半正定矩阵算术平方根的表示

利用特征根的Lagrange插值多项式，给出了半正定矩阵算法平方根的表示，即公式解，避免了求过渡矩阵的繁琐过程。当特征根难以求出而特征根的对称式易求时，半正定矩阵的算法平方根可直接由矩阵的本谢的性质来表示。     

记忆的奇迹

知道5476的平方根是多少吗?知道287的正弦是多少吗?心算大王鲁迪格尔·加姆能在几秒钟的时间内给出答案。这个德国青年经常到电视台作表演,大家看他的心算表演就像看魔术:这太神奇了,这小子简直是天才!据《纽约时报》报道,鲁迪格尔在学校的时候其实并不怎么出色,到20岁的时候才     

Failure prognostic of systems with hidden degradation process

Systems with a hidden degradation process are pervasive in the real world.Degrading critical components will undermine system performance and pose potential failures in the future.Prognostic aims at predicting potential failures before it evolves into faults.A prognostic procedure based on expectation maximization and unscented Kalman filter is proposed.System state,sensor measurement and hidden degradation process are viewed as data (incomplete or missing) in the expectation maximization method.System state and hidden degradation process are estimated by a unscented Kalman filter upon sensor measurements.Component-specific parameters in a degradation process are identified on the estimation of the degradation process.Residual life is measured by the median of estimated residual life distribution.The proposed procedure is verified by simulations on a first-order capacitor-resistance circuit with degrading resistance.Residual life estimation consists conservatively with the trend and is evaluated in terms of relative errors.Simulation results are reasonable.The proposed prognostic method expects applications in practice.     

集合平方根滤波同化AMSU-A辐射率的观测系统模拟试验

借助观测系统模拟试验,针对晴天和有降水两种天气状况,探究用集合平方根滤波同化卫星辐射率资料来改进中尺度天气预报模式初始场的可行性.试验结果表明:在晴天条件下,同化后的分析场较同化前背景场更加接近于真实场,尤其是对所选AMSU-A第5通道辐射率观测值贡献较大的那些层,如500,700,800 hPa3层位温的分析场相对背景场均方根误差分别减小了26%,15%和42%,同化效果显著.在有降水天气状况下,试验结果在特定的高度层上也表现出一定的正贡献,但总体而言对各气象要素场的改善均不及晴天时明显,说明该种天气类型下的卫星资料同化还有待进一步的研究.     

基于双平方根算子的保幅角度域成像

建立基于双平方根算子的保幅叠前深度偏移与地下人射角度的关系,应用单程波双平方根方程的保幅波动方程叠前深度偏移输出角度域共成像点道集及相应的成像结果,为后续的偏移速度分析和振幅分析提供可靠的数据.取代相对耗时的倾斜叠加法,应用基于精确投影的快速插值映射法抽取保幅角度域共成像道集.结果表明:基于双平方根求取偏移距域道集比基于单平方根方程更为方便直观,也更适合于角度域成像;保幅角度域偏移采用的成像条件不仅可以有效地补偿振幅和改善成像结果,而且克服传统炮域单程波保幅偏移中反褶积型成像条件的不稳定性.理论模型数据和实际资料试算结果进一步证明了所提角度域保幅偏移理论和算法的正确性和有效性.     

Modified state prediction algorithm based on UKF

The state prediction based on the unscented Kalman filter (UKF) for nonlinear stochastic discrete-time systems with linear measurement equation is investigated. Predicting future states by using the information of available measurements is an effective method to solve time delay problems. It not only helps the system operator to perform security analysis, but also allows more time for operator to take better decision in case of emergency. In addition, predictive state can make the system implement real-time monitoring and achieve good robustness. UKF has been popular in state prediction because of its advantages in handling nonlinear systems. However, the accuracy of prediction degrades notably once a filter uses a much longer future prediction. A confidence interval (CI) is proposed to overcome the problem. The advantages of CI are that it provides the information about states coverage, which is useful for treatment-plan evaluation, and it can be directly used to specify the margin to accommodate prediction errors. Meanwhile, the CI of prediction errors can be used to correct the predictive state, and thereby it improves the prediction accuracy. Simulations are provided to demonstrate the effectiveness of the theoretical results.     

基于双平方根算子叠前深度偏移成像技术的结构损伤成像与探测

介绍一种基于双平方根算子的叠前深度偏移方法用于结构损伤探测.首先推导上行波传播时间(走时)的全微分表达式,推导在频率波数域和频率空间域中,用源点和接收点坐标表示的双平方根算子波动方程.然后,用频率空间域的有限差分法及混合法进行双平方根算子的波场外推,推导关于炮点和检波点的差分方程,以及双平方根算子混合法波场外推公式.最后,用Marmousi数据体对结构损伤进行偏移成像.根据双程波动方程分析该方法的数值频散性、奇异性以及波场、位移、振幅、能量、动应力集中系数等力学特征,计算得到波场快照图和剖面图,达到对结构损伤成像的目的.数值算例证明了这种方法的适用性.     

无迹卡尔曼滤波在无线传感器网络节点定位中的应用

传统的基于距离的无线传感器网络节点定位技术,由于测距过程产生较大的误差,从而使定位精度不高.文中在基于接收信号强度(RSSI)测距、三边测量法初始定位的基础上,提出以接收信号强度为观测量,将无迹卡尔曼滤波(UKF)算法应用到节点精确定位中.通过仿真验证使用该方法后,相比以距离为观测量的UKF定位方法,节点的定位精度有一定的提高,并进一步定量的分析比较了两种实现模型下节点定位算法的误差概率分布.在此算法的基础上,通过权衡平均定位误差与算法运算复杂度之间的关系,给出最佳定位锚节点数量,并模拟具体环境,验证了文中节点定位算法的实用性.     

基于粒子群算法和平方根平淡卡尔曼滤波的北斗导航系统定位估计算法

为提高北斗定位系统(BDS)的估计精度,克服传统平淡卡尔曼滤波(UKF)算法中可能因状态量协方差矩阵失去正定性而导致滤波器发散的问题,将平方根平淡卡尔曼滤波(SRUKF)算法应用于BDS定位估计.在此基础上,为进一步提高SRUKF算法的性能,引入粒子群优化(PSO)算法,提出基于PSO和SRUKF算法的BDS定位估计(PSO-SRUKF)算法.结果表明,PSO-SRUKF算法可以降低系统噪声和测量噪声特性估计不准确带来的误差,有效提高了BDS定位精度和稳定性.