## 3 Numerical Simulation  
For the noise dataset, the random step increment slip method [26] was applied to classify each noise type into 200 groups as shown in Figure 4. The length of each intercepted signal is 512. In addition, the min-max normalization method was used to map the noise signal into intervals [0, 1]. The separated noise signals were taken as reference signals \(x(n)\) for ANC system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure Parameters** & **Loss Function** & **Estimators Number** & **Maximum Depth** \\ \hline
**Optimal Parameters** & Huber & 500 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The optimal GBDT structure parameters for NOISEX-92 noise dataset.  
Figure 3: The construction of GBDT for ANC.  
To verify the effectiveness of the proposed method, the simulation environment was built for the ANC system using the Python-based Pyromacoustics software v.1.1 package [27]. Pyromacoustics software package could easily create an enclosed space acoustic simulation. Then, the sound source signal and microphone signal can be designed conveniently, and the room impulse response (RIR) of the enclosed space can be obtained. As shown in Figure 5, a rectangular space of 2.2 m \(\times\) 1.1 m \(\times\) 1.2 m was designed. The noise source and error microphone were located at two ends of the enclosed space, and the control output was located near the error microphone.  
To make the simulation better resemble real scenarios, the ray tracing algorithm was used to simulate the transmission and reflection of noise in the enclosed space. Air absorption was set as 0.0015. The wall surface of the enclosed space was set as rough concrete, with its material absorption and material scattering changing with center frequency, as shown in Table 2.  
According to the simulation process shown in Figure 5, four simulation schemes were designed to verify the universality of the proposed methods. As shown in Figure 6, the four simulation schemes designed in this paper include rectangular enclosed space without obstacles, rectangular enclosed space with obstacles, trapezoidal enclosed space without obstacles and trapezoidal enclosed space with obstacles.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Center** & 125 & 250 & 500 & 1000 & 2000 & 4000 & 8000 \\
**Frequency (Hz)** & 0.02 & 0.03 & 0.03 & 0.03 & 0.004 & 0.07 & 0.07 \\
**Settering** & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.6 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parallel table of material absorption, material scattering and center frequency.  
Figure 4: The partition method for different types of noise data.  
Figure 5: ANC simulation schematic diagram.  
A key point of ANC simulation is to obtain the impulse response (IR) of the primary path, which is the basis of ANC algorithm design. The IR of the primary path is affected by different environments and different noise types, so the IR of the primary path must be obtained under four simulation schemes for each noise type as shown in Figure 7. The shape of the enclosed space has an important impact on the IR of the primary path. However, the impact of noise type on IR is not obvious. After obtaining the IR of different noise types in different simulation situations, it can get the primary noise by convolution operation between IR and the input noise. Then, the design and analysis of ANC algorithm can be carried out on the basis of the simulation results.  
Figure 6: Four simulation schemes for the ANC, (**a**) Obstacle-free Rectangular Enclosed Space (**b**) Rectangular Enclosed Space with Obstacle (**c**) Obstacle-free Trapezoidal Enclosed Space (**d**) Trapezoidal Enclosed Space with Obstacle.  
Figure 7: Impulse response of the primary path for different noise type under four simulation schemes.