Optimal Latin Hypercube Design Research Articles

On the crashworthiness analysis and design of a lateral corrugated tube with a sinusoidal cross-section

Thin-walled structures have been widely used as energy absorbers due to their light weight, high energy absorption efficiency and good machinability. However, the existing researches mainly focus on different sizes of tubes with the same shape, but the topological relationship of cross-sectional shape also has an important effect on the energy absorption of structure. In view of the fact that the existing corrugated tubes are mainly studied about the corrugation in the axial direction, we put forward a new type of lateral corrugated tube (LCTs) with a sinusoidal cross-section. The evolution of its cross-section could be controlled through the amplitude (A), the basic nominal diameter (R0) and the number of corrugations (N). In the meantime, a systematic crashworthiness study is carried out with multi-objective optimization design. The results show that A, N and the wall thickness (t) are the important parameters that affect the deformation mode and crashworthiness. Numerical simulation of axial compression of 16 different LCTs with different A and N shows that when N = 6 and N = 8, the SEA of the LCTs are increased by 27.91% and 27.24% respectively compared with that of the ordinary circular tube (CTs). Subsequently, the optimal Latin hypercube design method is used to determine the sample points and Kriging method is used to construct the surrogate models of specific energy absorption (SEA) and initial peak force. Finally, the multi-objective optimization of LCTs and CTs are carried out by using the non-dominated sorting genetic algorithm-II. The optimization results show that the LCTs has better crashworthiness than CTs, and the SEA is increased by 53.65% compared with the optimized design of the CTs. Compared with CTs, the SEA of the LCTs can be extended to a wider area, indicating that the LCTs has a wider range of application and design space than CTs.

Reliability-based robust design optimization of gap size of annular nuclear fuels using kriging and inverse distance weighting methods

ABSTRACTIn this study, the design optimization of the gap size of annular nuclear fuels used in pressurized water reactors (PWRs) was performed. For this, thermoelastic–plasticity–creep (TEPC) analysis of PWR annular fuels was carried out using an in-house code to investigate the performance of nuclear fuels. Surrogate models based on the kriging and inverse distance weighting models were generated using computational performance data based on optimal Latin hypercube design. Using these surrogate models, the gap size of PWR annular fuel was deterministically optimized using the micro-genetic algorithm to improve the heat transfer efficiency and maintain a lower level of stress. Reliability-based design optimization and reliability-based robust design optimization were conducted to satisfy target reliability and secure the robustness of the PWRs’ performance. The optimal gap size was validated through TEPC analysis and the optimum solutions were compared according to the approximate method and reliability index.

Structure design and multi-objective optimization of a novel crash box based on biomimetic structure

In order to improve the crashworthiness and energy absorption performance, this paper introduces the structural bionics to the structural design of crash box and proposes a novel structure. Taking the human tibia as a bionic object, the novel crash box is composed of a concave structure shell and an inner core filled with negative Poisson's ratio (NPR) structure material. In view of the gradient characteristics of the cancellous bone structure of the tibia, the NPR inner core is designed as a functional gradient distribution structure along the longitudinal direction of the crash box. Based on this, by combining the optimal Latin hypercube design and response surface methodology, a multi-objective optimization design is conducted for the novel crash box based on archive-based micro genetic algorithm (AMGA) and improved non-dominated sorting genetic algorithm (NSGA-II). Simulation results show that the novel crash box optimized by NSGA-II algorithm can improve the energy absorption characteristics and comprehensive crashworthiness more effectively, and make the collision process controllable and stable. The results of this paper can provide some reference for the design and optimization of the crash box.

A systematic design and optimization method of transmission system and power management for a plug-in hybrid electric vehicle

The transmission system together with power management will simultaneously affect the fuel economy of the plug-in hybrid electric vehicle (PHEV) with automated mechanical transmission (AMT). This paper strives to make three contributions to realize systematic design and optimization of the transmission and power management. Firstly, a design of experiment method is proposed to redesign the current transmission system of the PHEV with Optimal Latin Hypercube Design algorithm. Then, a co-optimization method is proposed to insight into the preferable speed ratios of the redesigned transmission system with multi-island genetic and dynamic programming algorithms. Finally, a Pontryagin’s Minimum Principle-based self-identification controller is proposed to realize adaptive power management control, based on a significant finding that the constant solution of the co-state from off-line iteration optimization can be approximately identified by the mean value of the co-state with time-moving in the self-identification controller. Results demonstrate that the current 6-speed ratio AMT can be reduced to 4, the fuel economy of the redesigned transmission system can be improved by 2.9% compared to the current transmission system and the self-identification controller can further improve the fuel economy of the PHEV compared to the conventional PI controller.

Optimization of the aerodynamic configuration of a tubular projectile based on blind Kriging

Based on optimal Latin hypercube design for computer experiments, blind Kriging surrogate model and sequential quadratic programming method, the optimal design of the aerodynamic configuration of a 30mm tubular projectile is carried out with the use of commercial softwares, such as UG, ICEM CFD, FLUENT etc. The aerodynamic configuration has been optimized to minimize the drag coefficients at different Mach numbers and maximize the kinetic energies at given flight ranges. The optimal configuration is obtained and discussed. Finally, the similarities and differences of the flow structure and aerodynamic characteristics between the original and optimal tubular projectiles are compared. The numerical optimal method proposed in this paper for optimizing the tubular projectile can provide important guidances for the aerodynamic configuration design of projectiles.

Multi-objective optimization of a novel crash box with a three-dimensional negative Poisson’s ratio inner core

The crash box can absorb energy from the beam as much as possible, so as to reduce the collision damage to the front part of the car body and protect the safety of passengers. This work proposes a novel crash box filled with a three-dimensional negative Poisson’s ratio (NPR) inner core based on an inner hexagonal cellular structure. In order to optimize and improve the crash box’s energy absorption performance, the multi-objective optimization model of the NPR crash box is established, which combines the optimal Latin hypercube design method and response surface methodology. Then, the microstructure parameters are further optimized by the multi-objective particle swarm optimization algorithm to obtain an excellent energy absorption effect. The simulation results show that the proposed NPR crash box can generate smooth and controllable deformation to absorb the total energy, and it can further enhance the crashworthiness through the designed optimization algorithm.

Hull form optimisation in waves based on CFD technique

ABSTRACTThe seakeeping behavior of a ship in waves is different from its behavior in calm water. The resistance and seakeeping performance of a ship must be considered in the early-stage design. Therefore, this paper proposes a hull form optimization framework aiming to achieve the minimum total resistance in waves using a computational fluid dynamics (CFD) technique. A sinusoidal wave is adopted to establish the numerical wave tank and the overset mesh technique is used to facilitate the motions of the ships in question. The total resistance of the hull in waves is regarded as the objective function which is calculated using the Reynolds averaged Navier–Stokes (RANS) method. The arbitrary shape deformation (ASD) technique is used to change the geometry. Under displacement and design variables, a hybrid algorithm is developed to evaluate the objective function combining the optimal Latin hypercube design (Opt LHD) and the non-linear programming by quadratic Lagrangian (NLPQL) algorithm. Finally, two examples of hull form optimization are presented and discussed for David Taylor Model Basin (DTMB) model 5512 and WIGLEY III cases. The results show the effectiveness of the optimization framework developed in the present study, which can lay the foundation for further optimization of full-scale ships.

Computational fluid dynamics-based hull form optimization using approximation method

ABSTRACTWith the rapid development of the computational technology, computational fluid dynamics (CFD) tools have been widely used to evaluate the ship hydrodynamic performances in the hull forms optimization. However, it is very time consuming since a great number of the CFD simulations need to be performed for one single optimization. It is of great importance to find a high-effective method to replace the calculation of the CFD tools. In this study, a CFD-based hull form optimization loop has been developed by integrating an approximate method to optimize hull form for reducing the total resistance in calm water. In order to improve the optimization accuracy of particle swarm optimization (PSO) algorithm, an improved PSO (IPSO) algorithm is presented where the inertia weight coefficient and search method are designed based on random inertia weight and convergence evaluation, respectively. To improve the prediction accuracy of total resistance, a data prediction method based on IPSO-Elman neural network (NN) is proposed. Herein, IPSO algorithm is used to train the weight coefficients and self-feedback gain coefficient of ElmanNN. In order to build IPSO-ElmanNN model, optimal Latin hypercube design (Opt LHD) is used to design the sampling hull forms, and the total resistance (objective function) of these hull forms are calculated by Reynolds averaged Navier–Stokes (RANS) method. For the purpose of this article, this optimization framework has been employed to optimize two ships, namely, the DTMB5512 and WIGLEY III, and these hull forms are changed by arbitrary shape deformation (ASD) technique. The results show that the optimization framework developed in this study can be used to optimize hull forms with significantly reduced computational effort.

Firing Accuracy Evaluation of Electromagnetic Railgun Based on Multicriteria Optimal Latin Hypercube Design

Electromagnetic railgun (EMRG) is a promising candidate weapon system for the future surface-fire support mission characterized by quick response, hypersonic velocity, and high damage efficiency. Since the huge power consumption during launching, priority should be given to the precise strike. Firing accuracy of EMRG, which refers to the closeness degree of the projectiles’ impact points to the target, is an important performance metric in the EMRG exterior ballistic performance assessment. To provide a systematic solution for the measure of firing accuracy, the assessment factors are formulated in detail. Then, a general framework, including trajectory simulation, data preprocessing, parameters estimation, and hit probability calculation, is proposed to evaluate EMRG firing accuracy. Considering the trajectory simulation experiments may be time consuming, a new multicriteria optimal Latin hypercube design method is presented to maintain the balance between experiment time and sampling performance. Finally, firing accuracy assessment of 16-kg projectiles is performed using the designed framework and proposed experimental design method. The result reveals that the circular error probability is about 5 km under current defined scenarios, which means the initial disturbances may have great impact on the firing accuracy of projectiles without guidance and control units.

Unsteady Aerodynamic Optimization of Airfoil for Cycloidal Propellers Based on Surrogate Model

An effective unsteady aerodynamic-optimization method of airfoil for cycloidal propellers is developed. Firstly, the class-function/shape-function transformation parameterization method is adopted to describe the airfoil profile with different geometrical parameters. Secondly, the sample points in the design space are selected using the optimal Latin hypercube design methodology. Thirdly, the actual aerodynamic performance of cycloidal propellers is simulated by using the time-dependent incompressible Reynolds-averaged Navier–Stokes computational fluid dynamics method and the sliding-mesh technique, which are verified by validation cases on an oscillating NACA 0012 airfoil and the baseline cycloidal propeller. Then, to replace the time-consuming computational fluid dynamics solver, kriging surrogate models are established using the sample data. Finally, the genetic algorithm is adopted to determine the optimized airfoil in the design space based on the constructed kriging models. Optimization is conducted on a micro- four-bladed cycloidal propeller with the NACA 0015 airfoil, and the results show that the figure of merit of the cycloidal propeller is increased by 18.31% at the design rotation speed. Although the optimization is conducted only at the design rotation speed, an appreciable improvement of the figure of merit can be achieved for a wide range of rotation speeds.

Multiobjective Design Optimization of Hypersonic Combinational Novel Cavity and Opposing Jet Concept

It attaches profound importance to conduct a survey on drag reduction and a thermal protection mechanism applied to the nose tip of hypersonic reentry vehicle due to severe aerodynamic drag and heating. The combinational forward-facing cavity and opposing jet configuration is an effective concept, and its performance could be partially improved when a maximum thrust nozzle contour is employed to substitute the conventional cavity configuration. However, the novel concept would not necessarily generate higher drag and heat reduction efficiency than the conventional one. Therefore, based on the verification of a numerical method, multiobjective design optimization of the combinational novel cavity and opposing jet concept is conducted to minimize both the drag force coefficient and heat load in the current study. The jet total pressure ratio and geometric dimensions are selected as design variables, and the sampling points are obtained numerically by using an optimal Latin hypercube design method. The multi-island genetic algorithm coupled with the kriging surrogate model integrated in Isight 5.5 has been employed to establish the approximate model and solve the Pareto-optimal front. The operating conditions located on the front are proved accurate by a computational fluid dynamics method, and higher drag and heat reduction efficiency can be realized than the conventional configuration at a relatively lower jet total pressure.

Surrogate-based multi-objective optimization of firing accuracy and firing stability for a towed artillery

Determination of general parameters is one of the most essential tasks in optimal structural designs to increase firing accuracy or firing stability, since they are two of the most important performance requirements in artillery designs. This paper presents a multi-objective optimization approach, based on multidisciplinary agent model method. An experiment verified artillery multi-body rigid-flexible coupled dynamic model was first presented. Sample library was generated by optimal Latin hypercube design algorithm and this dynamic model. Then a radial basis function-back propagation neural (RBF-BP series combine) network model was developed to predict firing parameters, used the sample library to train and test the validation of developed neural network model. Finally, an application case was given by NSGA-II and the max-min criterion, its results demonstrate the effectiveness of our method through comparing with its original value.

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.

Metamodel-assisted design optimization of piezoelectric flex transducer for maximal bio-kinetic energy conversion

Energy-harvesting devices have been widely used to generate electrical power from the bio-kinetic energy of human body movement. A novel piezoelectric flex transducer based on the Cymbal device has been proposed by other researchers for the purpose of energy harvesting. To further improve the efficiency of the device, optimal design of the piezoelectric flex transducer for maximum output power subject to stress and displacement constraints is carried out in this article. Sequential quadratic programming on metamodels generated with genetic programming from a 140-point optimal Latin hypercube design of experiments is used in the optimization. Finally, the optimal design is validated by finite element simulations. The simulations show that the magnitude of the electrical power generated from this optimal piezoelectric flex transducer harvesting device can be up to 6.5 MW when a safety design factor of 2.0 is applied.

Calibration methodology for energy management system of a plug-in hybrid electric vehicle

This paper presents a new analytical calibration method for energy management strategy designed for a plug-in hybrid electric vehicle. This method improves the actual calibration efficiency to reach a compromise among the conflicting calibration requirements (e.g. emissions and economy). A comprehensive evaluating indicator covering emissions and economic performance is constructed by using a radar chart method. A radial basis functions (RBFs) neural network model is proposed to establish a precise model among control parameters and the comprehensive evaluation indicator. The optimal Latin hypercube design is introduced to obtain the experimental data to train the RBFs neural network model. And multi-island genetic algorithm is used to solve the optimization model. Finally, an offline calibration example is conducted. Results validate the effectiveness of the proposed calibration approach in improving vehicle performance and calibration efficiency.

A modified particle swarm optimisation algorithm and its application in vehicle lightweight design

Particle swarm optimisation (PSO) is a global optimisation algorithm, which imitates the cooperation behaviour reflected in flocks of birds, fishes, etc. Because of its simple implementation and strong optimisation capacity, the PSO algorithm is becoming very popular in diverse engineering design applications. However, PSO is also seriously affected by the premature convergence problem similar to other global optimisation algorithms. It is generally known that diversity loss is one of the crucial impact factors. To improve the diversity of particles and enhance the algorithm's optimisation ability, the standard PSO algorithm is improved by a mutation operator, the optimal Latin hypercube design (OLHD) technique and boundary reflection method. Optimisation ability of the modified PSO is superior to the standard version through experimental comparison of eight benchmark functions. Combined with kriging surrogate model technique, the modified PSO algorithm is applied to a vehicle lightweight design problem. The frontal structure achieves 5.06 kg (13.95%) weight saving without performances loss after being optimised.

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.

Comparison study of sampling methods for computer experiments using various performance measures

This study compares the performance of popular sampling methods for computer experiments using various performance measures to compare them. It is well known that the sample points, in the design space located by a sampling method, determine the quality of the meta-model generated based on expensive computer experiment (or simulation) results obtained at sample (or training) points. Thus, it is very important to locate the sample points using a sampling method suitable for the system of interest to be approximated. However, there is still no clear guideline for selecting an appropriate sampling method for computer experiments. As such, a sampling method, the optimal Latin hypercube design (OLHD), has been popularly used, and quasi-random sequences and the centroidal Voronoi tessellation (CVT) have begun to be noticed recently. Some literature on the CVT asserted that the performance of the CVT was better than that of the LHD, but this assertion seems unfair because those studies only employed space-filling performance measures in favor of the CVT. In this research, we performed the comparison study among the popular sampling methods for computer experiments (CVT, OLHD, and three quasi-random sequences) with employing both space-filling properties and a projective property as performance measures to fairly compare them. We also compared the root mean square error (RMSE) values of Kriging meta-models generated using the five sampling methods to evaluate their prediction performance. From the comparison results, we provided a guideline for selecting appropriate sampling methods for some systems of interest to be approximated.