Space-filling Experimental Design Research Articles

Sequentially extending space-filling experimental designs by optimally permuting and stacking columns of the design matrix

Researchers make available computationally expensive designs for computer experiments for widespread use by cataloging them and providing online links. This paper presents an algorithm that augments space-filling designs (SFDs) by optimally permuting and stacking columns of the design matrix to minimize the maximum absolute pairwise correlation among columns in the new extended design. The algorithm enables researchers to augment an SFD sequentially with batches of additional design points, which improves column orthogonality and adds more degrees of freedom for fitting metamodels. We show this method improves the correlation and space-filling properties of the resulting designs and allows us to extend some classes of designs to higher dimensions that are not easily obtainable. Moreover, the resulting extended designs compare well with many leading software-generated SFDs created from scratch in the extended design space.

Numerical Optimization of Spray-Guided Spark Assistance for Cold Idle Operation in a Heavy-Duty Gasoline Compression Ignition Engine

This article describes the results of a response surface model (RSM)-based numerical optimization campaign for spray-guided spark assistance at cold operations in a heavy-duty gasoline compression ignition (GCI) engine. On the basis of an earlier work on spark-assisted GCI cold combustion, a space-filling design of experiments (DoE) method was first undertaken to investigate a multitude of hardware design variables and engine operating parameters. The main design variables included the number of injector nozzles, fuel split quantities and injection timings, and spark timing. The objective variables were engine combustion efficiency (ŋc), maximum pressure rise rate (MPRR), and engine-out nitrogen oxide (NOx) emissions. A total of 150 design candidates were automatically generated using the Sobol sequence method provided by the commercial software package, CAESES. Then, closed-cycle computational fluid dynamic (CFD) spark-assisted GCI simulations under cold idling operations were performed. The outcomes from the CFD-DoE design campaign were utilized to construct high-fidelity RSMs that allowed for further design optimization of the spark plug- and fuel injector-related design variables, along with fuel injection strategy parameters. A merit function with respect to objective variables was formulated with an appropriate weight assignment on each objective variable. Finally, the best design candidate was identified from the RSM-based optimization process and further validated in the CFD analysis. The best design candidate showed the potential to significantly improve combustion efficiency (ŋc > 90%) over the baseline at cold idle while satisfying MPRR and NOx emissions constraints (MPRR < 5 bar/CAD and NOx < 4.5 g/kWh).

Automatic optimization of centrifugal pump based on adaptive single-objective algorithm and computational fluid dynamics

It is important to reduce carbon emissions caused by the energy consumption of pumps. This study used a centrifugal pump with a specific speed of 89.6 as the research object to improve pump efficiency. The adaptive single-objective method was adopted as the automatic optimization tool with computational fluid dynamics, which includes optimal space-filling experimental design, Kriging response surface, and mixed-integer sequential quadratic programming. Eight geometric parameters from the meridian section and the plan of the impeller and diffuser were chosen as the design variables. The maximum efficiency under the design flow conditions was set as the optimization target. The Spearman correlation coefficient analysis results show that the sensitivity of each variable to efficiency and head. Compared with the original scheme, the optimal scheme showed a 2.75% increase in efficiency and a 1.17 m increase in head under the design flowrate. The internal flow field after optimization was also improved. An external characteristic experiment of the original and optimized pumps was performed to validate the numerical results. This automatic optimization method presents great potential to improve the hydraulic performance of centrifugal pumps at a lower cost.

Investigation of processing windows in additive manufacturing of AlSi10Mg for faster production utilizing data-driven modeling

To reduce production time and decrease production cost, the increase of layer thickness is an adequate option in powder bed fusion. In order to determine the relationships between process parameters in laser powder bed fusion (PBF-LB/M) and final porosity in AlSi10Mg, samples were processed following a space-filling experimental design in the present study. A total of 144 samples were fabricated considering layer thicknesses of 30 µm, 45 µm, 60 µm, and 90 µm. Afterwards, porosity was assessed using image analysis and computed tomography. Different types of defects were found as expected, however, fully dense parts were realized in case of every considered layer thickness. Predictive models were developed using data-driven approaches, eventually enabling multivariate analysis of the correlations and determination of appropriate processing conditions resulting in both low porosity of parts and high build rates.

Isovolumetric adaptations to space-filling design of experiments

A brief review of methods in design of experiments and criteria to determine space-filling properties of a set of samples is given. Subsequently, the so-called curse of dimensionality in sampling is reviewed and used as motivation for the proposal of an adaptation to the strata creation process in Latin hypercube sampling based on the idea of nested same-sized hypervolumes. The proposed approach places samples closer to design space boundaries, where in higher dimensions the majority of the design space volume is located. The same idea is introduced for Monte Carlo considering an affordable number of samples as an a-posteriori transformation. Both ideas are studied on different algorithms and compared using different distance-based space-filling criteria. The proposed new sampling approach then enables more efficient sampling for optimization especially for high-dimensional problems, i.e. for problems with a high number of design variables.

Savonius Wind Turbine Numerical Parametric Analysis Using Space-Filling Design and Gaussian Stochastic Process

Wind energy is an alternative source of clean energy to address the growing energy demand and provide pollution-free electricity. With the rapid development of urban areas, high wind energy resources such as high-rise building rooftops are excellent locations for urban wind turbine installation. One of the practical and simple urban wind turbines is the Savonius design. It has a simple design, easy to maintain, and is very affordable. This work focuses on the design evaluation of a Savonius wind turbine (SWT) by varying the rotor diameter, rotor height, and twist angle for urban applications. A transient computational fluid dynamics (CFD) approach is applied to assess the various design treatments using a space-filling design of experiments. To address the spaces in the hypercube statistical design, a sphere packing design method was adopted which suited the evaluation of computational simulations results such as that of the CFD. The Gaussian stochastic process model was applied to establish the trend of the parametric performance of the optimized SWT design through the model fitting. The results have shown that optimized SWT performs well with its self-starting capability compared to the traditional Savonius design. In addition, the optimized SWT has shown a better peak power coefficient compared with the results of previous works on the design of SWT.

A Computational Investigation of PPCI-Diffusion Combustion Strategy at Full Load in a Light-Duty GCI Engine

<div class="section abstract"><div class="htmlview paragraph">A two-stage PPCI-diffusion combustion process recently showed good potential to enable clean and fuel-efficient gasoline compression ignition (GCI) combustion at medium-to-high loads. By conducting closed-cycle 3-D CFD combustion analysis, a further step was undertaken in this work to evaluate and optimize the PPCI-diffusion combustion strategy at a full load operating point (2000rpm-23.5 bar IMEPcc) while keeping engine-out NOx below 1 g/kWh.</div><div class="htmlview paragraph">The light-duty GCI engine used in this investigation featured a custom-designed piston bowl geometry at a 17.0 compression ratio (CR), a high pressure diesel fuel injection system, and advanced single-stage turbocharging. A split fuel injection strategy was used to enable the two-stage PPCI-diffusion combustion process.</div><div class="htmlview paragraph">First, the injector spray pattern and swirl ratio effects were evaluated. In-cylinder air utilization and the PPCI-diffusion combustion process were notably influenced by the closed-cycle combustion system design. Among the different spray patterns at a swirl ratio of 0, the one with 120° spray inclusion angle, 8-hole, and 1.5 times total nozzle area (TNA) was favored due to enhanced late-stage fuel-air mixing and more rapid diffusion combustion. In the second step, a fuel injection strategy optimization campaign was performed through a space-filling Design of Experiments (DoE) approach. Overall, the optimized injector spray pattern and the optimized fuel injection strategy together were predicted to produce 5.1% lower ISFC and 50% soot reduction over the baseline. A competitive analysis showed the optimized PPCI-diffusion combustion strategy had the potential to generate substantially lower NOx and soot than a modern light-duty diesel engine at full load.</div></div>

A Lipschitz Matrix for Parameter Reduction in Computational Science

We introduce the Lipschitz matrix: a generalization of the scalar Lipschitz constant for functions with many inputs. Among the Lipschitz matrices compatible a particular function, we choose the smallest such matrix in the Frobenius norm to encode the structure of this function. The Lipschitz matrix then provides a function-dependent metric on the input space. Altering this metric to reflect a particular function improves the performance of many tasks in computational science. Compared to the Lipschitz constant, the Lipschitz matrix reduces the worst-case cost of approximation, integration, and optimization; if the Lipschitz matrix is low-rank, this cost no longer depends on the dimension of the input, but instead on the rank of the Lipschitz matrix defeating the curse of dimensionality. Both the Lipschitz constant and matrix define uncertainty away from point queries of the function and by using the Lipschitz matrix we can reduce uncertainty. If we build a minimax space-filling design of experiments in the Lipschitz matrix metric, we can further reduce this uncertainty. When the Lipschitz matrix is approximately low-rank, we can perform parameter reduction by constructing a ridge approximation whose active subspace is the span of the dominant eigenvectors of the Lipschitz matrix. In summary, the Lipschitz matrix provides a new tool for analyzing and performing parameter reduction in complex models arising in computational science.

Influence of energy density on selective laser sintering of carbon fiber-reinforced PA12

This work provides an in-depth investigation of the influence of laser energy density on the mechanical, surface, and dimensional properties of carbon fiber-reinforced PA12 parts manufactured by selective laser sintering (SLS). A space-filling design of experiments (DOE) was used to conduct the experimental trials to cover a wide range of laser sintering parameters. The consolidation mechanism was evaluated by microstructural and crystallization evolution of the samples produced at different energy densities, supported by mechanical testing, scanning electron microscopy (SEM), X-ray diffraction (XRD), and infrared spectroscopy (FTIR). Surface morphology was evaluated by profile measurements and SEM images. Laser sintering parameters had a significant influence on physical and mechanical properties, exhibiting complex and nonlinear behavior. Low energy density resulted in better dimensional accuracy, whereas intermediate laser energy resulted in the best mechanical properties. A trade-off could be seen when mechanical or dimensional properties were desired, and optimum energy values were strongly dependent on the criteria desired. All samples exhibited a brittle fracture behavior, with little plastic deformation present. Fracture mechanism occurred in the interlayer region or interface between carbon fiber and PA12, depending on the energy density applied. XRD analysis revealed a decrease in crystal fraction with increasing energy density. FTIR measurement suggested that polymer degradation at high energy densities could be present by both polymer chain scission and oxygen functional group decomposition and gas release upon laser heating of carbon fiber, resulting in lower mechanical properties.

Fast and simple dataset selection for machine learning

Abstract The task of data reduction is discussed and a novel selection approach which allows to control the optimal point distribution of the selected data subset is proposed. The proposed approach utilizes the estimation of probability density functions (pdfs). Due to its structure, the new method is capable of selecting a subset either by approximating the pdf of the original dataset or by approximating an arbitrary, desired target pdf. The new strategy evaluates the estimated pdfs solely on the selected data points, resulting in a simple and efficient algorithm with low computational and memory demand. The performance of the new approach is investigated for two different scenarios. For representative subset selection of a dataset, the new approach is compared to a recently proposed, more complex method and shows comparable results. For the demonstration of the capability of matching a target pdf, a uniform distribution is chosen as an example. Here the new method is compared to strategies for space-filling design of experiments and shows convincing results.

Evaluation of zero-dimensional stochastic reactor modelling for a Diesel engine application

Prediction of engine-out emissions with high fidelity from in-cylinder combustion simulations is still a significant challenge early in the engine development process. This article contributes to this fast evolving body of knowledge by focusing on the evaluation of NO x emission prediction capability of a probability density function–based stochastic reactor engine models for a Diesel engine. The research implements a systematic approach to the study of the stochastic reactor engine model performance, underpinned by a detailed space-filling design of experiments (DoE)-based sensitivity analysis of both external and internal parameters, evaluating their effects on the accuracy in matching physical measurements of both in-cylinder conditions and NO x output. The approach proposed in this article introduces an automatic stochastic reactor engine model calibration methodology across the engine operating envelope, based on a multi-objective optimization approach. This aims to exploit opportunities for internal stochastic reactor engine model parameters tuning to achieve good overall modelling performance as a trade-off between physical in-cylinder measurements accuracy and the output NO x emission predictions error. The results from the case study provide a valuable insight into the effectiveness of the stochastic reactor engine model, showing good capability for NO x emissions prediction and trends, while pointing out the critical sensitivity to the external input parameters and modelling conditions.

Space-filling experimental designs for constrained design spaces

ABSTRACTConventional space-filling experimental design provides uniform coverage of a hypercube design space. When constraints are imposed, the results may contain many infeasible points. Simply omitting these points leads to fewer feasible points than desired and a design of experiments that is not optimally distributed. In this research, an adaptive method is developed to create space-filling points in arbitrarily constrained spaces. First, a design space reconstruction method is developed to reduce the invalid exploration space and enhance the efficiency of experimental designs. Then, a synthetic criterion of uniformity and feasibility is proposed and optimized by the enhanced stochastic evolutionary method to obtain the initial sampling combination. Finally, an adaptive adjustment strategy of design levels is constructed to obtain the required number of feasible points. Various test cases with convex and non-convex, connected and non-connected design spaces are implemented to verify the efficacy of the proposed method.

History match of the Groningen field dynamic reservoir model to subsidence data and conventional subsurface data

AbstractThis paper presents the method applied to history-match the Groningen field dynamic model to conventional data (pressure data and water influx data) and to subsidence data, which is a novelty. Modelled subsidence is matched to subsidence data based on a simplified geomechanical model, which was built into the dynamic simulator.A two-tier method was used to first achieve a match on a field-wide scale using field-average history-match quantifiers, which was then further improved at a regional/well level using regional history-match quantifiers. The history match was assisted by a space-filling experimental design. The resulting model has a field-average match to pressure data of ±2.17bar with a measurement uncertainty of ±0.4bar, to water influx data of ±2m with a measurement uncertainty of ±0.5m, and to subsidence data of ±4cm with a measurement uncertainty of ±1cm.The output from this model is used as input for compaction, subsidence and production forecasts feeding into the hazard and risk assessment completed by NAM for the Groningen Winningsplan 2016.

Order of experimentation and advisability of corner measurements

Abstract Basically two questions are examined regarding the design of experiments. First, for what settings is the placement of design points in the corners of the input space advisable in order to achieve a good generalization performance. And second, what order of experimentation leads to the best model quality in early stages of the measurement process. The effect of the explicit addition of corner measurements to three space-filling experimental designs is investigated. It turns out that for most cases the incorporation of corner points harms the model quality. Two new methods to determine the order of experimentation are compared to one active learning strategy and a simple randomization of the measurement sequence. Both order determination methods prove to outperform the random sequences significantly and are only slightly inferior to the active learning strategy.

Hybrid Large-Eddy Simulation Optimization of a Fundamental Turbine Blade Turbulated Cooling Passage

An efficient methodology for shape optimization based on computational fluid dynamics is developed and applied to a fundamental turbulated square duct. The present study uses a hybrid large-eddy simulation turbulence modeling approach for all computational fluid dynamics evaluation, as it is shown to give much more reliable results over a range of geometries. Four geometric parameters defining the cross-sectional profile and angle of the turbulators were optimized for two competing performance metrics: heat transfer and pressure drop. An initial database of computational fluid dynamics runs, sampled from the design space using a space-filling design of experiments, is used as a starting point. A metamodel is then fitted through the training data in the database. The metamodel provides the means for fast approximation of the objective functions at new design points, allowing the use of a genetic algorithm for this multiobjective optimization. The resulting Pareto front is verified with a second round of computational fluid dynamics evaluations at the end. The optimization demonstrates the potential for improvement in thermal performance when using turbulators with an upstream ramp. Various metamodels are also explored for their ability to deal with design space nonlinearity and noisy data.

Cyclic Tests in Batch Mode of CO2 Adsorption and Regeneration with Sorbent Consisting of Immobilized Amine on a Mesoporous Silica

A series of CO2 adsorption tests were conducted in a fluidized bed vessel using an impregnated polyamine sorbent. This sorbent was cross-linked using a silyl derivative to improve its stability and hydrophobicity. The fluidization and adsorption behavior of this sorbent was characterized over a range of flows, temperatures, and CO2 concentrations. A Latin hypercube space-filling experimental design was implemented for each of three operating modes (nonreactive at ambient and flue gas temperatures, and in a reactive mode using 10–20% CO2) to evaluate hydrodynamics, thermal, and flue gas CO2 adsorption effects independently. It was found that the variable having the greatest impact on adsorption capacity was the duration of testing. The capacity degraded by about 10% over the 100 h of testing. The slope from all points in the hypercube matrix indicates the heat of adsorption is approximately 65.8 kJ/mol CO2, a value consistent with the literature.

Distance correlation-based nearly orthogonal space-filling experimental designs

In many real-world applications of optimisation, the required model (function) evaluations are determined by expensive and time-consuming physical experiments or numerical procedures. Within this context, the objective of experimental design is to obtain meaningful information based on a strongly limited number of experiments or function evaluations. In order to generate informative designs, space-filling and orthogonality are widely considered to be essential. In this study, we review several existing design performance metrics that address these criteria, and the distance correlation-based metric is proposed for achieving improved experimental design. Three closely related randomised sampling schemes are proposed to generate nearly orthogonal designs with good space-filling properties in real time. The effectiveness of our approach is demonstrated by numerical examples and an illustrative borehole model case study.

Initial Experimental Design Methodology Incorporating Expert Conjecture, Prior Data, and Engineering Models for Deposition of Iridium Nanoparticles in Supercritical Carbon Dioxide

The study and optimization of nanofabrication techniques in nanotechnology research is often challenging because experiments are costly to conduct in terms of time and money. In particular, for a new system that has not been previously studied at length, it is a challenge to efficiently plan the first round of experiments in the region of interest near the process optimum, and there may be multiple process inputs that must be optimized simultaneously. A purely statistical approach to this challenge would apply a space-filling experimental design, or, alternatively, domain knowledge could be applied to guide the experimental design. However, both of these approaches may waste precious resources by failing to sample efficiently near the desired process output. In this work, a novel technique termed “initial experimental design” (IED) is applied to combine the statistical and experimental approaches for planning the initial round of experiments for a new system that is related to a similar but nonidentical e...

A GRASP for simultaneously assigning and sequencing product families on flexible assembly lines

This paper introduces a new model and solution methodology for a real-world production scheduling problem arising in the electronics industry. The production environment is a high volume, just-in-time, make-to-order facility with volatile demand over many product families that are assembled on flexible lines. A distinguishing characteristic of the problem is the presence of non-traditional sequence-dependant setup costs, which complicate our ability to find high-quality solutions. The scheduling problem arose when product variety exceeded the mix that the existing lines could accommodate. A nonlinear integer programming formulation is presented for the problem of minimizing setup costs, and a greedy randomized adaptive search procedure (GRASP) is developed to find solutions. To select the GRASP parameter values, an efficient, space-filling experimental design method is used based on nearly orthogonal Latin hypercubes. The proposed methodology is tested on actual factory data and compared to a prior heuristic presented in the literature; our heuristic provides a cost savings in 7 out of the 10 cases examined, and an average improvement of 17.39 % which is shown to be highly statistically significant. This improvement is due in part to the introduction of a pre-processing step to determine preferential and non-preferential line assignment information.

Model-aided optimization and analysis of multi-component catalysts: Application to selective hydrogenation of cinnamaldehyde

Multi-component catalysts are widely used to exploit the component interactions with the aim to improve catalysis processes. This study applies a model-aided approach to determine the optimal compositions of carbon nanotubes (CNTs) supported Pt–Co–Fe catalysts for selective hydrogenation of cinnamaldehyde. The methodology integrates an iterative response surface methodology (RSM) for optimization, and global sensitivity analysis for interpreting the impact of components and their interactions on the achieved process yield. The RSM encapsulates the state-of-the-art space-filling experimental design, advanced data-based modeling, and model-aided optimization while considering prediction uncertainty. A high performance catalyst, 3.4%Pt-1.3%Co-2.6%Fe/CNT, is identified with 15 experiments, giving rise to 86.1% conversion, 86.4% selectivity and 74.4% yield. The sensitivity analysis identifies the role of the components and their interactions, which is consistent with reported literature results. For verification purpose, selected catalysts are characterized by using powder X-ray diffraction, transmission electron microscopy, and X-ray photoelectron spectroscopy. Overall, this paper establishes the presented methodology as a powerful tool for design of multi-component catalysts.