ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

基于Non stationary-CNN-Transformer的海浪有效波高预测

针对海浪有效波高序列波动性、随机性较强,难以精确预测以及模型无法高效挖掘深层特征间关系的问题,提出一种基于Non stationary-CNN-Transformer模型的海浪有效波高预测方法。首先,使用平稳化模块减弱海浪时序数据的非平稳性;其次,利用一维卷积神经网络(CNN)提取相关数据间的深层特征并构建特征向量;最后,使用含有平稳性注意力的Transformer描述波高序列的时间依赖性捕捉到序列之间的全局关系,通过逆归一化处理后获得有效波高预测结果。该方法可消除海浪时序数据的非平稳性,提升数据的预测效果,并具有优异的特征提取能力且善于处理大规模时间序列数据。在实验中应用澳大利亚的浮标实测数据,通过7组对比实验分别预测0.5、3、6、12和24 h的有效波高,对所提模型进行全方位、多角度的验证。算例研究结果表明,该文所提模型在不同时间段精度有明显提升。

Microstructure and mechanical properties of stationary shoulder friction stir welding joint of 2A14-T62 aluminum alloy

2A14-T62 butt joint was successfully welded by stationary shoulder friction stir welding(SSFSW)method.The results showed that using a pin with small shoulder could broaden the process window,and under a rotation speed of 2000 r/min and welding speed of 30 mm/min,joint with smooth surface,small reduction in thickness and little inner defects was obtained.The weld nugget zone was approx-imately circular,which was a unique morphology for SSFSW.The heat-affected zone(HAZ)and thermo-mechanically affected zone(TMAZ)were both quite narrow due to the lower heat input and slight mechanical action of the stationary shoulder.The fraction of high angle grain boundaries(HAGBs)exhibited a“W”shape along horizontal direction(from advancing side to retreating side),and the minim-um value located at HAZ.The average ultimate tensile strength and elongation of the joint were 325 MPa and 4.5%,respectively,with the joint efficiency of 68.3%.The joint was ductile fractured and the fracture surface contained two types of dimples morphology in different re-gions of the joint.Microhardness distribution in the joint exhibited a“W”shape,and the difference along the thickness direction was negli-gible.The joint had strong stress corrosion cracking susceptibility,and the slow stain rate tensile strength was 139 MPa.Microcrack and Al2O3 particulates were observed at the fracture surface.

Recent applications and chiral separation development based on stationary phases in open tubular capillary electrochromatography(2019–2022)

Capillary electrochromatography(CEC)plays a significant role in chiral separation via the double separation principle,partition coefficient difference between the two phases,and electroosmotic flow-driven separation.Given the distinct properties of the inner wall stationary phase(SP),the separation ability of each SP differs from one another.Particularly,it provides large room for promising applications of open tubular capillary electrochromatography(OT-CEC).We divided the OT-CEC SPs developed over the past four years into six types:ionic liquids,nanoparticle materials,microporous materials,biomaterials,non-nanopolymers,and others,to mainly introduce their characteristics in chiral drug separation.There also added a few classic SPs that occurred within ten years as supplements to enrich the features of each SP.Additionally,we discuss their applications in metabolomics,food,cosmetics,environment,and biology as analytes in addition to chiral drugs.OT-CEC plays an increasingly significant role in chiral separation and may promote the development of capillary electrophoresis(CE)combined with other instruments in recent years,such as CE with mass spectrometry(CE/MS)and CE with ultraviolet light detector(CE/UV).

Modeling Rainfall Intensity-Duration-Frequency (IDF) and Establishing Climate Change Existence in Uyo-Nigeria Using Non-Stationary Approach

This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.

On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.

Stationary Measures of Three-State Quantum Walks with Defect on the One-Dimension Lattice

In this paper, we focus on the space-inhomogeneous three-state on the one-dimension lattice, a one-phase model and a two-phase model include. By using the transfer matrices method by Endo et al., we calculate the stationary measure for initial state concrete eigenvalue. Finally we found the transfer matrices method is more effective for the three-state quantum walks than the method obtained by Kawai et al.

AN INFORMATIC APPROACH TO A LONG MEMORY STATIONARY PROCESS

Long memory is an important phenomenon that arises sometimes in the analysis of time series or spatial data.Most of the definitions concerning the long memory of a stationary process are based on the second-order properties of the process.The mutual information between the past and future I_(p−f) of a stationary process represents the information stored in the history of the process which can be used to predict the future.We suggest that a stationary process can be referred to as long memory if its I_(p−f) is infinite.For a stationary process with finite block entropy,I_(p−f) is equal to the excess entropy,which is the summation of redundancies that relate the convergence rate of the conditional(differential)entropy to the entropy rate.Since the definitions of the I_(p−f) and the excess entropy of a stationary process require a very weak moment condition on the distribution of the process,it can be applied to processes whose distributions are without a bounded second moment.A significant property of I_(p−f) is that it is invariant under one-to-one transformation;this enables us to know the I_(p−f) of a stationary process from other processes.For a stationary Gaussian process,the long memory in the sense of mutual information is more strict than that in the sense of covariance.We demonstrate that the I_(p−f) of fractional Gaussian noise is infinite if and only if the Hurst parameter is H∈(1/2,1).

基于条件独立性检验的非稳态因果发现方法

非稳态时间序列数据之间的因果关系发现是非常重要但极具挑战的问题。现有的工作主要假设观察数据随着时间或领域发生变化。上述假设使得相关方法需要引入时间或领域作为先验知识,无法应用于分段稳态的非稳态场景。因此,提出了一种基于条件独立性检验的非稳态因果关系发现算法。首先使用变化点检测方法来识别非稳态变化的时间点,然后将上一步的时间点进行区间划分,用基于条件独立性检验的时序因果关系发现算法推断局部稳态因果结构。在仿真和真实世界数据上的实验证明了该方法的有效性。

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.

华北局地大暴雨过程中多个β中尺度对流系统发生发展对比分析

利用常规地面高空观测、多普勒雷达、风廓线、VDRAS(Variational Doppler Radar Analysis System)和NCEP再分析资料,对2018年8月5—6日副热带高压(以下简称副高)控制下华北一次局地大暴雨过程中多个β中尺度对流系统触发和发展机制进行了分析。结果表明:这次大暴雨发生在副高控制下,处于高温、高湿气团中,大气层结极不稳定。暴雨由多个相继发展的中尺度对流系统造成,分别是太行山迎风坡上西南—东北向、华北平原地区保定一带南北向、保定至霸州附近西南—东北向和以雄安新区为中心东西向原地生消的准静止MCS-Ⅰ、MCS-Ⅱ、MCS-Ⅲ和MCS-Ⅳ,均属于β中尺度。在相似的环境中,不同中尺度对流系统触发机制有较大差异,太行山迎风坡上的MCS-Ⅰ是由近地层偏东暖湿气流在迎风坡与山风形成的辐合抬升触发;由辐射差异和前期强降水形成的局地冷池受MCS-Ⅰ影响再次加强后,其出流与环境风形成的两条地面辐合线分别触发了MCS-Ⅱ和MCS-Ⅲ,并组织对流沿辐合线呈带状发展;而超低空偏东风增强叠加冷池出流在地形抬升作用下促使沿山暖湿气团进一步抬升,使得原本消亡的MCS-Ⅰ再次重建。MCS-Ⅳ发展最旺盛、持续时间最长,是大暴雨中心的直接制造者,一方面MCS-Ⅱ与MCS-Ⅲ、MCS-Ⅰ与MCS-Ⅳ的两次合并过程,是MCS-Ⅳ增强、持久的重要原因;另一方面边界层偏东风急流为MCS-Ⅳ的发展提供了水汽和不稳定能量等有利条件,同时推动其左前方中尺度涡旋的发展,导致MCS-Ⅳ所在地的气旋性涡度大大增加,加强了以急流轴为中心的垂直次级环流发展,造成MCS-Ⅳ的发展维持,形成华北平原地区以雄安新区为中心的东西向大暴雨带。

丘陵地区10 m高度以下近地面风场实测及非平稳特性分析

为确定10 m高度以下风场特征以指导光伏支架结构设计,在陕西汉中某拟建光伏电站场址内开展了近地面风场实测.由于实测结果存在较高的低频能量,分别选用平稳模型和基于离散小波变换的非平稳模型,研究了10 m以下近地面风场的平均风速、湍流度、阵风因子、湍流积分尺度和风功率谱等特征参数,并与规范取值进行对比分析.结果表明:丘陵地区10 m以下近地面风场具有一定的非平稳特性;平稳模型会高估风的湍流强度和湍流积分尺度;非平稳模型较好地提取了时变平均风速,提高了样本的平稳性,且与光伏结构易发生共振的高频部分能量密度有所增大,能量接近Kaimal谱和von Karman谱,高于平稳模型结果,更具适用性.

基于虚拟激励法的大跨度桥梁非平稳随机振动分析闭合解

针对大跨度结构考虑地面空间运动的非一致地震响应分析问题,结合虚拟激励法,应用傅里叶分析建立了结构非平稳随机振动响应演变功率谱分析的频域方法。建立的方法完全基于频域执行,给出了响应演变功率谱的闭合解表达式。由于实现了确定性调制过程与随机过程的有效分离,应用离散傅里叶变换进行计算不需要较高的采样分析频率就可以获得较好精度的数值结果。数值算例研究了某斜拉桥的考虑地面运动空间效应非平稳随机地震响应,与通常时频分析方法进行对比,验证了本文频域方法的正确性和有效性。

非平稳随机地震激励下多层框架-摇摆墙结构的响应分析

框架-摇摆墙是一种可有效提高建筑抗震性和韧性的组合自复位结构,为充分了解其在地震下的随机响应特性,构建多自由度框架-摇摆墙结构的简化非线性方程,并利用等效线性化,基于响应的伪谐波行为假设,构建含时变参数的等效线性动力方程;基于随机平均的原理,得出控制响应幅值概率密度函数(PDF)的时间演变形式的福克-普朗克-科尔莫哥洛夫(FPK)方程,最终得出随机响应时间相关方差的一阶微分方程;并以某教学楼一榀框架为样本构建算例模型进行验证。结果表明:近似解析方法具有优异的精确度,在保证随机响应时间相关方差准确性的前提下,相对于传统的蒙特卡罗模拟(MCS)方法可提高分析的效率;在可分离形式和不可分离形式的非平稳地震动功率谱模型的结果中,随机响应方差曲线趋势与随机地震激励的形式相关,且在分段式调制非平稳谱作用下其分段点表现出很明显的不平滑现象;不同类型的随机地震激励扰动下的结果证明了此方法优异的适用性。

基于非稳态加性噪声模型的因果发现算法

因果发现旨在通过观测数据挖掘变量间的因果关系。现有的因果发现方法大多假定数据的产生过程是平稳的,然而在实际环境下往往不满足稳态假设,导致结果不可靠。研究发现,在一些场景中的非稳态扰动与时序信息高度相关。因此,在加性噪声模型基础上将非稳态扰动刻画为一项关于时序信息的函数,设计非稳态加性噪声模型,并给出非稳态加性噪声模型的识别条件,提出一种两阶段的因果关系学习算法。第1阶段利用回归计算得到变量残差,再检验残差与回归特征集的独立性从而选出叶子节点,迭代得到观测变量集的因果次序;第2阶段再次进行回归计算和独立性检验,消除第1阶段中冗余的因果关系,从而得到观测变量集的因果结构。实验结果表明,与基于约束的异构/非平稳因果发现、LPCMCI和Ti MINo算法相比,该算法在仿真数据集上取得了最优的效果,平均F1值达到0.85;而在真实因果结构数据集中,该算法的F1值平均提升41.12%,能够从非稳态数据集中恢复出更多因果结构的信息。

多轴平稳非高斯随机振动试验控制方法

多轴向平稳非高斯随机振动控制试验能够对指定响应信号的时、频域特征进行同时控制。提出了一种快速生成具有指定功率谱密度、斜度和峭度的平稳非高斯随机振动信号的方法。通过频率采样方法将目标功率谱密度设计成滤波器,利用非线性变换方法获取非高斯随机信号,再将此信号经过设计的滤波器以获得满足要求的非高斯随机信号。该方法简单、快速并克服了传统非线性变换方法的缺点。进一步将此方法应用于三轴向平稳非高斯随机振动试验中,给出了三轴向非高斯随机振动控制的闭环均衡步骤,此方法能够同时对信号的功率谱自谱、相干系数、相位差以及斜度和峭度进行解耦控制。进行了三轴向平稳非高斯随机振动控制试验,三个方向上加速度信号的功率谱密度、斜度和峭度控制效果均令人满意,满足工程应用要求。

双级可转导叶压气机性能研究

压气机的稳定性是保证压气机其他性能及燃气轮机正常运行的基础,而压气机存在着失速、喘振等不稳定现象,这种不稳定流动会严重影响整机运行的稳定性。导叶/静叶可调是一种防止喘振从而避免压气机进入失稳流动的有效措施。该文介绍了一个集成式压气机实验台,除了可进行高精度可转导叶性能研究外,还可进行压气机不同叶片综合性能和局部特性实验测量工作,且其数据采集集成系统可满足实时准确观测实验台相关参数的需求。通过实验与数值模拟相结合的方法对2.5级轴流压气机进行了研究,通过逐级调节进口导叶和一级静叶的旋转角度,获得了叶片调节角度与压气机效率之间的对应关系。

基于差分非平稳Transformer的液压支架立柱压力预测

液压支架立柱压力预测是回采工艺决策的重要依据,也是确保围岩稳定的基础信息之一。然而,液压支架立柱压力虽然具有一定的规律性,却无法用简单的数学模型进行预测;且在回采过程中,支架不接顶、顶板破碎、传感器检测误差等带来大量的随机噪声,使得压力数据劣化为非平稳时间序列,给压力的预测带来的很大的困难。本文在Transformer基础上,提出一种差分非平稳Transformer模型,在Transformer的编码器和解码器中分别引入差分归一化和反归一化操作,以提升序列的平稳性。同时,在Transformer中采用去平稳注意力机制,计算序列元素之间的关联关系,以增强模型的预测能力。在真实的煤矿支架立柱数据集上的对比实验表明,本文提出的差分非平稳Transformer的预测效果达到0.674,表现明显优于LSTM、Transformer和非平稳Transformer模型。

一种高斯-重尾切换分布鲁棒卡尔曼滤波器

为降低实际应用中由强未知干扰和仪器故障对观测造成的影响,减轻随机和未建模干扰对系统的侵蚀,从而提升系统在非高斯噪声环境下的状态估计精度,提高滤波器的鲁棒性能,提出了一种基于高斯-重尾切换分布的鲁棒卡尔曼滤波器(Gaussian-heavy-tailed switching distribution based robust Kalman filter,GHTSRKF)。首先,通过自适应学习高斯分布和一种重尾分布之间的切换概率将噪声建模为GHTS(Gaussian-heavy-tailed switching)分布,所设计的GHTS分布可以通过在线调整高斯分布和新的重尾分布之间的切换概率来对非平稳重尾噪声进行建模,具有虚拟协方差的高斯分布用于处理协方差矩阵不准确的高斯噪声。其次,引入两个分别服从Categorical分布与伯努利分布的辅助参数将GHTS分布表示为一个分层高斯形式,进一步利用变分贝叶斯方法推导了GHTSRKF。最后,利用一个仿真场景对几种不同的RKFs(robust Kalman filters)进行了对比验证。结果表明,所提出的GHTSRKF算法的估计精度对初始状态的选取不敏感,精度优于其他RKFs,它的RMSEs最接近噪声信息准确的KFTNC(KF with true noise covariances)的RMSEs(root mean square errors),且当系统与量测噪声是未知时变高斯噪声时,相比于现有的滤波器,GHTSRKF具有更好的估计性能,从而验证了GHTSRKF的有效性。

基于VMD-SE的电力负荷分量的多特征短期预测

为提高电力负荷的预测精度,提出一种基于VMD-SE的电力负荷分量的多特征短期预测方法。首先采用变分模态分解(VMD)将原始负荷分解为一系列模态分量与残差,VMD的分解层数由样本熵值(sample entropy,SE)确定;然后对比原始负荷与模态分量的SE值,重构为平稳分量和波动分量,来降低运算规模;同时利用皮尔逊相关系数来筛选特征变量,删除特征冗余,建立灰狼算法优化后的支持向量回归模型(GWO-SVR)和长短期记忆神经网络(LSTM)分别对平稳分量和波动分量预测;最后以某地区2018—2020年用电负荷为例进行实验。实验证明:此模型精准度高达94.7%,平均绝对百分误差降低到2.98%,具有更好的精准性和适用性。