A STUDY OF EXPERIMENTAL DESIGN OPTIMALITY FOR WIENER SYSTEMS

In the context of nonlinear dynamic system identification for Hammerstein systems, Rollins et al. (2003a) studied the information efficiency of the following two competing experimental design approaches: statistical design of experiments (SDOE) and pseudo-random sequences design (PRSD). The focus of this study is the Wiener system and evaluates SDOE against PRS under D-optimal efficiency. Three cases are evaluated and the results strongly support SDOE as the better approach.     

Theory of Sample Surveys

Orthogonal arrays are used widely in manufacturing and high-technology industries for quality and productivity improvement experiments. For reasons of run size economy or flexibility, nearly-orthogonal arrays are also used. The construction of orthogonal or nearly-orthogonal arrays can be quite challenging. Most existing methods are complex and produce limited types of arrays. This article describes a simple and effective algorithm for constructing mixed-level orthogonal and nearly-orthogonal arrays that can construct a variety of small-run designs with good statistical properties efficiently.     

二阶分块混料试验模型的D-最优设计

讨论了混料试验设计中的分块模型,并对可控向量x的各分量只有一个分段点且分段点都相同的连续分块混料试验模型给出了D-最优设计的解析解及结论证明。     

线性─对数混料模型参数估计D─最优区组设计

对含过程变量的三分量含下界约束的线性—对数混料模型，研究了参数估计的D—最优正交区组设计，并借助电子计算机给出了ε＝1％～10％的最优典型设计点．     

Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.     

Approximate Model Spaces for Model-Robust Experiment Design

Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.     

Improved Split-Plot and Multistratum Designs

Many industrial experiments involve some factors whose levels are harder to set than others. The best way to deal with these is to plan the experiment carefully as a split-plot, or more generally a multistratum, design. Several different approaches for constructing split-plot type response surface designs have been proposed in the literature since 2001, which has allowed experimenters to make better use of their resources by using more efficient designs than the classical balanced ones. One of these approaches, the stratum-by-stratum strategy has been shown to produce designs that are less efficient than locally D-optimal designs. An improved stratum-by-stratum algorithm is given, which, though more computationally intensive than the old one, makes better use of the advantages of this approach, that is, it can be used for any structure and does not depend on prior estimates of the variance components. This is shown to be almost as good as the locally optimal designs in terms of their own criteria and more robust across a range of criteria. Supplementary materials for this article are available online.     

最优混料试验轴设计

混料试验设计被广泛地应用在工农业生产和科学研究中。本文讨论了三、四分量二阶可加混料模型的最优轴设计问题,使用对称的轴设计,获得了它们的轴设计类上的D-,A-最优轴设计。     

On D-optimality based trust regions for black-box optimization problems

Various sequential derivative-free optimization algorithms exist for solving black-box optimization problems. Two important building blocks in these algorithms are the trust region and the geometry improvement. In this paper, we propose to incorporate the D-optimality criterion, well known in the design of experiments, into these algorithms in two different ways. Firstly, it is used to define a trust region that adapts its shape to the locations of the points in which the objective function has been evaluated. Secondly, it is used to determine an optimal geometry-improving point. The proposed trust region and geometry improvement can both be implemented into existing sequential algorithms.     

“Design of Experiments” for the Identification of Linear Dynamic Systems

One of the most important problems in direct digital controller design is to determine the process model from the sampled data. Goodness of the control depends considerably on the accuracy of the identified model. This paper investigates how to generate optimal input signal series for the identification of linear discrete-time systems in order to improve the accuracy of estimates. The determinant of the covariance matrix or of the inverse of the information matrix is considered as a measure of the error in the parameter estimates. Very simple methods are presented for the minimization of these criteria in case of an amplitude constrained input signal.