In this paper, a recurrent iieural network(RNN) is applied to approximating one to N many valued mappings. The RNN described in this paper has a feedback loop from an output to an input in addition to t h e conventional multi layer neural network(MLNN). The feedback loop causes dynamic output properties. T h e convergence property in these properties can be used for this. approximating problem.In order to avoid conflict by the overlapped target d a t a y*s to the same input I*, the input d a t a set (n, y*) and t h e target d a t a y* are presented to t h e network in learning phase. By this learning, the network function j(x, z ) which satisfies y* = j ( m , y") is formed. In recalling phase, t h e solutions y of y = f ( z , y ) a r e detected by t h e feedback dynamics of RNN. The different solutions for t h e same input x can be gained by changing the initial output value of y.It have been presented in our previous paper that t h e RNN can approximate many valued continuous mappings by introducing the differential condition to learning. However, if t h e mapping has discontinuity or changes of value number, it sometimes shows undesirable behavior. In this paper, the integral condition is proposed in order t o prevent spurious convergence and to spread t h e attractive regions to the approximating points.

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SUMMARYThis paper proposes frequency annealing (FA) as an optimization method which searches for the global optimal solution without using the derivative of the objective function. FA detects the global optimal solution efficiently by smoothing the objective function with a low-pass filter. The gradient of the low-pass filter, which is defined by a convolution integral, is approximated by the value of the objective function at a finite number of evaluation points defined according to the Gaussian probability density function. Thus, a gradient method without using the derivative of the objective function is realized. The effectiveness of the approximation of the low-pass filter gradient is verified by the variance analysis of the approximation value. It is shown that by defining the neighbor points with an adequate probability density function, the approximation accuracy is made independent of the dimension M. The usefulness of the approach is demonstrated by a two-dimensional problem and a simulation of perceptron training. FA can detect the global optimal solution even when the objective function has a local minimum or a discontinuity.

As a basic study of a practical method for predicting sound insulation performance of windows, this report presents a study of the sound reduction index of windows with single glazing below a critical frequency. First, results calculated by an existing theory for a single plate for the sound reduction indices are compared with measured results of actual windows to assess the theory’s applicability for evaluating the sound insulation performance of windows. Next, a regression analysis is employed to measured results of a certain number of actual windows to explore a further development of a more practical prediction. The following findings were obtained: (1) Sound reduction indices of actual fixed windows are predictable using Sewell’s transmission theory for a single plate. However, sound reduction indices of openable windows, especially those of sliding windows, are affected strongly by window frame gaps. Therefore, predicting sound reduction indices of all windows accurately is difficult if using only one theory. (2) The frequency slope of the window reduction index is much lower than that of the mass law. Regression analyses indicate that the frequency slope of the reduction index of all examined windows is 3.0 dB per octave, on average.