A parameter inversion method for the probability integral method based on robust ridge estimation

Abstract

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The probability integral method is one of the most widely used methods for predicting surface subsidence induced by underground mining in China. In its parameter calculation, the least square algorithm is commonly employed for fitting parameters. However, in the process of fitting parameters, the results are easily affected by ill-conditioned normal matrices and the interference of outliers, resulting in divergent problems. To solve these problems, the principle of robust ridge estimation was introduced in this paper, and a parameter calculation model for the probability integral method based on this principle (hereafter referred to as the established model) was established. Besides, a parameter calculation experiment with manual intervention was conducted in combination with engineering examples. The results demonstrate that the parameter calculation method based on robust ridge estimation can suppress the interference of outliers, overcome the problem of ill-conditioned matrix, and ensure the effectiveness and reliability of parameter estimation results. Compared with the conventional least squares method, the robust ridge estimation method demonstrates greater accuracy in predicting surface subsidence parameters, which validates its rationality and accuracy in underground mining engineering. The research findings provide technical support for obtaining similar parameters for surface subsidence in mining areas and hold significant engineering application value.

Keywords

• robust ridge estimation
• probability integral method
• parameter determination
• illconditioned normal matrix
• outliers