Design Of Computer Experiments Research Articles

On Construction of Nearly Orthogonal Latin Hypercube Designs

Orthogonal Latin hypercube designs are becoming popular in designing computer experiments. Available literature on construction of orthogonal or nearly orthogonal LHDs has one or more restriction in terms of either runs or factors. In this article, we have proposed a method of construction for obtaining nearly orthogonal Latin hypercube designs capable of accommodating flexible number of runs or factors.

Robust assessment of railway vehicle safety risks in operation using a proposed data-driven wheel profile generation approach: Design of computer experiments and surrogate models

Worldwide objectives for railway vehicles are increased capacity, faster travels and higher levels of safety. In the vehicle-track complex system, assessing and controlling the interactions between the wheels and the rail track is crucial to these goals. Wheel profiles are specifically designed to steer the vehicle and avoid derailment. Maintenance standards and train operating companies establish safe envelopes for wheel profile geometric parameters. A design of experiments is conducted to model relationships between allowable wheel parameters and expected vehicle safety risks, which is supported by condition monitoring data from operation. Such a robust assessment is missing in the literature. The applied methods consist of: (i) selection of predictors and pre-processing, based on literature, standards and a purely data-driven approach to generate wheel profiles; (ii) space-filling design, using Latin hypercube sampling; (iii) obtaining vehicle responses and post-processing, using a multibody dynamics commercial software and according to standards; (iv) surrogate modelling, using Gaussian processes and linear models; (v) sensitivity analysis, through Sobol indices; (vi) safety assessment, analysing response surfaces. Wheels with large flange height and thickness result in higher flange climb derailment risks. The proposed approach allows quantifying this risk as a function of profile parameters and mitigate it through maintenance actions.

A data-driven multiscale model for reactive wetting simulations

We describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

A Sequential Hybrid Optimization Algorithm (SHOA) to Solve the Hybrid Flow Shop Scheduling Problems to Minimize Carbon Footprint

In today’s world, a situational awareness of sustainability is becoming increasingly important. Leaving a better world for future generations is becoming the main interest of many studies. It also puts pressure on managers to change production methods in most industries. Reducing carbon emissions in industry today is crucial to saving our planet. Theoretical research and practical industry requirements diverge, even though numerous researchers have tackled various strategies to handle carbon emission problems. Therefore, this work considers the carbon emission problem of the furniture manufacturing industry in Hosur, Tamilnadu, India. The case study company has a manufacturing system that resembles a hybrid flow shop (HFS) environment. As the HFS scheduling problems are NP-hard in nature, exact solution techniques could not be used to solve the problems. Hence, a sequential hybrid optimization algorithm (SHOA) has been developed in this paper to minimize the carbon footprint. In the SHOA, the pigeon-inspired optimization algorithm (PIOA) is hybridized sequentially with the firefly algorithm (FA). A computational experimental design is proposed to analyze the efficiency of the introduced strategy, and the solutions indicate that the developed approach could reduce the carbon footprint by up to 9.82%. The results motivate us to implement the proposed algorithm in the manufacturing industry to reduce the carbon footprint.

A design and analysis of computer experiments based mixed integer linear programming approach for optimizing a system of electric vehicle charging stations

This paper formulates a mixed integer linear programming (MILP) model to optimize a system of electric vehicle (EV) charging stations. Our methodology introduces a two-stage framework that integrates the first-stage system design problem with a second-stage control problem of the EV charging stations and develops a design and analysis of computer experiments (DACE) based system design optimization solution method. Our DACE approach generates a metamodel to predict revenue from the control problem using multivariate adaptive regression splines (MARS), fit over a binned Latin hypercube (LH) experimental design. Comparing the DACE based approach to using a commercial solver on the MILP, it yields near optimal solutions, provides interpretable profit functions, and significantly reduces computational time for practical application.

Numerical investigation of the use of flexible blades for vertical axis wind turbines

This study proposes a novel vertical axis wind turbine (VAWT) design with flexible blades aiming to improve their energy extraction capability. The blade deformation is achieved using Ansys Fluent dynamic mesh and user-defined functions to control the position of the blades nodes at specific azimuthal angles. An optimization study is carried out using computational Fluid Dynamics (CFD) simulations and Design of Experiments (DOE) to get the optimal design parameters of the flexible blade at different Tip Speed Ratios (TSRs). In addition, a comparison between the DOE results of both 2D and 3D CFD simulations is achieved to assess the use of 2D simulations for optimization purposes. Also, a detailed numerical study of the aerodynamic performance of the turbine based on this new design is done to compare the rigid and flexible blade models' power coefficient and flow fields around the blades. Results of 2D and 3D CFD simulations show that the flexible blades are able to improve the power coefficient of the turbine by up to 66% and 32% respectively at low tip speed ratios diminishing gradually with increasing tip speed ratios. It is also noticeable that similar pattern in power coefficient results was obtained from the 2D and 3D simulations of both turbine models. This, in turn, demonstrates the efficacy of 2D simulations in accurately determining optimized design parameters while significantly reducing computational costs compared to 3D simulations.

Adaptive Gaussian process regression for efficient building of surrogate models in inverse problems

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model ys that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that ys is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.

Orthogonal designs for computer experiments constructed from sequences with zero autocorrelation

Designs for computer experiments constitute an important class of experimental designs. Computer experiments are used when the physical experiments are expensive or time-consuming and attracted a lot of attention in recent years. In this paper, we proposed a method for generating computer experiments with many factors and symmetric runs. These designs are suitable for computer experiments and are constructed using known sequences with zero autocorrelation function, such as T-sequences, Bases sequences, Normal sequences, and other. The results appear to be encouraging as the methodologies can transform the known sequences into designs for computer experiments without the need for a computer search. The generated designs have some favorable properties, including the symmetry in their runs which results in all the even orders effects being orthogonal to the main effects.

Programmable Melt Electrowriting to Engineer Soft Connective Tissues with Prescribed, Biomimetic, Biaxial Mechanical Properties

AbstractAppropriate load‐bearing function of soft connective tissues is provided by their nonlinear and often anisotropic mechanics. Recapitulating such complex mechanical behavior in tissue‐engineered structures is particularly crucial, as deviation from native tissue mechanics can trigger pathological biomechanical pathways, causing adverse tissue remodeling and dysfunction. Here, a novel method combining computational modeling, melt electrowriting (MEW), and design of experiments (DOE) is reported to generate scaffolds composed of sinusoidal fibers with prescribed biaxial mechanical properties, recapitulating the distinct nonlinear, anisotropic stress–strain behavior of three model tissues: adult aortic valve, pediatric pulmonary valve, and pediatric pericardium. Finite element analysis is used to efficiently optimize scaffold architecture over a broad parameter space, representing up to 65 conditions, to define MEW print parameters to achieve polycaprolactone scaffolds with target mechanical properties. Architectural parameters are further optimized experimentally using DOE and regression to account for uncertainties involved in the simulation, yielding functional scaffolds with accurate, prescribed mechanics. The prescribed architecture also primarily governs the mechanics of hybrid structures generated by casting cell‐laden fibrin hydrogel within the scaffolds. This high‐fidelity approach recapitulates biaxial mechanical properties over a broad range of mechanical nonlinearity and anisotropy and is generalizable for programmed biofabrication in a variety of tissue engineering applications.

Nested Maximum Entropy Designs for Computer Experiments

Presently, computer experiments with multiple levels of accuracy are widely applied in science and engineering. This paper introduces a class of nested maximum entropy designs for such computer experiments. A multi-layer DETMAX algorithm is proposed to construct nested maximum entropy designs. Based on nested maximum entropy designs, we also propose an integer-programming procedure to specify the sample sizes in multi-fidelity computer experiments. Simulated annealing techniques are used to tackle complex optimization problems in the proposed methods. Illustrative examples show that the proposed nested entropy designs can yield better prediction results than nested Latin hypercube designs in the literature and that the proposed sample-size determination method is effective.

The use of the Karhunen Loève expansion in the design of computer experiments

This article proposes the use of the Karhunen Loève expansion in the design of computer experiments when the Gaussian Process (GP) model is used to model the output, Y(x). We start by finding the K-L expansion in the case of the univariate and multivariate processes. When the analytical solution does not exist, we apply several methods of approximation, such as Haar wavelet functions and Fourier expansions. Numerical examples are presented to illustrate the idea of the approximations. We use the approximated model to select the maximum entropy sampling design.

Optimization of absorption refrigeration systems by the method of computational experiment design

Optimization of absorption refrigeration systems by the method of computational experiment design

Developing a Biomechanical Testing Setup of the Pelvis-Part II: Experimental Testing.

Biomechanical testbench emulating the physiological loading of the pelvis is crucial in developing reconstructive implants for fragility fractures of the pelvis. Additionally, it will help understand the influence of the common daily loading on the pelvic ring. However, most reported experimental studies were mainly comparative with simplified loading and boundary conditions. In Part I of our study, we described the concept of the computational experiment design to design and construct a biomechanical testbench emulating the gait movement of the pelvis. The 57 muscles and joints' contact forces were reduced to four force actuators and one support, producing a similar stress distribution. The experimental setup is explained in this paper and some experimental results are presented. In addition, a series of repeatability and reproducibility tests were conducted to assess the test stand capabilities of replicating the gait physiological loading. The calculated stresses and the experimentally recorded strains showed that the pelvic ring response to the loading always follows the loaded leg side during the gait cycle. Furthermore, the experimental results of the pelvis displacement and strain at selected locations match the numerical ones. The developed test stand and the concept of computational experiment design behind it provide guidelines on how to design biomechanical testing equipment with physiological relevance.

Developing a Biomechanical Testing Setup of the Pelvis-Part I: Computational Design of Experiments.

Biomechanics of the human pelvis and the associated implants are still a medical and engineering debated topic. Today, no biomechanical testing setup is dedicated to pelvis testing and associated reconstructive implants with accepted clinical relevance. This paper uses the computational experiment design procedure to numerically design a biomechanical test stand that emulates the pelvis physiological gait loading. The numerically designed test stand reduces the 57 muscles and joints' contact forces iteratively to only four force actuators. Two hip joints' contact forces and two equivalent muscle forces with a maximum magnitude of 2.3 kN are applied in a bilateral reciprocating action. The stress distribution of the numerical model of the developed test stand is very similar to that of the numerical model of the pelvis with all 57 muscles and joint forces. For instance, at the right arcuate line, the state of stress is identical. However, at the location of superior rami, there is a deviation ranging from 2% to 20% between the two models. The boundary conditions and the nature of loading adopted in this study are more realistic regarding the clinical relevance than state-of-the-art. The numerically developed biomechanical testing setup of the pelvis in this numerical study (Part I) was found to be valid for the experimental testing of the pelvis. The construct of the testing setup and the experimental testing of an intact pelvis under gait loading are discussed in detail in Part II: Experimental Testing.

Stochastic Computational Methods and Experiment Design

Stochastic Computational Methods and Experiment Design

Optimum design of stenter machine hot air supply chamber by coupling CFD & DOE

The efficiency of the textile hot air-drying process fundamentally requires the uniformity of the airflow that impinges on the textile fabric. Optimization of a stenter machine’s hot air supply chamber shape was conducted in this paper, based on the actual real-size model and considering both the outlet flow uniformity and the standard velocity deviation as responses. The purpose is to improve the airflow uniformity at the chamber outlet, and modifications applied to the baseline must be applicable to both old and next-generation stenter machines. Coupled Computational Fluid Dynamics and Design of Experiment (CFD-DoE) optimization on the stenter machine chamber geometry was carried out. The CFD model was validated by measuring the chamber outlet velocity using a 2D velocity scanner. After choosing seven factors based on mechanical manufacturing and fluid dynamics theories, a main effect screening design was conducted to highlight relevant factors that influence the outlet airflow distribution. By fixing the best categorical factors, a central composite design (CCD) was applied using three other continuous factors to generate a quadratic prediction model that could be used to simultaneously maximize and minimize the uniformity index (UI) and the standard deviation (SD), respectively. With the embedded JMP SAS desirability function, the optimal value was calculated based on a statistical approach. Those values were used to design an optimal stenter air supply chamber that has been simulated with Fluent CFD code to validate the statistical prediction model. Finally, optimized geometry was obtained and experimentally validated. Results show that this new chamber improved by 16.48% for the uniformity index and 38.07% for the standard deviation.

A class of space‐filling designs with low‐dimensional stratification and column orthogonality

AbstractStrong orthogonal arrays are suitable designs for computer experiments because of stratification in low‐dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space‐filling designs with more economical run sizes. These designs are not only column‐orthogonal but also enjoy a large proportion of low‐dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3‐orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by‐product.

Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s2×s or s×s2 grids, and most column pairs satisfy stratifications on s2×s2 grids. Moreover, many column pairs can achieve stratifications on s4×s2 and s2×s4 grids. Furthermore, the obtained space-filling ODs can have s6 levels, s4 levels, and mixed levels, as required for different needs.

Design and Analysis of Computer Experiments with both Numeral and Distributional Inputs

Nowadays stochastic computer simulations with both numeral and distributional inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This article studies the design and analysis issues of such computer experiments. First, we provide preliminary results concerning the Wasserstein distance in probability measure spaces. To handle the product space of the Euclidean space and the probability measure space, we prove that, through the mapping from a point in the Euclidean space to the mass probability measure at this point, the Euclidean space can be isomorphic to the subset of the probability measure space, which consists of all the mass measures, with respect to the Wasserstein distance. Therefore, the product space can be viewed as a product probability measure space. We derive formulas of the Wasserstein distance between two components of this product probability measure space. Second, we use the above results to construct Wasserstein distance-based space-filling criteria in the product space of the Euclidean space and the probability measure space. A class of optimal Latin hypercube-type designs in this product space are proposed. Third, we present a Wasserstein distance-based Gaussian process model to analyze data from computer experiments with both numeral and distributional inputs. Numerical examples and real applications to a metro simulation are presented to show the effectiveness of our methods.

Doubly Coupled Designs for Computer Experiments With Both Qualitative and Quantitative Factors

Doubly Coupled Designs for Computer Experiments With Both Qualitative and Quantitative Factors