Hierarchical VMD parameter selection for short-term HVAC load forecasting: A compact TCN-LSTM implementation

Abstract

Variational mode decomposition (VMD) separates heating, ventilation, and air-conditioning (HVAC) load into narrower-band signals, but the number of modes and the bandwidth-penalty parameter must be selected without using test-set outcomes. We evaluated a diagnostic-guided selection procedure using a multichannel temporal convolutional network (TCN) with long short-term memory (LSTM). The dataset comprised 2208 hourly observations from Wuhan Cigarette Factory in summer 2024. For each target, VMD used the preceding 168 h; the final 24 values from each mode served as TCN-LSTM input. Training-only diagnostics screened 64 parameter pairs using range-normalized reconstruction error, the coefficient of variation in mode-specific sample entropy, and the first-mode energy ratio. Sixteen pairs met the criteria. The eight lowest-scoring pairs formed a diagnostic shortlist, which was evaluated with seed 42 and then across seeds 42–44. The selected pair, K=7 and α=1500, yielded validation and test root-mean-square errors (RMSEs) of 2.113±0.079 and 2.253±0.161 kW across seeds 42–44 and 42–46, respectively. On the test segment, the reference 5,2000 and minimum-J admissible 8,1000 pairs yielded RMSEs of 2.243±0.094 and 2.285±0.161 kW, respectively. VMD-transformer with bidirectional LSTM (VMD-transformer-BiLSTM) and VMD-TCN-LSTM yielded 2.185±0.062 and 2.253±0.161 kW, respectively; Diebold–Mariano tests showed no consistent squared-loss difference across seeds. VMD-TCN-LSTM used 14 961 parameters, 73.8% fewer than VMD-transformer-BiLSTM. Excluding preprocessing and data handling, its single-sample network forward-pass time was 0.285±0.014 ms. Across 231 diagnostic-weight combinations, five pairs were selected, with seed-42 validation RMSE spanning 2.038–2.063 kW. Therefore, the procedure fixed VMD parameters without using test targets but did not establish an RMSE advantage over the reference pair.