Optimal Latin Hypercube Sampling Research Articles

Improvements in Probabilistic Strategies and Their Application to Turbomachinery

This paper discusses various strategies for probabilistic analysis, with a focus on typical engineering applications. The emphasis is on sampling methods and sensitivity analysis. A new sampling method, Latinized particle sampling, is introduced and compared to existing sampling methods. While it can increase the quality of surrogate models, an optimized Latin hypercube sampling is mostly preferable as it shows slightly better results. In sensitivity analysis, the difficulty lies in correlated input variables, which are typical in engineering applications. First, the Sobol indices and the Shapley values are explained using an intuitive example. Then, the modified coefficient of importance is introduced as a new sensitivity measure, which can be used to reliably identify input variables without functional influence. Finally, these results are applied to a turbomachinery test case. In this case, the flow field of a compressor row is investigated, where the blades are subjected to geometric variability. The profile parameters used to describe the geometric variability are correlated. It is shown that the variability of the maximum camber and the thickness of the leading edge have a decisive influence on the variability of the isentropic efficiency.

Enhancing thermal transfer in airfoil structures through advanced simulation techniques and MOPSO optimization

This research employs advanced simulation techniques by integrating Python, CAD, ANSYS Fluent, and other execution programs, to optimize the thermal transfer performance of an airfoil structure. The study involves a design of experiments (DOE) analysis employing optimal Latin hypercube (OLH) sampling to study the influence of airfoil structural parameters on Nu, f, and comprehensive heat index (CHI). Subsequently, multi-objective particle swarm optimization (MOPSO) is applied, resulting in a remarkable 93.4% increase in CHI, elevating it from 101.13 to 195.61. Experimental validation of the optimized airfoil structure demonstrates close agreement with simulated results, affirming the reliability of our numerical simulations. The results establish the superior heatexchange capabilities of the optimized airfoil structure over the unoptimized reference airfoil and the traditional circular structure. This research contributes significantly to the structural optimization of heat exchange equipment, particularly for configurations characterized by substantial height-to-diameter ratios.

Application of Artificial Neural Networks to Numerical Homogenization of the Precast Hollow-Core Concrete Slabs

The main goal of this work is to combine the usage of the numerical homogenization technique for determining the effective properties of representative volume elements with artificial neural networks. The effective properties are defined according to the classical laminate theory. The purpose is to create and train a rapid surrogate model for the quick calculation of the mechanical properties of hollow concrete slabs. First, the homogenization algorithm was implemented, which determines membrane, bending and transverse shearing properties of a given parametrized hollow-core precast slab reinforced with steel bars. The algorithm uses the finite element mesh but does not require a formal solution of the finite element method problem. Second, the learning and training artificial intelligence framework was created and fed with a dataset obtained by optimal Latin hypercube sampling. In the study, a multilayer perceptron type of artificial neural network was used. This allows for obtaining rapid calculations of the effective properties of a particular hollow-core precast slab by using a surrogate model. In the paper, it has been proven that such a model, obtained via complex numerical calculations, gives a very accurate estimation of the properties and can be used in many practical tasks, such as optimization problems or computer-aided design decisions. Above all, the efficient setup of the artificial neural network has been sought and presented.

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.

Structural optimization design of ice abrasive water jet nozzle based on multi-objective algorithm

To enhance the cleaning efficiency of the ice abrasive water jet (IAWJ), the nozzle in the jet structure was optimized. The cleaning effect of nozzle with different structural design is different. The design variables include the geometric parameters of the nozzle's structure and the flow process parameters of the jet. The maximum wall static pressure, outlet velocity and wash width are the optimization objectives. Based on the Optimal Latin Hypercube Sampling (OLHS) method, 50 sets of sample capacity were designed for simulation calculation. The parameter functions associated with the three objectives were fitted by MATLAB. The Competitive mechanism multi-objective particle swarm optimizer (CMOPSO) algorithm was used to optimize the nozzle to improve the cleaning effect, which was verified with the test results. The inlet pressure and outlet diameter are critical factors influencing the cleaning effect of the IAWJ. The maximum wall static pressure produced by the optimized nozzle is about 4.5% higher than that of the ordinary cosine nozzle. The cleaning effect of the optimized nozzle is 10% higher than that of the ordinary cosine nozzle, which is verified by the experiments. The optimization of the nozzle serves as a valuable reference for the nozzle structure design of the cleaning machine.

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.

Surrogate-based optimization design for surface texture of helical pair in helical hydraulic rotary actuator

A good surface texture design can effectively improve the tribological performance of the helical pair within a helical hydraulic rotary actuator(HHRA). However, the optimization design process can be time-consuming due to the multiple design variables involved and the complexity of the mathematical model. This paper proposes a modified efficient global optimization (MEGO) method for solving such demanding surface texture design challenges. The MEGO utilizes a Kriging model with the optimized Latin hypercube sampling (OLHS) for initial sampling and the proposed modified expected improvement (MEI) function for sequential sampling. A comparative study of several global optimization algorithms with the MEGO on the surface texture design is performed. Subsequently, surrogate-based optimization and parameter analysis are carried out, resulting in the identification of an optimal set of texture parameters. The findings reveal the superiority of the MEGO in both model prediction accuracy and refinement of minima. Moreover, compared to the base design, the friction coefficient can be reduced by up to 45.2%.

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.

Optimized design of wind turbine airfoil aerodynamic performance and structural strength based on surrogate model

Though offshore wind turbines have great potential for applications in ocean energy harvesting, their subject to complex unsteady aerodynamic loads. To obtain wind turbine airfoils with both aerodynamic performance and structural strength, an airfoil optimization method was proposed by adding the torsion constant to the objective function under the premise of improving the lift-to-drag ratio. The optimization method characterizes the airfoil geometric profile by using Class/Shape function transformation (CST) parameterization. The airfoil aerodynamics and the structural properties were solved by the computational fluid dynamics (CFD) method and Matlab program, respectively. To reduce the number of CFD calculations, a Kriging surrogate model was established. The combination of an optimized Latin hypercube sampling method and expected improvement (EI) points infill criteria is to improve surrogate modeling efficiency. The NREL 5 MW wind turbine blade was used as the research object. The NACA64618 with 18% relative thickness, the DU91-W2-250 with 25% and the DU97-W-350 with 35% were optimized by assigning different weights to aerodynamic and structural objectives based on airfoil position in the blade. The results showed that the aerodynamic performance of the optimized airfoils was improved. Subsequently, the three optimized airfoils were replaced in the same positions of the blade for lay-up design. The blade structural properties were calculated by finite element method (FEM) and it found that the blade torsion angle was reduced, which indicated that adding structural objectives in the airfoil optimization could enhance the blade structural performance.

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.

Intelligent Optimization Design of a Phononic Crystal Air-Coupled Ultrasound Transducer.

To further improve the operational performance of a phononic crystal air-coupled ultrasonic transducer while reducing the number of simulations, an intelligent optimization design strategy is proposed by combining finite element simulation analysis and artificial intelligence (AI) methods. In the proposed strategy, the structural design parameters of 1-3 piezoelectric composites and acoustic impedance gradient matching layer are sampled using the optimal Latin hypercube sampling (OLHS) method. Moreover, the COMSOL software is utilized to calculate the performance parameters of the transducer. Based on the simulation data, a radial basis function neural network (RBFNN) model is trained to establish the relationship between the design parameters and the performance parameters. The accuracy of the approximation model is verified through linear regression plots and statistical methods. Finally, the NSGA-II algorithm is used to determine the design parameters of the transducer. After optimization, the band gap widths of the piezoelectric composites and acoustic impedance gradient matching layer are increased by 16 kHz and 13.5 kHz, respectively. Additionally, the -6 dB bandwidth of the transducer is expanded by 11.5%. The simulation results and experimental results are consistent with the design objectives, which confirms the effectiveness of the design strategy. This work provides a feasible strategy for the design of high-performance air-coupled ultrasonic transducers, which is of great significance for the development of non-destructive testing technology.

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 and Multi-Objective Optimization Strategy of the Curing Profile for Autoclave Processed Thick Composite Laminates.

To mitigate the risk of manufacturing defects and improve the efficiency of the autoclave-processed thick composite component curing process, parameter sensitivity analysis and optimization of the curing profile were conducted using a finite element model, Sobol sensitivity analysis, and the multi-objective optimization method. The FE model based on the heat transfer and cure kinetics modules was developed by the user subroutine in ABAQUS and validated by experimental data. The effects of thickness, stacking sequence, and mold material on the maximum temperature (Tmax), temperature gradient (ΔT), and degree of curing (DoC) were discussed. Next, parameter sensitivity was tested to identify critical curing process parameters that have significant effects on Tmax, DoC, and curing time cycle (tcycle). A multi-objective optimization strategy was developed by combining the optimal Latin hypercube sampling, radial basis function (RBF), and non-dominated sorting genetic algorithm-II (NSGA-II) methods. The results showed that the established FE model could predict the temperature profile and DoC profile accurately. Tmax always occurred in the mid-point regardless of laminate thickness; the Tmax and ΔT increased non-linearly with the increasing laminate thickness; but the DoC was affected slightly by the laminate thickness. The stacking sequence has little influence on the Tmax, ΔT, and DoC of laminate. The mold material mainly affected the uniformity of the temperature field. The ΔT of aluminum mold was the highest, followed by copper mold and invar steel mold. Tmax and tcycle were mainly affected by the dwell temperature T2, and DoC was mainly affected by dwell time dt1 and dwell temperature T1. The multi-objective optimized curing profile could reduce the Tmax and tcycle by 2.2% and 16.1%, respectively, and maintain the maximum DoC at 0.91. This work provides guidance on the practical design of cure profiles for thick composite parts.

Efficient uncertainty quantification for seawater intrusion prediction using Optimized sampling and Null Space Monte Carlo method

Uncertainty in environmental modeling predictions, stemming from parameter estimation, is a crucial challenge that must be addressed to ensure effective decision-making. Limited field measurements, high computational costs, and a lack of guidance in estimating measurement uncertainty further compound this challenge, particularly for highly parameterized complex models. In this study, we propose a novel and computationally efficient framework for quantifying predictive uncertainty that can be applied to a range of environmental modeling contexts. The novel components of the framework include efficient parameter space sampling using an Optimized Latin hypercube sampling strategy, and applying the Null Space Monte Carlo method (NSMC) along with a developed filtering technique. The NSMC generates sample sets to calibrate the model while exploring the null space. This space contains parameter combinations that are not sufficiently supported by observations. The filtering technique omits low-potential parameter sets from undergoing model calibration. The framework was tested on the seawater intrusion (SWI) model of Wadi Ham aquifer in the United Arab Emirates (UAE) to investigate aquifer sustainability in 2050. Our results demonstrate the importance of incorporating direct and indirect measurements of heads, salinity, and geophysical survey data into the calibration dataset to reduce uncertainty in salinity predictions. The extent of SWI for multiple calibrated parameter sets varied by 4.5% to 11% relative to their means at two main pumping fields. We conclude, with a moderate to a high degree of certainty, that SWI is a serious threat to these fields, and actions are needed to protect the aquifer from salinization. Additionally, variations in SWI length under different geological conditions illustrate regions of high uncertainty that require further data collection. Our framework effectively reduced and quantified prediction uncertainty and provides decision-makers with critical information to inform risk management strategies.

Control Parameters Optimization of Accumulator in Hydraulic Power Take-Off System for Eccentric Rotating Wave Energy Converter

To improve the efficiency and stability of an eccentric rotating wave energy converter (ERWEC), the adaptive hydraulic power-take-off (PTO) system with an accumulator is designed and developed. Experiments are performed to analyze the effects of trigger pressure, delay time, and open state duration on average output power and power fluctuation index. The results show that the effects of those three control parameters of accumulator on output power are strongly coupled. The experimental examples are designed based on the optimal Latin hypercube sampling (OLHS) method, and the nonparameterized agent models of control parameters to output power indices are established based on the Gaussian process regression (GPR) method. With the help of sensitivity analysis, it is found that the coupled effect of delay time and open state duration on the power fluctuation index is greater than that on the average output power. Furthermore, the optimal combination of control parameters is obtained by non-dominated sorting genetic algorithm-III (NSGA-III), which improves the amount and stability of output power from a hydraulic PTO system. This paper is of important significance for parameter setting of hydraulic PTO systems with an accumulator for wave energy converter, and provides the basis for the real-time adjustment of control parameters under complex sea conditions.

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 hollow shaft direct drive motor

Surface permanent magnet synchronous motor (SPMSM) is widely used in low-speed and high torque permanent magnet synchronous motor. A multi-objective optimization method of hollow shaft direct drive motor (HSDDM) for double direct drive feed system (DDFS) is proposed in this paper. Several dimensions of HSDDM are considered in the proposed design procedure including pole embrace, thickness of magnet, eccentric distance, and air gap length. A multi-objective optimization model is established to minimize cogging torque, maximize efficiency, and minimize the magnet weight. The Optimized Latin hypercube sampling (OLHS) is used to design the experimental samples, and the sampling results are calculated by the finite element method (FEM). The Kring approximate model is established according to the sampling results. Based on the established approximate model, NSGA II multi-objective genetic algorithm is used to optimize the HSDDM. Compared with that before optimization, the efficiency after optimization is increased by 4.08%, the cogging torque is reduced by 86.78%, and the magnet weight is reduced by 20.24%. Eventually, the integration of NSGA-II and FEM provides an effective approach to obtain the optimal design of HSDDM.

Simulation uncertainty determination of single flank rolling tests using monte carlo simulation and skin model shapes for zero defect manufacturing of micro gears

Simulative gear rolling enables the integration of function-oriented quality assurance into production processes for Zero Defect Manufacturing (ZDM). A simulated single flank rolling test can be carried out using inline measurements. With the aim of integration for the control of production parameters and a functional forecast, this paper aims at an uncertainty evaluation of an analytic tooth contact analysis software. Based on optical measurements of focus variation technology and actual micro gear test facility procedures, task-specific simulation uncertainties for the four parameters of the single flank rolling inspection are evaluated. This approach uses an optimized Latin Hypercube Sampling (LHS) approach to generate artificial gear point clouds with specified deviations for a Monte Carlo simulation (MCS) based on an adaptive scheme of the Guide to the Expression of Uncertainty in Measurement (GUM) for determining model uncertainties. It was shown that the fast simulative results have a relatively low expanded uncertainty of less than 6 µm. The use case is a high-volume micro-production.

Study on an Assembly Prediction Method of RV Reducer Based on IGWO Algorithm and SVR Model

This paper proposes a new method for predicting rotation error based on improved grey wolf-optimized support vector regression (IGWO-SVR), because the existing rotation error research methods cannot meet the production beat and product quality requirements of enterprises, because of the disadvantages of its being time-consuming and having poor calculation accuracy. First, the grey wolf algorithm is improved based on the optimal Latin hypercube sampling initialization, nonlinear convergence factor, and dynamic weights to improve its accuracy in optimizing the parameters of the support vector regression (SVR) model. Then, the IGWO-SVR prediction model between the manufacturing error of critical parts and the rotation error is established with the RV-40E reducer as a case. The results show that the improved grey wolf algorithm shows better parameter optimization performance, and the IGWO-SVR method shows better prediction performance than the existing back propagation (BP) neural network and BP neural network optimized by the sparrow search algorithm rotation error prediction methods, as well as the SVR models optimized by particle swarm algorithm and grey wolf algorithm. The mean squared error of IGWO-SVR model is 0.026, the running time is 7.843 s, and the maximum relative error is 13.5%, which can meet the requirements of production beat and product quality. Therefore, the IGWO-SVR method can be well applied to the rotate vector (RV) reducer parts-matching model to improve product quality and reduce rework rate and cost.

Vibration Performance Analysis and Multi-Objective Optimization Design of a Tractor Scissor Seat Suspension System

The combination of characteristic parameters is the key and difficult point to improving the vibration attenuation of scissor seat suspension. This paper proposes a multi-objective optimization method based on entropy weight gray correlation to optimize the combination of characteristic parameters with better vibration attenuation. The differential equation of seat suspension motion is derived through mechanical analysis, and a simplified driver seat suspension single degree of freedom model is constructed. The range of spring stiffness and damper damping is calculated theoretically. Through main effect analysis and analysis of contribution, the main influencing factors of seat suspension vibration attenuation are studied, and the influence correlation of the main factors is analyzed. On this basis, the spring stiffness and damper damping are taken as control variables, and the upper plane acceleration, displacement, and transfer rate of the seat suspension are taken as optimization objectives. The Optimal Latin Hypercube Sampling (OLHS) was used to sample the Design of Experiments (DoE), fit the RBF surrogate model, and screen the optimal solution based on the MNSGA-II algorithm and entropy weight gray relation ranking method. The comparative analysis of the performance before and after optimization shows that the vibration reduction performance response indexes of the acceleration, displacement, and transmissibility of the optimized seats are increased by 66.41%, 2.31%, and 8.19%, respectively. The design and optimization method proposed in this study has a significant effect on the vibration reduction of seats, which provides a reference for the optimization of the vibration reduction performance of seat suspension.