Table 6 Flowrate estimation errors of different frameworks

From: Towards parameter identification in pipeline hydraulics: integrating data-driven discovery and knowledge embedding

Flowrate estimation

Frameworks

MAPE of case 3/%

MAPE of case 4/%

Pseudo-steady condition

Transient condition

Whole flow process

Pseudo-steady condition

Transient condition

Whole flow process

Outlet flowrate

Proposed Framework (KE-ANN)

0.283

1.204

0.296

0.097

0.291

0.169

Proposed Framework (NARX)

0.402

1.683

0.530

0.391

0.875

0.624

Conventional Framework

0.609

3.803

0.708

0.639

1.017

0.727

Inlet flowrate

Proposed Framework (KE-ANN)

0.395

0.693

0.422

0.112

0.351

0.151

Proposed Framework (NARX)

0.443

0.837

0.533

0.176

0.465

0.195

Conventional Framework

0.565

1.447

0.589

0.455

1.956

0.620

  1. Note: The smallest estimation errors are highlighted in bold.