Artificial intelligence-powered hybrid probability density prediction for ultra-short-term offshore wind power: A model integrating TVFEMD, R2CMSE, and MCQRNNG

The volatility of offshore wind power poses challenges for grid stability, necessitating reliable uncertainty quantification beyond deterministic forecasts. We propose a TRMG model that integrates time-varying filter empirical mode decomposition (TVFEMD), rapid refined composite multi-timescale entropy (R2CMSE), and an AI-based monotonic composite quantile regression neural network (QRNN) with Gaussian kernel estimation (MCQRNNG) for probabilistic prediction. Experiments conducted on TenneT offshore wind data demonstrated the TRMG’s strategic emphasis on uncertainty metrics over point accuracy. Compared to the EMD-based hybrid ERMG, TRMG reduces interval width by 53.846% (prediction interval normalized averaged width (PINAW): 0.036 vs. 0.078) and probabilistic error by 29.062% (pinball loss: 29.745 vs. 41.931 MW). Compared with the sample-entropy-based TSMG model, TRMG achieved superior coverage (prediction interval coverage probability: 0.841 vs. 0.403), 25.000% narrower intervals (PINAW: 0.036 vs. 0.048), and 70.555% lower distributional errors (pinball loss: 29.745 vs. 101.018 MW). Notably, when compared with the unconstrained quantile model TRQG with identical inputs, TRMG delivered 82.439% tighter intervals (PINAW: 0.036 vs. 0.205) through the monotonicity constraints of the MCQRNN, eliminated quantile crossing (0.000 vs. 0.510 MW for the two-layer QRNN), and provided the narrowest prediction bounds in the industry. The TRMG equips grid operators with decision-ready uncertainty estimates, which are essential for renewable integration and energy-security planning.