Research on Short-Term Load Forecasting of Distribution Stations Based on the Clustering Improvement Fuzzy Time Series Algorithm

An improved fuzzy time series algorithmbased on clustering is designed in this paper.The algorithm is successfully applied to short-term load forecasting in the distribution stations.Firstly,the K-means clustering method is used to cluster the data,and the midpoint of two adjacent clustering centers is taken as the dividing point of domain division.On this basis,the data is fuzzed to form a fuzzy time series.Secondly,a high-order fuzzy relation with multiple antecedents is established according to the main measurement indexes of power load,which is used to predict the short-term trend change of load in the distribution stations.Matlab/Simulink simulation results show that the load forecasting errors of the typical fuzzy time series on the time scale of one day and one week are[−50,20]and[−50,30],while the load forecasting errors of the improved fuzzy time series on the time scale of one day and one week are[−20,15]and[−20,25].It shows that the fuzzy time series algorithm improved by clustering improves the prediction accuracy and can effectively predict the short-term load trend of distribution stations.

Time series clustering of COVID-19 pandemic-related data

The COVID-19 pandemic continues to impact daily life worldwide.It would be helpful and valuable if we could obtain valid information from the COVID-19 pandemic sequential data itself for characterizing the pandemic.Here,we aim to demonstrate that it is feasible to analyze the patterns of the pandemic using a time-series clustering approach.In this work,we use dynamic time warping distance and hierarchical clustering to cluster time series of daily new cases and deaths from different countries into four patterns.It is found that geographic factors have a large but not decisive influence on the pattern of pandemic development.Moreover,the age structure of the population may also influence the formation of cluster patterns.Our proven valid method may provide a different but very useful perspective for other scholars and researchers.

Relationship Between Urban Road Traffic Characteristics and Road Grade Based on a Time Series Clustering Model： A Case Study in Nanjing, China

With the increasing number of vehicles in large-and medium-sized cities challenges in urban traffic management, control, and road planning are being faced. Taxi GPS trajectory data is a novel data source that can be used to study the potential dynamic traffic characteristics of urban roads, and thus identify locations that show a notable lack of road planning. Considering that road traffic characteristics on their own are insufficient for a comprehensive understanding of urban traffic, we develop a road traffic characteristic time series clustering model to analyze the relationship between urban road traffic characteristics and road grade based on existing taxi trajectory data. We select the main urban area of Nanjing as our study area and use the taxi trajectory data of a single month for evaluating our method. The experiments show that the clustering model exhibit good performance and can be successfully used for road traffic characteristic classification. Moreover, we analyze the correlation between traffic characteristics and road grade to identify road segments with planning designs that do not match the actual traffic demands.

Massive feature extraction for explaining and foretelling hydroclimatic time series forecastability at the global scale

Statistical analyses and descriptive characterizations are sometimes assumed to be offering information on time series forecastability.Despite the scientific interest suggested by such assumptions,the relationships between descriptive time series features(e.g.,temporal dependence,entropy,seasonality,trend and linearity features)and actual time series forecastability(quantified by issuing and assessing forecasts for the past)are scarcely studied and quantified in the literature.In this work,we aim to fill in this gap by investigating such relationships,and the way that they can be exploited for understanding hydroclimatic forecastability and its patterns.To this end,we follow a systematic framework bringing together a variety of–mostly new for hydrology–concepts and methods,including 57 descriptive features and nine seasonal time series forecasting methods(i.e.,one simple,five exponential smoothing,two state space and one automated autoregressive fractionally integrated moving average methods).We apply this framework to three global datasets originating from the larger Global Historical Climatology Network(GHCN)and Global Streamflow Indices and Metadata(GSIM)archives.As these datasets comprise over 13,000 monthly temperature,precipitation and river flow time series from several continents and hydroclimatic regimes,they allow us to provide trustable characterizations and interpretations of 12-month ahead hydroclimatic forecastability at the global scale.We first find that the exponential smoothing and state space methods for time series forecasting are rather equally efficient in identifying an upper limit of this forecastability in terms of Nash-Sutcliffe efficiency,while the simple method is shown to be mostly useful in identifying its lower limit.We then demonstrate that the assessed forecastability is strongly related to several descriptive features,including seasonality,entropy,(partial)autocorrelation,stability,(non)linearity,spikiness and heterogeneity features,among others.We further(i)show that,if such descriptive information is available for a monthly hydroclimatic time series,we can even foretell the quality of its future forecasts with a considerable degree of confidence,and(ii)rank the features according to their efficiency in explaining and foretelling forecastability.We believe that the obtained rankings are of key importance for understanding forecastability.Spatial forecastability patterns are also revealed through our experiments,with East Asia(Europe)being characterized by larger(smaller)monthly temperature time series forecastability and the Indian subcontinent(Australia)being characterized by larger(smaller)monthly precipitation time series forecastability,compared to other continental-scale regions,and less notable differences characterizing monthly river flow from continent to continent.A comprehensive interpretation of such patters through massive feature extraction and feature-based time series clustering is shown to be possible.Indeed,continental-scale regions characterized by different degrees of forecastability are also attributed to different clusters or mixtures of clusters(because of their essential differences in terms of descriptive features).

Method of Time Series Similarity Measurement Based on Dynamic Time Warping

With the rapid development of mobile communication all over the world,the similarity of mobile phone communication data has received widely attention due to its advantage for the construction of smart cities.Mobile phone communication data can be regarded as a type of time series and dynamic time warping(DTW)and derivative dynamic time warping(DDTW)are usually used to analyze the similarity of these data.However,many traditional methods only calculate the distance between time series while neglecting the shape characteristics of time series.In this paper,a novel hybrid method based on the combination of dynamic time warping and derivative dynamic time warping is proposed.The new method considers not only the distance between time series,but also the shape characteristics of time series.We demonstrated that our method can outperform DTW and DDTW through extensive experiments with respect to cophenetic correlation.

Clustering-Inverse: A Generalized Model for Pattern-Based Time Series Segmentation

Patterned-based time series segmentation (PTSS) is an important task for many time series data mining applications. In this paper, according to the characteristics of PTSS, a generalized model is proposed for PTSS. First, a new inter-pretation for PTSS is given by comparing this problem with the prototype-based clustering (PC). Then, a novel model, called clustering-inverse model (CI-model), is presented. Finally, two algorithms are presented to implement this model. Our experimental results on artificial and real-world time series demonstrate that the proposed algorithms are quite effective.

Evolutionary Multi-Tasking Optimization for High-Efficiency Time Series Data Clustering

Time series clustering is a challenging problem due to the large-volume,high-dimensional,and warping characteristics of time series data.Traditional clustering methods often use a single criterion or distance measure,which may not capture all the features of the data.This paper proposes a novel method for time series clustering based on evolutionary multi-tasking optimization,termed i-MFEA,which uses an improved multifactorial evolutionary algorithm to optimize multiple clustering tasks simultaneously,each with a different validity index or distance measure.Therefore,i-MFEA can produce diverse and robust clustering solutions that satisfy various preferences of decision-makers.Experiments on two artificial datasets show that i-MFEA outperforms single-objective evolutionary algorithms and traditional clustering methods in terms of convergence speed and clustering quality.The paper also discusses how i-MFEA can address two long-standing issues in time series clustering:the choice of appropriate similarity measure and the number of clusters.

Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine

The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter gamma and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values.. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.

Wind power time series simulation model based on typical daily output processes and Markov algorithm

The simulation of wind power time series is a key process in renewable power allocation planning,operation mode calculation,and safety assessment.Traditional single-point modeling methods discretely generate wind power at each moment;however,they ignore the daily output characteristics and are unable to consider both modeling accuracy and efficiency.To resolve this problem,a wind power time series simulation model based on typical daily output processes and Markov algorithm is proposed.First,a typical daily output process classification method based on time series similarity and modified K-means clustering algorithm is presented.Second,considering the typical daily output processes as status variables,a wind power time series simulation model based on Markov algorithm is constructed.Finally,a case is analyzed based on the measured data of a wind farm in China.The proposed model is then compared with traditional methods to verify its effectiveness and applicability.The comparison results indicate that the statistical characteristics,probability distributions,and autocorrelation characteristics of the wind power time series generated by the proposed model are better than those of the traditional methods.Moreover,modeling efficiency considerably improves.

Integrated parallel forecasting model based on modified fuzzy time series and SVM

A dynamic parallel forecasting model is proposed, which is based on the problem of current forecasting models and their combined model. According to the process of the model, the fuzzy C-means clustering algorithm is improved in outliers operation and distance in the clusters and among the clusters. Firstly, the input data sets are optimized and their coherence is ensured, the region scale algorithm is modified and non-isometric multi scale region fuzzy time series model is built. At the same time, the particle swarm optimization algorithm about the particle speed, location and inertia weight value is improved, this method is used to optimize the parameters of support vector machine, construct the combined forecast model, build the dynamic parallel forecast model, and calculate the dynamic weight values and regard the product of the weight value and forecast value to be the final forecast values. At last, the example shows the improved forecast model is effective and accurate.

A Novel Parallel Scheme for Fast Similarity Search in Large Time Series

The similarity search is one of the fundamental components in time series data mining,e.g.clustering,classification,association rules mining.Many methods have been proposed to measure the similarity between time series,including Euclidean distance,Manhattan distance,and dynamic time warping(DTW).In contrast,DTW has been suggested to allow more robust similarity measure and be able to find the optimal alignment in time series.However,due to its quadratic time and space complexity,DTW is not suitable for large time series datasets.Many improving algorithms have been proposed for DTW search in large databases,such as approximate search or exact indexed search.Unlike the previous modified algorithm,this paper presents a novel parallel scheme for fast similarity search based on DTW,which is called MRDTW(MapRedcuebased DTW).The experimental results show that our approach not only retained the original accuracy as DTW,but also greatly improved the efficiency of similarity measure in large time series.

Unicast Network Topology Inference Algorithm Based on Hierarchical Clustering

Network topology inference is one of the important applications of network tomography.Traditional network topology inference may impact network normal operation due to its generation of huge data traffic.A unicast network topology inference is proposed to use time to live(TTL)for layering and classify nodes layer by layer based on the similarity of node pairs.Finally,the method infers logical network topology effectively with self-adaptive combination of previous results.Simulation results show that the proposed method holds a high accuracy of topology inference while decreasing network measuring flow,thus improves measurement efficiency.

A Parallel Approach to Discords Discovery in Massive Time Series Data

A discord is a refinement of the concept of an anomalous subsequence of a time series.Being one of the topical issues of time series mining,discords discovery is applied in a wide range of real-world areas(medicine,astronomy,economics,climate modeling,predictive maintenance,energy consumption,etc.).In this article,we propose a novel parallel algorithm for discords discovery on high-performance cluster with nodes based on many-core accelerators in the case when time series cannot fit in the main memory.We assumed that the time series is partitioned across the cluster nodes and achieved parallelization among the cluster nodes as well as within a single node.Within a cluster node,the algorithm employs a set of matrix data structures to store and index the subsequences of a time series,and to provide an efficient vectorization of computations on the accelerator.At each node,the algorithm processes its own partition and performs in two phases,namely candidate selection and discord refinement,with each phase requiring one linear scan through the partition.Then the local discords found are combined into the global candidate set and transmitted to each cluster node.Next,a node performs refinement of the global candidate set over its own partition resulting in the local true discord set.Finally,the global true discords set is constructed as intersection of the local true discord sets.The experimental evaluation on the real computer cluster with real and synthetic time series shows a high scalability of the proposed algorithm.

Enhancing Time Series Clustering by Incorporating Multiple Distance Measures with Semi-Supervised Learning

Time series clustering is widely applied in various areas. Existing researches focus mainly on distance measures between two time series, such as dynamic time warping （DTW） based methods, edit-distance based methods, and shapelets-based methods. In this work, we experimentally demonstrate, for the first time, that no single distance measure performs significantly better than others on clustering datasets of time series where spectral clustering is used. As such, a question arises as to how to choose an appropriate measure for a given dataset of time series. To answer this question, we propose an integration scheme that incorporates multiple distance measures using semi-supervised clustering. Our approach is able to integrate all the measures by extracting valuable underlying information for the clustering. To the best of our knowledge, this work demonstrates for the first time that the semi-supervised clustering method based on constraints is able to enhance time series clustering by combining multiple distance measures. Having tested on clustering various time series datasets, we show that our method outperforms individual measures, as well as typical integration approaches.

Wind and Photovoltaic Power Time Series Data Aggregation Method Based on an Ensemble Clustering and Markov Chain

Reducing the input wind and photovoltaic power time series data can improve the efficiency of time sequential simulations.In this paper,a wind and photovoltaic power time series data aggregation method based on an ensemble clustering and Markov chain(ECMC)is proposed.The ECMC method can effectively reduce redundant information in the data.First,the wind and photovoltaic power time series data were divided into scenarios,and ensemble clustering was used to cluster the divided scenarios.At the same time,the Davies-Bouldin Index(DBI)is adopted to select the optimal number of clusters.Then,according to the temporal correlation between wind and photovoltaic scenarios,the wind and photovoltaic clustering results are merged and reduced to form a set of combined typical day scenarios that can reflect the characteristics of historical data within the calculation period.Finally,based on the Markov Chain,the state transition probability matrix of various combined typical day scenarios is constructed,and the aggregation state sequence of random length is generated,and then,the combined typical day scenarios of wind and photovoltaic were sampled in a sequential one-way sequence according to the state sequence and then are built into a representative wind and photovoltaic power time series aggregation sequence.A provincial power grid was chosen as an example to compare the multiple evaluation indexes of different aggregation methods.The results show that the ECMC aggregation method improves the accuracy and efficiency of time sequential simulations.

The Multisource Time Series Data Granularity Conversion Method

Granular information has emerged as a potent tool for data represen-tation and processing across various domains.However,existing time series data granulation techniques often overlook the influence of external factors.In this study,a multisource time series data granularity conversion model is proposed that achieves granularity conversion effectively while maintaining result consis-tency and stability.The model incorporates the impact of external source data using a multivariate linear regression model,and the entropy weighting method is employed to allocate weights andfinalize the granularity conversion.Through experimental analysis using Beijing’s 2022 air quality dataset,our proposed method outperforms traditional information granulation approaches,providing valuable decision-making insights for industrial system optimization and research.

Individual and combination approaches to forecasting hierarchical time series with correlated data:an empirical study

Hierarchical time series arise in manufacturing and service industries when the products or services have the hierarchical structure,and top-down and bottomup methods are commonly used to forecast the hierarchical time series.One of the critical factors that affect the performance of the two methods is the correlation between the data series.This study attempts to resolve the problem and shows that the top-down method performs better when data have high positive correlation compared to high negative correlation and combination of forecasting methods may be the best solution when there is no evidence of the correlationship.We conduct the computational experiments using 240 monthly data series from the‘Industrial’category of the M3-Competition and test twelve combination methods for the hierarchical data series.The results show that the regression-based,VAR-COV and the Rank-based methods perform better compared to the other methods.

Clustering Structure Analysis in Time-Series Data With Density-Based Clusterability Measure

Clustering is used to gain an intuition of the struc tures in the data.Most of the current clustering algorithms pro duce a clustering structure even on data that do not possess such structure.In these cases,the algorithms force a structure in the data instead of discovering one.To avoid false structures in the relations of data,a novel clusterability assessment method called density-based clusterability measure is proposed in this paper.I measures the prominence of clustering structure in the data to evaluate whether a cluster analysis could produce a meaningfu insight to the relationships in the data.This is especially useful in time-series data since visualizing the structure in time-series data is hard.The performance of the clusterability measure is evalu ated against several synthetic data sets and time-series data sets which illustrate that the density-based clusterability measure can successfully indicate clustering structure of time-series data.

Feature selection for energy system modeling: Identification of relevant time series information

Heuristic or clustering based time series aggregation methods are often used to reduce temporal complexity of energy system models by selecting representative days.However,these methods potentially neglect relevant information of time series(e.g.,distribution parameters).To identify relevant time series parameters,feature selection algorithms can be applied.The present research contributes by(a)developing a new feature selection approach based on clustering,nested modeling and regression(CNR)which is designed for applications requiring high selectivity and using different data sets,(b)comparing and evaluating CNR with feature selection methods available from the literature(e.g.,LASSO)and(c)identifying relevant information of the time series applied in energy system models,in particular those of demand,photovoltaic and wind.Results show that CNR achieves on average up to 101%lower mean absolute errors when methods are directly compared.Thus,CNR better identifies relevant information when the number of selected features is restricted.The disadvantage of CNR,however,is its high computational effort.A potential remedy to counter this is the combination with another method(e.g.,as pre-feature selection).In terms of relevant information,energy systems including photovoltaic are mainly characterized by the correlation between demand and photovoltaic time series as well as the range and the 35%quantile of demand.When energy systems include wind power,the minimum and mean of wind as well as the correlation between demand and wind time series are relevant characteristics.The implications of these findings are discussed.

A Fuzzy Time Series Model Based on Improved Fuzzy Function and Cluster Analysis Problem

Based on the improvement in establishing the relations of data,this study proposes a new fuzzy time series model.In this model,the suitable number of fuzzy sets and their specific elements are determined automatically.In addition,using the percentage variations of series between consecutive periods of time,we build the fuzzy function.Incorporating all these improvements,we have a new fuzzy time series model that is better than many existing ones through the well-known data sets.The calculation of the proposed model can be performed conveniently and efficiently by a MATLAB procedure.The proposed model is also used in forecasting for an urgent problem in Vietnam.This application also shows the advantages of the proposed model and illustrates its effectiveness in practical application.