制造误差的灰自助动态预报

Dynamic Prediction for Manufacturing Errors Using Grey Bootstrap

综合考虑灰色系统理论和Bootstrap统计理论的信息预报特点,建立制造误差的灰自助动态预报模型GBM(1,1),以解决信息预报中存在的一些问题。GBM(1,1)在灰微分建模时进行Bootstrap再抽样,更多地挖掘系统信息,从而更准确地预报系统真值及其分布区间的瞬态变化状况。在计算机仿真中,研究了各种随机误差系统例如正态分布、瑞利分布、均匀分布、三角分布以及混合分布等系统的预报问题,也涉及到一些系统误差例如上升趋势、下降趋势和周期趋势等误差的预报问题。在实际试验中,研究了滚动轴承套圈磨削圆度误差的预报问题。计算机仿真和试验研究表明,GBM(1,1)允许小的数据样本以及各种类型的随机误差与系统误差存在,预报的准确率可以达到95%以上。

Based on the information prediction characteristics of the grey system theory and bootstrapt statistics, a grey bootstrap model （GBM） of dynamic prediction for manufacturing errors was proposed to resolve problems about information prediction. Bootstrap resampling is used in the process of modeling the grey differential coefficient function to mine more information about systems, and the grey bootstrap model can predict transient state of the true value and its distributing interval exactly. Computer simulation was applied to deals with the prediction of many kinds of random errors such as normal distribution, Rayleigh distribution, triangular distribution, uniform distribution and mixed distribution etc, and prediction of some systematic errors such as increasing tendency errors, decreasing tendency errors and periodic change tendency errors were involved in it as well. Experiment was carried out to predict the roundness errors of grinding rolling beating rings. Computer simulation and experiment showed that the grey bootstrap model allows small sample, different type of random errors and systematic errors, and the percentage of accuracy can be up to above 95 %.