Optimal Latin Hypercube Sampling Method Research Articles

Hydrodynamic shape optimization of an autonomous and remotely-operated vehicle via a multi-surrogate model

The design requirements for the hydrodynamic performance of underwater vehicles vary significantly depending on the application. Optimization without an initial model results in challenges such as large design domains, nonlinear complexity, and high data requirements. To optimize the hydrodynamic performance during the design process, in this paper, a multi-surrogate model was employed to progressively design the shape of an autonomous and remotely-operated vehicle. Based on the data characteristics of different stages, this approach strikes a balance among data quantity, prediction accuracy, and multi-objective requirements. An artificial neural network prediction surrogate model was constructed based on the principle of the minimum prediction factor using the optimal Latin hypercube sampling method. During the optimization of the design domain, the optimum objective was to minimize the dimensionless force (G(x)). During the multi-objective optimization stage, a regression kriging surrogate model was constructed based on a support vector product. The optimization objectives were to maximize volume and minimize dimensionless forces. This enabled the overall design process to attain optimal Pareto solutions within the design domain while simultaneously ensuring high prediction accuracy and minimum data requirements. The results obtained are consistent with the simulation comparison, thus verifying the reliability of the entire optimization process.

Multiobjective optimization of laser welding parameters for P92 steel based on MFO/MOEAD-Kriging

P92 steel is used in steam equipment of thermal power plants and nuclear power plants. It needs to withstand high temperature and high pressure during service, so high-quality welds are required. Laser welding can easily obtain good weld quality and reduce the probability of coarse grains and welding defects in the heat-affected zone. Post-weld deformation, residual stress, and weld hardness are important indexes for evaluating weld quality, which largely depends on the combination of laser welding process parameters. The multiobjective optimization methods of moth-flame optimization (MFO) and multiobjective evolutionary algorithm based on decomposition under the Kriging model were compared in this research. It was found that the MFO algorithm has a faster optimization speed and better overall effect. The Optimal Latin hypercube sampling method was used to design the simulation test. The welding seam-forming process was simulated by the SYSWELD software. The Kriging model was used to make the nonlinear relationship between the process parameters and the weld quality indexes significant. A new data set was designed to evaluate the accuracy of the model. On this basis, the efficiency of the combination of process parameters optimized by the two algorithms was compared. The simulation and experimental results were in good agreement with the multiobjective optimization results of the MFO. In the experimental verification, the optimized weld quality was analyzed from the aspects of microstructure and mechanical properties. The results showed that the multiobjective optimization method quickly and effectively reduces the probability of weld quality defects in actual welding, thereby improving weld quality. This multiobjective optimization method provides valuable research ideas for engineering research and development to effectively shorten its development cycle.

Aerodynamic shape optimization of passenger car fender based on the FFD method

The research of this work focuses on optimizing the body fender of the CAERI AERO car model to decrease aerodynamic drag and improve aerodynamic performance. Five design regions of the body fender were selected and studied. The Free-Form Deformation (FFD) method was used to perform the mesh deformation process without re-modeling and re-gridding. The optimal Latin Hypercube Sampling method and Computational Fluid Dynamics (CFD) simulations are used to generate the sample points and obtain their responses. The relationships between the design variables and their responses, as well as the contributions of the main factors, were analyzed. After then, an optimization of decreasing drag using the Adaptive Simulated Annealing (ASA) algorithm was conducted based on the Radial Basis Function (RBF) model, and a set of convergent solution space sets is obtained. Finally, CFD simulations were performed on the ASA algorithm search results, and a comparison of the aerodynamic performance between the original fender and an optimal fender that selected from the solution spaces is presented. Using the FFD method and the surrogate model dramatically improves the computational efficiency in this study.

A construction strategy of Kriging surrogate model based on Rosenblatt transformation of associated random variables and its application in groundwater remediation

When using simulation-optimization models for optimizing the design of groundwater pumping-treatment plans for pollution, building a surrogate model for the numerical simulation model has become an effective means of overcoming the computational load of such models. However, previous studies often treated pumping time as a single optimization variable, leading to unnecessary excessive pumping. This paper considers the location, pumping rate, start time, and end time of each candidate pumping well as optimization variables, and proposes a Rosenblatt-transform-based optimal Latin hypercube sampling method for the associated random variables to ensure that the start time is less than or equal to the end time. This method is coupled with an adaptive sampling method based on batch local optimal solutions to construct a dynamic adaptive Kriging surrogate model for the numerical model, ensuring that the true value of the optimal remediation scheme is not lost. The results show that, at the final stage of remediation, the pollutant concentration in the 4 scenarios achieves comprehensive compliance. However, when considering the minimization of remediation costs as the evaluation criterion, the remediation scheme in scenario 1 (the pumping start and end times are independent optimization variables for all candidate pumping wells) is optimal. In the optimization design of groundwater pumping-treatment plans, the pumping wells should be arranged in the midstream and downstream regions of the contaminant plume and parallel to the regional flow direction. This paper provides a method reference for the construction and adaptive updating of surrogate models involving associated random variables, as well as guidance for the dynamic optimization of groundwater pumping and treatment at contaminated sites.

Design and optimization of bionic Nautilus volute for a hydrodynamic retarder

To reduce the energy loss of volute and improve the emergency braking performance of hydrodynamic retarder under design condition, a bionic volute optimization design method is proposed based on the Nautilus shell. First, the accuracy of the numerical method is verified by grid convergence analysis and experiments. Thereafter, the bionic parametric expression is performed based on the cross-section shape of the Nautilus shell. Subsequently, sample points are created using the Optimal Latin Hypercube sampling method and numerically simulated. Radial basis function neural network and multi-objective genetic algorithm are used for optimization. Finally, the flow field inside the volute and the braking performance of the hydrodynamic retarder are compared by numerical calculation and experiment. Results show that the internal flow field of the bionic volute is more uniform, the energy loss is reduced by 78.95%, and the oil flow speed is increased by 40.61%. In addition, the stable flow field can be established faster during braking, the peak torque can be increased by 6.15%, and the onset time can be advanced by 6.58%. The analysis of energy characteristics shows that the improved performance of the bionic volute can be attributed to its improved internal oil flow conditions, thus reducing the energy loss.

Multi-fidelity data-driven optimization design framework for self-piercing riveting process parameters

Due to its excellent performance, the self-piercing riveting (SPR) process has been widely used in auto body manufacturing in recent years. The need for efficient and reliable design of SPR process parameters is growing in industry. Traditional trial-and-error design methods rely on historical experience and can be limited by physical experimental materials and equipment. Data-driven methods rely on data accuracy and data volume, and data from a single source is often inadequate to meet design needs. To address these issues, a multi-fidelity data-driven optimization design framework is proposed in this paper. The most significant feature of this framework is the fusion of physical experiment data and simulation data to build surrogate models. In this framework, a modified optimal Latin hypercube sampling method and a multi-fidelity surrogate model based on transfer learning and neural networks are proposed for SPR process. This multi-fidelity surrogate model can use a very small amount of experiment data to modify the surrogate model built on simulation data based on transfer learning, so that the model predictions can more closely match the physical experiment results at a lower modeling cost. Benefit from this method, the proposed framework can balance the contradiction between design accuracy and development cost compared to a single-fidelity data-driven framework. The application cases show that the prediction errors of the multi-fidelity models are <0.1 mm for the key geometric parameters of the SPR joint. As verified by physical experiments, the rivets and dies selected by the framework are the optimal solutions within the optional range. To the authors' knowledge, this is the first time that a multi-fidelity modeling method has been introduced to the field of SPR process, to solve the process parameter optimization design problem. Further, the method is not limited to the use of SPR process but can be applied as a paradigm in other engineering optimization design problems, especially in joining process parameter design problems.

Sensitivity Analysis of RV Reducer Rotation Error Based on Deep Gaussian Processes

The rotation error is the most important quality characteristic index of a rotate vector (RV) reducer, and it is difficult to accurately optimize the design of a RV reducer, such as the Taguchi type, due to the many factors affecting the rotation error and the serious coupling effect among the factors. This paper analyzes the RV reducer rotation error and each factor based on the deep Gaussian processes (DeepGP) model and Sobol sensitivity analysis(SA) method. Firstly, using the optimal Latin hypercube sampling (OLHS) approach and the DeepGP model, a high-precision regression prediction model of the rotation error and each affecting factor was created. On the basis of the prediction model, the Sobol method was used to conduct a global SA of the factors influencing the rotation error and to compare the coupling relationship between the factors. The results show that the OLHS method and the DeepGP model are suitable for predicting the rotation error in this paper, and the accuracy of the prediction model constructed based on both of them is as high as 95%. The rotation error mainly depends on the influencing factors in the second stage cycloidal pinwheel drive part. The primary involute planetary part and planetary output carrier's rotation error factors have little effect. The coupling effects between the matching clearance between the pin gear and needle gear hole (δJ) and the circular position error of the needle gear hole (δt) is noticeably stronger.

Multi-objective optimization of the geometric parameters of a pressure-swirl nozzle

ABSTRACT The geometric parameters of the pressure-swirl nozzle demonstrate a significant effect on the atomization performance such as the spray cone angle and mass flow rate. However, these objectives are incompatible, and obtaining a nozzle geometric parameter that optimizes all the atomization performances is difficult. The effectiveness of the nozzle optimization process is typically low, resulting in high costs. To this purpose, an enhanced CBSO-Kriging surrogate model was developed to solve this expensive black box problem, and the spray cone angle and mass flow rate were optimized using a multi-objective optimization algorithm. Firstly, the optimal Latin hypercube sampling method was used to generate 65 sets of sample points, and the corresponding response values were calculated using CFD simulation. The established surrogate model of atomization performance can predict the atomization characteristics of the nozzle with arbitrary shape. The correlation between the key geometric parameters and the spray cone angle and the mass flow rate was determined on this basis. Then, to find the optimal geometric parameters for the nozzle, the NSGA-II algorithm was used. In comparison to the initial model, the optimization results show that the spray cone angle and mass flow rate increased by 4.26% and 37.74%, respectively.

Identification of nonparametric thermodynamic model and optimization of ocean thermal energy conversion radial inflow turbine

Turbine is one of the key components of ocean thermal energy conversion system, and its aerodynamic performance and geometric structure directly affect the performance of the system. At present, the design methods of radial inflow turbines can be roughly divided into three categories: trial method, best velocity ratio method and screening method, which follow no concrete rules and are not comprehensive, and rely mostly on the designers' experience. This study proposes a fully data-based non-parametric model identification and optimization method for ocean thermal energy conversion radial inflow turbines is proposed, and takes the 25 kW R134 working fluid turbine of the ocean thermal energy conversion system as an example for verification and analysis. First, the optimal Latin hypercube sampling method was used to complete the experimental design with seven initial thermodynamic parameters as independent variables. And then according to the test data and the Gaussian process regression identification, the non-parametric turbine thermodynamic model was obtained. At last, on the basis of this model, the NSGA-III multi-objective optimization algorithm was used to optimize the design with the goal to achieve maximum efficiency and minimum diameter, and the optimized results were obtained. The results show that the non-parametric model based on the Gaussian process proposed in this study has higher accuracy, and the optimization results obtained based on this model are more efficient and have a more compact structure. The research work described in this study saves time and cost for completing the aerodynamic performance design of the turbine and further improving the expansion efficiency of the radial inflow turbine. It is of great significance for the practical application of promoting ocean thermal energy conversion.

Optimization strategy for curing ultra-thick composite laminates based on multi-objective genetic algorithm

Thermal gradient and temperature overshoot during the curing process of ultra-thick carbon fibre composite have a major impact on its properties. We present a strategy to optimize the curing process based on the surrogate model and genetic algorithm. Firstly, a FE model based on heat transfer was developed for curing a 30 mm thick laminate and validated by experimental data. Then a multi-objective optimization strategy was developed by combining the optimal Latin hypercube sampling method, elliptical basis function (EBF) neural network model and non-dominated sorting genetic algorithm-II (NSGA-II). It is found that the optimized cure cycle can effectively reduce the undesirable maximum DoC (Degree of cure) gradient and the temperature gradient leading to improved mechanical properties for the 30 mm thick laminate.

The effect of micromechanics models on mechanical property predictions for short fiber composites

The Tandon-Weng (T-W), the Halpin-Tsai (H-T) micromechanical models and a novel numerical implementation of asymptotic homogenization method (NIAH) for determining the stiffness of unidirectional orientation short fiber composites are compared. Based on rigorous mathematical theory, NIAH can be easily implemented using commercial software as a black box as representative volume approaches. Representative volume element (RVE) models were generated using random sequential adsorption technique (RSA) based on the optimal Latin hypercube sampling method. For arbitrary fiber orientation, the NIAH approach was compared with orientation averaging with the T-W and the H-T micromechanical models. Agreement between the three approaches in predicting the effective properties of short fiber composites was found to be excellent. Finally, the results calculated with the three approaches were compared with experimental values. It is shown that the three approaches in this paper are in quite good agreement with measured values. However, for random oriented short fiber composites with fiber length and fiber diameter distribution, the NIAH method still can provide calculated results with sufficient prediction accuracy, and the other two methods are not any more effective.

Multi-objective optimization of deployable composite cylindrical thin-walled hinges with progressive damage

The deployable composite cylindrical thin-walled (DCCTW) hinges have application prospects as deployable structures of satellite and solar array, but the mechanical characteristics of the DCCTW hinges have not been considered comprehensively. Taking progressive damage into consideration, the mechanical properties of DCCTW hinges have been reassessed, and a new optimal design method is presented in this paper. Firstly, a simplified model of DCCTW hinge was established. Both analytical and numerical analyses of the simplified model have been conducted. Secondly, the finite element (FE) method has been used to analyze the folding and torsional behavior of DCCTW hinge based on progressive damage theory. Thirdly, design of experiment (DOE) has been carried out using optimal Latin hypercube sampling method. The surrogate model has been established based on the DOE process and elliptical basis functions (EBF). Sensitivity analysis of mass, peak moment of folding, torsional failure angle, and peak moment of torsion have been conducted. Lastly, considering lightweight, the higher peak moment of folding and torsion, the optimization was implemented by multi-objective particle swarm optimization (MOPSO) algorithm, two different optimal designs of DCCTW hinge have been obtained at the same time. The maximum relative error between FE analysis results and optimal design results with the surrogate model is 7.46%, which also reflects the accuracy of the surrogate model. The proposed optimization method can be applied to optimize other composite flexible hinges in consideration of progressive damage.

Accuracy analysis of a parallel positioning mechanism with actuation redundancy

A forward accuracy analysis method based on Lie-group theory and screw theory is proposed to analyze the pose error of parallel mechanisms with actuation redundancy. Both the input uncertainty and components stiffness were considered. The method was applied to study the accuracy performance of a positioning mechanism, which has the potential to be used for the positioning of satellite antenna, camera, astronomical telescope and so on. The advancement of the method is that it models the elastic deformation and passive joint motions together by motion vector and limb stiffness matrix, which greatly simplifies the constraints modeling process. Mean value and standard deviation of the pose errors under different working conditions were obtained by optimal Latin hypercube sampling method, which reduces the sampling size on the premise of ensuring the precision. Finally, the robust optimization was employed to give further insight into the effects of redundant limb and mechanism structure on the accuracy performance of the actuation-redundant mechanism.

Optimization of the Heating Element in a Gas-Gas Heater Using an Integrated Analysis Model

Gas-gas heaters (GGHs) are used to reheat gases through desulfurization in coal-fired power plants to reduce low-temperature corrosion and white smoke. Wrinkled heating elements are installed inside the GGH to perform effective heat exchange. An optimization study of the heating element shape was conducted to reduce the differential pressure effectively and improve performance. An integrated analysis model was applied. Based on actual operational data, a computational fluid dynamic analysis was conducted on the L-type heating element and GGH system. The experiments applied the optimal latin hypercube sampling method, and numerical analysis was performed for each sample. Based on the response surface, the result of the sample was optimized through the pointer algorithm. For the integrated analysis model, validation was performed by comparison with the actual operational data, and the thermal-fluid characteristics of the heating element and GGH system were analyzed to set three parameters: plate angle, undulated angle, and pitch 1. From the optimization result, increases in the undulated angle and pitch 1 reduce the pressure drop by widening the heating element cross section. By increasing the plate angle, the heat transfer area is secured and the reduced heat transfer coefficient is compensated, improving the GGH performance.

A multiobjective aerodynamic optimization design of a high-speed train head under crosswinds

In this work, a multiobjective aerodynamic optimization of a high-speed train head was performed to improve the aerodynamic performance of the high-speed train running on an embankment under crosswinds. Seven optimization design variables were selected to control five regions on the train head. The total aerodynamic drag force, aerodynamic lift force, and aerodynamic side force of the head coach were set as the optimization objectives. The optimal Latin hypercube sampling method was used to obtain the values of the design variables of the sample points. The high-speed train head was deformed using the free-form deformation approach through which the mesh morphing was performed without remodeling and re-meshing. Then, the aerodynamic performances of the high-speed trains at the sample points were calculated using the computational fluid dynamics method. A Kriging surrogate model between the design variables and their optimization objectives was constructed. Then, the multiobjective aerodynamic optimization of the high-speed train head was performed using multiobjective genetic algorithms based on the Kriging model. Based on the results of the sample points, the relationships between the optimization design variables and the optimization objectives were analyzed, and the contributions of the primary factors to the optimization objectives were obtained. After optimization, a series of Pareto-optimal head shapes were obtained. The steady and unsteady aerodynamic performances of the train with an optimal head, which was selected from the Pareto-optimal head shapes, were compared with those of the original train.

Optimization of vehicle compartment low frequency noise based on Radial Basis Function Neuro-Network Approximation Model

For reducing the vehicle compartment low frequency noise, the Optimal Latin hypercube sampling method was applied to perform experimental design for sampling in the factorial design space. The thickness parameters of the panels with larger acoustic contribution was considered as factors, as well as the vehicle mass, seventh rank modal frequency of body, peak sound pressure of test point and sound pressure root-mean-square value as responses. By using the RBF(radial basis function) neuro-network method, an approximation model of four responses about six factors was established. Further more, error analysis of established approximation model was performed in this paper. To optimize the panel’s thickness parameter, the adaptive simulated annealing algorithm was im-plemented. Optimization results show that the peak sound pressure of driver’s head was reduced by 4.45dB and 5.47dB at frequency 158HZ and 134Hz respec-tively. The test point pressure were significantly reduced at other frequency as well. The results indicate that through the optimization the vehicle interior cavity noise was reduced effectively, and the acoustical comfort of the vehicle was im-proved significantly.

Optimization on the impeller of a low-specific-speed centrifugal pump for hydraulic performance improvement

In order to widen the high-efficiency operating range of a low-specific-speed centrifugal pump, an optimization process for considering efficiencies under 1.0Q d and 1.4Q d is proposed. Three parameters, namely, the blade outlet width b 2, blade outlet angle β 2, and blade wrap angle φ, are selected as design variables. Impellers are generated using the optimal Latin hypercube sampling method. The pump efficiencies are calculated using the software CFX 14.5 at two operating points selected as objectives. Surrogate models are also constructed to analyze the relationship between the objectives and the design variables. Finally, the particle swarm optimization algorithm is applied to calculate the surrogate model to determine the best combination of the impeller parameters. The results show that the performance curve predicted by numerical simulation has a good agreement with the experimental results. Compared with the efficiencies of the original impeller, the hydraulic efficiencies of the optimized impeller are increased by 4.18% and 0.62% under 1.0Q d and 1.4Qd, respectively. The comparison of inner flow between the original pump and optimized one illustrates the improvement of performance. The optimization process can provide a useful reference on performance improvement of other pumps, even on reduction of pressure fluctuations.

Profile Design and Multifidelity Optimization of Solid Rocket Motor Nozzle

This paper presents a new profile modeling method and multifidelity optimization procedure for the solid rocket motor contoured nozzle design. Two quartic splines are proposed to construct the nozzle divergent section profile, and the coefficients of the splines' functions are calculated by a fortran program. Two-dimensional axisymmetric and three-dimensional compressible Navier–Stokes equations with Re-Normalisation Group (RNG) k-ε turbulent models solve the flow field as low- and high-fidelity models, respectively. An optimal Latin hypercube sampling method produces the sampling points, and Kriging functions establish the surrogate model combining with the low- and high-fidelity models. Finally, the adaptive simulated annealing algorithm is selected to complete the profile optimization, with the objectives of maximizing the thrust and the total pressure recovery coefficient. The optimization improves the thrust by 4.27%, and enhances the recovery coefficient by 4.63%. The result shows the proposed profile modeling method is feasible and effective to enhance the nozzle performance. The multifidelity optimization strategy is valid for improving the computational efficiency.

An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing

This paper proposes a new optimal Latin hypercube sampling method (OLHS) for design of a computer experiment. The new method is based on solving sequencing and continuous optimisation using simulated annealing. There are two sets of design variables used in the optimisation process: sequencing and real number variables. The special mutation operator is developed to deal with such design variables. The performance of the proposed numerical strategy is tested and compared with three established OLHS methods, namely genetic algorithm (GA), enhanced stochastic evolutionary algorithm (ESEA) and successive local enumeration (SLE). Based on 30 test problems with various design dimensions and numbers of sampling points, the proposed method gives the best results. The method can generate an optimum set of sampling points within reasonable computing time; therefore, it can be considered as a powerful tool for design of computer experiments.

Metamodeling Development for Vehicle Frontal Impact Simulation

Abstract Response surface methods or metamodels are commonly used to approximate large computationally expensive engineering systems. Five response surface methods are studied: Stepwise Regression, Moving Least Square, Kriging, Multiquadric, and Adaptive and Interactive Modeling System. A real-world frontal impact design problem is used as an example, which is a complex, highly nonlinear, transient, dynamic, large deformation finite element model. To study the accuracy of the metamodel, the optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. The Root Mean Square Error (RMSE) is used as the error indicator. Convergence rate, widely used in the arena of the finite element method for evaluating new element’s performance, was exploited in this vehicle impact example.