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浙江大学学报(工学版)
浙江大学学报(工学版)  2024, Vol. 58 Issue (7): 1336-1345    DOI: 10.3785/j.issn.1008-973X.2024.07.003
计算机与控制工程     
基于KPCA和数据处理组合方法神经网络的半球谐振陀螺温度建模补偿方法
张晨(),汪立新*(),孔祥玉
火箭军工程大学 导弹工程学院，陕西 西安 710025
Temperature modeling and compensation method of hemispherical resonator gyro based on KPCA and grouped method of data handling neural network
Chen ZHANG(),Lixin WANG*(),Xiangyu KONG
School of Missile Engineering, Rocket Force University of Engineering, Xi’an 710025, China
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摘要：

针对半球谐振陀螺（HRG）的温度建模与补偿问题，提出基于核主成分分析（KPCA）和数据处理组合方法（GMDH）神经网络的建模补偿方法. 通过分析HRG的温度特性和大数据特征，初步确定网络模型的特征向量. 为了去除HRG输出数据的相关性和冗余性，引入KPCA并降低特征向量维度. 将特征向量代入GMDH神经网络训练，区分训练集和验证集以确定网络权值和网络结构，实现HRG温度漂移的建模与补偿. 实验结果表明，单一样本预测时，所提方法预测效果明显好于传统多项式模型；多样本预测时，在4种不同训练样本下，所提方法相比传统多项式模型精度分别提升了48.5%、54.0%、56.3%、68.4%，相比GMDH模型分别提升了3.6%、5.1%、3.8%、8.8%. 所提方法能够有效提高HRG在变温工况下的测量精度.
关键词： 半球谐振陀螺(HRG);  核主成分分析(KPCA);  数据处理组合方法(GMDH);  温度建模与补偿;  测量精度    
Abstract:

A modeling and compensation method based on kernel principal component analysis (KPCA) and grouped method of data handling (GMDH) neural network was proposed aiming at the temperature modeling and compensation of hemispherical resonator gyro (HRG). By analyzing the temperature characteristics and the big data characteristics of HRG, the eigenvectors of the network were initially selected. To remove the correlation and redundancy of the HRG outputs, KPCA was introduced and the eigenvector dimension was reduced. The eigenvectors were substituted into the GMDH neural network and the training set and the validation set were distinguished to determine the network weight and structure to model and compensate for the HRG temperature drift. Experiment results showed that the proposed method was significantly better than the traditional polynomial model for single-sample predictions; for multiple-sample predictions, under four different training samples, the accuracy of the proposed method was 46.5%, 51.5%, 54.6% and 65.3% higher than that of the traditional polynomial model, also 3.6%, 5.1%, 3.8% and 8.8% higher than that of the GMDH model. The proposed method effectively improved the measurement accuracy of HRG under variable temperature conditions.
Key words: hemispherical resonator gyro(HRG)    kernel principal component analysis(KPCA)    grouped method of data handling(GMDH)    temperature modeling and compensation    measurement accuracy
收稿日期: 2023-06-13 出版日期: 2024-07-01
CLC:  V 241.5  
基金资助: 国防科技创新特区基金资助项目（HHJJ-2022-0402）.
通讯作者: 汪立新     E-mail: buaa0318@163.com;wlxxian@sina.com
作者简介: 张晨（1993—），男，博士生，从事惯性系统、大数据处理研究. orcid.org/0009-0001-1310-8390. E-mail：buaa0318@163.com
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张晨
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引用本文:

张晨,汪立新,孔祥玉. 基于KPCA和数据处理组合方法神经网络的半球谐振陀螺温度建模补偿方法[J]. 浙江大学学报(工学版), 2024, 58(7): 1336-1345.

Chen ZHANG,Lixin WANG,Xiangyu KONG. Temperature modeling and compensation method of hemispherical resonator gyro based on KPCA and grouped method of data handling neural network. Journal of ZheJiang University (Engineering Science), 2024, 58(7): 1336-1345.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2024.07.003    或    https://www.zjujournals.com/eng/CN/Y2024/V58/I7/1336

图 1  数据处理组合方法的网络结构
图 2  主成分分析和数据处理组合方法神经网络模型
图 3  半球谐振陀螺的实验装置
图 4  半球谐振陀螺的参数变化曲线
图 5  扣除转台运动前后半球谐振陀螺转动角度
图 6  平滑前后半球谐振陀螺转动角度
图 7  去除未启动状态数据后的半球谐振陀螺转动角度
图 8  重采样后的半球谐振陀螺转动角速度
特征最大值最小值平均值
$ \sqrt f $69.934969.930969.9340
$ f $4890.88814890.33644890.7693
$ {f^2} $2.319 2×1072.391 5×1072.392 0×107
$ {\mathrm{d}}f $0.0042?0.00050.0008
$ \sqrt f \cdot {\mathrm{d}}f $0.2950?0.03290.0540
$ f \cdot {\mathrm{d}}f $20.6294?2.30083.7751
$ {f^2} \cdot {\mathrm{d}}f $1.008 9×105?1.125 3×1041.846 3×104
$ {({\mathrm{d}}f)^2} $1.7795×10?501.6851×10?6
$ \sqrt f \cdot {({\mathrm{d}}f)^2} $0.001201.1785×10?4
$ f \cdot {({\mathrm{d}}f)^2} $0.087000.0082
$ {f^2} \cdot {({\mathrm{d}}f)^2} $425.5719040.3035
表 1  样本初选特征向量的统计特性
特征最大值最小值平均值
${{\boldsymbol{X}}_1}$18.6932?95.12302.600 9×10?14
${{\boldsymbol{X}}_2}$9.5840?14.0542?7.9554×10?13
${{\boldsymbol{X}}_3}$6.1600?10.3414?1.988 5×10?13
表 2  样本经核主成分分析筛选后的特征向量统计特性
特征最大值最小值平均值
${\boldsymbol{Y}}$18.6932?95.12302.600 9×10?14
表 3  样本转动角速度的统计特性
图 9  样本2的预测曲线及误差曲线
样本RMSE
多项式预测KPCA-GMDH
20.000680.00064
30.003800.00300
40.004400.00290
50.004900.00470
60.004100.00370
70.000600.00050
表 4  不同样本预测结果的均方根误差
图 10  融合样本A拟合样本4的预测曲线及误差曲线
图 11  融合样本B拟合样本4的预测曲线及误差曲线
图 12  融合样本C拟合样本4的预测曲线及误差曲线
图 13  融合样本D拟合样本4的预测曲线及误差曲线
融合样本$\sigma $
多项式GMDHKPCA-GMDH
A0.02580.01380.0133
B0.03240.01570.0149
C0.02930.01330.0128
D0.03950.01370.0125
表 5  不同建模方法的误差标准差对比
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