Experimental Design Problem Research Articles

Least costly identification experiment for control

All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed-loop system and the actual closed-loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a “dual” point of view and in a closed-loop setting: given a maximum allowable control-oriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation during experimentation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.

New light on certain two level designs using Gröbner bases

Algebraic geometry can be used to solve identifiability problems in design of experiments as modern computational algebra packages such as Maple or CoCoA can be used. The point is that we regard the design as a set of polynomial solutions. Then, the Gröbner base theory allows one to identify the whole set of estimable effects (main or interactions) of the factors of the design. In this paper we applied Gröbner base theory in certain two level factorial designs.

Identification of multi-input systems: variance analysis and input design issues

This paper examines the identification of multi-input systems. Motivated by an experiment design problem (should one excite the various inputs simultaneously or separately), we examine the effect of an additional input on the variance of the estimated coefficients of parametrized rational transfer function models, with special emphasis on the commonly used FIR, ARX, ARMAX, OE and BJ model structures. We first show that, for model structures that have common parameters in the input–output and noise models (e.g. ARMAX), any additional input contributes to a reduction of the covariance of all parameter estimates. We then show that the accuracy improvement extends beyond the case of common parameters in all transfer functions, and we show exactly which parameter estimates are improved when a new input is added. We also conclude that it is always better to excite all inputs simultaneously.

Experimental design for groundwater modeling and management

This study aims to develop a methodology for data collection that accounts for the application of simulation models in decision making for groundwater management. Simulation model reliability is estimated by comparing the effects that a perturbation in the model parameter space has over the model output as well as over the solution of a multiobjective optimization problem. The problem of experimental design for parameter estimation is formulated and solved using a combination of genetic algorithm and gradient‐based optimization. Gaussian quadrature and Bayesian decision theory are combined for selecting the best design under parameter uncertainty. The proposed methodology is useful for selecting a robust design that will outperform all other candidate designs under most potential “true” states of the system. Results also show that the uncertainty analysis is able to identify complex interactions among the model parameters that may affect the performance of the experimental designs as well as the attainability of management objectives.

ON OPTIMAL INPUT DESIGN IN SYSTEM IDENTIFICATION1

System identification concerns the construction and validation of mathematical models of dynamical systems from experimental data. The objective of this contribution is to discuss new research directions in experiment design , e.g. how to design informative experiments which satisfy specifications on the resulting model quality and practical limitations such as constraints on input and output signals, but also experimental time. In particular, we discuss how input design is instrumental for alleviating the problem of modelling complex systems. Many optimal experiment design problems can be formulated as optimal control problems, but with nonstandard cost functions. A difficulty is that the solution often depends on the true system. To solve optimal control problems, we can exploit recent advances in numerical optimization for control design, including convex optimization and relaxation methods. As a more concrete example, we study how to estimate the ℋ∞ norm of a system.

A multi-sequential number-theoretic optimization algorithm using clustering methods

A multi-sequential number-theoretic optimization method based on clustering was developed and applied to the optimization of functions with many local extrema. Details of the procedure to generate the clusters and the sequential schedules were given. The algorithm was assessed by comparing its performance with generalized simulated annealing algorithm in a difficult instructive example and a D-optimum experimental design problem. It is shown the presented algorithm to be more effective and reliable based on the two examples.

Construction of a 21-Component Layered Mixture Experiment Design Using a New Mixture Coordinate-Exchange Algorithm

This article describes the solution to a unique and challenging mixture experiment design problem involving (1) 19 and 21 components for two different parts of the design, (2) many single-component and multicomponent constraints, (3) augmentation of existing data, (4) a layered design developed in stages, and (5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. A D-optimal approach was used to augment existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The traditional approach to building D-optimal mixture experiment designs is to generate a set of candidate points from which design points are D-optimally selected. The large number of mixture components (19 or 21) and many constraints defining each layer of the waste glass experimental region made it impossible to generate and store the huge number of vertices and other typical candidate points. A new coordinate-exchange algorithm applicable for constrained mixture experiments implemented in JMP® was used to D-optimally select design points without candidate points. The new coordinate-exchange algorithm for mixture experiments is described in this article.

Advances in Canadian forest hydrology, 1999–2003

AbstractUnderstanding key hydrological processes and properties is critical to sustaining the ecological, economic, social and cultural roles of Canada's varied forest types. This review examines recent progress in studying the hydrology of Canada's forest landscapes. Work in some areas, such as snow interception, accumulation and melt under forest cover, has led to modelling tools that can be readily applied for operational purposes. Our understanding in other areas, such as the link between runoff‐generating processes in different forest landscapes and hydrochemical fluxes to receiving waters, is much more tentative. The 1999–2003 period saw considerable research examining hydrological and biogeochemical responses to natural and anthropogenic disturbance of forest landscapes, spurred by major funding initiatives at the provincial and federal levels. This work has provided valuable insight; however, application of the findings beyond the experimental site is often restricted by such issues as a limited consideration of the background variability of hydrological systems, incomplete appreciation of hydrological aspects at the experiment planning stage, and experimental design problems that often bedevil studies of basin response to disturbance. Overcoming these constraints will require, among other things, continued support for long‐term hydroecological monitoring programmes, the embedding of process measurement and modelling studies within these programmes, and greater responsiveness to the vagaries of policy directions related to Canada's forest resources. Progress in these and related areas will contribute greatly to the development of hydrological indicators of sustainable forest management in Canada. Copyright © 2005 John Wiley & Sons, Ltd.

IDENTIFICATION OF A TWO-INPUT SYSTEM: VARIANCE ANALYSIS

This paper examines the identification of a single-output two-input system. Motivated by an experiment design problem (should one excite the two inputs simultaneously or separately), we examine the effect of the (second) input signal on the variance of the various polynomial coefficients in the case of FIR, ARX, ARMAX, OE and BJ models. A somewhat surprising result is to show that the addition of a second input in an ARMAX model reduces the variance of all polynomials estimates.

IDENTIFICATION OF QUANTUM SYSTEMS: MAXIMUM LIKELIHOOD AND OPTIMAL EXPERIMENT DESIGN FOR STATE TOMOGRAPHY

An optimal experiment design problem invoked by the Cramér-Rao Inequality is applied to the problem of quantum state tomography. The optimization problem is integer-combinatorial and we use an established relaxation which results in a convex programming problem whose solution can be used to guide a more efficient experiment.

Theory of model-based geophysical survey and experimental design

Enormous sums of money are invested by industry and scientific funding agencies every year in seismic, well logging, electromagnetic, earthquake monitoring and microseismic surveys, and in laboratory-based experiments. For each survey or experiment a design process must first take place. An efficient design is usually a compromise—a suitable trade-off between information that is expected to be retrieved about a model of interest and the cost of data acquisition and processing. In some fields of geophysics, advanced methods from design theory are used, not only to optimize the survey design, but also to shift this entire trade-off relationship between information and cost. In others, either crude rules of thumb are used or, indeed, expected model information is not optimized at all. This is the first part of a two-part tutorial that provides a theoretical framework from the field of statistical experimental design (SED), within which model-based survey and experimental design problems and methods can be understood. Specifically, these two articles describe methods that are pertinent to the detection and inference of physical properties of rocks in the laboratory, or in the earth. The choice of method to use when designing experiments depends greatly on how easily one can measure information. This in turn depends principally on whether the relationship between data that will be measured and model parameters of interest is approximately linear, or significantly nonlinear. Consequently, the first article focuses on the case where this relationship is approximately linear and the next (in next month's issue of TLE ) deals with theory for nonlinear design. The tutorial begins with an introduction to concepts in model-based SED theory. This is then extended to create a more general, theoretical framework of design for linear model-data relationships. The same techniques can be used to design model parameterizations that explain information contained in measured data …

Experimental designs for precise parameter estimation for non-linear models

This paper is concerned with the experimental design for precise parameter estimation in a model of known form. Emphasis is primarily placed on three flotation models in which the parameters appear in a non-linear fashion. The first part of the paper consists of a brief statement of the statistical concepts and procedures involved in obtaining precise estimates of parameters, the logic of the design criterion, and the general sequential design procedures. Based on of this background, the second part describes the experimental design problem of estimating the parameters in three different flotation recovery models. The numbers of sampling and different measuring times for these models to obtain the precise parameter estimates are present in the conclusion.

A comparison between the Gröbner bases approach and hidden projection properties in factorial designs

Screening designs are useful for situations where a large number of factors ( q ) are examined but only few ( k ) of these are expected to be important. Plackett–Burman designs have traditionally been studied for this purpose. Since these designs are only main effects plans and since the number of runs are greater than the number of active factors (main effects), there are plenty of degrees of freedom unused for identifying and estimating interactions of factors. Computational Algebraic Geometry can be used to solve identifiability problems in design of experiments in Statistics. The theory of Gröbner bases allows one to identify the whole set of estimable effects (main or interactions) of the factors of the design. On the other hand, the hidden projection property approach, that deals with the same identification problem, provides a measure of how efficient the identification of effects is. The advantages and disadvantages of both methods are discussed with application to a certain two level (fractional) factorial designs that arise from Plackett–Burman designs.

A Probabilistic Method for Detecting Multivariate Extreme Outliers

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the center of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its outlierness). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

Predictors of Species Sensitivity to Fragmentation

We reviewed empirical data and hypotheses derived from demographic, optimal foraging, life-history, community, and biogeographic theory for predicting the sensitivity of species to habitat fragmentation. We found 12 traits or trait groups that have been suggested as predictors of species sensitivity: population size; population fluctuation and storage effect; dispersal power; reproductive potential; annual survival; sociality; body size; trophic position; ecological specialisation, microhabitat and matrix use; disturbance and competition sensitive traits; rarity; and biogeographic position. For each trait we discuss the theoretical justification for its sensitivity to fragmentation and empirical evidence for and against the suitability of the trait as a predictor of fragmentation sensitivity. Where relevant, we also discuss experimental design problems for testing the underlying hypotheses. There is good empirical support for 6 of the 12 traits as sensitivity predictors: population size; population fluctuation and storage effects; traits associated with competitive ability and disturbance sensitivity in plants; microhabitat specialisation and matrix use; rarity in the form of low abundance within a habitat; and relative biogeographic position. Few clear patterns emerge for the remaining traits from empirical studies if examined in isolation. Consequently, interactions of species traits and environmental conditions must be considered if we want to be able to predict species sensitivity to fragmentation. We develop a classification of fragmentation sensitivity based on specific trait combinations and discuss the implications of the results for ecological theory.

Guided tissue regeneration for the treatment of periodontal intrabony and furcation defects. A systematic review.

Many clinical studies have demonstrated that guided tissue regeneration (GTR) is a successful treatment modality of periodontal reconstructive surgery and it has become an accepted procedure in most periodontal practices. The purpose of this structured review was to assess the efficacy of guided tissue regeneration (GTR) procedures in patients with periodontal osseous defects compared with surgical controls on clinical, radiographic, adverse, and patient-centered outcomes. It extends the scope of previous GTR systematic reviews, which were limited to randomized controlled studies, by the scope of outcome measures examined, and the duration of the study. In patients with periodontal osseous defects, what is the effect of physical barriers compared with surgical controls on clinical, radiographic, adverse, and patient-centered outcomes? An electronic search of the Cochrane Oral Health Group Trials Register and MEDLINE databases was performed. Manual searching of journals included Journal of Clinical Periodontology, Journal of Periodontology, and Journal of Periodontal Research up to January 2002. This manual search also included review of relevant bibliographies. Two manufacturers of GTR devices were contacted regarding unpublished data. Studies were selected for review if the evidence level was 3B (cohort) or above, at least 6 months duration, and compared a test GTR intervention with a surgical control. Studies with experimental design problems; histologic or microbiological investigations; or those with outcome measurements, study populations, or study duration not consistent with the inclusion criteria were excluded. Primary outcome measures for intrabony defects were: clinical attachment level (CAL) gain, probing depth reduction (PD), gingival recession (REC) reduction; for furcation defects: vertical probing attachment level (VPAL) gain, vertical probing depth reduction (VPD), horizontal probing depth reduction (HPD), horizontal open probing attachment level gain (HOPA), and vertical open probing attachment level gain (VOPA). Meta-analysis was performed to compare GTR procedures to other surgical treatments and to examine the resulting clinical outcomes. 1. For the primary outcome variables, in both intrabony-defect and furcation-defect studies, GTR was favored over open flap debridement (OFD) therapies (P < 0.0001). 2. No differences were detected among barrier types, but barrier types could explain some heterogeneity in the results. 3. Augmentation of the GTR barrier with a particulate graft enhanced VPD (P < 0.05), VPAL, and HOPA, but none of the intrabony outcomes. Overall, GTR is consistently more effective than OFD in the gain of clinical attachment and probing depth reduction in the treatment of intrabony and furcation defects.

Estimating Expected Information Gains for Experimental Designs With Application to the Random Fatigue-Limit Model

Expected gain in Shannon information is commonly suggested as a Bayesian design evaluation criterion. Because estimating expected information gains is computationally expensive, examples in which they have been successfully used in identifying Bayes optimal designs are both few and typically quite simplistic. This article discusses in general some properties of estimators of expected information gains based on Markov chain Monte Carlo (MCMC) and Laplacian approximations. We then investigate some issues that arise when applying these methods to the problem of experimental design in the (technically nontrivial) random fatigue-limit model of Pascual and Meeker. An example comparing follow-up designs for a laminate panel study is provided.

Bioassays and Field Studies for Allelopathy in Terrestrial Plants: Progress and Problems

Bioassays are an integral part of allelopathy research. The unsuitability of laboratory bioassays to explain field situations is discussed previously. In this article, we discuss progress in bioassay experimental design and several unresolved problems associated with research on allelopathy. The objectives of this article are to discuss problems related to (1) collection of allelopathic material for bioassay, (2) allelochemical quantification in bioassays, (3) selection of concentration of allelochemicals in bioassay, (4) selection of appropriate control, (5) interaction between allelochemicals and other substances, and (6) in situ allelochemical bioassays. We concluded that new experimental designs for in situ bioassay are needed that can account for the large number of confounding factors in a complex field environment, and can be linked to physiological monitoring of target species and biochemical monitoring of the growth medium.Referee: Dr. Stella Elakovich, Dept. of Chemistry and Biochemistry, University of Southern Mississippi, Hattiesburg, MS 390406-5043

On the Design of Optimally Informative Dynamic Experiments for Model Discrimination in Multiresponse Nonlinear Situations

We present a new method for determining optimally informative dynamic experiments for the purpose of model discrimination among several rival multiresponse nonlinear structured dynamic models generally described by systems of differential and algebraic equations (DAEs). A robust and efficient algorithm based on an extension to the dynamic case of the discrimination criterion put forth by Buzzi-Ferraris and Forzatti (Chem. Eng. Sci. 1984, 39, 81) is developed to calculate dynamic input trajectories by reformulation of the experiment design problem as an optimal control problem. We show that the new approach, by taking parametric uncertainty into account, can provide significant improvements in the ability to distinguish among a series of rival dynamic models over previous attempts to design dynamic experiments primarily based on parameter point estimates and thus maximizes the divergence of the model predictions without regard for uncertainty (Espie, D. M.; Macchietto, S. AIChE J. 1989, 35, 223). We illust...

Designing plant experiments for real-time optimization systems

This paper presents a new criterion to design plant experiments for model-based real-time optimization (RTO) systems. Experiments are designed by maximizing total expected profit over a future horizon. The objective function for designing plant experiments includes the gain in profit by reducing the offset and variability after the experiments and loss in profit before and during experimentation. Therefore, large plant movement from the optimum during experimentation and too many experiments are penalized by the profit loss term. By solving the experimental design problem, the time to start the experiments, the number of experiments and the experimental operating conditions are determined. The proposed experimental design approach is applied to the simulated Williams-Otto reactor, where it yields higher profit for several cases than achieved by standard RTO without experimentation.