关键词: 最小一乘法, 曲线拟合, 沉降, 预测

Abstract: The least absolute deviation (LAD) method has some favorable properties, including intuitiveness, robustness, zero-error, predictability and generalization, compared to the least square (LS) method. The LAD approximation is a "mini-mini approximation", which is minimization of the minimum absolute value of error. Because the best result of the mini-mini approximation must be zero, the zero-error principle is indeed the basic principle of LAD method. The realization of the LAD solution is achieved by a "representative" data processing mode. Because the disturbance induced by the data with big error is removed, the LAD method has a good robustness. Since the representative data are selected according to different applications, the LAD method is widely applicable. When the LAD method is applied to prediction, the endpoint data can be set to be zero-error data, yielding the unequal weights of the data which are closer to the end point. As a result, the endpoint data have the greatest weight, and have a basis without errors, making the proposed procedure more reasonable and more accurate. Based on three engineering cases, the LAD method is applied to predicting the settlement process of rock and soil foundation. By comparing with LS method, it is concluded that: 1) The stability of data processing of LDA method is better, the fluctuation range is smaller, and the forecasted result is more accurate; 2) Ccntradictory and unreasonable phenomenon no longer appear as in the data processing of LS method; 3) when t→∞, although the limit settlement values cannot be verified, the prediction of LAD method is more reasonable than those of LS method, since the LAD method is built on the basis without errors.

Key words: least absolute deviation method, curve fitting, settlement, forecast