Henrik Madsen

Michael Nauheimer, Rishi Relan, Uffe Høgsbro Thygesen et al.

The real-time fault monitoring and control of the Vacuum Assisted Resin Transfer Moulding (VARTM) production process requires a knowledge of the position of the epoxy flow-front inside the mould. Therefore, a fast and accurate flow-front tracking system capable of combining the underlying physics of the flow-front dynamics with the measured data is highly prized. Stochastic differential equations (SDEs) based grey-box models deliver a good trade-off between high fidelity models and data-driven black-box models for designing such a flow-front position tracking system. In this paper, we propose a simple yet novel coupled SDE based spatiotemporal grey-box model of the flow-front dynamics in case of missing sensor information. The proposed method uses the finite difference approximation of the spatial domain of the flow-front for estimating spatial flow pattern of the epoxy. Furthermore, to accommodate for the missing sensor data, we utilise a modified version of the continuous-discrete extended Kalman filter (CD-EKF) based estimation framework for SDEs that takes into consideration the effective dimension of the measurement space during the identification process. The performance of the method is evaluated for various common sensor faults scenarios at different levels of measurement noise and sampling rates.

Julien Leprince, Henrik Madsen, Jan Kloppenborg Møller et al.

Optimal decision-making compels us to anticipate the future at different horizons. However, in many domains connecting together predictions from multiple time horizons and abstractions levels across their organization becomes all the more important, else decision-makers would be planning using separate and possibly conflicting views of the future. This notably applies to smart grid operation. To optimally manage energy flows in such systems, accurate and coherent predictions must be made across varying aggregation levels and horizons. With this work, we propose a novel multi-dimensional hierarchical forecasting method built upon structurally-informed machine-learning regressors and established hierarchical reconciliation taxonomy. A generic formulation of multi-dimensional hierarchies, reconciling spatial and temporal hierarchies under a common frame is initially defined. Next, a coherency-informed hierarchical learner is developed built upon a custom loss function leveraging optimal reconciliation methods. Coherency of the produced hierarchical forecasts is then secured using similar reconciliation technics. The outcome is a unified and coherent forecast across all examined dimensions. The method is evaluated on two different case studies to predict building electrical loads across spatial, temporal, and spatio-temporal hierarchies. Although the regressor natively profits from computationally efficient learning, results displayed disparate performances, demonstrating the value of hierarchical-coherent learning in only one setting. Yet, supported by a comprehensive result analysis, existing obstacles were clearly delineated, presenting distinct pathways for future work. Overall, the paper expands and unites traditionally disjointed hierarchical forecasting methods providing a fertile route toward a novel generation of forecasting regressors.

Julien Leprince, Waqas Khan, Henrik Madsen et al.

Many sectors nowadays require accurate and coherent predictions across their organization to effectively operate. Otherwise, decision-makers would be planning using disparate views of the future, resulting in inconsistent decisions across their sectors. To secure coherency across hierarchies, recent research has put forward hierarchical learning, a coherency-informed hierarchical regressor leveraging the power of machine learning thanks to a custom loss function founded on optimal reconciliation methods. While promising potentials were outlined, results exhibited discordant performances in which coherency information only improved hierarchical forecasts in one setting. This work proposes to tackle these obstacles by investigating custom neural network designs inspired by the topological structures of hierarchies. Results unveil that, in a data-limited setting, structural models with fewer connections perform overall best and demonstrate the coherency information value for both accuracy and coherency forecasting performances, provided individual forecasts were generated within reasonable accuracy limits. Overall, this work expands and improves hierarchical learning methods thanks to a structurally-scaled learning mechanism extension coupled with tailored network designs, producing a resourceful, data-efficient, and information-rich learning process.

Bastian Schmidt Jørgensena, Jan Kloppenborg Møller, Peter Nystrup et al.

We introduce the open-source Python package NABQR: Neural Adaptive Basis for (time-adaptive) Quantile Regression that provides reliable probabilistic forecasts. NABQR corrects ensembles (scenarios) with LSTM networks and then applies time-adaptive quantile regression to the corrected ensembles to obtain improved and more reliable forecasts. With the suggested package, accuracy improvements of up to 40% in mean absolute terms can be achieved in day-ahead forecasting of onshore and offshore wind power production in Denmark.

Peder Bacher, Hjörleifur G. Bergsteinsson, Linde Frölke et al.

Systems that rely on forecasts to make decisions, e.g. control or energy trading systems, require frequent updates of the forecasts. Usually, the forecasts are updated whenever new observations become available, hence in an online setting. We present the R package onlineforecast that provides a generalized setup of data and models for online forecasting. It has functionality for time-adaptive fitting of dynamical and non-linear models. The setup is tailored to enable the effective use of forecasts as model inputs, e.g. numerical weather forecast. Users can create new models for their particular applications and run models in an operational setting. The package also allows users to easily replace parts of the setup, e.g. using neural network methods for estimation. The package comes with comprehensive vignettes and examples of online forecasting applications in energy systems, but can easily be applied for online forecasting in all fields.

Kenneth Leerbeck, Peder Bacher, Rune Junker et al.

A machine learning algorithm is developed to forecast the CO2 emission intensities in electrical power grids in the Danish bidding zone DK2, distinguishing between average and marginal emissions. The analysis was done on data set comprised of a large number (473) of explanatory variables such as power production, demand, import, weather conditions etc. collected from selected neighboring zones. The number was reduced to less than 50 using both LASSO (a penalized linear regression analysis) and a forward feature selection algorithm. Three linear regression models that capture different aspects of the data (non-linearities and coupling of variables etc.) were created and combined into a final model using Softmax weighted average. Cross-validation is performed for debiasing and autoregressive moving average model (ARIMA) implemented to correct the residuals, making the final model the variant with exogenous inputs (ARIMAX). The forecasts with the corresponding uncertainties are given for two time horizons, below and above six hours. Marginal emissions came up independent of any conditions in the DK2 zone, suggesting that the marginal generators are located in the neighbouring zones. The developed methodology can be applied to any bidding zone in the European electricity network without requiring detailed knowledge about the zone.