Initial Experimental Design Research Articles

Expected improvement in efficient experimental design supported by a global optimizer

To develop an efficient experimental design method for real process applications, the well-known expected improvement infill criterion, which is usually adopted in achieving the surrogate-based optimization, and the global optimizer DIRECT are combined as the core of the developed experimental method. The method iterates through initial experimental design, empirical modeling and model-based optimization to allocate informative experiments for the next iteration. Specifically, the Kriging regression is adopted as the surrogate model due to its demonstrated prediction accuracy and reliable prediction uncertainty. Adopting a suitable threshold value of the initial expected improvement during the optimization process, the experiments located by the global optimizer could accelerate the optimization process to reach the defined target. Three termination criterions for stopping the iterating process are proposed to meet the requirements of both the simulation optimization problems and the experimental systems. Three simulation test problems demonstrate the efficiency of the developed experimental design method.

Constrained Design Optimization Using Generative Topographic Mapping

High-dimensional design-optimization problems involving complex and time-consuming solvers present computational challenges and are expensive to execute. Even though surrogate models can replace these expensive problems with simpler models, the initial design of experiment for constructing these models effectively is still exponential to the dimension of the problem. Traditional screening methods in optimization reduce the dimension of the problem by discarding variables, which is undesirable. In this paper, a latent variable model called generative topographic mapping is proposed to reduce the dimension of the problem so as to facilitate an optimization search in a low-dimensional space without removing any variables from the design problem. The method works by transforming high-dimensional data to be embedded on a low-dimensional manifold. It is demonstrated on a two-dimensional Branin function subjected to nonlinear constraints and then applied to real engineering constrained optimization problems of an aircraft wing design and an aircraft compressor rotor. The model developed in this work proved to be more effective in dealing with constrained optimization problems by effectively learning the constraint boundary, hence finding feasible best designs when compared to other surrogate models like kriging.

Considerations for D-Optimal Sequential Design

Classical D-optimal design is used to create experimental designs for situations in which an underlying system model is known or assumed known. The D-optimal strategy can also be used to add additional experimental runs to an existing design. This paper demonstrates a study of variable choices related to sequential D-optimal design and how those choices influence the D-efficiency of the resulting complete design. The variables studied are total sample size, initial experimental design size, step size, whether or not to include center points in the initial design, and complexity of initial model assumption. The results indicate that increasing total sample size improves the D-efficiency of the design, less effort should be placed in the initial design, especially when the true underlying system model isn't known, and it is better to start off with assuming a simpler model form, rather than a complex model, assuming that the experimenter can reach the true model form during the sequential experiments. Copyright © 2013 John Wiley & Sons, Ltd.

Towards vulnerability minimization of grassland soil organic matter using metamodels

Vulnerability is the degree to which a human or environmental system is likely to experience harm due to a perturbation or a stress. This paper aims at proposing a generic quantitative method for climate change vulnerability assessment and to illustrate it on the particular case of the steady-state soil organic matter (SOM) of grassland thanks to PaSim, a mechanistic biochemical model. Based on literature review, we first present a model of concepts related to climate change vulnerability, and then we give our numerical method for vulnerability assessment. We documented all the different steps of our approach (from building of the initial design of experiments, to assessment of vulnerability with adaptation, through generating response surfaces and searching for vulnerability minima with different optimization methods). This study showed that steady-state SOM content will globally increase in future and that their vulnerability will decrease (due to higher increase of average values compared to the increased variability). Moreover, the analysis of the found vulnerability minima suggests both a reduction of vulnerability of SOM of adapted system and an increase of the gain by adaptation.

A Framework for Initial Experimental Design in the Presence of Competing Prior Knowledge

An initial experimental design criteria is proposed for optimization problems by combining multiple, potentially competing, sources of prior information—engineering models, expert opinion, and data from past experimentation on similar, nonidentical systems. By leveraging prior information, resources used for the initial experiments are already targeted toward the optimization problem, potentially reducing the total number of resources needed in follow-up experimentation. New methodology, applicable to both computer and physical experiments, is provided for incorporating and combining conjectured models and data into both the initial modeling and experimental design stages. As a result, the experimental design criteria is flexible in how it balances space filling and objective oriented properties in the presence of conjectured prior information. An application to a thin-film growth study is provided in addition to a detailed numerical study of the design properties.

Removal of Cd (II) by polystyrene-base chelating resins: adsorption properties and experiences of industrial wastewater treatment

This study involved the adsorption removal of Cd (II) by “green” chelating PS-DETA resins and its application in a column mode for industrial wastewater treatment. An initial factorial design of experiments showed that factors such as pH of the solution, agitation speed, and contact time were important. Competing adsorption of Cd (Ⅱ) and Zn (Ⅱ) onto the PS-DETA resins in binary system showed that the adsorption affinity may be in the following order: Cd (Ⅱ)##xgt;##xgt; Zn (Ⅱ). The adsorption kinetics for Cd (II) was found to follow pseudo-second-order reaction. Isotherm studies conducted at 5–500 mg/g of initial Cd (II) concentrations provided the maximum adsorption capacities of 92.1 mg/g for the PS-DETA resins. The Langmuir isotherm model was found to describe adsorption well indicating the monolayer adsorption process. It was evident from results of the desorption studies that desorption efficiency larger than 99.6% could be obtained for Zn (Ⅱ) and Cd (Ⅱ) with 0.1M HCl or HNO3. Data from a column study using PS-DETA resins for Cd (II) and Zn (II) from industrial wastewater showed that after approximately 760 BV, removal of Cd (II) achieved 50%. Hence, it was concluded that it was effective to remove Cd (II) from industrial wastewater with the column operation although the adsorption capacity of the PS-DETA resins for Cd (II) and Zn (II) was found to be less than the adsorption capacity obtained in the batch 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...

Performance Investigation and Optimization of a Vertical Axis Wind Turbine with the Omni-Direction-Guide-Vane

This paper aims to present an approach on optimizing the design of the omni-direction-guide-vane (ODGV) in order to maximise the performance of the vertical axis wind turbine (VAWT). An analytical model had been developed based on the continuity equation for assessing the impact of each design parameter of the ODGV to the VAWT performance. A 2-level full factorial design was further utilized for the verification of analytical findings with the aid of computational fluids dynamics (CFD) simulation. Three parameters, i.e. two guide vanes angles (θ and β) and ratio of VAWT diameter to distance between two guide vanes (b) were selected for the initial design of experiment (DOE) screening process. A total of 9 cases which include one centre point per block had been setup in CFD simulation. The DOE results suggested that the optimum point exists at the corner point (not at center point). Meanwhile, it was also pointed that strong interaction effect can be seen in θ with β, θ with b and β with b. It is worth to highlight that the analytical model overestimates the performance at larger θ since only one dimension steady flow is assumed.

Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light

We present initial results of the direct observation of the signature of localized light in an ultrafast laser-inscribed (ULI) disordered lattice that contains an array of evanescently coupled, one-dimensional optical waveguides in glass in which certain amount of disorder in refractive index was introduced. Numerical simulations were carried out to test the feasibility of the initial experimental design. Such configurable ULI disordered waveguide lattices should open up a platform for investigating the phenomenon of transverse localization of light and its statistical nature.

Response surface methodology with prediction uncertainty: A multi-objective optimisation approach

In the field of response surface methodology (RSM), the prediction uncertainty of the empirical model needs to be considered for effective process optimisation. Current methods combine the prediction mean and uncertainty through certain weighting strategies, either explicitly or implicitly, to form a single objective function for optimisation. This paper proposes to address this problem under the multi-objective optimisation framework. Overall, the method iterates through initial experimental design, empirical modelling and model-based optimisation to allocate promising experiments for the next iteration. Specifically, the Gaussian process regression is adopted as the empirical model due to its demonstrated prediction accuracy and reliable quantification of prediction uncertainty in the literature. The non-dominated sorting genetic algorithm II (NSGA-II) is used to search for Pareto points that are further clustered to give experimental points to be conducted in the next iteration. The application study, on the optimisation of a catalytic epoxidation process, demonstrates that the proposed method is a powerful tool to aid the development of chemical and potentially other processes.

A case study on statistical characterization and optimization of coercivity in cobalt ferrite nanoparticles

Characterization and optimization of material properties during synthesis and processing are frequent problems in materials science and engineering. In the present paper, the use of design of experiments (DOE) to characterize and improve coercivity in cobalt ferrite nanoparticles is described. The sequence of experiments was planned to capitalize on previous experimental runs available. Emphasis is placed on the rationale for choosing the additional runs. The results reveal that the choice of an adequate initial experimental design can save effort and resources in arriving at useful conclusions upon which subsequent experimental runs can be planned, capitalizing on the initial experimental structure. A region with attractive solutions in terms of coercivity, including a local maximum, was identified through the experimental sequences described in this case study.

Feasibility analysis of black-box processes using an adaptive sampling Kriging-based method

This paper presents a new approach for performing feasibility analysis over a multivariate factor space when the explicit form of a process model is lacking or when its evaluation is expensive. Specifically, two issues are addressed: feasibility evaluation of black-box processes using Kriging and development of an adaptive sampling strategy in order to minimize sampling cost, while maintaining feasibility space accuracy. Kriging is chosen as the interpolating technique for constructing a response surface of the feasibility function as a function of the uncertain parameters when a set of input–output data are available. The adaptive sampling strategy identifies critical regions and directs the search towards feasibility boundaries or where the Kriging prediction uncertainty is high. The average Kriging prediction error and cross-validation methods are used to validate the robustness of the produced model of the initial experimental design which is found to highly affect the final predicted feasible region.

Application of proteomic analysis to the study of renal diseases

Proteomics-based approaches are generating considerable data in clinical nephrology covering almost all aspects of the discipline. Proteomic experiments commonly involve fractionation and protein separation, followed by mass spectrometric analysis to identify proteins and peptides. Biostatistical and bioinformatical input is essential in such experiments, from initial experimental design to analysis of data. Standardization of procedures is an important research objective. Depending on study design, results can lead to biomarker discovery, mechanistic insight and identification of potential avenues for therapeutic intervention and treatment evaluation. Understanding proteomic information and its place in current clinical research and practice is fundamental. This Review describes proteomic experimentation and the concepts behind it, and gives an overview of its application to important areas in clinical nephrology including acute kidney injury, chronic kidney disease, end-stage renal disease, genetic diseases and fluid and electrolyte disorders, with a particular focus on biomarker discovery. The importance of future developments, such as the establishment of an infrastructure for a 'biomarker pipeline' with structured validation pathways for candidate biomarkers and development of clinical assays, is also discussed and some future perspectives are presented.

Model reduction by CPOD and Kriging

This paper proposes a novel approach for multi-objective optimization when the criteria of interest rely on a functional output from an expensive-to-evaluate numerical simulator. More specifically, the proposed method is developed in the frame of an automotive application. The aim of this application is to design the shape of an intake port in order to maximize the mass flow (denoted by Q) and the tumble (denoted by T), which both depend on a 3D velocity field obtained by numerical flow simulation. Since the considered flow simulator is time-consuming, using regular multi-objective genetic algorithms (MOGA) directly on integral quantities depending on the simulator output is prohibitive. Three different Reduced Order Models (ROMs) are presented. The first one consists in directly Kriging the integral quantities Q and T on the basis of the outputs computed at an initial design of experiments, and basing the optimization search on the sequentially obtained couples of response surfaces. The other methods explored in the present work consist in building a parametrized representation of the whole velocity field by different variants of the Proper Orthogonal Decomposition (POD). Instead of directly Kriging Q and T at un-sampled locations, the proposed technique is hence to proceed in two steps: first approximate the functional outcome by Kriging the POD coefficients, and then compute the integral quantities Q and T associated with the approximate 3D field. However, such an approach induces new difficulties since the truncated POD does not preserve the global (integrated) quantities, and that surrogate-based MOGA with this kind of POD are therefore likely to fail locating the (Q, T)-Pareto front accurately. This is what motivates to propose an original constrained POD method (called CPOD) meant to overcome the bias created by the truncation made in regular POD. More precisely, this means modifying the way of calculating the POD coefficients by imposing the integral quantities Q and T based on the truncated POD to match with the actual Q and T values obtained by flow simulation at the design of experiments. A detailed comparison of the Pareto sets obtained from the three ROMs demonstrates the interest of the CPOD approach.

Complexometric Determination of Mercury Based on a Selective Masking Reaction

In the first analytical chemistry course, students are introduced to the concepts of equilibrium in water solutions and classical (non-instrumental) analytical methods. Our teaching experience shows that "real samples" stimulate students' enthusiasm for the laboratory work. From this diagnostic, we implemented an optional activity at the end of the first analytical chemistry course. We suggested that the students propose a lab project that awakens their curiosity and perform it with the instructor's supervision. The project described here was one of the most interesting proposed experiments. The students' goal was to test the potential environmental leaching of mercury from common 12 V batteries that were improperly disposed, without following the specific environmental policies for this extremely harmful material. The battery labels did not specify the composition of electroactive ions. To simulate the disposal situation, the batteries were submerged in water for one month. The project consisted of an initial experimental design; a bibliographic search of classical methods for detection of the mercury ion; choice and optimization of the selected technique with standard solutions, pretreatment, and analysis of "real" samples; and conclusions. With these optional activities students are challenged to find a real-world problem and to solve a real analytical problem by thinking independently about a specific issue and searching literature about the proper analytical methods.

PIV-based investigations of animal flight

An overview is presented of the principles of estimation of fluid forces exerted upon solid bodies, based upon whole-field velocity measurements such as provided by PIV. The focus will be on the range of length and velocity scales characterised by the flight of large insects, birds, bats and small unmanned air vehicles, so that while viscous terms in the Navier-Stokes equations can many times be ignored in the quantitative analysis, understanding and measuring boundary-layer flows, separation and instability will ultimately be critical to predicting and controlling the fluid motions. When properly applied, PIV methods can make accurate estimates of time-averaged and unsteady forces, although even ostensibly simple cases with uncomplicated geometries can prove challenging in detail. Most PIV-based force estimates are embedded in some analytical model of the fluid-structure interaction, and examples of these with varying degrees of complexity are given. In any event, the performance and accuracy of the PIV method in use must be well understood as part of both the overall uncertainty analysis and the initial experimental design.

Model Migration for Development of a New Process Model

Data-based process models are usually developed by fitting input−output data collected on a particular process. The model built on one particular process becomes invalid with another similar process. Traditional data-based modeling methods have to completely rebuild a new process model on a similar process, leading to repetition of a large number of experiments, if process similarities between two similar processes are ignored. Effective use and extraction of these process similarities and migration of the existing process model to the new process can require a fewer number of experiments for the development of a new process model, resulting in savings of time, cost, and effort. In this paper, we present a model migration method that can quickly model a new process based on an existing base model and contrast information between the base model and the new process. The method developed involves a procedure of six steps: information extraction from the base model, initial design of experiments, slope/bias correction (SBC) to the base model, outlier detection and assessment, further design of experiments, and development of the new model by combining local difference models and the corrected base model. An example is provided to illustrate the new model development strategy for predicting injection molded part weight, taking advantage of an existing model.

Optimisation of sensitivity in the multi-elemental determination of 83 isotopes by ICP-MS as a function of 21 instrumental operative conditions by modified simplex, principal component analysis and partial least squares

The optimisation of the sensitivity in the ICP-MS determination of 83 isotopes, as a function of 21 operative parameters was performed by generating an initial experimental design that was used to define, by principal component analysis, the multi-criteria target function. The first PC, which contained an overall evaluation of the signal intensity of all isotopes, was used to rank the experiments. The modified simplex optimisation technique was then applied on the ranked experiments. The increase in signal intensity was, on the average, 3.9 times for the isotopes considered for the simplex procedure. When finally convergence was achieved, a PLS regression model calculated on the available experiments allowed to investigate the effect played by each factor on the experimental response. Simplex and PCA proved to be extremely effective to obtain the optimisation and to generate the multi-criteria target function: they can be suggested as an automatic method to perform the optimisation of the instrumental operative conditions.

Kriging Hyperparameter Tuning Strategies

Response surfaces have been extensively used as a method of building effective surrogate models of high-fidelity computational simulations. Of the numerous types of response surface models, kriging is perhaps one of the most effective, due to its ability to model complicated responses through interpolation or regression of known data while providing an estimate of the error in its prediction. There is, however, little information indicating the extent to which the hyperparameters of a kriging model need to be tuned for the resulting surrogate model to be effective. The following paper addresses this issue by investigating how often and how well it is necessary to tune the hyperparameters of a kriging model as it is updated during an optimization process. To this end, an optimization benchmarking procedure is introduced and used to assess the performance of five different tuning strategies over a range of problem sizes. The results of this benchmark demonstrate the performance gains that can be associated with reducing the complexity of the hyperparameter tuning process for complicated design problems. The strategy of tuning hyperparameters only once after the initial design of experiments is shown to perform poorly.

Use of Chemometrics To Optimize the Operation of an Ion Source

A chemometric approach has been used to optimize the Agilent multimode ion source. Initial factorial experimental design studies indicated that there was a significant degree of curvature in the experimental region, so further central composite design experiments were performed. Optimum conditions were found using statistical optimization tools, and these results were then validated. As a result, recommendations have been made for the value of each operational parameter in order to optimize response.