Table 2 Meaning and function of Libsvm regression model formulas.

(3)

f(x)

Predictive value

The estimated value of the target variable (such as propulsion speed) calculated by the Libsvm model based on input data

y

True value

The accurate value of actual measurement or known target variables (such as propulsion speed)

ε

Insensitive loss function parameters

Used to control the balance between fitting accuracy and model complexity

(4)

w

Weight vector

Determining the direction of the hyperplane affects the calculation of the distance between data points and the hyperplane

b

Threshold

Determine the position of the hyperplane in the feature space

(5)

C

Punishment factor (regularization parameter)

Control the degree of influence of outliers on the model

\(\xi_{i} ,\xi_{i}^{*}\)

Slack variable

Processing data points that fall outside the decision boundary to enhance model robustness

(6)

φ(x)

Nonlinear mapping function

Map raw data to high-dimensional space and handle nonlinear relationships

N

Number of samples

Determine the number of samples to participate in model training or computation

(7)

x_i,y_i

Sample data points

Representing different sample data of the input model for calculating kernel function values

γ

Kernel function parameters

Determine the shape of the Gaussian kernel function and adjust the model’s generalization ability