Accurate Time Series Research Articles

From heat demand to heat supply: How to obtain more accurate feed-in time series for district heating systems

Using the heating demand of the final customer as the heat supply input time series in investment or dispatch models of district heating systems could lead to erroneous results. Both thermal losses and the network’s transient behavior lead to a mismatch between heat demand and required heat supply and should be considered. Following the methodology of standard load profiles for natural gas usage, standard load profiles for district heating systems at the plant level are developed by analyzing the measured heat supply of four different district heating systems for multiple years. The derived standard load profiles can be used to consider network transients without a complex physical model. The correction of the transient behavior is coupled with three different options to consider thermal losses in the network. Considering the transient behavior leads to an average reduction in Root Mean Square Error of 35 % compared to the neglection of the transients. Compared to a direct forecast method, the proposed approach shows a 5 % decrease in Root Mean Square Error with an increase in peak load estimation accuracy by 7 percentage points. The proposed methodology is best coupled with loss distribution methods relying on a constant share of the actual load or on the grid’s flow and return temperatures. The proposed method and the published dataset aim to develop annual load profiles for data-scarce district heating networks to serve as an input parameter for long-term dispatch or investment problems.

Forecasting Scrub Typhus Cases in Eight High-Risk Counties in China: Evaluation of Time-Series Model Performance

Scrub typhus (ST) is expanding its geographical distribution in China and in many regions worldwide raising significant public health concerns. Accurate ST time-series modeling including uncovering the role of environmental determinants is of great importance to guide disease control purposes. This study evaluated the performance of three competing time-series modeling approaches at forecasting ST cases during 2012–2020 in eight high-risk counties in China. We evaluated the performance of a seasonal autoregressive-integrated moving average (SARIMA) model, a SARIMA model with exogenous variables (SARIMAX), and the long–short term memory (LSTM) model to depict temporal variations in ST cases. In our investigation, we considered eight environmental variables known to be associated with ST landscape epidemiology, including the normalized difference vegetation index (NDVI), temperature, precipitation, atmospheric pressure, sunshine duration, relative humidity, wind speed, and multivariate El Niño/Southern Oscillation index (MEI). The first 8-year data and the last year data were used to fit the models and forecast ST cases, respectively. Our results showed that the inclusion of exogenous variables in the SARIMAX model generally outperformed the SARIMA model. Our results also indicate that the role of exogenous variables with various temporal lags varies between counties, suggesting that ST cases are temporally non-stationary. In conclusion, our study demonstrates that the approach to forecast ST cases needed to take into consideration local conditions in that time-series model performance differed between high-risk areas under investigation. Furthermore, the introduction of time-series models, especially LSTM, has enriched the ability of local public health authorities in ST high-risk areas to anticipate and respond to ST outbreaks, such as setting up an early warning system and forecasting ST precisely.

A Hybrid Spiking Neurons Embedded LSTM Network for Multivariate Time Series Learning under Concept-drift Environment

Complicated temporal patterns can provide important information for accurate time series forecasting. Existing long short-term memory (LSTM) model with attention mechanism have achieved significant performance. However, the exponential decay of long-term memory of LSTM has not be resolved yet in these efforts, remaining a longstanding open problem in recurrent nature. This problem exhibits a bottleneck which restricts the performance of existing studies. Recently, spiking neural networks (SNNs) have shown high efficiency in capturing temporal patterns via the surrogate gradient (SG) method to resolve this issue. However, the concept-drift environment makes it impossible to pre-set the variance into the standard SG method due to time-varying data distribution. In this paper, we propose a novel adaptive and hybrid spiking (AHS) module embedded LSTM, collaborating with two attention mechanisms (called HSN-LSTM) to resolve above-mentioned problems. First, the AHS module is analyzed theoretically can remain long-term memory. Moreover, our smooth SG method avoids pre-setting of variance, which is not sensitive in the above scenarios. Besides, we use the negative log-likelihood function to adjust the attention score for alleviating the negative impact from the concept-drift. Experiment results show the HSN-LSTM outperformed the state-of-the-art models on several multivariate time series datasets.

Metrics and Evaluations of Time Series Explanations: An Application in Affect Computing

Explainable artificial intelligence (XAI) has shed light on enormous applications by clarifying why neural models make specific decisions. However, it remains challenging to measure how sensitive XAI solutions are to the explanations of neural models. Although different evaluation metrics have been proposed to measure sensitivity, the main focus has been on the visual and textual data. There is insufficient attention devoted to the sensitivity metrics tailored for time series data. In this paper, we formulate several metrics, including <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max short-term sensitivity (MSS)</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max long-term sensitivity (MLS)</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">average short-term sensitivity (ASS)</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">average long-term sensitivity (ALS)</i> , that target the sensitivity of XAI models with respect to the generated and real time series. Our hypothesis is that for close series with the same labels, we obtain similar explanations. We evaluate three XAI models, LIME, integrated gradient (IG), and SmoothGrad (SG), on CN-Waterfall, a deep convolutional network. This network is a highly accurate time series classifier in affect computing. Our experiments rely on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">data-</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">metric-</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">XAI hyperparameter-</i> related settings on the WESAD and MAHNOB-HCI datasets. The results reveal that (i) IG and LIME provide a lower sensitivity scale than SG in all the metrics and settings, potentially due to the lower scale of important scores generated by IG and LIME, (ii) the XAI models show higher sensitivities for a smaller window of data, (iii) the sensitivities of XAI models fluctuate when the network parameters and data properties change, and (iv) the XAI models provide unstable sensitivities under different settings of hyperparameters.

Comparison of Inversion Methods for Maize Canopy Time-Series LAI Based on SupReME Reconstructed Images

HighlightsThe Sentinel-2 images are reconstructed by the SupReME algorithm to obtain rich spatial features and consistent spectral reflectance.The reconstructed images are more advantageous for LAI estimation than the original images.The PROSAIL coupled RF model is verified to be an effective method for time-series LAI estimation at 10 m spatial resolution.Abstract. Accurate time-series crop leaf area index (LAI) monitoring can provide data support for field management and early yield estimation. The Sentinel-2 satellite has a high spatial, temporal, and spectral resolution, and its unique three red-edge bands provide an ideal data source for LAI estimation. However, the inconsistent spatial resolution of different bands hinders the application potential of Sentinel-2 images. In view of this problem, we focused on mining more information provided by the high spatial resolution bands of Sentinel-2 images using the Super-Resolution for Multispectral Multiresolution Estimation (SupReME) algorithm. Furthermore, The SNAP (Sentinel Application Platform) biophysical processor and the PROSAIL radiation transfer model coupled with Random Forest (RF) model were applied to estimate time-series LAI of maize canopy at 10 m spatial resolution, and the Leaf Area Index Wireless Sensor Network (LAINet) measurements were used for accuracy verification. Finally, the effectiveness of images reconstructed by SupReME and the two inversion methods for time-series LAI estimation were evaluated. The results showed that: (1) the Sentinel-2 images reconstructed by SupReME can improve spatial characteristics while maintaining spectral invariance, and they were more advantageous for LAI estimation than the original images; (2) The SNAP biophysical processor suits a quick large-scale estimation with robustness, while the PROSAIL coupled RF model achieved a higher coefficient of determination (R2) and a lower root mean square error (RMSE) (R2 increased by more than 0.1, RMSE decreased by more than 0.33) for time-series LAI estimation in this specific study area; (3) both inversion methods showed apparent underestimation at the late growth stage. This study verifies the feasibility of obtaining high spatial resolution images using a super-resolution algorithm for LAI inversion and provides the effect of two commonly used inversion methods for time-series LAI estimation at 10 m resolution. Keywords: Leaf area index, PROSAIL model, Random forest, SNAP biophysical processor, SupReME algorithm.

Optimized Gated Recurrent Unit for Mid-Term Electricity Price Forecasting

Electricity price forecasting (EPF) is important for energy system operations and management which include strategic bidding, generation scheduling, optimum storage reserves scheduling and systems analysis. Moreover, accurate EPF is crucial for the purpose of bidding strategies and minimizing the risk for market participants in the competitive electricity market. Nevertheless, accurate time-series prediction of electricity price is very challenging due to complex nonlinearity in the trend of electricity price. This work proposes a mid-term forecasting model based on the demand and price data, renewable and non-renewable energy supplies, the seasonality and peak and off-peak hours of working and non-working days. An optimized Gated Recurrent Unit (GRU) which incorporates Bagged Regression Tree (BTE) is developed in the Recurrent Neural Network (RNN) architecture for the mid-term EPF. Tanh layer is employed to optimize the hyperparameters of the heterogeneous GRU with the aim to improve the model’s performance, error reduction and predict the spikes. In this work, the proposed framework is assessed using electricity market data of five major economical states in Australia by using electricity market data from August 2020 to May 2021. The results showed significant improvement when adopting the proposed prediction framework compared to previous works in forecasting the electricity price.

Time Series Long-Term Forecasting of per Capita Electricity Consumption for Bangladesh

Bangladesh government has announced Vision-2041 of electricity generation and distribution to uplift the socio-economic conditions of Bangladesh. It is now entering into the list of middle-income countries and now planning for energy as one key measure to sustainable development. Policymakers are trying to forecast the future per capita electricity consumption and set up a feasible way of electricity generation over longer periods for sustainable development of Bangladesh through preventing underestimation or overestimation that could cause a huge loss in the financial sector of Bangladesh. This work focuses on long-term estimation of electricity consumption for Bangladesh, time series models have been used to forecast per capita electricity consumption from fiscal year (FY) 2019/20-2040/41 (next 22 years). An actual past historical data of FY 1976/77-2018/19 (43 years) has been analysed on Minitab 17 to get the most favourable time series model for forecasting per capita electricity consumption of Bangladesh. ARIMA has appeared as the most accurate time series model over the actual historical data of 43 years with the lowest MAPE, MAD, and MSD as 4.50, 3.23, and 15.40, respectively.

Ensemble learning‐based modeling and short‐term forecasting algorithm for time series with small sample

AbstractDue to missing data or a short sensing period, only a minimal amount of data can be captured in some IoT cases. Making accurate time series predictions with tiny samples is a huge task. To address this problem, this article proposes a time series modeling and prediction method based on gradient boosting. Our ensemble model is obtained by iteratively combining a set of simple learners. Each iteration inputs only part of the external attributes, thus solving the dimensional disaster problem. Simple learners are selected based on the attributes of the current input and can benefit from the researcher's expertise. In short‐term forecasting of electricity consumption, our method's average and maximum relative errors are 2.72% and 5.30%, respectively, which is much better than the reference approach.

Hydrological time series prediction by extreme learning machine and sparrow search algorithm

Abstract In general, accurate hydrological time series prediction information is of great significance for the rational planning and management of water resource systems. Extreme learning machine (ELM) is an effective tool proposed for the single-layer feedforward neural network in regression and classification problems. However, the standard ELM model falls into a local minimum with a high probability in hydrological prediction problems since the randomly assigned parameters (like input-hidden weights and hidden biases) often remain unchanged in the learning process. For effectively improving the prediction accuracy, this paper develops a hybrid hydrological forecasting model where the emerging sparrow search algorithm (SSA) is firstly used to determine the satisfying parameter combinations of the ELM model, and then the Moore–Penrose generalized inverse method is chosen to analytically obtain the weight matrix between the hidden layer and output layer. The proposed method is used to forecast the long-term daily runoff series collected from three real-world hydrological stations in China. Based on several performance evaluation indexes, the results show that the proposed method outperforms several ELM variants optimized by other evolutionary algorithms in both training and testing phases. Hence, an effective evolutionary machine-learning tool is developed for accurate hydrological time series forecasting.

A Long Short-Term Memory-based correlated traffic data prediction framework

Correlated traffic data refers to a collection of time series recorded simultaneously in different regions throughout the same transportation network route. Due to the presence of both temporal and spatial correlation properties between multiple time series data, accurate time series prediction becomes challenging. The accuracy of the traffic data prediction helps mitigating traffic congestion and establish a robust traffic management system. When a prediction algorithm fails to consider the correlations present in the dataset, the accuracy of the prediction results reduces. To overcome the prediction shortcomings, this study proposes a Long Short-Term Memory (LSTM)-based correlated traffic data prediction (LSTM-CTP) framework. The proposed LSTM-CTP framework was employed for two different real-time traffic datasets. These datasets were initially preprocessed to capture both temporal and spatial trends and the correlations between the collected data series. By employing LSTM, temporal and spatial trends were predicted. Further, the Kalman-filter approach was employed to obtain the final prediction by aggregating the temporal and spatial trend predictions. The performance of the proposed LSTM-CTP was evaluated using different performance metrics and compared with different time-series prediction algorithms. The proposed framework showed substantial improvements in prediction results compared to the other algorithms. Overall, the proposed LSTM-CTP framework can help control traffic congestion and ensure a more robust traffic management system in the future.

A DEEP LEARNING APPROACH TO ELECTRIC LOAD FORECASTING OF MACHINE TOOLS

The ongoing climate change and increasingly strict climate goals of the European Union demand decisive action in all sectors. Especially in manufacturing industry, demand response measures have a high potential to balance the industrial electricity consumption with the increasingly volatile electricity supply from renewable sources. This work aims to develop a method to forecast the electrical energy demand of metal cutting machine tools as a necessary input for implementing demand response measures in factories. Building on the results of a previous study, long short-term memory networks (LSTM) and convolutional neural networks (CNN) are examined in their performance for forecasting the electric load of a machine tool for a 100 second time horizon. The results show that especially the combination of CNN and LSTM in a deep learning approach generates accurate and robust time series forecasts with reduced feature preparation effort. To further improve the forecasting accuracy, different network architectures including an attention mechanism for the LSTMs and different hyperparameter combinations are evaluated. The results are validated on real production data obtained in the ETA Research Factory.

Using evolutionary algorithms for continuous simulation of long-term reservoir inflows

Data-driven models provide upgradeable environments to simulate inflow to reservoirs. An important aspect in the development of an adaptive neural fuzzy inference system (ANFIS) model is to choose the correct procedure (i.e. efficient and effective) to train the model. In this study, a daily timescale ANFIS-based model was developed to simulate aggregated monthly long-term inflow to the Ross River reservoir in northern Queensland, Australia. The suitability of different evolutionary algorithms (EAs) was evaluated to train an ANFIS-based model, including a genetic algorithm (GA), particle swarm optimisation (PSO), shuffled frog leaping algorithm, biogeography-based optimisation, harmony search algorithm, differential evolution algorithm, invasive weed optimisation (IWO) and a cultural algorithm. Four indices – the root mean square error, Nash–Sutcliffe efficiency, reliability index and vulnerability index – were used to measure the performance of the model. It was found that application of either IWO, GA or PSO provided accurate simulated inflow time series. The outputs obtained using the other EAs were not sufficiently accurate. Use of a coupled EA–ANFIS-based model was found to improve the accuracy of simulating long-term monthly inflow compared with other models used in a few previous recent studies.

Season- and Trend-aware Symbolic Approximation for Accurate and Efficient Time Series Matching

Processing and analyzing time series datasets have become a central issue in many domains requiring data management systems to support time series as a native data type. A core access primitive of time series is matching, which requires efficient algorithms on-top of appropriate representations like the symbolic aggregate approximation (SAX) representing the current state of the art. This technique reduces a time series to a low-dimensional space by segmenting it and discretizing each segment into a small symbolic alphabet. Unfortunately, SAX ignores the deterministic behavior of time series such as cyclical repeating patterns or a trend component affecting all segments, which may lead to a sub-optimal representation accuracy. We therefore introduce a novel season- and a trend-aware symbolic approximation and demonstrate an improved representation accuracy without increasing the memory footprint. Most importantly, our techniques also enable a more efficient time series matching by providing a match up to three orders of magnitude faster than SAX.

Temporal change of extreme precipitation intensity–duration–frequency relationships in Thailand

Abstract Due to climate change, many research studies have derived the updated extreme precipitation intensity–duration–frequency relationship (IDF curve) from forecasted sub-hourly rainfall intensity time series, which is one of the most important tools for the planning and designing of hydraulic infrastructures. In this study, the IDF curves (1990–2016) of the six regions and procedures are used in accordance with those of the Royal Irrigation Department (RID)’s study (1950–1988). Each set of IDF relationships consists of 81 intensity values which are the combination of nine durations and nine return periods. The intensity ratios of this study and RID are compared. A greater-than-1 ratio indicates extreme intensity increment from the past to the present. Considering 81 ratios for each region, the number of greater-than-1 ratios for the North, Northeast, Central, East, West, and South regions are 8, 2, 31, 34, 6, and 7, respectively. These ratio numbers are far below 81 which means that the majority of extreme rainfall intensities do not increase from the past to the present. The study found that using accurate historical sub-hourly rainfall time series to create a set of IDF curves would be more reliable than using forecasted rainfall modeling.

Prediction of COVID-19 pervasiveness in six major affected states of India and two-stage variation with temperature.

Coronavirus disease knocked in Wuhan city of China in December 2019 which spread quickly across the world and infected millions of people within a short span of time. COVID-19 is a fast-spreading contagious disease which is caused by SARS-CoV-2 (severe acute respiratory syndrome-coronavirus-2). Accurate time series forecasting modeling is the need of the hour to monitor and control the universality of COVID-19 effectively, which will help to take preventive measures to break the ongoing chain of infection. India is the second highly populated country in the world and in summer the temperature rises up to 50°, nowadays in many states have more than 40° temperatures. The present study deals with the development of the autoregressive integrated moving average (ARIMA) model to predict the trend of the number of COVID-19 infected people in most affected states of India and the effect of a rise in temperature on COVID-19 cases. Cumulative data of COVID-19 confirmed cases are taken for study which consists of 77 sample points ranging from 1st March 2020 to 16th May 2020 from six states of India namely Delhi (Capital of India), Madya Pradesh, Maharashtra, Punjab, Rajasthan, and Uttar Pradesh. The developed ARIMA model is further used to make 1-month ahead out of sample predictions for COVID-19. The performance of ARIMA models is estimated by comparing measures of errors for these six states which will help in understanding future trends of COVID-19 outbreak. Temperature rise shows slightly negatively correlated with the rise in daily cases. This study is noble to analyse the variation of COVID-19 cases with respect to temperature and make aware of the state governments and take precautionary measures to flatten the growth curve of confirmed cases of COVID-19 infections in other states of India, nearby countries as well.

Selego: robust variate selection for accurate time series forecasting

Naïve extensions of uni-variate prediction techniques lead to an unwelcome increase in the cost of multi-variate model learning and significant deteriorations in the model performance. In this paper, we first argue that (a) one can learn a more accurate forecasting model by leveraging temporal alignments among variates to quantify the importance of the recorded variates with respect to a target variate. We further argue that, (b) for this purpose we need to quantify temporal correlation, not in terms of series similarity, but in terms of temporal alignments of key “events” impacting these series. Finally, we argue that (c) while learning a temporal model using recurrence based techniques (such as RNN and LSTM—even when leveraging attention strategies) is difficult and costly, we can achieve better performance by coupling simpler CNNs with an adaptive variate selection strategy. Relying on these arguments, we propose a Selego framework (Selego is a word of latin origin meaning “selection”) for variate selection and experimentally evaluate the performance of the proposed approach on various forecasting models, such as LSTM, RNN, and CNN, for different top-X% variates and different forecasting time in the future (lead) on multiple real-world datasets. Experiments show that the proposed framework can offer significant (\(90-98\%\)) drops in the number of recorded variates that are needed to train predictive models, while simultaneously boosting accuracy.

An empirical evaluation of kernels for time series

There exist a variety of distance measures which operate on time series kernels. The objective of this article is to compare those distance measures in a support vector machine setting. A support vector machine is a state-of-the-art classifier for static (non-time series) datasets and usually outperforms k-Nearest Neighbour, however it is often noted that that 1-NN DTW is a robust baseline for time-series classification. Through a collection of experiments we determine that the most effective distance measure is Dynamic Time Warping and the most effective classifier is kNN. However, a surprising result is that the pairing of kNN and DTW is not the most effective model. Instead we have discovered via experimentation that Dynamic Time Warping paired with the Gaussian Support Vector Machine is the most accurate time series classifier. Finally, with good reason we recommend a slightly inferior (in terms of accuracy) model Time Warp Edit Distance paired with the Gaussian Support Vector Machine as it has a better theoretical basis. We also discuss the reduction in computational cost achieved by using a Support Vector Machine, finding that the Negative Kernel paired with the Dynamic Time Warping distance produces the greatest reduction in computational cost.

Evaluation of open photovoltaic and wind production time series for Norwegian locations

We investigate the accuracy of wind and photovoltaic time series in individual systems in Norway. To study the accuracy of the available open data sets, we compare the measured production from individual photovoltaic- and wind power plants to the open time series from Renewables.ninja and EMHIRES. Additionally, we try to adjust the wind speed based on the average wind speed from Global Wind Atlas 3.0 and Norwegian water resources and energy directorate's Wind Map to try to achieve more accurate wind speed time series that take into account the local wind conditions, since they are not well represented in the large resolution of the MERRA-2 data set used by Renewables.ninja. The results for photovoltaic production time series are promising, the correlation between production obtained from Renewables.ninja and measured production is above 0.72 and maximum capacity factor difference of 2.5%. For the case of wind production, production time series show considerable deviations depending on the specific wind farm (correlation between 0.51 and 0.91 depending on the case and year). Additionally, the adjustments only improve the time series in some of the wind farms, whereas in others the results are even less accurate than the Renewables.ninja time series compared to the measured data.

Performance degradation prediction of aeroengine based on attention model and support vector regression

Accurate performance degradation prediction of aeroengines can ensure the safety and reliability of the aircraft. Based on the mass long time series data of multiple state parameters, a novel performance degradation prediction method based on attention model (AM) and support vector regression (SVR) is proposed in this article. The AM uses the attention mechanism between encoder and decoder to realize weight distribution of different source samples, so as to realize time series prediction of state parameters. The SVR model is used to mine the mapping relationship between multiple state parameters and performance degradation. The performance degradation prediction results can be achieved by putting the time series prediction results of multiple state parameters into the SVR model. The turbofan engine degradation simulation dataset carried out using commercial modular aero-propulsion system simulation (C-MAPSS) is used to verify the effectiveness of the proposed method. The results demonstrate that it can get accurate time series prediction and performance degradation analysis results. Compared with other methods, the proposed attention model and support vector regression (AM-SVR) model has lower prediction error and higher stability when dealing with noised samples.

A novel robust prediction algorithm based on REMD-MWNN for AIOps

AIOps(Artificial Intelligence Operations) is emerging as one of the most important technology in industrial automation, and accurate time series prediction plays a crucial role in it. However, due to the non-linear and non-stationary characteristics of Ops(operations) data, traditional time series forecasting models can not effectively extract good enough sequence data features and result in poor forecasting accuracy. To fully extract the Ops data information and construct a robust prediction model, this paper proposes a hybrid model based on recursive empirical mode decomposition (REMD) and memory wavelet neural network (MWNN) to improve the forecasting accuracy of Ops data. In REMD-MWNN, we first use REMD to decompose the Ops data into multiple intrinsic modal functions (IMF) at different time scales. Then, to make full use of the historical information of the Ops data and reduce the running time, we designed a new memory recurrent neural network, namely MWNN. Next, use MWNN to predict multiple inherent IMFs respectively to obtain the predicted value of the corresponding subsequence. Finally, the final prediction result is obtained by reconstructing the prediction value of each subsequence. In the comprehensive experiment, we selected the Ops data of an open education platform. The experimental results show that, compared with other algorithms, the model proposed in this paper is highly competitive in predicting future changes and capturing the evolution mode of hidden factors. The experimental data involved in this paper can be downloaded from this website: https://github.com/1600383075/REMD-MWNN/tree/master/data.