Latin Hypercube Design Of Experiments Research Articles

Innovative time efficient method to optimize buildings’ performance using Design of Experiment, Polynomial Regression and Genetic Algorithms

Dynamic thermal simulation use is essential for studying complex building systems. One of the major challenges to widely deploy optimization in this field’ engineering and research is the high computational cost to perform the required simulation-based iterations. To participate in overcoming this hindrance, we propose in this paper an innovative time efficient Multiobjective Optimization methodology, based on coupling Latin Hypercube Design of Experiments to Artificial Neural Network polynomial regression and Genetic Algorithms (GA). This method allows to benefit from the robustness of Genetic Algorithms and from the rapidity of prediction of polynomial regression. RBD-FAST sensitivity Analysis indexes are also generated without any extra-time. We successfully applied the method to analyse and optimize a constrained 8-objectives problem with 13 input parameters in six climatic zones in Morocco.

Estimating Economic Losses from Cyber-Attacks on Shipping Ports: An Optimization-Based Approach

The Maritime Transportation System (MTS) accounts for more than 80% of global merchandise trade in volume and roughly a sixth of the Total Gross Output of the United States. Given that national and global economies depend upon efficient supply chains, port stakeholders must develop security plans to respond to all hazards, natural and manmade. Given recent cyber attacks affecting shipping ports, along with the multi-billion dollar cyber insurance gap, ports need to understand the tradeoffs between increased competitiveness and increased risk through investment in automation and advanced logistics technologies. This article addresses the need to understand the economic impact of cyber attacks that affect shipping port operations and thereby enable risk assessments that holistically evaluate interactions among port Information Technology (IT) and Operational Technology (OT) systems. We extend Boland et al's Dynamic Discretization Discovery (DDD) algorithm to include capacity constraints and delay arcs to accommodate commodities arriving late due to disruption. Using a Nearly-Orthogonal Latin Hypercube (NOLH) experimental design, we construct disruption profiles based on actual cyber attacks that specify the range of operational effects of IT/OT dependencies on stakeholder transportation assets. Economic loss functions for seven commodity categories based on the willingness to pay literature are used to compute delay costs so that stakeholders can estimate the range of economic and operational impacts within a disruption profile. Results based on data provided by Port Everglades, FL, illustrate impacts at $80,000 and $1.2M on average for cyberattacks on landlord port and terminal operator assets during the first week in October, 2017. The runtime performance of our DDD algorithm improves on the state of the art by an order of magnitude and on larger problem sizes based on real-world port networks.

Optimization design of heat pipe heat exchanger using response surface methodology

In this paper, Optimization design of heat pipe heat exchanger (HPHX) is processed utilizing the Response Surface Methodology (RSM). The response surface model was built by regressive analysis using Latin hypercube experimental design method and numerical simulation. Through response surface analysis, it is found that the two input variables affecting the performance of HPHX are the heat pipe pitch and the Inlet and outlet distance. Moreover, the maximum value of the overall performance factor on the response surface is searched using genetic algorithm, and the optimal values of four input variables are obtained.

Using the hierarchical Kriging model to optimize the structural dynamics of rocket engines

Traditional fine models are often inefficient in optimizing the dynamics of complex structural systems such as large liquid rocket engines. To enhance the design efficiency, this paper proposes a fast optimization method based on finite element modeling, central Latin hypercube experimental design with minimax criteria, hierarchical Kriging surrogate model, and combined multi-island genetic algorithm + nonlinear sequential quadratic programming approach. First, a low-frequency dynamic fine finite element model of the entire engine structure was established, and the sampling points were obtained by considering the experimental design and a hierarchical Kriging model that describes the relationship between the design variables of the engine structure parameters and the modal frequency characteristics. Next, the height of the frame, size of the gimbal mount, and stiffness and installation angle of the servo mechanism were considered as design variables. To satisfy the design requirements in terms of the first modal frequency of the engine structure and realize the optimal design of the modal characteristics, the global optimization of the high-precision Kriging model was performed in the design space by using the hybrid optimization algorithm. Finally, the optimization results were substituted into the finite element model to perform the modal analysis, and modal tests were conducted to verify the effectiveness of the optimization method in realizing large-scale structural system optimization. The results indicated that the first modal frequency of the engine structure was increased from 7.53 Hz to 11.50 Hz and the optimization results could satisfy the requirements for the dynamics design. The proposed optimization design method can considerably improve the optimization efficiency by ensuring high accuracy of the results. The presented modeling strategies and optimization concepts can be applied to several engineering applications and provide novel solutions for the dynamic optimization problems of large and complex structures.

Flame spray pyrolysis optimization via statistics and machine learning

Flame spray pyrolysis (FSP) is an important manufacturing process whereby nanomaterials are produced through the combustion of atomized fuel containing dissolved precursor elements. While FSP has the potential to enable the scalable production of a wide range of next generation energy materials, it also has a multi-scale, multi-physics character, and a large number of processing variables. Optimizing the process for desirable material outcomes by traditional approaches is challenging. In this work, the processing parameter space is explored via a new and efficient methodology that includes statistical methods such as Latin hypercube design of experiments, machine learning surrogate modeling, and Bayesian optimization. As a result, the FSP process is optimized for enhanced performance. Specifically, in-situ particle size measurements are used to tailor the production of silica nanoparticles for a low spread in particle diameters with respect to the mean particle diameter, resulting in an improvement of 25.5% over the baseline within 15 experimental trials. In the process, the analysis reveals distinct domains of primary particle and agglomerated particle formation.

Lumbar Spine Response of Computational Finite Element Models in Multidirectional Spaceflight Landing Conditions.

The goals of this study are to compare the lumbar spine response variance between the hybrid III, test device for human occupant restraint (THOR), and global human body models consortium simplified 50th percentile (GHBMC M50-OS) finite element models and evaluate the sensitivity of lumbar spine injury metrics to multidirectional acceleration pulses for spaceflight landing conditions. The hybrid III, THOR, and GHBMC models were positioned in a baseline posture within a generic seat with side guards and a five-point restraint system. Thirteen boundary conditions, which were categorized as loading condition variables and environmental variables, were included in the parametric study using a Latin hypercube design of experiments. Each of the three models underwent 455 simulations for a total of 1365 simulations. The hybrid III and THOR models exhibited similar lumbar compression forces. The average lumbar compression force was 45% higher for hybrid III (2.2 ± 1.5 kN) and 51% higher for THOR (2.0 ± 1.6 kN) compared to GHBMC (1.3 ± 0.9 kN). Compared to hybrid III, THOR sustained an average 64% higher lumbar flexion moment and an average 436% higher lumbar extension moment. The GHBMC model sustained much lower bending moments compared to hybrid III and THOR. Regressions revealed that lumbar spine responses were more sensitive to loading condition variables than environmental variables across all models. This study quantified the intermodel lumbar spine response variations and sensitivity between hybrid III, THOR, and GHBMC. Results improve the understanding of lumbar spine response in spaceflight landings.

Approximate relations between Manhattan and Euclidean distance regarding Latin hypercube experimental design

Among several existing distance measures, perhaps Euclidean distance is the most used tool to calculate distances and then Manhattan distance measure, though which distance measure is suitable depends on the problems. In the field of Design of Experiments (DoEs) especially in simulation domain Latin Hypercube design (LHD) is a well-known approach to find out design points for experiments/simulations. Generally, randomly generated LHDs show poor space-filling property. But space-filling is one of the most required impotent properties for DoE. So researchers search optimal LHD in the sense of space-filling. Some authors considered Euclidean distance measure on the other hand some other authors considered Manhattan distance measure to find out optimal LHD regarding space-filling. It is obvious that both optimal LHDs are not identical. So it is a crucial asked - which measure provided better space-filling? The main problem is that there is no any relation among the distance measures especially Euclidean distance measure and Manhattan distance measure. In this article we have established some relations and bounds between Euclidean distance measures and Manhattan distance measures in perspective of LHD. Finally some experimental results are compared namely maximin LHDs measured by both Euclidean distance measure and Manhattan distance measures by using some proposed transformation techniques.

Prediction of Left Ventricular Mechanics Using Machine Learning.

The goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.

Modeling and multi-objective optimization of a bionic crash box with folding deformation

Traditional crash box is unable to efficiently solve the problem of bending deformation during the collision process, which limits the energy absorption performance and crashworthiness. This paper introduces the structure of cactus into the design of crash box and attempts to redesign a new one with stable folding deformation. By imitating the cactus characteristic, the bionic crash box consists of two parts: one is the corrugated angular structure, and the other is its thickness functionally gradient distribution along the axial direction. Based on the sensitivity analysis, the parameters which have great influences on the energy absorption performance are selected as the design variables. The multi-objective optimization design is conducted based on response surface model and Latin hypercube design of experiment. Simulation results show that the bionic crash box can effectively weaken the damage to the autobody and improve the energy absorption performance through stable folding deformation.

Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem

The increasing demands for travelling comfort and reduction of carbon dioxide emissions have been considered substantially in the stage of conceptual aircraft design. However, the design of a modern aircraft is a multidisciplinary process, which requires the coordination of information from several specific disciplines, such as structures, aerodynamics, control, etc. To address this problem with adequate accuracy, the multidisciplinary analysis and optimization (MAO) method is usually applied as a systematic and robust approach to solve such complex design issues arising from industries. Since MAO method is tedious and computationally expensive, genetic programming (GP)-based metamodeling techniques incorporating MAO are proposed as an effective approach to minimize the wing stiffness of a large aircraft subject to aerodynamic, aeroelastic and stability constraints in the conceptual design phase. Based on the linear small-disturbance theory, the state-space equation is employed for stability analysis. In the process of multidisciplinary analysis, aeroelastic response simulations are performed using Nastran. To construct metamodels representing the responses of the interests with high accuracy as well as less computational burden, optimal Latin hypercube design of experiments (DoE) is applied to determine the optimized distribution of sampling points. Following that, parametric optimization is carried out on metamodels to obtain the optimal wing geometry shape, elastic axis positions and stiffness distribution, and then the solution is verified by finite element simulations. Finally, the superiority of the GP-based metamodel technique over genetic algorithm is demonstrated by multidisciplinary design optimization of a representative beam-frame wing structure in terms of accuracy and efficiency. The results also show that GP metamodel-based strategy for solving MAO problems can provide valuable insights to tailoring parameters for the effective design of a large aircraft in the conceptual phase.

A novel integrated process–machine approach for designing customized milling machines

This paper provides a novel integrated approach for designing customized milling machines. Static stiffness matching design of milling machine is carried out according to the static stiffness requirement at TCP. Rapid evaluation approach of milling stability of milling machine with position-dependent has been developed. The theoretical model which can describe the relationships between and among milling stability, dynamic stiffness, and natural frequency has been established. Dynamic characteristics’ simulation of milling machine has been carried out based on CAD/CAE co-simulation analysis platform. The structural component mass can be changed by changing the critical dimension, and then, the rule of structural component mass influence on the natural frequency of the milling machine can be obtained by optimal Latin hypercube experimental design method. The lightweight design of milling machine has been achieved according to the rule. The approach improves the rapidity, parameterization, and digitization of customized milling machine design.

Coupled thermal–structural analysis and multi-objective optimization of a cutting-type energy-absorbing structure for subway vehicles

With the aim of improving passive safety protection in subway vehicles, this paper investigates a cutting energy-absorbing structure by means of experiment and simulation. The proposed structure comprises a cutting knife, an energy-absorbing tube, and a support tool. The Johnson-Cook material model is used to study the coupled thermal–structural cutting energy-absorbing process, and a finite-element model of the cutting energy-absorbing structure is validated using data from a cutting collision experiment. The sensitivity of each factor is discussed using extreme difference analysis to identify the effects of the cutting depth, cutting width, and cutting knife rake angle on the energy absorbed (EA) and the peak cutting force (PCF). Based on sample points obtained from an optimal Latin-hypercube experimental design, a relationship between the crashworthiness index and the design variables is formulated using polynomial-response-surface and radial-basis-function surrogate models. Through comprehensive error analysis, the most accurate surrogate model is used to optimize the crashworthiness of the structure. The multi-objective particle swarm optimization algorithm is applied to multi-objective optimization to obtain the maximum EA and minimum PCF. The weighting factor plays an important role in selecting the ideal Pareto solution, and the optimal solution is determined using the minimum distance selection method. The results allow us to determine the structure with the best crashworthiness, for which EA = 991 kJ and PCF = 1441 kN.

Hierarchical Optimization of Landing Performance for Lander with Adaptive Landing Gear

A parameterized dynamics analysis model of legged lander with adaptive landing gear was established. Based on the analysis model, the landing performances under various landing conditions were analyzed by the optimized Latin hypercube experimental design method. In order to improve the landing performances, a hierarchical optimization method was proposed considering the uncertainty of landing conditions. The optimization problem was divided into a higher level (hereafter the “leader”) and several lower levels (hereafter the “follower”). The followers took conditioning factors as design variables to find out the worst landing conditions, while the leader took buffer parameters as design variables to better the landing performance under worst conditions. First of all, sensitivity analysis of landing conditioning factors was carried out according to the results of experimental design. After the sensitive factors were screened out, the response surface models were established to reflect the complicated relationships between sensitive conditioning factors, buffer parameters and landing performance indexes. Finally, the response surface model was used for hierarchical optimization iteration to improve the computational efficiency. After selecting the optimum buffer parameters from the solution set, the dynamic model with the optimum parameters was simulated again under the same landing conditions as the simulation before. After optimization, nozzle performance against damage is improved by 5.24%, the acceleration overload is reduced by 5.74%, and the primary strut improves its performance by 21.10%.

Prediction Accuracy of Collision Indicators for Minibuses Based on an Approximate Model

An approximate model can be used to replace the real model to reduce the computing time and guarantee the feasibility of optimization. However, the approximate model must meet the required accuracy. The higher the accuracy of the approximate model, the higher the reliability of optimization results. In this study, a finite element model for the 40% offset impact of minibus was established, with the thickness of 10 plates in the front of the car body as the design variable and peak acceleration of B pillar lower end, the total mass, and the intrusion volume of dashboard beam, steering column hole, and clutch pedal as the response values. We obtained 70 sample points by the Latin hypercube experimental design method and built approximate models of design variables and the response. Then, we compared the relative error scatter, mean relative error, and decision coefficient of the response surface approximate model, radial basis function network approximate model, kriging approximate model, and orthogonal polynomial approximate model. Results show that the prediction accuracy of the response surface approximate model and radial basis function network approximate model in the peak acceleration of B pillar lower end and the intrusion volume of the steering column hole and clutch pedal does not meet the requirement. The orthogonal polynomial approximate model has a high prediction accuracy in total mass, but its prediction accuracy in other responses does not meet the requirement. In addition, all three approximate models are obviously influenced by the linear relationship between the response and the variables. The kriging approximate model meets the required prediction accuracy of the four responses and is less affected by the linear relationship. Thus, the kriging approximate model is suitable to replace the original model. Then, particle swarm optimization can be performed to optimize the kriging approximate model. This study shows that the kriging approximate model has high fitting precision, and the optimization results reach the expected aim.

Computational modeling and analysis of thoracolumbar spine fractures in frontal crash reconstruction

Objective: This study aimed to reconstruct 11 motor vehicle crashes (6 with thoracolumbar fractures and 5 without thoracolumbar fractures) and analyze the fracture mechanism, fracture predictors, and associated parameters affecting thoracolumbar spine response.Methods: Eleven frontal crashes were reconstructed with a finite element simplified vehicle model (SVM). The SVM was tuned to each case vehicle and the Total HUman Model for Safety (THUMS) Ver. 4.01 was scaled and positioned in a baseline configuration to mimic the documented precrash driver posture. The event data recorder crash pulse was applied as a boundary condition. For the 6 thoracolumbar fracture cases, 120 simulations to quantify uncertainty and response variation were performed using a Latin hypercube design of experiments (DOE) to vary seat track position, seatback angle, steering column angle, steering column position, and D-ring height. Vertebral loads and bending moments were analyzed, and lumbar spine indices (unadjusted and age-adjusted) were developed to quantify the combined loading effect. Maximum principal strain and stress data were collected in the vertebral cortical and trabecular bone. DOE data were fit to regression models to examine occupant positioning and thoracolumbar response correlations.Results: Of the 11 cases, both the vertebral compression force and bending moment progressively increased from superior to inferior vertebrae. Two thoracic spine fracture cases had higher average compression force and bending moment across all thoracic vertebral levels, compared to 9 cases without thoracic spine fractures (force: 1,200.6 vs. 640.8 N; moment: 13.7 vs. 9.2 Nm). Though there was no apparent difference in bending moment at the L1–L2 vertebrae, lumbar fracture cases exhibited higher vertebral bending moments in L3–L4 (fracture/nonfracture: 45.7 vs. 33.8 Nm). The unadjusted lumbar spine index correctly predicted thoracolumbar fracture occurrence for 9 of the 11 cases (sensitivity = 1.0; specificity = 0.6). The age-adjusted lumbar spine index correctly predicted thoracolumbar fracture occurrence for 10 of the 11 cases (sensitivity = 1.0; specificity = 0.8). The age-adjusted principal stress in the trabecular bone was an excellent indicator of fracture occurrence (sensitivity = 1.0; specificity = 1.0). A rearward seat track position and reclined seatback increased the thoracic spine bending moment by 111–329%. A more reclined seatback increased the lumbar force and bending moment by 16–165% and 67–172%, respectively.Conclusions: This study provided a computational framework for assessing thoracolumbar fractures and also quantified the effect of precrash driver posture on thoracolumbar response. Results aid in the evaluation of motor vehicle crash–induced vertebral fractures and the understanding of factors contributing to fracture risk.

Maximum energy conversion from human motion using piezoelectric flex transducer: A multi-level surrogate modeling strategy

Conventional engineering design optimization requires a large amount of expensive experimental tests from prototypes or computer simulations, which may result in an inefficient and unaffordable design process. In order to overcome these disadvantages, a surrogate model may be used to replace the prototype tests. To construct a surrogate model of sufficient accuracy from limited number of tests/simulations, a multi-level surrogate modeling strategy is introduced in this article. First, a chosen number of points determined by optimal Latin Hypercube Design of Experiments are used to generate global-level surrogate models with genetic programming and the fitness landscape can be explored by genetic algorithms for near-optimal solutions. Local-level surrogate models are constructed then from the extended-optimal Latin Hypercube samples in the vicinity of global optimum on the basis of a much smaller number of chosen points. As a result, an improved optimal design is achieved. The efficiency of this strategy is demonstrated by the parametric optimization design of a piezoelectric flex transducer energy harvester. The optimal design is verified by finite element simulations and the results show that the proposed multi-level surrogate modeling strategy has the advantages of faster convergence and more efficiency in comparison with the conventional single-single level surrogate modeling technique.

Numerical investigation of driver lower extremity injuries in finite element frontal crash reconstruction

ABSTRACTObjective: Lower extremity injuries are the most frequent Abbreviated Injury Scale (AIS) 2 injury for drivers in frontal crashes. The objective was to reconstruct 11 real-world motor vehicle crashes (2 with AIS 2+ distal lower extremity injury and 9 without lower extremity injury) and to analyze the vehicle parameters and driver attributes that affect injury risk.Methods: Eleven frontal crashes were reconstructed with a finite element simplified vehicle model (SVM) using a semi-automated optimization method. The SVM was tuned to each corresponding vehicle and the Total HUman Model for Safety (THUMS) Ver 4.01 was scaled and positioned in a baseline configuration to mimic the documented precrash driver posture. The event data recorder crash pulse was applied as the boundary condition for each case. Additionally, for the 2 cases with lower extremity injury, 120 simulations to quantify the uncertainty and response variation were performed varying the following parameters using a Latin hypercube design of experiment (DOE): seat track position, seatback angle, steering column angle, steering column position, and D-ring height. Injury metrics implemented within THUMS were calculated from the femur, tibia, and ankle and cross-compared among the 11 baseline cases using tibia index and multiple injury risk functions. Kinetic and kinematic data from the 120-simulation DOE were analyzed and fit to regression models to examine any causal relationship between occupant positioning and lower extremity injury risk.Results: Of the 11 real-world crashes, both cases with lower extremity injuries resulted in elevated tibia axial forces and resultant bending moments, compared to the 9 cases without lower extremity injury. The average tibia index of the 2 cases with distal lower extremity injury (left: 1.79; right: 1.19) was higher than that in the 9 cases without lower extremity injury (left: 1.16, P =.024; right: 0.82, P =.024). An increased risk of AIS 2+ tibia shaft (33.6%), distal tibia and hindfoot (20.0%), as well as ankle malleolar (14.5%) fracture was also observed for the injured compared to the noninjured cases. Rearward seat track position, reclined seat back angle, and reduced seat height were correlated with elevated tibia axial force and increased tibia index, imposing additional lower extremity injury risk.Conclusions: This study provides a computational framework for assessing lower extremity injuries and elucidates the effect of precrash driver posture on lower extremity injury risk while accounting for vehicle parameters and driver attributes. Results from the study aid in the evaluation of real-world injury data, the understanding of factors contributing to injury risk, and the prevention of lower extremity injuries.

Discrete Element Model Calibration Using Multi-Responses and Simulation of Corn Flow in a Commercial Grain Auger

Abstract. Grain augers are primary grain conveying equipment in agriculture. Quantitative prediction of dynamic grain flow in grain augers using discrete element modeling (DEM) has potential to support simulation-based engineering design of grain handling equipment. The objective of this study was to develop a DEM corn model using a multi-response calibration methodology and validation of combine-harvested corn flow in a commercial grain auger. Using a Latin hypercube design of experiment (DOE) sampling from four particle interaction DEM parameters values, 27 DEM simulations were generated for four DEM corn shape approximations (1-sphere, 2-spheres, 5-spheres, and 13-spheres) to create virtual DEM experiments of bucket-discharged and anchor-lifted angle of repose (AOR) tests. A surface meta-model was developed using the DEM interaction parameters as predictor variables, and normalized AOR expressed as a mean square error (MSE), i.e., the sum of square differences between DEM simulations and laboratory-measured AOR. Analysis of the MSE percentiles with lower error differences between DEM simulations and laboratory AOR and the computational effort required per simulation (h per simulation) showed that the 2-spheres DEM model had better performance than the 1-sphere, 5-spheres, and 13-spheres models. Using the best stepwise linear regression models of bucket AOR MSE (R2 of 0.9423 and RMSE of 94.56) and anchor AOR MSE (R2 of 0.5412 and RMSE of 78.02) and a surface profiler optimization technique, an optimized 2-spheres DEM corn model was generated. The DEM predicted AOR with relative errors of 8.5% for bucket AOR and 7.0% for anchor AOR. A DEM grain auger simulation used as a validation step also showed good agreement with the laboratory-measured steady-state mass flow rate (kg s-1) and static AOR (degrees) of corn piled on a flat surface, with DEM prediction relative error ranging from 2.8% to 9.6% and from 8.55% to 1.26%, respectively. Keywords: Corn, DEM, Discharge angle of repose, Discrete element modeling, Grain auger, Lift angle of repose.

Empirical modelling of hydraulic pumps and motors based upon the Latin hypercube sampling method

The effectiveness of orthogonal and Latin hypercube (LHS) experimental design strategies was compared in axial piston pump and radial piston motor testing. Stratified sampling via LHS was used to create test plans of varying sample size. Pump flow and motor torque-loss models were derived from the experimental results based on a comprehensive list of physically significant terms. The effectiveness of the sampling plans was evaluated by tracking the evolution of model errors using progressively sequenced regression. Progressively sequenced regression identified the minimum sample size required to achieve data saturation by incrementally increasing the number of data points included in the regression analysis. It was found that LHS produced higher fidelity models but reached data saturation no sooner than the orthogonal method. These results demonstrate the merit of combining LHS with progressively sequenced regression to improve empirical model fidelity and determine minimum sample-size requirements in hydraulic pump and motor testing.

Radial Basis Functional Model of Multi-Point Dieless Forming Process for Springback Reduction and Compensation

Springback in multi-point dieless forming (MDF) is a common problem because of the small deformation and blank holder free boundary condition. Numerical simulations are widely used in sheet metal forming to predict the springback. However, the computational time in using the numerical tools is time costly to find the optimal process parameters value. This study proposes radial basis function (RBF) to replace the numerical simulation model by using statistical analyses that are based on a design of experiment (DOE). Punch holding time, blank thickness, and curvature radius are chosen as effective process parameters for determining the springback. The Latin hypercube DOE method facilitates statistical analyses and the extraction of a prediction model in the experimental process parameter domain. Finite element (FE) simulation model is conducted in the ABAQUS commercial software to generate the springback responses of the training and testing samples. The genetic algorithm is applied to find the optimal value for reducing and compensating the induced springback for the different blank thicknesses using the developed RBF prediction model. Finally, the RBF numerical result is verified by comparing with the FE simulation result of the optimal process parameters and both results show that the springback is almost negligible from the target shape.