Optimal Latin Hypercube Design Research Articles

Parametric optimization of rearview mirror structure based on a multi-island genetic algorithm

To quickly find the structural parameters of a particular mirror that produces the least amount of aerodynamic noise, the rearview mirror of a passenger car is taken as the research object and an optimization platform is established based on Isight software in this paper. The mirror structure is parameterized in Sculptor, and several sample models are constructed using the optimal Latin hypercube design (OLHD). Then, by simulating each sample model, the sound pressure level of the Curle source at the side window surface monitoring point was obtained. The relationship between the mirror structure and the wind noise at the point is fitted using the Kriging approximation model after the calculation is completed. Finally, the values at each point decreased when the changes at positions 1, 2, 3, and 4 were 2.5 mm, 3.91 mm, 4.5 mm, and 3.6 mm, and the sound pressure level at monitoring point 4 decreased the most, with a reduction of 3.76 dB in wind noise compared with the original model.

Optimization of unsteady jet control flow method for aerodynamic drag reduction of heavy truck model

The aerodynamic drag reduction of ground vehicles is crucial for meeting the increasingly strict emission standards. In this context, a potential approach to achieve this objective is to use active flow control techniques. Many active flow control techniques have been applied for ground vehicles, and the unsteady jet device has been proven to have better control energy efficiency than some other flow actuators. Therefore, this study focuses on applying this unsteady jet technique to a realistic truck model. The main parameters of the control flow device, including jet amplitude, jet angle, and control frequency were optimized to reduce the aerodynamic drag of the truck model and achieve the maximum control energy efficiency. Numerical studies were performed based on the CFD method with the k-ω SST turbulence model. A 25-level optimal Latin Hypercube design experimental study was conducted. The optimization method based on the Kriging response surface model and genetic algorithm was chosen to determine the optimal solution. The results show that the maximum energy efficiency is 9.174 % using the unsteady jet devices with the optimal parameters on the small-scale truck model.

An EGO-based online model updating method for hybrid simulation

Hybrid simulation combines experimentally testing of physical substructures with computational simulation of numerical substructures to replicate structural responses under earthquakes. When numerical substructure involves parts that are similar to physical substructure, measured responses of physical substructure are often used to update similar parts within numerical substructure, aiming to improve accuracy of seismic assessment. This study proposes an efficient global optimization based approach for online model updating in hybrid simulation (HSMU-EGO) involving multiple key components yet with only one physically tested in laboratory. Kriging meta-model is constructed for the response error between the numerical model for updating and the experimental substructure, while efficient global optimization and optimal Latin hypercube design are integrated for parameter estimation to minimize the response error. Computational simulations are conducted for a simple steel braced frame and a complex concrete continuous bridge to comprehensively evaluate the performance of HSMU-EGO in the presence of constitutive parameter and model errors. The proposed method is demonstrated to effectively and efficiently improve the accuracy of hybrid simulation in almost all cases. Compared with Unscented Kalman Filter (UKF), this proposed HSMU-EGO provides more suitable alternative when prior information is limited for the physical substructure.

RBF-Based Integrated Optimization Method of Structural and Turning Parameters for Low-Floor Axle Bridge

The axle bridge plays a crucial role in the bogie of low-floor light rail vehicles, impacting operational efficiency and fuel economy. To minimize the total cost of the structure and turning of axle bridges, an optimization model of structural and turning parameters was built, with the fatigue life, maximum stress, maximum deformation, and maximum main cutting force as constraints. Through orthogonal experiments and multivariate variance analysis, the key design variables which have a significant impact on optimization objectives and constraints (performance responses) were identified. Then the optimal Latin hypercube design and finite element simulation was used to build a Radial Basis Function (RBF) model to approximate the implicit relationship between design variables and performance responses. Finally, a multi-island genetic algorithm was applied to solve the integrated optimization model, resulting in an 8.457% and 1.1% reduction in total cost compared with the original parameters and parameters of sequential optimization, proving the effectiveness of the proposed method.

Research on Multi-Objective Optimization on Explosion-Suppression Structure-Nonmetallic Spherical Spacers

Intense burning phenomena (fire disasters) need to be prevented in the combustible gas utilization and transportation processes to ensure industrial safety. Nonmetallic spherical spacers (NSSs) have been investigated and applied in lots of explosive atmospheres to prevent explosion execution in a confined space. In this work, a novel fuzzy-based analytic hierarchy process (FAHP) is developed to take into account the uncertainty in decision-making and effectively solve the problem of factor weight allocation in multi-objective optimization. Optimal Latin Hypercube Design (Opt LHD), Chebyshev Orthogonal Polynomials (COP), and Adaptive Simulated Annealing (ASA) were combined. A multi-objective optimization method is proposed for the structural parameter optimization problem on NSSs in order to achieve conflicting multiple-objective optimization of low displacement rate and minimal deformation. That is to say, the small volume (low displacement rate) and high explosion-suppression performance (minimal deformation) of NSSs were optimized simultaneously. The results show that, compared with the original NSS model’s deformation (2.85 mm) and displacement rate (3.63%), the optimized NSSs with weight allocation had optimized the deformation by 12.98% and displacement rate by 6.1%. Compared with the optimized design model of NSSs without weight allocation with a deformation of 2.75 mm and a displacement rate of 3.48%, the deformation has been optimized by 9.82%, and the displacement rate has been optimized by 2.0%. It was verified that the proposed method is effective. At the same time, it was verified that the suppression effect of NSSs can be enhanced by changing the shape of the NSS spacer reasonably by experimental verification.

Research on the lightweight design and multilevel optimization method of B‐pillar of hybrid material based on side‐impact safety and multicriteria decision‐making

AbstractThis paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

Optimization Method of Multi-parameter Coupling for a Hydraulic Rolling Reshaper Based on Factorial Design

A hydraulic rolling reshaper is an advanced shaping technology with superior protection for casings, and the structural parameters of the reshaper affect its shaping effect on deformed casing directly. To improve the shaping capacity of the reshaper, a multi-parameter coupling optimization method of hydraulic rolling reshaper is proposed to optimize the design of the factors with significant influence under the premise of screening multi-structural parameters. In this paper, according to the working principle of the reshaper, considering the contact nonlinearity between the hydraulic rolling reshaper and deformed casing, as well as the material nonlinearity of the casing, a parametric finite element model of the hydraulic rolling reshaper repairing the shrinkage deformation of casings was developed. The remarkable factors were screened by factorial design, the sample points were generated by optimal Latin hyper-cube design (OLHD), and the response surface models were established by stepwise regression. Therefore, with the maximum plastic deformation of casings as the objective function, the maximum equivalent stress, residual stress, and the plastic deformation of casings as the constrained conditions, an optimized mathematical model for a reshaper was constructed, and the genetic algorithm (GA) is performed to obtain the optimal combination of parameters. The results showed that the optimal reshaper made the shaping process safe and effective, the plastic deformation of casings after single shaping was increased by 11.38 %, and the shaping effect was better (96.48 %), which can effectively improve the safety performance and shaping ability of the reshaper.

Energy Management Strategy Optimization for a Novel Electric‐hydraulic Power Coupling Vehicle Considering the Influence of Multiple Driving Cycles

Hydraulic hybrid technology can further improve the economy of electric vehicles (EV). In this article, a novel electric‐hydraulic power coupling vehicle (EHPCV), which is endowed with multiple drive modes and energy regenerative braking modes, is investigated. The electric‐hydraulic power coupler (EHPC) is an innovative device for realizing power coupling and conversion. The design and optimization of the energy management strategy (EMS) are key to ensuring the efficient and stable operation of the hybrid electric vehicle. Based on the analysis of energy flow, a rule‐based EMS (RB‐EMS) is built. To achieve more reasonable energy management of the EHPCV in random driving environments, the article proposes an optimization framework for the EMS based on multiple driving cycles. More precisely, a multiobjective optimization mathematical model is established with the goal of maximizing the battery state of charge and minimizing velocity error. Moreover, the optimal Latin hypercube design is used to select the design variables that have a significant impact on the optimization objective. Definitively, the nondominated sorting genetic algorithm II algorithm combines with RB‐EMS to optimize the control parameters. The verification results show that the optimized EMS enables the EHPCV to have superior economic advantages.

Sequential Latin hypercube design for two-layer computer simulators

The two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of the first-layer simulator (also called the inner simulator) are partial inputs of the second-layer simulator (also called the outer simulator). How to design experiments by considering the space-filling properties of inner and outer simulators simultaneously is a significant challenge that has received scant attention in the literature. To address this problem, we propose a new sequential optimal Latin hypercube design (LHD) by using the maximin integrating mixed distance criterion. A corresponding sequential algorithm for efficiently generating such designs is also developed. Numerical simulation results show that the new method can effectively improve the space-filling property of the outer computer inputs. The case study about composite structures assembly simulation demonstrates that the proposed method can outperform the benchmark methods.

Searching for optimal Latin hypercube designs by a local greedy strategy

The Latin hypercube design (LHD), because of its one-dimensional projection uniformity, is commonly used in computer experiment. The randomly generated LHD may have too many concentrated design points, and factors may be highly correlated. In this article, we suggested a local greedy strategy for searching optimal LHDs. Our strategy consists of two parts. One is a swap process for doing a local greedy search in a polynomial time. The other is a simulated annealing process for jumping out of the possible local optima. Our strategy is flexible and adapts to various space-filling criteria of LHDs. The simulated experiments illustrated that our proposed algorithm can produce LHDs with well space-filling property and orthogonality. Compared to other classical design algorithms, our algorithm performed better on the criteria related to the point distance and the column correlation. Moreover, for the response surface approximation, the Kriging model using our produced optimal LHD performed more robust on the surface prediction.

Study on the Optimal Design Method of the Containment Ring for an Air Turbine Starter

The airworthiness standards of transport category airplanes clearly stipulate that the equipment containing high-energy rotors must be shown by test that it can contain any failure of a high-energy rotor that occurs at the highest speed. The air turbine starter (ATS) is typical equipment containing high-energy rotors, and the manufacturers of ATS attach great importance to research on structural containment and weight reduction. In this paper, an optimal design method for a U-type containment ring is proposed. The method adopts the optimal Latin hypercube design, numerical simulation, response surface modeling, and genetic algorithm to achieve the multi-parameter optimal design of the containment ring section. By combining simulation and experiment, the influence weights of different structural parameters of the containment ring on the residual kinetic energy of debris and the containment ring volume were analyzed. The influence of different structural parameters of a U-type containment ring on containment results was studied, and a containment test was carried out to verify the containment capability of an optimized containment ring. The results show that the thickness of the containment ring has the greatest influence on the residual kinetic energy of the debris, and the weight ratio is 38%. The maximum radial deformation of the optimized containment ring can reach 22.3%, which means that the energy absorption effect of the containment ring on the disk fragments is significantly improved. With the same containment capability, the weight reduction effect of an optimized containment ring can reach 26.5%. The research results can provide weight reduction optimization methods and design theoretical guidance for U-type containment structures.

The analysis and optimization of thermal sensation of train drivers under occupational thermal exposure.

Prolonged exposure of train drivers to thermal discomfort can lead to occupational safety and health (OSH) risks, causing physical and mental injuries. Traditional method of treating human skin as a wall surface fail to observe accurate skin temperature changes or obtain human thermal comfort that adapts to the thermal environment. This study employs the Stolwijk human thermal regulation model to investigate and optimize the thermal comfort of train drivers. To minimize the time-consuming design optimization, a pointer optimization algorithm based on radial basis function (RBF) approximation was utilized to optimize the train cab ventilation system design and enhance drivers' thermal comfort. The train driver thermal comfort model was developed using Star-CCM+ and 60 operating conditions were sampled using an Optimal Latin Hypercube Design (Opt LHD). We analyzed the effects of air supply temperature, air supply volume, air supply angle, solar radiation intensity and solar altitude angle on the local thermal sensation vote (LTSV) and overall thermal sensation vote (OTSV) of the train driver. Finally, the study obtained the optimal air supply parameters for the Heating Ventilation and Air Conditioning (HVAC) in the train cabin under extreme summer conditions, effectively improving the thermal comfort of the driver.

Theoretical error formation and evaluation of acoustic source localization for cluster-based techniques

In this paper, the formation of theoretical error is presented to investigate the acoustic source localization (ASL) error that can be expected from traditional L-shaped, cross-shaped, square-shaped, and modified square-shaped sensor cluster arrangements. The response surface model based on the optimal Latin hypercube design is developed to theoretically study the effects of sensor placement parameters on the error evaluation index of root mean squared relative error (RMSRE) for the four techniques. The ASL results from the four techniques with the optimal placement parameters are analyzed theoretically. The relevant experiments are conducted for verifying the above theoretical research. The results show that the theoretical error, formed by the difference between the true and the predicted wave propagation directions is related to arrangement of sensors. The results also show that the sensor spacing and the cluster spacing are the two parameters that affect the ASL error most. Between these two parameters the sensor spacing has the stronger influence. The RMSRE increases with an increasing sensor spacing and a decreasing cluster spacing. Meanwhile, the interaction effect of placement parameters should be also emphasized, especially that between the sensor spacing and the cluster spacing for the L-shaped sensor cluster-based technique. Among the four cluster-based techniques, the newly modified square-shaped sensor cluster-based technique shows the smallest RMSRE and not the largest number of sensors. This research on error generation and analysis will provide guidance for the optimal sensor arrangements in cluster-based techniques.

Development of an overtopping wave absorption device for a wave-making circulating water channel

With the improvement of the stable flow generation function of circulating water channels (CWCs), CWCs are gradually developing toward multi-functionality. The wave test capability of a CWC is limited by its short test section; so, an efficient wave absorption device is required. This paper proposes the design concept of an overtopping wave absorption device (OWAD). An optimization design of the device by combining CFD and simulation-based design (SBD) is presented. The SBD system included optimal Latin hypercube design (Opt LHD), SVR, and particle swarm optimization (PSO). The reflection coefficient was used to estimate the wave absorption device performance. Numerical analysis was performed using the Unsteady Reynolds Averaged Navier–Stokes (URANS) solver and the boundary wave generation method, and was verified and validated via a procedure recommended by International Towing Tank Conference (ITTC). Under two wave conditions, four different OWAD design variables (slope angle, porosity, extension depth, and extension height) were optimized using the SBD system to minimize the reflection coefficient. Based on optimization results, the OWAD was assembled and its wave dissipation performance was confirmed experimentally. Installing an OWAD caused the reflection coefficient to be reduced from 0.161 to 0.089 for short-wave design conditions and from 0.528 to 0.128 for long-wave design conditions. A wave absorption test also showed that the wave absorption performance of the OWAD is significantly better than that of honeycomb and multiple porous plate wave absorption devices. The OWAD produces not only lower reflection coefficients but also smoother wave surfaces due to its two-dimensional structures.

Assessment of an Optimal Design Method for a High-Energy Ultrasonic Igniter Based on Multi-Objective Robustness Optimization

The current deterministic optimization design method ignores uncertainties in the material properties and potential machining error which could lead to unreliable or unstable designs. To improve the design efficiency and anti-jamming ability of a high-energy ultrasonic igniter, a Six Sigma multi-objective robustness optimization design method based on the response surface model and the design of the experiment has been proposed. In this paper, the initial structural dimensions of a high-energy ultrasonic igniter have been obtained by employing one-dimensional longitudinal vibration theory. The finite element simulation method of COMSOL Multiphysics software has been verified by the finite element simulation results of ANSYS Workbench software. The optimal igniter design has been achieved by using the proposed method, which is based on the finite element method, the Optimal Latin Hypercube Design method, Grey Relational Analysis, the response surface model, the non-dominated sorting genetic algorithm, and the mean value method. Considering the influence of manufacturing errors on the igniter’s performance, the Six Sigma method was used to optimize the robustness of the igniter. The Eigenfrequency analysis and the vibration velocity ratio calculation were conducted to verify the design’s effectiveness. The results reveal that the longitudinal resonant frequency of the deterministic optimization scheme and the robustness optimization scheme are closer to the design’s target frequency. The relative error is less than 0.1%. Compared with the deterministic optimization scheme, the vibration velocity ratio of the robustness optimization scheme is 2.8, which is about 15.7% higher than that of the deterministic optimization scheme, and the quality level of the design targets is raised to above Six Sigma. The proposed method can provide an efficient and accurate optimal design for developing a new special piezoelectric transducer.

A Shift Schedule to Optimize Pure Electric Vehicles Based on RL Using Q-Learning and Opt LHD

Range anxiety is a problem that restricts the development of pure electric vehicles. For this reason, much research starts from a shift schedule and strives to improve mileage. However, the proposed shift schedules have poor adaptive ability and are not suitable for dynamic conditions. In this paper, a shift schedule based on reinforcement learning (RL) is proposed, which uses Q-learning for optimization. However, the massive state variables and huge Q table in the state space put forward higher requirements on the computing power and storage space of the controller. Traditionally, the application of RL algorithms needs to rely on expensive GPU devices. To reduce high costs, we use an innovative treatment method, the optimal Latin hypercube design (Opt LHD), which is used for sampling, and state reduction is performed on the state space. Based on the above, the mileage is effectively improved by applying the shift schedule based on RL.

Shape Optimization of the Streamlined Train Head for Reducing Aerodynamic Resistance and Noise

Aiming to improve the comprehensive aerodynamic performance of a high-speed train, a multi-objective shape optimization method for a streamlined train head is proposed in this work. The shape of the streamlined train head is parameterized with some spline curves. The optimization design variables are uniformly sampled using the optimal Latin hypercube design method. The aerodynamic resistance and dipole noise sources are chosen as the optimization objectives, which can be obtained through the computational fluid dynamics (CFD) method. An approximate calculation model is established by the radial basis function neural network so as to effectively predict the values of optimization objectives. The error between the predicted values and actual values of the aerodynamic resistance is less than 1%, and that of the dipole noise source is less than 3 dB, which demonstrate the validity of the approximate calculation model. In the optimization process, the algorithm NSGA-II is adopted to update the values of the optimization design variables, and the approximate calculation model is used to calculate the optimization objectives, which greatly reduces the optimization computation time of the streamlined head shape. Through iterative computation of the optimization algorithm in the design space, each optimized design variable shows a trend of convergence, and the aerodynamic resistance and dipole noise source generally show a decreasing trend. The Pareto front is corrected by the CFD method after optimization. The aerodynamic resistance can be reduced by up to 4.5%, and the dipole noise source can be reduced by up to 3.9 dB.

CFD-based multi-objective optimization of the duct for a rim-driven thruster

Rim-driven thruster (RDT) is a new integrated thruster that has attracted much attention recently. The RDT provides the benefits of reducing vibration and noise and increasing useable volume by mounting the propulsion motor stator into the duct and fusing the motor rotor with the propeller blades. The calculation method of RDT considering the motor gap was discussed and validated. A simulation-based design optimization framework was proposed for the particularity of RDT ducts. The parametric reconstruction of the duct was executed based on the Bézier curve. The optimal Latin hypercube design method was used to generate samples, and the approximate model was developed based on the radial basis function (RBF) neural network. The fitting R2 of efficiency, minimum pressure, blade thrust, and total thrust of the approximate model reached 0.998, 0.955, 0.998, and 0.990, respectively. On this basis, the NSGA-II was employed to optimize the duct with minimum pressure and efficiency as the optimization objectives. Sensitivity analyses indicate that the optimization objectives are significantly affected by the nozzle size, followed by the internal nozzle profile. The typical Pareto solutions were verified by CFD calculation, and the duct optimization can improve efficiency by 3.3% or minimum pressure by 5.3%.

Multiobjective Optimization Design for a MR Damper Based on EBFNN and MOPSO

The structural parameters of the magnetorheological (MR) damper significantly affect the output damping force and dynamic range. This paper presents a design optimization method to improve the damping performance of a novel MR damper with a bended magnetic circuit and folded flow gap. The multiobjective optimization of the structural parameters of this MR damper was carried out based on the optimal Latin hypercube design (Opt LHD), ellipsoidal basis function neural network (EBFNN), and multiobjective particle swarm optimization (MOPSO). By using the Opt LHD and EBFNN, determination of the optimization variables on the structural parameters was conducted, and a prediction model was proposed for further optimization. Then, the MOPSO algorithm was adopted to obtain the optimal structure of the MR damper. The simulation and experimental results demonstrate that the damping performance indicators of the optimal MR damper were greatly improved. The simulation results show that the damping force increased from 4585 to 6917 N, and the gain was optimized by 50.8%. The dynamic range increased from 12.4 to 13.2, which was optimized by 6.4%. The experimental results show that the damping force and dynamic range of the optimal MR damper were increased to 7247 N and 13.8, respectively.

Aerodynamic Shape Optimization Design of the Air Rectification Cover for Super High-Speed Elevator

To reduce the aerodynamic load of super high-speed elevators, in this paper, the coefficient of drag [Formula: see text] and the coefficient of yawing moment [Formula: see text] of the elevator are selected as optimization objectives for the optimization of the air rectification cover (ARC) shape. The elliptic curve method was used to build the parametric model of the ARCs, six design variables were selected, and the design space of the ARC was determined. With the optimal Latin hypercube design method, the training points were selected, and the computational fluid dynamics numerical simulation was conducted to calculate the corresponding responses. Then, the relationship between the design variables and the responses was analyzed. The radial basis function (RBF) surrogate model of the relationship between the design variables and responses was constructed. Finally, the non-dominated sorting genetic algorithm-II (NSGA-II) was employed to optimize the shape of the ARC. The results show that the [Formula: see text] and [Formula: see text] decrease by 16.51% and 60.92%, respectively, compared with the unoptimized ARC, indicating that the ARC designed in this paper is optimized and can effectively reduce the aerodynamic load. Furthermore, among all the design variables, the bluntness of the ARC in the [Formula: see text]-direction has the most significant effect on the aerodynamic load, and the height of the ARC ([Formula: see text] and [Formula: see text]) has the second most significant effect on the aerodynamic load of elevators.