Autoregressive Moving Average Method Research Articles

Generation and validation of comprehensive synthetic weather histories using auto-regressive moving-average models

As energy system design moves to more complex methods of optimisation including machine learning there is a significant need for more weather data than is available. One method to solve this is using synthetic data models such as the auto-regressive moving-average (ARMA) model which has been frequently utilised to create such data. This paper looks at extending the ARMA algorithm to generate solar components through the use of clearsky detrending, maintaining vector relationships and by leveraging physical relationships. The method for the creation of entirely synthetic weather data files including key weather variables for energy system analysis is presented. Furthermore, a detailed comparison of energy system simulations utilising both real and synthetic data is made using NREL’s System Advisor Model. Whilst good agreement is made for the solar variables, and other weather variables, ARMA methods often fail to capture the standard deviation and skew of annual weather distributions. Vector-ARMA is shown to maintain correlations between variables and thus generate data sets that perform similarly in energy system design. It is finally shown that the ARMA method fails to preserve day-today correlations in weather variables and thus over-predicts optimal energy storage by 21% for a residential solar application.

A method for compensating random errors in MEMS gyroscopes based on interval empirical mode decomposition and ARMA

The random error in micro-electro-mechanical systems (MEMS) gyroscopes is one of the major aspects that limit measurement accuracy. In order to address the inaccurate extraction of noise and trend during the signal preprocessing, as well as the subjectivity in autoregressive moving average (ARMA) model ordering, this paper proposes a method based on interval empirical mode decomposition and ARMA model. In the proposed method, the original signal is decomposed into a series of intrinsic mode functions (IMFs) and a residual through empirical mode decomposition (EMD). Based on the Hellinger distance and autocorrelation function, IMFs are then classified into noise IMFs, hybrid IMFs, and signal IMFs. The improved sand cat swarm optimization is utilized to optimize the ordering process of the ARMA model. The improved adaptive filter is adopted to compensate the random error, and the compensated signal is reconstructed with the signal IMFs and residual to obtain the final output. Experiments show that under static conditions, the proposed method could reduce the root mean square error (RMSE) by 52.6% and 33.3%, respectively, compared with the traditional EMD and ARMA methods. Under dynamic conditions, the proposed method could reduce the RMSE by 51.1% and 37.1%, respectively, compared with the traditional EMD and ARMA methods. The proposed method could effectively compensate the random error and improve the measurement accuracy of MEMS gyroscopes.

In praise of Prais-Winsten: An evaluation of methods used to account for autocorrelation in interrupted time series.

Interrupted time series are increasingly being used to assess the population impact of public health interventions. These data are usually correlated over time (auto correlated) and this must be accounted for in the analysis. Typically, this is done using either the Prais-Winsten method, the Newey-West method, or autoregressive-moving-average (ARMA) modeling. In this paper, we illustrate these methods via a study of pneumococcal vaccine introduction and explore their performance under 20 simulated autocorrelation scenarios with sample sizes ranging between 20 and 300. We show that in terms of mean square error, the Prais-Winsten and ARMA methods perform best, while in terms of coverage the Prais-Winsten method generally performs better than other methods. All three methods are unbiased. As well as having good statistical properties, the Prais-Winsten method is attractive because it is decision-free and produces a single measure of autocorrelation that can be compared between studies and used to guide sample size calculations. We would therefore encourage analysts to consider using this simple method to analyze interrupted time series.

Crop yield prediction in agriculture based on climatic conditions and ground water level prediction for southern regions

The main aim of this project is to predict the rainfall ,ground water level and temperature for next ten years to predict the crop yield. The prediction of crop yield based on previous years downfall, temperature and ground water level results in taking necessary steps to improve crop yield in future years.Understanding crop yield can help ensure food security and reduce impacts of climate change. Crops are sensitive to various weather phenomena such as temperature, weather and rainfall. Therefore, it becomes crucial to incorporate these features when predicting the yield of a crop. Forecasting is a complicated process. In this work, ARMA (Auto Regressive Moving Average) method is employed to forecast crop yield. Past ten years of knowledge set is taken for temperature, rainfall and ground water level for our country. Moreover, classification of downfall, temperature and ground water level data set records is done using ANN approach to predict the model for future test record data sets. It will be helpful in analyzing crop yield in the past and so as to predict the future levels.

Multistage Model Predictive Control Co-Risk Dispatch for Coupled Electricity and Heat System

The energy transition can facilitate the rapid development of the coupled electricity and heat system (CEHS), accommodating the higher share of renewable energy. However, uncertain renewable energy sources (RESs) and overlimit risk can bring significant challenges for the safe operation of the CEHS. Considering uncertain RESs integration and overlimit risk within the upper and lower bounds jointly with high probability, the multistage model predictive control (MPC) co-risk dispatch model for the CEHS can be proposed in this paper. The model can hedge against the operational risk for the multistage rolling dispatch. In the context of the multistage real-time risk dispatch, the MPC framework is presented, which contains three processes, autoregressive moving average (ARMA) model prediction process, risk-based optimization process, and penalty-based feedback correction process. In the prediction process, the ARMA method can be employed to accurately predict the RESs power, which is characterized as the merit of the short-term forecast. In the optimization process, the violation risk of overlimit chance constraints caused by the output power fluctuation can be mitigated using the distributionally robust chance-constrained (DRCC) under the Wasserstein ambiguity set. The tractable approximation reformulation can be obtained by adopting the Worst-Case Conditional Value-at-Risk (WC-CVaR) approximation method. In the feedback correction process, penalty-based load shedding and RESs spillage can lower the risk level by minimizing the risk penalty cost. In the numerical case, the risk performance analysis based on the modified Barry Island system is implemented. The analysis demonstrates that the daily average violation probability $V_{p}$ can be mainly affected by the Wasserstein radius $\rho $ while the total cost $C_{obj}$ can be affected by the violation probability $\varepsilon $ . The dispatch energy for the CEHS is obtained using the proposed approach, which outperforms the existing robust optimization (RO) approach.

Statistical analysis and ARMA modeling for the big data of marathon score

Summary Aims Statistical analysis for the big data of marathon score. Methods Taking the Boston Marathon as an example and using statistical analysis, this paper studies the distribution of all players’ performances in 2001–2018 from the multiple perspectives of age, gender and digital statistics in the context of big data. A series of valuable information and research conclusions that are instructive for the organizers and participants of the event are obtained. Then an autoregressive moving average (ARMA) model for the statistics of male and female entrants’ average finishing time is established and the ARMA model has excellent explanation and prediction ability for the marathon average result. The statistical analysis and modeling method of big data for marathon results proposed in this paper based on Boston can also be extended to other cities and events. In addition, the ARMA method can also be used to model other marathon statistics according to the needs of researchers.

A New Ionospheric Model for Single Frequency GNSS User Applications Using Klobuchar Model Driven by Auto Regressive Moving Average (SAKARMA) Method Over Indian Region

The single-frequency users of Global Navigation Satellite System (GNSS) require an effective mathematical model that mitigate the dominant errors due to ionospheric delays. Klobuchar model approximately reduces ionospheric effect up to 50% through its coefficients in the navigation message, which is not sufficient for the GNSS single frequency users at critical applications. Hence, a new model, for Single Frequency GNSS User Applications using Klobuchar model driven by Auto Regressive Moving Average Method (SAKARMA) is proposed to forecast and enhance the precision of ionospheric delay estimations for GNSS users. The hourly VTEC maps are obtained from the Assimilated Indian Regional Vertical Total Electron Content (AIRAVAT) by the process of data assimilation using the Kalman filter exclusively for the Indian region (longitude: 65°E to 100°E; latitude: 5°N to 40°N) using 26 GPS TEC stations over Indian region. The accuracy of the SAKARMA model is investigated using the AIRAVAT maps for various Indian geographic regions during both geomagnetic quiet and disturbed conditions of September month in 2016 year. Furthermore, in order to test SAKARMA model, a dual-frequency Navigation with Indian Constellation (NavIC) receiver located at the KL Education Foundation, Guntur, India (geographic: 16.37°N, 80.37°E; geomagnetic: 7.44°N, 153.75°E) is used to collect the observations during 2 - 12 September 2017. Furthermore, SAKARMA model is also validated with Klobuchar model, Klobuchar-style coefficients provided by the Center for Orbit Determination in Europe (CODE) (CODKlob) Model, BeiDou System (BDS2) Model and NeQuick 2 Model over a low latitude NavIC station in forecasting the ionospheric delays. The experimental results of SAKARMA for NavIC have revealed that the MAPE for proposed SAKARMA model is 9-17% (accuracy: 83-91%), while 34-53% (accuracy: 47-66%) for the Klobuchar model. Thus, the results illustrate that the proposed SAKARMA model is capable of predicting the ionospheric delays for single frequency GNSS/NavIC users.

Wind-Tunnel Study of the Autoregressive Moving-Average Flutter Prediction Method

This paper presents an experimental study of flutter prediction via autoregressive moving-average (ARMA) system identification and the use of a linear stability parameter. System identification at subcritical (preflutter) conditions is based on measured structural responses to excitation by natural air turbulence. The current study investigates the application aspects of the methodology in a dedicated wind-tunnel experiment. An elastic wing was designed and manufactured using rapid prototyping and tested in a subsonic wind tunnel all the way to flutter. Structural responses were recorded by accelerometers, strain gauges, and fiber-optic sensors (measuring strains). The data were filtered, averaged, and used for system identification and flutter prediction. The study focuses on the prediction characteristics and accuracy, method applicability with various dynamic data, and signal processing techniques. It was shown that both accelerations and strains provide good data for system identification and accurate flutter prediction, even when sparse and short records are used. Averaging significantly improves the flutter onset prediction and its confidence bounds. The study results support the feasibility of using the ARMA method for flutter flight test.

State of Health Estimation for Lithium-ion Batteries Based on Fusion of Autoregressive Moving Average Model and Elman Neural Network

This paper proposes a fusion model based on the autoregressive moving average (ARMA) model and Elman neural network (NN) to achieve accurate prediction for the state of health (SOH) of lithium-ion batteries. First, the voltage and capacity degradation variation of the battery are acquired through the battery lifecycle data, and the health factor related to the battery aging is selected according to the variation of the voltage profile. Second, the empirical mode decomposition (EMD) is employed to process the capacity degradation data and eliminate the phenomenon of tiny capacity recovery, and multiple data sequences, as well as the related residue, are extracted, then the grey relational analysis (GRA) between sub-sequences and health factor are discussed. Furthermore, the ARMA model and Elman NN model are respectively built by training the subsequent time series data and residue data. Finally, all the individual predictions are combined to generate the estimated SOH sequences. The experimental validation is performed to manifest that the addressed fusion method performs the SOH prediction with satisfactory accuracy, compared with the single ARMA method and Elman NN model.

Crustal deformation and strain analysis in Nepal from GPS time-series measurement and modeling by ARMA method

High-precision Global Positioning System (GPS) measurements from 2002 to 2017 in Nepal has been analyzed and modeled with Autoregressive Moving Average (ARMA) method. The measured velocities of the GPS sites in ITRF-2014 indicate ~ 6–12 mm/year N–S convergence inside the Nepal between India and Tibet. This convergence occurs in the southern and western border of Nepal, but it is negligible to the eastern border of Nepal. ARMA-modeled result of India-fixed velocities is able to successfully model (within ~ 0.5 mm/year) the current measured velocities in Nepal. Synthetic or modeled velocities using ARMA method and measured velocity have difference ~ 2 mm/year at some sites. This indicates the possibility of very small level of a ductile deformation. In the present best-fit ARMA model, the modeled velocities ~ 8–10 mm/year convergence taken up from northern to southern boundaries of Nepal indicates slip along active Main Himalayan Thrust (MHT) which is the cause of change in tectonic strain and may be able to trigger earthquakes inside the country. Dislocation modeling of active MHT is also carried out in the study using GPS vertical displacement. The geometric model of the MHT is characterized by a rectangular plane with dip angle of 9.5° and the reverse kinematics with a slip of 19 mm/year. The thrust is located at a depth of 20 km. In addition, the regional deformation of the Nepal has been checked by baseline measurement and coordinate stability of GPS sites for the different zones. The baseline divergence and convergence of nearest GPS sites have been tested using triangular sites. The summary of regional deformation implies N–S convergence only and rules out any type of E–W convergence. Finally, the investigation of observed and modeled strain confirms that there is no significant strain accumulation due to localized regional deformation or earthquakes specific to the active dislocations and faults. This suggests that the convergence from northern to southern boundaries of Nepal is associated with the slip along the MHT only.

COMPARING TIME SERIES FORECASTING METHODS TO ESTIMATE WIND SPEED IN KIRIKKALE REGION

Due to the non-storable nature of electric energy, short-term and long-term electricity generation and consumption forecast are critical to keeping electricity market in balance. In addition, the production estimate of wind energy is parallel to the estimate of wind speed. Since wind speed forecasts includes seasonal and time-dependent trends, time series forecasting methods produce successful results in wind energy forecasting. However, choosing the most appropriate time series forecasting method for short-term and long-term production forecasts is of special importance. In this study, short-term and long-term wind speed estimations were made for the wind turbine at Kirikkale University by using Exponential Smoothing (ES) and ARMA (Auto Regressive Moving Average) methods. The most suitable methods for forecasting short-term and long-term wind speed have been determined with the obtained results.

Assessment of Advanced Flutter Flight-Test Techniques and Flutter Boundary Prediction Methods

The paper presents an experimental study, conducted by the Israel Air Force, aimed at the assessment of several advanced flutter flight-test techniques that are designed to improve the efficiency and accuracy of flutter tests. These include the autoregressive moving-average and operational modal analysis system identification methods, the use of various system stability parameters, and the use of atmospheric turbulence versus prescribed flaperon motion as the source of structural response excitation. The methods are evaluated based on data from a dedicated transonic flight test of the F-16 platform. All of the tested methods are able to accurately predict the instability onset. The operational modal analysis method has the advantage that it does not require a priori knowledge of the instability mechanism, whereas the autoregressive moving-average method is easier to implement and straightforward to use in real time. Excitation by atmospheric turbulence is found to be adequate in the current test case, in which the modes are lightly damped and highly suitable for system identification methods that rely on stochastic inputs. The use of autoregressive moving-average and operational modal analysis methods based on responses to atmospheric turbulence appears to offer an accurate and cost-effective flutter testing methodology.

A Two-Factor Autoregressive Moving Average Model Based on Fuzzy Fluctuation Logical Relationships

Many of the existing autoregressive moving average (ARMA) forecast models are based on one main factor. In this paper, we proposed a new two-factor first-order ARMA forecast model based on fuzzy fluctuation logical relationships of both a main factor and a secondary factor of a historical training time series. Firstly, we generated a fluctuation time series (FTS) for two factors by calculating the difference of each data point with its previous day, then finding the absolute means of the two FTSs. We then constructed a fuzzy fluctuation time series (FFTS) according to the defined linguistic sets. The next step was establishing fuzzy fluctuation logical relation groups (FFLRGs) for a two-factor first-order autoregressive (AR(1)) model and forecasting the training data with the AR(1) model. Then we built FFLRGs for a two-factor first-order autoregressive moving average (ARMA(1,m)) model. Lastly, we forecasted test data with the ARMA(1,m) model. To illustrate the performance of our model, we used real Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Dow Jones datasets as a secondary factor to forecast TAIEX. The experiment results indicate that the proposed two-factor fluctuation ARMA method outperformed the one-factor method based on real historic data. The secondary factor may have some effects on the main factor and thereby impact the forecasting results. Using fuzzified fluctuations rather than fuzzified real data could avoid the influence of extreme values in historic data, which performs negatively while forecasting. To verify the accuracy and effectiveness of the model, we also employed our method to forecast the Shanghai Stock Exchange Composite Index (SHSECI) from 2001 to 2015 and the international gold price from 2000 to 2010.

Coordination of energy storage systems and DR resources for optimal scheduling of microgrids under uncertainties

Wind energy integration into microgrids, has introduced new challenges to energy management systems because of its intermittent behaviour. Owing to continuous changes in generation and consumption, the energy price is volatile. This study proposes a new two-stage stochastic framework for day-ahead scheduling of microgrids. Uncertainties associated to wind power generation, real-time electricity price and load demand are considered. Different scenarios are generated using autoregressive moving-average method and then are reduced using fast-forward technique. On the first stage, the microgrid master controller determines the procured energy from the day-ahead market and commitment states of distributed energy resources (DERs). In the second stage, the purchased energy from the real-time market and schedules of committed DERs are obtained. The problem is modelled using mixed-integer linear programming approach and is solved via CPLEX® optimizer. Both grid-connected and stand-alone modes of operation are investigated. Despite of high operation cost in island mode, coordination of energy storage systems, incentive-based and price-based demand response (DR) programmes affect economy of microgrids. The framework is examined on a test microgrid. Results show that both of the releasing the microgrid master controller authority and DR resources result in significant saving in operating; especially in emergency conditions such as islanded mode.

Comparison of autoregressive moving average and state space methods for monthly time series modelling of Labrador and South-East Quebec river flows

Time series data such as monthly stream flows can be modelled using time series methods and then used to simulate or forecast flows for short term planning. Two methods of time series modelling were reviewed and compared: the well-known auto regressive moving average (ARMA) method and the state-space time-series (SSTS) method. ARMA has been used in hydrology to model and simulate flows with good results and is widely accepted for this purpose. SSTS modelling is a more recently developed method that is relatively unused for hydrologic modelling. This paper focuses on modelling the stream flows from basins of different sizes using these two time series modelling methods and comparing the results. Three rivers in Labrador and South-East Quebec were modelled: the Romaine, Ugjoktok and Alexis Rivers. Both models were compared for accuracy of prediction, ease of software use and simplicity of model to determine the preferred time series methodology approach for modelling these rivers. The SSTS was considered very easy to use but model diagnostics were found to require a high level of statistical understanding. Ultimately, the ARMA method was determined to be the better method for the typical engineer to use, considering the diagnostics were simple and the monthly flows could be easily simulated to verify results.

ARMA Prediction of SBAS Ephemeris and Clock Corrections for Low Earth Orbiting Satellites

For low earth orbit (LEO) satellite GPS receivers, space-based augmentation system (SBAS) ephemeris/clock corrections can be applied to improve positioning accuracy in real time. The SBAS correction is only available within its service area, and the prediction of the SBAS corrections during the outage period can extend the coverage area. Two time series forecasting models, autoregressive moving average (ARMA) and autoregressive (AR), are proposed to predict the corrections outside the service area. A simulated GPS satellite visibility condition is applied to the WAAS correction data, and the prediction accuracy degradation, along with the time, is investigated. Prediction results using the SBAS rate of change information are compared, and the ARMA method yields a better accuracy than the rate method. The error reductions of the ephemeris and clock by the ARMA method over the rate method are 37.8% and 38.5%, respectively. The AR method shows a slightly better orbit accuracy than the rate method, but its clock accuracy is even worse than the rate method. If the SBAS correction is sufficiently accurate comparing with the required ephemeris accuracy of a real-time navigation filter, then the predicted SBAS correction may improve orbit determination accuracy.

Estimation of Electromechanical Modes from Ambient PMU Data in China Southern Power Grid

Online estimation of electromechanical oscillation modes using ambient PMU data is adopted for monitoring the China Southern Power Grid (CSG). After some preprocessing steps, the ambient PMU data is processed by ARMA (Autoregressive Moving average) method, different identification results are obtained from multiple PMU sites. Then by utilization of a clustering method, oscillation modes representing the system operating conditions are derived. In this paper, we report on the preliminary results in CSG and restriction on the ambient data usage is explained. Application of ambient data analysis for oscillation event study is also proposed to judge the oscillation type by comparing the estimated damping ratio value before and during ringdown period. Some suggestions on further ambient data analysis study are also discussed.

Detection of obstructive sleep apnea by estimation of oral and nasal cavity cross-section areas from acoustic recordings of snore

Obstructive sleep apnea (OSA) refers to the condition in which a person’s breathing is paused while asleep, or the airflow is decreased, due to obstruction in the upper respiratory airway. In severe cases, OSA can cause complete arousals and deprive the patient from normal sleep. Surgical intervention is sometimes recommended, but accurate identification of the site of obstruction can be difficult. In the present study, we devised signal processing methods to estimate the site and the severity of airflow obstruction from recordings of sounds of snore. The vocal tract, the oral and the nasal cavity are modeled as three branches joining at the pharynx. Each branch consists of cylindrical segments whose cross-section areas can vary during snoring. Estimation of these cross-section areas consists of two steps: First, an auto-regressive moving-average method is applied to find the linear coefficients of a pole-zero model that optimally accounts for the recorded sound. Then, the Levinson-Durbin algorithm is applied to convert the coefficients to ratios of cross-section areas between adjacent segments. The present method is applied to a set of recorded snore samples during clinically confirmed apnea episodes, and results are compared with those of simple snore. Effectiveness of the method is analyzed statistically.

Automated T2* measurements using supplementary field mapping to assess cardiac iron content

To develop and evaluate an algorithm that automatically identifies high-susceptibility areas and excludes them from T(2) * measurements in the left ventricle (LV) for myocardial iron measurements. An autoregressive moving average (ARMA) model was implemented on multigradient echo scans of 24 patients (age range 3-45 years, 10 male/14 female). Voxels with relatively high susceptibility (>3 Hz/mm) were flagged and deselected from the T(2) * calculations for iron quantification. The mean, standard deviation, and coefficient of variation (CoV) of the ARMA-defined region were compared to the CoV of four distinct regions of the LV and the entire LV using a Student's t-test (α = 0.05). The CoV of T(2) * values obtained by the ARMA method are comparable with that in the interventricular septum (IS), where susceptibility was the lowest (CoV = 0.31). The ARMA method provides a greater area (51.9 ± 13.7% of the LV) to measure T(2) * than that using the IS alone (21.1 ± 3.4%, P < 0.0001). Areas where low susceptibility are measured corroborate with areas reported in previous studies that investigated T(2) * variations throughout the LV. An automated method to measure T(2) * relaxation in the LV with minimal effects from susceptibility has been developed. Variability is reduced while covering more regions for cardiac T2 * calculation.

Stochastic prediction of fatigue loading using real-time monitoring data

Accurate characterization and prediction of loading, while properly accounting for uncertainty, are essential for probabilistic fatigue damage prognosis. Three different techniques – rainflow counting, the Markov chain method, and autoregressive moving average (ARMA) modeling – are investigated for stochastic characterization and reconstruction of the fatigue load history. The ARMA method is extended in this paper by introducing random coefficients and probabilistic weights, to account for the uncertainty in the selection of the model, inherent variability in loading, and uncertainty due to sparse data. A continuous model updating approach based on real-time monitoring data is developed and applied to all the three techniques mentioned above. The relation between prediction accuracy and updating interval is evaluated quantitatively. A quantitative model validation approach using Bayesian hypothesis testing is proposed to assess the confidence in load prediction from all the three methods.