Latin Hypercube Design Method Research Articles

Pre-swirl system의 유량계수 향상을 위한 Pre-swirl nozzle의 형상 최적화 전산해석 연구

Optimization process of pre-swirl nozzle geometry was conducted to improve the discharge coefficient of pre-swirl system by using CFD. The optimization of pre-swirl nozzle shape covered the converging angle and the location of the converging nozzle. Optimization process included Optimal Latin Hyper-cube Design method to get the experimental points and the Kriging method to create the response surface which gives candidate points. The process was finished when the difference between the predicted value and CFD value of candidate point was less than 0.1%. This paper compared the Reference model, Initial model which is the first model of optimization and Optimized model to study flow characteristics. Finally, the discharge coefficient of Optimized model is improved about 17 % to the Reference model.

Crashworthiness research and optimisation design of sandwich multi-cell conical tube under axial impact

A novel sandwich multi-cell conical (SMC) tube was designed and analysed by using Abaqus/Explicit. The performances of three different conical tubes, i.e., ordinary conical tube, four cell conical tube and SMC tube, were compared. The variables that influence the performances of crashworthiness were investigated. Then, according to this investigation the optimisation goal and design variables are determined. Optimal Latin hypercube design method was adopted to define the sample points for establishing and evaluating the surrogate model. Finally, a numerical simulation on the sample points was performed by utilising Abaqus/Explicit. The surrogate model with three different indicators, i.e., the specific energy absorption, the maximum crush force, and the crush force efficiency, was constructed by using kriging method and the simulation results. The accuracy of surrogate model was evaluated with four distinct methods. Finally, the non-dominated sorting genetic algorithm-II was utilised to optimise the multi-objective problem.

Crashworthiness research and optimisation design of sandwich multi-cell conical tube under axial impact

A novel sandwich multi-cell conical (SMC) tube was designed and analysed by using Abaqus/Explicit. The performances of three different conical tubes, i.e., ordinary conical tube, four cell conical tube and SMC tube, were compared. The variables that influence the performances of crashworthiness were investigated. Then, according to this investigation the optimisation goal and design variables are determined. Optimal Latin hypercube design method was adopted to define the sample points for establishing and evaluating the surrogate model. Finally, a numerical simulation on the sample points was performed by utilising Abaqus/Explicit. The surrogate model with three different indicators, i.e., the specific energy absorption, the maximum crush force, and the crush force efficiency, was constructed by using kriging method and the simulation results. The accuracy of surrogate model was evaluated with four distinct methods. Finally, the non-dominated sorting genetic algorithm-II was utilised to optimise the multi-objective problem.

Phenomenological two-phase multi-zone combustion model for direct-injection diesel engines

This paper proposed a quasi-dimensional combustion model from a new observed two-phase penetration and combustion phenomenon in diesel spray. In the model, fuel spray was divided into two of liquid and gas phase areas. Considering the phenomenon that separation of gas and liquid phase in diesel spray occurs during spray penetration, gas and liquid area of spray are discretized respectively. Liquid phase areas play important role in fuel mass transport, however gas phase areas are the main region for fuel combustion in the model. Fuel and air mixing rate of gas phase zone is the key for the calculation of combustion rate. Validation experiments are designed by using optimal Latin hypercube design method. Comparison of calculations and experiments show that the model is able to predict diesel engine performance at different engine speeds, loads, and injection pressure and timing, and provides guidance for the design of engines.

Mathematical Methods Applied to Economy Optimization of an Electric Vehicle with Distributed Power Train System

This research presents mathematical methods to develop a high-efficiency power train system for a microelectric vehicle (MEV). First of all, to get the optimal ratios of a two-speed gearbox, the functional relationship of energy consumption and transmissions is established using the design of experiment (DOE) and min-max fitting distance methods. The convex characteristic of the model and the main and interactive effects of transmissions on energy consumption are revealed and hill-climbing method is adopted to search the optimal ratios. Then, to develop an efficient and real-time drive strategy, an optimization program is proposed including shift schedule, switch law, and power distribution optimization. Particularly, to construct a mathematical predictive distribution model, firstly Latin hypercube design (LHD) method is adopted to generate random and discrete operations of the MEV; secondly the optimal power distribution coefficients under various LHD points are confirmed based on offline genetic algorithm (GA); then Gauss radial basis function (RBF) is utilized to solve the low-precision problem in polynomial model. Finally, simulation verifications of the optimized scheme are carried out. Results show that the proposed mathematical methods for the optimizations of transmissions and drive strategy are able to establish a high-efficiency power train system.

A deterministic sequential maximin Latin hypercube design method using successive local enumeration for metamodel-based optimization

Space-filling and projective properties of design of computer experiments methods are desired features for metamodelling. To enable the production of high-quality sequential samples, this article presents a novel deterministic sequential maximin Latin hypercube design (LHD) method using successive local enumeration, notated as sequential-successive local enumeration (S-SLE). First, a mesh-mapping algorithm is proposed to map the positions of existing points into the new hyper-chessboard to ensure the projective property. According to the maximin distance criterion, new sequential samples are generated through successive local enumeration iterations to improve the space-filling uniformity. Through a number of comparative studies, several appealing merits of S-SLE are demonstrated: (1) S-SLE outperforms several existing LHD methods in terms of sequential sampling quality; (2) it is flexible and robust enough to produce high-quality multiple-stage sequential samples; and (3) the proposed method can improve the overall performance of sequential metamodel-based optimization algorithms. Thus, S-SLE is a promising sequential LHD method for metamodel-based optimization.

Multi-objective optimization method of precision forging process parameters to control the forming quality

To control the precision forging product forming quality, a multi-objective optimization method for process parameters design was proposed by applying Latin hypercube design method and response surface model approach. Meanwhile, the deformation homogeneity and material damage of forging product was first presented for evaluating the forming quality. Then, as a case of study, the radial precision forging for a hollow shaft with variable cross section and wall thickness was carried out. The 3D rigid-plastic finite element (FE) model of the radial precision forging was established. The parameters on the forming quality evaluation function study were discussed to investigate the multi-objective optimization model. Non-dominated sorting genetic algorithm-II (NSGA-II) was adopted to obtain the Pareto-optimal solutions. A compromise solution was selected from the Pareto solutions by using the mapping method. Experiments with the same parameter settings were compared with the simulations. After conducting radial forging and mechanical property experimental study on the forging product by multi-objective optimization process parameters, the feasibility of the multi-objective optimization method for the precision forging product forming quality was verified.

Mean compressive stress constitutive equation and crashworthiness optimization design of three novel honeycombs under axial compression

Taking typical type of honeycomb as research object, three types of novel honeycombs are studied on the aspects of theoretical prediction under axial crushing. The simplified super folding element (SSFE) theory is applied to estimate the energy dissipation of the typical elements. Taking the inertia effects into account, dynamic mean compressive stress calculating equation is further deduced by utilizing the dynamic enhancement coefficient. In order to validate these theoretical solutions, LS-DYNA is used to simulate the axial loading of three novel honeycombs. The analytical results correlate with these simulation results in an ideal manner. During the multi-objective optimization deign, optimal Latin hypercube design (OLHD) method is used to select sampling points in the design space. Meanwhile, the response surface method (RSM), as an accurate surrogate modeling method, is adopted to obtain a maximum specific energy absorption per mass (SEAm) capacity and minimum peak crushing stress (σpeak). These results yielded from the optimization indicate that the bending cellular honeycomb (BC-H) has the best energy absorption performance under the same limitation of σpeak. Furthermore, the theoretical equations proposed are utilized to validate the simulation results of three optimal structures. The theoretical predictions show excellent agreement with these simulation values, which hence illustrate the feasibility and efficiency of the crashworthiness optimization method based on surrogate models and finite element analysis techniques.

Parametric study and multi-objective crashworthiness optimisation of reinforced hexagonal honeycomb under dynamic loadings

Hexagonal honeycombs have exhibited significant advantages in energy absorption and they are increasingly used as absorbers under crush conditions. Rather than restating details of the existing traditional regular hexagonal honeycomb, this paper introduces reinforced hexagonal honeycomb. The full-scale elaborator finite-element model created through LS-DYNA is validated by available theoretical solutions and experimental results. Afterwards, the validated simulation model is further applied to do a number of parametric studies on the reinforced hexagonal honeycomb under dynamic impact. The parameters such as stiffener thickness, expanding angle, cell length, cell wall thickness, impact mass, impact velocity and end constraint are employed to determine their relative effects on crushing behaviour of the reinforced hexagonal honeycomb. In the multi-objective crashworthiness optimisation, optimal Latin hypercube design method is used to select the sampling design points from the design space. To obtain a maximum specific energy absorption per mass ( ) capability and minimum initial peak stress ( ), response surface method, which is an accurate surrogate modelling method is adopted. The optimisation results show that the reinforced hexagonal honeycomb has a better energy absorption performance within the same limit of . This research is hence significant in providing technical support in potential applications of the reinforced hexagonal honeycomb used as crashworthiness structures.

Crushing analysis and crashworthiness optimization design of reinforced regular hexagon honeycomb sandwich panel

Abstract Honeycomb sandwich panels (HSP) have exhibited significant advantages in light weight and energy absorption, and they have been widely applied in the automotive, aerospace, transportation and defense industries. Rather than restating details of the existing standard regular hexagon HSP (R0-HSP), this paper introduces single-rib reinforced regular hexagon HSP (R1-HSP) and double-rib reinforced regular hexagon HSP (R2-HSP). The mechanical characteristics of these three structures are first investigated by series full-scale elaborator models through LS-DYNA. It is found that the R1-HSP has the best crashworthiness performance under axial impact regarding specific energy absorption per unit (SEAm and SEAv) when the peak crashing stress (σ peak) is less important. Secondly, the thickness matching effect between stiffener and cell wall is analyzed with equivalent apparent density index to evaluate the contribution of the change of deformation model to the general mechanical properties. Consequently, stiffener thickness of 2.0 times and 1.5 times that of cell wall are found to be the most optimal options for R1-HSP and R2-HSP, respectively. To optimize the crashworthiness of the R1-HSP, optimal Latin hypercube design method is used for selection of sampling design points in the design space. And in the meantime, an accurate surrogate modeling method, or more specifically named as response surface method, is adopted to formulate the SEAm, SEAv and σ peak functions. The results yielded from the optimization indicate that the R1-HSP is superior to R0-HSP both in SEAm and SEAv under the same limitation of σ peak. This research is significant in providing technical support in the extended applications of different HSPs used as crashworthiness structures, and it has essential reference value in low volume and low mass energy absorber design.

Research on Lightweight Multi-Objective Optimization for Closed Body-in-White Structure

The 100% frontal crash and side impact performances of a passenger car are analyzed and compared with tests. The structural optimization of the Closed Body-in-White (BIW) is divided into two stages which are 100% frontal crash safe part optimization and side impact safe part optimization. Use the Optimal Latin hypercube (Opt LHD) design method to generate sample points. Take the Radial Basis Functions (RBF) neural network method to establish optimization approximation model. The non-dominated sorting genetic algorithm (NSGA-II) was used to conduct multi-objective collaborative optimization design. The results show that the total mass of the closed BIW is reduced 9.745kg; the light weight rate was 10.27%. The Crashworthiness performance of the closed BIW does not change obviously.

Multiobjective Optimization of Precision Forging Process Parameters Based on Response Surface Method

In order to control the precision forging forming quality and improve the service life of die, a multiobjective optimization method for process parameters design was presented by applying Latin hypercube design method and response surface model approach. Meanwhile the deformation homogeneity and material damage of forging parts were proposed for evaluating the forming quality. The forming load of die was proposed for evaluating the service life of die. Then as a case of study, the radial precision forging for a hollow shaft with variable cross section and wall thickness was carried out. The 3D rigid-plastic finite element (FE) model of the hollow shaft radial precision forging was established. The multiobjective optimization forecast model was established by adopting finite element results and response surface methodology. Nondominated sorting genetic algorithm-II (NSGA-II) was adopted to obtain the Pareto-optimal solutions. A compromise solution was selected from the Pareto solutions by using the mapping method. In the finite element study on the forming quality of forging parts and the service life of dies by multiobjective optimization process parameters, the feasibility of the multiobjective optimization method presented by this work was verified.

Lightweight of Aluminum Alloy Bumper Based on High-Speed Crash Component Test

High-speed crashworthiness characteristics of aluminum alloy bumper were investigated both experimentally and numerically, and then lightweight deign was performed based on these studies. After the simulation results were analyzed, chose plate thickness matching as an optimization direction and got crashworthiness indicators: cross-sectional force, energy absorption, and specific energy absorption (SEA). Design of experiment (DOE) for initial 25 sampling points, which provide input data for approximation, is implemented using the optimal Latin hypercube design (OLHD) method. Polynomial response surface (PRS) models, which are used to approximate LS-DYNA simulation models, are built using the moving least square (MVS), whose all coefficients of determination are over 0.97, indicated high accuracy. The simulation results of optimal designs, which are obtained after 52 iterations of genetic algorithms (GA), show that the mass loss of 30.8%, while energy absorption increase of 4% , SEA increase of 50.3%, and crushing forces decline.

Exploring optimum power unit of propulsion system for high altitude airship

Different schemes of a propulsion system have a distinguished influence on the overall performance of high altitude airship. There is an optimum power, called optimum power unit, to achieve the lowest propulsion system and energy system weight for a high altitude airship. The paper represents an optimization model of the optimum power unit for a high altitude airship. Firstly, the optimal Latin hypercube design method is applied to obtain the sample points of the distributed low power propulsion system. Secondly, the surrogate model, which is used to establish the optimization model, is obtained by responding surface method based on these sample points. The computational model of the energy system is obtained by the airship’s location and the working time. Finally, the multi-island genetic algorithm is used to find the optimum power unit for a typical high altitude airship. Furthermore, the optimization work under different typical power levels and diameters is carried out to verify the effectiveness of the optimum power unit design method. It has been found that the identical result validates the effectiveness of the optimum power unit design method.

Application of a Method on Optimization of Thin-Walled Column's Crashworthiness Based on Metamodel

In this paper the crashworthiness of a thin-walled column is selected as the optimization goal and its section gauge size parameters are defined as variables. We use Optimal latin hypercube design method and ASA optimization method respectively to define sampling design points and find optimal design in Kriging metamodel, constructed using function values in FEM results at sampling design points. A design space updating method is introduced in this paper to reduce computational consumption and improve accuracy by several rounds of metamodeling and optimization, practice shows that object parameter SEA in each round converge to a final one, constrained by the demand of no weight added. High accuracy and rapid convergence of this method will be verified by comparison between results by this method and FEM.

A Predictive Distribution Model for Cooperative Braking System of an Electric Vehicle

A predictive distribution model for a series cooperative braking system of an electric vehicle is proposed, which can solve the real-time problem of the optimum braking force distribution. To get the predictive distribution model, firstly three disciplines of the maximum regenerative energy recovery capability, the maximum generating efficiency and the optimum braking stability are considered, then an off-line process optimization stream is designed, particularly the optimal Latin hypercube design (Opt LHD) method and radial basis function neural network (RBFNN) are utilized. In order to decouple the variables between different disciplines, a concurrent subspace design (CSD) algorithm is suggested. The established predictive distribution model is verified in a dynamic simulation. The off-line optimization results show that the proposed process optimization stream can improve the regenerative energy recovery efficiency, and optimize the braking stability simultaneously. Further simulation tests demonstrate that the predictive distribution model can achieve high prediction accuracy and is very beneficial for the cooperative braking system.

Optimization Strategy Using Dynamic Radial Basis Function Metamodel Based on Trust Region

To improve the design quality and optimization efficiency of complicated engineering systems such as flight vehicle, metamodel based optimization is applied widely. Trust region is imported into the metamodel optimization and the updating strategy for sampling space using trust region is proposed and then the optimization strategy using dynamic radial basis function metamodel based on trust region is proposed. The metamodel is constructed with radial basis function and initial sampling points selected by Maximin latin hypercube design method. Global optimization algorithm is employed to optimize current metamodel to find the potential global optimum of the true optimization problem. According to the current known information, the trust region sampling space is updated. During optimization process, the new sampling points in the trust region sampling space are added, and the metamodel is updated, until the potential global optimum of the true optimization problem is satisfied the convergence conditions. The optimization strategy is validated by using five benchmark numerical test problems and an I-beam design problem. As the optimization results shown, the capability of TR-DRBF in both aspects of optimization efficiency and global convergency is good compared with the study fruit inland and overseas at present. Especially for high dimension problems, the performance of TR-DRBF is appealing.

New sampling scheme for neural network-based metamodelling with application to air pollutant estimation

Purpose A new method for the design of experiments (DOE) or sampling technique is proposed, using a distance weight function and the k-means theory. The radial basis function neural network metamodelling approach is used to evaluate the performance of the proposed DOE by using an n-degree of test function, applied to the complex nonlinear problem of spatial distribution of air pollutants. A comparison study is included to analyse the performance of the proposed technique against available methods such as the n-level full fractional design method and the Latin Hypercube Design method. Method For one design objective and n number of input design variables, a set of input-output training dataset are { } n j m i x x x x x x X i j j j i ,.., 1 , ,.., 1 ) ,.., , ;....; ,..., , ) ( ) 2 ( ) 1 ( ) ( 1 ) 2 ( 1 ) 1 ( 1 = = = and { } m i y y y Y i ,..., 2 , 1 ,..., , ) ( ) 2 ( ) 1 ( = = , where m is the

CRASHWORTHINESS DESIGN FOR HONEYCOMB STRUCTURES UNDER AXIAL DYNAMIC LOADING

For a honeycomb structure used for absorbing crash energy and protecting the safety of human or instruments, the bigger the specific energy absorption (SEA) is, the more popular it would be when the peak crushing stress (σp) was retained small enough. In order to improve the energy absorption capacity, crashworthiness optimization for honeycomb structures with various cell specifications are studied in this paper. Detailed numerical models are established for those honeycomb structures by using an explicit finite element method code LS-DYNA. The numerical simulation results are then used as the design samples for constructing metamodels. The optimal Latin hypercube design (OLHD) method is employed for the selection of sampling design points in the design space, and the polynomial functions, radial basis functions (RBF), Kriging, multivariate adaptive regression splines (MARS), and support vector regression (SVR) are utilized to formulate the two optimal objectives SEA and σp. It is found that the polynomial function is the most efficient in constructing the crashworthiness metamodels of honeycombs among the above-mentioned methods. Then, the polynomial function models of SEA and σp are chosen as the surrogate models in the crashworthiness optimization. In order to further validate the polynomial function models, the polynomial function models of SEA and σp are compared with the analytical solutions based on Wierzbicki's theory and Kunimoto and Yamada's theory, respectively. An excellent correlation has been established. As such, the multi-objective particle swarm optimization algorithm (MOPSOA) is applied to obtain the Pareto front of SEA with σp of the honeycomb structures with various cell specifications, which has resulted in a range of optimal designs of honeycomb structures by the multi-objective optimization.