Kazunori Nagasaka

Neuro-fuzzy ID3: a method of inducing fuzzy decision trees with linear programming for maximizing entropy and an algebraic method for incremental learning

Abstract ID3 is a popular and efficient method of making a decision tree for classification from symbolic data without much computation. Fuzzy reasoning rules in the form of a decision tree, which can be viewed as a fuzzy partition, are obtained by fuzzy ID3. The aims of this paper are: (1) Not only the learning from examples but also the interview with domain specialists are needed for knowledge acquisition in expert systems. In order to avoid dangerous simplification of the tree by discarding partial knowledge of the experts, a measure of uncertainty with maximizing entropy is applied to fuzzy ID3. (2) Basically the tree based learning is nonincremental or single step. An algebraic method to facilitate incremental learning like the neural nets is adapted and the fuzzy decision tree which consists of B-spline membership function is regarded as three layered neural network. (3) Prototypes of expert system for estimation of wheel wear characteristics and surface roughness in abrasive cut-off are developed.

Orthogonal and successive projection methods for the learning of neurofuzzy GMDH

Abstract A neural GMDH (group method of data handling) family of modelling algorithm emulates the self-organizing activity of the central nervous system, and discovers the structure (functional form) of empirical models that include many input variables. A generalized successive projection method is developed for the accelerated learning algorithm of the GMDH type model whose partial descriptions are represented by the radial basis functions network. (1) For the learning of partial descriptions of the perceptron type GMDH, a combined algorithm of the successive projection method and the orthogonal projection method is developed. (2) For the learning of the network type GMDH, a successive projection method is derived as the solution of an optimization problem in which the Minkowski norm of distance travelled (step size) is minimized. Their performances are compared with the instantaneous learning algorithms such as the least mean square. Several examples show the validity of the methods.

A neurofuzzy approach to variational problems by using Gaussian membership functions

Abstract In this paper we propose a neurofuzzy direct solution method for variational problems in which the cost function of an integral form is minimized. We deal with two nonlinear systems; one is a direct drive (DD) manipulator systems, and the other is a trailer-truck system. The DD manipulator system is described by a continuous-time dynamical model, and the trailer-truck system is described by a discrete-time dynamical model. The problem is to find trajectories which minimize the cost function of an integral form. The trajectories of state variables and input variables are represented by fuzzy models that consists of Gaussian membership functions. The networks of Gaussian functions are trained by the steepest-descent method to minimize the cost function. The proposed neurofuzzy approach provides a direct solution method of the variational problems by using Gaussian functions. The function is regarded as a simplifie fuzzy reasoning model and called neurofuzzy.

The establishment of a tool life equation considering the amount of tool wear

Abstract A new tool life equation is proposed: in this equation the cutting conditions and the amount of tool wear are treated as independent variables. The model is constructed so that it fits a process of tool wear which follows three stages, i.e. rapid initial wear followed by gradual or little wear and finally very rapid or catastrophic wear. The model is compared with the multiplication and polynomial models with respect to the accuracy and the applicability to optimization of the cutting process. A sensitivity analysis of the model was carried out by investigating the effect of parameter variation on the accuracy of the model. A convenient technique is suggested for application of the model to practical use.

Structural learning with M-apoptosis in neurofuzzy GMDH

There have been many studies of mathematical models of neural networks. However, there is always a problem of determining their optimal structures because of the lack of prior information. Apoptosis is the mechanism responsible for the physiological deletion of cells and appears to be intrinsically programmed. We propose a procedure, named M-apoptosis, for the structure clarification of neurofuzzy GMDH model whose partial descriptions are represented by the radial basis functions network. The proposed method prunes unnecessary links and units from the larger network to identify, and to further clarify the network structure by minimizing the Minkowski norm of the derivatives of the partial descriptions. The method is validated in the numerical examples of function approximation and the classification of Fishers Iris data.

Optimum combination of operating parameters in abrasive cut-off

Abstract For optimization of abrasive cut-off operation, wheel wear equation must be identified before the operation is optimized. The equation is obtained by using GMDH algorithm with successive determination of trends containing interactive terms. In the model equation factors of grinding fluid are taken into consideration in addition to the factors of wheel, work material, feed (table speed) and wheel speed. For the identification of the model wheel wear tests are performed under the experimental design treating the above-mentioned factors as independent variables. The grinding ratio (output in the model) can be predicted for combinations of various factors using the model. With the wheel wear equation and machining cost model, the optimum combination of wheel, fluid, feed and wheel speed can be selected for a given work material. The relationships between these variables and the costs are investigated.

Computed tomography by neuro-fuzzy inversion

Moody and Darken (1989) proposed a network architecture which uses a single internal layer of locally-tuned processing units to learn real-valued function approximations. The network can be reinterpreted as both neural networks and fuzzy rules. Hence, we call it neuro-fuzzy and proposes method of geophysical computerized tomography. The line integrals of Gaussian radial basis functions can be obtained in a simple manner and the spatial distribution is calculated from the line integrals along rays in a plane. With this method, detailed pictures of the spatial distribution of attenuation or propagation velocity can be reconstructed from a small number of measured data.

Identification of a grinding wheel wear equation of the abrasive cut-off by the modified GMDH

Abstract A grinding wheel wear equation is identified by the GMDH (Group Method of Data Handling) algorithm with successive determination of polynomial trends containing interactive terms, considering chemical compositions and mechanical properties of work materials, abrasive grain, grain size, grade, wheel speed and feed. The established model enables the grinding to be predicted for all combinations of work materials, grinding wheels and grinding conditions, and serves as an aid in the optimization of the grinding process.

Selection of the optimum number of hidden layers in neuro-fuzzy GMDH

An adaptive learning network (ALN) of group method of data handling (GMDH) type with error backpropagation is proposed, in which Gaussian radial basis functions (RBF) networks are applied to the partial descriptions of the GMDH. Optimum number of hidden layers in the ALN is selected applying the differential minimum bias criterion (DMC) and the Akaikes information criterion. The validity of these two criteria are confirmed with the cross validation technique and the average mean log-likelihood.<<ETX>>

Neuro-fuzzy minimum torque change control of DD manipulator

A minimum torque-change model of a robotic manipulator was proposed by Uno et al. (1989), in which a function of torque change is minimized. The objective function depends on the nonlinear dynamics of the manipulator. A trajectory with best performance was obtained by the iterative scheme using the method of variational calculus and dynamic optimization theory. Though the method is computationally economical, it seems to be a control theoretic approach rather than a neuro scientific one. In this paper, the authors propose a direct solution method of this variational problem using Gaussian radial basis functions. The function can be regarded as both a three layered neural network (Moody and Darken, 1989) and a simplified fuzzy reasoning model.