Construction of prediction system of properties of multi-component materials

本文的研究目的是对作者提出的“小面积线性插值法”进行改进，使其适用于各种实际系统，而“小面积线性插值法”在数据均匀分布在组成平面上的系统中是非常有效的，而在数据不均匀分布的系统中，特别是在数据稀疏分布的区域，对该方法的线性插值逼近效果较差。1999年，我们尝试将样条插值与“小面积线性插值法”结合使用。这大大提高了在数据分散稀疏的地区的预测能力。2000年，我们尝试将该方法扩展到使用外推法预测数据区域外的区域。当然，预计这将适用于靠近数据区域的区域。我们采用拉格朗日法结合改进的“小面积线性插值法”外推数据区域外的属性。因此，如果预测点在“数据长度”的10%之外，则可以以小于3%的误差预测属性。“数据长度”是指用于外推点的组合长度。如果预测点在“数据长度”的20%之外，则预测的误差范围为7%。这种改进的“小面积线性插值法”适用于预测多组分体系的所有连续变化的性质，但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.