Efficient global optimization (EGO) was applied to the multi-objective design and knowledge discovery of a supersonic transport (SST) wing. The objective functions considered here are employed to maximize the lift-to-drag ratio at supersonic cruise, to minimize the sonic boom intensity and to minimize wing structural weight, simultaneously. The EGO process is based on Kriging surrogate models, which were constructed using several sample designs. Subsequently, the solution space could be explored through the maximization of expected improvement (EI) values that corresponded to the objective function of each Kriging model because the surrogate models provide an estimate of the uncertainty at the predicted point. Once a number of solutions have been obtained for the EI maximization problem by means of a multi-objective genetic algorithm (MOGA), the sample designs could be used to improve the models' accuracy and identify the optimum solutions at the same time. In this paper, 108 sample points are evaluated for the constructions of the Kriging models. In order to obtain further information about the design space, two knowledge discovery techniques are applied once the sampling process is completed. First, through functional analysis of variance (ANOVA), quantitative information is gathered and then, self-organizing maps (SOMs) are created to qualitatively evaluate the aircraft design. The proposed design process provides valuable information for the efficient design of an SST wing.

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Self-Organizing Map (SOM) proposed by Kohonen is a kind of the Neural Networks and using for the competitive learning. It is difficult to specify the learning parameters for SOM, because the neighborhood radius, which is a one of learning parameter, depends on the scale of the problem or map space, and the users of SOM code usually find the proper value through a trial and error process. In this circumstance, the authors propose a SOM that has several neighborhood radii, which is similar to the temperature parallel Simulated Annealing (SA) method. In this method, several neighborhood radii conduct competitive learning in parallel, and a highly evaluated neighborhood radius is dynamically selected. Furthermore, the authors propose the new evaluation function of the map, in order to evaluate the proposed method quantitatively. The results of the map evaluation with the proposed evaluation function were consistent with those of visual evaluation. The results are compared with those of the conventional SOM, to demonstrate the effectiveness of the proposed method.

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Presently, ultrasonic and electromagnetic waves are often used for the quantitative nondestructive testing of concrete. The evaluation of material deterioration and detection of defects in concrete are carried out using ultrasonic waves. On the other hand, the positions of reinforced bars can be reconstructed by using electromagnetic waves. In order to gain a better understanding of ultrasonic and electromagnetic waves in concrete, it is useful to model the wave propagation and scattering process explicitly in the time domain. This study presents a technique for numerical time domain modelings of ultrasonic and electromagnetic waves. Our simulation tool is based on a combination of the finite integration technique (FIT) and an image-based modeling approach. The FIT is a grid-based spatial discretization method that works in conjunction with a leap-frog-type explicit scheme. In the image-based modeling approach, geometries of concrete are determined using a digital image, e.g., a cross-sectional image or CT data. Then the processed pixel or voxel data are directly fed into the FIT. We demonstrate simulations of the contact ultrasonic method and electromagnetic radar method for concrete. The utility of the image-based FIT is validated with experimentally measured data.

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