Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods

 We look at the task of computing the time-evolution of a non-linear system for a long time, in our case under random external influences. Our specific example is the fatigue evaluation of a wind turbine. To facilitate such a computation, we look at a reduction of the computational effort by projecting everything on a low-dimensional basis. In this case we take the Karhunen-Loève basis generated from running the model a little while under the random loading. It is important that the error which is caused by this reduction process can be controlled. We estimate the error by dual or adjoint methods. This in turn allows the process of model reduction to be performed adaptively. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.     

基于动态约简的增量贝叶斯分类算法的研究

朴素贝叶斯由于条件独立性假设使其分类效果不明显,同时在处理海量数据时缺乏灵活性。针对以上情况,提出一种基于动态约简的增量贝叶斯分类算法。算法首先利用(F-λ)广义动态约简计算出数据集的核属性,然后根据训练集的先验信息构造分类器对测试实例进行分类,最后利用类置信度进行选择性增量学习,增强处理增量数据的能力。实验结果表明,该算法在处理属性少的小量数据时,分类效果有一定的改善,在处理多属性大量数据时,分类效果明显提高。     

面向主题的微博热门话题舆情监测研究——以“北京单双号限行常态化”舆情分析为例

社交媒体舆情监测是社交媒体分析的热点研究问题,学界和工业界取得了很多研究成果。但目前针对热门话题舆情监测研究中,往往只在整体上关注事件舆情趋势,而没有对事件内部不同的讨论主题进行分析。鉴于此,该研究将主题分类模型引入到舆情监测中来,并在此基础上,以时间为脉络进行面向主题的情感分析。并以“北京市单双号限行常态化”这一微博话题为例进行实证研究,通过各个时段 “北京市单双号限行常态化”这一微博话题群体情感倾向变化的分析,为舆情的监测提供对象和时点选择的参考建议。
     

Supervised classification of share price trends

Share price trends can be recognized by using data clustering methods. However, the accuracy of these methods may be rather low. This paper presents a novel supervised classification scheme for the recognition and prediction of share price trends. We first produce a smooth time series using zero-phase filtering and singular spectrum analysis from the original share price data. We train pattern classifiers using the classification results of both original and filtered time series and then use these classifiers to predict the future share price trends. Experiment results obtained from both synthetic data and real share prices show that the proposed method is effective and outperforms the well-known K-means clustering algorithm.     

On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.