一类改进最大熵方法的可调参数分析

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

Logistic和Lotka-Volterra模型参数的灰色估计方法研究

根据灰色系统建模原理,对Logistic模型中的参数进行了估计,将此方法应用于Gause(1934)草履虫实验数据的拟合,并与已有拟合结果对比,说明此方法是有效的.然后将其推广至两种群的Lotka—Volterra模型参数的确定,来研究山西省人口—经济系统的发展演化状况,得出了满意的结果.     

基于半参数回归模型的最小一乘局部线性算法

根据最小一乘准则,推导出最小一乘局部线性估计的计算方法,并通过对模拟数据的计算和分析,对比最小一乘核算法和最小二乘局部线性算法,验证了最小一乘局部线性算法是一种有效的,稳健的估计方法,并且有降低边界效应的作用．     

汶川地震断裂带岩脉矿物拉曼谱峰特征

对汶川地震断裂带深溪沟出露的基岩错动面两侧岩脉中的石英矿物进行了拉曼谱峰测定, 并根据所测石英的464 cm-1拉曼谱峰向高波数的偏移量估算了断裂带中的压应力分布。测试结果表明, 错动面附近岩脉中石英的464 cm-1拉曼谱峰向高波数偏移量为3.29 cm-1, 相应的压应力值为368.63 MPa, 明显低于错动面两侧应力积累, 这可能是由于错动面的多次活动导致了应力不断得到释放。断裂南东盘(下盘)远离错动面, 岩脉中石英的464 cm-1拉曼谱峰向高波数偏移量具有增加的趋势, 相应的应力积累也逐渐增强, 距错动面21 m处的石英样品的464 cm-1拉曼谱峰向高波数偏移4.40 cm-1, 相应压应力可达到494.77 MPa。剖面北西盘(上盘)在距错动面10 m处, 样品464 cm-1拉曼谱峰的偏移量达到最大值, 相应的应力积累为519.87 MPa, 其后远离错动面应力积累开始减弱, 在北西盘17 m处, 应力积累骤然下降至400.37 MPa。在西北盘距错动面27 m处, 岩脉石英的464 cm-1拉曼谱峰向高波数偏移量下降至3.21 cm-1, 应力已经减弱到359.59 MPa, 这可能是由于该处位于断裂带的边缘, 远离错动面, 受到了较小的断层活动的影响。因此, 汶川地震断裂带内的应力虽然得到部分释放, 但剩余的应力分布并不均匀, 而且在局部还存在较高的应力积累, 这反应了断裂带中岩石的力学性质在空间上具有不均匀性。     

用单个矢量水听器基于DEMON线谱的双目标分辨

不同目标的解调线谱频率是不同的。本文提出了一种在DEMON谱域内对双目标测向的方法,它具有较好的抗相干及非相干干扰能力,表明单个矢量水听器也能分辨多目标。文中叙述了利用DEMON线谱测向的原理,给出了轴频提取及双目标DEMON线谱分离的方法,对DEMON线谱区分双目标的能力做了仿真分析。     

基于复小波包分形理论的爬壁机器人故障检测

通过研究爬壁式机器人的控制和运动特征，提出一种基于复小波包分形理论的故障检测方法．利用复小波包的平移不变性，将爬壁式机器人传感器输出信号分解成独立的频谱，并进行阀值处理和重构，从而有效去除高频噪音并提取故障的特征频率；依据信号分形维数的多尺度不变性，在嵌入维数空间，采用维数最大距离法，确定复小波包域故障信号的关联雏数．仿真实验表明，爬壁式机器人在各种异常工作模式下的故障信号关联维数能比较真实地反映其故障状态空间，同时也验证了故障信号的关联维数低于正常信号的关联维数作为故障发生与否的定量判据的正确性．     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

Analysis of large experimental datasets in electrochemical impedance spectroscopy

An approach for the analysis of large experimental datasets in electrochemical impedance spectroscopy (EIS) has been developed. The approach uses the idea of successive Bayesian estimation and splits the multidimensional EIS datasets into parts with reduced dimensionality. Afterwards, estimation of the parameters of the EIS-models is performed successively, from one part to another, using complex nonlinear least squares (CNLS) method. The results obtained on the previous step are used as a priori values (in the Bayesian form) for the analysis of the next part. To provide high stability of the sequential CNLS minimisation procedure, a new hybrid algorithm has been developed. This algorithm fits the datasets of reduced dimensionality to the selected EIS models, provides high stability of the fitting and allows semi-automatic data analysis on a reasonable timescale. The hybrid algorithm consists of two stages in which different zero-order optimisation strategies are used, reducing both the computational time and the probability to overlook the global optimum. The performance of the developed approach has been evaluated using (i) simulated large EIS dataset which represents a possible output of a scanning electrochemical impedance microscopy experiments, and (ii) experimental dataset, where EIS spectra were acquired as a function of the electrode potential and time. The developed data analysis strategy showed promise and can be further extended to other electroanalytical EIS applications which require multidimensional data analysis.     

Computing the conditioning of the components of a linear least‐squares solution

In this paper, we address the accuracy of the results for the overdetermined full rank linear least‐squares problem. We recall theoretical results obtained in (SIAM J. Matrix Anal. Appl. 2007; 29 (2):413–433) on conditioning of the least‐squares solution and the components of the solution when the matrix perturbations are measured in Frobenius or spectral norms. Then we define computable estimates for these condition numbers and we interpret them in terms of statistical quantities when the regression matrix and the right‐hand side are perturbed. In particular, we show that in the classical linear statistical model, the ratio of the variance of one component of the solution by the variance of the right‐hand side is exactly the condition number of this solution component when only perturbations on the right‐hand side are considered. We explain how to compute the variance–covariance matrix and the least‐squares conditioning using the libraries LAPACK (LAPACK Users' Guide (3rd edn). SIAM: Philadelphia, 1999) and ScaLAPACK (ScaLAPACK Users' Guide. SIAM: Philadelphia, 1997) and we give the corresponding computational cost. Finally we present a small historical numerical example that was used by Laplace (Théorie Analytique des Probabilités. Mme Ve Courcier, 1820; 497–530) for computing the mass of Jupiter and a physical application if the area of space geodesy. Copyright © 2008 John Wiley & Sons, Ltd.