Variational Inference Based Kernel Dynamic Bayesian Networks for Construction of Prediction Intervals for Industrial Time Series With Incomplete Input

Prediction intervals (PIs) for industrial time series can provide useful guidance for workers. Given that the failure of industrial sensors may cause the missing point in inputs, the existing kernel dynamic Bayesian networks (KDBN), serving as an effective method for PIs construction, suffer from high computational load using the stochastic algorithm for inference. This study proposes a variational inference method for the KDBN for the purpose of fast inference, which avoids the time-consuming stochastic sampling. The proposed algorithm contains two stages. The first stage involves the inference of the missing inputs by using a local linearization based variational inference, and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices. To verify the effectiveness of the proposed method, a synthetic dataset and a practical dataset of generation flow of blast furnace gas (BFG) are employed with different ratios of missing inputs. The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.      

The reconstruction of abnormal segments in HJ-1A/B NDVI time series using MODIS: a statistical method

HJ-1A/B is the first small satellite constellation built by China for environmental and disaster monitoring and forecasting. The satellite group has a 2-day repetition cycle and 30 m spatial resolution (charge coupled device camera). Thus, HJ-1A/B can provide hyper-temporal normalized difference vegetation index (NDVI) time series with a medium–high spatial resolution. However, the quality of the HJ NDVI time series can be abnormally low due to a number of factors, such as cloud cover, continuous fog, and haze. In the rainy season or in areas with serious atmospheric pollution, low-quality series often appear in succession, which is referred to as an abnormal segment. Neither the composition method nor quality flags satisfactorily solve this problem; therefore, a large amount of noise and long periods of abnormally low values often remain in HJ NDVI time series. This article presents a method to reconstruct the abnormal segments in HJ NDVI time series with the assistance of Moderate Resolution Imaging Spectroradiometer (MODIS) NDVI time series. The cointegration test was adopted to decide whether MODIS can be used for the reconstruction of NDVI time series for the corresponding HJ image pixels. Statistical quality control methods were used for singling out the abnormal segments in the HJ NDVI time series and establishing an error correction model that combines MODIS and HJ NDVI time series to perform the reconstruction. The study area is located in Jiangsu Province, China. Four-year (2009–2012) HJ multispectral images that cover the study area were used. The results show that abnormal segments in the HJ NDVI time series can be corrected using the proposed method. In a particular year, this method can decrease the root mean square error between the HJ NDVI time series and the reference sequence by 52.5%.     

基于多元时间序列的自适应贪婪高斯分段算法

现有多元时间序列分段算法中分段点的选择以及分段个数的确定往往需要分别独立完成,大大增加了算法的计算复杂度.为解决上述问题,提出一种基于多元时间序列的自适应贪婪高斯分段算法.该算法将多元时间序列各个分段所对应的数据解释为来自不同多元高斯分布的独立样本,进而将分段问题转化为协方差正则化的最大似然估计问题进行求解.为提高学习效率,采用贪婪搜寻方法使每个段的似然值最大化进而近似地找到最优分段点,并且在搜寻的过程中利用信息增益方法自适应地获取最优的分段个数,避免分段个数确定和分段点选择分别独立进行,从而减少计算的复杂度.基于多种领域的真实数据集实验结果表明,所提出方法的分段精度以及运行效率均优于传统方法,并且能够有效完成多元时间序列的异常检测任务.     

基于分段极值DTW距离的时间序列相似性度量

在时间序列相似性的研究中,通常采用的欧氏距离及其变形无法对在时间轴上发生伸缩或弯曲的序列进行相似性度量,本文提出了一种基于分段极值DTW距离的时间序列相似性度量方法可以解决这一问题。在动态时间弯曲(DTW)距离的基础上,本文定义了序列的分段极值DTW距离,并阐述了其完整的算法实现。与传统的DTW距离相比,分段极值DTW距离在保证度量准确性的同时大大提高了相似性计算的效率。文中最后运用MATLAB作对比实验,并给出实验结果数据,验证了该度量方法的有效性与准确性。     

Novel Online Methods for Time Series Segmentation

To efficiently and effectively mine massive amounts of data in the time series, approximate representation of the data is one of the most commonly used strategies. Piecewise Linear Approximation is such an approach, which represents a time series by dividing it into segments and approximating each segment with a straight line. In this paper, we first propose a new segmentation criterion that improves computing efficiency. Based on this criterion, two novel online piecewise linear segmentation methods are developed, the feasible space window method and the stepwise feasible space window method. The former usually produces much fewer segments and is faster and more reliable in the running time than other methods. The latter can reduce the representation error with fewer segments. It achieves the best overall performance on the segmentation results compared with other methods. Extensive experiments on a variety of real-world time series have been conducted to demonstrate the advantages of our methods.     

Granulation-based symbolic representation of time series and semi-supervised classification

We present a semi-supervised time series classification method based on co-training which uses the hidden Markov model (HMM) and one nearest neighbor (1-NN) as two learners. For modeling time series effectively, the symbolization of time series is required and a new granulation-based symbolic representation method is proposed in this paper. First, a granule for each segment of time series is constructed, and then the segments are clustered by spectral clustering applied to the formed similarity matrix. Using four time series datasets from UCR Time Series Data Mining Archive, the experimental results show that proposed symbolic representation works successfully for HMM. Compared with the supervised method, the semi-supervised method can construct accurate classifiers with very little labeled data available.     

基于多尺度的时间序列固定分段数线性表示

针对目前的时间序列线性表示方法多采用启发式方法提取局部特征点作为分段点,容易陷入局部最优化,不能很好地表示时间序列全局特征,而且多采用单一的拟合误差作为阈值,不能准确预计分段数量,不利于后期进行的时间序列分析应用的问题。提出了一种新的固定分段数的表示方法--PLR_BTBU,首先根据二叉树层次遍历的思想,提取时间序列全局特征点将时间序列初始分段,再通过斜率变化特征将整个时间序列符号化,以各初始分段内的符号特征来确定各初始分段中的分段点分布,最后采用一种改进的固定分段数的自底向上融合算法,将各个子序列逐步融合到要求的分段数。实验结果表明,与已有的方法相比,该方法不仅较好地保留时间序列的全局特征,而且拟合后的时间序列和原时间序列之间的拟合误差更小。     

RPAA：一种基于时间特性的时间序列建模表示

滑动聚集平均近似PAA（Piecewise Aggregate Approximation）是一种表示时间序列的方法，它通过时间序列上滑动一个等宽的滑动窗口将时间序列分成小的区段。考虑到时间序列的时间特性q-不同区段的影响，本文提出了一种改进表示RPAA（Reversed Piecewise Aggregate Approximation）。RPAA表示对处于不同时间段的序列赋以不同的影响因子，具有线性时间复杂度，并且证明了RPAA满足下界定理，因而能够进行实际的查询。最后的实验表明该表示是有效的。     

基于相关系数的多变量异常数据段的检测

工业报警系统普遍存在报警过多的问题,为了获取过程变量的正常与异常历史数据段,从而设计工业报警系统的动态报警阈值,进行性能评估和优化,提出了一种基于过程变量之间的相关系数进行异常数据段检测的改进方法。该检测方法将相关系数和数据段长度作为分段依据,对过程变量的多元时间序列进行分段,采用Spearman秩相关系数获取变量之间的相关关系,从而检测出不符合正常趋势的异常数据段。仿真算例和工业案例表明该方法可真实地反映过程变量之间的相关关系,并准确检测出所存在的异常数据段。     

基于DFS的工程图多层次图块信息提取

针对工程图信息提取过程中的图块多层次引用问题,利用深度优先搜索算法对引用图块信息进行提取。建立图块多层次引用关系,介绍节点深度定义、目标节点判定方法及引用图块搜索策略,设计多层次引用路径搜索算法,并开发应用程序模块,实现多层次引用图块的信息提取。应用结果表明,该方法的提取准确率较高。     

Automatic spectral analysis with missing data

The current computational power and some recently developed algorithms allow a new automatic spectral analysis method for randomly missing data. Accurate spectra and autocorrelation functions are computed from the estimated parameters of time series models, without user interaction. If only a few data are missing, the accuracy is almost the same as when all observations were available. For larger missing fractions, low-order time series models can still be estimated with a good accuracy if the total observation time is long enough. Autoregressive models are best estimated with the maximum likelihood method if data are missing. Maximum likelihood estimates of moving average and of autoregressive moving average models are not very useful with missing data. Those models are found most accurately if they are derived from the estimated parameters of an intermediate autoregressive model. With statistical criteria for the selection of model order and model type, a completely automatic and numerically reliable algorithm is developed that estimates the spectrum and the autocorrelation function in randomly missing data problems. The accuracy was better than what can be obtained with other methods, including the famous expectation–maximization (EM) algorithm.     

A global NDVI and EVI reference data set for land-surface phenology using 13 years of daily SPOT-VEGETATION observations

Time series of vegetation indices (VIs) obtained by remote sensing are widely used to study phenology on regional and global scales. The aim of the study is to design a method and to produce a reference data set describing the seasonal and inter-annual variability of the land-surface phenology on a global scale. Specific constraints are inherent in the design of such a global reference data set: (1) the high diversity of vegetation types and the heterogeneous conditions of observation, (2) a near-daily resolution is needed to follow the rapid changes in phenology, (3) the time series used to depict the baseline vegetation cycle must be long enough to be representative of the current vegetation dynamic and encompass anomalies, and (4) a spatial resolution consistent with a land-cover-specific analysis should be privileged. This study focuses on the SPOT (Satellite Pour l’Observation de la Terre)-VEGETATION sensor and its 13-year time series of reflectance values. Five steps addressing the noise and the missing data in the reflectance time series were selected to process the daily multispectral reflectance observations. The final product provides, for every pixel, three profiles for 52 × 7-day periods: a mean, a median, and a standard deviation profile. The mean and median profiles represent the reference seasonal pattern for variation of the vegetation at a specific location whereas the standard deviation profile expresses the inter-annual variability of VIs. A quality flag at the pixel level demonstrated that the reference data set can be considered as a reliable representation of the vegetation phenology in most parts of the Earth.     

基于残差连接长短期记忆网络的时间序列修复模型

传统的时间序列缺失修复方法通常假设数据由线性动态系统产生,然而时间序列更多地表现为非线性。为此,提出了基于残差连接长短期记忆（LSTM）网络的时间序列修复模型,称为RSI-LSTM,用来有效捕获时间序列的非线性动态特性,并且挖掘缺失数据和最近的非缺失数据之间的潜在关联。具体来说,就是采用LSTM网络对时间序列的非线性动态特性进行建模,同时引入残差连接来挖掘历史值与缺失值的联系,从而提升模型的修复能力。首先使用RSI-LSTM对单变量日供电量数据集的缺失数据进行修复,然后在第九届电工数学建模竞赛A题的电力负荷数据集上,引入气象因素作为RSI-LSTM的多变量输入,以提升模型对时间序列缺失值的修复效果。此外,使用了两个通用的多变量时间序列数据集以验证模型的缺失修复能力。实验结果表明,在单变量和多变量数据集上,RSI-LSTM的缺失值修复效果均优于LSTM,得到的均方误差（MSE）总体下降了10%。     

Adaptive sequential segmentation of piecewise stationary time series

The problem of adaptive segmentation of time series with abrupt changes in the spectral characteristics is addressed. Such time series have been encountered in various fields of time series analysis such as speech processing, biomedical signal processing, image analysis and failure detection. Mathematically, these time series often can be modeled by zero mean gaussian distributed autoregressive (AR) processes, where the parameters of the process, including the gain factor, remain constant for certain time intervals and then jump abruptly to new values. Identification of such processes requires adaptive segmentation: the times of parameter jumps have to be estimated thoroughly to constitute boundaries of “homogeneous” segments which can be described by stationary AR processes. In this paper, a new effective method for sequential adaptive segmentation is proposed, which is based on parallel application of two sequential parameter estimation procedures. The detection of a parameter change as well as the estimation of the accurate position of a segment boundary is effectively performed by a sequence of suitable generalized likelihood ratio (GLR) tests. Flow charts as well as a block diagram of the algorithm are presented. The adjustment of the three control parameters of the procedure (the AR model order, a threshold for the GLR test and the length of a “test window”) is discussed with respect to various performance features. The results of simulation experiments are presented which demonstrate the good detection properties of the algorithm and in particular an excellent ability to allocate the segment boundaries even within a sequence of short segments. As an application to biomedical signals, the analysis of human electroencephalograms (EEG) is considered and an example is shown.     

热带地区Landsat干季数据的无效像元修复方法研究

热带地区完整中分辨率时间序列遥感数据对于地表过程及地表扰动观测具有重要应用价值。针对热带地区Landsat数据存在云、雾污染及传感器本身缺陷导致的大量数据缺失问题，在现有的条带数据缺失填充算法（GNSPI）基础上，提出三次修复法。该方法能自动识别当前待修复像元前后48 d内有效参考像元，继而经三次修复法实现当前缺失数据的修复。实验结果表明：三次修复法整体平均修复精度（R²）可达0.88，该方法弥补了GNSPI填充算法需要整幅参考影像不存在无效像元方可执行的苛刻要求，提高了有效观测像元的利用率，对于获取热带地区长时间序列有效观测数据具有重要意义。     

基于ST-DCGAN的时序交通流量数据补全

时序交通流量数据作为一种新型城市数据,对智能交通和智慧城市的发展有着重要的意义,但是由于各种原因使得收集的交通数据存在大量的缺失,因此如何有效地补充缺失流量数据成为目前急需解决的问题。提出的ST-DCGAN模型利用了基于DCGAN网络的思想,引入补全损失函数和判别损失函数作为模型新的目标函数,通过生成器和鉴别器相互博弈的原理学习区域流量数据之间的时空特征性,在常规的缺失数据补全的基础上利用数据生成思想进行了区域时序交通流量数据的补全,从而为交通流量缺失值提出一种新的补全方法。实验以北京TaxiBJ GPS开源数据集为基础,并用RMSE评估函数分析上述算法对缺失交通流量补全的效果,实验结果表明提出的方法与所比较补全方法相比,效果更好。     

基于分段特征及自适应加权的DTW相似性度量

利用动态时间弯曲（DTW）技术在原始多元时间序列进行相似性度量时时间复杂度较高,且DTW在追求最小弯曲距离的过程中可能会出现过渡拉伸和压缩的问题。提出一种基于分段特征及自适应加权的DTW多元时间序列相似性度量方法。对原始时间序列在各个变量维度上进行统一分段,选取分段后拟合线段的斜率、分段区间的最大值和最小值以及时间跨度作为每一段的特征,实现对原始序列的大幅降维,提高计算效率。在DTW计算最佳弯曲路径的过程中为每个点设置自适应代价权重,限制弯曲路径中点列的重复使用次数,改善时间序列因过度拉伸或压缩所导致的度量精度低的问题,以得到最优路径路线。实验结果表明,该方法能很好地度量多元时间序列之间的相似性,在多个数据集上都能取得较好的度量结果。     

工业过程数据中缺失值处理方法的研究

针对工业生产中过程数据的缺失问题,首次提出了运用多重填补方法处理工业过程的缺失数据.阐述了常用的缺失数据处理方法,指出各方法的优缺点.在此基础上,通过建立回归模型,针对多变量工业数据中缺失值较少和较多时的两种情况,分别用删除含缺失值的个案,简单填补和多重填补(MI)3种方法对数据进行处理,利用处理后的新数据集进行数据挖掘,预测目标变量的值,并对预测结果进行分析比较.实验结果表明,多重填补方法的处理效果最好,为工业数据的缺失值处理提供了有用的策略.     

基于SOM的散乱数据点集的B样条曲面重建

利用自组织映射神经网络(SOM)技术对散乱数据点集进行B样条曲面重建时,往往存在网络学习时间过长和学习效果不理想等问题。提出了一种新的神经元初始化方法和分块学习算法,该算法首先运用主元素分析方法(PCA)对散乱数据进行分块,将拓扑结构为四边形的输出层神经元初始化在每块散乱数据的最小二乘平面上进行网络学习和训练,将分块学习得到的各网格曲面拼接成一个整体;然后对该整体网格曲面的边界和内部单独学习,得到一张逼近待重建曲面的双线性B样条曲面;最后对该B样条曲面误差进行了修正。实例证明,该算法可以明显地减少SOM网络学习时间,并改善网络学习效果。     

Improving Phoneme Classification Performance Using Observation Context–Dependent Segment Models

This article describes a novel method that models the correlation among acoustic observations in contiguous speech segments. The basic idea behind the method is that acoustic observations are conditioned not only on the phonetic context but also on the preceding acoustic segment observation. The correlation between consecutive acoustic observations is modeled by mean trajectory polynomial segment models (PSM). This method is an extension of conventional segment modeling approaches in that it describes the correlation of acoustic observations not only inside segments but also between contiguous segments. It is also a generalization of phonetic context (e.g., triphone) modeling approaches because it can model acoustic context and phonetic context at the same time. Using the proposed method in a speaker-independent phoneme classification test resulted in a 7 to 9% relative reduction of error rate as compared with the traditional triphone segmental model system and a 31% reduction as compared with a similar triphone hidden Markov model (HMM) system.