Short Term Forecasting Performances of Classical VAR and Sims-Zha Bayesian VAR Models for Time Series with Collinear Variables and Correlated Error Terms

Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.

Error term concerning number of subgroups of group Z_(m)×Z_(n) with m^(2)+n^(2)≤x

Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.

Tong-type identity and the mean square of the error term for an extended Selberg class

In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3(n). The aim of this paper is to generalize Tong's method to a class of Dirichlet series L(s) which satisfies a functional equation. Let a(n) be an arithmetical function related to a Dirichlet series L(s), and let E(x) be the error term of ′n xa(n). In this paper, after introducing a class of Diriclet series with a general functional equation(which contains the well-known Selberg class), we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L(s). This kind of Tong-type truncated formula could be used to study the mean square of E(x) under a certain assumption. In other words, we reduce the mean square of E(x) to the problem of finding a suitable constant σ*which is related to the mean square estimate of L(s). We shall represent some results of functions in the Selberg class of degrees 2–4.

The error term in Nevanlinna' s inequality

An upper bound is given for the error term S( r, { aj}, f) in Nevanlinna’s inequality. Forgiven positive increasing functions p and φ withWe prove thatholds, with a small exceptional set of r, for any finite set of points {aj} in the extended plane and any meromorphic function f such that Ψ (r( r, f)) = 0 (P (r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.

On the error term in Weyl’s law for the Heisenberg manifolds (Ⅱ)

In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.

ANALYSES OF ERRORS IN MEDIUM-TERM NUMERICAL FORECAST PRODUCTS FOR THE SUBTROPICAL HIGH 1998

By statistic and dynamic analyses, we have come to the following conclusions: (1) The ECMWF medium-term numerical forecast can forecast medium-term activity of subtropical high, and the accuracy rate of forecast cannot have large improvement by translational corrections. (2) The important cause for the ECMWF medium-term numerical forecast to have errors in 1998 is that the astronomical tide is not included in the model. (3) Two indexes are found from which it can be judged that ECMWF medium-term numerical forecast will have errors if the astronomical tide is ignored in the model : ① When the 54.7?line under the moon of the nodical month astronomical singularities coincides with the trough-line of the subtropical jet flow from 50癊 to 150癊 on the 500 hPa level at 2000 L.T. of the same day, and is approximately vertical (α>60? with the isotherm, then the day 0 2 days after the appearance of the nodical month astronomical singularities is defined as the initial day. Then in three successive days after the initial day, ECMWF medium-term numerical forecast of the northern latitude of the 588 line at 120 癊 will have continuous errors as large as two latitudes (7/9). Otherwise, it won’t have continuous errors (13/13). ② Otherwise, if the 54.7 ?line is in the range of a low pressure between two high pressures, then there is a dispersive error on the day of the nodical month astronomical singularities (5/7). There is not any error (6/6) otherwise.

ADS-B Reception Error Correction Based on the LSTM Neural-Network Model

Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites.

基于第十三代国际地磁参考场模型在中国区域特征分析与研究

根据最新的第十三代国际地磁参考场模型(IGRF13),计算了2015—2020年中国区域地磁场模型七要素长期变化速率,并在此基础上分析我国区域地磁场长期变化特征。通过分析计算我国28个地磁台的IGRF13模型值与实际地磁场的长期变化速率、差值及均方误差,结果显示:IGRF13模型所显示的地磁场长期变化与我国区域地磁场实际观测变化基本一致,但在局部区域也存在差异,IGRF13模型能够体现中国区域地磁场的特征。应用IGRF13模型数据时需要考虑局部区域与台站实际观测数据的误差。

计及误差信息的自适应超短期风速预测模型

为提升超短期风速预测精度,提出一种计及误差信息的自适应混合预测模型。应用自适应噪声的完备集合经验模态分解模型与鲸鱼优化的变分模态分解模型分别对风速样本数据与预测误差进行分解,同时计算各子序列的模糊熵以判断序列复杂程度。在此基础上,应用鲸鱼优化的长短期网络预测复杂程度较高的序列,差分自回归移动平均模型预测复杂程度较低的序列。最后,将初始风速预测结果和风速误差预测值相加得到基于误差修正的超短期风速预测值。结果表明,修正预测误差与考虑分解策略可有效提升点预测的性能,与基准模型相比,所提模型在多场景下均具备优良的预测精度。

复杂环境下基于自监督LSTM网络的导航误差建模补偿

针对复杂环境下惯导系统存在交互影响和导航误差难以辨识的问题,提出了一种基于自监督长短期记忆(LSTM)网络智能组合模型的导航误差补偿方法。模型中的自监督温变速率模块不受到温度传感器精度的限制,从而实时计算更精确的温变速率,进一步提升了模型导航误差辨识的能力。在实验部分,基于多种复杂环境下的实验数据,通过消融实验验证了自监督模块的有效性。以飞行数据的北向速度为例,补偿前后的最大速度绝对误差分别为1.607 m/s和0.357 m/s。实验结果说明了所提方法可以减小复杂环境下的速度和位置误差,从而提升惯性导航精度.

基于混合特征双重衍生和误差修正的风电功率超短期预测

随着风电渗透率的不断提高,对风电功率进行精准、可靠的预测是提升风电消纳水平的有效措施。针对功率预测时风电数据种类不足和特征数量稀缺的问题,提出基于混合特征双重衍生和误差修正的风电功率超短期预测模型。首先,在原始功率特征中施加混沌噪声,构造出多条混沌扰动特征,改善原始功率特征分布过于单一的状况。其次,提出基于免疫算法的特征衍生算法,挖掘风电功率数据的潜在信息,增加优质特征数量,进而构建误差预测模型,通过预测风电功率预测误差修正风电功率预测结果,进一步提升预测准确率。最后,基于比利时风电场实际运行数据进行算例分析。所提模型预测效果较好,且相较其他传统预测模型精确度更高,验证了所提模型的有效性。

基于SVM-STL-LSTM的区域短期电力负荷预测研究

针对区域电力负荷的时间序列数据随机性强、预测精度低及单一模型的数据特征提取能力差等问题,提出了一种支持向量机(SVM)、STL时序分解法、长短期记忆神经网络(LSTM)组合的电力负荷预测模型。该模型利用SVM对时间序列的电力负荷数据进行初始预测,并通过STL时序分解法对残差序列进行时序分解,从而提高残差序列的稳定性,减小其随机性,最后用LSTM对SVM的预测误差进行修正。试验结果证明,该方法利用误差修正可有效处理随机性强的数据,有利于预测结果的稳定性,提高预测精度。

基于考虑误差修正的非线性自适应权重组合模型的光伏发电功率预测

为了提高光伏电站光伏发电功率预测精度,解决极限梯度提升模型、长短期记忆模型2种传统单一模型及传统组合模型极限梯度提升-长短期记忆模型的光伏发电功率预测结果滞后、预测效果易突变、预测误差较大、线性拟合性较差等不足,基于极限梯度提升算法、长短期记忆算法和线性自适应权重,提出一种考虑误差修正的非线性自适应权重极限梯度提升-长短期记忆模型进行光伏发电功率预测;分别使用极限梯度提升算法和长短期记忆算法训练得到2种单一模型,将2种单一模型的初步预测值和真实值组成新的训练数据集,利用神经网络算法训练所提出的模型,对2种单一模型的初步预测值分配自适应权重系数,并根据训练时所提出模型的预测值大小分段统计预测误差的分布,预测时根据所提出模型的预测值在预测结果的基础上累加误差均值从而进行误差修正,进一步提高所提出模型的预测精度;利用Python语言分别对所提出的模型、传统组合模型和2种传统单一模型在晴天、阴天和雨天的光伏发电功率预测性能进行仿真。结果表明:与极限梯度提升-长短期记忆模型、极限梯度提升模型、长短期记忆模型相比,所提出模型的均方根误差分别减小28.57%、 39.39%、 49.79%,平均绝对误差分别减小44.25%、 53.33%、 64.8%,决定系数分别增大1.43%、 2.38%、 3.34%,所提出的模型更有效地减小了传统单一模型的光伏发电功率预测误差,优化了传统组合模型的权重系数;3种天气条件下所提出模型的光伏发电功率预测误差相对最小且稳健性最强,验证了所提出模型的有效性。

大规模电力工程数据价值深度挖掘算法设计研究

针对传统电力工程数据处理方法中存在的不可追溯且不易统一管理等问题,文中基于数据挖掘的思想提出了一种电力工程数据价值分析预测模型。该模型采用Boosting算法将多个预测树结构组合形成极端梯度提升树模型,从而实现对非线性数据的深入分析,且经过多次迭代后,可以使训练准确度与学习效果得到显著提升。通过采用改进的双向长短时记忆网络,增强了模型处理时序性数据的能力。同时还使用误差倒数法将两个算法模型相结合,使其具有更高的预测精度。在实验测试中,所提算法的预测结果更贴近实际值,且其MAPE及RMSE测试指标分别为0.201%和0.039%,在所有对比算法中均为最优,可以对电力工程数据价值进行准确的分析和预测。

EO-REEVMD-BILSTM的两阶段超短期风电功率预测

为提升风电功率的预测精度,提出一种基于平衡优化器优化算法的两阶段超短期风电功率预测方法。通过建立一种适用于风电功率预测的回归包络熵适应度目标模型,利用平衡优化器算法寻优VMD分解参数,实现对原始风电功率信号的合理分解,有效减小分解损失。基于BILSTM神经网络模型分别预测分解的模态分量,根据叠加各分量的预测结果获得初步风电预测功率序列,利用误差预测值纠正上一阶段预测结果。以土耳其某地区提供的风电功率数据作为实际算例,通过仿真实验与实测风电功率比较。结果表明:文中所提方法的RMSE与MAE仅为28.3781与17.4297,R^(2)为0.9986,明显低于BILSTM等单一预测模型与其他组合预测方法,验证了文中方法的有效性。

基于LSTM网络的分散式电采暖负荷仿真分析

基于等效热参数模型的分散式电采暖负荷存在参数识别困难、仿真误差大,不能满足电网调节需求的问题,为此提出基于长短时记忆网络的分散式电采暖负荷仿真模型。首先,根据分散式电采暖负荷与建筑物之间的传热过程,确定模型参数。然后,结合模型输入变量与输出变量确定长短时记忆网络参数,建立负荷模型。并通过对测试集输入数据中的室内温度进行动态更新,实现了长时间尺度的温度仿真。接着,为衡量模型的准确性,提出了纵向与横向两种维度上的模型误差评价指标。最后,算例分析结果表明,相比于分散式电采暖负荷二阶等效热参数模型,基于长短时记忆网络的分散式电采暖负荷模型仿真结果的纵向误差与横向误差更小,模型精度更高。

基于LSTM人工神经网络的电力系统负荷预测方法

针对电力市场环境下短期电力系统负荷预测准确性较低的问题,提出了一种基于LSTM人工神经网络的组合预测模型。分析了LSTM神经网络和其变体GRU神经网络在进行负荷预测时学习时序特征的独特优势,并以卷积神经网络作为负荷数据的特征提取层,结合GRU网络构建了组合模型,通过建立残差预测模型对结果进行修正。仿真结果表明,具有记忆功能的神经网络预测效果要优于ANN和SVM模型,且所提出残差预测模型的负荷预测平均相对误差约为1.79%,其准确性高于单一算法的负荷预测模型。

基于低秩稀疏表达的弹性最小二乘回归学习

为了克服重定向最小二乘回归模型容易破坏回归目标的结构的缺点,提出了一种基于低秩稀疏表达的弹性最小二乘回归学习模型LRSR-eLSR。模型以最小二乘回归为基础,不使用严格的0-1标签矩阵作为目标矩阵,而是引入边距约束来直接从数据中学习回归目标,可以在保持回归目标低秩结构的同时,增加回归模型的灵活性。而且,为了捕获数据的结构信息,利用了数据的低秩表示来保持数据的结构。在计算的过程中,考虑问题求解的复杂性,使用了核范数正则化代替秩函数。除此之外,模型还引入了一个带有L 2,1范数的稀疏误差项来补偿回归误差,这有利于学习更灵活地变换。模型还对投影矩阵施加额外的正则化项,来避免过拟合问题。实验结果表明:在4个公开的数据集上,所提模型的识别准确率优于其他方法;在COIL-20数据集中,识别率可达到98%。

基于改进演化博弈模型的网络防御决策方法

针对网络防御决策的误差干扰和实时响应问题,该文提出一种改进演化博弈模型(IEGM)和网络防御决策方法。首先,借鉴经典伺服系统模型,用微分假设量化表示防御方对攻击策略的短期预测效应,加快模型收敛速度,提升防御决策效率。其次,分析攻防博弈中的误差产生机理,量化定义网络防御中的观测误差,提出改进复制动力学方程,加强模型对信息偏差的容忍度。在此基础上,建立改进演化博弈模型,证明了模型能够收敛至纳什均衡解的微小ε-邻域,给出了相应的稳定性分析,并设计了一种网络防御决策方法。理论分析和仿真结果表明,所提模型能够克服观测误差影响,给出偏差数量级在0.01%的最优防御纯策略,且在强干扰环境下,防御决策的响应速度相较于其他3种经典决策模型最高可以提升64.06%。改进模型和防御决策方法能够有效提升防御决策的响应时效性和对观测误差的适应性。

基于LSTM与牛顿迭代的两轴系统轮廓误差控制

针对轮廓误差影响运动系统精度的问题,提出结合长短期记忆神经网络(LSTM)和牛顿迭代法对轮廓误差进行预测、通过转换任务坐标系对轮廓误差进行补偿的方法.在运动平台上提取特征轮廓与数据,将牛顿迭代法应用于对轮廓误差的计算,通过计算出的轮廓误差对优化后的LSTM神经网络进行训练,建立更准确的轮廓误差预测模型.通过转换任务坐标系,将预测的轮廓误差作为前馈补偿到参考轮廓中,提高轮廓控制性能.通过试验对比PID、迭代法和神经网络法,利用随机NRBUS轨迹验证泛化性,表明提出的方法能够有效地预测并控制轮廓误差,在精密运动控制领域有良好的应用前景.