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摘要:
受不确定性影响，数字孪生模型与真实系统存在误差，需要对其进行修正，定量评估模型的不确定性，作为使用模型时选取的依据。但是卫星数字孪生模型具有多动态、多空间尺度、多物理场耦合的特性，数值求解时会出现微分方程的刚性问题和偏微分方程的多尺度问题，如果从系统级上对众多遥测参数同时进行修正会造成结果不收敛。提出一种卫星数字孪生模型的多粒度协商修正框架。通过遥测参数的相关性和频域特征分析对参数进行分组。建立卫星各子系统和部件不同粒度的模型，按需构建多粒度数字孪生模型。研究了卫星不同层次组成结构之间的耦合关系，提出协商修正方法。利用真实在轨遥测数据对框架进行验证，研究结果表明：所提方法较未使用的均方根误差精度提升了50%以上，修正结果更具备系统性、完备性。
Abstract:The uncertainty of the model should be statistically assessed as the foundation for model selection, as there are errors between the digital twin model and the actual system that must be reduced. However, the satellite digital twin model exhibits multi-dynamic, multi-spatial scale, and multi-physical field coupling properties. Additionally, the numerical solution will reveal the stiffness problem of ordinary differential equations and the multi-scale problem of partial differential equations. If many telemetry parameters are updated at the system level, the results will not converge. A multi-granularity and negotiation model updating framework for satellite digital twin method was proposed. The parameters were grouped by correlation analysis and frequency domain analysis. Multi-granularity digital twin models were built based on the requirements, and various granularity models of satellite subsystems and components were produced. The coupling relationship between the satellite structure of different levels was studied, and a negotiation updating method was proposed. Real on-orbit telemetry data were used to verify the framework. According to the research findings, the proposed method updating approach outperforms the unused one by over 50% in terms of accuracy, and the updating results are more thorough and methodical.
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Key words:
- digital twin /
- model updating /
- cluster /
- multi-granularity modeling /
- negotiation update
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图 1 卫星数字孪生模型多粒度协商修正框架和应用
Figure 1. Framework and application of multi-granularity and negotiation model updating method for satellite digital twin
图 2 遥测量与数字卫星之间距离计算
Figure 2. Calculation of distance between telemetry parameters and digital satellite model
图 9 不同分组个数方案下修正结果比较
Figure 9. Comparison of updating results under different grouping number schemes
图 10 各个遥测量均方根误差随迭代次数的变化
Figure 10. Variation of each remote measurement root mean square error with the number of iterations
图 11 修正后仿真值与遥测值的对比
Figure 11. Comparison of updated simulation values with telemetry values
图 13 均方根误差随协商阈值的变化曲线
Figure 13. Root mean square error change curve with the negotiation threshold
表 1 典型卫星遥测参数
Table 1. Typical satellite telemetry parameters
子系统 典型遥测量 姿轨控子系统 星上时间，地球惯性系下轨道位置、速度，星敏测量四元数，陀螺测量角速度，太敏测量太阳角，地敏测量姿态角，磁强计测量值，飞轮测量转速，飞轮控制指令，磁力矩器指令，推力器及各种部件的开关指令，飞行控制模式，帆板转角等 电源子系统 帆板、母线、负载、蓄电池的开关状态、电压、电流，充放电调节器、分流器、电源控制器、配电器等工作状态等 推进子系统 氧化剂贮箱、燃料箱、高压气瓶的压强、流量，各种阀门的开关指令等 热控子系统 各个节点测温敏感器的温度测量值，温控敏感器状态，加热器状态等 测控子系统 信噪比，伪距，载波多普勒值，通信状态，通信数据等 载荷子系统 相机开关，拍照数据等 
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表 2 遥测参数-模型粒度隶属度
Table 2. Membership functions of telemetry parameters and model granularity
变量 隶属度值 姿轨控子系统 电源子系统 热控子系统 位置,速度,姿态角,角速度 1 0 0 飞轮转速 1 0 0 帆板输出电流, 蓄电池电压,
充放电电流0.5 1 0.5 帆板温度 0.5 0 1
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表 3 瓢虫一号卫星系统组成
Table 3. System composition of Ladybird 1 satellite
系统组成 内容 姿轨控子系统 陀螺, 星敏, 太敏, 磁强计，飞轮, 磁力矩器, 控制器 电源子系统 太阳帆板, 蓄电池, 各种用电部件 热控子系统 壁板, 加热器, 各种发热部件
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表 4 瓢虫一号卫星工况参数
Table 4. Initial values of Ladybird 1 satellite
轨道六要素 姿态 初始时刻 { 6908636 m, 0, 97.84°, 53.4°, 271°, 30° }{−80.5°, 179.7°, 111.6°} 2018-12-07 13:00:02
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表 5 待修正的遥测量和状态量
Table 5. Telemetry parameters and state parameters to be updated
遥测量 状态量 轨道位置、速度、姿态角、角速度、飞轮转速、帆板输出电流、蓄电池电压、充放电电流、飞轮电压、帆板温度 轨道位置初值、速度初值、姿态角初值、角速度初值、飞轮转速初值、飞轮电机电压初值、帆板光电转换因子、帆板温度补偿系数、电池充电系数和放电系数、蓄电池电池额定充放电电压、帆板初始温度
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表 6 粒度选取结果
Table 6. Model granularity selection results
变量 姿轨控子系统 电源子系统 热控子系统 轨道位置、速度 原理级 功能级 功能级 姿态角、角速度 原理级 功能级 功能级 飞轮转速 原理级 功能级 功能级 帆板输出电流，蓄电池电压，蓄电池充电电流，蓄电池放电电流，飞轮电压，帆板温度 原理级 原理级 原理级
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表 7 各遥测量的均方根误差
Table 7. Root mean square error of telemetry parameters
组别 变量名 修正前均方根误差/% 修正后均方根误差/% 仅分组 分组+协商 第1组 x轴位置分量 6.784 0.043 0.042 y轴位置分量 6.754 0.042 0.040 z轴位置分量 6.062 0.044 0.043 x轴速度分量 5.573 0.046 0.042 y轴速度分量 5.734 0.055 0.052 z轴速度分量 6.640 0.018 0.014 总遥测量 6.251 0.011 0.010 第2组 滚转角 4.003 0.044 俯仰角 8.647 0.016 偏航角 11.351 0.020 x轴角速度 7.424 1.027 y轴角速度 11.849 2.206 z轴角速度 8.833 3.526 总遥测量 9.029 1.330 第3组 飞轮1转速 34.164 7.071 飞轮2转速 40.169 7.730 飞轮3转速 20.167 4.110 飞轮4转速 26.435 5.187 总遥测量 31.426 6.196 第4组 帆板输出电流 4.625 2.548 0.331 电池充电电流 5.565 3.849 1.324 电池放电电流 6.613 3.549 1.354 电池电压 7.646 2.438 1.387 飞轮1电压 6.024 5.394 1.031 飞轮2电压 6.846 5.303 1.104 飞轮3电压 6.248 6.129 1.435 飞轮4电压 7.045 5.450 1.521 帆板温度 12.540 3.671 2.671 总遥测量 6.472 5.484 1.426
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