Design And Analysis Of Computer Experiments Research Articles

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.

Wire ropes with diamond beads for multi-wire machines optimization by means of DoE: Numerical models and choice of design parameters

This paper reports FEM model’s development to optimize the stress–strain state of wire ropes used in multi-wire machines for cutting hard blocks of stone: numerical models and experimental observations were carried out with the company Pedrini SpA ad Unico Socio, located in Carobbio degli Angeli, Bergamo (Italy). The aim of the paper is to develop a numerical FEM model useful to understand the mechanical driving forces and highlight the damage mechanisms of wire ropes with diamond beads, in order to increase service life of these important cutting tools. DoE (Design of Experiments) and DACE (Design and Analysis of Computer Experiments) were applied to the numerical models to optimize the design of the wire ropes with diamond beads. Microscope observations and penetrating liquids method were used to analyze the damaged wire ropes. Fatigue, corrosion, and contact fatigue problems were observed and the effect of the centering of the beads on the wire rope was studied. Full scale and in service tests were carried out too, to better understand the behavior of the wire ropes mounted on real cutting multi-wire machines.

Use of Hybrid Surrogate in Sampling Process for Design and Analysis of Computer Experiments (DACE) applied on Multivariable Problems

Use of Hybrid Surrogate in Sampling Process for Design and Analysis of Computer Experiments (DACE) applied on Multivariable Problems

A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling.

This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle.

Addressing state space multicollinearity in solving an ozone pollution dynamic control problem

High ground-level ozone concentrations constitute a serious air quality problem in many metropolitan regions. In this paper, we study a stochastic dynamic programming (SDP) formulation of the Atlanta metropolitan ozone pollution problem that seeks to reduce ozone via reductions of nitrogen oxides. The initial SDP formulation involves a 524-dimensional continuous state space, including ozone concentrations that are highly correlated. In prior work, a design and analysis of computer experiments (DACE) based approximate dynamic programming (ADP) solution method was able to conduct dimensionality reduction and value function approximation to enable a computationally-tractable numerical solution. However, this prior work did not address state space multicollinearity. In statistical modeling, high multicollinearity is well-known to adversely affect the generalizability of the constructed model. This issue is relevant whenever an empirical model is trained on data, but is largely ignored in the ADP literature. We propose approaches for addressing the multicollinearity in the Atlanta case study and demonstrate that if high multicollinearity is ignored, the resulting empirical models provide misleading information within the ADP algorithm. Because many SDP applications involve multicollinear continuous state spaces, the lessons learned in our research can guide the development of ADP approaches for a wide variety of SDP problems.

Efficient approximate dynamic programming based on design and analysis of computer experiments for infinite-horizon optimization

The approximate dynamic programming (ADP) method based on the design and analysis of computer experiments (DACE) approach has been demonstrated as an effective method to solve multistage decision-making problems in the literature. However, this method is still not efficient for infinite-horizon optimization considering the required large volume of sampling in the state space and high-quality value function identification. Therefore, we propose a sequential sampling algorithm and embed it into a DACE-based ADP method to obtain a high-quality value function approximation. Considering the limitations of the traditional stopping criterion (Bellman error bound), we further propose a 45-degree line stopping criterion to terminate value iteration early by identifying an optimally equivalent value function. A comparison of the computational results with those of other three existing policies indicates that the proposed sampling algorithm and stopping criterion can determine a high-quality ADP policy. Finally, we discuss the extrapolation issue of the value function approximated by multivariate adaptive regression splines, the results of which further demonstrate the quality of the ADP policy generated in this study.

DESIGN OF EXPERIMENTS USED IN COMPUTER TRIALS: A SUPPORTIVE METHOD FOR PRODUCT DEVELOPMENT

ABSTRACT The study proposes the development of a framework that can take advantage of the Design and Analysis of Computer Experiments (DACE) more efficiently. The need for rapid product development cycles creates a demand for tools that aid in decision making. One of these tools is Computer Aided Engineering which uses the Finite Element Method that requires a long time to be executed. The philosophy of Design of Experiments and the construction of empirical models have been used together with physical simulations. After a theoretical review, two cases were applied to product development and the results were analyzed. A theoretical framework based on the experience gained from the empirical studies conducted was proposed. Despite the existence of many studies on the subject where mathematical and statistical aspects are explored, there is a lack of studies related to practical and operational issues regarding the application of DACE.

Data mining for state space orthogonalization in adaptive dynamic programming

Dynamic programming (DP) is a mathematical programming approach for optimizing a system that changes over time and is a common approach for developing intelligent systems. Expert systems that are intelligent must be able to adapt dynamically over time. An optimal DP policy identifies the optimal decision dependent on the current state of the system. Hence, the decisions controlling the system can intelligently adapt to changing system states. Although DP has existed since Bellman introduced it in 1957, exact DP policies are only possible for problems with low dimension or under very limiting restrictions. Fortunately, advances in computational power have given rise to approximate DP (ADP). However, most ADP algorithms are still computationally-intractable for high-dimensional problems. This paper specifically considers continuous-state DP problems in which the state variables are multicollinear. The issue of multicollinearity is currently ignored in the ADP literature, but in the statistics community it is well known that high multicollinearity leads to unstable (high variance) parameter estimates in statistical modeling. While not all real world DP applications involve high multicollinearity, it is not uncommon for real cases to involve observed state variables that are correlated, such as the air quality ozone pollution application studied in this research. Correlation is a common occurrence in observed data, including sources in meteorology, energy, finance, manufacturing, health care, etc.ADP algorithms for continuous-state DP achieve an approximate solution through discretization of the state space and model approximations. Typical state space discretizations involve full-dimensional grids or random sampling. The former option requires exponential growth in the number of state points as the state space dimension grows, while the latter option is typically inefficient and requires an intractable number of state points. The exception is computationally-tractable ADP methods based on a design and analysis of computer experiments (DACE) approach. However, the DACE approach utilizes ideal experimental designs that are (nearly) orthogonal, and a multicollinear state space will not be appropriately represented by such ideal experimental designs. While one could directly build approximations over the multicollinear state space, the issue of unstable model approximations remains unaddressed. Our approach for handling multicollinearity employs data mining methods for two purposes: (1) to reduce the dimensionality of a DP problem and (2) to orthogonalize a multicollinear DP state space and enable the use of a computationally-efficient DACE-based ADP approach. Our results demonstrate the risk of ignoring high multicollinearity, quantified by high variance inflation factors representing model instability. Our comparisons using an air quality ozone pollution case study provide guidance on combining feature selection and feature extraction to guarantee orthogonality while achieving over 95% dimension reduction and good model accuracy.

Numerical optimization of tungsten monoblock tile in EAST divertor

The ITER-like tungsten divertor with toroidally symmetric 1mm×1mm chamfers on monoblock tiles has been installed in EAST in 2014. Hot spots were experimentally observed mostly along the toridial facing gaps between two columns of W/Cu monoblock units, which are often aggravated by installation misalignment. These hot spots can significantly degrade the power handling capability of W divertor and need to be alleviated.A numerical optimization model for tile chamfering design is built based on the finite element method (FEM), in which the numerical experiments are designed by the uniform table. The calculation results in ANSYS for these experiments are then processed employing the code Design and Analysis of Computer Experiments (DACE) in which the Kriging method is adopted to reconstruct a response surface. The optimum geometry can be derived from the minimum point on the surface. The results show that, under 200 MW/m2 parallel heat flux with an inclination angle of 3° with respect to tile surface, the maximum temperature on W tile with a 0.5mm misalignment can be decreased to 2084°C by adopting an optimized single-sided chamfer, 1.8 times lower than 1mm×1mm symmetrically chamfered tile. The optimum chamfering geometry has a strong dependence on the inclination angle of plasma flux to tile surface. As a result, the monoblock tiles in a flat cassette module need to be chamfered differently to adapt to the varied inclination angles.

Elaborated Analysis of Force Model Parameters in Milling Simulations with Respect to Tool State Variations

Geometric physically-based simulation systems for milling processes can provide the possibility to analyze and predict characteristically behaviors of a certain process. The parametrization of the simulation models is a crucial task when optimizing the quality of the simulation prediction. In order to determine tool load, process forces have to be calculated. Thus, the parametrization of the cutting force model that is mainly subject to the processed material and tool characteristics has a versatile impact on the simulation results. However, the tool state is expected to be constant within common milling simulations and therefore tool state variations like several tool wear effects are not represented. The tool state is defined through the geometric constitution of the cutting edges of the tool. This paper aims to analyze tool wear effects by re-calibrating the parameter values of the force model within the simulation system. To validate the simulation system, several milling experiments were conducted. In order to induce a fast change of the tool state within the process and to provoke high tool loads, the powder metallurgic high speed steel 1.3344 was machined. Advanced surrogate modeling techniques from the design and analysis of computer experiments (DACE) were applied to analyze the contribution of the force model parameter values. The fitting of the surrogate model is performed by means of sequential design of experiments. This allows the retrieval of sets of fitting parameter combinations for each tool state with a relatively small amount of simulation runs compared to genetic algorithms or gradients based methods. The surrogate models are exploited to analyze the behavior of the force model parameter values over the varying tool states. Approaches for further research are recommended and potential practical applications are discussed.

Biogeography-based optimization of a variable camshaft timing system

Automotive simulations often prohibit the use of traditional optimization techniques because these simulations are complex and computationally expensive. These two qualities motivate the use of evolutionary algorithms and meta-modeling techniques respectively. In this work, we apply biogeography-based optimization (BBO) to optimize radial basis function (RBF)-based lookup table controls of a variable camshaft timing system for fuel economy. Also, we reduce computational search effort by finding an effective parameterization of the problem, optimizing the parameters of the BBO algorithm for the problem, and estimating the cost of a portion of the candidate solutions in BBO with design and analysis of computer experiments (DACE). We find that we can improve fuel economy by 1.7% over the original control parameters, and we find a tradeoff in population size, and an optimal value for mutation rate. Finally, we find that we can use a small number of samples to construct DACE models, and we can use these models to estimate a significant portion of the candidate solutions each generation to reduce computation effort and still obtain good BBO solutions.

Error Metrics and the Sequential Refinement of Kriging Metamodels

Metamodels, or surrogate models, have been proposed in the literature to reduce the resources (time/cost) invested in the design and optimization of engineering systems whose behavior is modeled using complex computer codes, in an area commonly known as simulation-based design optimization. Following the seminal paper of Sacks et al. (1989, “Design and Analysis of Computer Experiments,” Stat. Sci., 4(4), pp. 409–435), researchers have developed the field of design and analysis of computer experiments (DACE), focusing on different aspects of the problem such as experimental design, approximation methods, model fitting, model validation, and metamodeling-based optimization methods. Among these, model validation remains a key issue, as the reliability and trustworthiness of the results depend greatly on the quality of approximation of the metamodel. Typically, model validation involves calculating prediction errors of the metamodel using a data set different from the one used to build the model. Due to the high cost associated with computer experiments with simulation codes, validation approaches that do not require additional data points (samples) are preferable. However, it is documented that methods based on resampling, e.g., cross validation (CV), can exhibit oscillatory behavior during sequential/adaptive sampling and model refinement, thus making it difficult to quantify the approximation capabilities of the metamodels and/or to define rational stopping criteria for the metamodel refinement process. In this work, we present the results of a simulation experiment conducted to study the evolution of several error metrics during sequential model refinement, to estimate prediction errors, and to define proper stopping criteria without requiring additional samples beyond those used to build the metamodels. Our results show that it is possible to accurately estimate the predictive performance of Kriging metamodels without additional samples, and that leave-one-out CV errors perform poorly in this context. Based on our findings, we propose guidelines for choosing the sample size of computer experiments that use sequential/adaptive model refinement paradigm. We also propose a stopping criterion for sequential model refinement that does not require additional samples.

Update-based evolution control: A new fitness approximation method for evolutionary algorithms

Evolutionary algorithms are robust optimization methods that have been used in many engineering applications. However, real-world fitness evaluations can be computationally expensive, so it may be necessary to estimate the fitness with an approximate model. This article reviews design and analysis of computer experiments (DACE) as an approximation method that combines a global polynomial with a local Gaussian model to estimate continuous fitness functions. The article incorporates DACE in various evolutionary algorithms, to test unconstrained and constrained benchmarks, both with and without fitness function evaluation noise. The article also introduces a new evolution control strategy called update-based control that estimates the fitness of certain individuals of each generation based on the exact fitness values of other individuals during that same generation. The results show that update-based evolution control outperforms other strategies on noise-free, noisy, constrained and unconstrained benchmarks. The results also show that update-based evolution control can compensate for fitness evaluation noise.

Optimization Design for the Stationary Platen Based on Uniform Design

Design and analysis of computer experiments (DACE) can solve the optimization design problem for stationary platen effectively. In this paper the method of uniform design is applied to obtain the design of computer experiments which is employed in the optimization design of the stationary platen. 3 factors (11 levels for each factor) are selected. The approximate Kriging model is built on the basis of the FEA results. 10 design points are selected randomly to verify the prediction ability of the Kriging model. The results show that the maximum of the relative error is 2.53% and the minimum is 0.63%. The approximate model built in this paper is practical in the optimization design of the stationary platen. The steps proposed in this paper are also suitable for the optimization design problems with complicated geometry or finite element model.

Mass-Optimized Design of Guyed Wind Turbine Tower Using Struts

Continuing upscaling trends in turbine height, rotor diameter, and rated power have resulted in massive, expensive tower structures. A modified guyed tower concept with struts (GTS) is proposed for saving material, and the basic design is made for a 2.5MW turbine. The tower and cable dimensions are optimized for lowest system cost given yield constraints. DACE (design and analysis of computer experiments) methods of sampling and surrogate model optimization are used for efficient parameter study and optimization of the ABAQUS finite element model using DAKOTA software. The resulting design is highly effective in transferring turbine loads from the tower to the cables. A mass savings of 41% is calculated vs. conventional structures, and further investigation of the GTS is recommended for both onshore and offshore applications. Additionally, the concept of retowering older turbines is introduced and proposed as an economic alternative to the common practice of repowering old wind farms with larger, new machines. The GTS is specifically suited to this application. Lastly, the design methodology developed for this study is shown to be effective and efficient; it can be applied for the massoptimization of similar cablesupported truss structures.

Comparison of several heuristic approaches to calibration of WATCLASS hydrologic model1☆

The purpose of this study is to find a computationally inexpensive calibration method of a hydrologic model for predicting river flows. The approach is called the surrogate model optimization (SMO), which relies on optimizing a surrogate model instead of the original model that requires significantly more computing time. The proposed SMO method combines the Latin hypercube sampling (LHS) method and a statistical approach called the “Design and Analysis of Computer Experiments (DACE)”. To investigate the performance of this approach, the Monte Carlo sampling and LHS results are compared with the results of the proposed SMO. As the case study, the prediction results of WATCLASS hydrologic model over Smokey river watershed using MC, LHS and SMO are presented. The proposed SMO is shown to be significantly faster than traditional calibration methods based on Monte Carlo simulation or other global optimization methods.

Adaptive value function approximation for continuous-state stochastic dynamic programming

Approximate dynamic programming (ADP) commonly employs value function approximation to numerically solve complex dynamic programming problems. A statistical perspective of value function approximation employs a design and analysis of computer experiments (DACE) approach, where the “computer experiment” yields points on the value function curve. The DACE approach has been used to numerically solve high-dimensional, continuous-state stochastic dynamic programming, and performs two tasks primarily: (1) design of experiments and (2) statistical modeling. The use of design of experiments enables more efficient discretization. However, identifying the appropriate sample size is not straightforward. Furthermore, identifying the appropriate model structure is a well-known problem in the field of statistics. In this paper, we present a sequential method that can adaptively determine both sample size and model structure. Number-theoretic methods (NTM) are used to sequentially grow the experimental design because of their ability to fill the design space. Feed-forward neural networks (NNs) are used for statistical modeling because of their adjustability in structure-complexity . This adaptive value function approximation (AVFA) method must be automated to enable efficient implementation within ADP. An AVFA algorithm is introduced, that increments the size of the state space training data in each sequential step, and for each sample size a successive model search process is performed to find an optimal NN model. The new algorithm is tested on a nine-dimensional inventory forecasting problem.

Semianalytical Bubble-Flow Models for the Development of a Novel Bubble-Column Simulator

The simulation of bubble columns is a computationally expensive task because of the complexity of the hydrodynamics. A novel bubble-column simulation approach attempts to increase the computational efficiency by accounting for the flow regions around individual bubbles with an algebraic flow model. To improve the accuracy and reduce the number of parameters of the flow model, the linear combination of the creeping and potential flow analytical solutions is considered as a first approximation, which is found to accurately model large portions of the flow field within the considered operating range (Re ≤ 270). The residual consists of significant nonlinear features, e.g., bubble wake, for which two statistically based strategies, i.e., Design and Analysis of Computer Experiments (DACE) and regression with empirical models, are evaluated. Both resulted in good fits, with the DACE strategy making fewer assumptions about the data, however, requiring more parameters. The combination of analytical and empirical models is therefore recommended for use as an accurate algebraic approximation of the flow field.

Response surface strategies in constructing statistical bubble flow models for the development of a novel bubble column simulation approach

Bubble columns represent a substantial contribution to chemical industrial equipment and due to their complex hydrodynamics are difficult and computationally expensive to simulate. A model of the flow structure around a single bubble is required for the development of a computationally efficient alternative model. The flow structure data obtained from CFD is highly non-linear, which lends itself to a Design and Analysis of Computer Experiments (DACE) approach. The situation differs from conventional DACE applications since high resolution data is summarized, which allows different sampling criteria, correlation functions and optimization criteria to be evaluated in an assessable manner. A modified powered exponential correlation function is introduced, which in conjunction with a gradient based space-filling design resulted in an averaged 8 times smaller mean squared error compared to other correlation design combinations. Furthermore, sequentially fitting the data is shown to produce the best overall fits, when used in combination with space-filling designs.

Constrained probabilistic multi-objective optimization of shot peening process

Shot peening is a cold working process used for improving the fatigue strength of metallic components. An optimum set of peening parameters must increase the residual compressive stress (RCS), but reduce the surface roughness and cold work for improving the fatigue strength. The optimization is made robust to avoid any unfeasible solution that may arise out of random variations of input variables. The current study uses the well-known Design and Analysis of Computer Experiments (DACE) methodology for optimization, which is better than the conventional Design of Experiments (DoE) approach. It employs a finite element method based unit cell approach to determine the RCS, surface roughness and cold work of a given material. Radial basis functions are used to develop the meta-models. A genetic algorithm (GA) is employed for finding a robust and optimum set of shot peening parameters for a given material. With this approach, the operator will achieve the optimum solution specified by the designer.