Data-driven high-precision model identification and time series prediction for maglev train suspension systems
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摘要:
针对EMS型磁浮列车悬浮控制系统因高维、强非线性及开环不稳定特性导致的机理建模精度不足与鲁棒性差等问题，提出一种基于贝叶斯优化（BO）算法改进长短期记忆网络（LSTM）的悬浮系统高精度模型辨识及时间序列预测方法。搭建了单自由度磁悬浮系统试验平台，通过控制器跟踪包含正弦、脉冲及白噪声的复杂激励信号，采集了覆盖系统动态特性的控制电压与悬浮间隙时序数据，并采用滑动窗口法重构输入输出序列；构建了长短期记忆网络模型以捕捉悬浮系统的时间依赖特征；为解决人工调参难以兼顾效率与性能的问题，引入了贝叶斯优化算法，选取高斯过程作为概率代理模型，以期望改进作为采集函数，将模型在验证集上的平均绝对误差作为目标函数，对LSTM模型的隐藏层神经元数量、初始学习率及L2正则化系数进行全局寻优。研究结果表明：经贝叶斯优化后的模型能够精准预测悬浮间隙的关键状态变化，预测误差稳定在±0.1 mm以内，且误差分布符合正态分布特征，表明消除了模型的结构性偏差；与未优化的LSTM模型相比，其在测试集上的平均绝对误差降低了48.04%，均方根误差降低了41.83%。该方法能有效解决悬浮系统建模中超参数整定困难的问题，显著提升模型的预测精度与泛化能力，为磁浮列车的高精度悬浮控制器设计及实时状态监测提供了可靠的模型基础。
Abstract:In response to low modeling accuracy and poor robustness in the suspension control systems of EMS-type maglev trains caused by high dimensionality, strong nonlinearity, and open-loop instability, a high-precision model identification and time series prediction method was proposed based on a long short-term memory (LSTM) improved by the Bayesian optimization (BO) algorithm. First, an experimental platform for a single-degree-of-freedom magnetic suspension system was built. A controller was used to track complex excitation signals, including sine, pulse, and white noise. Time series data of the control voltage and suspension gap covering the dynamic characteristics of the system were collected. The input and output sequences were reconstructed using the sliding window method. Second, an LSTM model was constructed to capture the time-dependent features of the suspension system. In response to the difficulty of manual parameter tuning in balancing efficiency and performance, the BO algorithm was introduced. A Gaussian process was selected as the probabilistic surrogate model, and the expected improvement was used as the acquisition function. The mean absolute error of the model on the validation set was set as the objective function. A global optimization was performed for the number of hidden layer neurons, initial learning rate, and L2 regularization coefficient of the LSTM model. Research results show that after BO, the model can accurately predict the key state changes of the suspension gap. The prediction error stabilizes within ±0.1 mm, and the error distribution conforms to a normal distribution, indicating that the structural deviation of the model is eliminated. Compared with the unoptimized LSTM model, the mean absolute error on the test set is reduced by 48.04%, and the root mean square error is decreased by 41.83%. This method effectively solves the difficulty of hyperparameter setting in suspension system modeling, and significantly improves the prediction accuracy and generalization ability of the model, providing a reliable model foundation for the design of high-precision suspension controllers and real-time condition monitoring of maglev trains.
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图 5 单自由度磁悬浮试验台
Figure 5. Single-degree-of-freedom magnetic suspension experiment platform
表 1 数据集原始序列格式
Table 1. Raw sequence format of dataset
时间 数据点 $ {t}_{1} $ $ {u}_{1},{z}_{1} $ $ {t}_{2} $ $ {u}_{2},{z}_{2} $ $ {t}_{3} $ $ {u}_{3},{z}_{3} $ ⋮ ⋮ $ {t}_{n} $ $ {u}_{n},{z}_{n} $ 
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表 2 超参数优化区间设置
Table 2. Hyperparameter optimization range configuration
超参数 优化区间 学习率 [0.000 1，0.1] 隐藏层单元数 [64, 256] L2正则化系数 [0.000 01，0.01]
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表 3 BO-LSTM模型超参数设置
Table 3. Setting of hyperparameters of BO-LSTM model
参数 设定值 训练轮次 100 批量大小 50 学习率 0.015 2 LSTM神经元数 153 L2正则化系数 $ 1.104\times {10}^{-5} $
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表 4 模型总体评价指标对比
Table 4. Comparison of overall model evaluation metrics
模型 MSE RMSE MAE MAPE LSTM 0.000 6 0.025 1 0.020 4 0.002 076 BO-LSTM 0.000 2 0.014 6 0.010 6 0.001 080 下降比例/% 66.67 41.83 48.04 47.98
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