Time series data classification for real-time diagnostics has been widely explored using machine learning methods. Traditional machine learning classification models, such as logistic regression (LR) [4], support vector machines (SVM) [5], decision trees (DT) [6], random forests (RF) [7] and k-nearest neighbors (KNN) [8], have been commonly used. Users must manually compute and input statistical or physical features to classify time series data using these traditional machine-learning techniques. To overcome these limitations, research has increasingly focused on classification models based on deep learning, which integrates feature extraction and selection within the model itself.

Since introducing the backpropagation algorithm and convolution operations, convolutional neural network (CNN)-based models have gained attention in classification tasks. AlexNet [9], for instance, used ReLU as the activation function in the basic convolution layers and employed max-pooling. The residual neural network (ResNet) [10], introduced in 2016, was the first CNN model to add skip-connections, addressing the chronic problem of gradient vanishing in deep learning. In 2017, densely connected convolutional networks (DenseNet) were proposed to overcome ResNet’s limitations [11]. Unlike the simple summation of skip-connections in ResNet, DenseNet concatenates outputs depth-wise. Although initially designed for image recognition, these models have been widely adapted for time series classification by performing convolution operations in 1D. The computational complexity of 1D CNNs is significantly lower than that of 2D CNNs under the same conditions, making them easier to train. As a result, 1D CNNs have been employed in various applications, such as real-time electrocardiogram (ECG) monitoring and vibration-based structural damage monitoring [12]. In this paper, we aim to analyze and classify time series data using DenseNet, a model that can effectively capture local features in the data due to its densely connected layers.

The following discusses prior studies that performed time-frequency analysis on sensor data collected in underwater environments. In underwater environments, hydrophone sensor data is the most commonly used time-series data. Sheng et al. acquired time-domain hydrophone sensor data for ship-radiated noise recognition, decomposing the input signal into frequency components using an auditory filter bank inspired by the cochlea [13]. This approach enabled end-to-end time-frequency analysis, with the auditory filter optimized for ship classification based on the relationship between center frequencies and bandwidths. However, this method is unsuitable for underwater cutting tasks, which involve unclear characteristic frequencies and are performed at various depths and on diverse cutting materials. Yingchun et al. applied the Hilbert transform to hydrophone sensor data to create time-frequency images used as inputs [14]. However, generating suitable time-frequency images requires prior domain knowledge. Additionally, this approach requires extensive preprocessing steps for image generation, and 2D neural networks are computationally more complex than 1D networks, making integration into real-time monitoring systems challenging. Therefore, this study proposes and applies a time-frequency analysis method that considers the diversity of underwater cutting environments and target materials, using a parallel input structure for 1D signals to facilitate easier integration with monitoring systems. While frequency domain analysis is commonly applied to acoustic signals from hydrophones [15], it is less frequently used for pressure signals. Camci et al. analyzed the frequency domain of underwater pressure to study the flow within the rim seal cavity region, excluding low-frequency pressures from the analysis by considering them as noise [16]. Similarly, in this study, we observed abnormally high amplitudes in the low-frequency range, accounting for about 1% of the total frequency range in the underwater pressure signal. To address this, we applied zero-padding to the affected areas before using them in the analysis.

This section discusses previous studies that used parallel-configured networks to process input data in various ways. Gan et al. introduced a parallel DenseNet-BiLSTM to simultaneously consider small- and large-scale features in ECG signals [17]. Although this method is designed to capture a wide range of signal features, it only applies to time-domain signals and does not consider the frequency domain. Fan et al. proposed a parallel ResNet to assess road pavement condition and safety by accounting for different types of cracks [18].

While this approach applied a parallel structure to analyze multivariate signals simultaneously, it did not analyze each signal across multiple domain spaces. In this paper, we propose a deep learning model that not only inputs multivariate sensor data but also uses a parallel DenseNet structure to simultaneously learn both the time and frequency domains of the sensor data.

The proposed structure of the adaptive weighted parallel 1D-DenseNet is illustrated in Fig. 1. The four preprocessed input signals are fed into the one-dimensional densely connected convolutional network(1D-DenseNet) in a parallel configuration. This parallel structure of DenseNet extracts temporal and frequency features of each sensor through densely connected convolution operations. Consequently, the model minimizes the loss of local features caused by the mixing of multi-domain signals during the computation process. The outputs from each DenseNet are flattened and then multiplied by the adaptive weight parameter (AWP), resulting in a single weighted output that is concatenated. The AWP assigns weights to emphasize local features according to their importance, with the vector having the same size as the flattened DenseNet output, thus adjusting the weights among the features of the multivariate signals to ensure stable concatenation. Although the AWP is initially set to the same value across all elements before training, its values are optimized during the learning process. The concatenated weighted output is then passed through a Fully-Connected (FC) layer to determine the presence of cutting. Since this study aims to perform binary classification for the presence of cutting, the FC layer reduces the concatenated weighted output to two values. These two values represent probabilities of cutting presence and are trained to minimize the Cross-Entropy with the true labels. The proposed network structure, as described, extracts local features from multivariate signals, emphasizes them according to their importance, and ultimately determines the presence of underwater cutting. The advantages of proposed network structure are validated through cutting state prediction experiments using sensor data obtained from actual underwater remote cutting experiments. Additionally, an ablation study will be conducted to evaluate the contributions of each component of the network.

This study employs a DenseNet to process time-series data. Due to the skip connections between layers in DenseNet, the input to each layer is a collection of the outputs from all previous layers. This design grants DenseNet a superior ability to extract local features compared to other models. DenseNet is constructed by repeatedly stacking a set of Dense blocks and transition layers, as shown in Fig. 2. Upon receiving the model’s input, it undergoes a 7 7 convolution (Conv) with a kernel size of 7, followed by a 3 3 max pooling, before being passed to the first Dense block. The output of the final Dense block directly proceeds to the FC layer for classification, bypassing any transition layers. Each Dense block consists of 1 1 and 3 3 Conv layers, batch normalization (BN), and the ReLU activation function, which enhance feature extraction. The number of Conv layers within each Dense block is determined based on the dataset. Transition Layers, composed of BN, ReLU, 1 1 Conv, and 2 2 average pooling, accelerate the model’s execution.

The 1D-DenseNet is a network that has been modified to process one-dimensional data by adapting the two-dimensional convolution operations used in the standard DenseNet to one dimension [19]. Despite this modification, the powerful local feature extraction capabilities inherent to DenseNet are preserved, making it highly effective for time-series data classification.

In this study, four types of multi-domain, multivariate signals are used as model inputs. While this allows the model to learn diverse information, it also poses the challenge of reduced convergence due to discrepancies between domains. To address this, we propose the application of AWP that assesses the importance of each input and enables the model to adjust weights accordingly. The output of the final Dense block in DenseNet is flattened into a 1-dimensional matrix and passes through a FC layer. The output of the FC layer is then processed through a Softmax function to represent probabilities for each classification label. In the case of parallel network configurations, the outputs of each parallel branch are concatenated into a single FC layer. AWP is applied at this stage by multiplying each output by a vector-shaped matrix, which is the same size as the parallel outputs, before concatenation. Consequently, each index of the DenseNet output is multiplied by its respective weight before concatenation. Initially, AWP is filled with weights like 0 or 1. Since AWP is not a simple matrix but is computed with gradients, its values are updated during the backpropagation process as training progresses. Thus, by the end of training, the values of AWP are optimized according to the importance of the input data and applied as weights to the inputs. This approach not only enhances the convergence of the model in handling multivariate signals but also allows the model to focus on and learn from region-specific features that carry significant information. The loss function used for training is Cross-Entropy. Cross-Entropy is employed to measure the difference between two probability distributions and is used in classification tasks to compare the actual data distribution with the model's predicted distribution. The formula is given in Eq. 1.

N denotes the number of batch elements, x represents the input batch, p_i and q_i represent the actual data distribution and the predicted distribution, respectively.

To train the adaptive weighted parallel 1D-DenseNet, Python 3.12.4 and PyTorch 2.3.1 libraries were used. All training was conducted on a computer with an Intel Core i7-13700 CPU (2.10 GHz), 32GB of memory, and an NVIDIA GeForce RTX 3060 graphics card. As mentioned in Section 3.2, the number of repetitions for Conv layers within the Dense blocks should be set according to the dataset. In this study, the network was configured with four Dense blocks, with 3, 6, 12, and 6 repetitions of Conv layers, respectively. The Adam optimizer was used as the optimizer, following Eqs. 2.1, 2.2, and 2.3.

The hyperparameters β₁ and β₂ were set to 0.9 and 0.999, respectively, and the L2 penalty weight decay λ was set to 10⁻⁴ to mitigate overfitting. The ɛ value for numerical stability was set to 10⁻⁸. The initial learning rate was set to 10⁻⁵, and a multi-step scheduler was applied with a step size of 20 and γ of 0.2. The entire training process was conducted over 100 epochs with a batch size of 16.

Data obtained from an underwater laser-cutting robot operated by the Korea Atomic Energy Research Institute (KAERI) was used to validate the proposed network structure's effectiveness. The experimental setup is configured as shown in Fig. 3. The TX200 robot arm, which has 6 degrees of freedom, is remotely controlled by an operator to perform the cutting. The robot arm head has a laser head and an auxiliary gas supply device. The high-power laser beam emitted from the laser head cuts the specimen, while the high-speed airflow from the auxiliary gas supply device removes the molten material. The robot arm head is also fitted with a hydrophone and pressure sensor alongside the cutting device. Data is acquired through the sensors mounted next to the cutting device, allowing for direct capture of signals generated during the cutting operation.

The cutting process is divided into six stages, as shown in Fig. 3(d). Steps 2 (slow cutting), 3 (normal cutting), and 4 (abnormal cutting) all involve attempting to cut using the laser. In Steps 2 and 3, the laser reaches the end of the specimen, resulting in smooth cutting. In contrast, abnormal cutting occurs when the laser does not fully reach the end of the specimen due to the rapid movement of the laser head, leading to incomplete cutting. Our goal is to perform a binary classification between the cutting state (Steps 2 and 3) and the idle state (the remaining stages).

Despite requiring significantly less user intervention in feature extraction than traditional machine learning, deep learning still necessitates a thorough preprocessing process to achieve high classification performance. In this study, we perform preprocessing on raw sensor signals in the following order: up-sampling, sliding window, FFT, and scaling. Up-sampling is used to augment insufficient data or fill in gaps. We apply up-sampling to unify the data sizes obtained from the two types of sensor signals used in this study. The data is then reconstructed using a sliding window. When treating a window as a single input, more local information can be learned compared to considering each datum point as an input. Additionally, class imbalance is a major issue in classification tasks. Data imbalance can be mitigated by setting a larger sliding delay in underrepresented regions during the sliding window process. The sliding window process is illustrated in Fig. 4.

An FFT is performed for each window that has been reconstructed to a fixed size. The FFT results in N/2 datum points if the window size is N. Since the time-frequency signals are input into a parallel network with the same structure, the frequency signals must also have a size of N. Therefore, the remaining N/2 datum points are filled in using zero-padding. The signals, now unified in size, exhibit significant scale differences depending on the type of sensor. To eliminate the model's bias toward specific signals that may arise from this disparity, each data point is normalized using a MinMax scaler before input to the network

The experimental process lasts 140 seconds, and the hydrophone and pressure sensors have sampling rates of 50,000 and 12,800 Hz, respectively. Due to the sensor sampling rates and the experimental duration, 7,000,000 time series data points were acquired from the hydrophone, and 1,792,000 data points were acquired from the pressure sensor. The time series raw data obtained from both sensors are shown in Fig. 5.

The preprocessing is carried out according to the method described in Section 4.2. First, to unify the input sizes of the two sensor data streams, the pressure data is up-sampled to the same size as the hydrophone data using linear interpolation. The entire raw data is then reconstructed using a window of 1000 data points. Since the cutting state accounts for a relatively small proportion of the experimental process, data augmentation applies a sliding delay of 400 to the windows for the normal cut range. FFT is performed on each window. Low-frequency regions corresponding to 1% of the frequency domain in the pressure data are considered noise and zero-padded. An additional 500 zero-padding is added to the FFT results to maintain the original window size. As a result, the cutting state data size for pressure and hydrophone data is (4249, 2, 1000), and the size of the idle state data is (4450, 2, 1000). By stacking the results from the two sensors, a total of (8699, 4, 1000) preprocessed data is obtained. The 8699 preprocessed data points are split into training and validation datasets at a ratio of 0.8:0.2, resulting in 6,959 samples for the training dataset and 1,740 samples for the validation dataset.

The training result shows that both the train and validation sets converged smoothly. The loss graph for each training epoch is shown in Fig. 6(a). As training progressed, the values of the adaptive parameters, initially set to 1, were updated properly. The average parameter values for each input during the training process are illustrated in Fig. 6(b) and the final values are listed in Table 1. The adaptive parameters multiplied by each of the four inputs are optimized to reflect the contribution of the input values to classification performance as training progresses. Fig. 6(b) shows the changes in the average values of the adaptive parameters over the training epochs. It can be observed that each parameter value optimizes smoothly without significant fluctuations during the training process. The final average values of the optimized adaptive parameters are presented in Table 1 upon completion of the training. As a result, the final optimized value of the adaptive parameter corresponding to the time-domain hydrophone was calculated to be 0.9870, which is the highest among the parameters. This indicates that the time-domain hydrophone has the greatest impact on diagnosing the underwater cutting state.

Fig. 7 presents the confusion matrix summarizing the prediction results on the validation set after the completed model training. The accuracy was calculated as 98.85%, and the F1-score was 0.9888. These results confirm that the proposed adaptive weighted parallel 1D-DenseNet effectively performs on real experimental data.

The performance of the proposed model was compared with that of several representative classification models on the case study data. We compared the classification performance of machine learning models introduced in Section 2.1 (LR; Logistic Regression, SVM; Support Vector Machine, DT; Decision Tree, RF; Random Forest, KNN; K-Nearest Neighbor) and a deep learning model with FC layers that does not use convolution. The same preprocessing procedures were applied. The results are shown in Table 2.

Among the traditional machine learning models, RF achieved the highest performance with an accuracy of 92.38% and an F1-score of 0.9245. The FC layer model yielded an accuracy of 80.80% and an F1-score of 0.7971, demonstrating similar performance to the traditional machine learning models. In contrast, the adaptive weighted parallel 1D-DenseNet significantly improved performance over the traditional baseline models. This result indicates that the experimental dataset used in this study requires classification through deep learning models with complex architectures, suggesting that the proposed network structure is well-suited for this task.

The proposed network’s main techniques can be categorized into DenseNet, parallel structure, and adaptive weighting. An ablation study was conducted to evaluate how each technique contributes to improving classification performance. First, to assess the impact of the parallel structure, we compared the case where four time-series signals are input into a standard

1D-DenseNet versus a parallel-structured 1D-DenseNet. To isolate the effect of the parallel structure, adaptive weighting was not applied in this comparison. The second ablation study was conducted to evaluate the impact of adaptive weighting. In this study, the initial values of the AWP were set to 0 and 1 to compare classification performance. This was compared to the parallel 1D-DenseNet from the first ablation study, which did not include weighting, to assess the contribution of adaptive weighting and the effect of initial weights. The results are summarized in Table 3.

When the parallel structure was not used, the accuracy was 88.56%, and the F1 score was 0.8547. Using the parallel structure resulted in approximately a 10% improvement in accuracy, achieving an accuracy of 98.10% and an F1-score of 0.9807. When AWP was applied with an initial value of 0, the performance was quantitatively the same as that of the parallel structure DenseNet without weighting. This suggests that the focus on learning within DenseNet may have prevented effective updating of the AWP during training. Finally, setting the initial value of the AWP to 1 achieved the best performance, with an accuracy of 98.85% and an F1-score of 0.9888. This indicates that the proposed method significantly improved classification performance, incorporating both the parallel structure and adaptive weighting. Additionally, by comparing the accuracy of each case during the training process, as shown in Fig. 8, differences in convergence on the validation set can be observed. This indicates that the AWP helps prevent overfitting on the training dataset and improves validation accuracy. Therefore, based on Fig. 8, it has been confirmed that Case 4, which features the adaptive weighted parallel 1D-DenseNet with an initial parameter value of 1, excels in convergence stability.

The ablation study demonstrates that a parallel structure network is most suitable for extracting features from multivariate time series signals. Additionally, it was observed that applying adaptive weighting before concatenating parallel outputs impacts classification performance and convergence stability. Thus, the effectiveness of the proposed adaptive weighted parallel 1D-DenseNet has been validated for the case study dataset.

This paper proposes a deep-learning classification model for monitoring underwater remote cutting. The adaptive weighted parallel 1D-DenseNet demonstrated effective performance on the experimental dataset, showing significant improvements over traditional methods. Despite its high performance, future research needs to address the following areas.

Firstly, the dataset labels need to be corrected. The dataset used in this study was obtained by performing the cutting process in six sequential stages. Consequently, the stages were separated, and the data were segmented according to the timing of the remote-control commands. As a result, the data were not acquired discretely and may include transient characteristics between stages. Such inaccurate labeling could impact classification performance, so using datasets acquired separately for each cutting stage could lead to a more accurate model. In this study, binary classification was performed to distinguish between the cutting and idle states to minimize the impact of transient intervals between stages. Therefore, abnormal cutting intervals may contain various features, such as robot movement or laser termination. Using datasets acquired for each cutting stage would allow for more granular labeling and could help the model better understand the data distribution.

Secondly, future research should include a parametric study of the deep learning model. For models with high classification performance, differences in learning conditions or initial values can significantly affect the results. In this study, cases with adaptive parameters initialized to 0 and 1 were compared solely to validate the effectiveness of the adaptive parameters. Since these parameters are directly multiplied with the output of DenseNet, the choice of initial values can significantly impact the results. Therefore, further research is needed to find optimized initial values. Another important aspect of the parametric study is the number of Conv layer repetitions within the Dense block. Thus, it is necessary to determine the appropriate number of repetitions based on the difficulty of the other given data.