According to traditional concepts, the movement of overlying strata and surface damage caused by coal mining in horizontal coal seams are symmetrical in terms of spatial distribution. However, in a lot of engineering practices, this symmetry has not been discovered. We often use the symmetry function to establish the profile prediction function of the surface damage, which results in a large difference between the prediction result and the actual situation. To solve this problem, this paper takes subsidence velocity as an example. Firstly, the spatial distribution functions of subsidence velocity on both sides were deduced theoretically. Through comparison, it is found that the change rate of the spatial distribution curve of the coal pillar side subsidence velocity is smoother than that of the goaf side and the subsidence velocity curves are skewed to the left. Secondly, based on the idea of lossless propagation of harmonic waves and idealizing the propagation environment, the spatial propagation relationship of surface subsidence velocity in the time domain is established. Then, the Box–Cox transform function is introduced to improve the normal distribution probability density function, and a new dynamic subsidence prediction model based on the Box–Cox transformation is obtained, which is suitable for the full mining stage. The model is tested by practical cases, the prediction accuracy is better than 7%, and the prediction results can meet the needs of engineering prediction accuracy (10%). The results of this research can enrich the existing subsidence prediction theory and provide theoretical and technical support for the prediction of dynamic surface damage caused by similar mining.

中文翻译：

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基于波无损传播思想的水平煤层表面动态损伤预测模型

按照传统概念，水平煤层采煤造成的覆岩运动和地表破坏在空间分布上是对称的。然而，在很多工程实践中，这种对称性并没有被发现。我们经常使用对称函数来建立表面损伤的轮廓预测函数，导致预测结果与实际情况存在较大差异。为了解决这个问题，本文以沉降速度为例。首先从理论上推导出两侧沉降速度的空间分布函数。通过比较，发现煤柱侧沉降速度空间分布曲线的变化率比采空区平缓，沉降速度曲线向左倾斜。其次，基于谐波无损传播的思想，理想化传播环境，建立了地表沉降速度在时域的空间传播关系。然后，引入Box-Cox变换函数改进正态分布概率密度函数，得到了一种新的基于Box-Cox变换的动态沉降预测模型，适用于全采阶段。模型经实际案例检验，预测精度优于7%，预测结果可以满足工程预测精度（10%）的需要。