# Noise Source Diagnosis Method Based on Transfer Path Analysis and Neural Network
## 2 Converter Cabinet System and Transfer Path Analysis Method
### Transfer Path Analysis Method  
The primary objective of transmission path analysis is to reduce the complexity of the system into an analysis model of incentive source transmission path target point. By analyzing the contribution of the excitation source transmitted to the designated target point, the main sound source can be located, giving instructions for system noise control. The noise sound pressure or vibration level at the target point is equal to the sum of the energy propagated along various paths to the evaluation point by each excitation source under working load excitation, assuming that the entire converter cabinet system is linearly invariant. When considering both structural sound and airborne sound, the target point noise can be expressed as  
\[P_{l}(t)=\sum_{i=1}^{\mu}P_{li}(t)+\sum_{j=1}^{y}P_{lj}(t) \tag{1}\]  
The number of transmission paths for the structural and acoustic loads, respectively, are indicated by \(u\) and \(v\) in the equation. \(P_{l}(t)\) is the total contribution response of the \(l\)-th target point; \(t\) is a time variable; \(P_{li}(t)\) is the contribution of the structural load of the \(i\)-th path to the target point \(l\); \(P_{lj}(t)\) is the contribution of the air load of the \(j\)-th path to the target point \(l\). Figure 2: Partial enlarged view of installation site. Through the reference point signal and the transfer function from the path point to the reference point when the converter cabinet is working, the load at the path point when the converter cabinet is working can be obtained by using the inverse matrix method. \[ \begin{bmatrix}F_{1}\\ \vdots\\ F_{n}\end{bmatrix} = \begin{bmatrix}H_{X_{1}/F_{1}}&H_{X_{1}/F_{2}}&\dots&H_{X_{1}/F_{ n}}\\ \vdots&\vdots&\ddots&\vdots\\ H_{X_{m}/F_{1}}&H_{X_{m}/F_{2}}&\dots&H_{X_{m}/F_{n}}\end{bmatrix} ^{-1} \begin{bmatrix} a_{1}\\ \vdots\\ a_{m}\end{bmatrix}  \tag{2}\]  
which can be simplified as  
\[\left[F\right]_{n}=\left[H\right]^{-1}_{m\times n}\left[a\right]_{m} \tag{3}\]  
The term \(m\) in the equation represents the number of reference points, and \(n\) represents the number of path points. \(\left[F\right]_{n}\) represents the load at the path point. Term \(\left[H\right]_{m\times n}\) is the transfer function matrix from the path point to the reference points. Term \(a_{m}\) represents the acceleration response of the reference point during operation. The number of reference points \(m\) (\(m=26\)) and path points \(n\) (\(n=13\)) tested satisfy the matrix statically indeterminate condition: \(m\geq 2n\), ensuring sufficient accuracy when solving the inverse matrix. \(\left[H\right]_{m\times n}^{-1}=\left(\left[H\right]^{T}\left[H\right]\right)^ {-1}\left[H\right]^{T}\) is created when \(m>n\) and takes the place of \(\left[H\right]_{m\times n}^{-1}\). Singular value decomposition (SVD) for \(\left[H\right]\), which is transformed into orthogonal space through SVD, is performed concurrently in order to prevent calculation errors brought on by improperly conditioned matrices. Different singular values and singular vectors in the system matrix represent various linear independences or independent terms. Utilizing LMS TPA software (Siemens LMS Test.Lab 17A), perform SVD decomposition on the frequency response function matrix to determine the load at the working path point based on the measured data. The target point response is calculated by calculating the load at the path point and the transfer function from the path point to the target point. \[ \begin{bmatrix}P_{1}\\ \vdots\\ P_{q}\end{bmatrix} = \begin{bmatrix}H_{P_{1}/F_{1}}&H_{P_{1}/F_{2}}&\dots&H_{P_{1 }/F_{n}}\\ \vdots&\vdots&\ddots&\vdots\\ H_{P_{q}/F_{1}}&H_{P_{q}/F_{2}}&\dots&H_{P_{q}/F_{n}}\end{bmatrix}\begin{bmatrix} F_{1}\\ \vdots\\ F_{n}\end{bmatrix}