The empirical foundation of this study consists of two distinct infrasound datasets that capture a wide array of geophysical phenomena and natural hazards. The first dataset is derived from the library of typical infrasonic signals (LOTIS), an open-source repository designed to facilitate the study of non-stationary atmospheric acoustic waves (Bryan et al., 2018; Zhao et al., 2024). These data were primarily recorded by the infrasound sensor array located at Windless Bight, Antarctica (sensor bandwidth: 0.01–0.2 Hz; the relative coordinates of example channels CHF1–CHF4 are shown in Fig. 1). This high-latitude monitoring site provides a unique environment for capturing a diverse range of Earth system events, including atmospheric gravity waves (AGW) triggered by auroras, microbaroms (MB), mountain associated waves (MAW), and infrasound generated by volcanic eruptions (VE). By including these natural hazard precursors alongside complex background noise, the dataset provides a rigorous baseline for testing the discriminative power of the proposed model. The dataset division follows the approach described in the reference, as detailed in Table 1.

The other infrasound dataset used in this study consists of field-measured data obtained from the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO). Due to high frequency of occurrence and the close resemblance of waveform characteristics and time-frequency distributions to those of nuclear explosions, natural earthquakes and chemical explosions represent significant sources of interference (Wang et al., 2022; Chang and Cui, 2013). Therefore, this dataset specifically emphasizes infrasound events generated by natural earthquakes and chemical explosions. Table 2 lists the number of events and waveforms for each category of infrasound in the catalog. The monitoring system runs continuously and actively 24 h a day, 7 d a week. Because each infrasound event is simultaneously captured by multiple sensors within a single station array as well as by multiple stations across the network, a one-to-many relationship is established between an event and its recordings. As a result, every event produces multiple waveforms.

Partial event information is summarized in Table 3.

The amount of infrasound data used in this study is limited. To make more efficient use of the data, the infrasound data are divided into three sub-datasets, and it is ensured that infrasound data from the same event are included in only one subset, thereby preventing the risk of data leakage. Table 4 displays the number of samples and events in the three subsets.

The data division approach is designed to minimize the correlation between the test set and the training set as much as possible, ensuring the reliability of the classification outcomes (Tan et al., 2021). The division methodology is illustrated in Fig. 2, beginning with the division of data into three event-based subsets containing 244, 298, and 247 raw signals respectively. Each subset undergoes log-scattering feature extraction, generating six feature sets per original signal (when the number of scattering paths is six), resulting in a total of 4734 input groups. In the classification experiments, one feature subset was sequentially employed as the test set, while the other two were utilized for training. The final metric was derived by averaging the results from these three independent classification trials.

For Branch 1, the scattering features derived from the wavelet scattering transform exhibit strict temporal locality preservation, necessitating a sequential modeling network that balances the capture of long-range dependencies with computational efficiency. Unlike the BiLSTM (Bidirectional Long Short-Term Memory), the BiGRU (Bidirectional Gated Recurrent Unit) utilizes a simplified gating mechanism, which significantly reduces parameter complexity while maintaining the ability to model long-term dependencies in sequential data (Cho et al., 2014; Hochreiter and Schmidhuber, 1997). This design enhances parameter convergence efficiency on limited-sample infrasound datasets and effectively mitigates the risk of overfitting.

However, the traditional BiGRU architecture utilizes only the final hidden state as the sequential representation, while the intermediate hidden states generated during the process are not directly incorporated into the final output computation. This approach implicitly assumes the Markov property, where ht is expected to encode the entire historical information. According to the principle of entropy increase in information theory, as the sequence length grows, the information entropy of the hidden state exhibits an exponential decay trend, leading to the gradual loss of early temporal features. Consequently, the final hidden state overly focuses on the final features, affecting the model's ability to model the entire sequence. To address this issue, a Global Attention (GA) mechanism (Luong et al., 2015; Zhang et al., 2024a) is introduced, which aims to mitigate information loss and enhance global interactive representation. This mechanism preserves information across both channel and spatial dimensions, thereby improving the performance of the neural network. The schematic diagram of the GA-BiGRU architecture is shown in Fig. 7.

The scalar at(s) represents the weight of the hidden state hs at time step s relative to all hidden states. 7at(s)=exp⁡(score(ht,hs))∑s′exp⁡(score(ht,hs′)) By combining the weights at(s) of all t hidden states, the weight vector at is obtained. The term ct(s) denotes the context vector at time step s, which is computed by multiplying the hidden state hs with its corresponding weight at(s). The global context vector ct for the entire sample is computed by summing across all time steps. 8ct=∑s=1Txat(s)hs where Tx is the number of sequence length. The target hidden state ht and context vector ct are concatenated to form an attention-enhanced vector ht̃. 9ht̃=tanh(Wc[ct;ht]) Finally, ht̃ is fed into a Softmax layer to produce the classification probability yt. 10p(yt|y<t,x)=softmax(Wsht̃) Through the aforementioned method, GA learns the weights of each time step of the BiGRU, comprehensively considering all hidden states and assigning scores to emphasize important features while suppressing irrelevant ones. This method not only fully leverages the strengths of BiGRU in processing sequential data but also addresses the limitation of traditional methods in insufficiently capturing key features through the attention mechanism, thereby significantly enhancing the model's performance.

The design of Branch 2 aims to leverage the distinct time-frequency feature distributions between the two types of infrasound events (Fig. 5). To this end, this branch incorporates a lightweight CNN architecture, centered around a multi-scale convolutional structure and a hierarchical feature extraction mechanism. Specifically, this branch utilizes parallel multi-scale convolutional kernels to capture different characteristics across varying receptive fields: smaller-scale kernels focus on capturing fine-grained fluctuations and local structures in the signal, while larger-scale kernels are used to extract energy distribution trends and macro patterns over extended time ranges. Through this multi-scale collaborative mechanism, the model can simultaneously respond to both local anomalies and global evolutionary patterns in infrasound signals. To further address the risk of overfitting in limited-data scenarios, this branch abandons traditional deep convolutional networks in favor of a shallower architecture with fewer parameters and a more streamlined structure. This design enhances its sensitivity and robustness to key spatial features (such as energy distribution and structural patterns). Through the aforementioned multi-scale and hierarchical processing, Branch 2 can effectively capture discriminative spatial structures across different time intervals, significantly improving the differentiation capability of infrasound events. The architecture is shown in Fig. 8.

Four convolution layers are utilized to extract features, ensuring the lightweight nature of the MSCI-Net. The first two layers utilize kernels of sizes 9 × 1 and 7 × 1 to expand the receptive field, enabling the rapid capture of global features, which are essential for understanding the overall structure and trends of infrasound signals. In the third layer, multiple convolution layers are parallelized with varying kernel sizes at the same network level (Li et al., 2024). This allows for the fusion of information filtered at different scales and effectively reduces information loss without increasing the network depth. Before the fully connected layer, a 1 × 1 convolutional kernel is applied. This is specifically designed for small-sample infrasound signal processing, aiming to reduce parameter counts and enhance nonlinearity, thereby improving the modeling capability for infrasound signals. The LeakyReLU activation function is introduced after the convolution layers to replace the conventional ReLU (Rectified Linear Unit). LeakyReLU retains a small gradient in the negative region, mitigating information loss and gradient vanishing issues caused by feature compression, as detailed in Eq. (11). 11σ(x)=xifx≥0γxifx<0(γ=0.01) Additionally, a small stride is adopted, allowing the convolutional kernels to scan the signal step-by-step, thereby capturing both local details and global features. To enhance translational invariance and improve the MSCI-Net's robustness to minor temporal shifts, MaxPooling layers are incorporated. Furthermore, to address the non-stationarity of infrasound signals and their sensitivity to environmental noise, which complicates the data distribution, a batch normalization layer is employed to accelerate convergence, stabilize the training process, and suppress noise interference. Dropout is also introduced to randomly deactivate a portion of neurons (i.e., the fundamental computational units that receive input signals, compute a weighted sum, and apply a nonlinear activation function) during training, reducing MSCI-Net complexity and preventing overfitting. Ultimately, the MSCI-Net employs two fully connected layers that serve as a critical bridge from feature integration to classification decision-making. While convolutional layers excel at extracting local features, these features remain spatially or temporally fragmented. The first fully connected layer (with 64 neurons) performs global integration of these highly abstract yet scattered “local feature fragments.” Through weighted summation and nonlinear activation functions, it learns complex high-order combinatorial relationships among them, thereby forming a compact global representation that incorporates all contextual information. Subsequently, the second fully connected layer maps this 64-dimensional global representation to the final sample label space. Each of neurons directly corresponds to an output category. Subsequently, the Softmax function generates the classification probability for each branch. This design, through multi-scale convolutional kernel configurations, a lightweight architecture, and anti-interference mechanisms, significantly enhances the extraction capability for complex infrasound signal features and the robustness of classification, while maintaining computational efficiency.

Through the strategic use of multi-scale convolutional kernels, a lightweight architecture, and robust anti-interference mechanisms, this branch significantly boosts the Infra-Net's ability to extract complex features from infrasound signals and enhances classification robustness.

Leveraging information fusion theory (Zhang et al., 2025, 2024c; Dai et al., 2024), Infra-Net employs its novel confidence-based decision-making module to integrate the results of the two branches, achieving enhanced classification robustness.

As shown in Fig. 9, the confidence-based decision-making module is conducted in the following stages. In the information collection stage, after feature extraction through the logarithmic wavelet scattering network, a single 1 × N infrasound signal yields a q×l set of logarithmic wavelet scattering features. Each q×1 scattering feature is treated as a distinct feature view for parallel assessment. Subsequently, the logarithmic wavelet scattering features are input into both the MSCI-Net and GA-BiGRU networks, which independently produce l sets of classification probability values corresponding to the same signal, denoted as (piA,piB) and (pia,pib), respectively, where (i=1, 2, …, l), q denotes the dimension of the scattering coefficients and l represents the number of scattering paths.

At the local fusion node, for each signal, the average of the l sets of probability values output by each network are calculated, which can be expressed as follows: 12(pA,pB)=1l∑i=1lpiA,1l∑i=1lpiB,13(pa,pb)=1l∑i=1lpia,1l∑i=1lpib.

The l collection nodes per branch are merged into one using the confidence-based averaging method (Eqs. 12–13), resulting in local integrated classification probabilities being obtained for each branch. This approach calculates the decision probability for a single signal across two branches by averaging the confidence of each column of scattering coefficients from the same signal, thereby mitigating the potential bias of a single-view representation through ensemble evaluation.

At the global fusion output node, to achieve a complementary advantage between the two branches, the second step of the confidence-based decision-making module is necessary. The final event category confidence is defined as the inner product of the output probabilities from both networks, which is denoted as 14(P1,P2)=(PA⋅Pa,PB⋅Pb). The ultimate classification outcome is determined by the event category corresponding to Max(P1,P2). The inner product operation in Eq. (14) combines the confidence levels of two networks through multiplication, emphasizing the joint support of both branches for the same category. The magnitude of the inner product value directly reflects the strength of the joint support of the two branches for that category. Therefore, the inner product value can serve as a measure of joint confidence, which helps enhance the reliability of the final decision.

In summary, by integrating temporal, spatial, and logarithmic wavelet scattering features, Infra-Net constructs a more diversified feature space. Subsequently, through a parallel network architecture and a confidence fusion strategy, it effectively enhances the reliability of the results, achieving robust and accurate classification of interference infrasound signals in natural hazards monitoring.

Before training the Infra-Net, it is necessary to customize the Infra-Net's parameters. The number of hidden layer units in the BiGRU, the learning rate for training, and the maximum number of iterations all impact the recognition results. The optimal combination of these three parameters is determined using the enumeration method and grid search optimization (Abbaszadeh et al., 2022). The BiGRU network includes two layers, which contain 512 and 256 hidden layer units. The Adam optimizer is employed, and cross-entropy is utilized as the loss function. The initial learning rate is 0.001, it is reduced to 0.0001 after 400 training epochs, and the maximum number of epochs is set to 500, with a minimum of 400 training samples per epoch.

As shown in Table 5, the confusion matrix allows us to compute four statistical quantities: true positives, false positives, false negatives, and true negatives.

Three indices are utilized to evaluate the classification performance of the Infra-Net: the accuracy (ACC), precision (P), and F1 score. The recall (R), the rate of true positive identification, is also considered. The specific definitions of each index are as follows: 15ACC=TP+TNTP+FP+TN+FN,16P=TPTP+FP,17R=TPTP+FN,18F1=2×R×PR+P. In addition, due to the highly pronounced uneven distribution of samples across various categories in the LOTIS dataset, Cohen's Kappa was further employed as a supplementary metric for evaluating model performance, to prevent the misleadingly optimistic assessment produced by traditional metrics such as accuracy under imbalanced data conditions. Cohen's Kappa is an important statistical measure used to evaluate the consistency and reliability between the predictions of a classification model and the true labels. Unlike accuracy, which only focuses on the proportion of correctly classified samples, this coefficient incorporates a correction for “random agreement”, eliminating the influence of random factors in the classification results. Thus, it provides a more robust and accurate measure of model performance. Especially in scenarios with highly skewed class distributions, Cohen's Kappa better reflects the model's true discriminative capability beyond random guessing. Its calculation formula is as follows: 19Cohen's Kappa=po-pe1-pe, where, po is the observed proportional agreement, representing the actual proportion of agreement between evaluators across all samples. pe is the expected random agreement proportion, calculated assuming evaluators classify independently and randomly.

First, experiments were conducted using the LOTIS dataset. Figure 10 shows classification results for Branch 1 (Fig. 10a), Branch 2 (Fig. 10b), and Infra-Net (Fig. 10c) using logarithmic wavelet scattering features. The limited data length only permits a threefold scattering feature path expansion. Experiments (a) and (b) generate three independent classifications per signal without decision fusion, yielding input counts of original signals × 3. Conversely, (c)'s confidence-based decision-making module fuses three results into single outputs, maintaining original signal counts. Thus, (a) and (b) contain threefold more features than (c). It can be seen that the classification accuracy reached above 98 % when using only one of the branches designed in this study, which is comparable to or even better than the classification results reported by Bryan et al. (2018) and Zhao et al. (2024) on the same dataset, both in terms of accuracy and time efficiency. Notably, compared with Zhao et al., which requires 10 000 iterations to achieve a maximum accuracy of 99.07 %, Branch 2 only needs 300 iterations to reach a result of 99.35 %, and the classification accuracy for AGW, MAW and VE events can all reach 100 %. Ultimately, when using Infra-Net for classification, the overall classification accuracy stabilizes at 100 %, yielding very excellent results. When facing the classification of different categories of infrasound signals, it is only necessary to adjust the number of neurons in the final fully connected layer of Infra-Net to match the corresponding number of categories, without requiring further modifications to the model architecture.

For the comparative experiments, state-of-the-art wavelet scattering-based methods along with advanced techniques currently employed in infrasound classification were selected, including WST-AMResNet-18 (Liu et al., 2025), WST-Trans (Shirodkar et al., 2025), WST-BiLSTM (Zhang et al., 2024b), and MS-SE-ResNet (Tan et al., 2024). The results are summarized in Table 6.

As can be observed from the Table 6, Infra-Net not only achieved the highest classification accuracy but also exhibited a significantly higher Cohen's Kappa compared to the other three models. The elevated Kappa value indicates a high level of agreement between the model's predictions and the ground truth labels, substantially surpassing the level expected by random chance. This demonstrates that the performance advantage of Infra-Net does not stem from biases in the training data distribution but is rather attributable to its stronger feature discrimination capability. Furthermore, it validates the robustness under class-imbalanced conditions.

In summary, experiments with different classification methods on this dataset demonstrate that Infra-Net consistently achieves the best performance, thereby validating its superior capability in multi-class interference infrasound signal recognition. Subsequently, the field-measured CTBTO dataset will be employed for evaluation.