In the actual random phenomena, the objective signal usually shows a complex fluctuation pattern apart from a standard Gaussian distribution due to the diversified causes of fluctuation. Furthermore, the observation data are very often contaminated by the external noise of arbitrary distribution type. In this paper, a new state estimation algorithm for the stochastic system with a random excitation of non-Gaussian distribution type is proposed by introducing a form of expansion expression with parameter differential type for the conditional probability density function. It is noticeable that the proposed wide sense digital filter is constructed in a hierarchical form based on the direct use of the well-known Kalman's filtering algorithm. Therefore, non-Gaussian properties of the fluctuation and various nonlinear correlation information are reflected hierarchically in this estimation algorithm. Finally, the effectiveness of the theory is experimentally confirmed too by applying it to the actual data in the room acoustical field.

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This paper discusses a determining algorithm for the three-dimensional convex hull which is well-fitted to deal with interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution and is available for set operations. The paper also deals with the application of this algorithm to specific interference problems. The proposed algorithm is devised to determine the smallest convex polyhedron containing a concave polyhedron given by a solid model beforehand, as a solid model having the same data structure as that of the concave polyhedron. It features the use of Euler operators, a general method for determining a solid model. This means that the proposed algorithm does not depend on the data structure of a solid model and that all convex polyhedrons obtained during the process of determining a three-dimensional convex hull are also in the form of solid model. Because of such a feature, the three-dimensional convex hull determined by the algorithm can be used for set operations with the given concave polyhedrons, and therefore, the algorithm provides a convenient approach to interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution. As an example of the application of the proposed algorithm to practical purposes, this paper also discusses a study on the extraction of undercuts in mold design using this algorithm. The findings indicate that the proposed algorithm is useful in solving such practical problems.

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We discuss the application of the expert system technology to the flatness control problem of the aluminum foil rolling process. Our expert system can adjust the target shape pattern on line for the automatic flatness control system according to the material characteristics and operating conditions. We have modelled the knowledge structure and inference mechanism in the target shape adjustment process that has been done by the experts and developed an expert system. This system has ability to solve the conflict between rules, and keeps consistency in actions. This system infers adaptively considering applied results of the past inference to accomodate the change of the characteristics of the rolling process. Further our model is useful for a class of adjustment problems in the process control.

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We show the Inductive capability or generality of a connectionist learning depends on the network architecture. It is shown that the conventional network architecture is inadequate for representing and learning complex nonlinear structure of the continuous mapping. We propose a new network architecture, high-order functional networks, with some nonmonotonic functional units as input units. It is shown that a high-order functional network trained with backpropagation can generalize and infer the nonlinear structure between the continuous variables. Nonlinear mappings are characterized by the positions and the number of their extreme points and the curvatures at the extreme points. It is shown that the combination of the, high-order functional input units and the sigmoid-type hidden units make it possible to realize and acquire a proper internal representation of the network and that extracts those features of the task domain.

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In this paper, a pattern recognition system by neurons with signum function is considered. The entire pattern recognition system is constructed by an invariance net of neurons with signum function and a trainable descrambler with CONE. The invariance net can be designed to produce a set of outputs that are insensitive to translation and rotation of the input patterns. The original patterns can be reproduced in standard position by the trainable descrambler. The system presented here produces a noise tolerant mapping and has a fast convergence rate with CNR algorithm.

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