Table 3 Meaning and function of model performance evaluation indicators.

From: A comprehensive investigation of the relationship between propulsion speed and water influx in coal mine TBM inclined shaft projects

Formula

Parameter

Meaning

Role in the model

(8)

(9)

(10)

(11)

yi

Actual observations

As the learning foundation of the model; Used for model evaluation; Reflect the real situation

\(\overline{y}\)

Model prediction value

Test the generalization ability of the model; Provide decision support; Optimize the model

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{y}_{i}\)

Mean of actual values

As a reference benchmark; Used for data standardization and normalization;Auxiliary model analysis

\(\sum\limits_{i = 1}^{N} {(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{y}_{i} - y_{i} )^{2} }\)

Residual sum of Squares

Reflects the size of the error in model prediction

\(\sum\limits_{i = 1}^{N} {(y_{i} - \overline{y})^{2} }\)

Total sum of squares

Reflects the degree of fluctuation of the data itself

N

Number of samples

Reliability of results; Stability of indicators; Model comparative effectiveness

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{y}_{i} - y_{i}\)

Residual

Evaluate the fitting effect of the model; Detect outliers and outliers