The dataset utilized in this study is the CTU-UHB database (Chuda´cˇek et al., 2014), an open-access repository comprising 552 recordings obtained at University Hospital in Brno (UHB) during the period of 2010–2012. Each recording is composed of two components: the cardiotocography (CTG) and clinical data. The CTG data are captured using three distinct methods: ultrasound Doppler probe, direct scalp measurement, or a hybrid approach. The CTG data encompass FHR and uterine contractions sampled at a rate of 4 Hz, resulting in four data points per second for each parameter.

The clinical data include information regarding fetal status and parameters concerning puerperal and newborn infants. Table 1 displays a portion of the clinical statistics obtained from the CTU-UHB database. Umbilical artery pH serves as a recognized marker for fetal acidemia, a condition associated with neonatal complications, such as multiple organ dysfunction in newborns (Sehdev et al., 1997; van den Berg et al., 1996). Studies have shown a relationship between FHR and variations in umbilical artery pH (Singh et al., 2021). Consequently, we employed the umbilical artery pH values from the clinical data to classify our dataset into two separate groups in Figure 1. In accordance with the established criterion that a pH value exceeding 7.15 signifies a normal condition, a total of 439 samples were classified as normal, and 113 samples were categorized as pathological based on their pH value (Comert et al., 2018).

During the data collection process, missing signals and artifacts may arise in the original data due to external factors such as limitations in data acquisition by ultrasound probe and maternal and fetal movement, necessitating the preprocessing of data. The process is as follows:

(1) The original data are divided into 1-min segments, each containing 240 points. Then, the number of zero-value points f 0 are counted, and the data loss rate LR is calculated according to Eq. 1.

Due to too many missing signals in some recordings, the number of recordings in the dataset decreased to 550, with 439 normal recordings and 111 pathological recordings.

There are only 550 recordings in the dataset, and the ratio of normal recordings and pathological recordings is 4:1. The limited number of recordings and the ratio of normal to pathological readings can easily cause model overfitting. The length of recordings varies from 60 to 90 min. Under the instruction of obstetricians, we take 20-min signals to do further analysis. Thus, the dataset can be augmented by window slicing (Liang and Lu, 2023). The specific process is given as follows:

Step 1: For an FHR time series T = t 1 , t 2 , … , t n , choose the length of slicing window s and step length k ;

Step 2: Obtain the first slice with a window T 1 = t 1 , … , t s ;

Step 3: Move the window to get T 2 = t k + 1 , … , t k + s , ..., T m = t m k + 1 , … , t m k + s and stop the process when m k + s > n .

Figure 2 shows the signals before and after preprocessing. In this article, we chose s = 4800 and k = 600 , which implies generating 20-min samples with the beginnings of two adjacent samples that are 2.5 min apart. An example of a slice operation is shown in Figure 3.

After data augmentation, the number of normal samples increased to 6382 from 439, and the number of pathological samples increased to 1615 from 111. Because the two classes were still imbalanced, we chose 1,615 from 6,382 normal samples randomly to create a new dataset with all pathological samples.

An LSTM is a special kind of RNN designed to solve the problem of long-term dependency (Hochreiter and Schmidhuber, 1997).

The workflow of the LSTM cell at time t is as follows: the hidden state of the previous moment and the input of the current moment enter the forget gate, input gate, and output gate for calculation and then update the cell state and hidden state. The input gate can decide what new information can be stored in the cell state, and the output gate determines what information can be output based on the cell state. The forget gate can decide what information will be discarded from the cell state. The calculation process is according to Eqs 3–8. f t = σ W f h h t − 1 + W f x x t + b f . (3) i t = σ W i h h t − 1 + W i x x t + b i . (4) c t ∼ = ⁡ tanh W c h ∼ h t − 1 + W c x ∼ x t + b c ∼ . (5) c t = f t ⋅ c t − 1 + i t ⋅ c t . ∼ (6) o t = σ W o h h t − 1 + W o x x t + b o . (7) h t = o t ⋅ ⁡ tanh c t . (8)

The architecture of LSTM cell is shown in Figure 4.

In clinical practice, obstetricians primarily utilize nonstress testing (NST) as the main modality for evaluating prenatal FHR. The SOGC (Liston et al., 2007) guidelines stipulate that interpreting NST results requires assessing various parameters, including baseline FHR, baseline variability, accelerations, and deceleration, each of which must be evaluated across different time intervals. For instance, the baseline FHR denotes the mean level of FHR over a 10-min period, excluding any accelerations, decelerations, or notable variability, and requires a minimum of 2 min of uninterrupted observation.

In contrast, acceleration and deceleration are typically evaluated within a time frame of less than 30 s. Consequently, the model must possess the capability to encompass both enduring characteristics that signify the general pattern in FHR data and fleeting characteristics that indicate minor fluctuations in specific areas. In accordance with this principle, we adopt the strategy of training numerous models by downsampling the data at varying frequencies. Downsampling is a prevalent technique in the processing of time series data. Downsampling facilitates the hybrid model in extracting data features across various time scales, thereby mitigating computational expenses and eliminating data redundancy (Liu et al., 2021).

Subsequently, each dataset undergoes downsampling by distinct sampling intervals before being inputted into diverse time-scale LSTM models. These outputs of multi-scale models are aggregated using weights to yield the ultimate result, represented by the final result vector y denoting the probability of data belonging to each category. The computation process is according to Eqs 9, 10. y = Σ i = 1 n ω i y i . (9) Σ i = 1 n ω i = 1 , (10) where y i is the output vector of the i -th model and ω i is the corresponding weight value of i -th model. The architecture of multi-scale LSTM networks is shown in Figure 5.

The confusion matrix is a commonly utilized tool for assessing the efficacy of models in classification tasks (James et al., 2013). In the context of the binary classification discussed in this article, a confusion matrix with dimensions of two rows and two columns represents the frequency of four distinct prediction outcomes.

The metrics employed in our study include accuracy (ACC), specificity (SP), precision (PR), recall, F1-score, and area under the curve (AUC). ACC provides a comprehensive measure of the accuracy of predictions, while SP emphasizes the proportion of accurately identified negative samples. The constraints of electronic fetal monitoring contribute to a notable false positive rate in obstetric diagnoses. Inaccurate identification of pathological conditions may result in unwarranted medical interventions (Li et al., 2019). Therefore, it is imperative to consider precision and recall metrics, which evaluate the accuracy of positive predictions and the proportion of successfully detected positive samples. The F1-score represents the harmonic mean of PR and recall, while the quality index is calculated as the geometric mean of SP and sensitivity. The metrics mentioned above are calculated according to Eqs 11–15. A C C = T P + T N T P + F P + T N + F N . (11) S P = T N T N + F P . (12) PR = T P T P + F P . (13) R e c a l l = T P T P + F N . (14) F 1 − s c o r e = 2 ⋅ PR ⋅ R e c a l l PR + R e c a l l . (15)

The experiment was carried out utilizing the PyTorch deep learning framework in Python, along with additional packages such as Numpy and Scikit-learn. The hardware configuration includes an Intel(R) Core (TM) i9-10900X CPU @ 3.70 Hz and an NVIDIA GeForce RTX 2080Ti.

The hybrid model is composed of two LSTM layers, three full connection layers, and an output layer, with each LSTM layer containing 512 hidden units. In order to address overfitting, a dropout rate of 0.2 is applied before the full connection layer. The output dimension is reduced to 2 through the full connection layers, with the final activation function being softmax for classification. The optimizer used is Adam, and the loss function employed is cross-entropy. To enhance the convergence of the network, we implemented a learning rate decay strategy during the training process consisting of 2,000 epochs. The initial learning rate was set at 0.001 and decreased by a factor of 10 after 500 and 1000 epochs.

The models were trained using a 10-fold cross-validation approach, where the dataset was partitioned into 10 subsets, each containing 323 samples. Nine subsets were utilized to train the model, while the remaining subset was used to test its performance. Following the training and testing of 10 models on the test set, the mean and standard deviation of the results were calculated.

Initially, the experiments were conducted to examine the impact of varying sampling rates on the efficacy of the model. The results presented in Table 2 indicate that the model exhibits optimal performance at a sampling rate of 10. Specifically, ACC and F1-score metrics demonstrate an improvement of approximately 5% compared to the next highest-performing model, while the SP and PR metrics show an enhancement of approximately 4.5%. The model’s performance improves with increasing sampling intervals, potentially due to its enhanced ability to discern between normal and pathological data by capturing long-term features. Furthermore, larger sampling intervals serve to diminish the impact of noise signals within the data.

Three different multi-scale models were constructed by manipulating the quantity and magnitude of the component models. Multi-scale Model 1 comprises four sampling rates: 4, 6, 8, 10. Multi-scale Model 2 utilizes models with sampling rates of 4, 8, and 10, whereas multi-scale Model 3 exclusively integrates models with sampling rates of 8 and 10. The superior performance of all multi-scale models over the single models is evident in Table 2, indicating that the incorporation of multi-scale features aids in mitigating overfitting to some degree and enhances categorization accuracy. Multi-scale Model 1 demonstrates superior performance on ACC, recall, F1-score, and AUC, suggesting that incorporating diverse time-scale features enhances classification accuracy. Conversely, Model 3 exhibits higher SP and PR but comparatively lower performance on other evaluation criteria. The ROC curve depicted in Figure 6 illustrates the discriminative capabilities of single models versus multi-scale models, with the latter showcasing an enhanced ability to distinguish between two classes.

In this research, we introduce a multi-scale LSTM model integrated with models that target various time scales. Experimental analyses were carried out on both single and multi-scale models. The results demonstrate that multi-scale LSTM models outperform regular LSTM models in various performance metrics. Specifically, among the single models tested, the model with a sampling rate of 10 exhibited the highest classification accuracy. Incorporating alternative sampling rates into the model resulted in enhancements across all performance indicators, including ACC (85.73% vs. 83.28%), SP (85.32% vs. 82.47%), PR (85.53% vs. 82.84%), recall (86.13% vs. 84.09%), F1-score (85.79% vs. 83.42%), and AUC (0.9180 vs. 0.8667).

To illustrate the importance of our model, the outcomes of both machine learning (Comert et al., 2018; O’Sullivan et al., 2021; Ben Barek et al., 2023) and deep learning approaches (Liu et al., 2021; Singh et al., 2021) utilizing the identical dataset are presented in Table 3. Our model exhibits superior performance in terms of ACC, SP, PR, recall, and AUC compared to the aforementioned machine learning methods (Liu et al., 2021; Singh et al., 2021). Furthermore, when compared to a specific model (Liu et al., 2021), our model demonstrates notably higher levels of ACC, SP, and recall. It is worth noting that the model discussed (Singh et al., 2021) achieves an ACC of 69.6%, potentially attributed to the limitations of CNNs in capturing temporal features effectively. This observation suggests that our model possesses enhanced classification capabilities.

In conclusion, the proposed model demonstrates enhanced performance in the classification of FHR. This model offers several advantages, including directly classifying FHR signals without the need for complex feature extraction processes and ensuring immediate discrimination. Additionally, incorporating various time-scale signals enables the model to effectively learn both long-term and short-term features, thereby optimizing overall performance.