阶跃函数高精度逼近的结构拓扑优化方法

为了提高ICM(Independent Continuous and Mapping,即独立、连续及映射)方法求解结构拓扑优化问题的效率,本文改进了阶跃函数及其反函数的近似逼近函数——磨光函数和过滤函数。首先,分别对ICM方法的磨光函数和过滤函数按其近似性质进行了分类,分别提出了左磨函数及上磨函数和快滤函数、慢滤函数诸概念。然后得到了区分左磨函数和上磨函数、快滤函数和慢滤函数的两个判别定理;并得到了上磨函数、快滤函数、左磨函数及慢滤函数的对应定理。进而给出了磨光函数和过滤函数的使用准则及构造方法。采用高精度逼近阶跃函数的指数类函数做左磨函数,建立近似程度更高的结构拓扑优化模型。上述策略带来了模型非线性程度的提高,增加了求解难度。为此,针对该模型给出了精确对偶映射下的序列二次近似解法。最后,以位移约束下结构重量最轻化问题为例,叙述了相应的算法。与以往采用幂函数做磨光函数时算例结果的比较表明,该模型的提法合理,算法更加有效。由于提高了对阶跃函数及其反函数的逼近程度,从而显著减少了优化迭代的次数。     

Time series prediction using kernel adaptive filter with least mean absolute third loss function

In this paper, a novel kernel adaptive filter, based on the least mean absolute third (LMAT) loss function, is proposed for time series prediction in various noise environments. Combining the benefits of the kernel method and the LMAT loss function, the proposed KLMAT algorithm performs robustly against noises with different probability densities. However, an important limitation of the KLMAT algorithm is a trade-off between the convergence rate and steady-state prediction error imposed by the selection of a certain value for the learning rate. Therefore, a variable learning rate version (VLR–KLMAT algorithm) is also proposed based on a Lorentzian function. We analyze the stability and convergence behavior of the KLMAT algorithm and derive a sufficient condition to predict its learning rate behavior. Moreover, a kernel recursive extension of the KLMAT algorithm is further proposed for performance improvement. Simulation results in the context of time series prediction verify the effectiveness of the proposed algorithms.     

基于新型滤波器-HABF的SINS传递对准仿真

传统动基座传递对准主要采用扩展卡尔曼滤波技术。但在动基座传递对准的非线性、非高斯条件下,这种基于模型线性化和高斯假设的滤波方法在估计系统状态及其方差时误差较大且可能发散。混合退火粒子滤波针对非线性、非高斯系统状态的在线估计问题,提出一种新的基于序贯重要性抽样的粒子滤波算法。在滤波算法中,用状态参数分解和退火系数来产生重要性概率密度函数,此概率密度函数综合考虑了转移先验、似然、噪声的统计特性以及最新的观察数据,因此更接近于系统状态的后验概率。实验仿真结果表明,这种基于混合退火粒子滤波器不仅比扩展卡尔曼滤波提高了传递对准的精度,而且又比传统的粒子算法减少了时间。     

不完全测量系统鲁棒SGQKF的传递对准滤波器设计和稳定性分析

针对复杂环境下运载体观测信息不完全测量并且存在随机干扰不确定的传递对准问题,研究了不完全测量随机不确定系统的鲁棒稀疏网格求积分(H_∞-SGQKF)的高斯逼近滤波算法。基于非线性离散系统的最优贝叶斯滤波框架和间断观测滤波算法以及不确定性扰动噪声下的H_∞范数的鲁棒SGQKF算法,给出了不完全测量的稀疏网格求积分的高斯逼近滤波算法;通过非线性系统随机稳定性理论,分析并给出了系统估计误差和估计误差方差有界的充分条件,同时给出了系统稳定的不完全测量时的丢包率临界值,证明间断观测条件下的不完全测量H_∞-SGQKF算法是稳定的。通过传递对准仿真试验和某型激光捷联式惯性导航系统的跑车试验对该算法进行了验证。结果表明,该方法比未采用鲁棒的不完全测量的稀疏网格求积分滤波的传递对准精度有所提高,说明不完全测量的鲁棒稀疏网格求积分滤波算法是正确的、稳定的,并且具有鲁棒性能。     

EPF算法在惯导非线性初始对准中的应用

介绍了作为粒子滤波理论基础的递推贝叶斯估计的基本概念,说明了重要性函数对于粒子滤波器的设计是至关重要的。随后,给出了一种将EKF算法作为重要性函数的EPF算法,并提出将其用于静基座条件下的惯导系统非线性初始对准,通过计算机仿真对比了EPF和EKF的估计效果。仿真结果表明,EPF算法较传统的EKF算法对准时间更快,对准精度更高。     

基于级联FIR滤波器的系泊精对准算法

舰船的系泊环境存在风浪和浪涌,这些因素引起捷联惯导系统对准过程中的不确定性干扰加速度,提出一种基于级联FIR低通数字滤波器的惯性系Kalman滤波精对准算法。高频随机干扰加速度在通过级联FIR低通数字滤波器后被滤除,近似周期性干扰通过积分运算,正负部分基本抵消,因此该算法可以有效抑制系泊环境下的不确定性干扰。江上系泊对准结果为:水平精度0.02°,航向精度0.06°。试验结果表明该方案能有效完成精对准,对准精度达到中等导航精度要求。     

A numerical method for accelerating the rate of convergence of the SIMPLE-like algorithm for flow through a thin filter

The control volume, finite difference method and the k-? tubulence model are employed in a numerical simulation of the turbulent fluid flow both outside and inside a blunt cylindrical sampler which houses a paper filter in its chamber. The presence of a paper filter, which has a very large resistance, results in a large pressure drop across the filter and this causes difficulties in making the SIMPLE or the SIMPLEC scheme converge. In order to improve the rate of convergence of the SIMPLE-like algorithm when the resistance of the filter is very large, an average pressure correction formula is proposed. Based on global mass conservation, a line average pressure correction for the paper filter is derived using a modified Darcy law for a porous medium. A combination of this formula and the SIMPLE-like algorithm can rapidly build up the pressure drop across the filter and hence dramatically improve the rate of convergence of the iterative scheme. Comparisons of the convergence histories and the numerical results for the fluid flow when using SIMPLE and SIMPLEC with the average pressure correction method show that the average pressure correction method for dealing with the paper filter significantly accelerates the rate of convergence of the iterative scheme.     

Operational modal filter and its applications

In the paper, the procedure for the estimation of modal filter coefficients from output-only data is presented. The basic concept of the procedure consists in frequency response functions synthesis based on the knowledge of an operational modal model. A method of operational mode shapes scaling is described. The method is then compared with the classical modal filter and with modal filtration of responses spectra, which is sometimes used as a solution for modal filtration based on the output-only data. Each solution is applied to load identification and damage detection. The study shows the method verification on data obtained from laboratory experiment.     

一种基于遗传模糊推理的自适应容错滤波算法

针对常规卡尔曼滤波在组合导航中容错性不足的问题,提出了一种基于遗传模糊推理的自适应容错滤波算法。首先建立了基于模糊推理的自适应滤波模型,利用模糊推理系统的输出对组合导航系统的量测噪声实时进行调整,以实现状态的精确估计,进而达到容错目的。接着利用自适应遗传算法对模糊推理系统的隶属度函数参数进行了优化,提高了系统的输出精度,改进了传统模糊建模中系统精度取决于专家知识是否完备的问题。最后以SINS/GPS组合导航系统为平台进行了仿真,并在系统工作中间时刻引入量测噪声故障。验证结果表明遗传模糊推理自适应滤波算法比常规卡尔曼滤波具有更强的容错能力和总体精度,在仿真中,平均位置和速度均方根误差分别降低了20.87%和41.94%。     

自适应Kalman和零相移滤波算法在重力信号处理中的对比

为了有效消除海洋重力仪测量信号的噪声,提高重力数据的获取精度,根据随机过程理论,借助基于二阶高斯一马尔可夫异常位模型的重力异常协方差函数,得到海洋重力测量中重力异常信号的状态方程.对sage-husa滤波算法和零相移算法进行了理论分析,为了抑制零相移滤波器的首尾数据畸变,求解了滤波器的初始状态.根据实测重力数据,进行了去噪仿真试验.理论分析和仿真结果表明,sage-husa与零相移滤波算法均能较好地抑制采样重力数据中的噪声干扰,但零相移滤波算法的性能优于sage-husa滤波器.     

基于鲁棒滤波的无人机着陆相对导航方法

针对无人机在移动平台上进行起降时的相对导航问题,提出了一种基于鲁棒高阶容积滤波的惯导/视觉相对导航方法。建立了相对导航系统模型,基于无人机与移动平台之间的相对运动给出了系统的相对惯导方程,并针对系统中传感器的量测特性给出了导航敏感器的测量方程。针对相对导航系统非线性较强且量测噪声不符合高斯分布等问题,在高阶容积滤波的基础上,结合Huber-based量测更新方程,设计了鲁棒高阶容积滤波相对导航滤波器,该方法具有较高的估计精度,且对混合高斯噪声有鲁棒性。相对姿态采用四元数表示,为保证四元数的归一化,在设计相对导航滤波器时采用修正的罗德里格斯参数表示姿态误差。仿真结果表明,该方法可以准确地给出无人机与移动平台之间的相对位置、速度和姿态信息,且估计精度高于扩展卡尔曼滤波、Huber-Based滤波以及高阶容积卡尔曼滤波。     

Experimental study on vibrations of a nonwoven fabric cylindrical filter

Unexpected vibrations on a cylindrical filter made of nonwoven fabrics were clarified experimentally. Two types of filter with length L=1.8 m and 3.7 m, both 45 cm in diameter and 1.08 mm in thickness, were used. This is a new type of aeroelastic vibration phenomenon because the filter is a closed cylindrical vessel. In addition, the flow velocity of inner air was very slow and inner air flowed out slowly from the filter surface. The velocity distribution of air flow from a fan duct as well as the frequency and amplitude of the filter vibration were measured for two types of filter. By setting up a roll core panel at the outlet of the fan duct, we could rectify the outflow and suppressed the vibration of the shorter filter with L=1.8 m. However, this method was not adequate for the longer filter with L=3.7 m, and we could suppress the vibration by shielding the inner surface of the filter at the top region.     

Dual estimation of partially observed nonlinear structural systems: A particle filter approach

Dual estimation consists of tracking the whole state of partially observed systems, and simultaneously estimating unknown model parameters. In case of nonlinearly evolving systems, standard filtering procedures may provide unreliable model calibrations, either because of estimates affected by bias or due to diverging filter response. In this paper, we propose a particle filter (PF) wherein particles, i.e. system realizations evolving in a stochastic frame, are first sampled from the current probability density function of the system and then moved towards the region of high probability by an extended Kalman filter. We show that the proposed filter works much better than a standard PF, in terms of accuracy of the estimates and of computing time.     

Improved probability hypothesis density filter for multitarget tracking

Multitarget tracking (MTT) is important in radar and/or sonar surveillance systems. However, as a popular implementation of MTT, the standard probability hypothesis density (PHD) filter has computerized intractability and imprecise estimation. To overcome these drawbacks, an improved PHD filter is proposed in this paper. First, we apply particle approximation to achieve the closed-form solution to the PHD propagations. Afterward, the weight formula is simplified by the method of kernel estimate. Meanwhile, the excess weights of newborn particles are increased to survival particles on average. As a result, the overestimated target number and the missed detection are balanced, and the accuracy of MMT is improved by our lemmas. Finally, simulations are presented to compare the performance of the proposed filter with that of the standard one. The results show that our filter can achieve MTT with better performance.     

基于卡尔曼滤波的信息融合算法优化研究

通过比较采用联邦卡尔曼滤波的状态向量融合和量测信息融合,得出量测信息融合优于状态向量融合,因为只有当卡尔曼滤波一致时状态向量融合才有效.采用基于最小均方差估计的观测值加权融合法融合了多传感器数据,保持了观测向量的维数.这种方法具有高效性.为了提高该算法的速度和精度,对系统的量测空间进行了等价变换,而等价系统的状态空间却没有改变.给出了等价变换前后的系统误差方差阵和状态估计均一致性的证明.把矩阵分析中的L-D分解算法运用到该算法中以避免计算矩阵的逆,从而改善了算法的稳定性和精度.举例验证了所设计算法的这些优点,给出了采用联邦卡尔曼滤波和所优化滤波算法的状态估计和误差的仿真结果,并依次进行了分析.经过这种优化,算法的精度和速度得到很大提高,已经应用到实际工程中.     

结构拓扑优化中不同过滤函数间关系的探讨

为了确定结构拓扑优化中不同过滤函数间的关系, 深入研究了ICM方法中的 过滤函数, 针对幂函数形式的过滤函数, 利用均匀化方法的思想, 结合最小二乘法, 确定了 单元重量和单元刚度的过滤函数, 然后采用数值模拟的方法, 探讨了重量过滤函数和刚度过 滤函数之间的关系, 最后提出过滤函数幂指数系数的概念, 得出刚度过滤函数随重量过滤函 数变化的规律.     

自适应Kalman滤波在SINS初始对准中的应用

为了提高捷联惯导系统的对准精度和收敛速度,提出了一种基于Sage-Husa自适应滤波算法的初始对准方法。针对方位小失准角的情况,推导出精对准误差模型和自适应Kalman滤波方程。常规Kalman滤波算法,在噪声统计特性已知的情况下,使用比较方便;多数情况下,噪声统计特性是处于未知状态,从而引入自适应Kalman滤波算法。它利用观测到的数据自动进行噪声统计特性的在线估计和修正,使系统达到最佳的滤波效果。通过仿真验证,该自适应滤波算法有效地提高了收敛速度和对准精度。     

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements, the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.     

Evaluation of steerable filter for detection of fibers in flowing suspensions

Steerable filters are concluded to be useful in order to determine the orientation of fibers captured in digital images. The fiber orientation is a key variable in the study of flowing fiber suspensions. Here, digital image analysis based on a filter within the class of steerable filters is evaluated for suitability of finding the position and orientation of fibers suspended in flowing suspensions. In sharp images with small noise levels, the steerable filter succeeds in determining the orientation of artificially generated fibers with well-defined angles. The influence of reduced image quality on the orientation has been quantified. The effect of unsharpness and noise is studied and the results show that the error in orientation is less than 1° for moderate levels. Images from two flow cases, one laminar shear flow and one turbulent, are also analyzed. The fiber orientation distribution is determined in the flow-vorticity plane. For the laminar case a comparison is made to a robust, but computationally more expensive, method involving convolutions with an oriented elliptic filter. A good agreement is found when comparing the resulting fiber orientation distributions obtained with the two methods. For the turbulent case, it is demonstrated that correct results are obtained and that the method can handle overlapping fibers.     

基于自适应联邦滤波的传递对准算法

为了提高传递对准的对准速度和对准精度,研究了基于自适应联邦滤波的"速度 姿态角"传递对准的算法,在状态变量中加入了安装误差角和挠曲变形角,在算法中进行了估计并补偿。为了保证滤波的实时性,采用联邦滤波的方法,分别建立了速度匹配子滤波器、姿态角匹配子滤波器和主滤波器的模型,给出了状态方程和量测方程。在子滤波器中利用模糊控制器对噪声特性进行了自适应调整以解决系统噪声和量测噪声是未知情况下滤波发散或者精度不高的缺点从而增强系统的鲁棒性。最后在载体匀速直线加三轴摇摆的运动模型下进行了仿真,结果表明该方法能够有效地估计安装误差角和部分挠曲变形角,并且能够以一定精度完成初始对准。