Revisiting prior distributions,Part II: Implications of the physical prior in maximum entropy analysis

The well-known “Maximum Entropy Formalism” offers a powerful framework for deriving probability density functions given a relevant knowledge base and an adequate prior. The majority of results based on this approach have been derived assuming a flat uninformative prior, but this assumption is to a large extent arbitrary (any one-to-one transformation of the random variable will change the flat uninformative prior into some non-constant function). In a companion paper we introduced the notion of a natural reference point for dimensional physical variables, and used this notion to derive a class of physical priors that are form-invariant to changes in the system of dimensional units. The present paper studies effects of these priors on the probability density functions derived using the maximum entropy formalism. Analysis of real data shows that when the maximum entropy formalism uses the physical prior it yields significantly better results than when it is based on the commonly used flat uninformative prior. This improvement reflects the significance of the incorporating additional information (contained in physical priors), which is ignored when flat priors are used in the standard form of the maximum entropy formalism. A potentially serious limitation of the maximum entropy formalism is the assumption that sample moments are available. This is not the case in many macroscopic real-world problems, where the knowledge base available is a finite sample rather than population moments. As a result, the maximum entropy formalism generates a family of “nested models” parameterized by the unknown values of the population parameters. In this work we combine this formalism with a model selection scheme based on Akaike’s information criterion to derive the maximum entropy model that is most consistent with the available sample. This combination establishes a general inference framework of wide applicability in scientific/engineering problems.     

1961—2016年祁连山区季节性干旱综合指数特征分析

采用Z指数和熵权理论,构建了干旱综合指数作为干旱强度评价标准,对祁连山区季节性干旱特征及其空间分布规律进行了深入剖析。结果表明:1961—2016年季节性干旱强度普遍减弱,其中春秋两季显著减弱,夏季明显减弱;尽管20世纪60—70年代、90年代为季节性干旱频发与重发时段,但从2000年以来夏旱与冬旱却比较频繁,不容忽视。干旱强度由强到弱依次为冬季、夏季、春季和秋季,冬季干旱程度最强;在干旱波动性上秋季最强,冬季次之,春季最弱。春夏秋三季南侧比北侧干旱,冬季北侧比南侧干旱,其中冬季干旱范围最为广泛,尤以酒泉为中心的北侧区域最为显著。在研究时段内祁连山南北两侧干旱强度逐渐减弱,南侧明显减弱,枯草期干旱强度减弱程度尤为显著。本研究为祁连山区干旱评价提供了参考依据。     

Estimating the spatial distribution of dredged material disposed of at sea using particle-size distributions and metal concentrations

We present a method to estimate the spatial distribution of dredged material disposed of at sea. Using both dredged sediments and samples of sea-bed sediment from near the Rame Head disposal site, Plymouth, UK, we applied entropy analysis to the <63 μm sediment fraction and combined the results with the trace metal data in the same fraction, to form a series of groups. We interpret the distribution of sediments in one group (F1) to approximate the distribution of material affected by the disposal site. This distribution includes locations close to the disposal site, and also locations <4 km to the SE and SW, <6 km to the NW and <2 km to the N. This approach demonstrates the feasibility of using trace metal analysis of particular grain size fractions to reduce uncertainty in interpreting the spatial distribution of impacts of dredge disposal.     

基于PSR模型的胶州湾生态安全评价研究

科学有效地评价胶州湾生态安全程度,是胶州湾地区可持续发展的前提。文章基于PSR模型建立评价指标体系,利用AHP-熵权法确立指标权重,对2007—2016年胶州湾生态安全的发展状况进行了综合评价,并从压力、状态、响应3个方面对影响胶州湾生态安全的主要因素进行系统分析。研究结果表明:胶州湾生态安全指数整体呈波动上升态势,但在2010—2013年略有下降,并在2014年有大幅度的回升直至2016年。生态安全指数在0.4～0.6间波动,整体处于"一般"的生态安全状态。最后,文章提出通过坚持控制入海污水排放量和环境污染,加强海洋生态保护修复与海洋保护区建设,进一步完善胶州湾生态安全保护相关法律制度,注重海洋科技人才培养等方式来促进胶州湾地区生态安全水平的提高。     

宁夏倾斜固体潮潮汐因子熵的变化

应用宁夏银川台和石嘴山台倾斜固体潮观测数据计算了潮汐因子γ值,进一步计算了γ值的熵值,并对各熵值曲线进行分析,结果认为γ值熵在震前的异常表现比较突出,熵值变化到最低时,很有可能是应变积累到最大程度,即进入了临震状态。     

形变观测数据的多异常形态统一识别

地震前兆数据中的形变观测数据变化复杂,地球物理场变化和环境干扰等信息识别与剔除是与地震相关现象分析的关键.传统的信号识别主要采用回归分析、经验模态分解、频域信号分解等方法,但它们难以统一识别高幅值变化（尖峰、阶跃）与高频变化波形.本文利用信息熵参与形变时序数据的自动化分段构造子序列,一定程度上避免了这两种波形被分割的弊端,然后以统计描述方式表达子序列,最后利用角度异常因子（Angle-Based Outlier Factor,ABOF）和局部异常因子（Local Outlier Factor,LOF）构建对数函数定义离群点,以解决统一识别高幅度变化与高频率变化的问题.实验表明,对于特征向量维度变化的情况,LOF-ABOF算法的计算效率呈线性变化关系;在特征表达策略改变的情况下,该算法对高幅值变化和高频变化的异常识别效果良好.本文所提供方法可以检测出高幅值变化与高频率变化的异常形态,为地震前兆数据中形变观测数据"前兆信号"的识别提供指导与参考,为深入认识地震现象及其产生机理奠定基础.     

阵风锋自动识别算法的试验研究

利用江苏省6部S波段全相参多普勒天气雷达测得的2007-2011年28个阵风锋观测实例,检验多普勒天气雷达的阵风锋自动识别算法的效果。该算法主要包括熵函数模板的反射率强度边界识别、风切变算法,并综合依据径向速度及谱宽进行阵风锋识别。在阵风锋的识别中,多普勒速度的径向切变有利于判别雷达波束垂直于阵风锋边界的辐合,旋转切变可更好地显示平行于波束的阵风锋边界。在参与检测的28个个例中,成功检测出的有13个;因雷达资料质量影响,7个个例检测出部分阵风锋;8个个例未检测到阵风锋。经过检验,该算法的识别效果较好,但仍存在一些不足,需要进一步完善雷达资料的质量控制,和对低层弱切变特征的提取研究。     

基于PSE模型的矿业城市经济发展脆弱性研究

脆弱性是可持续发展的一个时间函数和空间函数.区域经济发展过程是一个不断抑制脆弱性实现螺旋式上升的过程.矿业城市经济发展的脆弱性具有典型的"压力(P)-敏感(S)-弹性(E)"的特征.据此,构建了一个矿业城市经济发展脆弱性评价模型,结合主成分分析法和熵值法,选取东北地区矿业城市作为案例进行评价,从脆弱性的视角来研究矿业城...     

Estimation of ecological high flow

Floods can destroy fish habitat. During a flood a fish has to seek shelters (refuges) to survive. It is necessary to know the maximum discharge that the fish can sustain against the strong current. Ecological and hydraulic engineers can simulate the flow condition of high flow for designing the refuge when restoring and enhancing the rivers are needed. Based on the average ratio of the mean and maximum velocities invariant with time, discharge and water level, this paper tries to introduce the concept of ecological high flow. The mean‐maximum velocity ratio can be used to estimate the mean velocity of the river. If the maximum velocity of the cross section is replaced by the maximum sustained swimming speeds of fish, the mean velocity of ecological high flow can be calculated with the constant ratio. The cross‐sectional area can be estimated by the gage height. Then the ecological high flow can be estimated as the product of mean velocity of ecological high flow multiplied by the cross‐sectional area. The available data of the upstream of the Dacha River where is the habitat of the Formosan landlocked salmon were used to illustrate the estimation of the ecological high flow. Any restoration project at Sonmou that try to improve the stream habitat can use the ecological high flow to design the hydraulic structure at suitable location to offer refuges for the Formosan landlocked salmon that is an endangered species in Taiwan Copyright © 2005 John Wiley & Sons, Ltd.     

Modelling the pre-failure instabilities of sand

A simple incremental model describing the pre-failure behaviour of granular soils is presented. The model describes both the dry/fully drained and undrained response. It takes into account an initial anisotropy of soil and an initial state defined as either contractive or dilative. A physically sound definition of loading/unloading is assumed, which differs from elasto-plastic approaches. The model is based on extensive empirical data and gives predictions conformable with experimental results. It also describes pre-failure instabilities of granular soils, both dry/fully drained and undrained. The Hill’s criterion was used to examine stability. It was shown that this condition can be formulated either in terms of the effective stresses or by the total stresses. In the extreme cases of either dry/fully drained or undrained conditions, these alternative formulations are equivalent. This is not so in the case of partial drainage of pore water and associated volumetric deformations as well as pore pressure changes. The model describes the pre-failure instabilities well, and additionally allows for analytical derivation of the instability line. It was shown that the second order work, appearing in the Hill’s condition, is equivalent to the entropy source.