Hybrid Deep Learning Model for Fault Diagnosis in Centrifugal Pumps: A Comparative Study of VGG16, ResNet50, and Wavelet Coherence Analysis

Abstract

Significant in various industrial applications, centrifugal pumps (CPs) play an important role in ensuring operational efficiency, yet they are susceptible to faults that can disrupt production and increase maintenance costs. This study proposes a robust hybrid model for accurate fault detection and classification in CPs, integrating Wavelet Coherence Analysis (WCA) with deep learning architectures VGG16 and ResNet50. WCA is initially applied to vibration signals, creating time–frequency representations that capture both temporal and frequency information, essential for identifying subtle fault characteristics. These enhanced signals are processed by VGG16 and ResNet50, each contributing unique and complementary features that enhance feature representation. The hybrid approach fuses the extracted features, resulting in a more discriminative feature set that optimizes class separation. The proposed model achieved a test accuracy of 96.39%, demonstrating minimal class overlap in t-SNE plots and a precise confusion matrix. When compared to the ResNet50-based and VGG16-based models from previous studies, which reached 91.57% and 92.77% accuracy, respectively, the hybrid model displayed better classification performance, particularly in distinguishing closely related fault classes. High F1-scores across all fault categories further validate its effectiveness. This work underscores the value of combining multiple CNN architectures with advanced signal processing for reliable fault diagnosis, improving accuracy in real-world CP applications.

1. Introduction

Centrifugal pumps (CPs) are increasingly used for a variety of industrial and commercial applications and contribute significantly to worldwide energy consumption [1]. However, unexpected CP failures can result in costly downtime and extensive repair needs, posing a major challenge for industries that rely on these systems. Therefore, it is essential to maintain continuous monitoring of CPs, which can be accomplished either through manual inspections by personnel or, more efficiently, by using advanced signal processing and artificial intelligence (AI) techniques [2,3,4]. Notably, “soft” malfunctions, such as those caused by mechanical seal defects or impeller irregularities, make up a significant portion of CP failures. This makes intelligent fault diagnosis and robust condition monitoring systems indispensable for predicting potential issues and handling risks before they lead to serious disruptions [5]. Recently, condition-based maintenance (CBM) has gained considerable traction as a preferred method for improving CP performance and efficiency in a cost-effective way. CBM enables the real-time assessment of equipment health by analyzing data collected from machinery operating under various conditions, allowing early detection and rectification of potential faults before they escalate into major issues [6,7,8].

CPs are vulnerable to both hydraulic and mechanical faults, with mechanical issues being more frequently encountered in practice [9]. Maintaining the reliable operation of CPs is strongly dependent on the early detection of these mechanical faults, particularly those involving impeller damage and mechanical seal failures [5,10,11,12,13]. These mechanical faults have a significant impact on the vibration signals produced by CPs, often causing abrupt, irregular vibration patterns that require careful analysis for accurate fault diagnosis. Signal processing plays a critical role in this diagnostic process, involving initial data preprocessing and the extraction of relevant features [14,15]. This process uses various techniques across the temporal, frequency, and time–frequency domain (TFD) analyses, enabling comprehensive insights into the underlying fault characteristics [16,17,18].

Various studies have introduced a range of approaches for diagnosing faults in rotating machinery, each offering unique methodologies to address the challenges in this domain. One such technique utilizes wavelet coefficients within an energy-based framework to analyze signal features effectively. Additionally, advanced strategies have emerged that combine statistical-time features with nonlinear manifold learning and hierarchical neural networks, allowing for a more robust analysis. Convolutional neural networks (CNNs) are also employed to automate feature extraction, providing efficient and scalable solutions for fault detection [19]. Other methods utilize the Walsh Transform [20], linear discriminant analysis [21], and informative ratio principal component analysis to achieve dimensionality reduction and refine feature classification, collectively enhancing the precision and speed of fault detection across diverse applications [9]. Another innovative technique calculates kurtogram spectra to train convolutional encoders using supervised contrastive loss, followed by a linear classifier fine-tuned for fault classification [22]. This combination of kurtogram analysis and deep learning substantially improves the detection and classification of faults in a supervised learning context. In related studies, Ullah et al. [23] propose a deep learning-based approach for detecting faults using vibration data. This method uses a CNN and convolution auto encoder (CAE) for feature extraction and an artificial neural network (ANN) for classification. Similarly, Zaman et al. [24] introduced a novel method for classifying centrifugal pump conditions by combining signal processing and deep learning. By transforming vibration signals into Sobel–Edge scalograms, the method intensifies fault-related information, which a CNN then uses to effectively classify faults. Siddique et al. [25] propose an approach for pipeline leak detection by enhancing AE scalogram images with leak-augmentation techniques. This method uses deep learning components, specifically CNNs and CAEs, to identify patterns and assess pipeline health, ultimately achieving precise evaluation through a shallow ANN. Each of these methods advances fault detection and condition monitoring by incorporating sophisticated machine learning and deep learning algorithms, driving improved performance and reliability in fault diagnosis across rotating machinery and pipelines.

Deep learning methods have proven exceptionally effective for extracting meaningful features and performing precise fault classification, making them highly suitable for complex fault detection tasks [26,27,28,29,30,31,32,33]. These techniques are capable of automatically learning relevant features directly from data, enabling a high level of generalization and adaptability across different fault types. CNNs, one of the most prominent deep learning approaches, excel at extracting highly discriminative features from image data, making them ideal for classification tasks within fault detection contexts. Additionally, various types of autoencoders are used for tasks such as data compression, anomaly detection, and data generation, as they efficiently extract essential features from input data while reducing dimensionality and preserving important patterns [34]. Generative Adversarial Networks (GANs) are frequently used for data augmentation, where they learn the underlying distribution of the original data to generate new, synthetic samples, effectively addressing data scarcity issues and enhancing model robustness [35]. While these techniques are powerful, their performance hinges on the quality and relevance of the input data’s features. Neural component analysis has also shown efficacy in monitoring industrial processes, enhancing the accuracy of fault detection and diagnosis. When integrated with deep learning models, it strengthens the system’s diagnostic capacity and facilitates more proactive maintenance strategies. Altogether, these advanced methods hold significant potential for refining maintenance practices, optimizing operational efficiency, and minimizing unscheduled downtimes across various industries.

In this study, the vibration signal data from the CP setup undergoes a detailed processing sequence to ensure accurate fault detection and classification. Initially, noise is removed from the raw signal data through mean removal, a step designed to enhance signal clarity by filtering out unwanted noise elements that could interfere with subsequent analysis. By performing mean removal, the data becomes more representative of the actual vibration patterns generated by the CP, which is important for identifying subtle, fault-related anomalies. Following noise reduction, the signals are transformed into time–frequency scalograms using the WCA. This transformation is particularly advantageous as it generates a two-dimensional representation of the signal, combining both time and frequency domain information. Such dual-domain information allows for a more comprehensive analysis of the CP’s operating conditions, capturing transient and frequency-dependent characteristics that are essential for detecting subtle fault indicators that might be missed in single-domain analyses. The next phase involves feature extraction using two well-established deep learning models, VGG16 and ResNet. These models are known for their ability to capture highly discriminative features from complex data inputs. VGG16, with its layered architecture, excels at learning intricate patterns in the data, while ResNet’s residual connections allow it to handle deeper layers without degradation, effectively capturing both high-level and fine-grained features [36]. By using both models, this study ensures a more robust and enriched feature extraction process, where each model complements the other by extracting different types of salient features from the scalograms. To maximize the depth of information available for classification, all extracted features are combined into a hybrid feature pool. This hybridization consolidates the strengths of both VGG16 and ResNet, resulting in a comprehensive set of features that improves the model’s ability to differentiate between normal and faulty states with greater precision. Fine-tuning is applied to this feature pool to optimize the feature representations for the specific task at hand, ensuring that only the most relevant information contributes to the final classification stage. Finally, classification is performed using an ANN, chosen for its capability to manage and process complex, multi-dimensional feature sets. By using an ANN as the classifier, this study takes advantage of its flexibility and accuracy in decision-making, ensuring reliable differentiation between different fault categories. This study’s novelty and primary contributions lie in the suitable integration of signal denoising, WCA-based time–frequency analysis, dual-model feature extraction, hybrid feature pooling, and ANN-based classification. This approach not only enhances the accuracy of fault detection in CPs but also demonstrates the effectiveness of combining advanced signal processing techniques with deep learning models for comprehensive condition monitoring.

This paper is further classified as follows: Section 2 explains the proposed methodology followed by the technical background in Section 3. Section 4 covers the results and discussions along with a detailed description of the experimental setup. This paper is concluded in Section 5 with future recommendations.

2. Proposed Method for Fault Diagnosis in Centrifugal Pumps

In this study, vibration signals from a centrifugal pump are processed through a structured sequence to enhance fault detection accuracy. Figure 1 depicts the complete flow diagram of the proposed method. The process begins with mean removal to eliminate any inherent bias, ensuring that the signals accurately reflect actual vibration patterns. This initial noise reduction step is of key importance as it lays the foundation for a more refined analysis. Following this, the signals undergo transformation through the WCA, which creates time–frequency representations that retain both temporal and frequency information. This dual-domain approach makes the data ideal for CNN-based feature extraction by capturing complex signal characteristics that are essential in fault detection.

For feature extraction, two pre-trained CNN models, VGG16 and ResNet50, are utilized due to their strengths in capturing detailed and meaningful features, particularly beneficial in scenarios with limited sample sizes. Each model offers unique advantages: VGG16’s deep structure is effective at identifying intricate patterns, while ResNet50’s residual connections allow it to capture significant features across multiple layers. This fusion of features uses the strengths of each model, providing a comprehensive and optimized feature pool.

Post fusion, additional fully connected layers are added to refine the model’s capacity for fault classification. This setup is specifically designed for the centrifugal pump data, ensuring that the model learns from the hybrid feature pool with high precision. The training process is executed using the Adam optimizer with a learning rate of 0.001, and categorical cross-entropy is used as the loss function, well suited for multi-class classification.

This method represents a robust solution by combining the strengths of VGG16 and ResNet50 architectures. The fusion of complementary features, followed by fine-tuning with a dataset specific to centrifugal pumps, yields a significant improvement in classification accuracy. This integrated approach highlights the effectiveness of hybrid feature fusion, making it a powerful tool for advancing condition monitoring and fault detection in centrifugal pumps. The proposed model is validated using experimental data from the centrifugal testbed. The results demonstrate the robustness and generalization ability of the model, achieving accurate fault detection across various fault conditions. Visualizations, including confusion matrices and accuracy curves, showcase the model’s effectiveness in fault classification. In Figure 1, N, MSH, MSS, and IF represent the normal, mechanical seal hole, mechanical seal scratch, and impeller fault, respectively.

3. Technical Background

3.1. Wavelet Coherence Analysis

WCA is a powerful signal processing tool used to evaluate the correlation between two time-domain signals across various frequency ranges. This approach is particularly useful in analyzing vibration signals from rotating machinery, such as centrifugal pumps, where faults manifest as distinct patterns across time and frequency domains. WCA enables a precise comparison between signals under normal and faulty conditions, helping to identify early signs of equipment malfunction [23].

In this study, vibration signals are captured from the centrifugal pump under multiple operational states, including a baseline (healthy) state and various fault conditions: IF, MSS, MSH, and NC, as shown in Figure 2. These signals are denoted as $x_{s1}\left(t\right)$ for the baseline state and $x_{s2}\left(t\right)$ for the faulty states, providing a foundation for comparing pump behaviors across different scenarios. To analyze these signals, the wavelet transform decomposes each signal into its frequency components over time, revealing transient features critical to fault diagnosis. The wavelet transforms $W_x(a,\tau )$ of a signal $x\left(t\right)$ at scale $\alpha$ and time $\tau$ are given by Equation (1) as below:

$$W_x\left(a,\tau \right)={\displaystyle \frac{1}{\sqrt{a}}}{\int }_{-\infty }^{+\infty }x\left(t\right)·\varnothing \left({\displaystyle \frac{t-\tau }{a}}\right)$$

(1)

In Equation (1), $\varnothing \left(t\right)$ is the chosen wavelet function, typically the Morlet wavelet for its effectiveness in time–frequency localization. The cross-wavelet transform examines the coherence between $x_{s1}\left(t\right)$ and $x_{s2}\left(t\right)$ by calculating their synchronized behavior across time and frequency. The coherence between these signals, which ranges from 0 (no coherence) to 1 (perfect coherence), is calculated as follows:

$$Coherance={\displaystyle \frac{\left|W_{x_{s1-}{x}_{s2}}(a,\tau )\right|}{\sqrt{\left|W_{x_{s1}}\left(a,\tau \right)\right|}·\left|W_{x_{s2}}\left(a,\tau \right)\right|}}$$

(2)

In Equation (2), $W_{x_{s1-}{x}_{s2}}(a,\tau )$ represents the cross-wavelet transform. This coherence function provides a visual representation of how closely the signals align over time and across frequency bands, with brighter colors in the wavelet coherence spectrum indicating higher coherence values. The wavelet coherence spectrum serves as an insightful diagnostic tool. Yellow regions signify high coherence, typically seen in normal operation or specific stable fault states. Blue regions indicate low coherence, often associated with faults that introduce significant deviations, such as MSHs. Green regions suggest transitional dynamics, representing gradual or minor disturbances. Each coherence spectrum includes a Cone of Influence, demarcated by a dashed line, which identifies areas where boundary effects might reduce accuracy. By focusing on coherence variations, WCA offers a robust framework for detecting transient and frequency-specific patterns associated with faults, providing essential insights for centrifugal pump maintenance and fault diagnosis.

3.2. Feature Extraction Using VGG16 and ResNet50

Effective and discriminant feature extraction is vital for accurate fault diagnosis, especially given the complex, non-linear patterns present in AE signals. In this hybrid approach, two pre-trained deep convolutional neural networks VGG16 and ResNet50 are used in parallel to extract complementary features from the scalograms of these signals. This parallel approach supports the unique strengths of both networks, enhancing the diagnostic model’s capability to identify different fault types.

3.2.1. VGG16: Capturing Fine-Grained Features

VGG16 is a 16-layer deep CNN architecture known for its simplicity and depth, which consists of 13 convolutional layers and 3 fully connected layers. Each convolutional layer uses small 3 × 3 filters, followed by max-pooling layers to down-sample the spatial dimensions, which helps the model capture hierarchical feature patterns [37]. The architecture is designed to progressively learn fine-grained features from low-level edges to high-level object representations through successive convolutional layers. The feature extraction process in VGG16 can be represented as follows:

$$F=ReLU(W\cdot X+b)$$

(3)

In Equation (3), $F$ represents the extracted features, $W$ and $b$ are the weights and biases of the convolutional layer, and ReLU is the Rectified Linear Unit activation function. This activation function introduces non-linearity into the model, enhancing its ability to capture complex patterns in the input scalograms. Figure 3 shows the basic architecture diagram of VGG16.

3.2.2. ResNet50: Learning Multi-Scale Features with Residual Connections

ResNet50 introduces a deeper network structure capable of learning multi-scale features. ResNet50 is a 50-layer CNN that uses residual learning through skip connections, allowing layers to “skip” over others and connect directly to deeper layers. This architecture prevents the vanishing gradient problem in deep networks, ensuring that meaningful features are learned even in deeper layers. Each residual block in ResNet50 can be mathematically expressed as follows:

$$y=F\left(x,\left\{W_i\right\}\right)+x$$

(4)

In Equation (4), $x$ is the input to the block, $F\left(x,\left\{W_i\right\}\right)$ is the residual function representing the convolutional layers within the block, and $y$ is the output after adding the input $x$ back to the residual function. This formulation helps the network learn identity mappings, facilitating the extraction of both fine and coarse features essential for distinguishing between different fault conditions. Figure 4 shows the ResNet50 architecture with residual blocks as below:

In this study, VGG16 and ResNet50 work in parallel to extract features from the scalograms. VGG16 focuses on fine-grained, hierarchical features, while ResNet50 captures complex, multi-scale patterns. The outputs from both networks are combined through feature fusion, creating a rich, comprehensive feature set that sums up diverse aspects of the input features. This fused feature set enhances fault classification accuracy by providing a detailed representation of both local and global patterns. By combining the strengths of VGG16 and ResNet50, the model can effectively distinguish between normal and faulty states in centrifugal pumps, ensuring powerful and accurate fault diagnosis. The detailed parameters of the pre-trained models used in this study are summarized in

Table 1. Parameters of the pre-trained models used.

Parameter	VGG16	ResNet50
Number of Layers	16	50
Total Parameters	138 million	23.6 million
Input Size	224 $\times$ 224	224 $\times$ 224
Dropout Rate	0.5	-
Feature Vector Size	4096	2048
Pre-trained Dataset	ImageNet	ImageNet
Learning Rate	0.001	0.001
Optimizer Used	SGD	Adam
Pooling	MaxPooling	Global Average Pooling
Regularization	Dropout	Residual Learning
Model Depth	Sequential	Residual Blocks

. VGG16, with its sequential 16-layer architecture and a total of 138 million parameters, is tailored for extracting fine-grained, hierarchical features through MaxPooling and dropout regularization (0.5) to mitigate overfitting. On the other hand, ResNet50, comprising 50 layers and 23.6 million parameters, leverages its residual block-based design to efficiently capture multi-scale patterns with Global Average Pooling and residual learning. Both models were pre-trained on the ImageNet dataset and fine-tuned for the specific requirements of this study using a learning rate of 0.001, with SGD used for VGG16 and Adam for ResNet50. This complementary configuration enables the model to balance the strengths of both architectures, resulting in a fused feature set that represents both local and global patterns comprehensively. The inclusion of these parameter details underscores the thoughtful design and fine-tuning of the feature extraction stage, which is critical for ensuring accurate and robust fault diagnosis in centrifugal pumps.

3.3. Artificial Neural Network (ANN)

After feature fusion, the resulting high-dimensional feature set requires effective classification to distinguish between various fault types. For this purpose, an ANN is used, designed with multiple fully connected layers to optimize classification performance on the fused features. The ANN architecture begins with a series of fully connected layers that further refine and interpret the fused feature set. These layers act as dense, nonlinear combinations of the extracted features, enabling the network to learn high-level abstractions. Each fully connected layer is followed by a Rectified Linear Unit ReLU activation function, which introduces non-linearity and enhances the model’s capacity to extract complex patterns [38]. The output from each fully connected layer can be represented as follows:

$$y=ReLU(W\cdot F+b)$$

(5)

In Equation (5), $W$ and $b$ are the weight and bias terms of the layer, $F$ represents the input feature vector, and $y$ is the activated output. The ANN then progressively transforms these features, focusing on distinctions relevant to different classes i.e., IF, MSS, MSH, and NC.

Following the initial training on fused features, the ANN undergoes fine-tuning to adapt specifically to the target dataset. This involves adjusting the network’s weights using the target-specific dataset of the centrifugal pump, enabling the model to extract subtle, domain-specific characteristics in the data. Fine-tuning enhances the ANN’s ability to generalize well across classes, significantly improving classification accuracy. Figure 5 shows the ANN architecture with multiple hidden layers.

The ANN architecture summarized in

Table 2. ANN model summary.

Parameter	Details
Input Shape	(224, 224, 3)
Base Models	ResNet50 (output size: 2048), VGG16 (output size: 128)
Flatten Layers	ResNet50: (2048), VGG16: (128)
Feature Concatenation	ResNet50 and VGG16 features into a single vector (2176)
Dense Layer 1	Units: 64, Activation: ReLU, Trainable Parameters: 8256
Dense Layer 2	Units: 4 (for classification), Activation: Softmax
Output Layer	Units: 4 (for classification), Activation: Softmax

was designed to effectively classify the hybrid feature set obtained from the ResNet50 and VGG16 models. By concatenating the features extracted by ResNet50 (output size: 2048) and VGG16 (output size: 128), a unified feature vector of size 2176 was created, capturing both fine-grained and multi-scale patterns essential for fault classification. This vector was processed through a two-layer dense network, with the first dense layer (64 units, ReLU activation) refining the feature representations, followed by the output layer (4 units, Softmax activation) tailored to classify the four fault conditions (Normal, MSH, MSS, and IF). This architecture was carefully optimized to balance computational efficiency and classification accuracy, ensuring the model’s robustness in distinguishing subtle fault characteristics. The inclusion of this detailed ANN configuration ensures clarity and transparency in the methodology, while emphasizing the comprehensive nature of the proposed approach.

4. Results and Performance Evaluation

The effectiveness of the proposed method is assessed using vibration signals data obtained from an actual CP testbed. Since the primary aim of this method is to detect and diagnose faults in CPs, this section begins with Experimental Setup and Data Acquisition, followed by comparison of the proposed model with existing state of the art methods.

4.1. Experimental Setup and Data Acquisition

In this study, we used a CP, specifically the PMT-4008 model (Hanil, Gwangju, Republic of Korea), mostly used in industrial applications, powered with a 5.5 kW motor. The system was managed via a panel equipped with essential components: a switch, temperature and water supply regulators, speed and flow rate controllers, pressure gauges, and display screens. The fluid transport system consists of steel pipes connected to two tanks: a main tank and a buffer tank. The main tank was set at an elevation to provide the net positive suction head (NPSH) required at the pump’s inlet, ensuring continuous operation of the CP. The experimental setup, illustrated in Figure 6 and Figure 7, operated within a closed-loop design. Upon initializing the setup, water began circulating throughout this loop. To collect vibration data from the CP, four accelerometers were strategically placed: two directly on the pump casing and two at the mechanical seal and impeller locations. Each sensor’s output was routed to a recording system, where the signals were subsequently digitized using a National Instruments 9234 device at a signal monitoring station.

Table 3. Specifications of the data acquisition system.

Name of Device	Details
Accelerometer (622b01)	Frequency Range: 0.4–10 kHz Sensitivity: 100 mV/g (10.2 mV/g (ms2)) ± 5%
DAQ System (NI9234)	Frequency Range: 0–13.1 MHz Specifications: Four analog input channels with 24-bit ADC resolution

provides the details about the data acquisition system.

During testing, vibration data from the CP was gathered using four accelerometers, operating consistently at 1733 rpm over a period of 300 s with a sampling frequency of 25.6 kHz.

In this study, we evaluate the proposed method’s generalizability by testing it on a dataset collected at a constant pressure of 3 bars. This dataset was acquired using the data acquisition system and includes vibration signals for four different conditions of the CP: MSH, MSS, IF, and NC. Each condition reflects a different health state of the CP, and the dataset comprises a variety of samples representing these states.

Table 4. Data acquisition summary.

Testing Condition	Samples Count	Pressure (Bars)
Normal	317	3.0
IF	304	3.0
MSH	317	3.0
MSS	315	3.0

provides a clear summary of the dataset’s structure and contents.

One of the leading causes of mechanical seal failure is excessive pressure. During pump installation, springs are employed to maintain contact between the seal’s rotating and stationary components, preventing leaks. Maintaining optimal pressure is essential for the correct compression of these springs. However, if the pressure exceeds a certain limit, the seal faces endure excessive force, causing them to overheat and transforming the lubricant between them into gas. Compounding this, dirt particles may become trapped between the seal faces under increased spring pressure, which, without adequate lubrication, can lead to scratches, holes, or even brittleness on the seal surfaces. If unresolved, these issues result in premature seal failure, potentially causing significant pump damage. To address these concerns, this study introduces faults like holes and scratches into a mechanical seal, collecting vibration data to analyze the adverse effects of such premature failures. The goal is to identify and understand these faults to enhance the reliability and lifespan of mechanical seals in pump systems.

Mechanical seals comprise two main parts: a stationary seal and a rotating seal. In this investigation, both seals had a diameter of 38 mm. Observations revealed a controlled defect in the rotating seal, a perforation measuring 2.8 mm in diameter and depth, while the stationary seal remained intact. This defect was purposefully introduced to simulate an imperfect barrier and assess the inherent vulnerabilities in mechanical seal apertures. This study explores the impact of such flaws on the performance and durability of mechanical seals in pumps, advancing the understanding of how these imperfections influence operational reliability. In mechanical seals, the rotating part often displays surface abrasion, while the stationary part remains unaffected. This study highlights a specific surface defect in the form of a scratch, measuring 2.5 mm in width, 10 mm in length, and 2.8 mm in depth. Such damage compromises seal performance and reliability. Examining this type of surface abrasion is critical to understanding its effects on the efficiency and longevity of seals, offering insights to improve the maintenance and performance of mechanical seals in pump systems.

Crevice corrosion is a common problem impacting impeller functionality. This type of corrosion creates a nonuniform surface on the impeller, with overlapping apertures of varying sizes that resemble insect bores in wood. These are formed due to external erosion of the impeller’s surface. Over time, shear stress causes these small openings to expand, potentially leading to significant cracks, fatigue, and ultimately catastrophic failure of the impeller. To study this fault, an impeller was deliberately altered to introduce a crevice corrosion defect, allowing for the collection of vibration data from the compromised impeller. This research aims to gain insights into the effects of crevice corrosion on impeller performance, contributing to improved fault detection and maintenance strategies for industrial pump systems. For this study, three cast iron impellers, each with a diameter of 161 mm, were used. Two impellers remained in normal condition, while a controlled defect was created in the third by removing a section of metal. Figure 8 illustrates the vibration signals recorded from this altered impeller, ensuring operational consistency across components. The analysis of these signals provides critical insights into the impact of this defect on impeller performance. The impeller defect measured 2.5 mm in width, 18 mm in length, and 2.8 mm in depth, as shown in Figure 9. This study thus contributes to a deeper understanding of impeller-related faults and enhances fault detection techniques in pump systems.

4.2. Performance Metrics for Comparisons

This study employs a rigorous processing sequence on CP vibration signals to enhance fault detection accuracy. Noise reduction through mean removal ensures data clarity, followed by WCA scalograms that combine time and frequency domains, capturing subtle fault characteristics. Features are extracted using VGG16 and ResNet, creating a hybrid feature pool that utilizes the unique strengths of each model. Fine-tuning this pool allows precise classification using an ANN, optimized for fault differentiation. The integrated approach combining noise reduction, WCA, dual-model feature extraction, and ANN classification demonstrates effective condition monitoring for CPs. The proposed approach’s effectiveness is assessed by comparing it with traditional methods using several performance metrics, including accuracy, precision, recall, and F1 score. The mathematical formulas used to compute these metrics are presented in Equations (6)–(9).

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{(\mathrm{T}\mathrm{N}+\mathrm{T}\mathrm{P})}{(\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N})}}\times 100\mathrm{\%}$$

(6)

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}}\times 100\mathrm{\%}$$

(7)

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}\times 100\mathrm{\%}$$

(8)

$$\mathrm{F}1-\mathrm{S}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}={\displaystyle \frac{2\mathrm{T}\mathrm{P}}{2\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}}}={\displaystyle \frac{2\times (\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\times \mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l})}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

(9)

In classification, a True Positive (TP) is when the classifier correctly identifies positive samples, while a True Negative (TN) occurs when it accurately identifies negative samples. A False Positive (FP) arises when the classifier incorrectly labels negative samples as positive, and a False Negative (FN) happens when positive samples are mistakenly classified as negative.

4.3. Comparative Analysis of Fault Diagnosis Methods

To evaluate the proposed model’s effectiveness in CP fault detection, a structured processing sequence was applied, beginning with mean removal to eliminate bias in vibration signals, ensuring they accurately reflect true vibration patterns. The signals were then transformed using the WCA, providing time–frequency representations that capture essential temporal and frequency characteristics for CNN-based feature extraction. For this purpose, two pre-trained CNN models, VGG16 and ResNet50, were chosen for their complementary strengths: VGG16’s deep architecture captures intricate data patterns, while ResNet50’s residual connections allow it to extract nuanced features across multiple layers. Individually, these models achieved accuracies between 91% and 93%; however, by using a hybrid approach that combines features from both models, overall accuracy improved to over 96.39%, as shown in

Table 5. Performance scores of proposed and comparison models.

Model	Accuracy	Precision	Recall	F1-Score
Proposed Model	96.39%	0.96	0.97	0.96
Wen et al. [36]	91.57%	0.92	0.92	0.92
Kumaresan et al. [37]	92.77%	0.93	0.93	0.93

, creating a comprehensive and optimized feature pool. After feature fusion, additional fully connected layers were introduced to enhance classification accuracy, tailored to the centrifugal pump dataset. The model was trained using the Adam optimizer with a learning rate of 0.001 and categorical cross-entropy as the loss function, ideal for multi-class classification tasks. Performance was assessed through training and validation accuracy and loss curves as shown in Figure 10, which showed stable convergence with validation accuracy exceeding 95% and low training loss. These plots were also plotted for the comparison methods as shown in Figure 11 and Figure 12. The confusion matrix revealed minimal errors across all fault types as shown in Figure 13. Furthermore, as seen from the t-SNE visualization in Figure 14, the proposed model displayed distinct clustering for each class, indicating the model’s ability to capture discriminative features effectively. This approach, combining VGG16 and ResNet50 features with targeted fine-tuning, demonstrates a robust solution for condition monitoring and fault detection in centrifugal pumps, highlighting the potential of hybrid CNN models for complex diagnostic tasks. While the methodology achieves excellent accuracy, its computational complexity and dependency on high-quality vibration data could pose challenges for real-time applications. These aspects are important considerations for future research to ensure broader industrial applicability and operational scalability.

In the first comparison, the model by Wen et al. [36] utilized a ResNet50-based transfer convolutional neural network (TCNN) for fault diagnosis in CPs. This model applied transfer learning with ResNet50 as a feature extractor on signal-to-image transformed vibration data, achieving around 91.57% accuracy in the test phase. Training and validation curves showed stable convergence, and the model exhibited high classification accuracy with minimal misclassifications, particularly for the “Normal” and “Impeller” classes. However, the confusion matrix and t-SNE plot indicated some overlaps between certain fault classes, especially between MSH and MSS, affecting its discriminative power as shown in Figure 13 and Figure 14, respectively. In contrast, the proposed hybrid model, combining VGG16 and ResNet50 architectures with WCA based feature extraction, achieved higher overall accuracy, outperforming the reference model on the same dataset. The hybrid model’s fusion of features in the proposed method from both CNN architectures allowed for richer, complementary representations, enabling clearer fault class separation and improved classification reliability. This comparison highlights the benefits of hybrid feature fusion, demonstrating how combining CNN strengths and multi-domain representations can enhance fault detection accuracy in complex, multi-class scenarios.

Similarly, Kumaresan et al.’s [37] study used the VGG16 model with transfer learning to classify weld defects. By leveraging the model’s pre-trained convolutional layers on ImageNet, they froze these layers and fine-tuned only the fully connected layers to adapt to their specific dataset. This approach allowed VGG16 to serve as a powerful feature extractor, capturing essential patterns in the weld defect imagery while keeping computational costs lower than training from scratch. The model achieved a strong testing accuracy of 93% when tested on our dataset, showing its ability to generalize well even with limited data. However, it faced challenges in distinguishing closely related defect types; the confusion matrix and t-SNE plot revealed some overlap among classes, particularly between MSH and MSS, indicating difficulties in feature separation within complex, high-dimensional spaces as shown in Figure 13 and Figure 14, respectively. In comparison, our hybrid model, which combined VGG16 and ResNet50 with WCA for feature extraction, achieved higher accuracy with clearer class distinctions. The hybrid approach produced a more precise confusion matrix with minimal misclassifications, yielding only minor overlaps, particularly in MSH and MSS. This improvement highlights the benefits of combining complementary feature extraction methods for enhanced fault detection accuracy.

In summary, the proposed model combines WCA with VGG16 and ResNet50 for hybrid feature extraction, achieving superior fault detection with a test accuracy of 96.39%. WCA’s dual-domain transformation enables both CNNs to capture complementary features, resulting in better class separation and high F1-scores. In contrast, the ResNet50-based model by Wen et al. reached 91.57% accuracy with overlapping classes, and Kumaresan et al.’s VGG16 model achieved 92.77% but struggled with similar overlap issues. The proposed model’s hybrid structure, using multi-scale and detailed features, provides a richer representation, enhancing fault-class discrimination in complex scenarios. In addition to accuracy metrics, the model’s performance was validated using t-SNE plots and confusion matrices, which showed minimal class overlaps and high classification precision across all fault categories. These results underscore the robustness of the proposed hybrid model in addressing complex fault conditions in centrifugal pumps. Future work will explore lightweight architectures and optimization techniques to reduce computational overhead without compromising performance.

5. Conclusions

In conclusion, this study presents a hybrid model integrating WCA with VGG16 and ResNet50 for enhanced fault detection and classification in complex datasets by combining WCA’s dual-domain representation with the complementary strengths of VGG16 and ResNet50; the model effectively captured intricate fault characteristics, outperforming individual CNN models. The proposed model demonstrated superior performance and has improved the accuracy by almost 5% as compared to the ResNet50-based model and 4% as compared to the VGG16-based model. Also, the proposed model exhibits strong feature separation with minimal class overlap, as confirmed by the t-SNE plots and confusion matrix, whereas the comparison models encountered limitations in distinguishing closely related classes, particularly in high-dimensional feature spaces. The hybrid approach’s enhanced feature extraction and class discrimination capabilities underscore its robustness and applicability for fault diagnosis in centrifugal pumps.

Future work will explore strategies to quantify and optimize this balance, aiming to reduce computational overhead without compromising diagnostic performance. Further investigation into time-wave plots for challenging fault types, such as MSH and MSS, will also be conducted to identify unique temporal features for improving fault classification. Additionally, testing the model on larger, more diverse datasets and exploring advanced fusion techniques or alternative CNN architectures will further validate its generalizability and enhance its applicability to various industrial scenarios.