Construction of prediction system of properties of multi-component materials

本研究的目的是改进“小区域线性插值法”，使其适用于各种实际系统，而“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是非常有效的，而在数据不均匀分布的系统中效果较差，特别是在数据稀疏分散的区域，对这种方法进行线性内插逼近。1999年，我们尝试将样条插值法和“小区域线性插值法”结合使用。在2000年，我们尝试将这种方法推广到数据区外的地区进行预测。当然，这预计适用于数据区附近的区域。我们使用拉格朗日方法和改进的“小区域线性插值法”一起外推数据区外的属性。结果，在预测点在“数据长度”之外10%的情况下，预测属性的误差小于3%是可能的。“数据长度”是指用来外推点的合成长度。这种改进的“小区域线性插值法”适用于预测多组分体系的所有连续变化的性质，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.