Hydraulic support straightening method based on maximum correntropy Kalman filtering algorithm
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摘要: 现有液压支架调直方法受到传感器测量误差和液压支架推移误差的影响，使得调直误差较大；且在非高斯量测噪声环境下，传统基于卡尔曼滤波（KF）算法的调直方法对液压支架轨迹的预测准确度低，无法达到理想的调直效果。针对上述问题，提出了一种基于最大熵卡尔曼滤波（MCKF）算法的液压支架调直方法。首先根据液压支架的位置坐标和工作面推进方向确定调直参考直线；然后根据液压支架调直原理构建液压支架线性推移系统的状态方程和观测方程，经MCKF算法处理后得到液压支架推移后的预测轨迹；最后根据液压支架预测轨迹与调直参考直线解算出每架液压支架的推移距离补偿量，从而达到调直目的。仿真结果表明：与现有基于KF算法的调直方法相比，基于MCKF算法的液压支架调直方法能够有效降低量测噪声和过程噪声对液压支架直线度的影响，特别当量测噪声服从非高斯分布时，该方法的均方误差平均值仅为4.76 mm，远小于基于KF算法的调直方法的均方误差，可以更加准确地预测液压支架的真实轨迹，使调直后液压支架的直线度误差降低了36%，有效提高了调直精度，且液压支架直线度误差只与本次调直过程有关，有效避免了累计误差。Abstract: The existing hydraulic support straightening method is affected by the sensor measurement error and the hydraulic support moving error, which make the straightening error larger. In the non-Gaussian measurement noise environment, the traditional Kalman filter (KF) straightening method has low accuracy in predicting the trajectory of the hydraulic support, and cannot achieve the ideal straightening effect. In order to solve the above problems, a hydraulic support straightening method based on maximum correntropy Kalman filtering (MCKF) algorithm is proposed. Firstly, the straightening reference line is determined according to the position coordinates of the hydraulic support and the advancing direction of the working face. Secondly, the state equation and observation equation of the linear moving system of hydraulic support is constructed according to the straightening principle of hydraulic support. After MCKF algorithm processing, the predicted trajectory of hydraulic support after moving is obtained. Finally, the moving distance compensation amount of each hydraulic support is calculated according to the predicted trajectory of the hydraulic support and the straightening reference line, so as to achieve the purpose of straightening. The simulation results show that the hydraulic support straightening method based on the MCKF algorithm can effectively reduce the influence of measurement noise and process noise on the straightness of the hydraulic support compared with the existing straightening method based on the KF algorithm. When the measurement noise obeys non-Gaussian distribution, the average of mean square error of the method is only 4.76 mm, which is far less than the mean square error of the straightening method based on the KF algorithm. The real trajectory of the hydraulic support can be predicted more accurately, which reduces the straightening error of the hydraulic support by 36% after straightening. The method thus effectively improves the straightening precision. The straightening error of the hydraulic support is only related to this straightening process, which effectively avoids the accumulated error.
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图 2 高斯噪声条件下液压支架初始轨迹
Figure 2. Initial trajectory of hydraulic support under condition of Gaussian noise
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图 3 高斯噪声条件下液压支架推移轨迹
Figure 3. Moving trajectory of hydraulic support under condition of Gaussian noise
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图 4 高斯噪声条件下KF算法与MCKF算法预测轨迹的MSE
Figure 4. Mean square errors of prediction trajectory of KF algorithm and MCKF algorithm under condition of Gaussian noise
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图 5 高斯噪声条件下液压支架直线度误差随推移次数变化曲线
Figure 5. Variation curves of the straightness error of hydraulic support with moving number under condition of Gaussian noise
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图 6 非高斯噪声条件下液压支架初始轨迹
Figure 6. Initial trajectory of hydraulic support under condition of non-Gaussian noise
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图 7 非高斯噪声条件下液压支架推移轨迹
Figure 7. Moving trajectory of hydraulic support under condition of non-Gaussian noise
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图 8 非高斯噪声条件下KF算法预测轨迹与MCKF算法预测轨迹的MSE
Figure 8. Mean square errors of prediction trajectory of KF algorithm and MCKF algorithm under condition of non-Gaussian noise
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