Probabilistic Forecasting Model Research Articles

Probabilistic-Forecasting-Based Admission Control for Network Slicing in Software-Defined Networks

Network slicing is one the key features of software-defined networks (SDNs) and can be used in next-generation communication networks. Admission control of network slices is the basis of providing the heterogeneous quality-of-service performance guarantee and maximizing the optimization objectives of the network operator. Various admission control mechanisms have been proposed in the literature, including those based on traffic forecasting. However, recurrent neural network-based probabilistic forecasting models have not been given thorough consideration for slice admission control. In this study, the network slicing scheme design problem is formulated mathematically, with an equivalent formulation of the constrained bandwidth-sharing scheme. Then, a DeepAR-based slice admission control mechanism is proposed for sequential decision making for network slice requests in SDN, with the support of the SDN controller. An improved variant is further proposed with a closed-loop parameter update mechanism. The experiments based on real-world historical traffic data validate the effectiveness of the proposed mechanisms, with metrics, including revenue, resource reservation and utilization ratios, and service admission ratio.

PyCSEP: A Python Toolkit for Earthquake Forecast Developers

Abstract The Collaboratory for the Study of Earthquake Predictability (CSEP) is an open and global community whose mission is to accelerate earthquake predictability research through rigorous testing of probabilistic earthquake forecast models and prediction algorithms. pyCSEP supports this mission by providing open-source implementations of useful tools for evaluating earthquake forecasts. pyCSEP is a Python package that contains the following modules: (1) earthquake catalog access and processing, (2) representations of probabilistic earthquake forecasts, (3) statistical tests for evaluating earthquake forecasts, and (4) visualization routines and various other utilities. Most significantly, pyCSEP contains several statistical tests needed to evaluate earthquake forecasts, which can be forecasts expressed as expected earthquake rates in space–magnitude bins or specified as large sets of simulated catalogs (which includes candidate models for governmental operational earthquake forecasting). To showcase how pyCSEP can be used to evaluate earthquake forecasts, we have provided a reproducibility package that contains all the components required to re-create the figures published in this article. We recommend that interested readers work through the reproducibility package alongside this article. By providing useful tools to earthquake forecast modelers and facilitating an open-source software community, we hope to broaden the impact of the CSEP and further promote earthquake forecasting research.

Sparse Gaussian Process Regression for Landslide Displacement Time-Series Forecasting

Landslide hazards are complex nonlinear systems with a highly dynamic nature. Accurate forecasting of landslide displacement and evolution is crucial for the prevention and mitigation of landslide hazards. In this study, a probabilistic landslide displacement forecasting model based on the quantification of epistemic uncertainty is proposed. In particular, the displacement forecasting problem is cast as a time-series regression problem with limited training samples and must be solved by statistical inference. The epistemic uncertainty of the landslide displacement series is depicted by the statistical properties of the function space constituted by the nonlinear mappings generated by the sparse Gaussian process regression. Data for our study was collected from the study area located in northwestern China. Other state-of-the-art probabilistic forecasting models have also been utilized for comparative analysis. The experimental results confirmed the superiority of the sparse Gaussian process in the modeling of landslide displacement series in terms of forecasting accuracy, uncertainty quantification, and robustness to overfitting.

Real-time probabilistic sediment concentration forecasting using integrated dynamic network and error distribution heterogeneity

Sediment forecasting at a dam site is important for the operation and management of water and sediment in a reservoir. However, the forecast results generally have some uncertainties, which may hinder the operation of the dam. In this study, a real-time sediment concentration probabilistic forecasting model is proposed based on a dynamic network model. Under this framework, the Elman neural network (ENN) and nonlinear auto-regressive with exogenous inputs (NARX) neural network models were established for sediment concentration forecasting with different lead times. A hybrid algorithm, which combined the Levenberg–Marquardt algorithm and real-time recurrent learning, was used to train the model. Using the aforementioned method, the sediment concentration was forecast for at the Sanmenxia Dam, China, and, subsequently, the forecast results were evaluated. Among the selected lead time, the results at 5 h exhibited the highest accuracy and practical significance. Compared with the ENN model, the sediment concentration peak error using the NARX neural network was reduced by 4.5%, and the sediment yield error was reduced by 0.043%. Therefore, the NARX neural network was selected as the deterministic sediment forecasting model. Additionally, the probability density function of the sediment concentration was derived based on the heterogeneity of the error distribution, and the sediment concentration interval, with different confidence levels, expected values, and median values, was forecast. The Nash–Sutcliffe coefficient of efficiency for the sediment concentration, as forecasted based on the median value, was the highest (0.04 higher than that using a deterministic model), whereas the error of the sediment concentration peak and sediment yield remained unaltered. These results indicated the accuracy and superiority of the proposed real-time sediment probabilistic forecasting hybrid model.

Probabilistic forecasting informed failure prognostics framework for improved RUL prediction under uncertainty: A transformer case study

The energy transition towards resilient and sustainable power plants requires moving from periodic health assessment to condition-based lifetime planning, which in turn, creates new challenges and opportunities for health estimation and prediction. Probabilistic forecasting models are being widely employed to predict the likely evolution of power grid parameters, such as weather prediction models and probabilistic load forecasting models, that precisely impact on the health state of power and energy components. These models synthesize forecasting knowledge and associated uncertainty information, and their integration within asset management practice would improve lifetime estimation under uncertainty through uncertainty-aware probabilistic predictions. Accordingly, this paper presents a probabilistic prognostics method for lifetime planning under uncertainty integrating data-driven probabilistic forecasting models with expert-knowledge based Bayesian filtering methods. The proposed concepts are applied and validated with power transformers operated in two different power generation systems and obtained results confirm that the proposed probabilistic transformer lifetime estimate aids in the decision-making process with informative lifetime distributions and associated confidence intervals.

An empirical study on probabilistic forecasting for predicting city-wide electricity consumption

In the competitive framework of the electricity markets, demand forecasting with high accuracy is invaluable for governmental institutions and power generation industry. By providing a basis for sound decision-making in energy management, it supports the decision makers to build capacity to meet the demand. In this research, we use electricity consumption data from 81 cities in Turkey to create global probabilistic forecasting models. For this purpose, we implement two prevailing probabilistic forecasting methods, namely, DeepAR and Deep State Space (DeepState) models. We compare the performances of these models against well-known statistical forecasting models (e.g., ARIMA), machine learning models (e.g., gradient boosting, and random forests), and deep learning models (e.g., long short term memory networks (LSTM) and gated recurrent unit networks (GRU)). Our results show that LSTM and GRU outperform others in terms of point forecasting performance, whereas DeepAR and DeepState models provide a better probabilistic forecasting performance for longer prediction horizons. We find that the global forecasting methods successfully leverage multiple time series (as in the case of 81-city forecasting data), however, mainly due to the relatively simple structure of the electricity datasets, they do not lead to meaningful performance gain over simpler models

Probabilistic forecasting of remotely sensed cropland vegetation health and its relevance for food security

In a world where climate change, population growth, and global diseases threaten economic access to food, policies and contingency plans can strongly benefit from reliable forecasts of agricultural vegetation health. To inform decisions, it is also crucial to quantify the forecasting uncertainty and prove its relevance for food security. Yet, in previous studies both these aspects have been largely overlooked. This paper develops a methodology to anticipate the agricultural Vegetation Health Index (VHI) while making the underlying prediction uncertainty explicit. To achieve this aim, a probabilistic machine learning framework modelling weather and climate determinants is introduced and implemented through Quantile Random Forests. In a second step, a statistical link between VHI forecasts and monthly food price variations is established. As a pilot implementation, the framework is applied to nine countries of South-East Asia (SEA) with consideration of national monthly rice prices. Model benchmarks show satisfactory accuracy metrics, suggesting that the probabilistic VHI predictions can provide decision-makers with reliable information about future cropland health and its impact on food price variation weeks or even months ahead, albeit with increasing uncertainty as the forecasting horizon grows. These results - ultimately allowing to anticipate the impact of weather shocks on household food expenditure - contribute to advancing the multidisciplinary literature linking vegetation health, probabilistic forecasting models, and food security policy.

Random Noise vs. State-of-the-Art Probabilistic Forecasting Methods: A Case Study on CRPS-Sum Discrimination Ability

The recent developments in the machine-learning domain have enabled the development of complex multivariate probabilistic forecasting models. To evaluate the predictive power of these complex methods, it is pivotal to have a precise evaluation method to gauge the performance and predictability power of these complex methods. To do so, several evaluation metrics have been proposed in the past (such as the energy score, Dawid–Sebastiani score, and variogram score); however, these cannot reliably measure the performance of a probabilistic forecaster. Recently, CRPS-Sum has gained a lot of prominence as a reliable metric for multivariate probabilistic forecasting. This paper presents a systematic evaluation of CRPS-Sum to understand its discrimination ability. We show that the statistical properties of target data affect the discrimination ability of CRPS-Sum. Furthermore, we highlight that CRPS-Sum calculation overlooks the performance of the model on each dimension. These flaws can lead us to an incorrect assessment of model performance. Finally, with experiments on real-world datasets, we demonstrate that the shortcomings of CRPS-Sum provide a misleading indication of the probabilistic forecasting performance method. We illustrate that it is easily possible to have a better CRPS-Sum for a dummy model, which looks like random noise, in comparison to the state-of-the-art method.

Completed Review of Various Solar Power Forecasting Techniques Considering Different Viewpoints

Solar power has rapidly become an increasingly important energy source in many countries over recent years; however, the intermittent nature of photovoltaic (PV) power generation has a significant impact on existing power systems. To reduce this uncertainty and maintain system security, precise solar power forecasting methods are required. This study summarizes and compares various PV power forecasting approaches, including time-series statistical methods, physical methods, ensemble methods, and machine and deep learning methods, the last of which there is a particular focus. In addition, various optimization algorithms for model parameters are summarized, the crucial factors that influence PV power forecasts are investigated, and input selection for PV power generation forecasting models are discussed. Probabilistic forecasting is expected to play a key role in the PV power forecasting required to meet the challenges faced by modern grid systems, and so this study provides a comparative analysis of existing deterministic and probabilistic forecasting models. Additionally, the importance of data processing techniques that enhance forecasting performance are highlighted. In comparison with the extant literature, this paper addresses more of the issues concerning the application of deep and machine learning to PV power forecasting. Based on the survey results, a complete and comprehensive solar power forecasting process must include data processing and feature extraction capabilities, a powerful deep learning structure for training, and a method to evaluate the uncertainty in its predictions.

Sparse Variational Gaussian Process Based Day-Ahead Probabilistic Wind Power Forecasting

In this paper, we present a probabilistic wind power forecasting (PWPF) model via quantification of epistemic uncertainty and aleatory uncertainty. Concretely, the epistemic uncertainty is described by the statistical characteristics of function space constituted by all wind power forecasting (WPF) mappings through Gaussian process (GP) frameworks. In particular, we adopt the sparse variational Gaussian process to address inference complexity and hyperparameters determination issues, which impede the performance of existing GP-based PWPF models. It introduces inducing variables and variational inference to minimize the difference between the approximated sparse GP model and the original GP, whereby a variational distribution is introduced to explicitly represent the inducing variables. All parameters are optimized via gradient descent optimization based on likelihood maximization. Experiments based on an open dataset demonstrate that the proposed model is comparable to state-of-the-art in terms of continuous ranked probability score, and robust to overfitting.

Execution of synthetic Bayesian model average for solar energy forecasting

Accurate photovoltaic (PV) forecasting is quite crucial in planning and in the regular operation of power system. Stochastic habit along with the high risks in PV signal uncertainty and a probabilistic forecasting model is required to address the numerical weather prediction (NWP) underdispersion. In this study, a new synthetic prediction process based on Bayesian model averaging (BMA) and Ensemble Learning is developed. The proposed model is initiated by the improved self-organizing map (ISOM) clustering K-fold cross-validation for the training process. To provide desirable learning model for different input samples, three learners including long short-term memory (LSTM) network, general regression neural network (GRNN), and non-linear auto-regressive eXogenous NN (NARXNN) are employed. The proposed BMA approach is combined with the output of the learners to obtain accurate and desirable outcomes. Different models are precisely compared with the obtained numerical results over real-world engineering test site, that is, Arta-Solar case study. The numerical analysis and recorded results validate the performance and superiority of the proposed model.

Generative Probabilistic Wind Speed Forecasting: A Variational Recurrent Autoencoder Based Method

In this paper, a novel framework for probabilistic wind speed forecasting (PWSF) based on variational recurrent autoencoders (VRAEs) via a generative perspective is proposed. Compared with a traditional optimization objective maximizing the conditional likelihood of the target wind speed directly, a novel optimization objective maximizing the likelihood of the complete wind speed sequence is proposed to better model the temporal relationship within the complete wind speed sequence. As directly maximizing the proposed objective is intractable, we show that it can be alternatively achieved via the help of the VRAE learning principle. The framework of the proposed VRAE based PWSF is composed of two phases, training a VRAE with maximizing the variational lower bound of the likelihood of the complete wind speed sequence and forecasting the target wind speed from the generative perspective through the approximate posterior learned by the VRAE. Computational results demonstrate that the proposed method outperforms other benchmarking deterministic and probabilistic forecasting models in terms of the negative form of continuous ranked probability score (CRPS*). Compared with other benchmarking models for probabilistic forecasting, the proposed method achieves better sharpness and overall quality of prediction intervals (PIs) as well as a comparable reliability. Results verify advantages of the proposed VARE based PWSF method.

Objective and Probabilistic Long-Range Forecasts of Summertime Air Temperatures in South Korea Based on Gaussian Processes

Abstract We propose the objective long-range forecasting model based on Gaussian processes (OLRAF-GP), focusing on summertime near-surface air temperatures in June (1-month lead), July (2-month lead), and August (3-month lead). The predictors were objectively selected based on their relationships with the target variables, either from observations (GP-OBS) or from observations and dynamical climate model results from APEC Climate Center multimodel ensemble (APCC MME) for the period with no observed data (GP-MME). The performances of the OLRAF-GP models were compared with the model with predetermined predictors from observations (GP-PD). Both GP-MME and GP-OBS outperformed GP-PD in June [Heidke skill score (HSS); HSS = 0.46, 0.72, and 0.16 for mean temperature] and July (HSS = 0.53, 0.3, and 0.07 for mean temperature). Furthermore, GP-MME mostly outperformed GP-OBS and GP-PD in August (HSS = 0.52, 0.28, and 0.5, respectively, for mean temperature), implying larger contributions of the additional predictors from MME. OLRAF-GP models, especially GP-MME, are expected to better forecast summertime temperatures in regions where existing models have been struggling. We find that the physical processes associated with the notable predictors are aligned with those in previous studies, such as the attribution of the La Niña conditions in the previous winter, the related Indian Ocean capacitor effect, and the impacts of wintertime Polar/Eurasia pattern. These results imply that the mechanisms of the objectively selected predictors can be physically meaningful, and their inclusion can improve model performance and efficiency. Significance Statements This study aims to improve the long-range probabilistic forecasting of summertime near-surface temperatures for regions where the climate variability is not sufficiently explained by well-known key predictors. We propose objective and probabilistic forecasting models that use objectively selected predictors either from observations or from observations and results of the dynamical climate model. The overall skill scores of the proposed models (overall HSS = 0.33, 0.39) for the case study site of South Korea are higher than the model with predetermined predictors (overall HSS = 0.19). We also find that the mechanisms of the objectively selected predictors can be physically meaningful, and their inclusion can improve model performance and efficiency.

Applications of Probabilistic Forecasting in Smart Grids: A Review

This paper reviews the recent studies and works dealing with probabilistic forecasting models and their applications in smart grids. According to these studies, this paper tries to introduce a roadmap towards decision-making under uncertainty in a smart grid environment. In this way, it firstly discusses the common methods employed to predict the distribution of variables. Then, it reviews how the recent literature used these forecasting methods and for which uncertain parameters they wanted to obtain distributions. Unlike the existing reviews, this paper assesses several uncertain parameters for which probabilistic forecasting models have been developed. In the next stage, this paper provides an overview related to scenario generation of uncertain parameters using their distributions and how these scenarios are adopted for optimal decision-making. In this regard, this paper discusses three types of optimization problems aiming to capture uncertainties and reviews the related papers. Finally, we propose some future applications of probabilistic forecasting based on the flexibility challenges of power systems in the near future.

Using the Residual Network Module to Correct the Sub-Seasonal High Temperature Forecast

The high temperature forecast of the sub-season is a severe challenge. Currently, the residual structure has achieved good results in the field of computer vision attributed to the excellent feature extraction ability. However, it has not been introduced in the domain of sub-seasonal forecasting. Here, we develop multi-module daily deterministic and probabilistic forecast models by the residual structure and finally establish a complete set of sub-seasonal high temperature forecasting system in the eastern part of China. The experimental results indicate that our method is effective and outperforms the European hindcast results in all aspects: absolute error, anomaly correlation coefficient, and other indicators are optimized by 8–50%, and the equitable threat score is improved by up to 400%. We conclude that the residual network has a sharper insight into the high temperature in sub-seasonal high temperature forecasting compared to traditional methods and convolutional networks, thus enabling more effective early warnings of extreme high temperature weather.

A k‐nearest neighbor‐based averaging model for probabilistic PV generation forecasting

AbstractProbabilistic forecasting of PV generation is crucial in uncertainty management to reinforce PV‐integrated power systems for long‐term planning. In this context, developing a reliable probabilistic forecast model is challenging due to weather conditions' stochastic nature and varying daily PV production patterns at multiple time instants. Due to varying probability distribution patterns, a nonparametric approach, such as quantile regression, is challenging to approximate the forecast error distribution. A forecast combination concept that yields impressive probabilistic forecasting results has rarely been utilized for PV generation forecasting. The use of complementary and sensible point forecasters characterizing different aspects of intricate PV production patterns in a k‐nearest neighbor quantile regression averaging framework is the proposed probabilistic forecasting model. The proposed forecasting model's accuracy is assessed with real‐world PV generation data from the USA for multi‐time instants. The probabilistic forecast performance of the proposed quantile k‐nearest neighbors regression averaging model is evaluated against the traditional quantile regression averaging, quantile regression forests, quantile k‐nearest neighbors, basic quantile regression, and regression bootstrapping in terms of the forecast (quantiles and prediction intervals) accuracy, using relevant error measures and scores. The proposed model has superior performance compared to the other models, as indicated by the lowest forecast errors and scores.

The probabilistic solar particle event forecasting (PROSPER) model

The Probabilistic Solar Particle Event foRecasting (PROSPER) model predicts the probability of occurrence and the expected peak flux of solar energetic particle (SEP) events. Predictions are derived for a set of integral proton energies (i.e., E > 10, > 30, and > 100 MeV) from characteristics of solar flares (longitude, magnitude), coronal mass ejections (width, speed), and combinations of both. Herein the PROSPER model methodology for deriving the SEP event forecasts is described, and the validation of the model, based on archived data, is presented for a set of case studies. The PROSPER model has been incorporated into the new operational advanced solar particle event casting system (ASPECS) tool to provide nowcasting (short term forecasting) of SEP events as part of ESA’s future SEP advanced warning system (SAWS). ASPECS also provides the capability to interrogate PROSPER for historical cases via a run-on-demand functionality.

Generation of Proxy GIM‐TEC for Extreme Storms Before the Era of GNSS Observations

AbstractFor the first time, we reconstructed global distribution of both the total electron content disturbance W index and TEC values for eight extreme storms (Dst < −250 nT) occurred before the epoch of GNSS observations in solar cycle 22. We created a model based on superposed epoch analysis of the training set of GIM‐W maps of nine SC23 extreme storms. Global GIM‐W index maps are calculated from 15‐min UPC GIM‐TEC (UQRG) as the logarithmic deviation of instantaneous TEC from the monthly median GIM‐MTEC empirical model. We introduced the storm phase metrics for main and recovery phases of the positive ionosphere disturbance (the WU‐index), the negative disturbance (the WL‐index) and the ring current (the Dst‐index). The probabilistic forecasting model (Pmodel) for SC22 GIM‐Wx maps is developed based on GIM‐W maps of the SC23 training set. The storm phase distribution Φx for the eight SC22 extreme storms is calculated from the proxy time shift (lag) of peak WUmax and WLmin relative to Dstmin. Proxy GIM‐TECx maps are calculated by adjusting the GIM‐MTEC median to the GIM‐Wx prediction. Validation of the technique based on data of UPC and JPL for four intense ionospheric storms showed a root‐mean‐square error less than 3 TECU. The proposed technique can be applied for both the past and future forecasting of GIM‐W index and GIM‐TEC maps.

Ensemble Deep Learning-Based Non-Crossing Quantile Regression for Nonparametric Probabilistic Forecasting of Wind Power Generation

Probabilistic forecasting that quantifies the prediction uncertainties is crucial for decision-making in power systems. As a prevalent nonparametric probabilistic forecasting approach, traditional machine learning-based quantile regression encounters the quantile crossing problem. This paper proposes a novel ensemble deep learning based non-crossing quantile regression (EDNQR) model for probabilistic wind power forecasting, which does not need any distribution assumption and demonstrates high generalization ability. A unique non-crossing quantile regression strategy is proposed to generate monotonous quantiles with deep learning models. The exponential stacking mapping method is proposed to guarantee the monotonicity of quantiles, and Huber norm pinball loss is introduced for deep learning quantile regression model training. To improve the generalization capability, a two-stage ensemble framework is proposed to integrate homogeneous and heterogeneous deep learning models. The newly-trained base model considers the training performance of the last base model, which benefits the performance boosting of the ensemble model. To overcome the complexity of conventional weight optimization-based model integration, an overall quantile loss index is proposed to serve as an indicator to directly integrate both the homogeneous and heterogeneous deep learning base models. Comprehensive numerical studies based on actual wind farm data validate the superior performance of the proposed EDNQR model in terms of reliability, overall skill and generalization ability.

Probabilistic LSTM-Autoencoder Based Hour-Ahead Solar Power Forecasting Model for Intra-Day Electricity Market Participation: A Polish Case Study

This article presents the selection of an appropriate deep learning Long Short-Term Memory (LSTM) based probabilistic hour-ahead forecasting model for a grid connected industrial solar PV power plant located in Poland. It has a 317 kW peak power capacity and is connected with a metallurgical plant producing steel for car parts. The purpose of the study is to present a model that could be used by the plant to participate in the Polish intra-day electricity market. Four different LSTM models were investigated which include the vanilla model, the stacked LSTM model, the Bi-directional LSTM model and the LSTM-Autoencoder model. Out of the investigated models it was observed that the LSTM-Autoencoder model was the best performing one in terms of reliability. The average Root Mean Squared Error (RMSE) and the average Mean Absolute Error (MAE) for the Autoencoder model over 100 runs were 15.59 kW and 8.36 kW which represent 4.9% and 2.6% of the peak power respectively. Moreover, it was observed that it has the shortest width for the 95% confidence interval of only 0.5% for both the RMSE and the MAE. In terms of accuracy the best performing model was the LSTM bi-directional model with the average RMSE and MAE values of 12.87 kW and 6.91 kW which represent 4% and 2.1% of the peak power. The 95% confidence intervals width for both the RMSE and MAE over the 100 runs were 0.8% and 0.5% respectively.