Christine M. Anderson-Cook

Fraction of Design Space to Assess Prediction Capability of Response Surface Designs

Variance Dispersion Graphs (VDGs) are useful summaries for comparing competing designs on a fixed design space. However, they do not give all useful information about the prediction capability of a design. We propose the Fraction of Design Space (FDS) technique, which addresses some of the shortcomings of VDGs. The new technique gives the researcher more detailed information by quantifying the fraction of design space where the scaled prediction variance (SPV) is less than or equal to any pre-specified value. The FDS graph gives the researcher information about the distribution of the SPV in the region based on the ranges and proportions of possible SPV values. Several variations on the graph, including plotting the variance of the estimated mean response, are also presented to allow for specialized consideration of different designs. The FDS technique complements the use of VDGs to give the researcher more insight into the prediction capability of a design. Several standard designs with different numbers of factors are studied with both methods.

Probabilistic model for the chloride-induced corrosion service life of bridge decks

Abstract A statistical model to determine the time to first repair and subsequent rehabilitation of concrete bridge decks exposed to chloride deicer salts that incorporates the statistical nature of factors affecting the corrosion process is developed. The model expands on an existing deterministic model using statistical resampling techniques. Emphasis was placed on the diffusion portion of the diffusion-cracking model. Data collected for the time for corrosion deterioration after corrosion initiation can be readily incorporated into the model. Data for the surface chloride concentration, apparent diffusion coefficient and clear cover depth were collected from 10 bridge decks built in Virginia. Several ranges of the chloride corrosion initiation concentration, as determined from the available literature, were investigated. The resampling techniques known as the simple and parametric bootstrap were used to predict time to first repair and rehabilitation based on the observed field data. The two methods provide results that substantially agree for all decks investigated.

Impact of specification changes on chloride-induced corrosion service life of bridge decks

Abstract A model was developed to determine the time to first repair and to subsequently rehabilitate concrete bridge decks exposed to chloride deicer salts. Said model incorporates the statistical nature of factors affecting the corrosion process. The time to first repair and rehabilitate was predicted for 10 bridge decks built in Virginia between 1981 and 1994. The model was validated using historical service life data for 129 bridge decks built in Virginia between 1968 and 1972. The time for rehabilitation predicted for the newer set of bridge decks was approximately 13 years longer than the normalized time for rehabilitation projected for the older bridge decks. The increase in time for rehabilitation for the newer set of bridge decks was attributed to a reduction in the specified maximum water/cement ratio and increase in clear cover depth. The probabilistic model is shown to be an advancement over the deterministic model currently in use.

A genetic algorithm with memory for mixed discrete–continuous design optimization

This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.

Fraction of Design Space Plots for Assessing Mixture and Mixture-Process Designs

Variance dispersion graphs are useful tools for evaluating various types of designs, including mixture and mixture-process designs. They allow an experimenter to see patterns of scaled prediction variances (SPV) throughout a design space. We introduce a complementary fraction of design space (FDS) plot that provides additional information on the distribution of the SPV throughout a design space. These plots display the fraction of design space where the SPV is less than or equal to specific values. The FDS plots for combined mixture-process experiments also show which of the two types of variables has more influence on the SPV. The FDS plots for mixture and mixture-process experiments are developed and then demonstrated with several examples.

Genetic algorithm for mixed integer nonlinear programming problems using separate constraint approximations

This paper describes a new approach for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation.The additions involve memory as a function of both discrete and continuous design variables, and multivariate approximation of the individual functions responses in terms of several continuous design variables. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.

Three-Dimensional Variance Dispersion Graphs for Mixture-Process Experiments

In a mixture experiment, the design factors are the proportions of the components of a mixture, and the response variables depend only on these component proportions. In addition to the mixture components, the experimenter may be interested in other variables that can be varied independently of one another and of the mixture components. Such mixture-process experiments are common in industry. There are many strategies based on different design criteria that are used to create designs involving both types of variables. We develop variance dispersion graphs (VDGs) to evaluate mixture-process designs and illustrate how the graphs are used with two examples.

A second order model for cylindrical data

Modeling cylindrical data, comprised of a linear component and a directional component, can be done using Fourier series expansions if we consider the conditional distribution of the linear component given the angular component. This paper presents the second order model which is a natural extension of the Mardia and Sutton (1978) first order model. This model can be parameterized either in polar or Cartesian coordinates, and allows for parameter estimation using standard multiple linear regression. Characteristic of the new model, how to compare the adequacy of the fit for first and second order models, and an example involving wind direction and temperature are presented.

A Genetic Algorithm with Memory for Mixed Discrete-Continuous Design Optimization

This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.

A Tutorial on One-Way Analysis of Circular-Linear Data

Some industrial applications lead to observations that are characterized by a bivariate response where one observation is an angle or direction and the other is linear. These data are frequently called cylindrical data since they can be represented by p..