基于WTLS的井筒变形监测算法及方案设计

针对基于最小二乘的常规井筒变形监测算法中,系数矩阵往往包含观测值误差影响,难以解算出井筒变形最优解,提出一种抗差加权整体最小二乘算法。该算法通过同时对待求参数和系数矩阵进行估计,克服常规最小二乘系数矩阵受观测值随机误差影响;同时结合IGGⅢ三段权函数抗差因子,调整各观测值权函数,消除观测值粗差对最终变形估计值的影响,得到最优的井筒变形值。最后分别采用模拟和实测井筒数据对算法进行了验证,结果表明:当观测值含有随机误差时,整体最小二乘算法优于最小二乘,但都无法抵御观测粗差影响;抗差加权整体最小二乘算法可以有效抵御观测粗差,修正观测随机误差影响,且精度优于抗差最小二乘;采用抗差加权整体最小二乘算法对实测井筒变形数据进行解算结果与实际相符,可以增强变形监测结果的可靠性,提高井筒变形量精度。

Shaft deformation monitoring scheme design and algorithm based on WTLS

Since the coefficient matrix affected by the observation errors in the traditional least squares (LS) algorithm，it is hard to calculate the optimal solution of shaft deformation.A weighted total least squares (WTLS) algorithm was proposed.The algorithm can mitigate the influence of stochastic observation errors on coefficient matrix.With IGGIII weight function and robust factors，the influence of observation gross errors on the final estimated deformation can be greatly eliminated.Finally both the simulating data and the field data on shaft deformation were used to verify the algorithm.It shows that WTLS algorithm is better than the LS in terms of the condition of observation with stochastic errors，but both algorithms fail to deal with the gross error.Robust WTLS algorithm can eliminate the gross error and weaken the influence of stochastic observation errors，and the deformation of robust WTLS is more accuracy than that of robust LS.The deformation results of field data solved with robust WTLS agree with the real situation，which improve the reliability and accuracy of shaft deformation.