Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
-
Rongcai Wang
and
Xisheng Jia
Abstract
Diesel engines find extensive application in various production sectors, including industry and agriculture. Strengthening the condition monitoring and fault diagnosis of diesel engines is of paramount importance in ensuring the smooth operation of production systems. Timely detection and elimination of defects play a crucial role in maintaining the normal functioning of these systems. Significant temperature fluctuations during the operation of diesel engines are often associated with malfunctions, including ignition failure, abnormal intake, and exhaust processes. Hence, the application of infrared thermography (IRT) for collecting infrared images of diesel engines and conducting quantitative analysis of the temperature distribution in these images has proven to be a faster and more efficient method for recognizing the health status of diesel engines, compared to other fault diagnosis methods. In recent years, there has been a growing interest in deep learning (DL) for fault diagnosis in various industries. This emerging trend has attracted significant attention from researchers. Convolutional neural network (CNN) has garnered significant attention owing to the exceptional capability in extracting image features. Therefore, the article presents a new fault diagnosis method for diesel engines using IRT and CNN. The proposed method involves conducting adaptive histogram equalization for image enhancement, followed by employing Softmax regression for pattern recognition. Finally, two sets of self-made experimental data are used to investigate the impact of temperature variations on fault diagnosis performance and to validate the efficacy of the proposed method in comparison with three DL methods. The findings indicate that this method exhibits superior performance in the realm of diesel engine fault diagnosis.
1 Introduction
Diesel engines, as a common type of reciprocating machine, serve as the primary power source for various equipment and find extensive application in agricultural production, petroleum equipment, defense technology, military industry, ship transportation, and other domains. Therefore, enhancing the dependability of diesel engines and guaranteeing the seamless functionality hold immense importance [1]. Diesel engines are susceptible to a range of faults during high-speed and heavy-duty operation due to the intricate and challenging working conditions, as well as certain inherent manufacturing defects. These faults have a significant impact on production efficiency and can even lead to major safety accidents [2]. Through the implementation of real-time condition monitoring and fault diagnosis techniques, the defects can be promptly identified and rectified. Additionally, appropriate maintenance measures can be implemented to effectively mitigate the risk of catastrophic fault and significant economic losses.
Currently, in the field of mechanical equipment fault diagnosis, sensor technologies commonly employed include vibration signals [3–5], sound signals [6], temperature signal analysis [7], as well as oil [8] and infrared image analysis [9–11]. The sensitivity and maintenance costs of the aforementioned methods [12] in the context of mechanical equipment fault diagnosis are illustrated in Figure 1.
Sensitivity and maintenance costs of various sensor technologies.
Based on the findings presented in Figure 1, it is evident that the higher sensitivity of the sensor technology allows for the detection of abnormalities in mechanical equipment through signal analysis. However, accurately pinpointing and resolving faults is not currently feasible, leading to lower accuracy in fault diagnosis and subsequently higher maintenance costs. Conversely, as the sensitivity of the sensor technology decreases, the identification and characterization of faults become clearer, resulting in reduced maintenance costs. However, the decrease in sensitivity also increases the likelihood of equipment failure.
Among the fault diagnosis methods mentioned above, vibration signals are widely applied in fault diagnosis of diesel engines [13–15], primarily due to the ease of measurement and ability to capture crucial dynamic information of mechanical equipment, including the reciprocating motion of piston connecting rod components, crankshaft rotation, and valve opening and closing [16,17]. However, the analysis of vibration signals is subject to certain inherent limitations. The limitations include the need for contact measurement, the presence of complex noise pollution, and the requirement for local detection. Furthermore, the collection process of vibration signals typically takes place in challenging working environments, such as those with high temperatures or oil and gas-filled equipment surfaces. These conditions can easily result in signal measurement distortion and even damage to the sensors [18]. Additionally, the positioning of vibration signal sensors is typically conducted during equipment shutdown, resulting in certain losses associated with the shutdown process.
The structure and composition of diesel engines exhibit a high degree of complexity, while the working environment is characterized by harsh conditions. When faults arise, it is common to observe abnormal occurrences such as heightened friction, unusual vibrations, and fluctuations in temperature [19]. In recent years, temperature signals have garnered significant attention from scholars both domestically and internationally, owing to the abundant information regarding the condition of mechanical equipment [20–22]. In recent years, infrared thermography (IRT) has emerged as a promising non-contact and non-destructive testing technique for acquiring temperature data of devices [23]. The infrared thermal camera serves as the central element of the IRT system, enabling the remote monitoring of equipment surface temperatures. It is capable of converting temperature distributions into infrared images, which can be visually displayed. Compared to contact temperature measurement, IRT offers a simpler and more intuitive approach. By analyzing the abundant fault information present in infrared images, IRT enables a comprehensive assessment of the equipment’s fault status. Currently, IRT has been extensively and effectively applied in the domains of equipment condition monitoring and fault diagnosis, as depicted in Figure 2. Furthermore, a comprehensive examination and synthesis of the fundamental principles, current application status, and procedural framework of IRT can be found in the literature [24].
Related IRT application scenarios: (a) Defect detection of chips, (b) power facility troubleshooting, (c) evaluation of material extrusion fatigue, (d) inspection of building structure and internal facilities, (e) lumbar intervertebral disc examination in medical field, and (f) condition monitoring of the wind turbine gearbox.
This article aims to leverage the distinctive benefits of IRT to propose a novel approach for fault diagnosis of diesel engines. The proposed method is designed to achieve precise and efficient fault diagnosis. In this study, infrared images of diesel engines exhibiting various fault states were acquired using an infrared thermal camera. Subsequently, CNN was employed to automatically extract the distinguishing features from the infrared images. Finally, the utilization of a softmax regression (SR) classifier is deployed to effectively classify different fault types of the diesel engine. The efficacy of this method is validated through the analysis of experimental data obtained from a high-pressure common-rail diesel engine.
The subsequent sections of the article are structured as follows: Section 2 provides a comprehensive review of relevant literature, while also analyzing the current research state in the field. In Section 3, the article provides a concise introduction to the related background knowledge of the fault diagnosis method proposed, as well as an overview of the fault diagnosis method framework. Section 4 offers a comprehensive overview of the fundamental elements of the diesel engine system and the data acquisition system. Additionally, it examines the procedural approach to fault diagnosis. In Section 5, the article introduces two self-made datasets, as well as the parameter settings of the network models that are relevant to this study. Section 6 provides a discussion and comparison of the experimental results, thereby verifying the efficacy of the proposed method. Finally, conclusions and contributions of the article are summarized in Section 7.
2 Related literature review and their limitations
In recent years, experts and scholars from various countries have conducted numerous meaningful studies on the significant application value of IRT in the field of mechanical equipment fault diagnosis. This is due to the unique advantages of IRT in temperature measurement. Extracting image histogram features is considered a straightforward and efficient method for representing features. Younus et al. [25] introduced a novel approach for fault diagnosis of rotating machinery by using infrared image histogram features. Principal component analysis (PCA) and independent component analysis (ICA) were deployed during the feature extraction phase. Finally, support vector machine (SVM) was applied to classify the various fault states of rotating machinery. In a separate investigation conducted by Younus and Yang [26], the application of the two-dimensional discrete wavelet transform (DCT) was employed to decompose infrared images of rotating machinery. By extracting the histogram feature parameters of each layer following decomposition, the Mahalanobis distance and relief algorithm were applied for feature extraction. Subsequently, fault pattern recognition was performed using SVM and linear discriminant analysis (LDA). Widodo et al. [27] employed a self-organizing map (SOM) artificial neural network (ANN) to detect the faults in the rotor system and rolling bearings. The authors extracted histogram features from infrared images, such as mean, variance, standard deviation, central moment, entropy, kurtosis, maximum, and minimum, to identify misalignment, imbalance, looseness, and defects in the outer ring, inner ring, rolling body, and cage of rolling bearings. Bagavathiappan et al. [28] used IRT as a remote sensing technique to capture the atypical temperature patterns on the surface of a machine, successfully implementing the method for real-time monitoring of the blower impeller end bearing, shaft, and motor in the exhaust system of a nuclear power plant, effectively preventing the occurrence of major malfunctions. Janssens et al. [29] introduced a novel automated system for fault diagnosis of bearings using IRT, with a specific focus on rotating machinery bearings as the subject of investigation. By utilizing various feature parameters, including temperature standard deviation, Gini coefficient, and optical moment, SVM was employed to classify bearing fault types that are challenging to diagnose with conventional techniques, such as the absence of lubricating oil. In a separate study [19], random forest (RF) was employed to conduct early fault diagnosis of rotating machinery by extracting the Gini coefficient from infrared images. Glowacz and Glowacz [11] proposed a novel method for extracting features from infrared images, which involves selecting the difference region of the image as the fault feature and classifying the fault patterns using K-means, K-nearest neighbor (KNN), and BP network. Li et al. [30] introduced a novel method for fault diagnosis of variable-speed rotating machinery using IRT. The feature parameters of infrared images were extracted based on the bag of visual word (BoVW), and the identification of various fault types of rotating machinery was achieved through the implementation of SVM.
Currently, within the realm of diesel engine fault diagnosis, the prevailing approaches primarily encompass the construction of dynamic models [31] and the implementation of condition monitoring techniques [32]. The construction of dynamic models primarily relies on the principles of mechanical equipment dynamics. By developing a dynamic model that accurately represents the mechanical properties of diesel engines, this study aims to investigate the correlation between variations in dynamic parameters and system malfunctions. Consequently, the ultimate goal is to achieve effective fault diagnosis for diesel engines. The limitations of this particular method are rooted in the challenges associated with constructing a model and its limited ability to generalize, thereby complicating the practical application process. To date, the diagnosis method based on condition monitoring has emerged as the most extensively employed approach in the particular field, which achieves real-time fault diagnosis of diesel engines through online monitoring and collection of related signals that can effectively characterize the fault state of diesel engines. The method involves several steps, including signal preprocessing, feature extraction, and pattern recognition, to accurately identify and diagnose faults in real-time. The commonly employed methods for condition monitoring encompass vibration analysis [33], temperature monitoring [34], noise analysis [18], abrasive particle detection [35], and instantaneous torque method [36].
With the rapid advancement and extensive application of artificial intelligence (AI) technology, fault diagnosis methods that rely on signal processing, feature extraction, and machine learning (ML) have garnered increasing attention and research [37,38]. During the operation of diesel engines, the measurement of vibration signals provides a convenient means to directly observe and analyze the dynamic variations of the equipment. Hence, vibration signal analysis has emerged as the predominant approach in the field of diesel engine fault diagnosis. Flett and Bone [39] introduced a novel approach for fault diagnosis of the diesel engine valve train. Aiming to address common issues in the valve train, such as valve spring deformation and abnormal clearance, the study employed the extraction of improved root mean square (RMS) to achieve accurate diagnosis results. Meanwhile, the naive Bayes classifier was applied for this purpose. Kowalski et al. [40] have proposed a novel intelligent fault diagnosis method for impulse diesel engines commonly used in marine and land transportation. The method is based on extreme learning machine (ELM) and demonstrates the ability to accurately classify 15 common fault states of diesel engines. A comparative analysis between SVM and KNN has been conducted to establish the superiority of the proposed method. Ramteke et al. [41] conducted a study where vibration and sound signals were collected to assess the wear status of diesel engines, employing fast Fourier transform (FFT) and short-time Fourier transform (STFT) for signal processing and extracting statistical feature parameters. Based on the features, ANN was used to effectively classify different types of wear faults.
Based on the above literature, it becomes evident that the fault diagnosis methods proposed in these studies lack significant accuracy. This can be attributed to the fact that infrared images are not subjected to enhancement techniques prior to feature extraction and fault classification. When acquiring infrared images, various factors such as circuit conditions, detector performance, space environment, and channel transmission errors can significantly impact the quality of the images. The issues often result in problems such as low contrast, blurred texture, and loss of details, which in turn adversely affect subsequent computer processing and recognition tasks. Image enhancement is a widely applied method in the preprocessing of infrared images. Its objective is to accentuate or refine certain features of the image, such as edges, contours, and contrast, with the aim of improving the visual impact of the image or making it more suitable for computer-based processing. Furthermore, it is important to acknowledge that image enhancement does not fundamentally change the quantity of feature information conveyed by infrared images. Instead, it merely adjusts the dynamic range of feature information to a certain degree, facilitating the extraction of features and the identification of images by computer systems.
Image enhancement can be broadly categorized: including spatial domain and frequency domain, such as histogram equalization [42–44], grayscale transformation [45], spatial domain filtering [46,47], and frequency domain filtering [48,49]. The precise categorization is shown in Figure 3.
Classification of frequently employed techniques for image enhancement.
Currently, histogram equalization (HE) is widely employed as a prevalent technique in the field of image enhancement. The gray-scale histogram of an image is a representation of the distribution of gray-scale values, which provides an intuitive visualization of the frequency of each gray-scale level across all pixels in the image, effectively describing the overall gray-scale distribution. The primary objective of HE is to employ the cumulative distribution function to convert the grayscale histogram of the original image from a relatively concentrated grayscale interval to a uniform distribution across all grayscale ranges. By performing nonlinear stretching on the image, the pixel values are redefined to achieve a more balanced distribution of pixels within a specific grayscale range, as shown in Figure 4.
Schematic graph of histogram equalization.
HE effectively enhances the contrast of the image [50]. However, the application of HE can significantly change the contrast of the entire image, potentially resulting in the loss of local detail information [51]. In recent years, the adaptive histogram equalization (AHE) has garnered significant attention and research interest [52,53]. AHE performs equalization according to the local regions of the image, avoiding the problem of excessive enhancement or distortion caused by global equalization, preserving image details, improving the effectiveness of image enhancement, and making it more conducive to the next step of feature extraction.
Despite some progress in the field of diesel engine fault diagnosis, there are still some limitations associated with the application of conventional ML methods, including the inadequate capacity to extract intricate features from raw data and the inability to accurately identify interference information within the data. Up to now, research studies on fault diagnosis of mechanical equipment using IRT are still limited, and it is characterized by four main problems:
The majority of existing research on fault diagnosis of diesel engines primarily concentrates on the analysis of a single fault mode. However, in the practical operation of diesel engines, the state often involves a complex fault mode where multiple faults occur simultaneously. Therefore, it is not practical to study diesel engine fault diagnosis only in single fault mode.
Most of the existing fault diagnosis methods based on IRT need to manually extract the features of infrared images. Because infrared images contain rich and complex status information, the process of feature selection needs a lot of professional field prior knowledge and engineering experiments, which greatly affects the efficiency of fault diagnosis and the final classification results.
The application of IRT in the domain of mechanical equipment fault diagnosis is currently constrained to conventional rotating machinery, such as rolling bearings, rotor systems, and shafts. However, there exists a dearth of both theoretical and applied investigations pertaining to reciprocating mechanical equipment, such as diesel engines.
In practical industrial applications, faults may manifest under varying temperature conditions. When there is a variation in the temperature distribution of mechanical equipment, the corresponding distribution of fault information on infrared images also changes. This, in turn, poses a challenge in extracting features that remain unaffected by temperature fluctuations. However, the existing fault diagnosis methods that rely on IRT fail to take into account the impact of temperature fluctuations on the outcomes of fault diagnosis.
To address the research gap, this article concentrates on typical fault modes of diesel engines. It employs an infrared thermal camera to capture infrared images under different fault modes and subsequently applies deep learning (DL) methods for extracting fault characteristics from the infrared images at different temperatures. The primary advantage of DL resides in its inherent capability to automatically extract features from images, thereby overcoming the limitations associated with manual feature extraction methods. Additionally, DL exhibits strong image-processing capabilities [54]. In the context of mechanical equipment fault diagnosis, there exist four commonly used DL models: deep neural network (DNN) [55], recurrent neural network (RNN) [56,57], stacked automatic encoder (SAE) [58], and convolutional neural network (CNN) [59]. In the aforementioned models, CNN is capable of automatically and efficiently extracting deep-level features from images, which is achieved through key operations such as convolution and pooling [60], which help to mitigate information loss that may occur during manual processing. In the meantime, CNN employs the approach of local connection and weight sharing, which serves two purposes: first, it reduces the number of weights, thereby facilitating network training and optimization [61]. Secondly, it decreases the model’s complexity, consequently mitigating the risk of overfitting. CNN exhibits significant advantages in the analysis of two-dimensional images, as it possesses the capability to extract various image features, encompassing color, texture, shape, and image topology. The proposed method exhibits strong robustness and computational efficiency when applied to image processing, particularly in tasks involving the identification of displacement, scaling, and other types of distortion invariance. Therefore, this article employs CNN to extract features from infrared images across various fault states.
3 Methodology
3.1 Adaptive histogram equalization
AHE is a sophisticated image processing technique to enhance the contrast of images. Unlike global HE, which aims to equalize the entire image, AHE operates by equalizing the local image based on the grayscale distribution within specific regions of the image, achieving a more effective enhancement effect. Therefore, AHE is considered more appropriate for enhancing the local contrast of images and capturing finer image details. The fundamental concept of AHE involves the partitioning of an image into multiple regions, with the application of HE to each local region, which mitigates the issue of excessive enhancement resulting from global HE, while simultaneously preserving the local characteristics of images. The following is the specific application process of AHE.
The image should be divided into multiple not overlapping local regions. The dimensions of each region can be modified based on the specific attributes of the application scenario and the image. Typically, the dimensions of each region are 8 × 8, 16 × 16 or 32 × 32 pixels. As AHE operates in local regions, each local region can be processed independently. The presence of overlapping regions aids in preserving the image’s continuity and smoothness, while also preventing the formation of conspicuous boundaries.
The grayscale histogram needs to be calculated for each region. To obtain the grayscale histogram for each region, it is necessary to calculate it separately for each region. The calculation method for the grayscale histogram can be represented by the following equation:
(1)where h(k) denotes the count of pixels with a grayscale level of k, w(i, j) represents the weight assigned to pixel (i, j), f(i, j) represents the grayscale level of pixel (i, j), and δ(x) is the Kronecker function. Specifically, when x equals 0, δ(x) is equal to 1; otherwise, its value is 0. N and M correspond to the width and height of the image, respectively.
The cumulative distribution function needs to be calculated for each region. For the grayscale histogram of each region, the cumulative distribution function can be calculated using the following equation:
(2)In Eq. (2), the variable c(k) denotes the cumulative sum of the quantity of pixels having a grayscale level equal to or less than k.
Calculate the mapping function for each respective region. The calculation of the mapping function for each region’s cumulative distribution function is expressed as follows:
(3)Among the variables used in the context, s(k) denotes the grayscale level of a pixel after mapping, where k represents the original grayscale level. L represents the total number of grayscale levels present in the image.
HE is conducted for each region. For each region, the pixels contained within it are assigned a grayscale value through the utilization of a mapping function.
The processed regions should be merged into a single image.
The size of the local region in AHE is set to 8 × 8 in the article.
3.2 Convolutional neural network
CNN is composed of a series of convolution layers, activation layers, batch normalization layers, pooling layers, and fully connected layers. It can automatically extract features from the input data and apply the features to perform tasks such as classification, recognition, and prediction. It has achieved good results in image recognition, speech recognition, natural language processing, and other fields. In the CNN model, the convolution layer extracts features through a sliding filter (a set of convolution kernels), the pooling layer reduces the dimension of features through down-sampling, and the fully connected layer maps features to specific output classes. The basic process of CNN is shown in Figure 5, and the following sections will provide a detailed description of the different layers of CNN.
Typical architecture of CNN.
3.2.1 Convolutional layer
Convolution operation is a fundamental operation in CNN, wherein a set of convolutional kernels is employed to conduct convolution calculations on input data, resulting in the generation of feature maps. Each new feature map is obtained by convolving the local features of the input data, a process referred to as “local perception.” During the process of obtaining the feature map through convolution operation, the convolution kernel remains constant in order to achieve “weight sharing.” The mathematical representation of the convolution operation is as follows:
where the variable
3.2.2 Batch normalization layer
The inclusion of a batch normalization layer in CNN is intended to enhance both the training speed and overall performance of the network. By applying input normalization to each layer, the stability of the input distribution is enhanced, thereby mitigating the issues of gradient vanishing and exploding. Consequently, the approach facilitates the training process by accelerating its convergence. The process of batch normalization can be represented as follows [22]:
where
3.2.3 Activation layer
The activation layer is typically positioned following the convolutional layer. By incorporating nonlinear mapping functions such as Sigmoid, Tanh, ReLU, etc., the CNN’s expression and generalization capabilities can be enhanced, allowing it to effectively address intricate nonlinear problems. Compared to activation functions such as Tanh and Sigmoid, the ReLU offers several advantages. Firstly, ReLU effectively mitigates the issue of gradient disappearance, ensuring more stable training of neural networks. Additionally, ReLU exhibits faster calculation speed and better convergence, further enhancing its appeal as an activation function. The mathematical representation of the output of ReLU can be expressed using the following equation:
where let x represent the input value and f(x) denote the corresponding output value. When the input value is greater than or equal to zero, the output value is equal to the input value. Conversely, when the input value is less than zero, the output value is zero.
3.2.4 Pooling layer
The pooling layer serves as a crucial component in the down-sampling process, aiming to decrease the dimensions of images or feature maps while preserving the essential characteristics. This reduction in size not only helps to minimize computational expenses but also mitigates the risk of overfitting. The pooling operations commonly employed in various applications encompass maximal pooling and average pooling. The encoding of positional information in features makes the maximal value of the feature map more informative in terms of information content, as opposed to the average value. Therefore, when conducting pooling operations, it is common to use maximal pooling, which can be expressed as follows:
where W represents the width of the maximal pooling area.
3.2.5 Fully connected layer
The fully connected layer is commonly deployed as either the output layer or an intermediate layer within a neural network to facilitate dimensional transformation. It is employed for the purpose of classifying or regressing input features. In the CNN model, the outputs of the convolutional layer, pooling layer, and activation function ReLU are typically linked via one or more fully connected layers in order to generate G-dimensional vectors for the purpose of pattern recognition. Here, G represents the total number of classes. The fully connected layer is characterized by a high number of parameters, which can lead to overfitting. Hence, it is common practice to employ regularization techniques, such as L1 and L2 regularizations, in conjunction to minimize the number of parameters in the fully connected layer.
3.3 SR
SR is a model used for multi-classification tasks, where it addresses the classification problem by mapping the input vector to a probability vector. The application of this approach offers several benefits, including rapid training speed and robust interpretability of output results. Consequently, it has found extensive application in various domains such as image classification, natural language processing, recommendation systems, face recognition, etc. [62]. Meanwhile, in the context of multi-classification problems, SR serves as a classifier that is frequently integrated with other models, such as CNN and RNN, as the output layer in DL. The primary function of SR is to determine the fault state by computing the probability that the samples to be classified are associated with each fault class label. The particular model is depicted in Figure 6.
SR model.
The subsequent section outlines the procedural steps and mathematical derivation of the SR theory.
Data Input. Assuming a dataset with m samples, each containing n features, the input data are represented by X . The dimension of X is (m, n).
Provide explicit values for the weights and biases. The weight matrix, denoted as W , is employed in the context to represent the dimensions of (n, k), where k signifies the number of classes. Additionally, the bias vector, denoted as b , possesses a dimension of k.
Constructing a linear model. For every given sample X , the score under each class is calculated as Z = WX + b . The dimension of Z is represented as (m, k).
The Softmax function is substituted. To transform the scores of each sample within each class into probability values, the softmax function is applied, denoted as y = softmax ( Z ). The Softmax function is defined by the following equation:
(9)where i denotes the score of the current sample belonging to the ith class, and j represents all classes.
The introduction of the loss function is discussed. Cross entropy is commonly employed as the loss function, and it can be mathematically expressed as follows:
(10)where the variable y represents the true label, while the variable
Update parameters. The gradient of the loss function with respect to the weight and offset is calculated, and the parameters are updated using the gradient descent method. The process can be expressed as follows:
(11)In Eq. (11), the symbol α denotes the learning rate, which serves the purpose of regulating the magnitude of each iteration’s step in the gradient descent algorithm.
Pattern recognition. For the given input sample, the probability value for each class should be calculated, and the class with the highest probability value should be selected as the predicted result.
4 The proposed system for fault diagnosis of diesel engines
The diesel engine fault diagnosis system proposed in the article is depicted in Figure 7. The system comprises four modules, namely, infrared image acquisition, image preprocessing, CNN-based adaptive feature extraction, and SR classifier. First, it is necessary to gather infrared images of the diesel engine in various conditions, including normal condition (NC), single cylinder misfire (SCM), multi-cylinder misfire (MCM), and air filter blockage (AFB). Before feeding the infrared images into the feature extraction module, it is necessary to preprocess them, which involves several steps, such as grayscale processing, capturing the region of interest (ROI) in the images, and applying AHE algorithm to enhance the contrast of the ROI. Finally, the image feature parameters extracted by CNN are divided into training and testing sets. These sets are then directly inputted into the fault pattern recognition process of the SR classifier.
Fault diagnosis system of the diesel engine.
4.1 The proposed IRT-CNN-based fault diagnosis method
This section aims to present the proposed method for fault diagnosis of diesel engines, which is based on IRT and CNN. CNN possesses two primary advantages in the extraction of image feature parameters. First, CNN has the capability to autonomously extract deep features from images without relying on prior knowledge or human subjective experience in feature design and extraction. This ability reduces the influence of human involvement in the process. Secondly, in contrast to traditional fully connected networks, CNN employs techniques such as local connection, weight sharing, and spatial pooling. On one hand, the reduction in the number of weights simplifies the training and optimization process of the network. On the other hand, it also decreases the complexity of the model, thereby mitigating the risk of overfitting and enhancing the extraction of translation invariant features. The flow chart illustrating the IRT-CNN-based fault diagnosis method for diesel engines, as proposed in the article, is presented in Figure 8.
Procedure of the proposed method.
As shown in Figure 7, the methodology comprises three primary stages. In the initial phase, infrared image data is gathered for the diesel engine across various fault states. In the subsequent phase, CNN is employed to develop a fault diagnosis model for diesel engines. The model aims to extract fault characteristics from infrared images. Finally, the fault features collected under various fault states are fed into the SR classifier to perform fault pattern recognition of the diesel engine. It is noteworthy that the application of IRT-CNN based fault diagnosis method, as proposed in the article, does not necessitate any prior understanding of the fault mechanism or parameter configurations of the diesel engine. This method exhibits robust self-learning capabilities and is easily applicable, making it highly adaptable for fault diagnosis of diesel engines.
4.2 Infrared image acquisition
When analyzing the infrared image signals, the variation in temperature of the diesel engine cylinder head serves as an indicator not only of the combustion conditions within the cylinder, but also provides valuable insights into the operational status of the ignition system, fuel supply system, and the reciprocating impact of the piston. Therefore, collecting infrared images of the diesel engine cylinder head for the purpose of fault pattern recognition holds significant relevance and practical importance. In this study, infrared image data acquisition is dependent on the utilization of a high-pressure common-rail diesel engine test bench. Figure 9 illustrates the fundamental structure and layout of the diesel engine condition monitoring system. This system primarily consists of a diesel engine and its control panel, an infrared thermal camera, and a data acquisition system. The diesel engine type employed in the experiment is CA6DF3-20E3, and the corresponding operational parameters are presented in Table 1.
(a) IRT-based diesel engine condition monitoring system; (b) diesel engine test bench.
Working parameters of the diesel engine
| Items | Values |
|---|---|
| Common-rail mode | BOSCH electronic control common-rail system |
| Air intake mode | Supercharged intercooling |
| Rated power | 155 kW |
| Rated speed | 2300 rpm |
| Maximal torque | 760 N m |
| Compression ratio | 17.4 |
| Total displacement | 6.7 L |
| Number of cylinders | 6 |
| Number of valves per cylinder | 2 |
As shown in Figure 9(a), the high-pressure common-rail diesel engine test bench comprises two main components, namely the diesel engine and the control panel. The control panel is responsible for managing the initiation, ignition, and shutdown of the diesel engine, while the accelerator pedal is used for executing acceleration and deceleration maneuvers. The control panel’s dashboard enables real-time monitoring of various parameters such as speed, intake pressure, fuel rail pressure, and water temperature of the diesel engine. This allows for the detection of any sudden abnormalities or irregularities.
In this experimental study, the MAG32 infrared thermal camera was applied for the purpose of capturing infrared images, as depicted in Figure 9. The pertinent parameters of the infrared thermal camera are presented in Table 2.
Parameters configuration of the infrared thermal camera
| Configuration parameters | Values |
|---|---|
| Equipment type | MAG32, China |
| Infrared detector type | Uncooled focal plane |
| Image resolution | 384 × 288 |
| Frame rate | 50 fps |
| Measuring range | ‒20°C–150°C |
| Environmental temperature | 20°C |
| Measuring sensitivity | 0.02°C |
| Emissivity | 0.94 |
| Test distance | 1.2 m |
| Palette | High contrast |
The temperature measurement process of an infrared thermal camera can be influenced by various factors, including environmental temperature, measurement distance, and the emissivity of the object’s surface. Infrared thermal cameras can be used for temperature correction to compensate for the above factors. The surface emissivity of an object is defined as the ratio of the radiant energy emitted by the object at a specific temperature T to the radiant energy emitted by a blackbody at the same temperature. The characterization of the thermal radiation characteristics of an object’s surface and the calculation of thermal radiation energy transfer are crucial parameters. The object’s thermal radiation and thermal conduction characteristics are of great significance for engineering design and research, which are influenced by various factors such as temperature, surface material, and spectral wavelength. The emissivity of the object surface ranges from 0 to 1, and any variations in emissivity within a specific wavelength and temperature range can be disregarded. The emissivity values of various common materials within a specific temperature range are presented in Table 3.
Emissivity of common materials in a certain temperature range
| Materials and status | Temperature (°C) | Emissivity |
|---|---|---|
| Blackbody | All temperatures | 1.00 |
| Polished (oxidized) aluminum | 50–500 (200–600) | 0.04–0.06（0.11–0.19） |
| Polished copper | 115 | 0.023 |
| Matte brass plate | 50∼350 | 0.22 |
| Polished steel | 100 | 0.07 |
| Newly rolled steel | 20 | 0.24 |
| Polished iron | 425–1025 | 0.14–0.38 |
| Rusty iron plate | 19 | 0.69 |
| Water | 0–100 | 0.95–0.96 |
| Human skin | 36 | 0.98 |
| Coal (carbon) | 25–30 | 0.93 |
| Various colors of oil paint | Below 100°C | 0.92–0.96 |
In the present study, the application of green paint on the surface of the engine cylinder block is investigated. With regard to the data presented in Table 3, the emissivity value is determined to be 0.94. During the experiment, four common fault states were simulated for the diesel engine, namely NC, SCM, MCM, and AFB. Among them, simulating single cylinder misfire and multi-cylinder misfire by disconnecting the cylinder ignition power cord, and installing an intake hood to simulate AFB. The malfunction of the diesel engine is shown in Figure 10.
(a) NC, ①–⑥ are the six cylinders, respectively, (b) SCM, (c) MCM, (d) AFB.
Set the engine speed to 500 revolutions per minute (rpm) and use the infrared thermal camera to acquire infrared images in the following manner.
Step 1. Choose one fault class from the four simulated fault states.
Step 2. Set the environmental parameters of the infrared thermal camera. Before commencing the experiment, it is observed that the temperatures of the diesel engine test bench and the surrounding environment are initially similar, which can be attributed to the gradual reduction in temperature difference between the diesel engine and the environment as a result of continuous heat transfer. Eventually, it is possible for the temperature to reach equilibrium. At present, the laboratory thermometer indicates a temperature of 20°C. The minimum temperature of the first infrared image, captured by the infrared thermal camera, is extracted for each of the four fault states, as depicted in Figure 11.
The minimum temperature profile of the diesel engine cylinder surface: (a) NC, (b) SCM, (c) MCM, and (d) AFB.
As shown in Figure 10, the minimum temperatures observed on the surface of the diesel engine cylinder remain consistently close to 20°C across all four fault states. In the experiment, the environmental temperature parameter of the infrared thermal camera is set to 20°C.
Step 3. At the constant speed of a diesel engine of 500 rpm, infrared images are collected every 10 s.
Step 4. The duration for image acquisition is set to 25 min in order to allow the highest temperature on the surface of the cylinder to reach a stable state. In the experiment, the temperature stabilizes at approximately 52°C. A total of 150 infrared images are collected for each fault class. The maximum temperature profile of the diesel engine cylinder surface the temperature is displayed in Figure 12.
The maximal temperature profile of the diesel engine cylinder surface: (a) NC, (b) SCM, (c) MCM, and (d) AFB.
Step 5. Cool the diesel engine to the environmental temperature and repeat the aforementioned steps for the remaining fault classes until the data collection process is concluded.
4.3 The process of infrared image enhancement
Before implementing image enhancement for infrared images, it is necessary to first extract the ROI from infrared images. This initial step serves to simplify the complexity of subsequent image processing tasks and effectively reduce the overall amount of image data. The research should primarily concentrate on the thermal dynamics of the diesel engine cylinder block, which experiences substantial variations in temperature. At the same time, it can also emphasize the primary information contained within the image, thereby facilitating subsequent image processing and analysis. The ROI plays a crucial role in an image as it encompasses significant information that requires careful consideration. Selecting the ROI can enhance the ability to capture pertinent information, optimize the speed and efficiency of image processing, and facilitate improved image recognition and classification by algorithms. Infrared images depicting the fault state of the diesel engine running steadily for a duration of 10 min are selected, as illustrated in Figure 13. The temperature unit is °C.
Infrared images of the diesel engine: (a) NC, (b) SCM, (c) MCM, (d) AFB.
As shown in Figure 13(a), the infrared image reveals notable brightness and high temperature in the diesel engine cylinder region. Additionally, the brightness near the turbocharger is also prominent, indicating the highest temperature point in the entire image. In Figures 13(b) and 13(c), SCM and MCM occurred in the diesel engine, resulting in a decrease in the temperature of the corresponding cylinder block region. In Figure 13(d), it can be observed that the temperature in the vicinity of the turbocharger is significantly higher compared to other conditions. AFB can lead to suboptimal engine intake, which in turn can result in a dense fuel-air mixture, incomplete combustion, and inadequate airflow for turbocharger cooling. In addition, it should be noted that certain extraneous variables, such as the presence of power lines and experimental equipment, can introduce substantial interference to infrared images, thereby affecting the suitability for subsequent analysis. Therefore, the ROI extraction from infrared images is advantageous for subsequent feature extraction studies and serves to mitigate the impact of interfering factors. The resolution of infrared images obtained in the study is 384 × 288. After isolating the engine block region, the resolution is reduced to 355 × 49, as depicted in Figure 14.
ROI of a diesel engine infrared image under NC.
After the ROI extraction from infrared images, the size of the images decreased significantly from 324 kb to 51.1 kb. The size reduction suggests that the ROI extraction can effectively reduce the amount of data that needs to be processed, leading to enhanced speed and efficiency in image processing. The extracted ROI from infrared images is inputted into the AHE-based image enhancement module, as shown in Figure 15.
(a) ROI of infrared images under NC; (b) ROI of infrared images under NC after image enhancement.
The analysis of Figure 15 reveals that AHE has a notable impact on enhancing the visual quality of images. It effectively improves the color distribution and enhances the effect on feature extraction by adapting to the grayscale distribution in various regions.
5 Experimental study
5.1 Experiment dataset description
During the operation of the diesel engine, the surface temperature of the cylinder block experiences a certain degree of fluctuation. However, over time, it stabilizes at a temperature of approximately 52°C, after initially rising from 20°C. We collected 150 infrared images for each fault class. The article employs four commonly used DL models, namely CNN, DNN, RNN, and SAE, to analyze infrared images and identify fault modes of diesel engines.
In the present experimental study, two self-made experimental datasets, namely dataset 1 and dataset 2, after ROI extraction and AHE-based image enhancement, are employed to validate the efficacy and precision of the proposed method. Among the datasets, dataset 1 comprises 600 infrared image samples, with 150 samples collected from each of the four fault classes. On the other hand, dataset 2 is a sample grid that encompasses five time regions: region 1 (0–5 min), region 2 (5–10 min), region 3 (10–15 min), region 4 (15–20 min), and region 5 (20–25 min). Each time region consists of 120 samples (four fault classes × 30 samples). For instance, Figure 16 displays the infrared images depicting four different fault states of the diesel engine in region 2.
Infrared images of the diesel engine after AHE-based image enhancement: (a) NC, (b) SCM, (c) MCM, and (d) AFB.
As reflected in Figure 16, it is difficult to visually distinguish the fault class when analyzing infrared images under different fault states. Due to the phenomenon of thermal conduction, the variations observed in infrared images of different fault classes are minimal. In the present study, a partitioning scheme was employed where 80% of the available data samples were allocated for training purposes, while the remaining 20% were reserved for evaluating the model’s generalization ability and real-world performance. Tables 4 and 5 provide detailed descriptions of individual regions of dataset 1 and dataset 2, respectively.
Detailed description of dataset 1
| Fault class | Class label | Number of training set images | Number of test set images |
|---|---|---|---|
| NC | 1 | 120 | 30 |
| SCM | 2 | 120 | 30 |
| MCM | 3 | 120 | 30 |
| AFB | 4 | 120 | 30 |
Detailed description of individual regions in dataset 2
| Fault class | Class label | Number of training set images | Number of test set images |
|---|---|---|---|
| NC | 1 | 24 | 6 |
| SCM | 2 | 24 | 6 |
| MCM | 3 | 24 | 6 |
| AFB | 4 | 24 | 6 |
5.2 Parameter settings of the involved DL methods
In this article, the AlexNet model in CNN is employed to extract fault features present in infrared images of diesel engines. AlexNet has significantly enhanced the accuracy of image recognition by leveraging several advantages. These include a deep network structure, a substantial number of convolutional layers and pooling layers, the application of the ReLU activation function, and the incorporation of dropout technology. The advancements have demonstrated the superiority of CNN in the field of image recognition, establishing AlexNet as a significant milestone in the field of DL. We used the pre-trained AlexNet model and made certain parameter adjustments to it according to the characteristics of the dataset employed.
AlexNet necessitates an input image size of 227 × 227 × 3, encompassing 5 convolutional layers, 3 pooling layers, and 3 fully connected layers. The filter consists of convolutional kernels of sizes 11 × 11, 5 × 5, and 3 × 3. Subsequently, a fully connected layer is employed to compute the probability of four classes and facilitate pattern recognition. The detailed structure is presented in Table 6. To showcase the effectiveness of the CNN-based method, various DL methods such as DNN, RNN, and SAE, which have been prominent in recent years, were compared and analyzed. These methods were then applied to the task of fault pattern recognition of diesel engines. In the context of RNN, LSTM is used to perform image classification. On the other hand, the DNN model employs MLP for the purpose of fault pattern recognition. The specific parameter configurations for the aforementioned methods are presented in Table 7.
Parameter settings of AlexNet
| Layer type | Number of kernels | Size of input map | Size of output map | Size of kernel | Stride | Padding |
|---|---|---|---|---|---|---|
| Input layer | / | 227 × 227 × 3 | / | / | / | / |
| Convolutional layer 1 | 96 | 227 × 227 × 3 | 55 × 55 × 96 | 11 × 11 | 4 × 4 | 0 |
| Pooling layer 1 | 1 | 55 × 55 × 96 | 27 × 27 × 96 | 3 × 3 | 2 × 2 | / |
| Convolutional layer 2 | 256 | 27 × 27 × 96 | 27 × 27 × 256 | 5 × 5 | 1 × 1 | 2 × 2 |
| Pooling layer 2 | 1 | 27 × 27 × 256 | 13 × 13 × 256 | 3 × 3 | 2 × 2 | / |
| Convolutional layer 3 | 384 | 13 × 13 × 256 | 13 × 13 × 384 | 3 × 3 | 1 × 1 | 1 × 1 |
| Convolutional layer 4 | 384 | 13 × 13 × 384 | 13 × 13 × 384 | 3 × 3 | 1 × 1 | 1 × 1 |
| Convolutional layer 5 | 256 | 13 × 13 × 384 | 13 × 13 × 256 | 3 × 3 | 1 × 1 | 1 × 1 |
| Pooling layer 3 | 1 | 13 × 13 × 256 | 6 × 6 × 256 | 3 × 3 | 2 × 2 | / |
| Fully connected layer 1 | / | 6 × 6 × 256 | 4096 | / | / | / |
| Fully connected layer 2 | / | 4096 | 2048 | / | / | / |
| Fully connected layer 3 | / | 2048 | 4 | / | / | / |
| Output layer | / | 4 | 4 | / | / | / |
Parameter settings of comparison methods
| Comparison method | Network size | Activation function | Classifier |
|---|---|---|---|
| MLP | [52185, 512, 256, 128, 4] | ReLU | Softmax |
| LSTM | [52185, 100, 100, 4] | Sigmoid | Softmax |
| SAE | [52185, 1024, 512, 128, 4] | ReLU | Softmax |
Note: The input image size of the above three methods is 355 × 49 × 3.
6 Result analysis
6.1 Fault diagnosis results of diesel engines under dataset 1
The objective of the article is to evaluate the effectiveness of the proposed CNN-based fault diagnosis method for diesel engines. However, it should be noted that this investigation does not take into account the impact of temperature variations on the surface of the diesel engine cylinder block. For the purpose of conducting a comparative analysis, this study employed various DL methods, including MLP, LSTM, and SAE. These methods were deployed to dynamically extract features of infrared images captured in mixed temperature regions and accurately classify the fault state of the diesel engine. The confusion matrix depicting the fault diagnosis results of the aforementioned four methods can be observed in Figure 17.
Classification results of four methods: (a) CNN; (b) MLP; (c) LSTM; (d) SAE.
From the analysis of Figure 17, it is evident that the CNN-based method exhibits the highest fault diagnosis accuracy, regardless of temperature variations during diesel engine operation. Moreover, it demonstrates the capability to effectively differentiate between the four fault states of the diesel engine. When diagnosing diesel engine faults, MLP, LSTM, and SAE exhibit a higher number of misclassifications compared to the CNN-based method. Additionally, the classification accuracy is significantly lower than that of CNN-based methods. Simultaneously, to mitigate the influence of randomness in DL methods, each method performs 10 times of training and testing on dataset 1. This is done to determine the mean and standard deviation of the diagnostic accuracy, as presented in Table 8.
Classification results of dataset 1
| Methods | Average classification accuracy | Standard deviation |
|---|---|---|
| CNN | 97.67% | 0.0072 |
| MLP | 87.67% | 0.0934 |
| LSTM | 83.33% | 0.0456 |
| SAE | 88.50% | 0.0423 |
From the analysis of Table 8, it is evident that the CNN-based fault diagnosis method exhibits the highest classification accuracy and the lowest standard deviation, which achieves an accuracy rate that is 10.36% higher than the second-highest method based on SAE. The average testing accuracy of the LSTM model is the lowest, measuring only 83.33%. In relation to the stability of algorithms, the CNN-based method proposed in the article demonstrates a significant advantage over the other three DL methods. It is worth noting that MLP exhibits the highest standard deviation of 0.0934. Furthermore, MLP, LSTM, and SAE have a certain degree of mistaken identification between classes 2 and 3. In contrast, CNN demonstrates 100% accuracy in correctly identifying SCM and MCM. In conclusion, the CNN-based method proposed in this article demonstrates superior feature extraction capabilities in the recognition of diesel engine fault states.
6.2 Fault diagnosis results of diesel engines under dataset 2
In the engineering application of diesel engines, it is important to acknowledge that functional failures can potentially arise at any stage of operation. Therefore, with the objective of mitigating potential premature failures, this article seeks to showcase the efficacy of the method proposed in the research by segmenting the complete operational process of the diesel engine into five distinct regions. Simultaneously, the fault diagnosis results are compared with DL methods such as MLP, LSTM, and SAE to showcase the superior performance of the CNN-based fault diagnosis method proposed in the article. For the purpose of fault pattern recognition, the aforementioned four DL methods were employed on datasets from five different time regions. Each method was subjected to ten training and testing sessions, and the corresponding classification results are presented in Table 9 and Figure 18, respectively.
Classification results of dataset 2
| Methods | Time regions | Average | |||||
|---|---|---|---|---|---|---|---|
| 0–5 min | 5–10 min | 10–15 min | 15–20 min | 20–25 min | |||
| CNN | Accuracy | 70.42% | 97.50% | 100% | 100% | 100% | 93.58% |
| Std | 0.0657 | 0.0204 | 0 | 0 | 0 | 0.0172 | |
| MLP | Accuracy | 66.25% | 92.07% | 95.00% | 96.67% | 100% | 90.00% |
| Std | 0.0684 | 0.0472 | 0.0520 | 0.0583 | 0 | 0.0452 | |
| LSTM | Accuracy | 55.42% | 93.75% | 96.67% | 97.50% | 100% | 88.67% |
| Std | 0.0813 | 0.0208 | 0.0583 | 0.0534 | 0 | 0.0428 | |
| SAE | Accuracy | 36.67% | 92.08% | 98.33% | 88.33% | 87.92% | 80.67% |
| Std | 0.1302 | 0.0292 | 0.0276 | 0.0717 | 0.0683 | 0.0654 | |
Note: Std represents the standard deviation.
Diagnostic accuracy of CNN, MLP, LSTM, and SAE in five time regions.
From the analysis of Table 9 and Figure 18, it is evident that among the five time regions of dataset 2, CNN-based fault diagnosis method exhibits the highest average classification accuracy. Furthermore, when considering all four methods, CNN also achieves the highest overall classification accuracy, reaching an impressive 93.58%. MLP demonstrates the second-highest average classification accuracy among the four methods, achieving an accuracy of 90%. The remaining two approaches, namely LSTM and SAE, exhibit comparatively lower average classification accuracy of 88.67 and 80.67%, respectively. On the contrary, the CNN-based method proposed in the article exhibits strong algorithm stability, as evidenced by its consistently low standard deviation of average classification accuracy. Among the four DL methods evaluated, the CNN-based method consistently achieves the lowest standard deviation of 0.0172 across five time regions and overall. The standard deviation of the average accuracy of SAE is the highest, reaching a value of 0.0654.
Furthermore, it is evident that during the initial time region, the classification accuracy of the four DL methods is relatively low. This can be attributed to the fact that in the early stage of diesel engine operation, the temperature of the cylinder and the environmental temperature are similar. Consequently, the training data for the model is inadequate, leading to interference in subsequent fault pattern recognition. The analysis results presented above indicate that the CNN-based fault diagnosis method proposed in the article is capable of effectively extracting fault features from infrared images of diesel engines.
The conclusion is supported by the fact that all four methods employed in the study use the SR classifier for final pattern recognition. Furthermore, by conducting a comparative analysis, it becomes evident that the surface temperature of the diesel engine cylinder block exhibits a gradual increase across the dataset of five consecutive time regions. It is noteworthy that CNN demonstrates the highest accuracy in fault diagnosis and the lowest standard deviation of average accuracy. The aforementioned statement suggests that the CNN-based method, as proposed in the article, exhibits superior algorithm stability and anti-interference capability when it comes to fault diagnosis of diesel engines caused by temperature fluctuations.
6.3 Effect evaluation of image enhancement
In this article, the image pre-processing stage involved the application of AHE for infrared image enhancement. As depicted in Figure 14, image enhancement has resulted in a notable improvement in contrast for infrared images. To examine the impact of image enhancement on the feature extraction process of CNN, the features obtained after the final fully connected operation of CNN are chosen for visualization, as shown in Figure 19.
Comparison of feature visualization: (a) pre- and (b) post-AHE.
It can be clearly seen from Figure 19 that after AHE-based image enhancement, the feature distribution becomes more concentrated, with the distribution range of Dimension 1 and Dimension 2 reduced by half, and the feature separation degree has been improved, thereby facilitating subsequent feature extraction and pattern recognition.
To provide additional evidence on the impact of image enhancement on fault state recognition of diesel engines, we conducted training and testing using various methods including CNN, MLP, LSTM, and SAE on dataset 3 obtained from dataset 1 without undergoing any image enhancement. The network parameters remained constant, and the classification results are presented in Table 10 and Figure 20.
Classification results of dataset 3
| Methods | AHE | Average accuracy | Comparison |
|---|---|---|---|
| CNN | Y | 97.67% | 1.65% |
| N | 96.08% | ||
| MLP | Y | 87.67% | 11.80% |
| N | 78.42% | ||
| LSTM | Y | 83.33% | 2.66% |
| N | 81.17% | ||
| SAE | Y | 88.50% | 1.72% |
| N | 87.00% |
Comparison of diagnostic accuracy of CNN, MLP, LSTM, and SAE.
It is worth noting that the raw data used in the research process of this article is consistent with a previous article published by the author [63]. It is reasonable to say that the fault diagnosis results before applying AHE-based image enhancement in Table 10 of this article should be consistent with the results for Dataset 3 in Table 10 of the previous article. However, due to the unpredictability of DL methods, there may be significant differences in the results of each training and testing. Therefore, it can be explained that in this article, after retraining and testing the dataset 10 times, the results have shown some differences compared to the previous article. However, this difference is relative and does not affect the scientificity and accuracy of the results in this article. The results in Table 10 fully demonstrate the effectiveness of the AHE-based image enhancement method.
In Table 10 and Figure 20, the variable Y denotes the application of AHE for image enhancement, while the variable N signifies the absence of AHE in image enhancement. Table 10 demonstrates that when using the above four DL methods for feature extraction, AHE-based image enhancement can effectively improve fault diagnosis accuracy. Among the various models considered, the MLP-based method exhibited the most significant enhancement in fault diagnosis accuracy, achieving a notable increase of 11.80%. The fault diagnosis accuracy of the other three DL methods has also shown improvement to varying degrees following the application of AHE.
6.4 Generalization ability verification of CNN
To elaborate on the generalization ability [64] of the CNN for infrared image classification under study, we have set up a situation where the training dataset is unbalanced. For dataset 1, we randomly deleted 20% of the infrared images under class label 1, which means there are still 120 infrared images left under this label. Among them, the training set and test set contain 96 and 24 images, respectively, and the infrared images under the other class labels remain unchanged. Set the epochs to 10 because in this case, the training accuracy curve and loss value curve of CNN have become stable, and then record the entire training and testing process time. The confusion matrix of the highest fault diagnosis accuracy of 10 times of training and test results is taken and presented, as shown in Figure 21.
Confusion matrix of fault diagnosis results.
The variation curves of fault diagnosis accuracy and loss value during the training process are shown in Figure 22.
The variation curves of accuracy and loss value: (a) accuracy, (b) loss value.
From Figure 21, it can be seen that even with reduced training data under class label 1, the fault diagnosis accuracy can still reach 99.12%, with an average accuracy of 97.28% and a standard deviation of 0.018. Furthermore, all test data under classs label 1 have been correctly identified. Therefore, the above facts are sufficient to prove the good generalization ability of the proposed CNN for infrared image classification.
In terms of hardware configuration, a computer of Windows 11 is used in this study, with 13th Gen Intel(R) Core(TM) i5-13600KF 3.50 GHz CPU, NVIDIA GeForce RTX 4060 GPU, and the RAM is 32GB DDR5. Moreover, the total number of iterations is 280, taking 25 s. The number of parameters of the CNN used in this article is about 60 M. Therefore, we can conclude that the method proposed in this article has the acceptable feasibility of online monitoring and can identify the real-time status of diesel engines accurately. In addition, due to the relatively large number of parameters, the model needs to be compressed and pruned in subsequent embedding tasks, and the hardware configuration of the computer needs to be improved.
7 Conclusions
This article introduces a highly efficient fault diagnosis approach for diesel engines, using the combination of IRT and CNN. In order to address four prevalent fault states of diesel engines, we have collected the corresponding infrared images. The effectiveness of the proposed method is verified in comparison to DL methods such as MLP, LSTM, and SAE. Simultaneously, the article investigates the impact of temperature variations on the fault diagnosis efficacy of DL methods. To summarize, the article makes the following key contributions:
This study proposes an effective fault diagnosis method for diesel engines by combining IRT with CNN. The proposed method is capable of automatically extracting fault features from infrared images and demonstrates excellent algorithm stability and anti-interference ability against temperature fluctuations.
The AHE-based image enhancement, proposed in the article, demonstrates its effectiveness in enhancing the fault diagnosis accuracy. Moreover, it exhibits a certain level of adaptability to DL methods, including CNN, MLP, LSTM, and SAE.
The experimental results demonstrate that the proposed CNN has a good generalization ability for infrared image classification and acceptable feasibility of online monitoring, and exhibits superior fault diagnosis performance and effectively identifies mixed faults (MCM) when compared to MLP, LSTM, and SAE.
In future research endeavors, the primary focus will be on addressing the issue of low accuracy in fault diagnosis during the early stages of diesel engine operation. This will involve conducting research on few-shot image classification, as acquiring an adequate amount of data is challenging.
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Funding information: The research work was funded by the National Natural Science Foundation of China (No. 71871219).
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Author contributions: Conceptualization: Rongcai Wang and Xisheng Jia; methodology: Rongcai Wang and Hao Yan; writing – original draft preparation: Rongcai Wang; writing – review and editing: Enzhi Dong and Yuan Li; and supervision: Zhonghua Cheng and Xisheng Jia. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: All data generated or analyzed during this study are included in this published article.
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Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
- Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
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- Comparative study of couple stress fluid flow using OHAM and NIM
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- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
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Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
- Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
