基于横坐标系的捷联惯导系统极区导航方法

现有惯性导航系统机械编排在极区(特别是地理极点附近)不适用。针对该问题,提出了适用于捷联惯性导航系统极区使用的横坐标系导航方法。构建出横坐标系参考框架,推导出横坐标系和常规坐标系之间位置、速度和姿态信息的转换关系,建立了横坐标系捷联惯导系统的机械编排,并在此基础上分析其误差传播特性。仿真分析表明:横坐标系可以解决采用现有机械编排时,极区经线圈快速汇聚和地理极点附近无北向基准所引起的问题,从而满足极区导航要求;同时,仿真结果验证了横坐标系捷联惯导系统中位置和航向误差漂移的特性。     

极区间接横向惯性导航方法

针对极区经线收敛引起的以真北向作为航向参考的导航算法失效问题,在横向惯性导航方法的基础上,提出了一种以游移方位坐标系为导航坐标系的间接横向惯性导航方法,以寻求全球导航时算法的内在统一性,保证平台惯导平稳切换时的流畅性。在横向地球椭球模型下,推导了横向游移坐标编排,建立了误差模型,并进行了仿真分析,并给出了间接横向导航方法下的全球导航流程。结果表明,导航坐标系相同情况下指北编排与间接横向编排极区性能不同的本质原因在于游移角误差的不同;间接横向惯性导航方法能够满足极区导航与穿越极点航行要求,航向角误差小于0.1'/h。     

基于神经网络的GPS深度融合弹载惯导模型

针对传统弹载惯性导航系统误差修正采用线性化模型,无法对非线性误差进行修正的缺点,提出一种基于神经网络的GPS深度融合弹载惯导模型。构建IMU六路脉冲数到发射惯性坐标系下视速度增量的非线性映射关系,利用GPS信息对网络误差模型进行训练,为GPS信号失效后的长航时惯性导航系统提供更高精度的误差修正模型。仿真实验结果表明,相较于纯惯性导航系统,所提模型能够在GPS信号失效后抑制惯导系统误差发散,速度精度提高76.56%,位置精度提高91.61%。     

建立惯性仪表安装误差数学模型的理论研究

安装误差对系统精度有较大的影响,对捷联惯性系统的影响尤为突出,为此从仿射坐标系的坐标变换理论入手,分析并推导了建立惯性仪表安装误差数学模型的坐标变换矩阵公式,为惯性仪表安装误差数学模型的建立、测试及在惯性导航系统中的补偿提供了理论依据。     

基于虚拟圆球法向量的极区惯性导航算法

提出了一种基于虚拟圆球法向量位置表示的具有全球范围适用性的惯性导航算法。避免了横坐标系、格网坐标系极区导航算法中参考椭球模型下曲率半径近似计算带来的误差问题,且不需要在极区算法和非极区算法之间进行复杂的切换。与地球坐标系下惯性导航算法相比,由于高度通道和水平通道的导航解算分开,便于通过阻尼抑制高度通道的误差发散问题。分别建立了高度通道和水平通道的误差微分方程,对极区和非极区惯性导航进行了统一的更加精确的误差特性分析。基于实际航海导航试验数据的仿真结果表明,相比横坐标系、格网坐标系极区导航算法,提出的极区导航算法形式简洁易实现,精度略高,且具有全球适用性。     

基于地速分解的高精度捷联惯性导航算法

传统的捷联惯性导航算法求解比力积分项采用了一阶近似方法,近似误差对高精度导航应用的影响是不可忽略的。为消除近似误差,提出了一种改进的捷联导航算法。在惯性坐标系中,将地速分解为比力地速与重力地速两部分,求出了能够完全补偿动态误差的比力积分变换项解析表达式,在此基础上得到了比力地速的精确解,并将其求解方法扩展应用于重力地速,在不改变传统导航算法实现框架的前提下,设计了高精度的捷联惯性导航算法。改进导航算法的精度与对偶四元数导航算法一致,而其实时性却与传统导航算法相当,获得了整体性能上的优势。     

单轴旋转调制捷联惯导系统倾斜角误差补偿

安装在单轴转位机构上的惯性测量单元(IMU),会因IMU坐标系与载体坐标系不重合而存在一定的倾斜角,此倾斜角会使得IMU在旋转过程中引入姿态误差,在很大程度上降低了系统的姿态输出精度。为了降低安装倾斜角对旋转式捷联惯导系统的影响,文章通过对旋转过程中因安装倾斜引起的姿态角误差进行了详细分析,然后运用实验和数据拟合的方法得出了倾斜角随转位机构变化的规律,最后对倾斜角产生的误差加以补偿。经仿真和实验验证表明,对倾斜角误差补偿后,单轴旋转式捷联惯性导航系统的水平姿态精度由原先的2°提高到0.05°范围以内,航向误差由原先的0.5°提高到0.005°,大大提高了旋转式捷联惯导系统的姿态精度,具有一定的工程应用价值。     

基于转台误差隔离的捷联惯导系统尺寸效应参数标定

针对捷联惯导系统尺寸效应参数标定问题,提出了一种基于转台误差隔离的改进标定方法。先标定出捷联惯导系统中加速度计间的相对位置关系,再基于尺寸效应误差最小原则,对载体坐标系原点位置进行优化,得出尺寸效应参数。克服了传统分立式标定方法的一些不足,从原理上降低了标定对转台的依赖。对于陀螺零偏稳定性优于0.005°/h,加速度计零偏稳定性优于2×10~(-5) g的捷联惯导系统:尺寸效应参数标定重复性小于0.01 mm(转速60°/s);在摇摆条件下(幅度30°,频率0.15 Hz),4000 s纯惯性导航平均定位误差由补偿前的3100 m以上减小到补偿后的150 m以内。     

中低纬度评估极区导航时IMU数据转换误差模型

为解决在中低纬度地区定量评估惯性导航系统极区性能的问题,开展了惯导IMU极区模拟转换误差分析与建模.首先,基于地球球体模型横向坐标系下导航参数不变的轨迹模拟转移规则,给出惯导IMU模拟极区输出转换修正量模型;之后,对模拟试验测试参考基准的位置、航姿、速度等误差进行理论分析,并在此基础上,详细推导了测试参考基准误差对IM...     

关于激光捷联惯性导航系统姿态算法的分析

圆锥误差和量化误差是激光捷联惯性导航系统姿态解算误差的两个最主要的误差源.从分析圆锥误差产生的机理出发,分别分析了以角度和角速度为计算参数的圆锥误差补偿算法,并对量化误差对圆锥误差补偿算法的影响进行了研究.通过理论分析和数字仿真,得出在实际工程应用中,采用角速度为输入信息的激光捷联惯性导航系统姿态算法应该在考虑量化误差的情况下,采用以角速度为计算参数的圆锥误差补偿算法.     

基于惯性参考系基准的快速传递对准方法

研究了以惯性参考系为基准的新型传递对准方法。推导了计算惯性坐标系和计算体坐标系传递对准动态误差模型,并给出了相应的"速度+姿态"观测方程。基于惯性参考系的对准方法通过链式法则将子惯导输出的姿态矩阵描述为三个变换矩阵之积,其中两个变换矩阵通过对准时间和主惯导提供的位置信息可得到精确求解,剩余的变换矩阵(子惯导体坐标系至惯性坐标系间的变换矩阵)通过子惯导陀螺仪的输出进行解算,其误差通过传递对准估计得到的失准角进行补偿。对提出的两种对准方法进行摇摆实验验证,方位对准误差优于4’(1)。与传统基于导航坐标系的方法相比,基于惯性坐标系的方法直接将误差定位到惯性坐标系上,具有算法简便的特点。     

光电积分式陀螺经纬仪用于发射阵地定向误差分析

为实现导弹快速精确的发射,必须准确标定导弹发射阵地基准射向。陀螺经纬仪的使用可有效标定阵地射向,同时陀螺经纬仪系统误差又使阵地基准方向产生偏差。在确定各种系统误差的基础上,对陀螺经纬仪系统误差中的第一项进行了分析,推导出其后三项引起导弹发射阵地定向的方位误差模型,定量分析了其对导弹落点横向偏差的影响,并进行了仿真。仿真数据为不同射程导弹对系统误差的具体指标要求提供了依据,为下一步研究光电积分式陀螺经纬仪在导弹发射阵地快速、精确定向奠定一定的基础。     

火星引力捕获动力学与动态误差分析

火星探测的制动捕获机会唯一,是影响任务成败的关键. 从限制性三体问题出发,推导了火星引力球、作用球与希尔球半径的计算公式,比较了三者的特点与适用范围,并结合作用球的定义与物理意义,给出了一种火星探测制动捕获段的工程定义. 在作用球范围内建立了火星制动捕获段动力学模型,给出了对捕获轨道精度产生影响的各项误差源. 通过蒙特卡洛仿真,定量分析了导航初始误差、发动机推力误差、制动点火时间误差等对捕获轨道近火点与远火点高度的影响,并对不同误差源可能导致的超差概率进行了分析,指出了影响捕获精度的主导误差源,可为我国未来火星探测制动捕获段的任务实施提供参考.      

Mathematical and Physical Constraints on Large-Eddy Simulations

We examine the mathematical constraints on the filtering operation in large-eddy simulation (LES), and the physical constraints on the formulation of subgrid scale (SGS) models. The mathematical constraints on filtering arise from the assumption of commutativity between the filtering operation and the differential operators: this breaks down for finite domains and for non-uniform filter kernels. The physical constraints on the modelling are twofold; invariance principles require any model to be invariant under a group of transformations: the most stringent of these being the principle of frame indifference. In addition, realizability requires that the SGS model should have the same mathematical properties as the term it replaces, which leads to further constraints on the modelling. Finally, we investigate the effects of commutation and realizability for two simulated cases: forced homogeneous isotropic turbulence in a box and fully developed channel flow. In particular, we look for correlations between the commutation errors and the non-realizable regions, and the large-scale resolved flow structures in the simulations. Received: 17 June 1996 and accepted 3 April 1997     

Thermoelasto-viscous Materials

A thermoelasto-viscous material is defined by a set of constitutive laws in which the stress, entropy, heat flux and free energy are functions of the present configuration, temperature, temperature gradient and the rate of change of all three of these. Here these materials are presented within the framework of Walter Noll’s new theory of simple materials, so that the constitutive laws are specified without the use of a frame of reference. The Coleman-Noll procedure is carried out, and the symmetry group of the material is also discussed, both without using a frame of reference. It is then shown what form the constitutive laws of a fluid thermoelasto-viscous material take when a frame of reference is considered. Finally, the governing equations for these materials are explicitly obtained and discussed. The results in this paper may serve as a foundation for new and better mathematical models to deal with phenomena such as heat transfer, heat exchanges and thermophoresis.     

A chassis-based kinematic formulation for flexible multi-body vehicle dynamics

This research proposed an efficient implicit integration method for the real-time simulation of flexible multi-body vehicle dynamics models. The equations of motion for the flexible bodies were formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. The proposed approach does not require evaluation of system Jacobian and its LU-decomposition in time loof of simulation. This is one of the key aspects that enable high computational efficiency of the proposed method. The numerical simulation results of the proposed approach were matched up with those of the conventional approach but the computation time can be reduced by applying the proposed method. The joint constraint and generalized force equations are the same as the equations for rigid vehicle dynamics models because the joints and forces between flexible bodies are connected by the RBE (rigid body element). On the various driving conditions, the numerical simulation results show that the proposed approach yields almost exact solutions compared to the conventional approach. And the proposed approach spends only 22.9% of conventional approach on computation time under CPU 3.2 GHz personal computer.     

Evaluating large eddy simulation results based on error analysis

The quantification of the prediction accuracy in large eddy simulations (LES) is very challenging due to various interacting errors associated with this approach. When dealing with errors in LES using implicit filtering, numerical and modeling errors have drawn the interest of many researchers. Little attention has been paid to other sources of discrepancies between LES results and reference data, namely sampling errors, influence of the initial conditions, improper boundary conditions or uncertainties issuing from reference data. A framework of metrics that includes all these issues is addressed in the present paper to study subgrid-scale (SGS) models for LES and to quantify their prediction accuracy and computational costs. The method is applied to a simple wall-bounded turbulent flow at moderate Reynolds number. It turns out from the results obtained with six commonly used SGS models that wall-adapting models (WALE and SIGMA) and localized dynamic models reproduce the physics of the flow field more faithfully, reveal a superior prediction accuracy and have a similar computational cost than models using van Driest wall damping. Especially at the viscous wall region (\(r^+<50\)), wall-adapting and localized dynamic models are more accurate, reflecting the proper near wall behavior of such models. Relying on the analysis of sources of various errors, uncertainties in LES are estimated and systematically assessed, and their influence on simulation results is quantified. Finally, engineering estimations of the required averaging time to obtain basic estimates of statistical quantities with a predetermined degree of accuracy are suggested.     

基于方位旋转调制的平台式惯导系统“一点校”

为了提高惯导系统长时间导航精度,需要在导航阶段对系统进行综校。设计了一种基于方位旋转调制技术的平台式惯导系统一点校方案。方位旋转调制技术可以有效地调制水平惯性敏感元件误差,降低其对系统工作精度的不利影响,这为"一点校"方案的实施提供了前提。分析了方位旋转式平台惯导系统的误差模型,得到了系统误差与误差源之间的解析关系。通过分析研究系统的误差传播特性,建立了方位陀螺漂移与系统位置误差的数学模型,完成了方位旋转式平台惯导系统的"一点校"方案设计,通过系统试验验证其有效性,方位陀螺常值漂移为0.003(°)/h的条件下,经10 h一点校,40 h一点校后,72 h定位误差小于1nmile,航向误差小于1′。     

What physical phenomena can be neglected when modelling concrete at high temperature? A comparative study. Part 1: Physical phenomena and mathematical model

The paper deals with modelling of hygro-thermal performance and thermo-chemical degradation of concrete exposed to high temperature. Several possible simplifications in modelling of heat and mass transport phenomena in heated concrete are considered and their effect on the results of numerical simulations is analyzed.A mathematical model of concrete at high temperature, already extensively validated with respect to experiments, is used as the reference model. It is based on mechanics of multiphase porous media and considers all important couplings and material nonlinearities, as well as different properties of water above the critical point of water, i.e. 647.3 K (374.15 °C).In this part of the paper, first physical phenomena, as well as heat and mass flux and sources in a concrete element are studied, both during slow and fast heating process, to examine the relative importance of different flux components. Then, the mathematical model of concrete at high temperature, developed by Authors in the last 10 years, is briefly presented and for the first time all the constitutive relationships of the model are summarized and discussed in detail. Finally, the method of numerical solution of the model equations is thoroughly presented.In the companion paper (part II) a brief literature review of the existing mathematical models of concrete at high temperature and a summary of their main features and physical assumptions will be presented. Then, extensive numerical studies will be performed with several simplified models, neglecting chosen physical phenomenon or flux components, to evaluate the difference between the results obtained with the simplified models and with the reference model. The study will concern hygric, thermal and degradation performance of 1-D and 2-D axisymmetric concrete elements during fast and slow heating. The analysis will allow us to indicate which simplifications in modeling of concrete at high temperature are practically and physically possible, without generating excessive errors with respect to the full reference model.     

The method of manufactured solutions applied to chaotic systems

In this paper, the method of manufactured solutions is applied to dynamical systems possessing chaotic behavior. This method is used in a non-traditional way to identify points with potential numerical errors and to improve computational efficiency. The numerical errors may be due to the selection of error tolerances in the integration of the ordinary differential equations, computer arithmetic precision, etc. Two classical chaotic models and two ship capsize models are examined. The current approach has similarities to entrainment methods in chaotic control theory, where entrainment refers to two dynamical systems having the same period, phase and amplitude. The convergent region from control theory is used to give a rough guide for identifying potentially catastrophic numerical errors for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models.