicle performance. This variation increases with the complexity of the vehicle; e.g., it is greater for heavy-duty vehicles than for passenger cars. This paper presents an efficient uncertainty quantification method based on uncertainty definition, propagation, and certification, with regard to the integrated performance of a heavy-duty vehicle. For the uncertainty definition of the design parameters, an analysis of variance is performed to select the parameters with the greatest effect on the performance, and various probability density functions are employed for these parameters. To predict the precise uncertainty propagation of the vehicle performance and reflect the design uncertainty in the real-world, a full vehicle model is constructed. Additionally, a Monte Carlo simulation (MCS) with surrogate models is performed to assess the efficiency and accuracy of the performance estimation. To efficiently develop the surrogate models, an adaptive-sampling method is used to reduce the required amount of sampling data. For certification of the required performance, the joint probability of correctness for the integrated performance is suggested for practical application, and a comparison of the probability results between the surrogate and dynamic vehicle models indicates the accuracy of MCS with a surrogate model. [ABSTRACT FROM AUTHOR]

Highlights • An integrated interface is developed to focus on concept design via Maple software. • Outlier analysis, screening, kriging model are adopted to the integrated interface. • Symbolic computation is implemented to reduce computational cost. • Design optimization of combat vehicle system is applied to the integrated interface. • Optimization time is reduced by the integrated interface and symbolic computation. Abstract A complex system is composed of several subsystems and numerous lower level components. It is inefficient to design the complex system at the system level by using high-fidelity models. A system level approach using a language-based model is required to design such a highly complex system before implementing a detailed design. However, as commercial process integration and design optimization software packages focus on detailed design, which uses the high-fidelity models, it is difficult to perform the design optimization of a highly complex system, such as a combat vehicle. Moreover, as commercial optimization software packages use numerical computation, the gradient calculation cost can increase, and the matrix computation process can be inefficient in terms of optimization time. Therefore, in this study, an integrated interface for efficient design optimization was developed to focus on concept design using a MODELICA language-based model. Additionally, the design variable screening by using analysis of variance, surrogate modeling through sequential design of experiments, and symbolic computation were used to solve the aforementioned problems. These were applied to the design optimization of the combat vehicle system to demonstrate the effectiveness of the integrated interface and symbolic computation. In conclusion, a concept design utilizing a MODELICA language-based model was achieved, and the optimization time achieved by symbolic computation was largely reduced in comparison to the optimization time achieved by numerical computation. [ABSTRACT FROM AUTHOR]

Complex systems like combat vehicles contain numerous subsystems and components. Therefore, simultaneous consideration of hierarchy of a system, subsystems, and components is necessary for optimization. Multidisciplinary design optimization techniques have been researched to design the complex system. However most of these techniques premise integration process of total system which requires great time and cost. To reduce time and cost for the integration process, we introduce a target cascading technique that optimizes complex hierarchy system with several subproblems of each subsystem and component. Another challenge is to improve the firing accuracy of combat vehicle under various uncertainties. Robust design is therefore necessary to improve the firing accuracy of combat vehicles. To utilize these two concepts in optimization process, statistical information of firing angle is used as linking variables for problem formulation of robust target cascading. Furthermore, analysis of variance, surrogate modeling and statistical approach evaluating firing accuracy are employed to enhance efficiency of optimization. Finally, optimum design of a combat vehicle is achieved by using robust target cascading while improving firing accuracy. [ABSTRACT FROM AUTHOR]