Table 3 Model evaluation metrics for Multi-parameter coupling Compensation.

From: Deep learning-based multi-parameter coupling compensation algorithm for clamp-on gas metering systems

Metric name

Calculation formula

Evaluation standard

Weight coefficient

Mean Absolute Error

\(\:MAE=\frac{1}{n}\sum\:_{i=1}^{n}\parallel\:{y}_{i}-{\widehat{y}}_{i}\parallel\:\)

< 0.5% excellent

0.30

Root Mean Square Error

\(\:RMSE=\sqrt{\frac{1}{n}\sum\:_{i=1}^{n}{\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2}}\)

< 0.3% excellent

0.25

Maximum Absolute Error

\(\:MA{E}_{max}={\text{m}\text{a}\text{x}}_{i}\parallel\:{y}_{i}-{\widehat{y}}_{i}\parallel\:\)

< 2.0% acceptable

0.20

Correlation Coefficient

\(\:R=\frac{\sum\:\left({y}_{i}-\stackrel{-}{y}\right)\left({\widehat{y}}_{i}-\stackrel{-}{\widehat{y}}\right)}{\sqrt{\sum\:{\left({y}_{i}-\stackrel{-}{y}\right)}^{2}\sum\:{\left({\widehat{y}}_{i}-\stackrel{-}{\widehat{y}}\right)}^{2}}}\)

> 0.95 excellent

0.15

Computational Time

\(\:{T}_{comp}=\frac{{t}_{inference}}{{t}_{baseline}}\)

< 1.5 acceptable

0.10