Table 14 Comparative assessment of multi-seasonal prediction metrics for ICEEMDAN-NCRBMO-AELM alongside representative hybrid prediction approaches on both training and validation datasets.

From: Hybrid prediction system for reliable multi-seasonal sustainable energy generation under meteorological and environmental volatility

Metrics

Hybrid approaches

Training set

Validation set

Mar

Jun

Sep

Dec

Mar

Jun

Sep

Dec

R2

ICEEMDAN-NCRBMO-AELM*

0.959*

0.873*

0.941*

0.979*

0.879*

0.865*

0.965*

0.863*

CPO-BITCN-BIGRU

0.928

0.810

0.902

0.951

0.854

0.806

0.959

0.783

PSO-BP

0.901

0.765

0.897

0.929

0.830

0.755

0.881

0.784

QRBI-LSTM

0.743

0.720

0.728

0.794

0.717

0.762

0.735

0.700

CNN-stacked-LSTM

0.949

0.844

0.926

0.963

0.848

0.839

0.942

0.837

CEEMDAN-iMPA-BiLSTM

0.793

0.636

0.790

0.815

0.781

0.624

0.837

0.703

Benchmark-ELM

0.785

0.659

0.781

0.812

0.778

0.634

0.810

0.656

Benchmark-LSTM

0.926

0.825

0.825

0.836

0.838

0.803

0.811

0.824

BKA-Transformer

0.946

0.851

0.934

0.966

0.859

0.842

0.961

0.844

MAE

ICEEMDAN-NCRBMO-AELM*

2.309*

4.279*

3.158*

3.138*

4.954*

4.514*

3.299*

3.428*

CPO-BITCN-BIGRU

4.406

6.839

5.161

3.308

6.592

7.284

4.542

6.711

PSO-BP

5.051

7.915

5.740

5.477

6.786

8.403

7.558

7.609

QRBI-LSTM

8.547

9.382

9.810

9.125

10.669

8.633

13.045

9.497

CNN-stacked-LSTM

3.602

6.273

4.329

2.714

6.355

6.417

4.881

5.696

CEEMDAN-iMPA-BiLSTM

7.198

11.750

8.344

7.962

8.521

13.787

9.453

9.712

Benchmark-ELM

7.513

9.927

8.595

9.104

8.838

12.376

10.680

11.894

Benchmark-LSTM

4.041

6.475

6.403

6.351

5.993

8.101

6.881

8.641

BKA-Transformer

2.436

4.523

3.627

3.664

6.937

7.829

4.355

4.073

RMSE

ICEEMDAN-NCRBMO-AELM*

3.987*

7.148*

5.258*

4.382*

8.071*

7.349*

5.384*

7.979*

CPO-BITCN-BIGRU

6.297

9.103

7.141

5.688

8.956

9.720

6.784

10.812

PSO-BP

6.872

10.295

7.636

7.204

9.760

10.799

9.807

10.871

QRBI-LSTM

11.350

11.774

12.483

11.906

13.047

10.512

15.421

13.693

CNN-stacked-LSTM

5.309

8.489

6.515

5.076

9.564

8.790

6.923

9.508

CEEMDAN-iMPA-BiLSTM

9.763

14.240

10.685

10.919

11.237

15.201

12.046

13.199

Benchmark-ELM

9.902

12.434

10.978

11.411

11.458

14.796

13.109

13.845

Benchmark-LSTM

5.999

9.858

8.823

8.577

9.799

10.646

9.473

10.112

BKA-Transformer

4.423

7.941

6.008

4.024

6.829

7.843

4.321

8.537

MA

ICEEMDAN-NCRBMO-AELM*

9.106*

16.044*

9.426*

6.877*

14.473*

17.219*

11.231*

11.255*

PE %

CPO-BITCN-BIGRU

20.893

32.175

22.019

12.756

26.541

33.820

14.332

28.094

PSO-BP

23.007

37.491

24.225

20.583

28.930

38.118

25.976

32.742

QRBI-LSTM

37.114

43.687

42.501

34.009

39.125

40.738

43.996

40.540

CNN-stacked-LSTM

15.700

21.352

15.867

12.184

20.449

21.906

13.218

22.671

CEEMDAN-iMPA-BiLSTM

33.918

47.240

35.803

30.932

36.057

48.164

31.889

41.336

Benchmark-ELM

34.551

45.388

36.216

34.975

36.632

47.027

35.590

45.469

Benchmark-LSTM

18.254

30.412

28.769

26.934

24.118

35.627

24.581

34.102

BKA-Transformer

11.124

18.856

12.102

9.458

17.756

23.491

11.403

14.082

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