最小二乘法对多周期函数的周期筛选优化

运用最小二乘法对多周期函数的周期进行筛选优化研究,对不同周期组引起的中误差精度做了分析与比对.     

Spectral pattern recognition in under-sampled functions

Fourier optics and an optical bench model are used to construct an ensemble of candidate functions representing variational patterns in an undersampled two dimensional functiong(x,y). The known sample functions(x,y) is the product ofg(x,y) and a set of unit impulses on the sample point patternp(x,y) which, from the optical point of view, is an aperture imposing strict mathematical limits on what the sample can tell aboutg(x,y). The laws of optics enforce much needed—and often lacking—conceptual discipline in reconstructing candidate variational patterns ing(x,y). The Fourier transform (FT) ofs(x,y) is the convolution of the FT's ofg(x,y) andp(x,y). If the convolution shows aliasing or confounding of frequencies undersampling is surely present and all reconstructions are indeterminate. Then information from outsides(x,y) is required and it is easily expressed in frequency terms so that the principles of optical filtering and image reconstruction can be applied. In the application described and pictured the FT ofs(x,y) was filtered to eliminate unlikely or uninteresting high frequency amplitude maxima. A menu of the 100 strongest remaining terms was taken as indicating the principle variational patterns ing(x,y). Subsets of 10 terms from the menu were chosen using stepwise regression. By so restricting the subset size both the variance and the span of their inverse transforms were made consistent with those of the data. The amplitudes of the patterns being overdetermined, it was possible to estimate the phases also. The inverse transforms of 9 patterns so selected are regarded as ensembles of reconstructions, that is as stochastic process models, from which estimates of the mean and other moments can be calculated.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

Recovery of Bathymetry from Altimeter Data

At present,there exist two methods used to recover the bathymetry from altimeter data,i.e.the deterministic method and the stochastic method.In this paper,the principles of the two methods are introduced first.Then according to the theory of leastsquare collocation,a modified statistical model for recovering bathymetry from altimeter data is proposed.The new model has been used for computing the ocean depth in the South China Sea from altimeter-derived gravity anomalies.Finally the predicted depths are compared with the ship-borne depth.It shows that they agree with each other very well.     

输入非线性方程误差系统的多新息辨识方法

针对输入非线性方程误差系统,即输入非线性受控自回归系统,研究了基于过参数化模型的多新息辨识方法和基于过参数化模型的递阶多新息辨识方法;研究了基于关键项分离原理的多新息辨识方法;使用辨识模型分解技术,研究了基于关键项分离原理的两阶段多新息辨识方法和三阶段多新息辨识方法.这些方法可以推广到其他输入非线性方程误差系统、输入非线性输出误差类系统、输出非线性方程误差类系统、输出非线性输出类系统、反馈非线性系统等.同时,给出了几个典型辨识算法的计算量、计算步骤和流程图.     

Mapping beech (Fagus sylvatica L.) forest structure with airborne hyperspectral imagery

Estimating forest structural attributes using multispectral remote sensing is challenging because of the saturation of multispectral indices at high canopy cover. The objective of this study was to assess the utility of hyperspectral data in estimating and mapping forest structural parameters including mean diameter-at-breast height (DBH), mean tree height and tree density of a closed canopy beech forest (Fagus sylvatica L.). Airborne HyMap images and data on forest structural attributes were collected from the Majella National Park, Italy in July 2004. The predictive performances of vegetation indices (VI) derived from all possible two-band combinations (VI_(i,j) = (R_i − R_j)/(R_i + R_j), where R_i and R_j = reflectance in any two bands) were evaluated using calibration (n = 33) and test (n = 20) data sets. The potential of partial least squares (PLS) regression, a multivariate technique involving several bands was also assessed. New VIs based on the contrast between reflectance in the red-edge shoulder (756–820 nm) and the water absorption feature centred at 1200 nm (1172–1320 nm) were found to show higher correlations with the forest structural parameters than standard VIs derived from NIR and visible reflectance (i.e. the normalised difference vegetation index, NDVI). PLS regression showed a slight improvement in estimating the beech forest structural attributes (prediction errors of 27.6%, 32.6% and 46.4% for mean DBH, height and tree density, respectively) compared to VIs using linear regression models (prediction errors of 27.8%, 35.8% and 48.3% for mean DBH, height and tree density, respectively). Mean DBH was the best predicted variable among the stand parameters (calibration R² = 0.62 for an exponential model fit and standard error of prediction = 5.12 cm, i.e. 25% of the mean). The predicted map of mean DBH revealed high heterogeneity in the beech forest structure in the study area. The spatial variability of mean DBH occurs at less than 450 m. The DBH map could be useful to forest management in many ways, e.g. thinning of coppice to promote diameter growth, to assess the effects of management on forest structure or to detect changes in the forest structure caused by anthropogenic and natural factors.     

基于 EEMD 和 Husrt 指数的 GNSS 基准站的垂向速率估计

连续的全球卫星导航系统(GNSS)基准站的坐标时间序列中包含了复杂的噪声信号、非构造形变及其它因素的影响,尤其在垂直方向,对GNSS基准站在国际地球参考框架(ITRF)下的运动速率估计产生了较大的干扰。为进一步提高速率精度,文中采用整体模态分解(EEMD)方法对GNSS基准站的垂向观测时间序列进行分解,并根据各种信号的Hurst值进行分类及重构为噪声信号、季节性信号和长期趋势信号,采用最小二乘方法拟合长期趋势信号得到垂向速率。通过对中国大陆构造环境监测网络(CMONOC)的GNSS台站从2001—2013年近13a的垂向坐标时间序列的实例分析,采用基于EEMD和Husrt指数的最小二乘法能够准确地估计GNSS基准站的垂向速率。     

岩土工程中的杂交边界点方法

改进了正则化的杂交边界点方法,提出了岩土工程中一种新的数值方法。该方法将基本解的源点布在边界上,避免了自由参数的选取,将修正变分原理同移动最小二乘法结合起来,不但有边界元降维的优点,而且还是一种真正的无网格方法,输入数据只是求解域上离散分布的点,后处理十分简便。同时它适合于处理岩土工程的无限域问题。数值算例表明,它是一种计算精度很高的数值方法,适合于岩土工程中的若干问题。     

PREDICTION OF FLOOD SEASON PRECIPITATION IN SOUTHWEST CHINA BASED ON IMPROVED PSO-PLS

In order to achieve the best predictive effect of the Partial Least Squares (PLS) regression model, Particle Swarm Optimization (PSO) algorithm is applied to automatically filter the optimal subset of a set of candidate factors of PLS regression model in this study. An improved version of the Particle Swarm Optimization-Partial Least Squares (PSO-PLS) regression model is applied to the station data of precipitation in Southwest China during flood season. Using the PSO-PLS regression method, the prediction of flood season precipitation in Southwest China has been studied. By introducing the precipitation period series of the mean generating function (MGF) extension as an alternative factor, the MGF improved PSO-PLS regression model was also build up to improve the prediction results. Randomly selected 10%, 20%, 30% of the modeling samples were used as a test trial; random cross validation was conducted on the MGF improved PSO-PLS regression model. The results show that the accuracy of PSO-PLS regression model and the MGF improved PSO-PLS regression model are better than that of the traditional PLS regression model. The training results of the three prediction models with regard to the regional and single station precipitation are considerable, whereas the forecast results indicate that the PSO-PLS regression method and the MGF improved PSO-PLS regression method are much better than the traditional PLS regression method. The MGF improved PSO-PLS regression model has the best forecast performance on precipitation anomaly during the flood season in the southwest of China among three models. The average precipitation (PS score) of 36 stations is 74.7. With the increase of the number of modeling samples, the PS score remained stable. This shows that the PSO algorithm is objective and stable. The MGF improved PSO-PLS regression prediction model is also showed to have good prediction stability and ability.     

基桩极限荷载的确定及其预测

由基桩静载试验数据建立目标函数，用非线性最小二乘法求解该目标函数的极小值，从而得到基桩极限荷载值。这一方法不仅可用于对单桩极限荷载的精确确定，也可用于对单桩极限荷载的预测，计算实例表明，该方法是很有效的，具有较大的实用价值。     

基于最小二乘平差的全极化SAR配准偏移量估计方法

全极化合成孔径雷达影像(PolSAR)相对单极化SAR影像有更加丰富的地表信息。为了提高SAR影像偏移量跟踪技术估算偏移量的精度,提出一种基于最小二乘平差法的全极化SAR数据偏移量估计方法。首先利用全极化SAR不同极化通道数据估算偏移量得到多个观测值,然后通过最小二乘平差法对多余观测值循环剔除粗差得到最优偏移量。文中选取美国科罗拉多州湖城(Lake city)区域的两景JPL无人机UAVSAR全极化SAR影像进行实验,结果表明,文中新方法具有良好的粗差探测和去除功能,相对于已有研究结果,在方位向和距离向的偏移量估算精度都有明显提高,达到15%~25%。新方法提高了偏移量跟踪估算偏移量的精度,这对利用偏移量跟踪技术监测滑坡、地震及冰川等有重要的意义。