Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

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.

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.

Dynamic Ensemble Multivariate Time Series Forecasting Model for PM2.5

In forecasting real time environmental factors,large data is needed to analyse the pattern behind the data values.Air pollution is a major threat towards developing countries and it is proliferating every year.Many methods in time ser-ies prediction and deep learning models to estimate the severity of air pollution.Each independent variable contributing towards pollution is necessary to analyse the trend behind the air pollution in that particular locality.This approach selects multivariate time series and coalesce a real time updatable autoregressive model to forecast Particulate matter(PM)PM2.5.To perform experimental analysis the data from the Central Pollution Control Board(CPCB)is used.Prediction is car-ried out for Chennai with seven locations and estimated PM’s using the weighted ensemble method.Proposed method for air pollution prediction unveiled effective and moored performance in long term prediction.Dynamic budge with high weighted k-models are used simultaneously and devising an ensemble helps to achieve stable forecasting.Computational time of ensemble decreases with paral-lel processing in each sub model.Weighted ensemble model shows high perfor-mance in long term prediction when compared to the traditional time series models like Vector Auto-Regression(VAR),Autoregressive Integrated with Mov-ing Average(ARIMA),Autoregressive Moving Average with Extended terms(ARMEX).Evaluation metrics like Root Mean Square Error(RMSE),Mean Absolute Error(MAE)and the time to achieve the time series are compared.

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.

Generic reconstruction technology based on RST for multivariate time series of complex process industries

In order to effectively analyse the multivariate time series data of complex process,a generic reconstruction technology based on reduction theory of rough sets was proposed,Firstly,the phase space of multivariate time series was originally reconstructed by a classical reconstruction technology.Then,the original decision-table of rough set theory was set up according to the embedding dimensions and time-delays of the original reconstruction phase space,and the rough set reduction was used to delete the redundant dimensions and irrelevant variables and to reconstruct the generic phase space,Finally,the input vectors for the prediction of multivariate time series were extracted according to generic reconstruction results to identify the parameters of prediction model.Verification results show that the developed reconstruction method leads to better generalization ability for the prediction model and it is feasible and worthwhile for application.

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.

Volatility in High-Frequency Intensive Care Mortality Time Series: Application of Univariate and Multivariate GARCH Models

Mortality time series display time-varying volatility. The utility of statistical estimators from the financial time-series paradigm, which account for this characteristic, has not been addressed for high-frequency mortality series. Using daily mean-mortality series of an exemplar intensive care unit (ICU) from the Australian and New Zealand Intensive Care Society adult patient database, joint estimation of a mean and conditional variance (volatility) model for a stationary series was undertaken via univariate autoregressive moving average (ARMA, lags (p, q)), GARCH (Generalised Autoregressive Conditional Heteroscedasticity, lags (p, q)). The temporal dynamics of the conditional variance and correlations of multiple provider series, from rural/ regional, metropolitan, tertiary and private ICUs, were estimated utilising multivariate GARCH models. For the stationary first differenced series, an asymmetric power GARCH model (lags (1, 1)) with t distribution (degrees-of- freedom, 11.6) and ARMA (7,0) for the mean-model, was the best-fitting. The four multivariate component series demonstrated varying trend mortality decline and persistent autocorrelation. Within each MGARCH series no model specification dominated. The conditional correlations were surprisingly low (<0.1) between tertiary series and substantial (0.4 - 0.6) between rural-regional and private series. The conditional-variances of both the univariate and multivariate series demonstrated a slow rate of time decline from periods of early volatility and volatility spikes.

Research on Pattern Matching Method of Multivariate Hydrological Time Series

The existing pattern matching methods of multivariate time series can hardly measure the similarity of multivariate hydrological time series accurately and efficiently.Considering the characteristics of multivariate hydrological time series,the continuity and global features of variables,we proposed a pattern matching method,PP-DTW,which is based on dynamic time warping.In this method,the multivariate time series is firstly segmented,and the average of each segment is used as the feature.Then,PCA is operated on the feature sequence.Finally,the weighted DTW distance is used as the measure of similarity in sequences.Carrying out experiments on the hydrological data of Chu River,we conclude that the pattern matching method can effectively describe the overall characteristics of the multivariate time series,which has a good matching effect on the multivariate hydrological time series.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

Computational Method for Extracting and Modeling Periodicities in Time Series

Periodicity is common in natural processes, however, extraction tools are typically difficult and cumbersome to use. Here we report a computational method developed in MATLAB through a function called Periods with the aim to find the main harmonic components of time series data. This function is designed to obtain the period, amplitude and lag phase of the main harmonic components in a time series (Periods and lag phase components can be related to climate, social or economic events). It is based on methods of periodic regression with cyclic descent and includes statistical significance testing. The proposed method is very easy to use. Furthermore, it does not require full understanding of time series theory, nor require many inputs from the user. However, it is sufficiently flexible to undertake more complex tasks such as forecasting. Additionally, based on previous knowledge, specific periods can be included or excluded easily. The output results are organized into two groups. One contains the parameters of the adjusted model and their F statistics. The other consists of the harmonic parameters that best fit the original series according to their importance and the summarized statistics of the comparisons between successive models in the cyclic descent process. Periods is tested with both, simulated and actual sunspot and Multivariate ENSO Index data to show its performance and accuracy.

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.

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.

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.

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.

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.

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.

Oil–water two-phase flow pattern analysis with ERT based measurement and multivariate maximum Lyapunov exponent

Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.