This paper describes the flexible implementation of approximation concepts in an MDO framework offered by the commercial-off-theshelf software package iSIGHT. Three different types of approximation models-Response Surface Modeling, Taylor Series Approximations, and Variable Complexity Modeling-are implemented in such a way that they may be used interchangeably in any combination to approximate any segment of an MDO analysis problem, as well as the complete system analysis sequence as a whole. The novelty of the implementation is in the fact that all approximation models are implemented as "smart" objects. Each of the objects possesses certain characteristics defined by the "tuning parameters" specific to each approximation type, and a suite of methods (actions) which operate on the data of each model. The concept of Response Surface Modeling is taken to the extreme of simplicity and efficiency by using a minimum number of design analyses for model construction and then gradually improving the quality of the model following the path of the optimizer The category of Taylor Series Approximations actually spans a whole suite of approximation techniques that are based on using the first derivatives of the response function. Applications demonstrate the utility and flexibility of the approach.

Morphological algorithms for the analysis of the microstructure and estimation of the physical properties of volcanic geological specimens are described. Various properties of materials, such as bulk viscosity, rigidity, tensile and compressive strengths, etc., depend on the microstructure of the material, which is typically composed of a mosaic of interlocking particles of different phases. The images of the geological microstructure are first separated into their constituent phases. The phase images can then be processed to estimate the percentage contribution of each phase, the total boundary per phase, phasephase contact boundaries, particle size distributions for each phase and angle of contact between particles. These morphological image measurements can then be used to characterize the physical properties of magma.

No abstract

Morphological algorithms1 for the parallel quantification and modeling of Gaussian image features are described. These algorithms are applicable to any image generation process which disthbutes the greyscale values according to a normal distribution. Morphological operators can be applied to the image data to obtain two parameter images, one consisting of mean positions and amplitudes and the other consisting of estimates of standard deviations, which are then used to "grow" (in parallel) the predicted Gaussian surfaces. Two methods to decompose and modulate the growth process (using the parameter images) are considered. One method grows the predicted Gaussian surface in terms of an approximating binomial distribution. The other method grows the desired Gaussian from smaller Gaussians of varying standard deviations.