Comparison of local and global approximators in multivariate chaotic forecasting of daily streamflow

ABSTRACT

Although it is conceptually assumed that global models are relatively ineffective in modelling the highly unstable structure of chaotic hydrologic dynamics, there is not a detailed study of comparing the performances of local and global models in a hydrological context, especially with new emerging machine learning models. In this study, the performance of a local model (k-nearest neighbour, k-nn) and, as global models, several recent machine learning models – artificial neural network (ANN), least square-support vector regression (LS-SVR), random forest (RF), M5 model tree (M5), multivariate adaptive regression splines (MARS) – was analysed in multivariate chaotic forecasting of streamflow. The models were developed for Australia’s largest river, the River Murray. The results indicate that the k-nn model was more successful than the global models in capturing the streamflow dynamics. Furthermore, coupled with the multivariate phase-space, it was shown that the global models can be successfully used for obtaining reliable uncertainty estimates for streamflow.     

Some results comparing Monte Carlo simulation and first order Taylor series approximation for steady groundwater flow

The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation.     

Seismic tomography in the Ostrava-Karviná mining region

The effective algorithm of seismic tomography was applied to the simultaneous determination of the velocity field in the medium and the location of hypocentres of events in the area of the underground seismological network in the Ostrava-Karviná mining region (OKR). Although the configuration of the network is unsuitable and the used data are relatively unreliable, after classifying the data it is possible to obtain representative information that demonstrates the existence of significant inhomogeneities of the medium in the area under study. In addition, it is possible to obtain more precise hypocentre parameters of local seismic events.     

Statistical distribution of surface elevation for the fourth order nonlinear random sea waves

Based upon the nonlinear model of random sea waves, the statistical distribution of wave surface elevation exact to the fourth order is derived as the truncated Gram-Charlier series,by calculating directly each order moment. The phenomenon found by Huanget al. that the agreement between observed data and investigated series deteriorates much more when the series is kept to λ₈ is explained. The effect of the approximation order on the truncation of series and the determination of coefficients is investigated. For themth order approximation, the derived series is truncated atH _3m-3 with the absence of H_3m-4, and the coefficients ofH _3m-3 andH _3m-6 are connected by a simple algebraic relation. Project supported by the National Natural Science Foundation of China.     

热液系统流体输运－化学反应耦合动力学综述

输运－反应模式通过连续质量守恒方程进行描述，它表示为主要组分的Ｎ＋Ｍ个耦合的非线性偏微分方程。这些方程可以通过有限差分或有限元等数值方法进行求解。利用准静态近似法，涉及平流、分子扩散和水动力弥散作用的地球化学系统的演化在时间上通过一系列静止状态模拟出来。模拟实际地质系统的动力学实验对输运－反应耦合动力学的应用具有十分重要的影响。     

准地转动量近似下风速切变线上的波动

利用准地转动量近似下的斜压两层大气的非线性方程组及非线性边界条件，研究了切变线上波动的稳定性，导出了切变线上孤立波解。较好地解释了切变线上易产生低涡等天气系统现象。     

Effects of topographic–isostatic masses on gravitational functionals at the Earth’s surface and at airborne and satellite altitudes

Topographic–isostatic masses represent an important source of gravity field information, especially in the high-frequency band, even if the detailed mass-density distribution inside the topographic masses is unknown. If this information is used within a remove-restore procedure, then the instability problems in downward continuation of gravity observations from aircraft or satellite altitudes can be reduced. In this article, integral formulae are derived for determination of gravitational effects of topographic–isostatic masses on the first- and second-order derivatives of the gravitational potential for three topographic–isostatic models. The application of these formulas is useful for airborne gravimetry/gradiometry and satellite gravity gradiometry. The formulas are presented in spherical approximation by separating the 3D integration in an analytical integration in the radial direction and 2D integration over the mean sphere. Therefore, spherical volume elements can be considered as being approximated by mass-lines located at the centre of the discretization compartments (the mass of the tesseroid is condensed mathematically along its vertical axis). The errors of this approximation are investigated for the second-order derivatives of the topographic–isostatic gravitational potential in the vicinity of the Earth’s surface. The formulas are then applied to various scenarios of airborne gravimetry/gradiometry and satellite gradiometry. The components of the gravitational vector at aircraft altitudes of 4 and 10 km have been determined, as well as the gravitational tensor components at a satellite altitude of 250 km envisaged for the forthcoming GOCE (gravity field and steady-state ocean-circulation explorer) mission. The numerical computations are based on digital elevation models with a 5-arc-minute resolution for satellite gravity gradiometry and 1-arc-minute resolution for airborne gravity/gradiometry.     

基于分数阶模型的磁流变阻尼器振动系统的预测控制

磁流变阻尼器因其可控阻尼的特性可以用于制作优质减振器,近年来,它与各种控制策略的结合设计已在工业振动控制领域得到了广泛的应用.研究表明,分数阶模型对磁流变阻尼器的拟合精度更高.本文使用分数阶模型描述磁流变阻尼器的粘弹特性,并利用Oustaloup近似方法得到易处理的分数阶传递函数近似值,离散化处理后选取输出跟踪输入的二次型性能指标设计了一种新的模型预测控制器.最后,通过仿真实验证明了该分数阶模型预测控制器具有良好的动态性能,验证了方案的可行性与稳定性.