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Featured Application: This paper mainly applies to the parameter inversion problem in mining subsidence under the condition of lack of empirical values. In this study conducted in the Shendong mining area, this paper tackles the challenge of estimating mining subsidence parameters in the absence of empirical values. The study employs a tailored pattern recognition method specifically designed for mining subsidence in a specific working face. The goal is to determine a globally approximate optimal solution for these parameters. Subsequently, this study utilizes the approximate optimal solution as an initial exploration value and harnesses the modular vector method to obtain stable, accurate, optimal solutions for the parameters. The results of the study demonstrate the effectiveness of the improved modular vector method. In simulation tests involving the subsidence coefficient, the main influence angle tangent value, the propagation angle of mining influence, and the deviation of the inflection point, the relative errors do not exceed 1.2%, 1.9%, 1.7%, and 7.9%, respectively. Furthermore, when subjected to random errors of less than 20 mm, the relative errors for each parameter remain below 2%. Even in conditions with 200 mm gross error, the relative error for each parameter does not exceed 5.1%, indicating high precision. In an engineering example, the root mean square error of the improved modular vector method's fitting result is 64.31 mm, constituting a mere 1.79% of the maximum subsidence value. This performance surpasses that of the genetic algorithm (70.47 mm), particle swarm algorithm (72.82 mm), and simulated annealing algorithm (75.45 mm). Notably, the improved modular vector method exhibits superior stability and reduced reliance on the quantity of measured values compared to the three aforementioned algorithms. The inversion analysis of predicted parameters based on the improved modular vector method, coupled with the probability integral method, holds practical significance for enhancing the accuracy of mining subsidence prediction. [ABSTRACT FROM AUTHOR]

In this study conducted in the Shendong mining area, this paper tackles the challenge of estimating mining subsidence parameters in the absence of empirical values. The study employs a tailored pattern recognition method specifically designed for mining subsidence in a specific working face. The goal is to determine a globally approximate optimal solution for these parameters. Subsequently, this study utilizes the approximate optimal solution as an initial exploration value and harnesses the modular vector method to obtain stable, accurate, optimal solutions for the parameters. The results of the study demonstrate the effectiveness of the improved modular vector method. In simulation tests involving the subsidence coefficient, the main influence angle tangent value, the propagation angle of mining influence, and the deviation of the inflection point, the relative errors do not exceed 1.2%, 1.9%, 1.7%, and 7.9%, respectively. Furthermore, when subjected to random errors of less than 20 mm, the relative errors for each parameter remain below 2%. Even in conditions with 200 mm gross error, the relative error for each parameter does not exceed 5.1%, indicating high precision. In an engineering example, the root mean square error of the improved modular vector method’s fitting result is 64.31 mm, constituting a mere 1.79% of the maximum subsidence value. This performance surpasses that of the genetic algorithm (70.47 mm), particle swarm algorithm (72.82 mm), and simulated annealing algorithm (75.45 mm). Notably, the improved modular vector method exhibits superior stability and reduced reliance on the quantity of measured values compared to the three aforementioned algorithms. The inversion analysis of predicted parameters based on the improved modular vector method, coupled with the probability integral method, holds practical significance for enhancing the accuracy of mining subsidence prediction.