回声状态网络(Echo state network, ESN)凭借其独特的动态系统建模机制，在时序数据分析等领域展现出显著优势，从而被广泛应用。然而，现有研究表明ESN仍存在若干亟待解决的理论缺陷。储层参数配置经验性选择严重制约了模型的自适应能力；同时储层神经元随机连接引发共线性问题导致网络记忆容量下降。针对以上问题，研究基于储层参数与拓扑结构的协同优化，提出了储层自适应优化方法。本文主要工作体现在以下三个方面：

(1) 针对回声状态网络储层参数随机选择导致网络预测性能不佳的问题，提出一种基于多策略鲸鱼优化算法(Multi-strategy whale optimization algorithm, MWOA)的回声状态网络参数优化方法。首先，MWOA通过池化机制增加种群的多样性；其次，利用迁移策略提高算法的局部搜索能力，避免算法陷入局部最优；最后，MWOA通过优先选择策略提高算法的鲁棒性和全局搜索能力。通过Mackey-Glass、Lorenz和短期电力负荷时间序列数据集进行仿真实验，结果表明，本文所提模型具有普适性，在预测精度和拟合性方面，优于已有经典算法。相比现有成果，该预测模型是可行且有效的。

(2) 针对回声状态网络储层存在大量冗余神经元导致高维状态空间矩阵产生共线性问题，提出一种融合多策略鲸鱼算法和强化学习的储层自适应优化方法。首先利用MWOA算法对ESN储层关键参数进行优化；其次引入互信息衡量储层神经元贡献度；最后结合强化学习的决策机制筛选对网络输出有效的神经元，从而简化网络结构，提高网络预测性能。通过Mackey-Glass、Lorenz和短期电力负荷时间序列数据进行仿真实验，结果表明，本文提出的方法实现了网络结构的简化和预测性能的提升。与其他预测模型比较，该方法在储层结构在达到最简时，预测性能也得到显著提升，证明了其在时间序列预测任务中的优越性。

(3) 针对瓦斯浓度时序数据存在复杂非线性动态特征及噪声干扰导致传统方法预测精度不足的问题，利用融合多策略鲸鱼算法和强化学习的回声状态网络自适应优化模型进行预测；此外，为了实现对瓦斯浓度异常情况的及时、有效预警的要求，采用三级预警指标体系，方便工作人员根据预警程度采取相应预警应急措施。最后基于山西某煤矿实际监测数据的实验验证表明，该模型相对于传统ESN，MWOA-QESN预测误差RMSE降低了57.10%，MAE降低了70.40%，相对于长短期记忆网络(Long Short-Term Memory, LSTM)，其预测误差RMSE降低了61.32%，MAE降低了68.69%，同时计算效率提升了17.56%，表明该模型能够有效地预测瓦斯浓度，并迅速判断预警情况，为煤矿安全管理提供了可靠的决策依据。

通过理论分析与实验验证充分证明了本文提出的回声状态网络储层自适应优化方法的有效性和可靠性，该方法不仅简化了对储层结构的规模，同时极大地提升了ESN对于时间序列的的预测性能，为回声状态网络的推广普及提供了参考。

Echo State Network (ESN), leveraging their unique mechanism for dynamic system modeling, demonstrate significant advantages in fields like time series data analysis and are thus widely applied. However, existing research indicates that ESNs still possess several theoretical flaws that require urgent resolution. The heavy reliance on empirical selection of reservoir parameters severely constrains the model's adaptive capability. Simultaneously, the random connectivity of reservoir neurons leads to collinearity issues, resulting in a decline in network memory capacity. To address these problems, this research proposes a reservoir adaptive optimization method based on the co-optimization of reservoir parameters and topological structure. The main contributions of this work are reflected in the following three aspects:

Firstly, to address the issue of suboptimal prediction performance in Echo State Networks (ESNs) resulting from the random selection of reservoir parameters, this paper proposes an ESN parameter optimization method utilizing the Multi-strategy Whale Optimization Algorithm (MWOA).The MWOA approach incorporates three key strategies: a pooling mechanism enhances population diversity; a migration strategy is employed to enhance the algorithm's local search capability and avoid it from falling into local optimality; and a preferential selection strategy improves the algorithm's robustness and global search capability. Simulation experiments conducted on the Mackey-Glass, Lorenz, and short-term electric power load time series datasets demonstrate the proposed model's strong generalization capability. Results show it outperforms established classical algorithms in both prediction accuracy and fitting performance. Compared to current state-of-the-art methods, this prediction model proves empirically validated as both feasible and effective.

Secondly, to address the collinearity issues arising from high-dimensional state space matrices caused by abundant redundant neurons within Echo State Network (ESN) reservoirs, this paper proposes a reservoir adaptive optimization method integrating the Multi-strategy Whale Optimization Algorithm (MWOA) with reinforcement learning.The proposed approach involves three core components: MWOA optimizes key ESN reservoir parameters; mutual information quantifies the contribution of reservoir neurons; and a reinforcement learning-based decision mechanism selects neurons effective for network output. This integrated strategy simplifies the network structure while enhancing prediction performance.Simulation experiments conducted on Mackey-Glass, Lorenz, and short-term electric power load time series datasets demonstrate that the proposed method successfully achieves both network simplification and improved prediction performance. Comparative analysis with other prediction models reveals that this method delivers significantly enhanced prediction performance while simultaneously achieving the most compact reservoir structure, proving its superiority in time series forecasting tasks..

Finally，to address the issues of complex nonlinear dynamic characteristics and noise interference in gas concentration time-series data, which lead to insufficient prediction accuracy of traditional methods, an adaptive optimization model of echo state network (ESN) integrating multi-strategy whale optimization algorithm (MWOA) and reinforcement learning (Q-learning) is proposed for prediction. Additionally, a three-level early-warning index system is adopted to meet the requirement of timely and effective early warning for abnormal gas concentration, facilitating staff to take corresponding emergency measures according to the warning level. Experiments based on actual monitoring data from a coal mine in Shanxi show that compared with the traditional ESN, the MWOA-QESN model reduces the prediction errors of RMSE by 57.10% and MAE by 70.40%. When compared with the Long Short-Term Memory (LSTM) network, its prediction errors of RMSE and MAE are reduced by 61.32% and 68.69% respectively, while the computational efficiency is improved by 17.56%. This indicates that the model can effectively predict gas concentration and quickly determine early warning situations, providing a reliable decision-making basis for coal mine safety management..

Theoretical analysis and experimental verification fully demonstrate the effectiveness and reliability of the proposed adaptive optimization method for the echo state network (ESN) reservoir. This method not only simplifies the scale of the reservoir structure but also significantly improves the prediction performance of ESN for time series, providing a reference for the popularization of echo state networks.

[1] Hartomo K D, Nataliani Y. A new model for learning-based forecasting procedure by combining k-means clustering and time series forecasting algorithms[J]. PeerJ Computer Science, 2021, 7: e534.

[2] 应鑫迪,厉晓华.结合改进算术优化算法与小波神经网络的网络流量预测模型[J].传感技术学报,2024,37(08):1350-1361.

[3] Wei D. Network traffic prediction based on RBF neural network optimized by improved gravitation search algorithm[J]. Neural Computing and Applications, 2017, 28: 2303-2312.

[4] Machine Learning; University of Calgary Describes Findings in Machine Learning [J]. Robotics & Machine Learning,2020.

[5] 王岩,陈耀然,韩兆龙等.基于互信息理论与递归神经网络的短期风速预测模型[J].上海交通大学学报,2021,55(09):1080-1086.DOI:10.16183/j.cnki.jsjtu.2020.433

[6] 丛爽,戴谊.递归神经网络的结构研究[J].计算机应用,2004,(08):18-20+27.

[7] 耿磊, 傅洪亮, 陶华伟, 卢远, 郭歆莹, 赵力. 基于动态卷积递归神经网络的语音情感识别[J/OL]. 计算机工程: 2023-03-29.

[8] 庄爱军. 基于WA-ESN的建筑起重机械故障检测[J]. 机械与电子,2021, 39(01): 67-75.

[9] Jaeger H, Haas H. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication[J]. science, 2004, 304(5667): 78-80.

[10] 刘丽丽, 刘玉玺, 王河山. 偏置剪枝叠式自编码回声状态网络的时序预测[J]. 计算机工程与设计, 2024, 45(01): 212-219.

[11] 李无言, 王志强, 蒋永年, 郭亚. 基于优化回声状态网络的溶解氧预测建模[J]. 控制工程, 2023, 30(03): 520-528.

[12] Liu C, Li Y L, Duan Z X, Chu Z S, Ma Z F. Echo state network-based robust tracking control for unknown constrained nonlinear systems by using integral reinforcement learning[J]. IEEE Access, 2024, 12: 15133-15144.

[13] 韩敏, 任伟杰, 许美玲. 一种基于L1范数正则化的回声状态网络[J]. 自动化学报, 2014, 40(11): 2428-2435.

[14] Xu M L, Han M. Adaptive elastic echo state network for multivariate time series prediction[J]. IEEE Transactions on Cybernetics, 2016, 46(10): 2173-2183.

[15] Wang Z G, Zeng Y R, Wang S R, Wang L. Optimizing echo state network with backtracking search optimization algorithm for time series forecasting[J]. Engineering Applications of Artificial Intelligence, 2019, 81: 117-132.

[16] Liu J X, Sun T N, Luo Y L, Yang S, Cao Y, Zhai J. Echo state network optimization using binary grey wolf algorithm[J]. Neurocomputing. 2020, 385: 310-318.

[17] Qiao J F, Wang L, Yang C L. Adaptive lasso echo state network based on modified Bayesian information criterion for nonlinear system modeling[J]. Neural Computing and Applications, 2019, 31(10): 6163-6177.

[18] Ahmed Z, Memon M Q, Memon A, Munshi P, Memon M J. Echo state network optimization using hybrid-structure based gravitational search algorithm with square quadratic programming for time series prediction[J]. International Arab Journal of Information. Technology, 2022, 19(3A): 530-535.

[19] Liu Z Y, Xu X H, Pan M Y, Loo C K, Li S X. Weighted error-output recurrent echo kernel state network for multi-step water level prediction[J]. Applied Soft Computing, 2023, 137: 110-131.

[20] Zhan Z H, Shi L, Tan K C, et al. A survey on evolutionary computation for complex continuous optimization[J]. Artificial Intelligence Review, 2022: 1-52.

[21] Liu Z, Li S, Pan M, et al. Grammatical structure detection by instinct plasticity based echo state networks with genetic algorithm[J]. Neurocomputing, 2022, 467: 173-183.

[22] Zhong S, Xie X, Lin L, et al. Genetic algorithm optimized double-reservoir echo state network for multi-regime time series prediction[J]. Neurocomputing, 2017, 238: 191-204.

[23] Chouikhi N, Ammar B, Rokbani N, et al. PSO-based analysis of Echo State Network parameters for time series forecasting[J]. Applied Soft Computing, 2017, 55: 211-225.

[24] Sergio A T, Ludermir T B. Reservoir computing optimization with a hybrid method[C]//2014 International Joint Conference on Neural Networks (IJCNN). IEEE, 2014: 2653-2660.

[25] Wang H, Yan X. Optimizing the echo state network with a binary particle swarm optimization algorithm[J]. Knowledge-Based Systems, 2015, 86: 182-193.

[26] Xue Y, Zhang Q, Neri F. Self-adaptive particle swarm optimization-based echo state network for time series prediction[J]. International Journal of Neural Systems, 2021, 31(12): 2150057.

[27] Chen H C, Wei D Q. Chaotic time series prediction using echo state network based on selective opposition grey wolf optimizer[J]. Nonlinear Dynamics, 2021, 104(4): 3925-3935.

[28] Duan H, Wang X. Echo state networks with orthogonal pigeon-inspired optimization for image restoration[J]. IEEE transactions on neural networks and learning systems, 2015, 27(11): 2413-2425.

[29] Strauss T, Wustlich W, Labahn R. Design strategies for weight matrices of echo state networks[J]. Neural computation, 2012, 24(12): 3246-3276.

[30] Bianchi F M, Livi L, Alippi C. Investigating echo-state networks dynamics by means of recurrence analysis[J]. IEEE transactions on neural networks and learning systems, 2016, 29(2): 427-439.

[31] Ozturk M C, Xu D, Principe J C. Analysis and design of echo state networks[J]. Neural computation, 2007, 19(1): 111-138.

[32] Xue Y, Yang L, Haykin S. Decoupled echo state networks with lateral inhibition[J]. Neural Networks, 2007, 20(3): 365-376.

[33] Jaeger H. Discovering multiscale dynamical features with hierarchical echo state networks[R]. Jacobs University Bremen, 2007.

[34] Wen S, Hu R, Yang Y, et al. Memristor-based echo state network with online least mean square[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 49(9): 1787-1796.

[35] 李丁园.回声状态网络结构设计及应用研究[D].吉林大学,2019.

[36] 伦淑娴,林健,姚显双.基于小世界回声状态网的时间序列预测[J].自动化学报,2015,41(09):1669-1679.DOI:10.16383/j.aas.2015.c150049

[37] Qiao J, Li F, Han H, et al. Growing echo-state network with multiple subreservoirs[J]. IEEE transactions on neural networks and learning systems, 2016, 28(2): 391-404.

[38] Yang C, Qiao J, Wang L, et al. Dynamical regularized echo state network for time series prediction[J]. Neural Computing and Applications, 2019, 31: 6781-6794.

[39] LeCun Y, Bengio Y, Hinton G. Deep learning[J]. nature, 2015, 521(7553): 436-444.

[40] Sun X, Li T, Li Q, et al. Deep belief echo-state network and its application to time series prediction[J]. Knowledge-Based Systems, 2017, 130: 17-29.

[41] Gallicchio C, Micheli A. Deep reservoir computing: A critical analysis[A]. In: ESANN 2016 - 24th. European Symposium on Artificial Neural Networks[C]. Bruges, Belgium, 2016. 497-502.

[42] 沈礼锋. 新型深度储备池计算方法研究 [D]. 华南理工大学,2018.

[43] 马晶, 王梅, 谯小伟, 曹文珮, 李娟生.ARIMA季节性模型在预测兰州市丙肝发病人数中的应用[J]. 中国卫生统计, 2022, 39(01): 98-100+105.

[44] 杨雨桐, 张利, 杨玖. 基于指数平滑法的噪声污染预测及应用[J].资源节约与环保, 2024(03): 74-78.

[45] 王燕丽. 改进粒子群算法优化回声状态网络的能源需求预测研究 [D]. 华中科技大学,2020.

[46] Yildiz I B, Jaeger H, Kiebel S J. Re-visiting the echo state property[J]. Neural Networks, 2012, 35: 1-9.

[47] Buehner M, Young P. A tighter bound for the echo state property [J]. IEEE Transactions on Neural Networks, 2006, 17(3): 820-824.

[48] Yao X S, Wang Z S, Zhang H G. Prediction and identification of discrete-time dynamic nonlinear systems based on adaptive echo state network[J]. Neural Networks, 2019, 113: 11-19.

[49] Li X, Bi F R, Yang X, Bi X Y. An echo state network with improved topology for time series prediction[J]. IEEE Sensors Journal, 2022, 22(6): 5869-5878.

[50] Ferreira A A, Ludermir T B, Aquino R. An approach to reservoir computing design and training []Expert Systems with Applications, 2013, 40(10):4172-4182

[51] Xu M L, Wang Y W, Time Series Prediction Based on Improved Differential Evolution and Echo State Network[J]. Acta Automatica Sinica, 2021, 47(7): 1589-1597.

[52] Xue Y, Zhang Q, Neri F. Self-adaptive particle swarm optimization-based echo state network for time series prediction[J]. International Journal of Neural Systems, 2021, 31(12): 2150057.

[53] Mirjalili S, Lewis A. The whale optimization algorithm[J]. Advances in engineering software, 2016, 95: 51-67.

[54] 潘悦悦,吴立飞,杨晓忠.一种多策略改进鲸鱼优化算法的混沌系统参数辨识[J]. 智能系统学报, 2024, 19(01): 176-189.

[55] Zhang M, Wang B, Zhou Y, et al. WOA-based echo state network for chaotic time series prediction[J]. Journal of the Korean Physical Society, 2020, 76: 384-391.

[56] Zhang M, Wang B, Zhou Y, et al. Prediction of chaotic time series based on SALR model with its application on heating load prediction[J]. Arabian Journal for Science and Engineering, 2021, 46: 8171-8187.

[57] Succetti F, Rosato A, Panella M. An adaptive embedding procedure for time series forecasting with deep neural networks[J]. Neural Networks, 2023, 167: 715-729.

[58] Wan R, Mei S, Wang J, et al. Multivariate temporal convolutional network: A deep neural networks approach for multivariate time series forecasting[J]. Electronics, 2019, 8(8): 876.

[59] Tian Z. Echo state network based on improved fruit fly optimization algorithm for chaotic time series prediction[J]. Journal of Ambient Intelligence and Humanized Computing, 2022, 13(7): 3483-3502.

[60] Chandra R. Multi-objective cooperative neuro-evolution of recurrent neural networks for time series prediction[C]//2015 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2015: 101-108.

[61] Na X, Han M, Ren W, et al. Modified BBO-based multivariate time-series prediction system with feature subset selection and model parameter optimization[J]. IEEE Transactions on Cybernetics, 2020, 52(4): 2163-2173.

[62] Guo X, Sun Y, Ren J. Low dimensional mid-term chaotic time series prediction by delay parameterized method[J]. Information Sciences, 2020, 516: 1-19.

[63] Chen X, Zhang H. Grey wolf optimization–based deep echo state network for time series prediction[J]. Frontiers in Energy Research, 2022, 10: 858518.

[64] Kraskov A, Stögbauer H, Grassberger P. Estimating mutual information[J]. Physical review E, 2004, 69(6): 138-151.

[65] LIU H, YU C, YU C, et al. A Novel Axle Temperature Forecasting Method Based on Decomposition, Reinforcement Learning Optimization and Neural Network[J]. Advanced Engineering Informatics, 2020, 44: 1-10.

[66] CHEN X, LUO X, JIN L, et al. Growing Echo State Network with an Inverse-free Weight Update Strategy[J]. IEEE Transactions on Cybernetics, 2022, 53(2): 753-764.

[67] LI Y, LI F. PSO-based Growing Echo State Network[J]. Applied Soft Computing, 2019, 85: 105774.

[68] 王磊,苏中,乔俊飞.基于增量式学习的正则化回声状态网络[J]. 控制与决策, 2022: 37(03): 661-668.

[69] 王磊,乔俊飞,杨翠丽,等.基于灵敏度分析的模块化回声状态网络修剪算法[J]. 自动化学报, 2019, 45(06): 1136-1145.

[70] 郭伟,姚欢,张昭昭,等.基于强化学习的储层神经元筛选优化方法[J/OL]. 控制与决策, 1-9[2024-04-15].

[71] Zhang T ,Song S ,Li S , et al.Research on Gas Concentration Prediction ModelsBased on LSTM Multidimensional Time Series[1.Energies,2019,12(1):161.

[72] 胡青松,郑硕,李世银,等.基于改进TCN-TimeGAN的矿井瓦斯浓度智能预测方法[J/OL].煤炭科学技术,1-10[2025-01-25].

[73] 郭风景,王斌,贾澎涛,等.基于梯度提升决策树的瓦斯浓度在线预测[J].中国煤炭,2023,49(10):61-67.