Single Time Series Research Articles

Estimating Permutation Entropy Variability via Surrogate Time Series.

In the last decade permutation entropy (PE) has become a popular tool to analyze the degree of randomness within a time series. In typical applications, changes in the dynamics of a source are inferred by observing changes of PE computed on different time series generated by that source. However, most works neglect the crucial question related to the statistical significance of these changes. The main reason probably lies in the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty. In this paper we propose a method to overcome this issue by using generation of surrogate time series. The analysis conducted on both synthetic and experimental time series shows the reliability of the approach, which can be promptly implemented by means of widely available numerical tools. The method is computationally affordable for a broad range of users.

Cohesive parcellation of the human brain using resting-state fMRI

BackgroundThe data burden for resting-state fMRI analysis rises with increasing resolutions available at ultrahigh fields. Therefore, a fundamental preprocessing step in brain network analysis is to reduce the data, usually by performing some kind of data parcellation. Most functional parcellations based on rsfMRI connectivity are synthesized from the dense connectome. In contrast, most network analyses begin by reducing each parcel to a single exemplar time series. This disconnect between parcel formation and usage assumes that parcel exemplars adequately represent their member voxels, which is not always the case for commonly used parcellations. New methodWe propose to parcellate the brain based on parcel cohesion, a measure of similarity between a parcel’s exemplar and its member voxels. A spatially constrained agglomerative hierarchical framework is used to synthesize parcels based on a minimum cohesion threshold, rather than a predetermined number of parcels. ResultsCohesive parcellation generally results in more parcels than existing approaches. The number of parcels scales with the amount of smoothing in preprocessing, yet retains adequate information to extract common intrinsic functional networks. Comparison with previous methodsCohesive parcellation performs better than several widely used anatomical, functional, and data-driven parcellations on the basis of parcel cohesion and comparably using several traditional measures of cluster validity. ConclusionCohesive parcellation ensures that the way parcels are synthesized directly corresponds to the way they are used in subsequent analyses. The resulting parcels are straightforward to interpret and optimal for downstream analysis.

Damage detection on the blade of an operating wind turbine via a single vibration sensor and statistical time series methods: Exploring the performance limits of robust methods

The study aims at damage detection on the blade of an operating Vestas V27 wind turbine via a single vibration response sensor under varying Environmental and Operating Conditions (EOCs), and through this, at exploring the performance limits of robust vibration-based Statistical Time Series type methods. Three trailing edge progressive, 15 cm, 30 cm, and 45 cm long, damage scenarios are examined using signals from a 104-day-long measurement campaign. The study is based on three robust methods: an Unsupervised Principal Component Analysis AutoRegressive model–based (U-PCA-AR) method, an Unsupervised Multiple Model AutoRegressive model–based (U-MM-AR) method, and an Unsupervised Principal Component Analysis Multiple Model AutoRegressive model–based (U-PCA-MM-AR) method. Comparisons with a nominal Unsupervised AutoRegressive model–based (U-AR) method and an 8-sensor–based method are also reported. The results of the study are based on a systematic and thorough assessment procedure using 7000 inspection experiments and confirm that single-sensor-based detection is indeed feasible via the aforementioned robust methods, with the best performance achieved by the U-PCA-MM-AR method which reaches up to 100% True Positive Rate at 4%, 1%, and 0% False Positive Rate for the 15, 30, and 45 cm damage scenarios, respectively. This performance is on par with that of the 8-sensor–based method and indicative of the high capabilities offered by the robust vibration-based Statistical Time Series type methods. The sensitivity of the methods with respect to the sensor location and the AutoRegressive model order is also examined.

Review of load forecasting based on artificial intelligence methodologies, models, and challenges

Accurate load forecasting can efficiently reduce the day-ahead dispatch stress of power system or microgrid. The overview of load forecasting based on artificial intelligence models are comprehensively summarized in this paper. As the steps of load forecasting based on artificial intelligence model mainly include data processing, setting up forecasting strategy and model forecasting, the paper firstly reviewed the data processing studies. According to the kinds of data obtained, the data can be classified into two categories: multivariate time series and single variate time series. Secondly the forecasting methodologies including one-step forecasting and rolling forecasting are summarized and compared. In addition, according to the form of the prediction results, point prediction, interval prediction and probability prediction are summarized. Thirdly, the paper reviews the artificial intelligence models used in load forecasting. In light of the application scenarios, it can be classified into single model and combination model. Finally, we also discussed the future trend for the research, such as fuzzy reasoning, intelligent optimization in forecasting, novel machine learning and transfer learning technologies, etc.

The North Atlantic Oscillations: Lead–Lag Relations for the NAO, the AMO, and the AMOC—A High-Resolution Lead–lag Analysis

Several studies examine cycle periods and the interactions between the three major climate modes over the North Atlantic, namely the Atlantic meridional overturning circulation (AMOC), the Atlantic multidecadal oscillation (AMO), and the North Atlantic oscillation (NAO). Here, we use a relatively novel high-resolution Lead–lag (LL) method to identify short time windows with persistent LL relations in the three series during the period from 1947 to 2020. We find that there are roughly 20-year time windows where LL relations change direction at both interannual, high-frequency and multidecadal, low-frequency timescales. However, with varying LL strength, the AMO leads AMOC for the full period at the interannual timescale. During the period from 1980 to 2000, we had the sequence NAO→AMO→AMOC→NAO at the interannual timescale. For the full period in the decadal time scale, we obtain NAO→AMO→AMOC. The Ekman variability closely follows the NAO variability. Both single time series and the LL relation between pairs of series show pseudo-oscillating patterns with cycle periods of about 20 years. We list possible mechanisms that contribute to the cyclic behavior, but no conclusive evidence has yet been found.

Toward Precise Localization of Abnormal Brain Activity: 1D CNN on Single Voxel fMRI Time-Series.

Functional magnetic resonance imaging (fMRI) is one of the best techniques for precise localization of abnormal brain activity non-invasively. Machine-learning approaches have been widely used in neuroimaging studies; however, few studies have investigated the single-voxel modeling of fMRI data under cognitive tasks. We proposed a hybrid one-dimensional (1D) convolutional neural network (1D-CNN) based on the temporal dynamics of single-voxel fMRI time-series and successfully differentiated two continuous task states, namely, self-initiated (SI) and visually guided (VG) motor tasks. First, 25 activation peaks were identified from the contrast maps of SI and VG tasks in a blocked design. Then, the fMRI time-series of each peak voxel was transformed into a temporal-frequency domain by using continuous wavelet transform across a broader frequency range (0.003–0.313 Hz, with a step of 0.01 Hz). The transformed time-series was inputted into a 1D-CNN model for the binary classification of SI and VG continuous tasks. Compared with the univariate analysis, e.g., amplitude of low-frequency fluctuation (ALFF) at each frequency band, including, wavelet-ALFF, the 1D-CNN model highly outperformed wavelet-ALFF, with more efficient decoding models [46% of 800 models showing area under the curve (AUC) > 0.61] and higher decoding accuracies (94% of the efficient models), especially on the high-frequency bands (>0.1 Hz). Moreover, our results also demonstrated the advantages of wavelet decompositions over the original fMRI series by showing higher decoding performance on all peak voxels. Overall, this study suggests a great potential of single-voxel analysis using 1D-CNN and wavelet transformation of fMRI series with continuous, naturalistic, steady-state task design or resting-state design. It opens new avenues to precise localization of abnormal brain activity and fMRI-guided precision brain stimulation therapy.

Forecasting Multiple Groundwater Time Series with Local and Global Deep Learning Networks.

Time series data from environmental monitoring stations are often analysed with machine learning methods on an individual basis, however recent advances in the machine learning field point to the advantages of incorporating multiple related time series from the same monitoring network within a ‘global’ model. This approach provides the opportunity for larger training data sets, allows information to be shared across the network, leading to greater generalisability, and can overcome issues encountered in the individual time series, such as small datasets or missing data. We present a case study involving the analysis of 165 time series from groundwater monitoring wells in the Namoi region of Australia. Analyses of the multiple time series using a variety of different aggregations are compared and contrasted (with single time series, subsets, and all of the time series together), using variations of the multilayer perceptron (MLP), self-organizing map (SOM), long short-term memory (LSTM), and a recently developed LSTM extension (DeepAR) that incorporates autoregressive terms and handles multiple time series. The benefits, in terms of prediction performance, of these various approaches are investigated, and challenges such as differing measurement frequencies and variations in temporal patterns between the time series are discussed. We conclude with some discussion regarding recommendations and opportunities associated with using networks of environmental data to help inform future resource-related decision making.

Optimized time series data clustering method for NN network

Time series data is a common sort of data that can be found in a variety of fields. Clustering time series data has a wide range of uses and has drawn scholars from several fields. A unique approach for shape-based time series clustering is proposed in this research. Using the complex network principle, it may reduce the bulk of data, enhance efficiency, and not reduce the effects. To begin, a one-nearest neighbour network is constructed using time series items that are comparable. The similarity is measured in this step using the triangle distance. Each node in the neighbour network represents a single time series object, whereas each connection indicates a neighbour relationship between nodes. Second, high-degree nodes are selected and used to cluster. Dynamic time warping distance function and hierarchical clustering algorithm are used in the clustering process. Finally, several studies are carried out using both synthetic and actual data. The findings demonstrate that the suggested approach is both efficient and effective.

건물에너지시스템 센서 네트워크에서의 백업 가상센서 성능 향상을 위한 시계열 데이터 다운스케일링 방법

Building system sensor networks measure and collect various information in buildings. Virtual sensors provide enormous potentials for improving and supplementing physical sensor-based building sensor networks. Virtual sensors are developed upon data collected from the sensor network and used for observation, backup, and prediction of system variables. A virtual sensor is a model which learns mathematical relations among input data to output the required variable. In this regard, aggregating various heterologous data (data fusion) has been important to obtain high-performance virtual sensors containing well-learned inner structures. However, fusing different data into single time series can be a difficult task due to the different sensing periods (data resolution). In this paper, a novel relational variable-based data downscaling method is suggested to tackle the limitations on building system data fusion. The effectiveness of the proposed method was evaluated with real operational datasets. The suggested method improved the performance of the virtual sensor by 30.2%.

Is purchasing powerparity hypothesis valid in ghana? an empirical assessment

The paper examines the theory of Purchasing Power Parity (PPP) hypothesis to determine whether the hypothesis is valid for Ghana for the period 1960 to 2013, by employing the Augmented Dickey-Fuller (ADF) test and the Kwiatkwski, Phillips, Schmidt and Shin (KPSS) test on a single time series data to test the unit root properties of the real exchange rate (Official exchange rate).It is found that the real exchangerate hasa unit root or are non-stationary in levels. The findings suggest that the purchasing power parity hypothesis is not valid for the period under discussion.

State space reconstruction techniques and the accuracy of prediction

If the data is dominated by deterministic dynamics, then a one-dimensional measurement of a single observable is sufficient to essentially reconstruct a potentially multidimensional state portrait of the entire governing dynamics. Our goal in this study was to find out which method of reconstruction is best to choose when the criterion is the quality of prediction of the studied observable. Several methods of reconstructing the state space portrait from a single time series were tested: uniform, non-uniform and weighted delay coordinates, an approach using principal components, and Xu’s differential reconstruction. In addition to predictability, we also evaluated the accuracy of estimating the complexity of a reconstructed attractor by a correlation dimension. We found that the numerical estimates of the correlation dimension were practically the same using different reconstructions. The prediction, on the other hand, was significantly influenced by the type of reconstruction. When trying to predict as accurately as possible, it is worth considering weighted delay coordinates, or approximations of derivatives instead of the standard uniform time delay embedding.

Temperature control load-regulation strategy based on multi-dimensional state queue method

The development of temperature control load is inevitable for people to improve the quality of life, but it has the same characteristics as the output of wind power generation, that is, randomness and intermittence. Therefore, the continuous access of temperature control load has an unprecedented challenge to the stability of power grid. However, the instability of the power grid caused by the input of wind power can be balanced by the temperature control load acting on the power grid. The research direction of this paper is the regulation of temperature controlled load household air source heat pump equipment on the power grid on the load side, which is constrained by meeting the user’s comfort. It is intended to achieve the goal of cutting peak and filling valley for the power grid side and reducing the wind rejection rate. The user side gets the economic compensation to cooperate with the power grid dispatching. At the same time, the power grid side improves the economic benefits by reducing the peak valley difference and reducing the occurrence of fan suspension. The main research contents are as follows: the thermodynamic equivalent model of single air source heat pump is established, and the aggregation model is established combined with Monte Carlo method. The simulation analysis shows that the air source heat pump group can participate in the regulation of load side; Using the prediction model of wind power based on meta learning, combined with single time series model and single linear regression model, the wind power is reasonably predicted; The multi-dimensional state queue method is used to improve the load characteristics and reduce the air rejection rate on the premise of meeting the user comfort; This paper expounds the distribution network level load regulation system, establishes the hierarchical load control structure, and makes the two-way interaction between the family compliance control system and the power grid a reality. In order to study the influence of user selection on regulation effect, according to the differences of user needs, we established three regulation strategies. Scheme A can achieve the most ideal regulation effect, and scheme B is slightly worse than scheme A. The most ideal control effect parameters can be obtained by scheme A, and the worst control effect parameters can be obtained by scheme C. Comparing the regulation effect parameters after scheme a and scheme C, based on the parameters of scheme C, the peak valley difference of scheme A is reduced by 18.30%, the peak to average ratio is reduced by 17.61% and the load variance is reduced by 18.12%. It is proved that the user can reduce the peak valley difference by using scheme A. Comparing the regulation effect parameters after scheme B and scheme C, compared with scheme C, the peak valley difference of scheme B is reduced by 11.80%, the peak to average ratio is reduced by 11.81%, and the load variance is reduced by 14.77%. It is proved that the regulation effect of scheme B can be reduced, but the effect is not as good as scheme A.

On the theory of random decrement

In this paper, we will give a short overview of the theory of the random decrement (RD) technique invented around 1970 by Henry Cole for structural response analysis, and introduced in the seventies as part of the Ibrahim time domain identification technique. The RD technique introduced by Cole and Ibrahim was an algorithm with uncertain meaning until Vandiver et al. and later Brincker et al. presented the theory of the RD functions as conditional expectations of the responses. Since the potential of seeing the RD functions as a conditional expectation, seem to remain un-released after 30–40 years of their ideas, we want in this paper to give an overview of the major findings. First, we will present a general framework for the theory of RD, and then we will use this to re-introduce the work of Vandiver in a simple way to obtain the theoretical solution for the level triggering condition for a single time series. We then generalize Vandiver’s result to the cross RD case where we are averaging on one time series and applying the condition to another time series. For this case, we obtain the general result of the RD function being proportional to the cross correlation function between the two considered signals. Finally, we consider the general triggering condition, where we are conditioning on both the signal itself and on its derivative, to obtain the so-called fundamental solution, where the RD function turns out to be a linear combination of the cross correlation function and its derivative. Finally, we will discuss different application issues, and illustrate how the fundamental solution can be used for identification taking advantage of the extended information from the derivative of the cross correlation function.

Prediction of Spot Price of Iron Ore Based on PSR-WA-LSSVM Combined Model

Aiming at the problems that the existing single time series models are not accurate and robust enough when it comes to forecasting the iron ore prices and the parameters of the traditional LSSVM model are difficult to determine, we propose a combined model based on Phase Space Reconstruction (PSR), wavelet transform and LSSVM (PSR-WA-LSSVM) to tackle these issues. ARIMA model, LSTM model, PSR-LSSVM model, and PSR-WA-LSSVM models were used for contrast simulation to forecast the spot price data of 61.5%PB powder from January 30, 2019, to February 1, 2021, in Ningbo Zhoushan port. The experimental results show that the PSR-WA-LSSVM combination model achieves better prediction results. At the same time, the model has a good performance in the multistep prediction of the iron ore price.

Missing Data Imputation in GNSS Monitoring Time Series Using Temporal and Spatial Hankel Matrix Factorization

GNSS time series for static reference stations record the deformation of monitored targets. However, missing data are very common in GNSS monitoring time series because of receiver crashes, power failures, etc. In this paper, we propose a Temporal and Spatial Hankel Matrix Factorization (TSHMF) method that can simultaneously consider the temporal correlation of a single time series and the spatial correlation among different stations. Moreover, the method is verified using real-world regional 10-year period monitoring GNSS coordinate time series. The Mean Absolute Error (MAE) and Root-Mean-Square Error (RMSE) are calculated to compare the performance of TSHMF with benchmark methods, which include the time-mean, station-mean, K-nearest neighbor, and singular value decomposition methods. The results show that the TSHMF method can reduce the MAE range from 32.03% to 12.98% and the RMSE range from 21.58% to 10.36%, proving the effectiveness of the proposed method.

Ground reaction forces and external hip joint moments predict in vivo hip contact forces during gait

Younger patients increasingly receive total hip arthroplasty (THA) as therapy for end-stage osteoarthritis. To maintain the long-term success of THA in such patients, avoiding extremely high hip loads, i.e., in vivo hip contact force (HCF), is considered essential. However, in vivo HCFs are difficult to determine and their direct measurement is limited to instrumented joint implants. It remains unclear whether external measurements of ground reaction forces (GRFs), a non-invasive, markerless and clinic-friendly measure can estimate in vivo HCFs. Using data from eight patients with instrumented hip implants, this study determined whether GRF time series data, alone or combined with other scalar variables such as hip joint moments (HJMs) and lean muscle volume (LMV), could predict the resultant HCF (rHCF) impulse using a functional linear modeling approach. Overall, single GRF time series data did not predict in vivo rHCF impulses. However, when GRF time series data were combined with LMV of the gluteus medius or sagittal HJM using a functional linear modeling approach, the in vivo rHCF impulse could be predicted from external measures only. Accordingly, this approach can predict in vivo rHCF impulses, and thus provide patients with useful insight regarding their gait behavior to avoid hip joint overloading.

Generalized ordinal patterns allowing for ties and their applications in hydrology

When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appears permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to overcome this problem. Often, time periods with constant values even have been counted as times of monotone increase. However, ties can contain valuable information which is disregarded by all of these approaches. To overcome this, a new approach is proposed: it explicitly allows for ties and, hence, considers more patterns than before. Ties are no longer seen as nuisance, but the information they carry is taken into account explicitly. Limit theorems in the new framework are provided, both, for a single time series and for the dependence between two time series. The methods are applied to hydrological data sets. In hydrology, it is common to distinguish five flood classes (plus ‘absence of flood’). Considering data vectors of these classes at a certain gauge in a river basin, one will usually encounter several ties. Co-monotonic behavior between the data sets of two gauges (increasing, constant, decreasing) can be detected by the method as well as spatial patterns. Thus, it helps to analyze the strength of dependence between different gauges in an intuitive way. This knowledge can be used to assess risk and to plan future construction projects.

Classification of Alzheimer’s Disease and Mild-Cognitive Impairment Base on High-Order Dynamic Functional Connectivity at Different Frequency Band

Functional brain connectivity networks obtained from resting-state functional magnetic resonance imaging (rs-fMRI) have been extensively utilized for the diagnosis of Alzheimer’s disease (AD). However, the traditional correlation analysis technique only explores the pairwise relation, which may not be suitable for revealing sufficient and proper functional connectivity links among brain regions. Additionally, previous literature typically focuses on only lower-order dynamics, without considering higher-order dynamic networks properties, and they particularly focus on single frequency range time series of rs-fMRI. To solve these problems, in this article, a new diagnosis scheme is proposed by constructing a high-order dynamic functional network at different frequency level time series (full-band (0.01–0.08 Hz); slow-4 (0.027–0.08 Hz); and slow-5 (0.01–0.027 Hz)) data obtained from rs-fMRI to build the functional brain network for all brain regions. Especially, to tune the precise analysis of the regularized parameters in the Support Vector Machine (SVM), a nested leave-one-out cross-validation (LOOCV) technique is adopted. Finally, the SVM classifier is trained to classify AD from HC based on these higher-order dynamic functional brain networks at different frequency ranges. The experiment results illustrate that for all bands with a LOOCV classification accuracy of 94.10% with a 90.95% of sensitivity, and a 96.75% of specificity outperforms the individual networks. Utilization of the given technique for the identification of AD from HC compete for the most state-of-the-art technology in terms of the diagnosis accuracy. Additionally, results obtained for the all-band shows performance further suggest that our proposed scheme has a high-rate accuracy. These results have validated the effectiveness of the proposed methods for clinical value to the identification of AD.

MarineTools.temporal: A Python package to simulate Earth and environmental time series

The assessment of the uncertainty about the evolution of complex processes usually requires different realizations consisting of multivariate temporal signals of environmental data. However, it is common to have only one observational set. MarineTools.temporal is an open-source Python package for the non-stationary parametric statistical analysis of vector random processes suitable for environmental and Earth modelling. It takes a single timeseries of observations and allows the simulation of many time series with the same probabilistic behavior. The software generalizes the use of piecewise and compound distributions with any number of arbitrary continuous distributions. The code contains, among others, multi-model negative log-likely functions, wrapped-normal distributions, and generalized Fourier timeseries expansion. Its programming philosophy significantly improves the computing time and makes it compatible with future extensions of scipy.stats. We apply it to the analysis of freshwater river discharge, water currents, and the simulation of ensemble projections of sea waves, to show its capabilities.

Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity

This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain connectivity inferences from a homogeneous group of subjects or discovering network differences among groups of signals collected under heterogeneous conditions. By recognizing that the GC of a single multivariate time series can be characterized by common zeros of vector autoregressive (VAR) lag coefficients, a group sparse prior is included in joint regularized least-squares estimations of multiple VAR models. Group-norm regularizations based on group- and fused-lasso penalties encourage a decomposition of multiple networks into a common GC structure, with other remaining parts defined in individual-specific networks. Prior information about sparseness and sparsity patterns of desired GC networks are incorporated as relative weights, while a non-convex group norm in the penalty is proposed to enhance the accuracy of network estimation in low-sample settings. Extensive numerical results on simulations illustrated our method’s improvements over existing sparse estimation approaches on GC network sparsity recovery. Our methods were also applied to available resting-state fMRI time series from the ADHD-200 data sets to learn the differences of causality mechanisms, called effective brain connectivity, between adolescents with ADHD and typically developing children. Our analysis revealed that parts of the causality differences between the two groups often resided in the orbitofrontal region and areas associated with the limbic system, which agreed with clinical findings and data-driven results in previous studies.