Computer-aided Experimental Design Research Articles

HOMOGENEOUS PLANS OF MULTI-FACTORY EXPERIMENTS ON QUASI-RANDOM R-ROBERTS SEQUENCES FOR SURROGATE MODELING IN A VORTEX STYLE STRUCTUROSCOPY

Context. The article is devoted to the creation of multifactorial experimental plans based on quasi-random recursive Roberts Rsequences. The object of the research is the process of creating computer-aided experimental design plans. The aim of the article is to create multifactorial, namely six- and seven-factor, uniform plans of experiments with low discrepancies, study of their projection properties and demonstrate their use on the example of surrogate modeling in eddy current structuroscopy.
 Method. An iterative method of unit hypercube even filling with reference points was used for constructing multidimensional experimental plans. It provides acceptable indicators of homogeneity and is realized on the basis of quasi-random nonparametric additive recursive Roberts R-sequences using irrational numbers, which, in turn, are obtained on the basis of the generalized Fibonacci sequence. The criterion for plans perfection is the assessment of homogeneity in terms of differences invariant with respect to the rotation of coordinates and re-marking and ordering of factors and which quantitatively characterize the deviation of the generated distribution from the ideal uniform.
 Results. Six- and seven-factor computer uniform experimental plans have been created for cataloging, which are characterized by low discrepancies and sufficiently high-quality projection properties. The tendency, which had been previously proved in the authors' research, for preserving these experimental plans characteristics in multidimensional factor spaces, which is observed with increasing number of plan points, has been confirmed. The evaluation of the quality of the created experimental plans is carried out both by visual analysis of the scattering matrix of all two-dimensional projections and by quantitative indicators of heterogeneity of the set of vectors that form the plan, namely centered and cyclic discrepancies.
 The example of the initial stage of creating a surrogate model to solve the problem of identifying profiles of electrophysical parameters in eddy current structuroscopy shows certain features of the application for created plans, in particular the transition from the plan for a unit hypercube to the plan in real factor space in the form of a hyperparallelepiped, which does not significantly affect its characteristics of homogeneity of the distribution of points.
 Conclusions. For the first time, the problem of creating six- and seven-factor uniform plans of experiments with low rates of centered and cyclic discrepancies based on R-sequences of Roberts was solved. The projection properties of the created experimental plans for different number of points were investigated. The method of constructing multidimensional computer plans of experiments taking into account the peculiarities of eddy current structuroscopy was improved. The use of six-dimensional experimental plans on the example of surrogate modeling in eddy current structuroscopy was demonstrated. The results of the study can be used in the construction of surrogate mathematical models of physical processes by any known methods of approximation.

Selection of representative calibration sample sets for near-infrared reflectance spectroscopy to predict nitrogen concentration in grasses

The effect of using representative calibration sets with fewer samples was explored and discussed. The data set consisted of near-infrared reflectance (NIR) spectra of grass samples. The grass samples were taken from different years covering a wide range of species and cultivars. Partial least squares regression (PLSR), a chemometric method, has been applied on NIR spectroscopy data for the determination of the nitrogen (N) concentration in these grass samples. The sample selection method based on NIR spectral data proposed by Puchwein and the CADEX (computer aided design of experiments) algorithm were used and compared. Both Puchwein and CADEX methods provide a calibration set equally distributed in space, and both methods require a minimum prior of knowledge. The samples were also selected randomly using complete random, cultivar random (year fixed), year random (cultivar fixed) and interaction (cultivar × year fixed) random procedures to see the influence of different factors on sample selection. Puchwein's method performed best with lowest RMSEP followed by CADEX, interaction random, year random, cultivar random and complete random. Out of 118 samples of the complete calibration set, 19 samples were selected as minimal number of representative samples. RMSEP values obtained for subsets selected using Puchwein, CADEX and using full calibration set were 0.099% N, 0.109% N and 0.092% N respectively. The result indicated that the selection of representative calibration samples can effectively enhance the cost-effectiveness of NIR spectral analysis by reducing the number of analyzed samples in the calibration set by more than 80%, which substantially reduces the effort of laboratory analyses with no significant loss in prediction accuracy.

Computer-aided design of experiments: an enabler of agile manufacturing

The ever-rising competition forces the modern organisations to provide variety of products and services that would suit individual customers within a very short period. The organisations which are able to meet this competitive strategy are said to have progressed towards agile manufacturing (AM). Modern researchers are striving to evolve enablers that would help the traditional manufacturing organisations to march towards AM goals. In this direction, this paper points out that the synergic power of two approaches, namely design of experiments (DOE) and computer-aided design (CAD), are inadequately exploited by both researchers and practitioners to achieve AM. In this context, the terminology computer-aided DOE (CADOE) is proposed. An implementation study is presented which revealed that CADOE would facilitate time compression and enhance accuracy, which are the major enablers of achieving AM.

On the selection of samples for multivariate regression analysis: application to near-infrared (NIR) calibration models for the prediction of pulp yield in Eucalyptus nitens

The effects of using reduced calibration sets on the development of near-infrared (NIR) calibration models for the prediction of kraft pulp yield in Eucalyptus nitens (Dean & Maiden) Maiden trees were explored. Three selection techniques based on NIR spectral data (CADEX (computer-aided design of experiments), DUPLEX, and SELECT algorithms) and one selection method based on a measured property (RANKING algorithm) were used for analysis and compared against a model using all data. The effect of using calibration sets of different sizes was also evaluated. All sample-selection methods resulted in models of similar performance compared with the model fitted using all samples. For calibration purposes, RANKING selection resulted in models with the lowest errors of cross-validation, followed by the DUPLEX, CADEX, and SELECT methods. In terms of validation, the SELECT and CADEX methods resulted in lower errors of prediction compared with the DUPLEX and RANKING algorithms. In general, cross-validation and prediction errors decreased as the number of calibration samples increased. These results show that it is possible to obtain adequate NIR calibration models with a reduced number of samples allowing the remaining samples to be used for model validation and that sample selection based on NIR spectral data alone is as successful as selection based on a measured property.

Bayesian computer-aided experimental design of heterogeneous scaffolds for tissue engineering

This paper presents a Bayesian methodology for computer-aided experimental design of heterogeneous scaffolds for tissue engineering applications. These heterogeneous scaffolds have spatial distributions of growth factors designed to induce and direct the growth of new tissue as the scaffolds degrade. While early scaffold designs have been essentially homogenous, new solid freeform fabrication (SFF) processes enable the fabrication of more complex, biologically inspired heterogeneous designs with controlled spatial distributions of growth factors and scaffold microstructures. SFF processes dramatically expand the number of design possibilities and significantly increase the experimental burden placed on tissue engineers in terms of time and cost. Therefore, we use a multi-stage Bayesian surrogate modeling methodology (MBSM) to build surrogate models that describe the relationship between the design parameters and the therapeutic response. This methodology is well suited for the early stages of the design process because we do not have accurate models of tissue growth, yet the success of our design depends on understanding the effect of the spatial distribution of growth factors on tissue growth. The MBSM process can guide experimental design more efficiently than traditional factorial methods. Using a simulated computer model of bone tissue regeneration, we demonstrate the advantages of Bayesian versus factorial methods for designing heterogeneous fibrin scaffolds with spatial distributions of growth factors enabled by a new SFF process.

Past developments and future opportunities in the design and analysis of crop experiments

A review of papers on the statistical design and analysis of experiments published in the Journal of Agricultural Science, Cambridge, over the last 100 years is presented. The development of significant ideas in the practical design of field experiments is reviewed. Some possible future developments in the design of spatial field trials and computer-aided design of experiments are discussed.

The complement regulator C4b-binding protein analyzed by molecular modeling, bioinformatics and computer-aided experimental design

Molecular modeling and bioinformatics have gained recognition as scientific disciplines of importance in the field of biomedical research. Molecular modeling not only allows to predict the three-dimensional structure of a protein but also helps to define its function. Careful incorporation of the experimental findings in the structural/theoretical data provides means to understand molecular mechanisms for highly complex biological systems. C4b-binding protein (C4BP) is composed of one β-chain and seven α-chains essentially built from three- and eight-complement control protein (CCP) modules, respectively, followed by a non-repeat carboxy-terminal region involved in polymerization of the chains. C4BP is involved in the regulation of the complement system and interacts with many molecules such as C4b, Arp, protein S and heparin. Here, we report experimental and computer data obtained for C4BP. Protein modeling together with site directed mutagenesis indicate that R39, R64 and R66 from the C4BP α-chain form a key binding site for heparin, suggesting that this region could be of major importance for interaction with C4b. We also propose that the first CCP of the C4BP β-chain displays a key hydrophobic surface of major importance for the interaction with the coagulation cofactor protein S.

ABSTRACTS

This article evaluates the literature that has been found to contribute to knowledge of the subject area. This literature review attempts to synthesize some of Taguchi's contributions to quality engineering and also provides a critical evaluation of his statistical methods. The role of computer-aided design of experiments was discussed. The findings provide the basis to combine Taguchi's engineering ideas with the principles of artificial neural networks. The findings also help to bring out the fourth generation of advancement in the industrial application of experimental design with the objectives of sensitivity analysis, predictive learning, and inverse modeling of systems and processes.

Algorithm AS 295: A Fedorov Exchange Algorithm for D-Optimal Design

Optimal design algorithms are particularly useful for creating designs in difficult situations, such as when experimental conditions enforce inconvenient block sizes. Several packages are now available for computer-aided design of experiments on personal computers (PCs) either in the form of Fortran source code or as easy-to-use commercial packages. Most of these packages could not find a good design for say a 23x 32 X 14 experiment in blocks of size 10. This kind of requirement is not unusual where there are say 14 species of timber or types of cheese, and the block size is dictated by the number of experimental runs which can be carried out in one day or from one batch of material. Our algorithm allows blocking, including the use of unequal block sizes. Another important application is in augmenting an experiment which has already been carried out. Our algorithm allows some of the candidate points, those in the experiment which has been carried out, to be forced into the design. Let X be an N x k matrix containing N possible or candidate design points. We want to find a subset of n out of the N points which maximizes the determinant D = IXnXn I

Efficient engineering through computer-aided design of experiments

Computer-aided design of experiments (CADOE) is discussed. Work performed using ECHIP software to meet quality and productivity goals for injection molded plastic components is detailed. An example of a fan shroud clearly shows that CADOE provides a powerful and efficient method for solving engineering problems. Although in some cases Taguchi methods may be slightly more accurate, CADOE methods such as ECHIP will usually find a solution to problems with a reduction in time and costs required. The actual time required to run the molding trials for the fan shroud was 3-0.5 h, plus 1 h of running time to confirm the predicted values on a faster molding cycle. >

コンピュータを活用する新しい統計学

The role of Behaviormetrics is to develop and apply quantitative methodologies for analizing phenomena concerning human behaviors in various fields. To quantify, it is unavoidable to carry out data analysis, sooner or later in the research process. Data analysis, for example, is indispensable for either building or testing models. Consequently, Behaviormetrics has a lot to do with Statistics, the branch of science concerning data and data analysis. Some standard methodologies for statistical data analysis are in particular useful for behaviormetricians. On the other hand, Statistics is undergoing a dramatic change due to the drastic improve ment of both computing environment and the ability of computer itself. First, as a result, with the easy access of computers, the population involving data analysis has been seeing a great increase, not restricted in the fields of natural sciences and technology, but also in the fields of social sciences and humanity. While this increase obviously reflects the availability of many new and easy-to-use softwares, it is also the mighty resource for developing even better softwares. Secondly, the computational revolution exerts direct influences on statistical theories themselves, which may be summarized by the appearence in Statistics in late 70's and early 80' s of so called computer-intensive methods. Some of these methods had been of mere theoretical interest to statisticians, but are ready to be put into practical use now. Some are, of course, totally innovative and unthinkable even 20 or 30 years ago. Here we introduce to our readers some of these new methods for data analysis and discuss their potentials for practical use in near future. We realize that time is needed for practitioners to be at ease with any of these methods. However, this is generally true for any new idea in science and technology, if we look back at the history. For example, factor analysis and many other multivariate statistical methods, once a world out of our reach, are now employed by many of us, as confidently as we handle the more usual t-test or analysis of variance(although we can' t say there exists no problem in the way of application). In the same way, we have sound reason to believe that the day should not be too long for many of these new methods, as powerful and versatile tools, to be applied widely and efficiently. In the sequel, we introduce some of these computer-intensive methods, discuss why and how they are conceived, and indicate the implications for applications. Our discussion is divided into two parts, with each of considerable length and relatively independent of the other. With ample practical examples, Part I gives an easy introduction to sevaral methods for data analysis which utilize computer intensively. Section1deals briefly with the historicalintimate relationship between computation and Statistics. Section 2 concerns nonlinear regression analysis. Section 3 discusses computer-aided design of experiments. It ends with a brief summary in Section 4. Our second part deals with bootstrap, which may be regarded as the typical example of computer-intensive methods in Statistics. This part covers almost all the research work about bootstrap and related studies untill the present day time. The historical background and aquick introduction to bootstrap are given in Section1and2, respectively. The applications of bootstrap to error estimation, mainly biases and variances, and to construction of confidence intervals, are given detailed treatment in Section3 and 4, respectively. Section 5 treats acomparatively less known application, i. e. regression analysis. We are especially ignorant of non-parametric regression. In carrying out bootstrapping, it is of great importance to find efficient resampling schemes, to save time and money, and this is the topic of Section6. Last section, Section7, is devoted to the discussion of many undergoing researches.

Grain Structure Interaction Between Cold and Hot Sputtered Aluminum Films

AbstractThe factors affecting the second layer grain structure of a two-aluminum-layer sputtered film were investigated with the use of a computer-aided experimental design and analysis program. A cold aluminum layer followed by a hotter aluminum layer has been described in the literature as a means of improving metal step coverage. Several factors were screened to determine the most important parameters by which the first layer influences the second. The two-layer interactions were determined by using scanning electron microscope (SEM) analysis to measure final grain structures. A model was generated from the experimental results that shows the influence of the first layer grain size on the second layer if the second sputter deposition is made above ∼300°C. The influence increases at higher temperatures. The results will be compared to grain growth models found in the literature.

Graphical and computer‐aided approaches to plan experiments

AbstractDesign of experiments is a quality technology to achieve product excellence, that is to achieve high quality at low cost. It is a tool to optimize product and process designs, to accelerate the development cycle, to reduce development costs, to improve the transition of products from R & D to manufacturing and to troubleshoot manufacturing problems effectively. It has been successfully, but sporadically, used in the United States. More recently, it has been identified as a major technological reason for the success of Japan in producing high‐quality products at low cost.In the United States, the need for increased competitiveness and the emphasis on quality improvement demands a widespread use of design of experiments by engineers, scientists and quality professionals. In the past, such widespread use has been hampered by a lack of proper training and a lack of availability of tools to easily implement design of experiments in industry.Three steps are essential, and are being taken, to change this situation dramatically. First, simple graphical methods, to design and analyse experiments, need to be developed, particularly when the necessary microcomputer resources are not available. Secondly, engineers, scientists and quality professionals must have access to microcomputer‐based software for design and analysis of experiments.1 Availability of such software would allow users to concentrate on the important scientific and engineering aspects of the problem by computerizing the necessary statistical expertise. Finally, since a majority of the current workforce is expected to be working in the year 2000, a massive training effort, based upon simple graphical methods and appropriate computer software, is necessary.2The purpose of this paper is to describe a methodology based upon a new graphical method called interaction graphs and other previously known techniques, to simplify the correct design of practically important fractional factorial experiments. The essential problem in designing a fractional factorial experiment is first stated. The interaction graph for a 16‐trial fractional factorial design is given to illustrate how the graphical procedure can be easily used to design a two‐level fractional factorial experiment. Other previously known techniques are described to easily modify the two‐level fractional factorial designs to create mixed multi‐level designs. Interaction graphs for other practically useful fractional factorial designs are provided. A computer package called CADE (computer aided design of experiments), which automatically generates the appropriate fractional factorial designs based upon user specifications of factors, levels and interactions and conducts complete analyses of the designed experiments is briefly described.1 Finally, the graphical method is compared with other available methods for designing fractional factorial experiments.

A statistical approach for characterizing chemical durability within a waste glass compositional region

In order to qualify nuclear waste forms for disposal in geological repositories, waste glass producers must adequately describe the properties of the glass. One of the most important of these properties is chemical durability (resistance to leaching). An approach for characterizing the chemical durability of a producer's waste glass form must take into account that the composition of the glass will vary during production. Thus, leach testing performed as part of the characterization effort must investigate the range of glasses that are likely to be produced. Also, the approach must account for the fact that only a limited number of compositional variations can be tested and that the leach test results will be subject to uncertainty. A statistical approach that satisfies these goals is presented. The statistical approach for characterizing the chemical durability of waste glasses in a specified compositional region involves the following steps: defining the compositional region of anticipated production glass, selecting a test matrix of compositions via computer-aided experimental design techniques, leach testing, empirical modeling of the leach test results, investigating glass component effects, and using statistical confidence statements to describe chemical durability over the compositional region. These steps are illustrated using the results of work performed at Pacific Northwest Laboratory for West Valley Nuclear Services.

Tools for Computer-Aided Design of Experiments

Computer packages have long been available to aid in the analysis of data. Only recently has the value of the computer in the data collection phase been recognized. This recognition has led to a proliferation of programs for the design of experiments. I..

Computer-Aided Design of Experiments—Some Practical Experiences

It does not appear to be widely recognized that a computer can be a useful aid in the design of experiments as well as in the analysis of the data. The computer can be particularly useful in the administration of an experimental program and in developing experimental plans for those situations in which the classic designs (e.g., factorial and response surface) are not applicable. Such situations include irregularly-shaped experimental regions, mixture experiments and formulation studies, the need to construct unusual fractions of factorial designs, and experimental plans to estimate the parameters in nonlinear models. Several examples are presented to illustrate the practical problems encountered and how computer algorithms can be helpful in developing useful experimental designs.