Table 7 Comparison of the prediction results of the different decomposition methods.

From: Novel hybrid data-driven modeling based on feature space reconstruction and multihead self-attention gated recurrent unit: applied to PM2.5 concentrations prediction

Dataset

Decomposition method

RMSE

/(µg/m3)

MAE

/(µg/m3)

SMAPE

/(%)

PCC

DA

MBE

Lanzhou

CEEMDAN-GRU

7.1517

4.2856

13.67%

0.9003

0.7174

-0.2237

STL-GRU

5.3648

3.0980

9.24%

0.9460

0.7464

0.1726

Xi’an

CEEMDAN-GRU

10.2638

7.4251

20.74%

0.9452

0.7826

-1.2538

STL-GRU

8.8417

5.7235

15.03%

0.9597

0.7935

-0.6880

Beijing

CEEMDAN-GRU

13.3516

9.4665

43.94%

0.8408

0.7721

0.4473

STL-GRU

14.7382

10.1124

41.86%

0.8031

0.6360

1.2777

Shijiazhuang

CEEMDAN-GRU

9.7250

7.3547

20.97%

0.9287

0.7899

-1.9463

STL-GRU

7.6280

5.7090

16.21%

0.9561

0.7971

-0.1310

Chengdu

CEEMDAN-GRU

5.9986

4.4002

15.13%

0.9475

0.7645

0.3757

STL-GRU

5.1486

3.9717

14.09%

0.9647

0.7754

0.8519

Lhasa

CEEMDAN-GRU

1.0983

0.7557

10.11%

0.9583

0.7868

0.0307

STL-GRU

1.4493

1.0628

13.52%

0.9256

0.6029

0.0198