Multi-Objective Optimization for Structure Crashworthiness Based on Kriging Surrogate Model and Simulated Annealing Algorithm

Multi-objective optimization of crashworthiness in automobile front-end structure was performed,and finite element model(FEM)was validated by experimental results to ensure that FEM can predict the response value with sufficient accuracy.Seven design variables and four crashworthiness indicators were defined.Through orthogonal design method,18 FEMs were established,and the response values of crashworthiness indicators were extracted.By using the variable-response specimen matrix,Kriging surrogate model(KSM)was constructed to replace FEM to refect the function correlation between variables and responses.The accuracy of KSM was also validated.Finally,the simulated annealing optimization algorithm was implemented in KSM to seek optimal and reliable solutions.Based on the optimal results and comparison analysis,the 9096-th iteration point was the optimal solution.Although the intrusion of firewall and the mass of optimal structure increased slightly,the vehicle acceleration of the optimal solution decreased by 6.9%,which fectively reduced the risk of occupant injury.

Multi-objective structural optimization and degradation model of magnesium alloy ureteral stent

Background:Mg alloys have attractive properties,including biocompatibility,biodegradability,and ideal mechanical properties.Moreover,Mg alloys are regarded as one of the promising candidates for manufacturing ureteral stents.This study proposed a multi-objective optimization method based on the Kriging surrogate model,NSGA-III,and finite element analysis to improve the degradation performance of Mg alloy ureteral stents.Methods:The finite element model for the degradation of Mg alloy ureteral stents has been established to compare the degradation performance of the stents under different parameters.Latin hypercube sampling was adopted to generate train sample points in the design space.Meanwhile,the Kriging surrogate model was constructed between strut parameters and stent degradation behavior.The NSGA-III was utilized to determine the optimal solution in the global design space.Results:The optimized stent achieved 5.52degradation uniformity(M),10degradation time(DT),and 4work time(FT).The errors between the Kriging surrogate model and the finite element calculation results were less than 6%.Conclusion:The optimized stent achieved better degradation performance.The degradation behavior of stents was dependent on the design parameters.The multi-objective optimization method based on the Kriging surrogate model and finite element analysis was effective in stent design optimization problems.

Rotary-scaling fine-tuning (RSFT) method for optimizing railway wheel profiles and its application to a locomotive

The existing multi-objective wheel profile optimization methods mainly consist of three sub-modules:(1)wheel profile generation,(2)multi-body dynamics simulation,and(3)an optimization algorithm.For the first module,a comparably conservative rotary-scaling finetuning(RSFT)method,which introduces two design variables and an empirical formula,is proposed to fine-tune the traditional wheel profiles for improving their engineering applicability.For the second module,for the TRAXX locomotives serving on the Blankenburg–Rubeland line,an optimization function representing the relationship between the wheel profile and the wheel–rail wear number is established based on Kriging surrogate model(KSM).For the third module,a method combining the regression capability of KSM with the iterative computing power of particle swarm optimization(PSO)is proposed to quickly and reliably implement the task of optimizing wheel profiles.Finally,with the RSFT–KSM–PSO method,we propose two wear-resistant wheel profiles for the TRAXX locomotives serving on the Blankenburg–Rubeland line,namely S1002-S and S1002-M.The S1002-S profile minimizes the total wear number by 30%,while the S1002-M profile makes the wear distribution more uniform through a proper sacrifice of the tread wear number,and the total wear number is reduced by 21%.The quasi-static and hunting stability tests further demonstrate that the profile designed by the RSFT–KSM–PSO method is promising for practical engineering applications.

Contrastive analysis and crashworthiness optimization of two composite thin-walled structures

For the safety protection of passengers when train crashes occur, special structures are crucially needed as a kind of indispensable energy absorbing device. With the help of the structures, crash kinetic-energy can be completely absorbed or dissipated for the aim of safety. Two composite structures(circumscribed circle structure and inscribed circle structure) were constructed. In addition, comparison and optimization of the crashworthy characteristic of the two structures were carried out based on the method of explicit finite element analysis(FEA) and Kriging surrogate model. According to the result of Kriging surrogate model, conclusions can be safely drawn that the specific energy absorption(SEA) and ratio of specific energy absorption to initial peak force(REAF) of circumscribed circle structure are lager than those of inscribed circle structure under the same design parameters. In other words, circumscribed circle structure has better performances with higher energy-absorbing ability and lower initial peak force. Besides, error analysis was adopted and the result of which indicates that the Kriging surrogate model has high nonlinear fitting precision. What is more, the SEA and REAF optimum values of the two structures have been obtained through analysis, and the crushing results have been illustrated when the two structures reach optimum SEA and REAF.

Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling using a Monte Carlo Approach with Kriging Model

Precise calculation of the trajectory of store separation is critical in assess-ing whether the store can be released safely.Store ejection is the initial stage of the releasing process and any uncertainty introduced at this stage will propagate through the whole trajectory.In this work,the impact of the uncertainties in ejector modeling on the simulation of a generic store separation is investigated by using a Monte-Carlo-based approach.To reduce the extremely large computation cost resulted from the direct use CFD in Monte Carlo simulation,the CFD solutions are represented by a time-dependent Kriging model,which is constructed at each time step by using the samples from the URANS simulations.The stochastic outputs,including the distri-bution of probability density function,expected value and 95%confidence interval of store separation trajectory,are obtained by the Monte Carlo simulations.The sensitiv-ity analysis is also carried out by using the Monte-Carlo-based method to determine the most significant variables in ejector modeling,which affect the output uncertainty.Our results show that ejector modeling is one of the main uncertainty sources of store separation simulation and the approximation in ejector modeling can cause a signifi-cant deviation,especially in the angular displacement.

Global aerodynamic design optimization based on data dimensionality reduction

In aerodynamic optimization, global optimization methods such as genetic algorithms are preferred in many cases because of their advantage on reaching global optimum. However,for complex problems in which large number of design variables are needed, the computational cost becomes prohibitive, and thus original global optimization strategies are required. To address this need, data dimensionality reduction method is combined with global optimization methods, thus forming a new global optimization system, aiming to improve the efficiency of conventional global optimization. The new optimization system involves applying Proper Orthogonal Decomposition（POD） in dimensionality reduction of design space while maintaining the generality of original design space. Besides, an acceleration approach for samples calculation in surrogate modeling is applied to reduce the computational time while providing sufficient accuracy. The optimizations of a transonic airfoil RAE2822 and the transonic wing ONERA M6 are performed to demonstrate the effectiveness of the proposed new optimization system. In both cases, we manage to reduce the number of design variables from 20 to 10 and from 42 to 20 respectively. The new design optimization system converges faster and it takes 1/3 of the total time of traditional optimization to converge to a better design, thus significantly reducing the overall optimization time and improving the efficiency of conventional global design optimization method.

Variable-fidelity optimization with design space reduction

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.