# A Machine Anomalous Sound Detection Method Using the IMS Spectrogram and ES-MobileNetV3 Network
## 3 Proposed Method
### Anomaly Detection Network  
In this study, we have chosen to employ MobileNetV3 [23] as the primary architecture for the sound detection network. The MobileNetV3 network builds upon the foundation of its predecessors, incorporating the deep separable convolution from MobileNetV1 and integrating the linear bottleneck and inverted residual structures of MobileNetV2. This approach effectively reduces computational demands while maintaining a compact structure. Furthermore, the MobileNetV3 network introduces the SE attention module within the inverted residual structure. The SE attention module dynamically adjusts the importance of different channels in the feature map by learning a set of channel weights. This dynamic adjustment facilitates feature selection and enhancement. However, in order to minimize computational overhead, the SE attention module conducts the dimensionality reduction operation on the feature matrix at the fully connected layer. This approach will lead to the loss of some information of the original data, resulting in the network not accurately restoring the original information. As a result, it may affect network performance while inevitably increasing the complexity of the model and the amount of calculation. In light of these considerations, this paper proposes an improved ES-MobileNetV3 network model for machine anomalous sound detection. The primary structure of the model is depicted in Figure 5. We have made modifications to the SE attention module of the MobileNetV3 network, replacing it with the Efficient Channel Attention (ECA) attention module [35], and implementing SoftPool [36] to replace the global average pooling of the ECA attention module. The ECA attention module presents a novel strategy for local cross-channel interaction, eliminating dimensionality reduction operations to obtain channel weights through adaptive one-dimensional convolution. The authors of [35] demonstrated the significance of avoiding dimensionality reduction in learning channel weights. Effective cross-channel interaction can reduce model complexity while preserving strong performance. By adaptively selecting the size of the one-dimensional convolutional kernel, we can define the scope of local cross-channel interaction, resulting in both reduced computational demands and performance optimization. In the ECA attention module, a global average pooling method is used to reduce the size of the feature map. Common pooling methods typically involve maximum pooling and average pooling, both of which will lead to the loss of some useful information. The average pooling performs average operations on the feature points in the feature region, which reduces the amount of computation but weakens the feature representation of the sound data. To address this issue, our approach aims to maintain more acoustic feature information during the down-sampling process, thus enhancing detection accuracy. We use the SoftPool operation instead of the average pooling operation in the ECA attention module. SoftPool continually updates gradient values during backpropagation, minimizing information loss in the pooling process while preserving the functionality of the pooling layer. The calculation process of SoftPool is shown in Figure 6. The feature region is defined as \(P\), and the size of the pooling kernel (\(R\)) is \(k\times k\). The SoftPool operation calculates the  
Figure 4: The IMS spectrogram of the machine Fan running sound. (**a**) log-Mel spectrogram; (**b**) SincNet spectrogram. corresponding feature weight according to the eigenvalues. The calculation process can be described as follows:  
\[w_{i}=\frac{e^{a_{i}}}{\sum\limits_{j\in R}e^{a_{j}}} \tag{9}\]  
where \(w_{i}\) denotes the weight, \(a_{i}\) denotes the value of a feature point, and the weight is calculated to ensure that the feature texture information can be transmitted more effectively. The output value of the SoftPool operation is produced through a standard summation of all weighted activations within the pooling kernel neighborhood, \(R\).