Probabilistic Forecasting Model Research Articles

Energy-saving potential benchmarking method of office buildings based on probabilistic forecast

Building energy consumption represents a substantial portion of China's total energy usage profile. Conducting a quantitative assessment of the energy-saving potential in buildings is crucial, as it aids in estimating the investment risk and payback period for energy-efficient projects. This evaluation also informs the development and formulation of policies promoting building retrofits and energy conservation. However, this field's present state of research exhibits a significant gap. This study takes 8 typical office buildings as case objects and conducts relevant research on quantitative evaluation of energy-saving potential. On the basis of quantile regression, three corresponding probabilistic forecasting models for building energy consumption are established by combining the classic time series prediction algorithm Long Short-Term Memory (LSTM) in data-driven methods, Gradient Boosting Decision Tree (GBDT) in known building energy benchmarking, and a relatively simple linear model. The evaluation results demonstrate that the LSTM-QR model can serve effectively as a probabilistic forecasting model for estimating building energy-saving potential. Based on the LSTM-QR model results, a quantitative evaluation method for building energy-saving potential benchmarking is proposed, utilizing linearized Cumulative Distribution Function (CDF) curves. This method can quantitatively assess the energy-saving potential of the studied buildings. By analyzing and comparing these buildings' hourly energy consumption data over the past three years, it is evident that the quantitative scoring results from this method can provide directional guidance for building renovation projects to enhance energy efficiency.

Probabilistic assessment of postfire debris-flow inundation in response to forecast rainfall

Abstract. Communities downstream of burned steep lands face increases in debris-flow hazards due to fire effects on soil and vegetation. Rapid postfire hazard assessments have traditionally focused on quantifying spatial variations in debris-flow likelihood and volume in response to design rainstorms. However, a methodology that provides estimates of debris-flow inundation downstream of burned areas based on forecast rainfall would provide decision-makers with information that directly addresses the potential for downstream impacts. We introduce a framework that integrates a 24 h lead-time ensemble precipitation forecast with debris-flow likelihood, volume, and runout models to produce probabilistic maps of debris-flow inundation. We applied this framework to simulate debris-flow inundation associated with the 9 January 2018 debris-flow event in Montecito, California, USA. When the observed debris-flow volumes were used to drive the probabilistic forecast model, analysis of the simulated inundation probabilities demonstrates that the model is both reliable and sharp. In the fully predictive model, however, in which debris-flow likelihood and volume were computed from the atmospheric model ensemble's predictions of peak 15 min rainfall intensity, I15, the model generally under-forecasted the inundation area. The observed peak I15 lies in the upper tail of the atmospheric model ensemble spread; thus a large fraction of ensemble members forecast lower I15 than observed. Using these I15 values as input to the inundation model resulted in lower-than-observed flow volumes which translated into under-forecasting of the inundation area. Even so, approximately 94 % of the observed inundated area was forecast to have an inundation probability greater than 1 %, demonstrating that the observed extent of inundation was generally captured within the range of outcomes predicted by the model. Sensitivity analyses indicate that debris-flow volume and two parameters associated with debris-flow mobility exert significant influence on inundation predictions, but reducing uncertainty in postfire debris-flow volume predictions will have the largest impact on reducing inundation outcome uncertainty. This study represents a first step toward a near-real-time hazard assessment product that includes probabilistic estimates of debris-flow inundation and provides guidance for future improvements to this and similar model frameworks by identifying key sources of uncertainty.

Hybrid model for intra-day probabilistic PV power forecast

Renewable generation forecasting has become an essential element of power system management because of the ever-increasing share of renewable power fed into the grid. Solar energy is one of the most common and well-known sources of energy in existing networks. Due to its intermittent and non-linear nature, accurate prediction of solar irradiance is essential for ensuring the reliable integration of photovoltaic (PV) plants with the grid system and for effectively managing supply and demand. The dispatching problem is typically addressed by generating a forecast for a few sample plants and scaling the result of these forecasts by the PV power generation capacity connected to the electric system. This research presents a comprehensive comparison of various methods for predicting PV power generation in fixed and single axis tracking PV systems at two different locations. These methods include time-series statistical regression, parametric physical approaches, machine learning (ML), and ensemble techniques, aimed at intra-day forecasts ranging from 1 to 6 h ahead. The study introduces a novel method for developing a parametric linear model for fixed PV systems and uses model output statistics (MOS) to improve forecast accuracy. Additionally, this study details various optimization algorithms designed to refine model parameters for creating a hybrid model. It also examines key factors influencing PV power forecasts and applies post-processing Kalman filter techniques. The study provides a detailed analysis of deterministic and probabilistic forecasting models, offering not just the most probable power production estimate, but also conveying the associated uncertainty. The results demonstrate a highly skilled ML based hybrid model to forecast PV power for different technologies at two different locations.

DiffPLF: A conditional diffusion model for probabilistic forecasting of EV charging load

Due to the vast electric vehicle (EV) penetration to distribution grid, charging load forecasting is essential to promote charging station operation and demand-side management. However, the stochastic charging behaviors and associated exogenous factors render future charging load patterns quite volatile and hard to predict. Accordingly, we devise a novel Diffusion model termed DiffPLF for Probabilistic Load Forecasting of EV charging, which can explicitly approximate the predictive load distribution conditioned on historical data and related covariates. Specifically, we leverage a denoising diffusion model, which can progressively convert the Gaussian prior to real time-series data by learning a reversal of the diffusion process. Besides, we couple such diffusion model with a cross-attention-based conditioning mechanism to execute conditional generation for possible charging demand profiles. We also propose a task-informed fine-tuning technique to better adapt DiffPLF to the probabilistic time-series forecasting task and acquire more accurate and reliable predicted intervals. Finally, we conduct multiple experiments to validate the superiority of DiffPLF to predict complex temporal patterns of erratic charging load and carry out controllable generation based on certain covariate. Results demonstrate that we can attain a notable rise of 39.58% and 49.87% on MAE and CRPS respectively compared to the conventional method.

Diff-MGR: Dynamic causal graph attention and pattern reproduction guided diffusion model for multivariate time series probabilistic forecasting

Time series probability forecasting provides insight into future evolution and its inherent uncertainty from past data. In order to obtain more accurate forecasting as the reliable basis for future decision-making and planning, a new probabilistic prediction model of multivariate time series Diff-MGR is proposed in this study. Diff-MGR innovatively proposes dynamic causal graph attention blocks and pattern reproduction guided prediction blocks to predict the future patterns. Compared with the existing methods, the former captures dynamic unidirectional information flow by using causal graph structure at different periods to provide a real representation of variable relationships. The latter completes a reliable mapping of historical patterns to the future based on the prior knowledge of pattern reproduction. Furthermore, Diff-MGR proposes a novel noise prediction network that can effectively capture dependencies in predicted future patterns and generate probability distributions of future sequences using a conditional diffusion model. Extensive experiments on several real datasets verify the effectiveness of Diff-MGR's components, and show it outperforms existing models in probabilistic forecasting performance.

Generating Synthetic Electricity Load Time Series at District Scale Using Probabilistic Forecasts

Thanks to various European directives, individuals are empowered to share and trade electricity within Renewable Energy Communities, enhancing the operational efficiency of local energy systems. The digital transformation of the energy market enables the integration of decentralized energy resources using cloud computing, the Internet of Things, and artificial intelligence. In order to assess the feasibility of new business models based on data-driven solutions, various electricity consumption time series are necessary at this level of aggregation. Since these are currently not yet available in sufficient quality and quantity, and due to data privacy reasons, synthetic time series are essential in the strategic planning of smart grid energy systems. By enabling the simulation of diverse scenarios, they facilitate the integration of new technologies and the development of effective demand response strategies. Moreover, they provide valuable data for assessing novel load forecasting methodologies that are essential to manage energy efficiently and to ensure grid stability. Therefore, this research proposes a methodology to synthesize electricity consumption time series by applying the Box–Jenkins method, an intelligent sampling technique for data augmentation and a probabilistic forecast model. This novel approach emulates the stochastic nature of electricity consumption time series and synthesizes realistic ones of Renewable Energy Communities concerning seasonal as well as short-term variations and stochasticity. Comparing autocorrelations, distributions of values, and principle components of daily sequences between real and synthetic time series, the results exhibit nearly identical characteristics to the original data and, thus, are usable in designing and studying efficient smart grid systems.

Probabilistic forecast of electric vehicle charging demand: analysis of different aggregation levels and energy procurement

Electric vehicles (EVs) are expected to be vital in transitioning to a low-carbon energy system. However, integrating EVs into the power grid poses significant challenges for grid operators and energy suppliers, especially regarding the uncertainty and variability of EV charging demand. Accurate forecasting of EV charging demand is essential for optimal power system integration, yet previous studies have often only considered point predictions that are inadequate for risk assessment. Therefore, this paper compares different probabilistic forecasting models for the short-term prediction of EV charging demand at various aggregation levels, using a large and novel dataset of over 350,000 charging processes at more than 500 locations across Germany. The performance of both machine learning and deep learning methods is evaluated against a naïve benchmark model, and the impact of data availability on the forecasting models is investigated. Further, the paper examines the effects of forecast accuracy on energy procurement, which has so far received minor attention in the literature. The results show that machine learning methods such as Ada Boosting and Random Forest yield robust results with a normalized root mean square error of 0.42 and 0.41 and a mean absolute scaled error of 0.36 and 0.34 at the highest aggregation level. Furthermore, the results show the influence of different site compositions on the forecast quality and how many charging points are likely to yield a robust forecast. Energy and fleet managers can use the described method to reliably predict the required energy quantities for fleets of sufficient size and procure them at low risk.

Probabilistic CDF-based load forecasting model in a power distribution system

The study searches for a probabilistic forecasting model for electric power demand based on the correlation between weather temperature and electric power demand using hourly time series data spanning a year. The model is based on the temperature and power demand data's cumulative probability distribution functions or CDFs. In probabilistic forecasting, a range of potential values and their associated probabilities are predicted in addition to a single value for a given range. The qualities of CDF modeling allow it to cover these uncertainties. For scenario 1, case 2, and case 3, the mean absolute percentage error (MAPE)-based forecasting accuracy for the hourly load demand is 3.93, 4.64, and 2.56, respectively. The Gaussian distribution-based CDFs' capacity to forecast outside of the present data range is an extra advantage. The world's electric power networks are growing increasingly intricate and unpredictable through the integration of several distributed energy resources (DERs) and cutting-edge technology from renewable energy resources (RERs). Other variables, such as variations in weather patterns, shifts in the status of the economy, or adjustments to energy policies, can also add to uncertainty and not be foreseen. A body of literature demonstrates a shortage of research on LTLF and general-purpose forecasting methods. The proposed approach is flexible and might establish a standard for many different forecasting tasks. The proposed method is intended to be a flexible strategy that may be used for different utilities with varying time horizons.

Dependence structure learning and joint probabilistic forecasting of stochastic power grid variables

Stochastic optimization is a promising approach to support a reliable and cost-efficient transition to a renewable generation-dominated power grid. However, utilization of this approach requires accurate and computationally affordable probabilistic forecasts that rigorously quantify the uncertainty in and the correlation between stochastic grid variables (wind/solar generation and load demand). We investigate and compare two types of probabilistic forecasting model architectures for jointly predicting stochastic variables in a power grid: sequence-to-sequence models and recursive one step ahead prediction models. A long short-term memory (LSTM) neural network model is chosen to represent sequence-to-sequence deep learning models and a periodic vector autoregressive (PVAR) model is chosen to represent the one step ahead recursive models. For each model architecture, we consider three forecasting approaches: predicting each time series variable separately, jointly predicting all time series variables of a given type (e.g., wind generation or load), or jointly predicting all time series variables. We quantify the predictive capability of these forecasting models with respect to accuracy degradation with increasing prediction horizon, ability to characterize uncertainty, and ability to capture cross-variable dependence structure. We train and test the forecasting models using publicly available zonal power supply and demand time series data for the French power grid. We find that different modeling architectures/approaches show superior forecasting capability for different prediction horizons. Our results show that in general, one step-ahead recursive (PVAR) models have high prediction accuracy for short forecast horizons, and sequence-to-sequence (LSTM) models have slower performance degradation for longer forecast horizons.

Interpretable transformer-based model for probabilistic short-term forecasting of residential net load

Short-term residential load forecasting is of great significance for the demand-side energy management of the grid and the home energy management of resident customers. The massive penetration of distributed renewable energy, especially small-scale solar photovoltaic (PV), in the residential sector urgently requires us to move from traditional load forecasting to net load forecasting. In recent years, deep learning techniques that can improve model forecasting performance have developed rapidly in the field of residential load forecasting. However, the opaque nature of deep learning makes its practical application very difficult. This paper proposes a Transformer-based probabilistic residential net load forecasting method that utilizes quantile regression to quantify uncertainty in future load demand. Meanwhile, to improve the interpretability of deep learning model, local variable selection network is developed to automatically select relevant features and provide feature-level explanations. Additionally, interpretable sparse self-attention mechanism is proposed to extract long-term temporal dependencies. Numerical experiments are carried out with data from real household smart meters. The results show that the proposed model outperforms other state-of-the-art forecasting models. In terms of point forecasting, compared with the most common deep time series forecasting model LSTM, the proposed model decreases by 21.3%, 27.3% and 20.9% On three point forecasting performance metrics. Compared with Vanilla Transformer, the proposed InterFormer decreases by 9.9%, 10.5% and 9.0% On three point forecasting performance metrics. In terms of probabilistic forecasting, compared with LSTM and Vanilla Transformer, the average pinball loss of the proposed model decreases by 26.2% and 17.0%, respectively. Additionally, and most importantly, our model provides users with explanations in terms of feature importance and temporal patterns.

A Rapid Intensification Deterministic Ensemble (RIDE) for the Joint Typhoon Warning Center’s Area of Responsibility

Abstract The Rapid Intensification Deterministic Ensemble (RIDE) is an operational method used to estimate the probability of tropical cyclone rapid intensification in the Joint Typhoon Warning Center’s area of responsibility. Inputs to RIDE are current intensity, storm latitude, intensity change forecasts from seven routinely available operational deterministic models of intensity change, and the number of those models exceeding their individual 90th percentile of intensity change. Deterministic model inputs come from four numerical weather prediction models, two statistical–dynamical models, and one purely statistical model. In RIDE, logistic regression combines the deterministic inputs to form a probabilistic rapid intensification forecast model. RIDE then also generates deterministic intensity forecasts from these probabilistic forecasts that serve as forecaster guidance and as input to intensity consensus aids. Results based on a year of independent verification suggest good reliability and discrimination with a general tendency to underpredict rapid intensification events, but with few false alarms. Significance Statement An operational tropical cyclone forecaster makes a forecast with deterministic and probabilistic intensity guidance tools at their disposal. These models have a varying degree of abilities for predicting both intensity change and rapid intensification. The forecaster faces a dilemma in how to combine this disparate guidance to anticipate rapid intensification events. Here, the RIDE model provides probability forecasts associated with rapid intensification at 12-, 24-, 36-, 48-, and 72-h lead times and associated deterministic forecasts. RIDE provides skillful rapid intensification forecasts and helps rectify this forecast dilemma.

An enhanced decomposition integration model for deterministic and probabilistic carbon price prediction based on two-stage feature extraction and intelligent weight optimization

Accurately predicting carbon price can promote the rational allocation of carbon resources, reducing carbon emissions and contributing to green development. The decomposition integration framework is widely applied for carbon price forecasting, but several problems remain. Thus, this paper innovatively proposes an enhanced decomposition integration model for deterministic and probabilistic carbon price forecasting, which combines two-stage feature extraction and intelligent weight optimization. In order to decrease the complexity of the data and fully extract the characteristics, two decomposition approaches are utilized. For reconstruction, fuzzy entropy is applied to balance model complexity and computing efficiency. Next, the combination forecasting model based on two deep learning models is built to circumvent the constraints of the single forecasting model, and the cuckoo search optimization method (CS) is utilized to find the weight of the combination model adaptively. Considering the differences in the contributions of each component, the optimal weighting strategy based on CS is then used to derive the final forecast. Ultimately, considering the probability interval can provide more helpful information, the decomposition integration framework is supplemented with Gaussian process regression relying on the mixed kernel function for interval prediction. In an empirical study of five carbon trading markets, the hybrid model developed in this paper exceeded all baseline models regarding prediction stability, proving that the developed model can make effective forecasting for the carbon trading business.

Long-term probabilistic streamflow forecast model with “inputs–structure–parameters” hierarchical optimization framework

Accurate, reliable, and stable streamflow forecasts are essential for risk assessment and decision making in water resources management. Owing to the limited value of deterministic forecasting, probabilistic forecasting incorporating probability and confidence intervals is achieved by optimizing the predictors and forecast equation while identifying forecast error features. The combination of deterministic forecasts and error identification can facilitate water resources management. This study improved the traditional forecast model’s inputs selection, structure designation, and error parameters calibration to propose a long-term probabilistic streamflow forecast model with hierarchical optimization of the predictors, forecast equation, and errors characteristics. The model develops information entropy theory to screen the driving predictor set, the long short-term memory (LSTM) model to conduct deterministic forecasts, and the generalized autoregressive conditional heteroskedasticity (GARCH) model to identify time-varying errors. The proposed model, used in some case studies to forecast the monthly streamflow of two lakes, Hongze and Luoma lakes in China, was evaluated using the multidimensional index method considering “accuracy–reliability–stability” performance. The results revealed the following: (1) Predictor screening based on information entropy investigates the statistical characteristics of predictors, thereby improving the reliability of streamflow forecasts. (2) The LSTM model exploits the response between the driving predictors and streamflow, whereas GARCH model identifies the time-varying features of forecast errors effectively, which reduces the probability of forecast failure and increases the accuracy and stability of probabilistic forecasts. (3) Under current meteorological observation conditions and forecasting capability, the proposed forecasts can extend the maximum forecast lead time from 1 month to 3 months. (4) The proposed model improves the accuracy (root mean square error: 6.7%–34.8%), reliability (Brier score: 15.3%–27.9%), and stability (mistaken distance: 36.4–52.6%) in comparison with the benchmark of the two case studies, indicating that “inputs–structure–parameters” hierarchical optimization provides effective forecast information for water resources management.

Multi-step probabilistic forecasting model using deep learning parametrized distributions

Multi-step probabilistic forecasting model using deep learning parametrized distributions

Probabilistic forecasting of daily COVID-19 admissions using machine learning

Abstract Accepted by: Aris Syntetos Accurate forecasts of daily Coronavirus-2019 (COVID-19) admissions are critical for healthcare planners and decision-makers to better manage scarce resources during and around infection peaks. Numerous studies have focused on forecasting COVID-19 admissions at the national or global levels. Localized predictions are vital, as they allow for resource planning redistribution, but also scarce and harder to get right. Several possible indicators can be used to predict COVID-19 admissions. The inherent variability in the admissions necessitates the generation and evaluation of the forecast distribution of admissions, as opposed to producing only a point forecast. In this study, we propose a quantile regression forest (QRF) model for probabilistic forecasting of daily COVID-19 admissions for a local hospital trust (aggregation of 3 hospitals), up to 7 days ahead, using a multitude of different predictors. We evaluate point forecast accuracy as well as the accuracy of the forecast distribution using appropriate measures. We provide evidence that QRF outperforms univariate time series methods and other more sophisticated benchmarks. Our findings also show that lagged admissions, total positive cases, daily tests performed, and Google grocery and Apple driving are the most salient predictors. Finally, we highlight areas where further research is needed.

Probabilistic carbon price prediction with quantile temporal convolutional network considering uncertain factors

Accurate carbon price projections can serve as valuable investment guides and risk warnings for carbon trading participants. However, the escalation of uncertain factors has brought numerous new hurdles to existing carbon price forecast methods. In this paper, we develop a novel probabilistic forecast model called quantile temporal convolutional network (QTCN) that can precisely describe the uncertain fluctuation of carbon prices. We also investigate the impact of external factors on carbon market prices, including energy prices, economic status, international carbon markets, environmental conditions, public concerns, and especially uncertain factors. Taking China's Hubei carbon emissions exchange as a study case, we verify that our QTCN outperforms other classical benchmark models in terms of prediction errors and actual trading returns. Our findings suggest that coal prices and EU carbon prices have the most significant effect on Hubei carbon price forecasting, while air quality index appears to be the least important. Besides, we demonstrate the great contribution of geopolitical risk and economic policy uncertainty to carbon price projections. The effect of these uncertainties is more pronounced when the carbon price is at a high quantile level. This research can offer valuable guidelines for carbon market risk management and provide new insight into carbon price formation mechanisms in the era of global conflict.

Research on rainbow probabilistic forecast model based on meteorological conditions in ZhaoSu region

AbstractAn analysis of artificial rainbow observations in ZhaoSu region from 2017 to 2019 shows that rainbows mainly occur between 16:00 and 22:00 (LST) from April to September. The analysis based on the meteorological observation in the same period shows that precipitation, temperature, wind force and cloud variety contribute to rainbow formation. Approximately 90% of rainbows appear one hour after rainfall, and 100% of rainbows occur when the Beaufort wind scale is less than level 8 following Beaufort wind scale (less than 20.9 m/s), the temperature is greater than 8°C, and the cloud amount is greater than 40%, respectively. A rainbow probabilistic forecast model is constructed based on five meteorological factors. The forecast ability of the model is independently assessed by comparing rainbow forecasts and its observation in 2020. The Brier score is 0.20, indicating that the objective model is effective for rainbow forecasts.

A novel multi-step ahead forecasting model for flood based on time residual LSTM

Climate change has significantly impacted hydrology, including extreme precipitation, and changing precipitation patterns that could lead to an increase in flooding. Life and property benefit from accurate and reliable multi-step flood forecasting. Recently, Recurrent Neural Network (RNN) have become increasingly popular among hydrology researchers for their ability to capture historical dependencies, simplify computations by ignoring intermediate hydrological processes, and provide higher prediction accuracy than traditional models. However, RNN-based flood prediction models face two significant challenges. Firstly, due to their strict time-serial, RNN suffer from gradient issues such as vanishing and exploding gradients, which can make training RNN models difficult. To address this issue, we propose a Residual Long Short-Term Memory (ResLSTM) model that incorporates time residual connections into the time connections of LSTM. Secondly, most flood prediction models output a deterministic value, but the natural hydrological characteristics of the basin are a nonlinear and complex system with many influencing factors that have some randomness. This requires the use of probabilistic methods to modeling. Thus, we introduce the probabilistic forecasting model Autoregressive Recurrent Networks (DeepAR) into our flood prediction model, which outputs a prediction interval rather than a deterministic value. Then, we build four flood probability prediction models by combining DeepAR and four enhanced RNN, including ResLSTM (ours), Long Short-Term Memory (LSTM), Gate Recurrent Unit (GRU), and Time Feedforward Connections Simple Gate Recurrent Unit (TFC-SGRU). The performance of these models is evaluated by the long-term hydrologic data of the Passaic and Ramapo River basins in the United States. The results demonstrate that the prediction interval of the four models is more adaptive to flood uncertainties. And the accuracy of peak flow prediction is nearly 100% within a 90% prediction probability interval. The temporal residual-based model is more accurate and robust than the original LSTM and GRU. We believe this study fills a research gap in multi-step-ahead flood probability prediction and improves the accuracy and reliability of flood prediction models.

An improved encoder-decoder-based CNN model for probabilistic short-term load and PV forecasting

An improved encoder-decoder-based CNN model for probabilistic short-term load and PV forecasting

Probabilistic accumulation grey forecasting model and its properties

In grey system theory, the performance of an established grey forecasting model largely depends on how efficiently the grey information can be measured from data. Most existing grey forecasting models use grey accumulating generators to obtain grey information. However, not all grey information helps improve the performance of grey forecasting models. Consequently, simple accumulation leads to the accumulation of error from invalid grey information, which deteriorates the model performance. To address this issue, valid and invalid grey information were defined in this study according their contributions to the model performance. Further, it was proposed to use a Bernoulli distribution to simulate the distribution of valid/invalid grey information. Based on that probability, a probabilistic accumulation operator was designed to compute grey information, and this grey information was utilized to establish a probabilistic accumulation operator-based grey forecasting model (PGM(1,1)). PGM(1,1) is advanced in terms of forecasting because it is not negatively affected by invalid grey information. PGM(1,1) was tested on five public datasets and compared to other grey models as well as a wide range of other forecasting models, achieving state-of-the-art performance. In addition, a comprehensive analysis was conducted to demonstrate how the forecasting performance benefits from identifying valid/invalid grey information in PGM(1,1).