WPD, as an extension of the Discrete Wavelet Transform (DWT), provides a more refined time-frequency analysis capability. Through recursive filtering and down-sampling processes, WPD not only iteratively decomposes low-frequency parts but also further segments high-frequency parts, thereby achieving multi-level decomposition. For an n-level decomposition, WPD can generate multiple different sets of coefficients or nodes, rather than just (n + 1) sets as in DWT. Although the total number of coefficients remains unchanged due to down-sampling, this provides greater flexibility in adapting to different signal characteristics. The basic process of WPD is shown in Figure 1.

The formula for WPD is as follows:

(1) $$ \begin{equation} \begin{aligned} P_{(t)}= \textstyle\sum_{j=-\infty}^{\infty} \alpha_{j k} \varphi_{j k}(t)+ \textstyle\sum_{j=0}^{\infty} \textstyle\sum_{k=-\infty}^{\infty} \beta_{j k} \varphi_{j k}(t) \end{aligned} \end{equation} $$

LSTM is a variant of the Recurrent Neural Network that can process sequential data while addressing the problems of gradient vanishing and gradient exploding that occur when training on long sequences. It allows the model to retain information from previous data, thereby further enhancing the model’s capability to capture the features of each sample, as shown in Figure 2.

An LSTM unit consists of an input gate, a forget gate, an output gate, and a cell state. The transition formulas at time t are as follows:

(2) $$ \begin{equation} \begin{aligned} \mathrm{Input~gate:} \left\{\begin{array}{c}i_{t}=\sigma\left(W_{i} \cdot\left[\begin{array}{ll}h_{t-1} & x_{t}\end{array}\right]+b_{i}\right) \\ \overline{C_{t}}=\tanh \left(W_{c} \cdot\left[\begin{array}{ll}h_{t-1} & x_{t}\end{array}\right]+b_{c}\right)\end{array}\right. \end{aligned} \end{equation} $$

(3) $$ \begin{equation} \begin{aligned} \mathrm{Forget~gate:} f_{t}=\sigma\left(W_{f} \cdot\left[\begin{array}{ll}h_{t-1} & x_{t}\end{array}\right]+b_{f}\right) \end{aligned} \end{equation} $$

(4) $$ \begin{equation} \begin{aligned} \mathrm{Output~gate:} \left\{\begin{array}{c}o_{t}=\sigma\left(W_{o} \cdot\left[h_{t-1} \quad x_{t}\right]+b_{o}\right) \\ h_{t}=o_{t} * \tanh \left(C_{t}\right)\end{array}\right. \end{aligned} \end{equation} $$

(5) $$ \begin{equation} \begin{aligned} \mathrm{Cell~state}: C_{t}=f_{t} * C_{t-1}+i_{t} * \overline{C_{t}} \end{aligned} \end{equation} $$

where x_t represents the sequence of the input unit, h_t denotes the hidden state of the unit, and C_t signifies the cell state. W_i, W_c, b_i, and b_c are the weight matrices and bias terms for the input gate; W_f and b_f are those for the forget gate; W_o and b_o are those for the output gate; and σ represents the sigmoid function.

The ECA mechanism is a lightweight attention module specifically designed for deep CNNs. It achieves performance gains with minimal increases in complexity by utilizing an appropriate cross-channel interaction strategy. This strategy is implemented via one-dimensional convolutions, which notably reduce model complexity while maintaining performance, as shown in Figure 3. The kernel size (k) for the convolution operation is adaptively selected based on the following formula to ensure adequate coverage of local cross-channel interactions:

(6) $$ \begin{equation} \begin{aligned} k=\varphi(D)=\left|\frac{\log _{2} D}{\gamma}+\frac{b}{\gamma}\right|_{o d d} \end{aligned} \end{equation} $$

Where k represents the size of the convolutional kernel. D represents the dimension of the input sequence. |n|_odd indicates the nearest odd number to n. Additionally, the mapping parameters γ and b are fixed at 2.0 and 1.0^[26], which enables the network to adaptively determine the optimal kernel size k based on the channel dimension D, ensuring efficient cross-channel interaction without manual tuning.

To achieve high-precision fault diagnosis of water injection pumps under complex industrial conditions, this paper proposes a multi-level Inception-LSTM network integrated with Wavelet-enhanced attention mechanism, termed MILN-WE. The overall architecture is designed to handle the non-stationary nature of vibration signals and the challenges of feature extraction from imbalanced data.

The proposed MILN-WE framework consists of three main stages: signal decomposition, multi-scale feature extraction, and feature fusion classification. The systematic flowchart of the MILN-WE is illustrated in Figure 4.

Specifically, the raw vibration signals collected from the water injection pump are first processed using a three-level WPD. A three-level decomposition was selected because it provides a sufficient frequency resolution to isolate subtle fault characteristics without introducing excessive computational complexity or over-segmenting the signal^[27,28]. This process decomposes the original complex signal into eight distinct frequency sub-bands. By transforming the 1D time-series signal into multiple frequency components, the model can capture subtle fault characteristics that are often submerged in noise in the original domain.

Subsequently, the features extracted from the eight frequency sub-bands are individually processed through the multi-scale Inception-LSTM branches. Within each branch, an ECA mechanism is integrated to adaptively recalibrate the importance of various feature channels. Unlike conventional hybrid models that typically rely on simple feature concatenation or late-stage attention pooling, this design leverages ECA to perform a non-dimensionality-reduction local cross-channel interaction specifically tailored for the independent WPD sub-bands. This advanced weighted fusion strategy allows the model to dynamically evaluate and effectively highlight fault-related transients while simultaneously suppressing background noise. To integrate information from different frequency domains, the enhanced latent features F_i from all branches are fused into a global representation F_S via a weighted summation strategy, expressed as F_S = ∑_iW_CiF_i (where i = 1, 2, ... 8), where W_Ci denotes the learned contribution weight of the i-th sub-band.

Finally, this fused feature map is mapped into the label space through a fully connected layer. A Softmax activation function is then employed to calculate the probability distribution across various fault types, where the category with the highest probability determines the final diagnostic result of the water injection pump.

In the fault diagnosis of water injection pumps, the complexity of vibration signals and the severe category imbalance in industrial environments present significant challenges. Traditional CNNs often employ a single-size convolutional kernel, which results in a fixed receptive field that may fail to capture diverse and subtle fault features, especially from minority class samples. To address this limitation, the proposed MILN-WE model utilizes a multi-scale Inception module instead of the standard CNN architecture. By incorporating parallel convolutional layers with different kernel sizes, the module can perceive local spatial features across multiple scales simultaneously. This design notably enhances the model’s ability to extract discriminative information from non-stationary signals and improves the diagnostic sensitivity for rare fault types, as shown in Figure 5. Specifically, to further enhance the discriminative power of the spatial features, local ECA modules are embedded within the Inception block following the Conv2-1 and Conv3-1 layers, prior to the feature concatenation.

To complement these spatial features, the architecture further integrates LSTM layers to model the temporal dependencies within the signal. The multi-scale feature maps generated by the Inception module are fed into the LSTM unit, which leverages its unique gating mechanisms—the input, forget, and output gates—to capture long-term correlations in the vibration sequences. By synergizing multi-scale spatial perception with temporal sequential modeling, the MILN-WE framework can derive highly robust and representative features from the sub-bands decomposed by WPD, providing a solid foundation for accurate fault classification under complex operational conditions.

Traditional feature concatenation or simple averaging fusion methods often overlook the varying contributions of different feature branches to the diagnosis of the current operating state, which can easily introduce redundant information and increase subsequent computational overhead. Therefore, during the feature enhancement and fusion stages, this paper introduces the ECA mechanism to perform adaptive weighted fusion of multi-scale features. It achieves cross-channel local interactions with an extremely low number of parameters, dynamically focusing on the most discriminative key features while avoiding information loss from feature dimensionality reduction. Specifically, complementing the local ECA modules inside the Inception blocks, an ECA-based global weighting mechanism is employed after the parallel Inception-LSTM branches and before the final classification layer to evaluate the eight frequency sub-bands. Through this design, the model captures cross-channel interactions via a non-dimension-reduction local cross-channel interaction strategy. This enables the network to adaptively assign higher weights to key feature channels that significantly contribute to fault diagnosis, while suppressing irrelevant background noise, thereby further enhancing the architecture’s overall performance under complex interference, as shown in Figure 6.

The ECA-based feature fusion process comprises three strategic phases. First, multi-scale features are compressed into channel descriptors via Global Average Pooling (GAP) to capture a global receptive field. Subsequently, instead of using computationally expensive fully connected layers, the module employs a one-dimensional convolution (1D Conv) with an adaptive kernel size k = φ(D) to facilitate Local Cross-Channel Interaction. This approach effectively captures local dependencies and avoids information loss from dimensionality reduction. Finally, the generated attention weights W_C1 to W_C8 are applied to the original features through element-wise multiplication and summation. By amplifying fault-sensitive features and suppressing redundant noise, this adaptive strategy notably enhances the discriminative power of the fused feature, ensuring precise identification of the 16 complex operating states.

The private water injection pump dataset is derived from the field operation data of an oil field in China. The water injection pump model used in this study is 3H-8/450II, as shown in Figure 7. Data collection was performed using 15 vibration sensors installed at different locations, the collected data were treated as independent single-channel input sequences. Additionally, all vibration signals were globally normalized prior to model training to eliminate amplitude variations caused by differences in distance and mounting positions between the sensors and the vibration sources, thereby ensuring that the diagnostic process is based on inherent time-frequency fault patterns. The specific installation positions of these sensors are listed in Table 1. The sampling frequency of the sensors is 8,192 Hz with a sampling duration of 1 s, meaning each sample contains 8,192 sampling points.

During the operation of the water injection pump, the motor at the power end drives the crankshaft to rotate, which in turn moves the plunger through the connecting rod, causing it to reciprocate within a high-sealing cylinder. The resulting ultra-high pressure pumps the sand-bearing fluid out of the hydraulic end. During this process, the pump head of the plunger pump is subjected to continuous high-intensity impacts. Under the constant erosion of the sand-bearing fluid, sealing components such as the plunger and valve seats are highly susceptible to wear and tear.

The dataset contains a total of 5,190 samples across 16 different states (including the normal operating state), covering various common failures of plunger pumps, such as plunger wear, pump head spring wear, and bearing bush wear. Figures 8-10 display the raw data sequence plots for some of these states. It can be observed that when the equipment is in a normal state, the cycles are clear, noise is relatively low, and the signal components are relatively simple. Conversely, when a fault occurs, the noise in the data increases notably, the data cycles change, and the underlying components become much more complex.

The sample sizes collected for each state are shown in Figure 11. In actual operations, field engineers strive to keep the machinery in a normal state as much as possible. When certain severe faults occur—such as plunger looseness, bearing bracket damage, or motor bolt looseness—the machine may be shut down immediately, forcing data collection to stop. This further increases the difficulty of diagnosing such faults. Consequently, there is a severe imbalance in the amount of data across different operating states, with the maximum gap between sample sizes exceeding 20 times. Therefore, it is difficult to use data reconstruction methods like resampling to supplement the number of minority class samples, and the quality of such supplemented data is hard to guarantee.

To strictly prevent data leakage between the training and testing phases, the continuous raw data sequences of each state are first chronologically divided into training, validation, and test sets. Specifically, based on the temporal order of data collection, the first 80% of the continuous time period for each state is designated as the training period. The subsequent 10% of the time period is allocated for validation, and the final 10% of the time period is strictly reserved for testing. Following this strict chronological division, a sliding window with overlap is independently employed to segment the data within each respective set to increase the data volume and ensure better training performance, as shown in Figure 12. Specifically, the width of the sliding window is 2,048 and the step size is 1,024. After independent segmentation, the total number of samples effectively generated reach 36,330.

In this experimental section, Accuracy, Precision, Recall, and F1-Score are employed as evaluation metrics to assess the diagnostic performance of the proposed models. Class-balanced CNN (CB-CNN)^[29] and SMOTE-CNN^[30] are selected as baseline methods, representing loss function-based improvement and oversampling-based approaches for handling class imbalance in water injection pump fault diagnosis, respectively. To further validate the contribution of individual modules in addressing sample imbalance, a comprehensive ablation study is conducted with traditional CNN as the reference model. Several variant architectures are constructed for comparison, including CNN-LSTM, Inception-LSTM, Inception-LSTM-ECA, CNN-LSTM-WE, Inception-LSTM-WPD, supervised contrastive learning^[31] (SCL), the deep-stable CNN^[32] (DSCNN), Inception-WE, and the proposed MILN-WE.

Each variant systematically excludes specific components from the complete architecture: CNN-LSTM removes WPD, Inception, and ECA modules; Inception-LSTM excludes the WPD and ECA modules; Inception-LSTM-ECA removes WPD module; CNN-LSTM-WE and Inception-WE remove the Inception and LSTM modules, respectively; and Inception-LSTM-WPD excludes the ECA module. This systematic comparison enables quantitative assessment of each module’s contribution to the overall diagnostic performance under imbalanced data conditions.

Based on the PyTorch deep learning framework, the proposed Multi-level Inception-LSTM network was constructed, integrating WPD and ECA mechanism. The hardware configuration included an Intel i5-13500HX CPU, an NVIDIA 4060 GPU, and 16GB of RAM. Based on the aforementioned independent data splitting strategy, the segmented samples from each state strictly maintain the 8:1:1 ratio for the training, validation, and test sets, respectively. This rigorous procedure ensures zero information crossover, resulting in 29,064 training samples, 3,633 validation samples and 3,633 testing samples.

Cross-Entropy Loss was employed as the loss function, and the Adam optimizer was used for model training. The learning rate was set to 0.002. To ensure statistical reliability and mitigate the influence of random initialization, all models evaluated in this study were independently trained and tested 5 times under the same hardware and software configurations. Within the Inception module, the kernel sizes for each convolutional layer are specified in Table 2, with a Batch Normalization layer added after each convolution. The LSTM module was configured with 2 layers. Additionally, as depicted in Figure 5, local ECA modules were integrated specifically after the Conv2-1 and Conv3-1 layers to enhance the cross-channel interaction capability of the Inception module.

The confusion matrix for the diagnostic results of the MILN-WE model is shown in Figure 13, where the horizontal axis represents the true labels and the vertical axis represents the predicted labels. The numbers within each colored block correspond to the number of samples classified into that category. As can be observed from the figure, except for fault samples of label 7, the number of misclassified samples for all other faults is below 10.

To verify the effectiveness of the improved method and evaluate its performance against common fault diagnosis algorithms for imbalanced data, other baseline models were trained using the same parameters for verification. Figures 14 and 15, and Table 3 illustrate the diagnostic performance comparison between the proposed model and eleven benchmark models: CNN, CB-CNN, SMOTE-CNN, CNN-LSTM, Inception-LSTM, Inception-LSTM-ECA, CNN-LSTM-WE, Inception-WE, and Inception-LSTM-WPD, SCL, DSCNN.

During the model training process, the proposed model achieved faster convergence speed in terms of both training and testing losses compared to other models. Regarding the testing set, the SMOTE-CNN, which incorporates SMOTE resampling, showed a performance similar to that of the traditional CNN model. This indicates that when facing severe data imbalance, resampling methods struggle to generate appropriate new data and fail to effectively distinguish minority class faults.

The diagnostic Accuracy, Precision, Recall and F1-Score of the proposed model on the test set reached 99.38%, 99.42%, 99.27%, and 99.34%, respectively, all of which showed improvements over the other benchmark models. Compared to the traditional CNN, the diagnostic accuracy improved by 6.05%. Compared with CB-CNN, a representative imbalance-aware fault diagnosis model based on improved loss function, the proposed MILN-WE model achieves a 3.24% improvement in diagnostic accuracy. Furthermore, when compared with SMOTE-CNN, which employs oversampling techniques for handling class imbalance, the diagnostic accuracy is enhanced by 5.28%. These results demonstrate that the proposed MILN-WE model exhibits better performance in addressing the imbalanced data diagnosis problem of plunger-type water injection pumps when compared with other advanced fault diagnosis methods.

Besides, during the process of network optimization, the diagnostic performance enhanced progressively. By comparing the diagnostic results of the proposed model with the Inception-LSTM-ECA, CNN-LSTM-WE, Inception-WE, and Inception-LSTM-WPD, SCL, DSCNN models, it is evident that each module contributes to the improvement of the final diagnostic accuracy. In summary, these results demonstrate the effectiveness and superiority of the proposed model for fault diagnosis under class-imbalanced conditions.

To verify the cross-platform robustness of the MILN-WE architecture, we extended our evaluation to a widely recognized public repository: the centrifugal multistage impeller blower dataset^[33].

In this validation phase, five operational states are considered: normal baseline (C0), along with four localized defects—outer-race (C1), inner-race (C2), rolling-element (C3), and gear (C4) failures. To mirror the sparsity of fault samples in actual industrial production, we intentionally constructed a non-uniform distribution. As detailed in Table 4, for classes C0-C2, 600 training and 180 testing samples per class are used; for minority classes C3 and C4, 200 training and 60 testing samples per class are used. Additionally, 10% of the training samples from each class are partitioned as a validation set during the training process. By testing the model on this skewed dataset, we can more effectively demonstrate MILN-WE’s proficiency in identifying underrepresented fault signatures amidst dominant healthy signals.

In the training process, the Adam optimizer was deployed for 50 epochs with a starting learning rate of 0.001. To prevent the model from overfitting, a decay strategy was integrated: the learning rate was reduced by 50% whenever the loss metric failed to decrease over 15 successive epochs. Additionally, we introduced Gaussian white noise with a signal-to-noise ratio of 1 into the raw vibration data to replicate the complex noise interference typically encountered in actual industrial operations.

As detailed in Table 5, our MILN-WE framework attained a 95.82% diagnostic accuracy. This performance shows higher diagnostic accuracy compared to the benchmark models, exhibiting improvements over CNN, SMOTE-CNN, CNN-LSTM, INCEPTION-LSTM-WPD, SCL, DSCNN by margins of 14.58%, 13.72%, 10.17%, 2.17%, 2.74%, and 1.25%, respectively. Beyond accuracy, our approach consistently yielded competitive results across the remaining evaluation metrics. These outcomes illustrate the model's capability to maintain effective fault identification on the public dataset, even under severe background noise conditions.