岩石抗剪强度计算的稳健回归模型及其应用

A Robust Regression Model and Its Application in Calculating Shear Strength of Rock

针对岩石抗剪强度确定中图解法和最小二乘法存在的问题:①只适用于实验数据相关性较高的情况,不适用于数据离散并有异常值存在的情况;②在处理由试验法获得的试验数据时,最小二乘法由于采用残差平方和,容易夸大试验数据中异常值的影响,提出了岩石抗剪强度参数的稳健回归分析方法。该方法在实验数据相关性差、数据离散并有异常值存在的情况下,具备削弱数据离散和对异常值进行定位的能力,提高了估计参数的稳健性和可靠性。该方法以残差的绝对值之和代替残差平方和,并通过复形法求得力学参数,避免了异常值的二次项,可有效地减少异常值的影响。通过工程实例表明,在试验数据的相关性较好时,两种方法的计算结果相差不大,但当试验数据的相关性较差,存在异常值时,稳健回归方法的计算结果要优于最小二乘法。

There are two problems in the graphic method and the Least Quares （LS） method in determining the shear strength of rock. （1） The experimental data should be highly correlated, and separate data and anomalous data are not suitable. （2） The effect of anomalous values in test data is markedly shown because of the quadratic sum of residual errors in the least squares method. This paper proposes a shear strength parameter （Robust） regression analysis method. This method can be applied to analyze experimental data with poor correlation, and with anomalous values, and the effects of discrete and abnormal positioning can be weakened to improve the robustness and reliability of estimated parameters. In order to reduce the effect of anomalous values in the test data, the sum of residual absolute value is used instead of the quadratic sum of residual errors in the robust regression method, then the quadratic terms of anomalous value could be avoided, and the effect of anomalous values could be reduced. It is shown that the results of the two methods are the same when the test data is good, but the results of the robust regression method are better than those obtained by the least squares method when there are anomalous values in the test data.