## 3 BPM Theory and Noise Label Set Generation  
Airfoil self-noise originates from the trailing edge of the airfoil and is one of the primary sources of aerodynamic noise in wind turbine blades, caused by instabilities within the boundary layer flow on the airfoil surface [18,19]. According to the classical BPM model, airfoil self-noise consists of five components:  
Figure 10: Part of the airfoil sample. Figure 9: Generate Airfoil set through Interpolation Using the B-spline. (**a**) Interpolation with RISOA21 and NACA64618 (**b**) Interpolation with S809 and NACA64418. 1. Turbulent Boundary Layer Trailing Edge Noise (TBL-TE) \[SPL_{TBLTE}=10 log_{10}\{10^{\frac{SPL_{s}}{10^{\frac{SPL_{s}}{10}}}}+10^{\frac{SPL_{ p}}{10}}\}\] (18) \[SPL_{s}=10 log_{10}(\frac{\delta_{s}^{*}M^{5}\bigtriangleup l\overline{D_{h}}}{ r^{2}})+G_{A}(\frac{St_{s}}{St_{1}})+(W_{1}-3)\] (19) \[SPL_{p}=10 log_{10}(\frac{\delta_{p}^{*}M^{5}\bigtriangleup l \overline{D_{h}}}{r^{2}})+G_{A}(\frac{St_{p}}{St_{1}})+(W_{1}-3)+\bigtriangleup W _{1}\] (20)  
In the equations: SPL\({}_{\rm P}\)--pressure surface noise, SPL\({}_{\rm S}\)--suction surface noise, \(\delta\)*--Thickness of the boundary layer at the trailing edge of the suction and pressure surfaces, St--Strouhal number, G\({}_{\rm A}\)--noise spectral shape function, W\({}_{1}\)--trailing edge noise amplitude function; \(\Delta\)W\({}_{1}\)--sound pressure level correction function, \(\Delta\)--the spanwise length of the airfoil. 2. Separated Flow Stall Noise (SEP) \[SPL_{SEP}=10 log_{10}(\frac{\delta_{p}^{*}M^{5}\bigtriangleup l\overline{D_{h}}} {r^{2}})+G_{B}(\frac{St_{s}}{St_{2}})+W_{2}\] (21)  
In the equations: G\({}_{\rm B}\)--Stall noise spectrum shape function, W\({}_{2}\)--Stall Noise Amplitude Function. 3. Laminar Boundary Layer Vortex Shedding Noise (LBL-VS) \[SPL_{LBLVS}=10 log_{10}(\frac{\delta_{p}M^{5}\bigtriangleup l\overline{D_{h}}} {r^{2}})+G_{1}(\frac{St^{\prime}}{St_{peak}^{\prime}})+G_{2}(\frac{Re}{St_{ peak}^{\prime}})+G_{3}(\alpha)\] (22)  
In the equations: The shape functions G\({}_{1}\), G\({}_{2}\), and G\({}_{3}\) are respectively dependent on the Reynolds number, Strouhal number, and angle of attack. 4. Tip Vortex Noise (TIP) \[SPL_{TIP}=10 log_{10}(\frac{M_{\max}^{3}M^{2}l_{tip}^{2}\overline{D_{h}}}{r^{2} })-30.5(log_{10}St^{\prime\prime}+0.3)^{2}+126\] (23)  
In the equations: M\({}_{\max}\)--Maximum mach number in the area of tip vortex formation, \(St^{\prime\prime}\)--The modified Stouhal number, I\({}_{\rm tip}\)--The span-wise extension of the tip vortex at the trailing edge. 5. Trailing Edge Bluntness Vortex Shedding Noise (TEB-VS) \[SPL_{TEBVS}=10 log_{10}(\frac{hM^{5.5}\bigtriangleup l\overline{D_{h}}}{r^{2} })+G_{4}(\frac{h}{\delta_{avg}^{*}},\psi_{TE})+G_{5}(\frac{h}{\delta_{avg}^{*} },\psi_{TE},\frac{St^{\prime\prime\prime}}{St_{peak}^{\prime\prime\prime}})\] (24)  
In the equations: \(h\)--Trailing Edge Thickness, G\({}_{\rm 4}\)--Spectrum at peak levels, G\({}_{\rm 5}\)--An auxiliary function for adjusting the shape of the spectrum. To verify the reliability of the BPM theory in predicting the self-noise of wind turbine airfoils, the prediction accuracy of the NACA0012 airfoil noise was evaluated by combining the BPM model with experimental data. When calculating the self-noise of the airfoil, the chord length was set to 30.48 cm, the observation angle was set to 90\({}^{\circ}\), the observer distance was set to 1.22 m, the incoming wind speed was 71.3 m/s, and the angles of attack were set at 0\({}^{\circ}\), 10.8\({}^{\circ}\), and 14.4\({}^{\circ}\). We used MATLAB together with the RFOIL program as a tool for calculating noise. The results are shown in Figure 11.  
By comparing the BPM predicted spectrum with experimental data, it can be seen that the results from BPM theory agree well with the experimental data, although there is a slight deviation below 2000 Hz. This model can be used to generate two-dimensional airfoil noise data in subsequent research, thereby enabling training for deep learning models.