Latin Hypercube Design Research Articles

Head injury metric response in finite element ATDs and a human body model in multidirectional loading regimes

Objective: The objective was to quantify head injury metric sensitivity of the 50th percentile male Hybrid III, THOR, and Global Human Body Models Consortium simplified occupant (GHBMC M50-OS) to changes in loading conditions in loading regimes that may be experienced by occupants of spaceflight vehicles or highly autonomous vehicles (HAVs) with nontraditional seating configurations.Methods: A Latin hypercube (LHD) design of experiments (DOE) was employed to develop boundary conditions for 455 unique acceleration profiles. Three previously validated finite element (FE) models of the Hybrid III anthropomorphic test device (ATD), THOR ATD, and GHBMC M50-OS were positioned in an upright 90°-90°-90° seat and with a 5-point belt. Acceleration pulses were applied to each of the three occupants in the ± X, +Y, and ± Z directions, with peak resultant acceleration magnitudes ranging from 5 to 20 G and times to peak ranging from 32.5 to 120.8 ms with duration 250 ms, resulting in 1,248 simulations. Head injury metrics included peak linear head acceleration, peak rotational head acceleration, head injury criteria (HIC15), and brain injury criteria (BrIC). Injury metrics were regressed against boundary condition parameters using 2nd order multiple polynomial regression, and compared between occupants using matched pairs Wilcoxon signed rank analysis.Results: Across the 416 matched-simulations that reached normal termination with all three models, HIC15 values ranged from 1.0–396.5 (Hybrid III), 1.2–327.9 (THOR), and 0.6–585.6 (GHBMC). BrIC ranged from 0.03–0.95 (Hybrid III), 0.03–1.21 (THOR), and 0.04–0.84 (GHBMC). Wilcoxon signed rank analysis demonstrated significant pairwise differences between each of the three occupant models for head injury metrics. For HIC15, the largest divergence between GHBMC and the ATDs was observed in simulations with components of combined underbody and rear impact loading. The three models performed most similarly with respect to BrIC output when loaded in a frontal direction. Both the GHBMC and the Hybrid III produced lower values of BrIC than the THOR on average, with the differences most pronounced in rear impact loading.Conclusion: In conclusion, observed differences between the occupant models’ head injury metric output were quantified. Loading direction had a large effect on metric outcome and metric comparability across models, with frontal and rear impacts with low vertical acceleration tending to be the most similar. One explanation for these differences could be the differences in neck stiffness between the models that allowed more rotation in the GHBMC and THOR. Care should be taken when using ATDs as human volunteer surrogates in these low energy events.

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.

Bayesian set pair analysis and machine learning based ensemble surrogates for optimal multi-aquifer system remediation design

Surrogate models are often adopted to substitute computationally intensive groundwater simulation models for aquifer management due to their high effectiveness and computing efficiency. However, solutions of using only one surrogate model are prone to large prediction uncertainty. This study compares individual surrogate models and an ensemble surrogate model in an optimal groundwater remediation design problem. Three machine learning based surrogate models (response surface regression model, artificial neural network and support vector machine) were developed to replace a high-fidelity solute transport model for predicting saltwater intrusion and assisting saltwater scavenging design. An optimal Latin hypercube design was employed to generate training and testing datasets. Set pair analysis was employed to construct a more reliable ensemble surrogate and to address prediction uncertainty arising from individual surrogate models. Bayesian set pair weights were derived by utilizing full information from both training and testing data and improved typical set pair weights. The individual and ensemble surrogate models were applied to the salinization remediation problem in the Baton Rouge area, southeast Louisiana. The optimal remediation design includes two conflicting objectives: minimizing total groundwater extraction from a horizontal scavenger well while maximizing chloride concentration difference to the MCL (maximum contamination level) at monitoring locations. NSGA-II (Non-dominated Sorting Genetic Algorithm II) was employed to solve the nonlinear optimization model and obtain Pareto-optimal pumping schedules. The optimal pumping schedules from ensemble surrogate models and individual surrogate models were verified by the solute transport model. The study found that Bayesian set pair analysis builds robust ensemble surrogates and accounts for model prediction uncertainty. The ensemble-surrogate-assisted optimization model provides stable and reliable solutions while considerably alleviating computational burden.

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering

Abstract We perform an ensemble of N-body simulations with 20483 particles for 101 flat wCDM cosmological models sampled based on a maximin distance sliced Latin hypercube design. By using the halo catalogs extracted at multiple redshifts in the range of z = [0,1.48], we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo–matter cross-correlation, and halo autocorrelation as a function of halo masses, redshift, separations, and cosmological models based on principal component analysis and Gaussian process regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of N-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo–matter cross-correlation, relevant for galaxy–galaxy weak lensing, with an accuracy better than 2% and the halo autocorrelation, relevant for galaxy clustering correlation, with an accuracy better than 4%. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the concentration–mass relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo–galaxy connection, such as the halo occupation distribution at the equation level, instead of using the mock catalogs to make accurate predictions of galaxy clustering statistics, such as galaxy–galaxy weak lensing and the projected correlation function for any model within the wCDM cosmologies, in a few CPU seconds.

Optimization of pre-swirl nozzle shape and radial location to increase discharge coefficient and temperature drop

Hole-type pre-swirl nozzle was optimized using CFD analysis and experiments. CFD methodologies were validated by comparing the CFD results with experiments. Four design variables were considered in the optimization process: Nozzle inlet length (L), outlet length (l), inlet diameter (D), and radial location (rp). The optimization process included the optimal Latin hypercube design sampling method with the Kriging surrogate model and genetic algorithm. The single-objective optimization was performed to maximize the discharge coefficient. Results showed that the optimized nozzle reduced total pressure losses and increased mass flow rate. Total temperature drop effectiveness was increased from 0.07 to 0.29. The total temperature in pre-swirl system could be characterized as the reduction in temperature by nozzle acceleration and elevation by aerodynamic losses due to friction and viscous effects in the system. The optimized model showed a discharge coefficient of 0.846, which was 31.7 % higher than the baseline condition. By improving the discharge coefficient the pre-swirl system reduced aerodynamic losses, and the mass flow rate was increased at certain pressure ratios or satisfied the pressure margin for blade cooling.

The nlrx r package: A next‐generation framework for reproducible NetLogo model analyses

Abstract Agent‐based models find wide application in all fields of science where large‐scale patterns emerge from properties of individuals. Due to increasing capacities of computing resources it was possible to improve the level of detail and structural realism of next‐generation models in recent years. However, this is at the expense of increased model complexity, which requires more efficient tools for model exploration, analysis and documentation that enable reproducibility, repeatability and parallelization. NetLogo is a widely used environment for agent‐based model development, but it does not provide sufficient built‐in tools for extensive model exploration, such as sensitivity analyses. One tool for controlling NetLogo externally is the r‐package RNetLogo. However, this package is not suited for efficient, reproducible research as it has stability and resource allocation issues, is not straightforward to be setup and used on high performance computing clusters and does not provide utilities, such as storing and exchanging metadata, in an easy way. We present the r‐package nlrx, which overcomes stability and resource allocation issues by running NetLogo simulations via dynamically created XML experiment files. Class objects make setting up experiments more convenient and helper functions provide many parameter exploration approaches, such as Latin Hypercube designs, Sobol sensitivity analyses or optimization approaches. Output is automatically collected in user‐friendly formats and can be post‐processed with provided utility functions. nlrx enables reproducibility by storing all relevant information and simulation output of experiments in one r object which can conveniently be archived and shared. We provide a detailed description of the nlrx package functions and the overall workflow. We also present a use case scenario using a NetLogo model, for which we performed a sensitivity analysis and a genetic algorithm optimization. The nlrx package is the first framework for documentation and application of reproducible NetLogo simulation model analysis.

Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.

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.

Modification of the Maximin and ϕp (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points

This article proposes a sampling technique that delivers robust designs, that is, point sets selected from a design domain in the shape of a unit hypercube. The designs are guaranteed to provide a statistically uniform point distribution, meaning that every location has the same probability of being selected. Moreover, the designs are sample uniform, meaning that each individual design has its points spread evenly throughout the domain. The sample uniformity (often measured via a discrepancy criterion) is achieved using distance-based criteria ( or Maximin), that is, criteria normally used in space-filling designs. We show that the standard intersite metrics employed in distance-based criteria (Maximin and (phi)) do not deliver statistically uniform designs. Similarly, designs optimized via centered L2 discrepancy or support points are also not statistically uniform. When these designs (after optimization based on intersite distances) are used for Monte Carlo type of integration, their statistical nonuniformity is a serious problem as it may lead to a systematic bias. This article proposes using a periodic metric to guarantee the statistical uniformity of the family of distance-based designs. The presented designs used as benchmarks in the article are only taken from the class of Latin hypercube designs, which forces univariate projections to be uniform and improves accuracy in Monte Carlo integration of some functions. Supplementary materials for this article are available online.

Thermo-mechanical optimization of metallic thermal protection system under aerodynamic heating

This paper details the application of the finite element model, Bayesian regularized neural network, and genetic algorithm for metallic thermal protection system parameter optimization. The object is to minimize the structure weight and satisfy multiple performance constraints which consist of the deformation of the top face sheet, the stress around the lug hole, the stress of the honeycomb core, and the inner temperature. Firstly, a high-fidelity thermo-mechanical coupled finite element model was established to investigate the thermal and mechanical properties of the metallic thermal protection system. Then, surrogate models were constructed based on the Bayesian regularized neural network which assigns a probabilistic nature to the network weights and biases and allows the network automatically and optimally penalize complex models. To guarantee full exploration of the design space, an optimal orthogonal-maximin Latin hypercube design was adopted and modified to generate preliminary sampling points. Finally, an approach for genetic algorithm constraint handling, stochastic ranking, was introduced and modified by multiple constraint ranking to handle constraints. In addition, a sensitivity analysis was performed to disclose the effects of individual design variables on the thermal and mechanical responses. The results indicate that the structure mass is decreased by 41.2 % when compared to the initial design and all the constraints are satisfied.

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.

A fast optimal Latin hypercube design method using an improved translational propagation algorithm

ABSTRACTTo further improve the space-filling quality and computational efficiency of the translational propagation algorithm, especially for high-dimensional and large-scale sampling problems, this article presents an improved translational propagation algorithm (iTPA). First, a novel uniform translating process is proposed to better allocate sample points. Second, the resizing process is improved to relieve its adverse influence on the space-filling quality. Comparative studies demonstrate the appealing merits of iTPA: (i) iTPA generally outperforms the existing optimization-based Latin hypercube design (LHD) methods; (ii) for high-dimensional and large-scale sampling problems, the computational efficiency of iTPA is dramatically improved and insensitive to sampling dimension and scale; (iii) iterations of iTPA can be used to enrich available LHDs and further upgrade the space-filling quality. Finally, an engineering example is presented to demonstrate the benefit of iTPA in improving the accuracy of surrogates.

Sampling Design Method of Fast Optimal Latin Hypercube

In engineering design optimization, the optimal sampling design method is usually used to solve large-scale and complex system problems. A sampling design (FOLHD) method of fast optimal Latin hypercube is proposed in order to overcome the time-consuming and poor efficiency of the traditional optimal sampling design methods. FOLHD algorithm is based on the inspiration that a near optimal large-scale Latin hypercube design can be established by a small-scale initial sample generated by using Successive Local Enumeration method and Translational Propagation algorithm. Moreover, a sampling resizing strategy is presented to generate samples with arbitrary size and owing good space-filling and projective properties. Comparing with the several existing sampling design methods, FOLHD is much more efficient in terms of the computation efficiency and sampling properties.

A hybrid meta-model based global optimization method for expensive problems

The meta-model based global optimization algorithms usually select the new promising points from a large set of points, which are generated using the Latin hypercube design (LHD) and evaluated by the meta-model. Once the poor points are generated by the random number based LHD, the desired results may not be obtained. In this work, a hybrid meta-model based global optimization method (HMGO) is proposed. In this method, three different meta-model, kriging, radial basis functions (RBF) and quadratic function (QF) are used together in the search process. And multiple sets of large points are generated and multiple screening strategy is used for the selection of the new promising points to avoid the poor points. Through test by six benchmark math function with the number of the variables ranging from 10 to 24 and compared with the famous efficient global optimization (EGO), the proposed method shows excellent accuracy, efficiency and robustness. The HMGO method is then applied in a vehicle lightweight design problem with 30 design variables, desired results have been obtained.

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.

Flexible sliced Latin hypercube designs with slices of different sizes

Sliced Latin hypercube designs (SLHDs) are widely used in various computer experiments. Literatures concerning the construction of SLHDs are all about constructing SLHDs with slices of the same size. However, in some cases, e.g. when an experiment with multiple computer models having different complexities or a sequential experiment with varying costs in different periods is considered, SLHDs with slices of different sizes are preferable. In this paper, we propose a new class of SLHD, named the flexible SLHD, in which the whole design is a Latin hypercube design (LHD), and each slice is also an LHD when its levels being properly collapsed, the difference lies in that its slices may have different run sizes. Several methods for constructing such designs are developed. Theoretical results on the constructed designs are derived, and discussion on the slice sizes of the constructed flexible SLHDs is provided. Furthermore, an optimization algorithm is developed to improve the space-filling property of the constructed SLHDs. The newly proposed flexible SLHD is also a special nested LHD (Qian in Biometrika 96:957–970, 2009), each of its slice can be viewed as a small LHD nested in the whole design.

A methodology for calibration of traffic micro-simulator for urban heterogeneous traffic operations

Traffic micro-simulation is a widely accepted tool in many countries for the evaluation and assessment of alternative design schemes. However, for several developing countries, replicating heterogeneous, non-lane based traffic in a micro-simulation framework is gaining increased importance and still remains a challenge due to its complexity. The present study demonstrates a methodology to calibrate a traffic micro-simulation model giving due consideration to vehicle-class specific driver behavior in an urban Indian scenario for a midblock section and an intersection approach in Kolkata. The sensitive parameters affecting the driver behavior were identified for every vehicle type using Latin Hypercube design, taking vehicle class specific travel time as a performance measure. Linear regression models were developed for each vehicle class considering the sensitive driving behavior parameters. The models highlight that the dependency of measure of effectiveness (MOE) of one vehicle type is not only limited to its own driver behavior but also on parameters of other vehicle classes. A genetic algorithm based optimization was adopted to obtain optimal parameter sets for different vehicle classes. The optimum values were found to vary significantly across all vehicle classes at a 95% confidence level. Single and multi-criteria calibration principles are also implemented to yield much more realistic results and subsequently minimizing weighted error for all vehicle classes. • A traffic micro-simulation calibration methodology for heterogeneous traffic is proposed. • Linear regression models using sensitive parameters were developed. • Genetic algorithm based optimization was adopted to obtain optimal parameter values. • Different sets of optimal driving behavior parameter for different vehicle classes are suggested. • The optimal parameter sets were found to vary significantly across vehicle classes.

Epistemic uncertainty-based reliability analysis for engineering system with hybrid evidence and fuzzy variables

With the rapid development of reliability analysis theory, the safety assessment for engineering systems with hybrid epistemic uncertainties has received increasing attentions. To overcome the imperfection of traditional single-uncertainty modeling methods, this paper introduces evidence variables and fuzzy variables simultaneously to describe the epistemic uncertain parameters. A novel dual-stage reliability analysis framework is presented, where the first stage incorporates the evidence information by the belief and plausibility measures; the second stage incorporates the fuzzy information by a membership function-like formula. To improve the computational efficiency of response bound prediction associated with various joint focal elements and λk-cut interval variables, a universal metamodel is constructed by radial basis functions in the global design space. The Latin Hypercube design method without overlapped data is adopted as the sampling strategy. Finally, two numerical examples verify the effectiveness of the proposed method in both mathematical theory and engineering application.

Global Optimisation of Car Front-End Geometry to Minimise Pedestrian Head Injury Levels

AbstractThe paper presents a multidisciplinary design optimisation strategy for car front-end profile to minimise head injury criteria across pedestrian groups. A hybrid modelling strategy was used to simulate the car- pedestrian impact events, combining parametric modelling of front-car geometry with pedestrian models for the kinematics of crash impact. A space filling response surface modelling strategy was deployed to study the head injury response, with Optimal Latin Hypercube (OLH) Design of Experiments sampling and Kriging technique to fit response models. The study argues that the optimisation of the front-end car geometry for each of the individual pedestrian models, using evolutionary optimisation algorithms is not an effective global optimization strategy as the solutions are not acceptable for other pedestrian groups. Collaborative Optimisation (CO) multidisciplinary design optimisation architecture is introduced instead as a global optimisation strategy, and proven that it can enable simultaneous minimisation of head injury levels for all the pedestrian groups, delivering a global optimum solution which meets the safety requirements across the pedestrian groups.

Tunability of Acoustic and Mechanical Behaviors in Breast Tissue Mimicking Materials.

In radiology practices, the ultrasound-guided breast biopsy is among the most commonly performed minimally invasive procedures. However, many radiology residents in their graduate residencies are found with little or no hands-on experience with ultrasound-guided breast procedures. To enhance safety, the problem can be solved by the use of anthropomorphic training phantoms which can provide the resident with realistic ultrasound imaging and needle insertion haptic feedback. Stiffness and acoustic properties of breast tissues vary between different people. The training breast phantom should be able to possess different acoustic and mechanical properties which conform the inconsistencies found in real tissues among people. Therefore, this paper investigates the tunability of acoustic and mechanical behaviors in breast tissue mimicking materials (TMMs). Experiments of central composite design (CCD) with a center point, four corner points, and an additional four axis points were used to fit the non-linear regression model of the speed of sound. The same design of experiment approach was then used to fit the second-order response surface of the attenuation coefficient. Suitable series of tissue mimicking materials for the glandular tissue and malignant lesion were suggested. Latin hypercube design method was conducted to evaluate the main factors that affected the mechanical property (Young's modulus) of tissue mimicking materials. The results showed that the recipe of tissue mimicking materials could be customized to possess different acoustic and mechanical properties which conform the inconsistencies found in real breast tissues.