Optimal embedding dimension and time delay.

Continuous monitoring and accurate measurement of required air volume in mine tunnels are crucial phenomena for mine safety However, air volume fluctuates and can become unstable which can lead to biased measurement in underground environment. In this paper, to accurately measure the mine tunnel air volume, the tunnel air volume, and related ventilation parameters are consistently monitored, and the real monitoring data is converted to interval numbers for representation. These interval numbers are then preprocessed using an Interval-type Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(In-CEEMDAN) to extract the essential features of the data. Then, the monitored data is processed using the phase space reconstruction technique to identify the most relevant influencing factors related to the air volume. The tunnel air volume and influencing factors are then input into different neural networks for air volume prediction. To further improve prediction accuracy, the predicted values of wind volume intervals from the single prediction method are transformed into triangular fuzzy numbers, and the generalized induced ordered weighted average operator is introduced for the combination of prediction results. The grey correlation method is selected as the optimization criterion, and the preference coefficients are used to transform the multi-objective optimization problem into a single-objective optimization problem. In order to reduce the prediction error, the L2 paradigm is combined with the gray correlation to construct a complete interval combination type air volume prediction model which considers multiple influencing factors. Finally, a sensitivity analysis was carried out to analyze the values of the preference coefficients in the model, and the final range of values was given. Experimental analysis using data from a coal mine in Inner Mongolia showed that the method could reduce Combined Weighted Mean Absolute Error(CWMAE) to a maximum of 5.0384, Combined Weighted Root of Mean Squares Error(CWRMSE) to 6.8889, and Combined Weighted Mean Absolute Percentage Error(CWMAPE) to 1.4756, which indicates that the method proposed in this study can effectively improve the prediction accuracy of the mine tunnel air volume.矿井巷道所需风量的持续监测与精准计量，是保障矿井安全生产的核心环节。然而，井下环境中风量会出现波动且状态失稳，进而导致计量结果出现偏差。针对矿井巷道风量精准计量的需求，本研究对巷道风量及相关通风参数进行持续监测，并将原始监测数据转换为区间数进行表征。随后采用自适应噪声完备集合经验模态分解（Interval-type Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, In-CEEMDAN）对该区间数数据进行预处理，以提取数据的本质特征。随后利用相空间重构技术对监测数据进行处理，以识别与风量相关的核心影响因素。将巷道风量及其影响因子输入至不同神经网络模型，开展风量预测任务。为进一步提升预测精度，将单一预测方法得到的风量区间预测值转换为三角模糊数，并引入广义诱导有序加权平均算子（Generalized Induced Ordered Weighted Average Operator）实现各预测结果的融合。选取灰色关联分析法作为优化准则，并通过偏好系数将多目标优化问题转化为单目标优化问题。为降低预测误差，结合L2范数与灰色关联分析，构建了兼顾多影响因子的完整区间组合式风量预测模型。最后，针对模型中的偏好系数开展敏感性分析，并给出其合理取值区间。采用内蒙古某煤矿的实测数据开展实验分析，结果显示本方法可将组合加权平均绝对误差（Combined Weighted Mean Absolute Error, CWMAE）降至5.0384以内，组合加权均方根误差（Combined Weighted Root of Mean Squares Error, CWRMSE）降至6.8889以内，组合加权平均绝对百分比误差（Combined Weighted Mean Absolute Percentage Error, CWMAPE）降至1.4756以内，表明本研究提出的方法可有效提升矿井巷道风量的预测精度。