Optimal Linear-Quadratic Model Designs (original) (raw)
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Technometrics, 2001
In this work, D−, G−, and A− efficiencies and the scaled average prediction variance, IV criterion, are computed and compared for second-order split-plot central composite design. These design optimality criteria are evaluated across the set of reduced split-plot central composite design models for three design variables under various ratios of the variance components (or degrees of correlation d). It was observed that D, A, G, and IV for these models strongly depend on the values of d; they are robust to changes in the interaction terms and vary dramatically with the number of, and changes in the squared terms.
Engineering Computations, 2008
PurposeTo reduce the computational complexity per step from O(n2) to O(n) for optimization based on quadratic surrogates, where n is the number of design variables.Design/methodology/approachApplying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitively expensive when the complexity of the simulation codes is large. Increasingly, response surface approximations (RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. For evaluation by the optimizer, RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number n of design variables in the problem. In this paper a novel technique to reduce the magnitude ...
Optimum experimental design for a regression on a hypercube-generalization of Hoel's result
Annals of the Institute of Statistical Mathematics, 1988
In the note Hoel's result (1965, Ann. Math. Statbt., 36, 1097-1106) is generalized to a large family of experimental design optimality criterions. Sufficient conditions for optimality criterion are given, which ensure existence of the optimum experimental design measure which is a product of design measures on lower dimensional domains.
2012
Most researchers conduct experiments on the Target-Performance Measure (e.g. mean) without considering the Noise-Performance Measure (e.g. signal-to-noise ratio). Robust Design is a technological breakthrough that enables efficient experimental and simulation methods to optimize parameters based on Performance Measures Independent of Adjustment (PerMIA). Robust Design minimizes sensitivity to noise factors. It uses orthogonal arrays as an efficient analytical method resorting to the 2-step optimization: 1) reducing variability; 2) reducing bias. Robust Design can be extended to optimize gradients rather than just points and thus represent a hypermodel for experimental research. The schematic for Robust Design is explained in this paper.
The optimal design of an experiment with blocks of size two for quadratic regression on one variable
Exact V-optimal designs are derived for an optometry experiment for the estimation of a quadratic polynomial in one explanatory variable. Two observations are made for each subject participating in the experiment, such that each subject serves as a block of two possibly correlated observations. The exact V-optimal designs are compared to the best possible three-level designs and to the continuous V-optimal designs.
Computer-Generated Minimal (and Larger) Response-Surface Designs: (II) The Cube
1991
Computer-generated designs in the sphere are described which have the minimal (or larger) number of runs for a full quadratic response-surface design. In the case of 3 factors, the designs have 10 through 33 runs; for 4 factors, 15 through 28 runs; for 5 factors, 21 through 33 runs; etc. Some of these designs are listed here in full; the others can be obtained from the authors. The designs were constructed by minimizing the average prediction variance. No prior constraints-such as a central composite structure-are imposed on the locations of the points. The program itself determines the optimal number of runs to make at the center. The best designs found have repeated runs at the center and the remaining runs at points well spread out over the surface of the sphere. There is a simple lower bound on the average prediction variance; this bound is attained by many of the designs.
Robust Parameter Design: A Response Surface Approach
Journal of Quality Technology, 1996
An alternative to Taguchi's robust parameter design has been recently presented. However, neither Taguchi's approach nor the alternative approach is capable of dealing satisfactorily with the frequently encountered siutations in which all the noise variables cannot be studied simultaneously. Based on the ideas from response surface modeling, linear models theory, and random effects models, we provide a method for estimation in the robust parameter design in such situations.
Using Genetic Algorithms to Generate Dw and Gw-Optimal Response Surface Designs in the Hypercube
Thailand Statistician, 2017
This article proposes and develops a genetic algorithm (GA) for generating response surface designs using weighted D and G optimality criteria (w D and w G). The numbers of input variables are 2,3 k and 4 with the number of design points , 1,..., 4 N p p p with 6,10 p and 16, respectively. In this research, weak heredity (WH) is assumed with 16 cases of prior probabilities assigned to the reduced models. For all cases, the designs are generated in a kdimensional hypercube design region. The weighted optimality criterion are used to compare the performance of GA designs with computer-generated designs (SAS OPTEX procedure).
A criterion for model-robust design of experiments
Proceedings of the 2004 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing, 2004., 2004
The paper considers the design of experiments for linear models with misspecification, of the form t(x) = Sigmai = 1 p thetasiPhii(x) + r(x), where r(x) is an unknown deviation from the regression model. Considering a modeling of this misspecification, the goal is to obtain robust designs which minimize the integral quadratic risk. A kernel-based representation (Gaussian process) is chosen
A new optimization criterion for robust parameter design — the case of target is best
The International Journal of Advanced Manufacturing Technology, 2008
Robust parameter design (RPD) is a set of techniques determining the levels of some set of controllable factors such that the sensitivity of the process to variations in another set of uncontrollable factors, the noise factors, is reduced; thus increasing the robustness of the process. The common assumption is that the noise factors can be controlled in an experimental environment. When this assumption does not hold true, a random effects model is applicable. Thus, if a fixed effects model is used for simplicity, an increase in the variance of the coefficient vector should be expected. In this article, we investigate the effects of this assumption, namely the effects of incorrect estimates of the regression parameters, on the final solution. Moreover, a new criterion is considered for optimization and the performance of this criterion is evaluated through a numerical example for the case of target is best.