Adaptive Data Analysis: Theoretical Results and an Application to Wind Power Forecasting
Authors
Vejling, Martin Voigt ; Kaaber, Morten Stig ; Andersen, Andreas Anton
Term
4. semester
Education
Publication year
2022
Submitted on
2022-05-31
Pages
113
Abstract
Dette speciale undersøger, om det at opdele tidsserier for Danmarks vindkraftproduktion i enklere dele (adaptiv dekomposition) kan forbedre forudsigelser én time frem. Vi afprøver fire metoder: empirisk modedekomposition (EMD), to compressive sensing-baserede metoder (teknikker til at genskabe signaler ud fra få målinger) og en PDE-EMD-variant, der bruger partielle differentialligninger til at stabilisere dekompositionen. Vi gennemgår relevant teori og viser også teoretiske egenskaber om entydighed for de compressive sensing-baserede metoder. Først testes metoderne på simulerede data og på faktiske data for dansk vindproduktion for at forstå deres egenskaber. Derefter anvendes de i én-times-forudsigelser og sammenlignes med to udbredte baselines: et long short-term memory (LSTM) neuralt netværk og autoregressive (AR) modeller. I en online opsætning, hvor modellen løbende opdateres i takt med nye målinger, præsterer PDE-EMD på niveau med baselines, mens EMD og de compressive sensing-baserede modeller klarer sig dårligere. I en offline opsætning, hvor hele datasættet kan behandles på forhånd, overgår EMD derimod markant de øvrige forudsigelsesmetoder. Resultaterne peger på, at dekompositionsbaserede forudsigelser fungerer særdeles godt offline, men at der kræves yderligere arbejde, før de er lige så robuste i en online kontekst.
This thesis examines whether breaking Danish wind power production time series into simpler building blocks (adaptive decomposition) can improve one-hour-ahead forecasts. Four methods are tested: empirical mode decomposition (EMD), two compressive sensing-based methods (techniques for reconstructing signals from few measurements), and a PDE-EMD variant that uses partial differential equations to stabilize the decomposition. The thesis presents the underlying theory and proves uniqueness properties for the compressive sensing approaches. We first assess each method on simulated data and real Danish wind production data to understand their behavior, and then use them for one-hour-ahead forecasting. Performance is compared against two common baselines: a long short-term memory (LSTM) neural network and autoregressive (AR) models. In an online setup, where models are updated continuously as new data arrive, PDE-EMD performs on par with the baselines, while EMD and the compressive sensing-based models perform worse. In an offline setup, where the full dataset can be processed in advance, EMD significantly outperforms the other forecasting methods. Overall, decomposition-based forecasting is very effective offline, but more work is needed to make it equally strong in online settings.
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