多学科设计优化中的不确定性建模

不确定性因素对复杂工程系统设计的影响贯穿整个设计过程.对多学科设计优化(MDO,Multidisciplinary Design Optimization)中不确定性的来源进行了总结和归类;建立了包含2个耦合学科的MDO系统分析输出结果的不确定性与设计变量输入数据误差和模型误差之间关系的数学模型,用于计算各种不确定性对系统性能的影响.算例分析结果和实验结果吻合,表明该数学模型有效可靠.经过扩展可用于估算包含多个耦合学科的MDO系统分析输出结果的不确定性,为鲁棒多学科设计优化方法的构建提供理论基础.      

基于误差四元数分解的刚体姿态跟踪滑模控制

对于转动惯量参数时变和参数不确定以及外部扰动和作用力矩方向偏差的刚体姿态跟踪系统,文章提出了采用滑模控制的方法。利用误差四元数建立数学模型,通过误差四元数分解进行反馈线性化得到指令角加速度;设计滑模控制律,实现指令角加速度跟踪。仿真结果表明,文章所求控制律对刚体姿态跟踪系统具有稳定性和鲁棒性。     

Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).     

利用OH夜气辉反演原子氧数密度时输入参数的不确定度对反演结果的影响

借助OH夜气辉辐射的光化学模式,由OH夜气辉辐射反演中间层-低热层区域的原子氧数密度时,输入参数的不确定性将导致反演得到的原子氧数密度具有不确定性.以在sudden death猝灭模式下通过OH(8-3)振动带体辐射率反演原子氧数密度为例,分别研究了大气参数和OH气辉辐射率的不确定度引起的反演不确定度、化学反应速率常数的不确定度引起的反演不确定度,以及所有输入参数的不确定度共同引起的反演不确定度,找出其不确定度对反演结果影响最大的参数.结果表明,三种反演不确定度均随着高度的升高而增大,温度和体辐射率的不确定度对第一种反演不确定度的贡献最大,反应速率常数b(8)和A(8-3)、的不确定度对第二种反演不确定度的贡献最大.     

知识与数据融合的可靠性定量模型建模方法

可靠性定量设计的关键是建立可靠性定量模型。现有的可靠性定量模型建模方法主要基于设计人员对产品对象故障规律的知识,包括故障模式、环境扰动、故障机理等。但知识固有的有限性和不完整性必然会给可靠性定量模型带来模型误差和输入参数的不确定性。针对这个问题,提出了基于贝叶斯理论融合知识和数据的可靠性定量模型建模方法,量化并更新模型误差和输入参数的不确定性。为此,首先说明了知识与数据融合的可靠性定量模型建模工作,建立了知识与数据融合的可靠性定量模型建模框架;接着阐述了基于贝叶斯理论的知识与数据融合原理;然后介绍了基于贝叶斯理论融合知识与数据的通用方法,并分别针对性能波动数据和性能退化数据2种常见数据类型进一步详细讨论了各自适用的贝叶斯融合方法;最后通过机载轴向柱塞泵的案例验证了前述方法的可行性和有效性。      

Accurate estimation of relative atmospheric density error on the example of uncertain geomagnetic activity information

Errors in neutral atmospheric density are the dominant contributor to unrealistic orbital state-vector covariances in low Earth orbits (LEO). Density uncertainty is caused by model-uncertainty at spatial scales below and within the model resolution, as well as input-uncertainty of the environmental parameters supplied to the semi-empirical atmospheric model.The paper at hand provides multiple contributions. First, analytic equations are derived to estimate the relative density error due to an input parameter uncertainty in any of the environmental parameters supplied to the model. Second, it is shown on the example of uncertain geomagnetic activity information, how to compute the required inputs to facilitate the accurate estimation of the relative density error.A clamped cubic splining approach for the conversion from geomagnetic amplitude (ap) to the kp index is postulated to perform this uncertainty propagation, as other algorithms were found unsuitable for this task. Results of numerical simulations with three popular semi-empirical models are provided to validate the set of derived equations. It is found that geomagnetic input uncertainty is especially important to consider in case of low global geomagnetic activity. The findings seamlessly integrate with prior work by the authors to perform density-uncertainty considering orbit estimation.     

Statistical validation of HZETRN as a function of vertical cutoff rigidity using ISS measurements

Measurements taken in Low Earth Orbit (LEO) onboard the International Space Station (ISS) and transit vehicles have been extensively used to validate radiation transport models. Primarily, such comparisons were done by integrating measured data over mission or trajectory segments so that individual comparisons to model results could be made. This approach has yielded considerable information but is limited in its ability to rigorously quantify and differentiate specific model errors or uncertainties. Further, as exploration moves beyond LEO and measured data become sparse, the uncertainty estimates derived from these validation cases will no longer be applicable. Recent improvements in the underlying numerical methods used in HZETRN have resulted in significant decreases in code run time. Therefore, the large number of comparisons required to express error as a function of a physical quantity, like cutoff rigidity, are now possible. Validation can be looked at in detail over any portion of a flight trajectory (e.g. minute by minute) such that a statistically significant number of comparisons can be made. This more rigorous approach to code validation will allow the errors caused by uncertainties in the geometry models, environmental models, and nuclear physics models to be differentiated and quantified. It will also give much better guidance for future model development. More importantly, it will allow a quantitative means of extrapolating uncertainties in LEO to free space. In this work, measured data taken onboard the ISS during solar maximum are compared to results obtained with the particle transport code HZETRN. Comparisons are made at a large number (∼77,000) of discrete time intervals, allowing error estimates to be given as a function of cutoff rigidity. It is shown that HZETRN systematically underestimates exposure quantities at high cutoff rigidity. The errors are likely associated with increased angular variation in the geomagnetic field near the equator, the lack of pion production in HZETRN, and errors in high energy nuclear physics models, and will be the focus of future work.     

飞行控制律评估与确认的μ分析方法

针对目前应用的网格法在实际使用中的不足,将μ分析方法应用到飞行控制律 的评估与确认中.以某型战斗机及为其设计的鲁棒飞行控制律为研究对象,采用相应的稳定 性准则,利用线性分式变换形式,考虑各种已知的不确定参数摄动,用μ分析方法实现了对 该准则的评估与确认.与传统网格法相比,基于μ分析的方法具有两个明显的优点,一是网 格间的点可以得到评估,二是不存在网格法的"维数灾"问题,从而提高了评估的可靠性和 效率.     

测量接收机与矢网测量衰减方法研究

介绍测量接收机与矢量网络分析仪测量衰减的原理，并对不确定度来源进行了分析。分别对低反射系数下，不同衰减量进行不确定度评定，表明衰减量在（10～60）dB范围内，两种标准测量不确定度相当；另外，采用两种测量标准对较大输入反射系数模值、不同相位下的阻抗调配器级联20dB固定衰减器作为被测件进行测试，最大偏差达到±0.31dB，矢量网络分析仪的测量不确定度（0.18dB），明显小于接收机测量不确定度（0.59dB）。     

测量接收机与矢网测量衰减方法研究

介绍测量接收机与矢量网络分析仪测量衰减的原理,并对不确定度来源进行了分析。分别对低反射系数下,不同衰减量进行不确定度评定,表明衰减量在(10～60) d B范围内,两种标准测量不确定度相当;另外,采用两种测量标准对较大输入反射系数模值、不同相位下的阻抗调配器级联20dB固定衰减器作为被测件进行测试,最大偏差达到±0. 31dB,矢量网络分析仪的测量不确定度(0. 18dB),明显小于接收机测量不确定度(0. 59dB)。     

Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed “HASDM-ML,” “CHAMP-ML,” and “MSIS-UQ” machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called “consider covariance sigma point (CCSP)” filter that can account for the density uncertainties during orbit propagation. As a test-bed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions.     

Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target

In this paper, a tube-based robust output feedback model predictive control method (TRMPC) is proposed for controlling chaser spacecraft docking with a tumbling target in near-circular orbit. The controller contains a simple, stable, Luenberger state estimator and a tube-based robust model predictive controller. Several practical challenges are also considered under dock-enabling conditions, such as the control saturation, velocity constraint, approach corridor constraint, and collision avoidance constraint. Meanwhile, uncertainties are carefully analyzed when designing the controller, including dynamics uncertainty, measurement error, and control deviation. The TRMPC ensures that all possible state trajectories with uncertainties lie in the minimum robust positively invariant set (mRPI, i.e., the so-called tube in this paper). The tube center is the solution of a nominal (without uncertainties) system. Another important contribution of this paper is to propose a technique where it is unnecessary to calculate the mRPI explicitly. Thereby, the ‘curse of dimensionality’ can be avoided for a six-dimensional system. To verify the feasibility of the proposed TRMPC strategy in the presence of uncertainties, two scenarios of autonomous rendezvous and docking (AR&D) are simulated. The simulation results show that the TRMPC method is more efficient in minimizing the uncertainties, fuel consumption, and computational cost, compared to the classic model predictive control (MPC) method.     

RLV再入神经网络自适应姿态控制器设计

可重复使用运载器（RLV）大包线再入过程中,广泛存在模型不确定与外界干扰,会给姿态控制器的设计带来不利影响,为此提出了一种神经网络自适应控制器设计方案。基于时标分离原理设计了快、慢双回路控制结构。在此基础上设计了径向基神经网络（RBFNN）自适应律,用于在线估计模型不确定和外界干扰力矩,并在控制器中进行补偿。仿真验证表明,RBFNN 自适应控制器能良好地完成姿态跟踪控制,有效地抑制干扰力矩对姿态控制的影响。自适应律能够在线估计真实的飞行器动态和外界干扰力矩,控制器具有抗扰动能力。     

考虑误差不确定性的航空安全预测新方法

航空安全精确预测对预防事故意义重大。目前航空安全预测主要是确定性预测，忽略了各类不确定性对预测影响。在确定性预测基础上，考虑误差不确定性开展航空安全预测，通过非参数方法获得航空安全预测误差不确定性描述，基于最高密度域求解一定可靠程度航空安全预测值最可能落入区间，量化不确定性引起航空安全预测结果的变动，从而确定该区间包含航空安全预测值的可靠程度，更好地认识被预测量在未来变化中可能存在的不确定性和面临的风险。以某航空公司1994—2015年航空安全数据为例，采用所提方法对航空安全开展预测，结果表明，所提方法能提供航空安全预测值及其更精确的不确定性变化范围，更有利于从不确定性角度对航空安全进行分析，解释航空安全预测结果的可能性水平，能为航空安全预警和管理提供理论依据。      

光栅式传动链误差测量系统的不确定度分析

为了进一步改善传动链误差测量系统的性能，以谐波减速器为被测对象，通过推导测量系统不确定度评定的一般方法，找出了测量系统的各个不确定度分量；通过分析系统中A类和B类不确定度，阐述了各个不确定度分量对整个测试系统的影响，提出了减少不确定度的相关措施，为优化传动误差测量系统的测量提供了指导。     

Backstepping sliding-mode control of stratospheric airships using disturbance-observer

In the presence of unknown disturbances and model parameter uncertainties, this paper develop a nonlinear backstepping sliding-mode controller (BSMC) for trajectory tracking control of a stratospheric airship using a disturbance-observer (DO). Compared with the conventional sliding mode surface (SMS) constructed by a linear combination of the errors, the new SMS manifold is selected as the last back-step error to improve independence of the adjustment of the controller gains. Furthermore, a nonlinear disturbance-observer is designed to process unknown disturbance inputs and improve the BSMC performances. The closed-loop system of trajectory tracking control plant is proved to be globally asymptotically stable by using Lyapunov theory. By comparing with traditional backstepping control and SMC design, the results obtained demonstrate the capacity of the airship to execute a realistic trajectory tracking mission, even in the presence of unknown disturbances, and aerodynamic coefficient uncertainties.     

基于本征旋转的刚体姿态跟踪系统滑模控制器

对于转动惯量参数时变和参数不确定以及外部扰动和作用力矩方向偏差的刚体姿态跟踪系统,提出了采用滑模控制的方法.利用误差四元数建立数学模型,通过本征旋转进行反馈线性化得到指令角加速度.设计滑模控制律,实现指令角加速度跟踪.仿真结果表明,所求控制律对刚体姿态跟踪系统具有全局稳定性和鲁棒性.     

视觉导航下基于H2/H∞的航迹跟踪

为了从理论上研究视觉导航系统的特性,首先在物理上将视觉导航系统划分为传感器(摄像头、激光测距仪)和视觉处理计算机。针对视觉处理计算机,建立视觉位置测量模型。将视觉位置测量模型的不确定性分为参数不确定性和输入干扰2种。然后通过仿真详细分析了视觉位置估计针对不同模型不确定性的敏感程度。最后在引入视觉位置测量模型不确定性的基础上研究H₂/H_∞混合鲁棒控制在航迹跟踪上的应用,并给出了保证航迹控制系统稳定性和跟踪性能情况下的视觉位置测量模型摄动范围,对计算机视觉算法的研究具有一定的指导意义。