Time Series Decomposition Method Research Articles

Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis

Abstract Various existed time-series decomposition methods, including wavelet transform, ensemble empirical mode decomposition (EEMD), local characteristic-scale decomposition (LCD), singular spectrum analysis (SSA), etc., have some defects for nonlinear system signal analysis. When the signal is more complex, especially noisy signal, the component signal is forced to decompose into several incomplete components by LCD and SSA. In addition, the wavelet transform and EEMD need user-defined parameters, and they are very sensitive to the parameters. Therefore, a new signal decomposition algorithm, symplectic geometry mode decomposition (SGMD), is proposed in this paper to decompose a time series into a set of independent mode components. SGMD uses the symplectic geometry similarity transformation to solve the eigenvalues of the Hamiltonian matrix and reconstruct the single component signals with its corresponding eigenvectors. Meanwhile, SGMD can efficiently reconstruct the existed modes and remove the noise without any user-defined parameters. The essence of this method is that signal decomposition is converted into symplectic geometry transformation problem, and the signal is decomposed into a set of symplectic geometry components (SGCs). The analysis results of simulation signals and experimental signals indicate that the proposed time-series decomposition approach can decompose the analyzed signals accurately and effectively.

Radiation situation dynamics at the Andreeva Bay site for temporary storage of spent nuclear fuel and radioactive waste over the period 2002–2016

The Coastal Technical Base (CTB) №569 at Andreeva Bay was established in the early 1960s and intended for the refueling of nuclear submarine reactors and temporary storage of spent nuclear fuel (SNF) and radioactive waste (RW). In 2001, the base was transferred to the Russian Ministry for Atomic Energy and the site remediation began. The paper describes in detail the radiation situation change at the technical site in Andreeva Bay from 2002–2016, the period of preparation for the most critical phase of remedial work: removal of spent fuel assemblies. The analysis of aggregated indicators and data mining were used. The article suggests the best number and location of checkpoints needed to ensure sufficient accuracy of the radiation situation description. The fractal properties of the radiation field are studied using the Hurst index. The relationship between checkpoints was assessed using the method of searching for checkpoint communities. The decrease in the integral of the ambient dose equivalent rate (ADER) at the technical site was evaluated by the method of time series decomposition. Three components of time series were identified: trend, seasonal and residual. The trend of the ADER integral over the technical site is a monotonic decreasing function, where the initial and final values differ tenfold. Taking into account that 137Cs dominates the radiation situation on-site, it is clear that the ADER due to the radionuclide decay will have decreased by 1.4 times. It is estimated that only a small proportion of 137Cs has migrated off-site. Therefore, approximately a sevenfold decrease in dose rate is mainly due to remediation activities of personnel. During the year, the seasonal component varies the ADER integral by a factor of two, due to snowfall. The residual component reflects the uncertainty of the ADER integral calculation and phases of active SNF and RW management. The methods developed are used to support the optimization of remediation work as well as regulatory supervision of occupational radiation protection.

Questioning the Influence of Sunspots on Amazon Hydrology: Even a Broken Clock Tells the Right Time Twice a Day

AbstractIt was suggested in a recent article that sunspots drive decadal variation in Amazon River flow. This conclusion was based on a novel time series decomposition method used to extract a decadal signal from the Amazon River record. We have extended this analysis back in time, using a new hydrological proxy record of tree ring oxygen isotopes (δ18OTR). Consistent with the findings of Antico and Torres, we find a positive correlation between sunspots and the decadal δ18OTR cycle from 1903 to 2012 (r = 0.60, p < 0.001). However, the relationship does not persist into the preceding century and even becomes weakly negative (r = −0.30, p = 0.11, 1799–1902). This result casts considerable doubt over the mechanism by which sunspots are purported to influence Amazon hydrology.

Non-oscillatory response to wind loading dominates movement of Scots pine trees

The response of four trees in a Scots pine (Pinus sylvestris L.) plantation to wind loading was studied using time series decomposition methods. For this purpose, wind speed and stem displacement time series recorded on a windy day were divided into intervals adjusted according to stem displacement. The real wind load acting on the sample trees during the intervals was estimated by the momentum flux at canopy top. To identify components in wind-induced stem displacement that are correlated with the wind, wavelet coherence was calculated. Results from these calculations indicate that the trees mainly responded to wind components with periods longer than their damped fundamental sway periods. Therefore, stem displacement data were decomposed into non-oscillatory and oscillatory components as well as noise using singular spectrum analysis. Results from singular spectrum analysis demonstrate that with increasing momentum flux, the importance of oscillatory components in the stem displacement time series decreases whereas the importance of non-oscillatory displacement components increases. The decreasing importance of the oscillatory components suggests that wind loading in the range of the damped fundamental sway period of the trees is inefficient and insignificant for total tree movement under non-destructive wind conditions. Consequently, there was no evidence of the occurrence of resonance effects between wind and tree response.

Stock composition of mutual funds and fund style: a time series decomposition approach towards testing for consistency

In this paper, we present a generic approach for checking the consistency between the proclaimed style of a mutual fund and the actual fund composition. We use a method of time series decomposition of stock prices to ascertain whether their inclusion in a particular style of fund is justified. It has been our contention that some share prices have a strong trend component in their time series, some show seasonality, while some share prices exhibit strong random component. We have chosen a sample of eleven equity- based mutual funds of varying styles, from Indian financial market and analyzed whether the style of the fund matches with the stock composition of the fund. We feel that the retail investors, who buy into certain funds on the basic trust that fund managers have the requisite expertise, should know whether the portfolio matches what they promise. A detailed analysis of the results show that, while in majority of cases the actual allocation of funds is consistent with the corresponding fund style, there have been some notable deviations too.

Stock composition of mutual funds and fund style: a time series decomposition approach towards testing for consistency

In this paper, we present a generic approach for checking the consistency between the proclaimed style of a mutual fund and the actual fund composition. We use a method of time series decomposition of stock prices to ascertain whether their inclusion in a particular style of fund is justified. It has been our contention that some share prices have a strong trend component in their time series, some show seasonality, while some share prices exhibit strong random component. We have chosen a sample of 11 equity-based mutual funds of varying styles, from Indian financial market and analysed whether the style of the fund matches with the stock composition of the fund. We feel that the retail investors, who buy into certain funds on the basic trust that fund managers have the requisite expertise, should know whether the portfolio matches what they promise. A detailed analysis of the results show that, while in majority of cases the actual allocation of funds is consistent with the corresponding fund style, there have been some notable deviations too.

Comparative study of three satellite image time-series decomposition methods for vegetation change detection

ABSTRACTSatellite image time-series (SITS) methods have contributed notably to detection of global change over the last decades, for instance by tracking vegetation changes. Compared with multi-temporal change detection methods, temporally highly resolved SITS methods provide more information in a single analysis, for instance on the type and consistency of change. In particular, SITS decomposition methods show a great potential in extracting various components from non-stationary time series, which allows for an improved interpretation of the temporal variability. Even though many case studies have applied SITS decomposition methods, a systematic comparison of common algorithms is still missing.In this study, the seasonal trend loess (STL), breaks for additive season and trend (BFAST) and multi-resolution analysis-wavelet transform (MRA-WT) were explored in order to evaluate their performance in modelling, monitoring and detecting land-cover changes with pronounced seasonal variations from simulated normal difference vegetation index time series. The selected methods have all proven their ability to characterize the non-stationary vegetation dynamics along with different physical processes driving the vegetation dynamics. Our results indicated that BFAST is the most accurate method for the examined simulated dataset in terms of RMSE, whereas MRA-WT showed a great potential for the extraction of multi-level vegetation dynamics. Considering the computational efficiency, both STL and MRA-WT outperformed BFAST.

Prediction of Oil Demand Based on Time Series Decomposition Method

The forecast of oil demand in large oil depot is the main basis for the allocation of oil and distribution. The accurate and efficient real-time forecast of oil demand is an important guarantee for the effective management and rational use of oil. In this paper, the amount of oil in and out of large oil depots is abstracted into time series model, and the main factors influencing the time series are extracted by time series decomposition method. The calculation process and the changing rules of these factors are studied, and the forecasting model of oil demand of large oil depot is constructed. The example shows that the time series decomposition method can realize the effective forecast of large oil depot demand.

Modeling and Extracting Load Intensity Profiles

Today’s system developers and operators face the challenge of creating software systems that make efficient use of dynamically allocated resources under highly variable and dynamic load profiles, while at the same time delivering reliable performance. Autonomic controllers, for example, an advanced autoscaling mechanism in a cloud computing context, can benefit from an abstracted load model as knowledge to reconfigure on time and precisely. Existing workload characterization approaches have limited support to capture variations in the interarrival times of incoming work units over time (i.e., a variable load profile). For example, industrial and scientific benchmarks support constant or stepwise increasing load, or interarrival times defined by statistical distributions or recorded traces. These options show shortcomings either in representative character of load variation patterns or in abstraction and flexibility of their format. In this article, we present the Descartes Load Intensity Model (DLIM) approach addressing these issues. DLIM provides a modeling formalism for describing load intensity variations over time. A DLIM instance is a compact formal description of a load intensity trace. DLIM-based tools provide features for benchmarking, performance, and recorded load intensity trace analysis. As manually obtaining and maintaining DLIM instances becomes time consuming, we contribute three automated extraction methods and devised metrics for comparison and method selection. We discuss how these features are used to enhance system management approaches for adaptations during runtime, and how they are integrated into simulation contexts and enable benchmarking of elastic or adaptive behavior. We show that automatically extracted DLIM instances exhibit an average modeling error of 15.2% over 10 different real-world traces that cover between 2 weeks and 7 months. These results underline DLIM model expressiveness. In terms of accuracy and processing speed, our proposed extraction methods for the descriptive models are comparable to existing time series decomposition methods. Additionally, we illustrate DLIM applicability by outlining approaches of workload modeling in systems engineering that employ or rely on our proposed load intensity modeling formalism.

Assessment and analysis of the chlorophyll-a concentration variability over the Vietnamese coastal waters from the MERIS ocean color sensor (2002–2012)

Spatio-temporal patterns of the chlorophyll-a concentration, Chla, have been assessed from the MEdium Resolution Imaging Spectrometer (MERIS) over the whole Vietnamese coastal waters from 2002 to 2012. For that purpose, six bio-optical algorithms already documented and based on different approaches have been tested over a large in situ data set collected at different seasons and locations along the Vietnamese coast. The OC5 algorithm (Gohin, Druon, and Lampert, 2002) presents the best performances and has been selected to assess Chla in the studied region. The notion of optimal bio-optical environment associated with the best performance of OC5 has been introduced. For suspended particulate matter concentration, SPM, lower than 100g·m−3, and colored dissolved organic matter, acdom(443), lower than 0.5m−1, Chla is estimated with an uncertainty of 36% and a bias of 5%. A Chla climatology has been generated and the temporal patterns (seasonal variability, long term trend, and irregular component) have been described using the Census-X-11 time series decomposition method. Three-dimensional hydrodynamical numerical simulations have been used to analyze the spatio-temporal patterns of Chla. The seasonal contribution dominates the variance of the signal, in good relationship with the dynamic of the mixed layer depth as well as with the occurrence of a seasonal upwelling induced by the summer monsoon. The irregular variability of Chla which may reach up to 35% of the total variance in the central part of the Vietnamese coast, can be explained through the surface kinetic energy and its standard deviation which is associated with small scales processes. A long term monotonic trend from about 2 to >5%·yr−1 (that is 20 to >50% from 2002 to 2012) have been noticed in different coastal areas where aquaculture activities exhibit a concurrence increase, ranging from 31% to 113% (in production weight) over the same time period. In situ measurements, and especially of nutrients, are however necessary to confirm the link between aquaculture activities and phytoplankton biomass long term evolutions.

Streamflow Prediction by Applying Generalized Regression Network with Time Series Decomposition Method

Precise and correct estimation of streamflow is important for the operative progression in water resources systems. The artificial intelligence approaches; such as artificial neural networks (ANN) have been applied for efficiently tackling the hydrological matters like streamflow forecasting in this study at upper Yangtze River. The objective is to investigate the certainty of monthly streamflow by applying artificial neural networks including Generalized Regression Network (GRNN). To overcome the non-linearity problem of streamflow, artificial neural networks integrated with discrete wavelet transform (DWT). Data has been analyzed by comparing the simulation outputs of the models with the correlation coefficient (R) root mean square errors (RMSE). It is found that the decomposition technique DWT has ability to improve the forecasting results as compare to single applied artificial neural networks. Moreover, all applied models are separately applies on the peak values as well which also have showed that intergrated model has more ability to catch the peak values

Variability of Ionospheric TEC and the Performance of the IRI-2012 Model at the BJFS Station, China

We studied variation characteristics of ionospheric total electron contents (TEC) and performance of the International Reference Ionosphere (IRI)-2012 model in predicting TEC at the BJFS (Beijing Fangshan station), China. Diurnal and seasonal variations were analyzed with TEC data derived from dual-frequency global positioning system (GPS) observations along with the solar activity dependence of TEC at the BJFS station. Data interpolated with information from IGS Global Ionosphere Maps (GIMs) were also used in the analysis. Results showed that the IRI-2012 model can reflect the climatic characteristics and solar activity dependence of ionospheric TEC. By using time series decomposition method, ionospheric daily averaged TEC values were divided into the periodic components, geomagnetic activity component, solar activity component and secular trend. Solar activity component and periodic components are supposed to be the main reasons which account for the difference between the GIMs TEC and the TEC from the IRI-2012 model.

Introduction to Time Series Analysis for Organizational Research

Organizational science has increasingly recognized the need for integrating time into its theories. In parallel, innovations in longitudinal designs and analyses have allowed these theories to be tested. To promote these important advances, the current article introduces time series analysis for organizational research, a set of techniques that has proved essential in many disciplines for understanding dynamic change over time. We begin by describing the various characteristics and components of time series data. Second, we explicate how time series decomposition methods can be used to identify and partition these time series components. Third, we discuss periodogram and spectral analysis for analyzing cycles. Fourth, we discuss the issue of autocorrelation and how different structures of dependency can be identified using graphics and then modeled as autoregressive moving-average (ARMA) processes. Finally, we conclude by describing more time series patterns, the issue of data aggregation, and more sophisticated techniques that were not able to be given proper coverage. Illustrative examples based on topics relevant to organizational research are provided throughout, and a software tutorial in R for these analyses accompanies each section.

Big Data Driven Mobile Traffic Understanding and Forecasting: A Time Series Approach

Understanding and forecasting mobile traffic of large scale cellular networks is extremely valuable for service providers to control and manage the explosive mobile data, such as network planning, load balancing, and data pricing mechanisms. This paper targets at extracting and modeling traffic patterns of 9,000 cellular towers deployed in a metropolitan city. To achieve this goal, we design, implement, and evaluate a time series analysis approach that is able to decompose large scale mobile traffic into regularity and randomness components. Then, we use time series prediction to forecast the traffic patterns based on the regularity components. Our study verifies the effectiveness of our utilized time series decomposition method, and shows the geographical distribution of the regularity and randomness component. Moreover, we reveal that high predictability of the regularity component can be achieved, and demonstrate that the prediction of randomness component of mobile traffic data is impossible.

Comparison of Two Time Series Decomposition Methods: Least Squares and Buys-Ballot Methods

This paper discusses comparison of two time series decomposition methods: The Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014), there exists a research gap for the choice of appropriate model for decomposition and detection of presence of seasonal effect in a series model. Estimates of trend parameters and seasonal indices are all that are needed to fill the research gap. However, these estimates are obtainable through the Least Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there is need to compare estimates of the two methods and recommend. The comparison of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE). The results from simulated series show that for the additive model; the summary statistics (ME, MSE and MAE) for the two estimation methods and for all the selected trending curves are equal in all the simulations both in magnitude and direction. For the multiplicative model, results show that when a series is dominated by trend, the estimates of the parameters by both methods become less precise and differ more widely from each other. However, if conditions for successful transformation (using the logarithmic transform in linearizing the multiplicative model to additive model) are met, both of them give similar results.

Forecasting of global horizontal irradiance by exponential smoothing, using decompositions

Time series methods are frequently used in solar irradiance forecasting when two dimensional cloud information provided by satellite or sky camera is unavailable. ETS (exponential smoothing) has received extensive attention in the recent years since the invention of its state space formulation. In this work, we combine these models with knowledge based heuristic time series decomposition methods to improve the forecasting accuracy and computational efficiency.In particular, three decomposition methods are proposed. The first method implements an additive seasonal-trend decomposition as a preprocessing technique prior to ETS. This can reduce the state space thus improve the computational efficiency. The second method decomposes the GHI (global horizontal irradiance) time series into a direct component and a diffuse component. These two components are used as forecasting model inputs separately; and their corresponding results are recombined via the closure equation to obtain the GHI forecasts. In the third method, the time series of the cloud cover index is considered. ETS is applied to the cloud cover time series to obtain the cloud cover forecast thus the forecast GHI through polynomial regressions. The results show that the third method performs the best among three methods and all proposed methods outperform the persistence models.

Statistical Prediction of the South China Sea Surface Height Anomaly

Based on the simple ocean data assimilation (SODA) data, this study analyzes and forecasts the monthly sea surface height anomaly (SSHA) averaged over South China Sea (SCS). The approach to perform the analysis is a time series decomposition method, which decomposes monthly SSHAs in SCS to the following three parts: interannual, seasonal, and residual terms. Analysis results demonstrate that the SODA SSHA time series are significantly correlated to the AVISO SSHA time series in SCS. To investigate the predictability of SCS SSHA, an exponential smoothing approach and an autoregressive integrated moving average approach are first used to fit the interannual and residual terms of SCS SSHA while keeping the seasonal part invariant. Then, an array of forecast experiments with the start time spanning from June 1977 to June 2007 is performed based on the prediction model which integrates the above two models and the time-independent seasonal term. Results indicate that the valid forecast time of SCS SSHA of the statistical model is about 7 months, and the predictability of SCS SSHA in Spring and Autumn is stronger than that in Summer and Winter. In addition, the prediction skill of SCS SSHA has remarkable decadal variability, with better phase forecast in 1997–2007.

Monitoring vegetation change and dynamics on U.S. Army training lands using satellite image time series analysis

Given the significant land holdings of the U.S. Department of Defense, and the importance of those lands to support a variety of inherently damaging activities, application of sound natural resource conservation principles and proactive monitoring practices are necessary to manage military training lands in a sustainable manner. This study explores a method for, and the utility of, analyzing vegetation condition and trends as sustainability indicators for use by military commanders and land managers, at both the national and local levels, in identifying when and where vegetation-related environmental impacts might exist. The BFAST time series decomposition method was applied to a ten-year MODIS NDVI time series dataset for the Fort Riley military installation and Konza Prairie Biological Station (KPBS) in northeastern Kansas. Imagery selected for time-series analysis were 16-day MODIS NDVI (MOD13Q1 Collection 5) composites capable of characterizing vegetation change induced by human activities and climate variability. Three indicators related to gradual interannual or abrupt intraannual vegetation change for each pixel were calculated from the trend component resulting from the BFAST decomposition. Assessment of gradual interannual NDVI trends showed the majority of Fort Riley experienced browning between 2001 and 2010. This result is supported by validation using high spatial resolution imagery. The observed versus expected frequency of linear trends detected at Fort Riley and KPBS were significantly different and suggest a causal link between military training activities and/or land management practices. While both sites were similar with regards to overall disturbance frequency and the relative spatial extents of monotonic or interrupted trends, vegetation trajectories after disturbance were significantly different. This suggests that the type and magnitude of disturbances characteristic of each location result in distinct post-disturbance vegetation responses. Using a remotely-sensed vegetation index time series with BFAST and the indicators outlined here provides a consistent and relatively rapid assessment of military training lands with applicability outside of grassland biomes. Characterizing overall trends and disturbance responses of vegetation can promote sustainable use of military lands and assist land managers in targeting specific areas for various rehabilitation activities.

Variability of suspended particulate matter concentration in coastal waters under the Mekong's influence from ocean color (MERIS) remote sensing over the last decade

Spatio-temporal patterns of suspended particulate matter, SPM, in coastal waters under the Mekong's influence are examined through remote sensing data collected from January 2003 to April 2012 by the MEdium Resolution Imaging Spectrometer (MERIS) at full spatial resolution (300×300m2). The first SPM climatology over this region is provided and the SPM temporal variation schemes (irregular variability, seasonal variability, and long term trend) are described using the Census-X-11 time series decomposition method. The different spatio-temporal patterns are then analyzed with regard to regional oceanographic and hydrologic conditions. The origin of the processes controlling the seasonality of the Mekong Delta plume is characterized. The increase of turbidity observed from June to December, starts with the Mekong sediment inputs which are maximum during the summer monsoon (the water discharge reaches its maximum in September/October). While the Mekong water discharge decreases, the concentration of suspended sediment keeps increasing in coastal waters during the following two/three months (November to January). This increase is explained by resuspension effects occurring in the shallow coastal areas. Due to higher wave energy and oblique orientation of the waves breaking near the coast, the winter monsoon triggers a high level of agitation and high value of resuspended material concentration which are submitted to a longshore current directed towards the South–West. Deposition (in front of the Delta) and erosion (northern and southern areas of the delta) areas are identified in good agreement with recent results obtained from a prognostic model. While the temporal variability is strongly dominated by the seasonal component, a long term trend of about −5% SPM concentration per year is observed in the pro-delta area and is attributed to the decrease of the Mekong river sediment output during the high flow season.

Dynamic linear models-based time series decomposition and its application on bearing fault diagnosis

Although various methods have been presented in the literature for rotating machine fault detection, it still remains a huge challenge to accurately extract features from non-stationary vibration signals with a high noise level, typically in the case of rolling element bearings faults diagnosis. Due to its random and non-stationary nature, fault related features are difficult to extract by common techniques and are usually overwhelmed by noise and macro-structural vibrations. In this paper, a new time series decomposition method based on a dynamic linear model is proposed, which provides time domain decomposition of a non-stationary signal into collections of latent components. The signal of a damaged bearing consists of exponentially decaying ringing that occurs periodically at the bearing characteristic defect frequency. Dynamic linear models with time-varying cyclical components provide a more generalized and adaptive description on rolling element bearings’ vibration signal with time-varying cyclical behavior. This allows the precise isolation of latent, quasi-cyclical bearing fault components via inferences on the time-varying parameters which characterize these components. An accelerated whole lifetime test of bearing has been performed to collect vibration data, which is utilized to validate the effectiveness of the proposed method.