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最小一乘法是一个既古典又新颖的方法,随着最小一乘解的实现问题近年来有大的突破,一些最小二乘法所不具有的优良特性,如直观性、稳健性、零误差性、可预测性、广义性等逐渐显现。最小一乘逼近是最小绝对值误差极小化的逼近,也称为“极小极小”逼近,由于极小极小逼近的最佳结果一定是零,所以零误差原理是最小一乘法的基本原理。最小一乘解是通过“代表式”的数据处理方式来实现的,由于排除了大误差数据的干扰,使最小一乘法具有较好的稳健性。而代表数据可按不同的应用而选择并确定,使应用具有了广泛性。对于预测而言,将端点数据设定为零误差数据,使数据的权重不再相等,而是往端点方向倾斜,端点数据具有最大的权重,且建立在无误差的基点上,这使得预测理论与模式变得合理,使预测的准确性得到保证。文中通过3个工程实例,介绍了最小一乘法在探索岩石或软土地基在沉降过程中的应用,其结果与最小二乘法的进行了比较,通过分析后给出如下主要结论:(1)最小一乘法的数据处理稳定性较好,波动幅度较小,预测结果较准;(2)一般不会出现最小二乘法数据处理中的矛盾及不合理的现象;(3)虽然时间t→∞的极限下沉量具有不可验证性,但最小一乘法的预测是建立在无误差的基点上,比最小二乘法的预测建立在有误差的基点上合理,加上有较好的稳健性,其结果更具参考性。
The least-squares method is a classical and novel method. As the problem of the least-squares solution has been greatly improved in recent years, some least-squares methods do not have some excellent characteristics such as intuition, robustness, zero error, Predictability, generality, etc. gradually appear. Least-squares approximation is the approximation of minimization of the absolute minimum error, also called the “minimax” approximation. Since the best result of the minimax approximation must be zero, the principle of zero error is the least-squares method The basic principle. The least-squares solution is realized by the data representation of “representative ”, which makes the least-squares method more robust by eliminating the interference of large error data. The representative data can be selected and determined according to different applications, so that the application has a wide range of applications. For the prediction, the endpoint data is set to zero error data, the data weight is no longer equal, but to the endpoint tilt, the endpoint data has the maximum weight, and based on error-free basis, which makes the prediction theory And the model becomes reasonable, so that the accuracy of the forecast is guaranteed. In this paper, the application of the least square method in exploring the settlement of rock or soft ground is introduced through three engineering examples. The results are compared with the least square method. The main conclusions are as follows: (1) The minimum The data processing of one-multiplication method has better stability and less fluctuation, and the prediction result is more accurate. (2) Contradictions and unreasonable phenomena in data processing of least-squares method generally do not appear. (3) Although the time t → ∞ The limit subsidence is untestabilistic, but the least-squares method is based on error-free basis, which is more reasonable than the least-squares method to predict with error, and has better robustness. The result More reference.