A Memory-Guided Anomaly Detection Model with Contrastive Learning for Multivariate Time Series

Some reconstruction-based anomaly detection models in multivariate time series have brought impressive performance advancements but suffer from weak generalization ability and a lack of anomaly identification.These limitations can result in the misjudgment of models,leading to a degradation in overall detection performance.This paper proposes a novel transformer-like anomaly detection model adopting a contrastive learning module and a memory block(CLME)to overcome the above limitations.The contrastive learning module tailored for time series data can learn the contextual relationships to generate temporal fine-grained representations.The memory block can record normal patterns of these representations through the utilization of attention-based addressing and reintegration mechanisms.These two modules together effectively alleviate the problem of generalization.Furthermore,this paper introduces a fusion anomaly detection strategy that comprehensively takes into account the residual and feature spaces.Such a strategy can enlarge the discrepancies between normal and abnormal data,which is more conducive to anomaly identification.The proposed CLME model not only efficiently enhances the generalization performance but also improves the ability of anomaly detection.To validate the efficacy of the proposed approach,extensive experiments are conducted on well-established benchmark datasets,including SWaT,PSM,WADI,and MSL.The results demonstrate outstanding performance,with F1 scores of 90.58%,94.83%,91.58%,and 91.75%,respectively.These findings affirm the superiority of the CLME model over existing stateof-the-art anomaly detection methodologies in terms of its ability to detect anomalies within complex datasets accurately.

Fine-Grained Multivariate Time Series Anomaly Detection in IoT

Sensors produce a large amount of multivariate time series data to record the states of Internet of Things(IoT)systems.Multivariate time series timestamp anomaly detection(TSAD)can identify timestamps of attacks and malfunctions.However,it is necessary to determine which sensor or indicator is abnormal to facilitate a more detailed diagnosis,a process referred to as fine-grained anomaly detection(FGAD).Although further FGAD can be extended based on TSAD methods,existing works do not provide a quantitative evaluation,and the performance is unknown.Therefore,to tackle the FGAD problem,this paper first verifies that the TSAD methods achieve low performance when applied to the FGAD task directly because of the excessive fusion of features and the ignoring of the relationship’s dynamic changes between indicators.Accordingly,this paper proposes a mul-tivariate time series fine-grained anomaly detection(MFGAD)framework.To avoid excessive fusion of features,MFGAD constructs two sub-models to independently identify the abnormal timestamp and abnormal indicator instead of a single model and then combines the two kinds of abnormal results to detect the fine-grained anomaly.Based on this framework,an algorithm based on Graph Attention Neural Network(GAT)and Attention Convolutional Long-Short Term Memory(A-ConvLSTM)is proposed,in which GAT learns temporal features of multiple indicators to detect abnormal timestamps and A-ConvLSTM captures the dynamic relationship between indicators to identify abnormal indicators.Extensive simulations on a real-world dataset demonstrate that the proposed algorithm can achieve a higher F1 score and hit rate than the extension of existing TSAD methods with the benefit of two independent sub-models for timestamp and indicator detection.

Generating Adversarial Samples on Multivariate Time Series using Variational Autoencoders

Classification models for multivariate time series have drawn the interest of many researchers to the field with the objective of developing accurate and efficient models.However,limited research has been conducted on generating adversarial samples for multivariate time series classification models.Adversarial samples could become a security concern in systems with complex sets of sensors.This study proposes extending the existing gradient adversarial transformation network(GATN)in combination with adversarial autoencoders to attack multivariate time series classification models.The proposed model attacks classification models by utilizing a distilled model to imitate the output of the multivariate time series classification model.In addition,the adversarial generator function is replaced with a variational autoencoder to enhance the adversarial samples.The developed methodology is tested on two multivariate time series classification models:1-nearest neighbor dynamic time warping(1-NN DTW)and a fully convolutional network(FCN).This study utilizes 30 multivariate time series benchmarks provided by the University of East Anglia(UEA)and University of California Riverside(UCR).The use of adversarial autoencoders shows an increase in the fraction of successful adversaries generated on multivariate time series.To the best of our knowledge,this is the first study to explore adversarial attacks on multivariate time series.Additionally,we recommend future research utilizing the generated latent space from the variational autoencoders.

Production performance forecasting method based on multivariate time series and vector autoregressive machine learning model for waterflooding reservoirs

A forecasting method of oil well production based on multivariate time series(MTS)and vector autoregressive(VAR)machine learning model for waterflooding reservoir is proposed,and an example application is carried out.This method first uses MTS analysis to optimize injection and production data on the basis of well pattern analysis.The oil production of different production wells and water injection of injection wells in the well group are regarded as mutually related time series.Then a VAR model is established to mine the linear relationship from MTS data and forecast the oil well production by model fitting.The analysis of history production data of waterflooding reservoirs shows that,compared with history matching results of numerical reservoir simulation,the production forecasting results from the machine learning model are more accurate,and uncertainty analysis can improve the safety of forecasting results.Furthermore,impulse response analysis can evaluate the oil production contribution of the injection well,which can provide theoretical guidance for adjustment of waterflooding development plan.

High-performance formaldehyde prediction for indoor air quality assessment using time series deep learning

Indoor air pollution resulting from volatile organic compounds(VOCs),especially formaldehyde,is a significant health concern needed to predict indoor formaldehyde concentration(Cf)in green intelligent building design.This study develops a thermal and wet coupling calculation model of porous fabric to account for the migration of formaldehyde molecules in indoor air and cotton,silk,and polyester fabric with heat flux in Harbin,Beijing,Xi’an,Shanghai,Guangzhou,and Kunming,China.The time-by-time indoor dry-bulb temperature(T),relative humidity(RH),and Cf,obtained from verified simulations,were collated and used as input data for the long short-term memory(LSTM)of the deep learning model that predicts indoor multivariate time series Cf from the secondary source effects of indoor fabrics(adsorption and release of formaldehyde).The trained LSTM model can be used to predict multivariate time series Cf at other emission times and locations.The LSTM-based model also predicted Cf with mean absolute percentage error(MAPE),symmetric mean absolute percentage error(SMAPE),mean absolute error(MAE),mean square error(MSE),and root mean square error(RMSE)that fell within 10%,10%,0.5,0.5,and 0.8,respectively.In addition,the characteristics of the input dataset,model parameters,the prediction accuracy of different indoor fabrics,and the uncertainty of the data set are analyzed.The results show that the prediction accuracy of single data set input is higher than that of temperature and humidity input,and the prediction accuracy of LSTM is better than recurrent neural network(RNN).The method’s feasibility was established,and the study provides theoretical support for guiding indoor air pollution control measures and ensuring human health and safety.

Identifying,exploring,and interpreting time series shapes in multivariate time intervals

We introduce a concept of episode referring to a time interval in the development of a dynamic phenomenon that is characterized by multiple time-variant attributes.A data structure representing a single episode is a multivariate time series.To analyse collections of episodes,we propose an approach that is based on recognition of particular patterns in the temporal variation of the variables within episodes.Each episode is thus represented by a combination of patterns.Using this representation,we apply visual analytics techniques to fulfil a set of analysis tasks,such as investigation of the temporal distribution of the patterns,frequencies of transitions between the patterns in episode sequences,and co-occurrences of patterns of different variables within same episodes.We demonstrate our approach on two examples using real-world data,namely,dynamics of human mobility indicators during the COVID-19 pandemic and characteristics of football team movements during episodes of ball turnover.

A Total Variation Based Method for Multivariate Time Series Segmentation

Multivariate time series segmentation is an important problem in data mining and it has arisen in more and more practical applications in recent years.The task of time series segmentation is to partition a time series into segments by detecting the abrupt changes or anomalies in the time series.Multivariate time series segmentation can provide meaningful information for further data analysis,prediction and policy decision.A time series can be considered as a piecewise continuous function,it is natural to take its total variation norm as a prior information of this time series.In this paper,by minimizing the negative log-likelihood function of a time series,we propose a total variation based model for multivariate time series segmentation.An iterative process is applied to solve the proposed model and a search combined the dynamic programming method is designed to determine the breakpoints.The experimental results show that the proposed method is efficient for multivariate time series segmentation and it is competitive to the existing methods for multivariate time series segmentation.

Multivariate Time Series Forecasting with Transfer Entropy Graph

Multivariate Time Series(MTS)forecasting is an essential problem in many fields.Accurate forecasting results can effectively help in making decisions.To date,many MTS forecasting methods have been proposed and widely applied.However,these methods assume that the predicted value of a single variable is affected by all other variables,ignoring the causal relationship among variables.To address the above issue,we propose a novel end-to-end deep learning model,termed graph neural network with neural Granger causality,namely CauGNN,in this paper.To characterize the causal information among variables,we introduce the neural Granger causality graph in our model.Each variable is regarded as a graph node,and each edge represents the casual relationship between variables.In addition,convolutional neural network filters with different perception scales are used for time series feature extraction,to generate the feature of each node.Finally,the graph neural network is adopted to tackle the forecasting problem of the graph structure generated by the MTS.Three benchmark datasets from the real world are used to evaluate the proposed CauGNN,and comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.

Exploring and visualizing temporal relations in multivariate time series

This paper introduces an approach to analyzing multivariate time series(MVTS)data through progressive temporal abstraction of the data into patterns characterizing the behavior of the studied dynamic phenomenon.The paper focuses on two core challenges:identifying basic behavior patterns of individual attributes and examining the temporal relations between these patterns across the range of attributes to derive higher-level abstractions of multi-attribute behavior.The proposed approach combines existing methods for univariate pattern extraction,computation of temporal relations according to the Allen’s time interval algebra,visual displays of the temporal relations,and interactive query operations into a cohesive visual analytics workflow.The paper describes the application of the approach to real-world examples of population mobility data during the COVID-19 pandemic and characteristics of episodes in a football match,illustrating its versatility and effectiveness in understanding composite patterns of interrelated attribute behaviors in MVTS data.

Rolling Iterative Prediction for Correlated Multivariate Time Series

Correlated multivariate time series prediction is an effective tool for discovering the chang rules of temporal data,but it is challenging tofind these rules.Recently,deep learning methods have made it possible to predict high-dimensional and complex multivariate time series data.However,these methods cannot capture or predict potential mutation signals of time series,leading to a lag in data prediction trends and large errors.Moreover,it is difficult to capture dependencies of the data,especially when the data is sparse and the time intervals are large.In this paper,we proposed a prediction approach that leverages both propagation dynamics and deep learning,called Rolling Iterative Prediction(RIP).In RIP method,the Time-Delay Moving Average(TDMA)is used to carry out maximum likelihood reduction on the raw data,and the propagation dynamics model is applied to obtain the potential propagation parameters data,and dynamic properties of the correlated multivariate time series are clearly established.Long Short-Term Memory(LSTM)is applied to capture the time dependencies of data,and the medium and long-term Rolling Iterative Prediction method is established by alternately estimating parameters and predicting time series.Experiments are performed on the data of the Corona Virus Disease 2019(COVID-19)in China,France,and South Korea.Experimental results show that the real distribution of the epidemic data is well restored,the prediction accuracy is better than baseline methods.

Simulating Temporally and Spatially Correlated Wind Speed Time Series by Spectral Representation Method

In this paper,it aims to model wind speed time series at multiple sites.The five-parameter Johnson mdistribution is deployed to relate the wind speed at each site to a Gaussian time series,and the resultant-Z(t)dimensional Gaussian stochastic vector process is employed to model the temporal-spatial correlation of mwind speeds at different sites.In general,it is computationally tedious to obtain the autocorrelation functions Z(t)(ACFs)and cross-correlation functions(CCFs)of Z(t),which are different to those of wind speed times series.In order to circumvent this correlation distortion problem,the rank ACF and rank CCF are introduced to Z(t)characterize the temporal-spatial correlation of wind speeds,whereby the ACFs and CCFs of can be analytically obtained.Then,Fourier transformation is implemented to establish the cross-spectral density matrix Z(t)mof,and an analytical approach is proposed to generate samples of wind speeds at different sites.Finally,simulation experiments are performed to check the proposed methods,and the results verify that the five-parameter Johnson distribution can accurately match distribution functions of wind speeds,and the spectral representation method can well reproduce the temporal-spatial correlation of wind speeds.

Multivariate time series imputation for energy data using neural networks

Multivariate time series with missing values are common in a wide range of applications,including energy data.Existing imputation methods often fail to focus on the temporal dynamics and the cross-dimensional correlation simultaneously.In this paper we propose a two-step method based on an attention model to impute missing values in multivariate energy time series.First,the underlying distribution of the missing values in the data is learned.This information is then further used to train an attention based imputation model.By learning the distribution prior to the imputation process,the model can respond flexibly to the specific characteristics of the underlying data.The developed model is applied to European energy data,obtained from the European Network of Transmission System Operators for Electricity.Using different evaluation metrics and benchmarks,the conducted experiments show that the proposed model is preferable to the benchmarks and is able to accurately impute missing values.

LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES

An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.

A multivariate grey incidence model for different scale data based on spatial pyramid pooling

In order to solve the problem that existing multivariate grey incidence models cannot be applied to time series on different scales, a new model is proposed based on spatial pyramid pooling.Firstly, local features of multivariate time series on different scales are pooled and aggregated by spatial pyramid pooling to construct n levels feature pooling matrices on the same scale. Secondly,Deng's multivariate grey incidence model is introduced to measure the degree of incidence between feature pooling matrices at each level. Thirdly, grey incidence degrees at each level are integrated into a global incidence degree. Finally, the performance of the proposed model is verified on two data sets compared with a variety of algorithms. The results illustrate that the proposed model is more effective and efficient than other similarity measure algorithms.

Latent ancestral graph of structure vector autoregressive models

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

LEARNING MULTIVARIATE TIME SERIES CAUSAL GRAPHS BASED ON CONDITIONAL MUTUAL INFORMATION

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis.This paper provides a method that employs both mutual information and conditional mutual information to identify the causal structure of multivariate time series causal graphical models.A three-step procedure is developed to learn the contemporaneous and the lagged causal relationships of time series causal graphs.Contrary to conventional constraint-based algorithm, the proposed algorithm does not involve any special kinds of distribution and is nonparametric.These properties are especially appealing for inference of time series causal graphs when the prior knowledge about the data model is not available.Simulations and case analysis demonstrate the effectiveness of the method.

Deep anomaly detection in horizontal axis wind turbines using GraphConvolutional Autoencoders for Multivariate Time series

Wind power is one of the fastest-growing renewable energy sectors instrumental in the ongoing decarbonizationprocess. However, wind turbines are subjected to a wide range of dynamic loads which can cause more frequentfailures and downtime periods, leading to ever-increasing attention to effective Condition Monitoring strategies.In this paper, we propose a novel unsupervised deep anomaly detection framework to detect anomalies in windturbines based on SCADA data. We introduce a promising neural architecture, namely a Graph ConvolutionalAutoencoder for Multivariate Time series, to model the sensor network as a dynamical functional graph. Thisstructure improves the unsupervised learning capabilities of Autoencoders by considering individual sensormeasurements together with the nonlinear correlations existing among signals. On this basis, we developeda deep anomaly detection framework that was validated on 12 failure events occurred during 20 months ofoperation of four wind turbines. The results show that the proposed framework successfully detects anomaliesand anticipates SCADA alarms by outperforming other two recent neural approaches.

The Analysis of Impact of Brexit on the Post-Brexit EU Using Intervented Multivariate Time Series

The UK is the most important partner of the EU in terms of economic and other fields due to the geographical proximity.It was one of the largest economies in the EU and its per capita income is higher than the EU average,so it is a net contributor to the EU.With UKs membership of the EU ended on 31 January 2019,there are concerns that the Brexit may have a significant impact on the EU,resulting in social,economic,political,and institutional changes,etc.in EU.While the impact of Brexit on the UK has always been the subject of considerable scholarly interest in recent years,there is relatively little literature on the impact of Brexit on the EU.This paper focuses on the evaluation of the impact of Brexit on the EU economy and other relevant aspects along three dimensions:GDP,PPP,Quarterly GDP growth.Employing powerful quantitative analysis technology that includes vector autoregression model,multivariate time series model with intervention variables,and autoregression integrated moving average,this paper obtains the important and novel evidence about the potential impact of Brexit on the EU economy,pointing out that Brexit is of far-reaching significance to the EU.This analysis uses several statistical models to screen out several key influencing factors,which can be used to predict the total GDP of EU in the next five years.The results show that EU economy will react negatively to"no-deal"Brexit,and its growth rate of economy will slow down significantly in next 5 years.Finally,we put forward relevant policy suggestions on how to deal with the negative impact of Brexit on EU.

A Hybrid Neural Network-based Approach for Forecasting Water Demand

Water is a vital resource.It supports a multitude of industries,civilizations,and agriculture.However,climatic conditions impact water availability,particularly in desert areas where the temperature is high,and rain is scarce.Therefore,it is crucial to forecast water demand to provide it to sectors either on regular or emergency days.The study aims to develop an accurate model to forecast daily water demand under the impact of climatic conditions.This forecasting is known as a multivariate time series because it uses both the historical data of water demand and climatic conditions to forecast the future.Focusing on the collected data of Jeddah city,Saudi Arabia in the period between 2004 and 2018,we develop a hybrid approach that uses Artificial Neural Networks(ANN)for forecasting and Particle Swarm Optimization algorithm(PSO)for tuning ANNs’hyperparameters.Based on the Root Mean Square Error(RMSE)metric,results show that the(PSO-ANN)is an accurate model for multivariate time series forecasting.Also,the first day is the most difficult day for prediction(highest error rate),while the second day is the easiest to predict(lowest error rate).Finally,correlation analysis shows that the dew point is the most climatic factor affecting water demand.

VAECGAN:a generating framework for long-term prediction in multivariate time series

Long-term prediction is still a difficult problem in data mining.People usually use various kinds of methods of Recurrent Neural Network to predict.However,with the increase of the prediction step,the accuracy of prediction decreases rapidly.In order to improve the accuracy of long-term prediction,we propose a framework Variational Auto-Encoder Conditional Generative Adversarial Network(VAECGAN).Our model is divided into three parts.The first part is the encoder net,which can encode the exogenous sequence into latent space vectors and fully save the information carried by the exogenous sequence.The second part is the generator net which is responsible for generating prediction data.In the third part,the discriminator net is used to classify and feedback,adjust data generation and improve prediction accuracy.Finally,extensive empirical studies tested with five real-world datasets(NASDAQ,SML,Energy,EEG,KDDCUP)demonstrate the effectiveness and robustness of our proposed approach.