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probability in the whale feeding process [18] , with:

(

· · cos(2 ) + if ≤ 0.5
+1
= (13)

− if ≥ 0.5

where the value interval of is [0, 1].
(c) Search for predation
The value of determines whether the whale swims toward the optimal individual or toward a random indi-
vidual, when | | ≤ 1, the whale chooses to swim toward the optimal individual [19] , as provided in Equations
(13) and (14); when | | > 1, the whale chooses to swim toward a random individual, which will enhance the
search ability of the whale population as a whole [20] , and the mathematical model equation is expressed as
follows:

= · − (14)

+1 = − · (15)

where rand is a random position vector.

2.2.4 WOA-Attention-GRU fatigue state recognition
The WOA is a heuristic optimization algorithm based on the principles of natural selection and biological be-
havior. Inspired by the hunting behavior of whales, it efficiently identifies the global optimal solution within
few iterations [21] . Furthermore, WOA circumvents the intricacies of parameter tuning, thus reducing the risk
of overfitting, which greatly benefits our handling of the problems with multiple parameters. In our work, the
role of WOA is to optimize the Attention-GRU model; to be precise, it seeks the optimal model parameters,
thereby maximizing the model’s accuracy on the fatigue driving behavior dataset. The algorithmic progres-
sion of the fatigue driving detection [22] , grounded in the synergy of the WOA and Attention-GRU, is visually
depicted in Figure 4. It encompasses three main components: whale optimization, processing of driving be-
havior data, and the establishment of the Attention-GRU neural network model. In the whale optimization
phase, the mean squared difference [mean squared error (MSE)] between the predicted fatigue level by the
Attention-GRU model and the true fatigue level serves as the fitness function. The aim is to ascertain a set
of hyperparameters that minimize this mean squared difference when fed into the Attention-GRU model [23] .
The mean squared deviation is expressed as follows:

1 Õ 2
= − (16)

=1
Where denotes the predicted value of fatigue level, indicates the true value of fatigue level, and
is the total number of fatigue samples.

In the WOA-Attention-GRU model, the overall framework can be divided into three main components: the
WOA part, the data processing part, and the Attention-GRU model part [Figure 4] [24] . In the data process-
ing part, we extract features from driving behavior data and conduct relevant analysis and selection. The main
stepsincludedatacollectionandpreprocessing: collectingdrivingbehaviordata,includingvehiclespeed,SWA,
acceleration, etc., and cleaning the data to remove outliers and noise, ensuring the data’s accuracy and relia-
bility. Subsequently, operational behavior features are extracted from the preprocessed data, including but
not limited to the rate of change of the SWA , vehicle acceleration, and braking frequency. These features are
then selected using correlation analysis methods closely related to driving fatigue. Through correlation and
preference analysis, the most representative features are selected as input variables for the model. In the whale
optimization part, WOA is used to optimize the hyperparameters of the Attention-GRU model. The main
steps include initialization: WOA encodes the initial values, including the number of iterations, batch size,