Deterministic Prediction Research Articles

The Future of Climate Modelling: Weather Details, Macroweather Stochastics—Or Both?

Since the first climate models in the 1970s, algorithms and computer speeds have increased by a factor of ≈1017 allowing the simulation of more and more processes at finer and finer resolutions. Yet, the spread of the members of the multi-model ensemble (MME) of the Climate Model Intercomparison Project (CMIP) used in last year’s 6th IPCC Assessment Report was larger than ever: model uncertainty, in the sense of MME uncertainty, has increased. Even if the holy grail is still kilometric scale models, bigger may not be better. Why model structures that live for ≈15 min only to average them over factors of several hundred thousand in order to produce decadal climate projections? In this commentary, I argue that alongside the development of “seamless” (unique) weather-climate models that chase ever smaller—and mostly irrelevant—details, the community should seriously invest in the development of stochastic macroweather models. Such models exploit the statistical laws that are obeyed at scales longer than the lifetimes of planetary scale structures, beyond the deterministic prediction limit (≈10 days). I argue that the conventional General Circulation Models and these new macroweather models are complementary in the same way that statistical mechanics and continuum mechanics are equally valid with the method of choice determined by the application. Candidates for stochastic macroweather models are now emerging, those based on the Fractional Energy Balance Equation (FEBE) are particularly promising. The FEBE is an update and generalization of the classical Budyko–Sellers energy balance models, it respects the symmetries of scaling and energy conservation and it already allows for both state-of-the-art monthly and seasonal, interannual temperature forecasts and multidecadal projections. I demonstrate this with 21st century FEBE climate projections for global mean temperatures. Overall, the projections agree with the CMIP5 and CMIP6 multi-model ensembles and the FEBE parametric uncertainty is about half of the MME structural uncertainty. Without the FEBE, uncertainties are so large that climate policies (mitigation) are largely decoupled from climate consequences (warming) allowing policy makers too much “wiggle room”. The lower FEBE uncertainties will help overcome the current “uncertainty crisis”. Both model types are complementary, a fact demonstrated by showing that CMIP global mean temperatures can be accurately projected using such stochastic macroweather models (validating both approaches). Unsurprisingly, they can therefore be combined to produce an optimum hybrid model in which the two model types are used as copredictors: when combined, the various uncertainties are reduced even further.

Using a hybrid optimal interpolation–ensemble Kalman filter for the Canadian Precipitation Analysis

Abstract. Several data assimilation (DA) approaches exist to generate consistent and continuous precipitation fields valuable for hydrometeorological applications and land data assimilation. Usually, DA is based on either static or dynamic approaches. Static methods rely on deterministic forecasts to estimate background error covariance matrices, whereas dynamic approaches use ensemble forecasts. Associating the two methods is known as hybrid DA, and it has proven beneficial for different applications as it combines the advantages of both approaches. The present study intends to explore hybrid DA for the 6 h Canadian Precipitation Analysis (CaPA). Based on optimal interpolation (OI), CaPA blends forecasts and observations from surface stations and ground-based radar datasets to provide precipitation fields over the North American domain. The application of hybrid DA to CaPA consisted of finding the optimal linear combination between (i) an OI based on the Regional Deterministic Prediction System (RDPS) and (ii) an ensemble Kalman filter (EnKF) based on the 20-member Regional Ensemble Prediction System (REPS). The results confirmed the known effectiveness of the hybrid approach when low-density observation networks are assimilated. Indeed, the experiments conducted for the summer without radar datasets and for the winter (characterized by very few observations in CaPA) showed that attributing a relatively high weight to the EnKF (50 % and 70 % for summer and winter, respectively) resulted in better analysis skill and a reduction in false alarms compared with the OI method. A deterioration in the moderate- to high-intensity precipitation bias was, however, observed during summer. Reducing the weight attributed to the EnKF to 30 % alleviated the bias deterioration while improving skill compared with the OI-based CaPA.

Deterministic and probabilistic ship pitch prediction using a multi-predictor integration model based on hybrid data preprocessing, reinforcement learning and improved QRNN

The deterministic and probabilistic prediction of ship motion is important for safe navigation and stable real-time operational control of ships at sea. However, the volatility and randomness of ship motion, the non-adaptive nature of single predictors and the poor coverage of quantile regression pose serious challenges to uncertainty prediction, making research in this field limited. In this paper, a multi-predictor integration model based on hybrid data preprocessing, reinforcement learning and improved quantile regression neural network (QRNN) is proposed to explore the deterministic and probabilistic prediction of ship pitch motion. To validate the performance of the proposed multi-predictor integrated prediction model, an experimental study is conducted with three sets of actual ship longitudinal motions during sea trials in the South China Sea. The experimental results indicate that the root mean square errors (RMSEs) of the proposed model of deterministic prediction are 0.0254°, 0.0359°, and 0.0188°, respectively. Taking series #2 as an example, the prediction interval coverage probabilities (PICPs) of the proposed model of probability predictions at 90%, 95%, and 99% confidence levels (CLs) are 0.9400, 0.9800, and 1.0000, respectively. This study signifies that the proposed model can provide trusted deterministic predictions and can effectively quantify the uncertainty of ship pitch motion, which has the potential to provide practical support for ship early warning systems.

Day‐ahead wind power ramp forecasting using an image‐based similarity search strategy

With the increase in penetration of wind generation on interconnected power systems, the importance of wind power ramp forecasting has continuously grown. Large power ramps caused by sudden weather changes raise more concerns due to their significant impact on the power system economics and stability. Correct wind power ramp forecasts can help the system operators and utility companies to tradeoff the risks when scheduling wind energy in the electricity market. In this paper, a day-ahead wind power ramp forecasting algorithm is developed to provide probabilistic ramp forecasts for look-ahead times up to 48 h using hourly wind speed forecasts from Environment Canada High Resolution Deterministic Prediction System (HRDPS). An image-based similarity search strategy has been designed to build a direct link between the wind speed forecasts and the wind power ramp prediction, thus reducing the impact of the uncertainty from both the power production forecast model and the ramp identification process on the forecasting accuracy. A performance assessment and validation of the proposed ramp event forecasting method is conducted by using the forecast and operation data from six investigated wind farms across Canada.

Dynamic Bayesian network for durability of reinforced concrete structures in long-term environmental exposures

Reinforced concrete (RC) structures under the marine environment may be subjected to chloride-induced corrosion of reinforcement, which significantly impacts the structural serviceability and reliability and further affects the sustainability and development of society. However, most of the existing durability assessment methods for RC structures only address their static and deterministic durability prediction and assessment at the design stage given the constant environment, ignoring the influences of stochastic environmental effects, uncertainties in structural properties, and inspection results. To this end, this paper proposes a dynamic Bayesian network (DBN) based durability assessment framework combined with a deterioration model that considers random changes in environmental parameters, convective chloride ion transport, and corrosion-induced cracking of concrete. In this framework, two-dimensional chloride transport and its influences on the durability deterioration assessment are concerned and achieved using the finite difference method. Besides, to reduce the deviations in probabilistic evaluation, the good-lattice-point-set-partially stratified-sampling (GLP-PSS) method is employed to establish a DBN framework. The proposed DBN framework is used for sensitivity analysis through a real-world example to examine the effects of the environmental model, chloride transport mode, and inspection results of concrete crack on durability assessment.

Estimating live-bed local scour around bridge piers in cohesionless sediments: applicability and bias of selected models

To design the foundation system of waterway bridges, Load and Resistance Factor Design guidelines suggest use of deterministic scour depth prediction models. Understanding the inherent bias of deterministic scour depth prediction models will advance the development of reliability index-based foundation design regime. Four bridge scour depth prediction models were assessed in terms of two statistical parameters, termed herein mean absolute percentage error (MAPE), and conservatism, percentage of cases the predicted scour depth exceeded the measured scour depth. Live-bed laboratory and field scour depth databases were used in analyses to quantify model scatter by comparatively assessing the computed scour depth versus measured data. For live-bed laboratory data, values of MAPE ranged from 23.5% to 59.8%, whereas conservatism ranged from 28.4% to 97.8%. For live-bed field data, conservatism varied from 93.3% to 95.1%, while MAPE ranged from 205.6% to 319%. Statistical models were applied to ascertain the biasness of the four deterministic models. Accuracy and conservatism of a given model were consequently adjusted through proposed modification factors. The proposed approach allows for the selection of a suitable modification factor to satisfy a target probability of deceedance or a target conservatism.

Probabilistic Prediction of Collisions between Cyclists and Vehicles Based on Uncertainty of Cyclists’ Movements

The uncertainty of cyclists’ movements has a significant impact on predicting the risk of collisions between cyclists and vehicles. The purpose of this study was to provide a method for assessing collision risk using probability, taking into account the uncertainty of cyclists’ movements. A cyclist model was first developed using a first-order Markov model. Then, based on Monte Carlo sampling, the distribution characteristics of the minimum distance and the time-to-collision (TTC) between the vehicle and the cyclist were extracted. By fitting these features, the probability density functions of the collision distance and TTC were estimated to derive the collision probabilities. The effectiveness of the collision probability prediction model was benchmarked against a deterministic crash risk prediction model (autonomous emergency braking [AEB] system) applied to three real-world cases previously reconstructed in an in-depth crash database. The results show that the collision probability prediction model can effectively predict the risk of collisions between cyclists and vehicles with better accuracy than AEB systems using a fixed trigger threshold. This study is a valuable reference for the development of advanced vehicle collision avoidance systems to protect cyclists and other vulnerable road users.

Can signal-to-noise ratio indicate prediction skill? Based on skill assessment of 1-month lead prediction of monthly temperature anomaly over Japan

We present a skill assessment of 1-month lead deterministic predictions of monthly surface air temperature anomalies over most part of Japan based on a large-ensemble climate model, SINTEX-F. We found that September is the most predictable and the only month in which the prediction skill beats the persistence. Interestingly, however, prediction of December becomes skillful (correlation skill: 0.67) when we select only years in which the signal-to-noise ratio of the predictions is relatively high. This means that the signal-to-noise ratio can partly indicate the prediction skill. The inter-member co-variability suggests that a combination of the tropical Pacific and western Indian Ocean surface temperature is the key for the prediction. Although seasonal climate prediction in the mid-latitude regions, such as Japan, is still challenging in general, providing the signal-to-noise ratio and the inter-member co-variability in addition to the real-time prediction might be useful for stakeholders to know how confident the individual prediction is, as well as its potential sources of predictability. Such information can be helpful to take necessary mitigation measures to reduce socio-economic losses associated with extreme climate.

Assessing spatial connectivity effects on daily streamflow forecasting using Bayesian-based graph neural network

Data-driven models have been widely developed and achieved impressive results in streamflow prediction. However, the existing data-driven models mostly focus on the selection of input features and the adjustment of model structure, and less on the impact of spatial connectivity on daily streamflow prediction. In this paper, a basin network based on graph-structured data is constructed by considering the spatial connectivity of different stations in the real basin. Furthermore, a novel graph neural network model, variational Bayesian edge-conditioned graph convolution model, which consists of edge-conditioned convolution networks and variational Bayesian inference, is proposed to assess the spatial connectivity effects on daily streamflow forecasting. The proposed graph neural network model is applied to forecast the next-day streamflow of a hydrological station in the Yangtze River Basin, China. Six comparative models and three comparative experimental groups are used to validate model performance. The results show that the proposed model has excellent performance in terms of deterministic prediction accuracy (NSE ≈ 0.980, RMSE≈1362.7 and MAE ≈ 745.8) and probabilistic prediction reliability (ICPC≈0.984 and CRPS≈574.1), which demonstrates that establishing appropriate connectivity and reasonably identifying connection relationships in the basin network can effectively improve the deterministic and probabilistic forecasting performance of the graph convolutional model.

A Novel Hybrid Machine Learning Model for Wind Speed Probabilistic Forecasting

Accurately capturing wind speed fluctuations and quantifying the uncertainties has important implications for energy planning and management. This paper proposes a novel hybrid machine learning model to solve the problem of probabilistic prediction of wind speed. The model couples the light gradient boosting machine (LGB) model with the Gaussian process regression (GPR) model, where the LGB model can provide high-precision deterministic wind speed prediction results, and the GPR model can provide reliable probabilistic prediction results. The proposed model was applied to predict wind speeds for a real wind farm in the United States. The eight contrasting models are compared in terms of deterministic prediction and probabilistic prediction, respectively. The experimental results show that the LGB-GPR model improves the point forecast accuracy (RMSE) by up to 20.0% and improves the probabilistic forecast reliability (CRPS) by up to 21.5% compared to a single GPR model. This research is of great significance for improving the reliability of wind speed, probabilistic predictions, and the sustainable development of new energy.

Real-time prediction of 6-DOF motions of a turret-moored FPSO in harsh sea state

Predicting the motions of a floating offshore structure could be useful for a motion compensation system and could provide useful early warning information for motion-sensitive operations. In this study, a deep learning (DL) model was developed to provide deterministic predictions of 6-DOF motions of a turret-moored floating production storage and offloading unit (FPSO) in a harsh sea state. These predictions rely purely on past time series of the motion itself. Training and test databases were obtained using a scaled model test in a wave basin. The 6-DOF motions were fed into the DL model simultaneously, and the predictive motion series was obtained from corresponding 6 standalone subnets. The prediction extended by approximately 15 s (one wave cycle) into the future with good accuracy for all 6-DOF motions. By concentrating the predictions in order, a 3-hour time series of the motions was reconstructed. Hyperparameter importance was also evaluated for dropout probability, number of RNN layers, number of fully connected layers, and number of neurons in each layer in terms of accuracy and training duration. Without the requirement for wave measurements, the proposed model is closer to real applications in offshore engineering.

A hybrid forecasting system with complexity identification and improved optimization for short-term wind speed prediction

Accurate wind speed prediction can relieve the pressure of peak regulation and frequency modulation of the power system and improve the acceptance capacity of wind power. In order to improve the forecasting accuracy of wind power, this paper proposes a hybrid wind power forecasting system. Firstly, the energy entropy theory (EVMD) is used to determine the number of VMD decompositions to solve the problem of VMD over-decomposition; secondly, the sample entropy (SE) is utilized to identify the complexity of the intrinsic mode functions (IMFs) of EVMD, and applied different methods to forecast. In addition, improved grey wolf optimizer (IGWO) is used to optimize the parameters of the prediction method. Finally, based on the kernel density estimation (KDE), this paper proposes to construct the prediction interval using the noise signal obtained by EVMD. Under the verification of two different datasets and comparative experiments, the MAPE of the deterministic prediction results reached 3.0985% and 7.1153% respectively. The coverage rate of nondeterministic prediction under 90% confidence reaches 95% and 96.67% respectively. The results show that the prediction effect of the proposed model is significantly better than that of other models, and it can provide strong support for the smooth operation of wind farms.

Coupled modelling of storm surge, circulation and surface waves in a large stratified lake

The wind-driven nature of large lakes suggests that the accuracy of meteorological inputs is essential for hydrodynamic modelling. Moreover, coupling between the meteorological inputs and density stratification may also influence the simulated lake behavior. To investigate wind-driven large lake processes, a high-resolution coupled Delft3D-SWAN model was applied to Lake Ontario to simulate storm surges, surface waves, and circulation during two recent storm events. In both events, the sustained wind speeds approached 20 m s−1; however, variations in wind direction and duration altered the lake's surface wave and storm surge responses. The influence of different atmospheric inputs was investigated by comparing results from two spatially varied atmospheric models: the Rapid Refresh (RAP) and the High-Resolution Deterministic Prediction System (HRDPS). Hydrodynamic simulations using HRDPS were marginally better, with maximum root mean squared errors (RMSE) between modelled and observed water levels of 0.07 m, compared to 0.08 m with RAP. Predictions of the magnitude and timing of the maximum wave heights varied based on wind fields, with differences between predicted peak wave heights of up to 0.4 m. Both events occurred during a stratified period, allowing for a comparative evaluation of the influence of baroclinic and barotropic processes on the simulated surface wave and storm surge results. Simulations including the vertical density gradient gave a better representation of current velocities with depth and resulted in an improved prediction of peak storm surge magnitudes and surface water level behavior following the storms, reducing the RMSE by up to 12%.

Probabilistic prediction model of steel to concrete bond failure under high temperature by machine learning

The interface bond performance between concrete and steel bars under high temperature has a crucial influence on the fire resistance design of the reinforced concrete (RC) structure, but there is no unified model for the prediction of the bond strength yet. Previous experimental studies have conducted plenty of RC member pull-out tests under high temperature, which could be collected as a comprehensive database. As a data-driven method, machine learning (ML) can efficiently establish the regression relationship between input features and output directly through the data. However, current studies usually use classic ML algorithms for establishing a deterministic prediction model, where only one scalar prediction would be provided and its confidence level is uncertain, which is not instructive for the users. Thus, based on previous experimental data, this paper uses the Natural Gradient Boosting (NGBoost) algorithm to establish a unified probabilistic prediction model for the bond strength between steel bars and concrete under high temperature, considering several key factors, such as fiber fraction, concrete compressive strength, bond strength under room temperature et al. By training on the collected 267 experimental data, the prediction results of the ML based model show that these models attain higher accuracy than those of empirical formulas, and the NGBoost based probabilistic prediction model has better prediction performance than the general deterministic ML models. Finally, the Shapley value method is used to explain the calculation results of the model, and compared with the statistical results such as variance and mean of the calculation results of the five empirical formulas, ML has obvious advantages.

A new framework for short-term wind power probability forecasting considering spatial and temporal dependence of forecast errors

Since deterministic prediction errors of wind power cannot be avoided, probabilistic prediction can adequately describe the uncertainty of wind power and, thus, provide further guidance to dispatching authorities for decision making. Current probabilistic prediction methods for wind power are still incomplete in mining its physical variation process. Therefore, this study constructs a new framework for short-term wind power probabilistic forecasting considering the spatio-temporal dependence of errors by mining the spatio-temporal characteristics of historical wind power data and numerical weather forecasts at numerical weather prediction (NWP). First, the deterministic prediction results are obtained by an improved deep belief network (DBN); then, a multi-location NWP is introduced to propose a multi-level error scenario partitioning method considering the spatio-temporal dependence property. Finally, a new error sample set is formed by reconstructing the kernel density estimation method to adapt the model, and the short-term wind power probability prediction at different confidence levels is carried out. It is, thus, concluded that the effectiveness of the overall framework under the probabilistic prediction considering spatio-temporal dependence is verified in a wind farm in Jilin, China, and the prediction accuracy is effectively and significantly improved compared with the same confidence level, and the coverage of the evaluation index prediction interval is improved by 1.23, 0.72, and 0.80%, and the average bandwidth of the prediction interval is reduced by 2.14, 1.40, and 0.63%, which confirms the proposed effectiveness and feasibility of the method.

Two-stage hybrid model for hydrological series prediction based on a new method of partitioning datasets

• A new method of dividing datasets based on PSO is proposed. • BNN incorporates Langevin dynamics in the parameter update step (LDBNN). • Integration of LDBNN, CEEMDAN, VMD and the proposed method yield the hybrid model. • The new data dividing method performs better than the traditional dividing method. • The hybrid model yields excellent point and interval predictions. Obtaining accurate point estimates and reliable interval prediction results for rainfall and runoff series is important to aid in water resource decision-making and planning management in a changing environment. In this paper, we propose a two-stage hybrid model (P-CVEE-LDBNN). The model uses the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods for data preprocessing and a Bayesian neural network (LDBNN) based on Langevin dynamics as a prediction model. Then, a new dataset partitioning method based on a particle swarm optimization algorithm, which is different from the traditional dataset partitioning method, is applied. A one-stage hybrid model (T-CEE-LDBNN) that integrates the CEEMDAN method and the traditional method of partitioning datasets, a one-stage hybrid model (P-CEE-LDBNN) that integrates the CEEMDAN method and the new method of partitioning datasets, and the two-stage hybrid P-CVEE-LDBNN model were compared. These models were applied to monthly runoff and monthly precipitation series from seven hydrological and meteorological stations in the Yellow River basin. The mean absolute error (MAE), absolute root mean squared error (RMSE), Nash–Sutcliffe efficiency (NSE), and correlation coefficient (R) were used to evaluate the predictive ability of the models. The containment ratio (CR), the average bandwidth (IW), and the average asymmetry degree (S) were used to evaluate the interval prediction results of the models. The results show that (1) the subset obtained with the new method of data partitioning considering statistical properties is more favorable for model prediction. (2) The second decomposition approach based on VMD is a reliable method that can significantly improve the prediction accuracy of the final model. (3) Compared with traditional neural networks that can only obtain deterministic point prediction results, Bayesian methods can provide intervals with prediction results, making the results of the two-stage hybrid P-CVEE-LDBNN model highly reliable.

Latent Heat Nudging in the Canadian High-Resolution (2.5 km) Regional Deterministic Prediction System

Abstract This study examines the application of latent heat nudging (LHN) for the assimilation of radar-derived precipitation rates in the 2.5-km High-Resolution Deterministic Prediction System (HRDPS) operated by Environment and Climate Change Canada. One goal of this study is to document the overall impact of applying LHN in the most recent operational implementation of the HRDPS. On average, for 110 forecasts conducted over a 2-month period in 2016, LHN is shown to improve a composite NWP index (measuring the average change in RMSE over many variables and observation types) by ∼1.5% compared to a control experiment with no LHN. For winds between 400 and 100 hPa, reductions in RMSE between 1% and 4% are found for lead times up to 48 h. For precipitation, improvements for lead times up to 6 h are shown. Another goal of this study is to quantify the relative contributions for certain components of the LHN implementation. The features being investigated are the inclusion of LHN within the assimilation cycle, the use of idealized heating profiles and the conservation of relative humidity. The 2-month forecasting experiments are conducted with these components deactivated in turn. By comparing these experiments, it is found that the inclusion of LHN in the assimilation cycle has the largest impact. It is also found that the use of idealized profiles in locations where precipitation is observed but not simulated is a critical aspect of this implementation of LHN. A case study is also provided to illustrate the impact of LHN on altitude winds.

Implementation of Scale-Dependent Background-Error Covariance Localization in the Canadian Global Deterministic Prediction System

Abstract The approach of applying different amounts of horizontal localization to different ranges of background-error covariance horizontal scales as proposed by Buehner and Shlyaeva was recently implemented in the four-dimensional ensemble–variational (4DEnVar) data assimilation scheme of the global deterministic prediction system (GDPS) at Environment and Climate Change Canada operations. To maximize the benefits from this approach to reduce the sampling noise in the ensemble-derived background-error covariances, it was necessary to adopt a new weighting between the climatological and flow-dependent covariances that increases significantly the role of the latter. Thus, in December 2021 the GDPS became the first operational global deterministic medium-range weather forecasting system to rely completely on flow-dependent covariances in the troposphere and the lower stratosphere. The experiments that led to the adoption of these two related changes and their impacts on the forecasts up to 7 days for various regions of the globe during the boreal summer of 2019 and winter of 2020 are presented here. It is also illustrated that relying more on ensemble-derived covariances amplifies the positive impacts on the GDPS when the background ensemble generation strategy is improved.

Simulating thaw-induced land cover change in discontinuous permafrost landscapes

Permafrost thaw is causing a rapid evolution of the lowland discontinuous permafrost regions of the Taiga Plains in Northern Canada and elsewhere in the Northern Hemisphere. Notably, this thaw is changing the spatial distribution of the dominant hydrologic land cover types (permafrost plateaus, fens, and isolated bogs) in parts of the Northwest Territories (NWT), Canada. Here, we develop a multinomial time series land cover model (TSLCM) to simulate historical land cover transitions, model spatial patterns of transition, and predict the long term evolution of land cover in the areas surrounding the Scotty Creek Research Station (SCRS), NWT, and similar discontinuous permafrost landscapes. The machine learning-based TSLCM is informed by a set of observed spatio-temporal variables. The independent variables represent driving factors of change, and include the estimated summertime land surface temperature anomaly (LST), the distance and a custom cost distance to land cover interfaces, time increment between initial and final states, and time-accumulated temperature; the dependent variable is classified land cover maps from 1970 to 2008. First, we applied both random forest (RF) and Multinomial Log-Linear Regression (MLR) methods to train a synthetic data model; the model which improves the performance of the TSLCM in extrapolating time series change by adding new data instances to the initial data set. We boosted the initial data by combining the predicted land cover change maps from synthetic data model and the real data set. Then, we evaluated a MLR, RF, and an extreme gradient boosting (XGBoost) model in their ability to simulate land cover change.The final results of this study show that the Ensemble Learning (EL) based approaches are capable of effectively representing historical land cover change and can produce physically consistent and plausible future land cover scenarios. Deterministic predictions from the TSLCM indicate that the permafrost plateaus’ coverage will continue to decrease, with corresponding decreases in isolated bogs’ coverage and their secondary runoff contributing areas.

Receding-Horizon Prediction of Vehicle Velocity Profile Using Deterministic and Stochastic Deep Neural Network Models

The paper firstly proposes a deterministic deep feedforward neural network model aimed at predicting the city bus velocity profile over receding time horizon based on the following inputs: actual vehicle position, actual velocity or short-term history of vehicle velocities, time of day and day of week. A systematic analysis of the influence of different input subsets, history interval length and prediction horizon length is carried out to find an optimal configuration of NN model inputs and hyperparameters. Secondly, a stochastic version of neural network prediction model is proposed, which predicts expectations and standard deviations of velocity patterns over the receding time horizon. The stochastic model prediction accuracy is verified against the recorded test dataset features, as well as by comparing the predicted velocity expectation with the deterministic model prediction and correlating the predicted velocity standard deviation with deterministic model prediction uncertainty metrics. The verification results indicate that: (i) the deterministic model velocity prediction accuracy is characterized by the R2 score greater than 0.8 for the prediction horizon length of 10 s and remains to be solid (greater than 0.6) for the horizon lengths up to 25 s; (ii) the actual vehicle position and the velocity history are the most significant input features, where the optimal value of history interval length lies in the range from 30 to 50 s; (iii) the stochastic model have only slightly lower accuracy of predicting the velocity expectation along the receding horizon when compared to the deterministic model (the root mean square error is higher by 2.2%), and it outputs consistent standard deviation prediction.