顾及起算数据误差的多点灰色模型在变形监测中的应用

Application of the Multivariable Grey Model in Deformation Monitoring in View of Initial Data Errors

分析了多点灰色模型利用最小二乘估计原理进行参数解算时无法顾及起算数据误差带来的影响。将混合最小二乘与多元整体最小二乘应用到多点灰色模型的参数估计中。首先利用QR分解将起算数据中常数列和误差项相分离;采用最小二乘和多元整体最小二乘分别进行解算建模;最后通过实验证明了优化的MGM(1,n)模型具有较高的建模和预测精度,能够为精密工程变形分析提供一定的参考和借鉴。

This paper analyzes the initial data errors is not preventable in the muhivariable grey model based on least square estimation, and proposes a muhivariable grey model based on the mix LS-MTLS. Firsly, the constant column and error block matrices are separated by using QR factorization approach; following, the least-square solution and the multivariate total least-squares solution are calculated the parameter respectively; finally, the experimental result shows that the proposes muhivariable grey model have better simulating and forecast accuracy, it can provide some reference for precision engineering measurement.