Construction of prediction system of properties of multi-component materials

研究的目的是改进作者提出的“小区域线性插值法”，使之适用于各种实际系统。“小区域线性插值法”在数据在组成平面上均匀分布的系统中非常有效，而在数据分布不均匀的系统中效果较差，1999年，我们尝试将样条插值与“小区域线性插值法”结合使用。2000年，我们尝试将该方法推广到数据区以外的区域，利用外推法进行预测。当然，预计这适用于接近数据区的区域。采用拉格朗日法外推数据区外的性质，并结合改进的“小区域线性插值法”。因此，在预测点在“数据长度”的10%之外的情况下，可以预测误差小于3%的属性。“数据长度”是指用于外推点的组成长度。当预测点在“数据长度”的20%范围内时，预测误差福尔斯在7%以内。这种改进的“小区域线性插值法”适用于多组分体系的所有连续变化的性质的预测，尽管我们对三组分硅酸盐玻璃的热膨胀系数和玻璃化转变温度进行了测试。

The object of the research is to improve "small-area linear interpolation method" which the author developed to be applicable to various actual systems While "small-area linear interpolation method" is very effective in a system where data are dispersed uniformly in the composition plane, it is less effective in a system where data are not dispersed uniformly, especially in an area where data are dispersed sparsely for linear interpolation approximation of this method.In 1999, we tried to use Spline interpolation together with "small-area linear interpolation method". This has improved prediction remarkably in the area where data are dispersed sparsely.In 2000, we tried to expand the method to prediction for the area outside of data area by use of extrapolation. This is, of course, anticipated to be applicable to the area close to data area. We used Lagrange method to extrapolate properties outside of data area together with the improved "small-area linear interpolation method". As a result, it has been possible to predict properties with error by less than 3% in the case a predicted point is in 10% outer of "data length". "Data length" means composition length which is used to extrapolate the point. The prediction falls to error range of 7% in the case a predicted point is in 20% outer of "data length".This improved "small-area linear interpolation method" is applicable to prediction of all properties which change continuously of multi-component system, although we tested this method for the thermal expansion coefficient and glass-transition temperature of three-component silicate glasses.