基于SVD方法的lNS传递对准的可观测性能分析

在惯导系统一般的误差动态方程和速度观测方程的基础上，建立了姿态传递对准所必需的弹、舰相对姿态误差方程和观测方程。介绍了基于动态系统可观测性矩阵奇异值分解的状态变量可观测度的分析方法。用奇异值分解的方法，对同时采用速度和姿态传递的INS对准模型，分析了系统变量的可观测性和可观测度，为对准方程的可观测性结构分解和误差估计性能的改善提供了必要的基础。     

GPS/SINS系统空中对准姿态角误差可观测性研究

提出一种新的判断系统可观测性和可观测度的方法,详细分析了机体各种运动对系统姿态角误差可观测性和可观测度的影响,并把该方法应用于组合导航系统的可观测性和可观测度的研究中。该方法利用了误差状态的最小二乘估计均方误差阵的特征值和特征向量,能判断系统的可观测度,避免进行卡尔曼滤波计算求协方差阵。仿真结果表明该方法简单、快速、有效。     

外场标定条件下捷联惯导系统误差状态可观测性分析

为了适应惯导系统的长期稳定使用和避免从机组上拆装的麻烦,实现惯组的外场标定是非常有意义的。在不依赖转台等设备的条件下,分析了仅依靠速度误差和位置误差信息时激光陀螺捷联惯组的误差参数的可观测性问题。首先从外场条件下系统误差的动态方程出发分析了捷联惯组的误差状态（姿态误差以及陀螺和加速度计的六个常值漂移）的可观测性并且进一步分析了误差状态估计的收敛速度以及受观测噪声的影响程度。分析表明,单一位置条件下在没有精确初始姿态误差信息的情况下惯性仪表零偏是不可观测的,为了较精确地估计出惯组的误差系数需至少将惯组摆放三个位置。最后对理论分析结果进行了仿真验证。     

Integration of topological modification within the modeling of multi-physics systems: Application to a Pogo-stick

The present work tackles the modeling of multi-physics systems applying a topological approach while proceeding with a new methodology using a topological modification to the structure of systems. Then the comparison with the Magos' methodology is made. Their common ground is the use of connectivity within systems. The comparison and analysis of the different types of modeling show the importance of the topological methodology through the integration of the topological modification to the topological structure of a multi-physics system. In order to validate this methodology, the case of Pogo-stick is studied. The first step consists in generating a topological graph of the system. Then the connectivity step takes into account the contact with the ground. During the last step of this research; the MGS language (Modeling of General System) is used to model the system through equations. Finally, the results are compared to those obtained by MODELICA. Therefore, this proposed methodology may be generalized to model multi-physics systems that can be considered as a set of local elements.     

M-P inverse method of topological variation of frame structures

In this paper a topological modification method for structural variations of space frame structures is studied by using the Moore-Penrose inverse theory and a new kind of factorization of the stiffness matrix. A set of explicit formulations of variations are obtained. A numerical example is given to illustrate the valid of the present method.     

Topological approach to solve frame structures using topological collections and transformations

The present work tackled the modeling of frame structures using a topological approach based on the concepts of topological collections and transformations. The topological collections are used to specify the interconnection law between the frame structures and the transformations that are used to describe their behavior. As a language allowing the application of this approach, we applied the MGS (Modeling of General System) language. To validate this approach, we studied the case of two- and three-dimensional frame structures. Then, the results obtained using the MGS language are presented and compared to those obtained by the structural calculation software by the finite-element method RDM6. For both studied cases, we find that the results obtained by MGS language based on the notions of topological collections and transformations and those obtained by the RDM6 software based on the finite element method are very close, which validates our approach. Using this topological approach, any structure can be characterized by local relations between its elements, thus making it possible to dissociate its topology and its physics. Indeed, in our topological approach, we separately define the topology of the studied frame structure and the local behavior law as well as the equilibrium equations of its various components. Therefore, this topological approach might be generalized to model complex systems which can be considered as a set of local elements linked by a neighborhood relationship.     

MSINS/GPS全组合系统可观测性分析

卡尔曼滤波是组合导航系统处理数据最常用的算法。首先给出PWCS可观测性定理,然后在G矩阵选星算法的基础上,设计了基于伪距/伪距率的MSINS/GPS紧耦合系统(TCS)的卡尔曼滤波器,在上述量测方程中加入基于GPS载波相位观测量的姿态测量方程,给出了有姿态测量信息的全组合系统(CIS)。最后证明了CIS满足PWCS定理条件,即可以用离散系统的选择可观测性矩阵(SOM)代替相应的连续系统的总可观测性矩阵(TOM)对系统进行可观测性和可观测度的分析。利用奇异值分解(SVD)理论给出了不同可见卫星数时CIS的可观测性分析结果。与不加入姿态观测信息的MSINS/GPS的TCS比较,计算结果表明CIS比TCS具有更好的可观测性和可观测度。     

Bandgap design of three-phase phononic crystal by topological optimization

Material topologies in phononic crystals take the key role in wave controlling. A genetic algorithm with a plane wave expansion method was adopted to optimize the three-phase phononic crystal for a larger relative band gap in both out-of-plane and in-plane wave modes. Fourier displacement property was used to calculate the structure function in the plane wave expansion. The mutation and crossover rates were calculated based on the adaptive GA method. Results indicate that the volume fraction and the symmetry are two key factors for the design of topological configurations. The relations between the key factors and the different topologies are correlated.     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

Energy release rate approximation for small surface-breaking cracks using the topological derivative

The topological derivative provides the variation of a response functional when an infinitesimal hole of a particular shape is introduced at a point of the domain. In this fracture mechanics work we use the topological derivative to approximate the energy release rate field associated with a small crack at any boundary location and at any orientation. Our proposed method offers significant computational advantages over current finite element based methods since it requires a single analysis, whereas the others require a distinct analysis for each crack location-orientation combination. Moreover, the proposed method evaluates the topological derivative in the non-cracked domain which eliminates the need for tailored meshes in the crack region.     

From imaging to material identification: A generalized concept of topological sensitivity

To establish a compact analytical framework for the preliminary stress-wave identification of material defects, the focus of this study is an extension of the concept of topological derivative, rooted in elastostatics and the idea of cavity nucleation, to 3D elastodynamics involving germination of solid obstacles. The main result of the proposed generalization is an expression for topological sensitivity, explicit in terms of the elastodynamic Green's function, obtained by an asymptotic expansion of a misfit-type cost functional with respect to the nucleation of a dissimilar elastic inclusion in a defect-free “reference” solid. The featured formula, consisting of an inertial-contrast monopole term and an elasticity-contrast dipole term, is shown to be applicable to a variety of reference solids (semi-infinite and infinite domains with constant or functionally graded elastic properties) for which the Green's functions are available. To deal with situations when the latter is not the case (e.g. finite reference bodies or those with pre-existing defects), an adjoint field approach is employed to derive an alternative expression for topological sensitivity that involves the contraction of two (numerically computed) elastodynamic states. A set of numerical results is included to demonstrate the potential of generalized topological derivative as an efficient tool for exposing not only the geometry, but also material characteristics of subsurface material defects through a local, point-wise identification of “optimal” inclusion properties that minimize the topological sensitivity at sampling location. Beyond the realm of non-invasive characterization of engineered materials, the proposed developments may be relevant to medical diagnosis and in particular to breast cancer detection where focused ultrasound waves show a promise of superseding manual palpation.     

A structural topological optimization method for multi-displacement constraints and any initial topology configuration

In density-based topological design, one expects that the final result consists of elements either black （solid material） or white （void）, without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multidisplacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.     

Sensitivity of the macroscopic elasticity tensor to topological microstructural changes

A remarkably simple analytical expression for the sensitivity of the two-dimensional macroscopic elasticity tensor to topological microstructural changes of the underlying material is proposed. The derivation of the proposed formula relies on the concept of topological derivative, applied within a variational multi-scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. The derived sensitivity—a symmetric fourth order tensor field over the RVE domain—measures how the estimated two-dimensional macroscopic elasticity tensor changes when a small circular hole is introduced at the microscale level. This information has potential use in the design and optimisation of microstructures.     

Correlation mechanism of friction behavior and topological properties of the contact network during powder compaction

The effect of friction behavior on the compacted density is significant, but the relationship between the topological properties of the contact network and friction behavior during powder compaction remains unclear. Based on the discrete element method (DEM), a DEM model for die compaction was established, and the Hertz contact model was modified into an elastoplastic contact model that was more suitable for metal-powder compaction. The evolution of the topological properties of the contact network and its mechanism during powder compaction was explored using the elastoplastic contact model. The results demonstrate that the friction behavior between the particles is closely related to the topological properties of the contact network. Side wall friction results in smaller clustering coefficient (CC) and excess contact (EC) in the lower region near the side wall. Corresponding to this phenomenon, the upper region near the side wall has more high-stress particles when the major principal stress threshold was considered, and the CC and EC are significantly higher than those in the other regions. This study provides a theoretical basis for improving powder compaction behavior.     

Substructured molecular dynamics using multibody dynamics algorithms

This paper reports a new research effort aimed at using efficient multibody dynamics methods to simulate coarse-grained molecular systems. Various molecular systems are studied and the results of nanosecond-long simulations are analyzed to validate the method. The systems studied include bulk water, alkane chains, alanine dipeptide and carboxyl terminal fragments of calmodulin, ribosomal L7/L12 and rhodopsin proteins. The stability and validity of the simulations are studied through conservation of energy, thermodynamics properties and conformational analysis. In these simulations, a speed up of an order of magnitude is realized for conservative error bounds with a fixed timestep integration scheme. A discussion is presented on the open-source software developed to facilitate future research using multibody dynamics with molecular dynamics.     

Moreau's hydrodynamic helicity and the life of vortex knots and links

This contribution to an issue of Comptes rendus Mécanique, commemorating the scientific work of Jean-Jacques Moreau (1923–2014), is intended to give a brief overview of recent developments in the study of helicity dynamics in real fluids and an outlook on the growing legacy of Moreau's work. Moreau's discovery of the conservation of hydrodynamic helicity, presented in an article in the Comptes rendus de l'Académie des sciences in 1961, was not recognized until long after it was published. This seminal contribution is gaining a new life now that modern developments allow the study of helicity and topology in fields and is having a growing impact on diverse areas of physics.     

捷联惯性系统对摇摆运动下的初始对准研究

建立了捷联惯性系统对摇摆运动及线运动下的误差模型，分析了系统状态的可观测性，比较了静基座与摇摆运动情况下的卡尔曼滤波器的估计效果，通过计算机仿真提出了有效的初始对准方法。     

Recent developments in multibody system dynamics

For the dynamical analysis of discrete mechanical systems the method of multibody systems is well qualified. The resulting equations of motion are solved by simulation codes and displayed by computer animation. The paper presents an approach for the efficient computation of motions and reactions.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

基于分子动力学与耗散粒子动力学串行耦合的面心立方金属粗粒化模型

通过全原子分子动力学(MD)与等温耗散粒子动力学(DPD)的串行耦合,提出了面心立方金属粗粒化模型的建立方法。该方法将一定数量的原子粗粒化为单个介观 DPD 粒子,假设 DPD 粒子间作用势的表达式为Sutton-Chen势函数形式,利用遗传算法,以 MD和DPD计算的单晶金属常温(298 K)等温线相一致为目标,确定了DPD粒子间作用势函数的参数。对单晶铜纳米棒的轴向拉伸开展 MD 和 DPD 对比模拟,发现在纳米棒弹性响应阶段,两者计算结果吻合较好,而屈服应力和屈服应变存在一定差距。建议在优化 DPD势函数参数时,引入更多的材料力学响应信息,进一步提高介观DPD模型的准确性。