## 1 Introduction  
Wind power bearings, as critical components of wind turbines, endure significant periodic loads during operation, further compounded by their high power capacity and large dimensions. These extreme working conditions can accelerate failure mechanisms, including surface wear and fatigue-induced pitting, thereby impacting the reliability and service life of the turbine [1, 2, 3, 4]. Traditional heat treatment techniques, including induction hardening [5, 6, 7], have been used to strengthen bearings and are capable of obtaining greater depths of hardened layers. Still, they are often characterized by high energy consumption, extended processing durations, and other inherent drawbacks such as surface cracking, large deformations, and soft bands. Laser quenching is a widely employed surface treatment that enhances the properties of material surfaces while maintaining their bulk characteristics. However, this process typically results in a relatively shallow hardened layer, usually less than 2 mm in depth [8, 9, 10, 11, 12], which fails to meet the requirements for prolongedoperation in heavy-duty bearings application. To address these issues, laser-induced hybrid hardening, primarily utilizing laser quenching supplemented by electromagnetic induction heating, was proposed for the first time by our research team. Subsequently, related research has been conducted on laser-induced hybrid hardening devices, microstructure simulation, temperature field simulation, performance regulation, and experimental studies. This method enables the formation of a hardened layer with large depth, small HAZ, and excellent performance [13,14]. However, current research on the laser-induced hybrid hardening process relies on approaches such as the 'test-and-improve' cycle, the 'orthogonal experiment' [15, 16, 17], and the 'finite element simulation' [18, 19, 20, 21], with a qualitative focus on the influence of process parameters. The presence of multiple heat sources in the laser-induced hybrid hardening process makes the variation of hardened layer characteristics complex and the process parameters more numerous. The non-linear relationship between these processing parameters and the hybrid phase transformation model poses a challenge in representing it through a simple parametric model.  
Neural network models have recently gained widespread application across various fields, among which artificial neural networks (ANN) and back-propagation neural networks (BPNN) are most common. Their primary advantage lies in learning iteratively, without predefined mathematical functions. This capability allows them to effectively model non-linear, multivariate data and address complex interactions between process parameters [22, 23, 24, 25, 26]. [PERSON] et al. [27] used different models to analyze the impact of melt pool temperature stability on part morphology in laser metal deposition. BPNN is the most accurate for future temperature control design. [PERSON] et al. [28] found that ANN outperforms RSM in predicting the mechanical properties of 3D-printed ABS. However, research on applying these methods to hybrid hardening remains limited.  
In this study, a Box-Behnken design (BBD) experiment is employed to construct a response surface model (RSM) [29, 30] and a back-propagation neural network optimized by the whale optimization algorithm [31] (WOA-BPNN) model [32]. These models are applied within the process interval to compare their predictive capabilities and to optimize the process model [33]. This study will serve as an estimator in the closed-loop control process, continuously adjusting process parameters during manufacturing and providing a reference for achieving high-efficiency, deep laser-induction hardening.