Innovative Application of Artificial Neural Networks for Effective Rotational Shaft Crack Localization

Rotational shafts are pivotal components in industrial settings and are responsible for transmitting torque and rotational motion. Despite their significance, these shafts are susceptible to faults, particularly cracks, which can adversely affect the system's performance and safety. Hence, efficient crack detection and diagnosis ensure safety, reliability, and cost-effectiveness. This research aims to develop an Artificial Neural Network (ANN) model that can effectively identify cracks occurring at different depths and locations in rotating shafts, which operate at varying rotational speeds. Vibration signals were obtained and subjected to preprocessing using a bandpass filter to isolate the shaft signals from other components. Subsequently, time-domain statistical features were extracted from the filtered signals. An optimal feature selection methodology was employed to rank the extracted features, and the highest-ranking features were chosen for training the ANN model. The findings of this research indicate that the developed model achieved a classification accuracy of 94.4%.


INTRODUCTION
Rotating shafts play a critical role as essential components in various industries where alternating loads are encountered, such as power plants, generators, compressors, aircraft engines, and wind turbines.These shafts are subjected to continuous rotation and are responsible for transmitting torque and rotational motion within the respective machinery.However, despite their vital function, rotating shafts are prone to various types of failures throughout their operational lifespan.These failures include misalignment or unbalance during the installation process, as well as the development of cracks, erosion, and wear during regular operation.The occurrence of such faults can have detrimental consequences, leading to diminished performance, equipment failure, and imposing significant financial burdens for repair or replacement.Under extreme operating conditions and subjected to repeated loads, rotating shafts are susceptible to local plastic deformation, which can give rise to surface flaws.Over time, these initial flaws have the potential to propagate and develop into cracks.When the stress intensity factors at the crack front exceed the critical stress intensity factor, the crack may undergo rapid propagation.This phenomenon can ultimately lead to catastrophic fatigue crack failure, posing significant risks and potential dangers [1].Despite their typical ductile nature, they can exhibit brittleness in fatigue fractures formed by cracks.Consequently, the early detection of cracks in rotor systems has become a matter of growing concern for engineers and researchers [2], [3].Detecting and diagnosing shaft cracks in rotor systems is crucial to preventing catastrophic failures, maintaining equipment reliability, and protecting personnel safety.
Currently, vibration-based fault detection is considered a practical and effective approach for diagnosing mechanical equipment [4].According to research by Malla and Panigrahi [5], vibration-based condition monitoring has been found to be highly successful in detecting machine faults or failures, with the capability of identifying up to 90% of such issues.This is because each component within a system or device possesses a specific vibration signature closely associated with the machine's operating conditions.Rotating machines typically consist of multiple components, such as shafts, bearings, pumps, gears, and fans.Any damage or failure to these components leads to abnormal vibrations compared to normal operational conditions.Complex vibration data is acquired from rotating machine components through signal processing techniques, which help resolve noise elimination, demodulation, and analysis issues and enhance technology for feature extraction when analyzing vibration signals from rotating machinery.Features of monitored signals are extracted using signal processing techniques to eliminate redundant information and analyze the corresponding patterns in the time and frequency domains and nonlinear features [6], [7].Features play a crucial role in fault detection in rotating machinery.Statistical features such as mean, standard deviation, skewness, and kurtosis are utilized to describe the overall features of the vibration signal, but they are limited in their ability to detect changes in the signal.
On the other hand, frequency-domain features, including energy, power spectral density, and root mean square, are derived from the Fourier transform of the signal and are highly sensitive to changes in the mechanical system, including shifts in natural frequency, damping, and stiffness, which are often indicative of damage or failure.Time-domain features, such as the time signal and its derivatives, and statistical parameters, such as mean, variance, and peak-to-peak value, are useful for the early detection of faults.The choice of fault diagnosis features depends on the fault type and the application's specific needs.The application of appropriate features can significantly enhance the accuracy and reliability of fault diagnosis in rotating machinery.However, it is not possible to identify fault patterns by directly removing features.Hence, the utilization of these characteristics in machine learning and artificial intelligence techniques is necessary to enable the categorization of faults.In the diagnosis of rotating equipment, classifiers and statistical learning approaches have been widely used, such as Artificial Neural Networks (ANN) [8][9][10][11], K-Nearest Neighbor (k-NN) [12][13][14], Decision Tree (DT) [15][16][17], Support Vector Machine (SVM) [18][19][20][21], and other algorithms.
Various studies have been conducted on rotating shaft fault diagnosis, providing valuable contributions and insights.Guan et al. [22] proposed two dynamic model variations to address shaft misalignment.Then, these models were subjected to both simulation and experimental evaluations.Bovsunovsky [23] presented a methodology that employs the principles of linear fracture mechanics to calculate the relative change in the compliance of a shaft caused by the presence of a crack.Huo et al. [24] presented a study that evaluated the performance and efficiency of crack fault detection through the utilization of wavelet packet decomposition (WPD) and empirical mode decomposition (EMD) in combination with multiscale entropy (MSE) for the diagnosis of rotating shaft faults.Gradzki et al. [25] proposed a novel signal-based methodology for detecting cracks in rotors utilizing auto-correlation and power spectral density functions derived from the vibration signals acquired at the bearings of the rotating shaft.Jeon et al. [26] created a noncontact method for identifying fatigue cracks in rotating steel shafts using aircoupled transducers.The method's efficacy was evaluated through experiments using ultrasonic data on real fatigue cracks on half-scale and full-scale steel shafts used in automobile assembly lines subjected to cyclic loading tests.Azeem et al. [27] employed a method of order analysis to detect misalignment and shaft cracks.The time-domain data obtained were transformed into spectra utilizing a Fast Fourier Transform (FFT), which was then used to conduct the order analysis in real-time.Sinou [28] studied the possible connections between nonlinear vibrations and the occurrences of higher-order antiresonances and structural modifications resulting from breathing cracks in rotor systems.In the context of using AI for fault classification, Jiang et al. [29] proposed a diagnostic method for faults in rotating machinery that employs the fusion of multi-sensor information, where all features are derived from vibration data in the time domain to form a fusion vector, and the SVM is utilized for classification.Rahmoune et al. [30] proposed a predictive control strategy for the high-pressure shaft speed of a gas turbine using ANN to monitor the vibratory behavior of the rotating machine.Yan et al. [31] presented a new algorithm for multi-sensor data fusion that utilizes the K-nearest neighbor classification method to identify imbalance, misalignment, and rub-impact in rotating machinery.Umbrajkaar et al. [32] employed a combination of ANN and SVM for the classification and assessment of shaft misalignment under varying load conditions.Zhao et al. [30] presented a method of fault diagnosis that employs a multi-input convolutional neural network (MI-CNN) was presented by Zhao et al. [33] for the classification of shaft misalignment and cracks in rotor systems.Liu Zhao et al. [34] proposed a novel method for diagnosing unbalance, misalignment, and contact-rubbing in rotating shafts based on the use of a convolutional neural network (CNN), discrete wavelet transform (DWT), and singular value decomposition (SVD).Seplveda and Sinha [35] proposed a smart vibration-based machine learning model (SVML) to diagnose rotor failures, including misalignment, shaft bow, looseness, and rubbing.Gangsar et al. [36] proposed a new approach to improve the accuracy of diagnosing unbalanced faults in rotating machinery using an SVM in combination with both time and frequency domains.Lee et al. [37] proposed a strategy for detecting shaft misalignment defects in rotating machinery through the use of an SVM for fault recognition, which was based on the analysis of the values of the components of the power spectrum in the frequency domain classified by the principal component analysis (PCA).Rao [38] utilized a combination of ANN and wavelet transforms to detect irregularities, such as open cracks or grooves on a rotating stepped shaft with multiple discs.Zamorano et al. [39] created a technique for choosing the mother wavelet in the wavelet packet transform method to improve the detection of cracks in rotating elements through SVM.
While examining the existing literature, it becomes apparent that the predominant focus of prior investigations in this field has centered on fundamental signal analysis.However, a notable gap contributing to inconsistent results and diminished accuracy in machine learning classifiers arises from the direct utilization of features extracted from signals without an intermediate preprocessing step.The absence of such preprocessing, involving techniques like noise reduction, filtering, or normalization, poses potential risks by introducing noise, distortions, or inconsistencies in the feature data.This directly impacts the performance and accuracy of machine learning classifiers.Thus, it is imperative to integrate suitable signal preprocessing techniques to mitigate these limitations and enhance the overall effectiveness of classifiers in analyzing and classifying vibration signals.To address these challenges, we advocate for robust signal preprocessing, specifically employing a bandpass filter applied to collected data.This critical preprocessing step significantly contributes to classifier performance enhancement and is, therefore, a crucial aspect of our proposed methodology.Furthermore, we underscore the paramount importance of feature selection alongside signal preprocessing.Researchers must diligently identify the optimal feature combination that captures and represents pertinent information within vibration signals, ultimately aiming for optimal results in terms of classification accuracy and overall performance.
This paper introduces an innovative application of ANN for detecting cracks in rotating shafts, critical components in various industries.The developed ANN model can identify cracks at different depths and locations, contributing to enhanced equipment reliability, safety, and cost-effectiveness.The practical applications include proactive maintenance through early crack detection, leading to improved equipment longevity.The automated capabilities of the ANN model offer a costeffective solution by reducing manual inspection efforts, saving time, and conserving resources.
In this paper, the development of an ANN model for the identification of crack depth and locations in rotating shafts operating at various rotational speeds is presented.To accomplish this objective, a test rig was designed and fabricated to provide a suitable platform for experimental investigations.Cracks of varying depths and locations were simulated in the shafts using a wire electrical discharge machine (WEDM).A data acquisition system was developed by integrating a micro-electromechanical system (MEMS) with data acquisition hardware and LabVIEW software.To improve the accuracy of the analysis, Bessel bypass filters were employed to filter the acquired vibration signals effectively.This filtering process successfully isolated the shaft vibration signals of interest, elimi-nating any extraneous signals originating from other components.Statistical features were derived from the filtered time-domain signals and subsequently utilized in the ReliefF feature ranking method.This method allowed for the identification of the most informative features.Finally, an AI classification model based on ANN was developed, incorporating the topranked features for the training of the model.The remainder of this paper is organized as follows Section 2 presents a comprehensive overview of the experimental procedures, encompassing details regarding the test rig, crack simulation, as well as the data acquisition system and signal processing techniques employed.The process of extracting and selecting relevant features using the ReliefF algorithm is examined in depth in Section 3. The classification model employed in this investigation is elaborated upon in Section 4. In Section 5, the obtained results are presented and analyzed.Finally, the conclusions drawn from this study are summarized in Section 6.

EXPERIMENTAL STUDY
This section provides details of the experimental test rig used to detect and diagnose cracks in a rotating shaft, crack fault simulation, and the data acquisition system, including hardware and software.

Test Rig Design
An experimental test setup was specifically designed and fabricated to evaluate shafts with a diameter of 20 mm and a length of 500 mm, as illustrated in Figure 1.This test rig consisted of a 0.75 kW three-phase electric motor, which was controlled by a Hyundai N700E variable frequency drive (VFD).In order to minimize misalignment, a flexible coupling was utilized to establish a connection between the shaft and the electric motor.
The experimental setup included a rotating disk with a diameter of 200 mm, a thickness of 35 mm, and a weight of 8 kg, which served as the load attached to the shaft.To ensure the secure placement of the accelerometer, the top edge of the bearing housing was machined, drilled, and threaded.An ADXL335 threeaxis accelerometer [40] was then mounted on the top edge of the bearing housing using two M3 bolts, guaranteeing its stability throughout the test operation.

Fault Simulation
This research encompassed the examination of an intact shaft (Healthy) in addition to nine shafts exhibiting cracks at different depths and locations, as presented in Table 1.These shafts were made of C45 carbon steel and measured 500 mm in length and 20 mm in diameter.The cracks were artificially simulated using a wire electrical discharge machine (WEDM) with a wire diameter of 0.25 mm and a cutting edge positioned at a 90-degree angle to the shaft's axis.Cracks were created at depths of 2 mm, 5 mm, and 8 mm, positioned at distances of 90 mm, 270 mm, and 410 mm from the edge of the shaft, respectively.Table 1 provides a comprehensive list of cases, while Figure 2-A visually depicts the shafts with simulated cracks.Additionally, Figure 2-B presents a side view showcasing the depths of the simulated cracks.
The case name for each experimental scenario was represented as a ratio of the crack depth to the crack location measured from the driven edge of the shaft.It is worth noting that the (Healthy) condition of the shaft, which was free of any cracks, was included as a reference point.
• Crest Factor (CF): is a measure of the peak-toaverage ratio of a waveform or signal.It is calculated by dividing the peak value of a signal by its RMS value.The crest factor is often used to assess the potential for audio and other signal distortion.
• Kurtosis (K): is a measure of the peakedness of a distribution.A distribution with a high kurtosis has a more peaked shape than a normal distribution, while a distribution with a low kurtosis has a flatter shape.
• Skewness (Sk): is a measure of the asymmetry of a distribution.Skewness can be positive, negative, or zero.A distribution with positive skewness is skewed to the right, a distribution with negative skewness is skewed to the left, and a distribution with zero skewness is symmetrical.
where xi is a signal for i = 1, 2,...,N.N is the number of data points, Vmax is the maximum value of (xi), μ is the signal value.

ReliefF Ranking Algorithm
The presence of a large number of features can pose challenges in the classification process, making it difficult to identify appropriate characteristics for classification purposes.Incorporating an excessive number of features can lead to increased operational complexity, reduced processing speed, and compromised classification accuracy, particularly when the available number of samples is limited [42].In such scenarios, the utilization of feature selection or dimensionality reduction methods becomes imperative to facilitate the classification process.Among these methods, the ReliefF algorithm stands out as one of the most effective filtering feature selection techniques.The Relief algorithm was first introduced by Kira in 1992 as a solution for two-class classification problems [43].This algorithm assigns weights to features according to their correlation with the class labels and selects those features whose weights exceed a specified threshold.The correlation is measured based on the features' ability to differentiate between samples in close proximity.The Relief algorithm has gained popularity due to its simplicity, efficiency, and satisfactory results.However, a notable limitation of the Relief algorithm is its capability to handle only two-class classification problems.To address this limitation, Kononenko pro-posed the ReliefF algorithm in 1994 [44], which extends the functionality of the Relief algorithm to handle multiclass classification problems.
In the context of multiclass classification problems, the ReliefF algorithm adopts a process where a sample Ri is randomly selected from the training dataset with class labels represented as C = {c1, c2, …, cl}.Subsequently, the algorithm identifies the k nearest neighbors of sample R i that share the same class label (referred to as near Hits) and assigns them labels H j (c)  (where j = 1, 2, …, k).Additionally, the algorithm identifies the k nearest neighbors of Ri that belong to other classes (known as near Misses), denoted as M j (c) (where j = 1, 2, …, k).These steps are repeated m times as part of the algorithm's execution [45].The assigned weight of feature A is adjusted as follows: where m is the iteration number, and diff(A, R 1 , R 2 ) represents the disparity between samples R 1 and R 2 in feature A. If A is continuous, the difference can be defined as: If A is discrete, then the diff can be defined as:

CLASSIFICATION MODEL
Artificial Neural Networks are computer structures inspired by the functioning of neurons in the human brain.
The first ANN was created by the psychologist Frank Rosenblatt in 1958.[46].An ANN is made up of a network of connected neurons that are stacked in layers.ANN typically comprises an input layer, an output layer, and at least one hidden layer.The number of input and output variables necessary to characterize the problem and its type determines the number of neurons in the input and output layers, while the trial-and-error approach decides the number of hidden layers and neurons each layer.illustrated in Figure 6, each neuron in a layer (except the input layer) adds the input value to the corresponding weight to generate a single threshold value.The single-value threshold is combined with a bias to obtain a net value (Net).
Finally, an activation function is applied to the net value to provide an output value.A supervised learning technique compares the input and output values and then uses a backpropagation algorithm to train the ANN model by altering the weights between each neuron in the various layers [47].Due to its superior performance, ANN has been used in many applications, including pattern identification, fault prediction and classification, voice recognition, handwritten and printed text recognition, and detection of heart disease and cancer detection [48][49][50][51][52].

Neural Network Mathematical Expression
The mathematical expression of an ANN model entails a sequential arrangement of interconnected computational units referred to as neurons, which are structured in layers.These neurons receive input, undergo computational operations, and generate an output.The network's input is represented by x i (n), the hidden layer output is represented by f, and the neural network's output is represented by y i (n).The weights connecting the input layer to the hidden layer and the hidden layer to the output layer are represented by w ij and w jk , respectively.The output vector of the hidden layer can be calculated using the following equation: where B j is the threshold of neurons in the hidden layer, N is the number of inputs, D represents the number of neurons in the hidden layer, and Q is the hyperbolic activation function in the hidden layer.Which is given by: While the time index n has been omitted for simplicity, the output of the final output layer can be calculated as: where B k is the threshold for the neuron of the output layer, and E is the number of neurons in the output layer.The output of the ANN may then be expressed as:

Neural Network Model Design
Orange Data Mining Software [53] was utilized in this research to design the ANN model, whose data processing flows are presented in Figure 7.The development of the ANN model involved an iterative process of experimentation and parameter tuning, encompassing various aspects such as the number of layers, neurons, solver, and activation function.Initially, a preliminary version of the ANN model was created with a single hidden layer and default parameter values.This initial model was then trained and evaluated to assess its classification accuracy.Subsequent iterations involved making several adjustments to enhance the performance of the ANN model.After multiple iterations, an optimal configuration was determined, which four hidden layers, with 60, 40, 40, and 40 neurons allocated to each respective layer.Detailed information regarding the classifier's characteristics can be found in Table 3.

RESULTS AND DISCUSSION
This research employed an ANN approach to identify and diagnose the depth and location of cracks in rotating shafts operating at three different rotational speeds (1200, 1800, and 2400 rpm).
The experiment involved the investigation of an intact shaft alongside nine shafts with cracks at various depths and locations, as outlined in Table 1.The vibration data collected from the shafts were filtered and analyzed.Subsequently, five statistical features were extracted, and the ReliefF ranking algorithm was employed to designate the highest-ranked feature from each axis.
The ANN model received a dataset consisting of 2400 samples for each case, resulting in the formation of a matrix containing 24000 samples across 15 features.The data sampler allocated 80% of these samples for training the ANN model, with the remaining 20% reserved for testing the model.
The cases were examined under two distinct scenarios, denoted as S1 and S2.In Scenario S1, a total of fifteen features were obtained by extracting five timedomain features from the filtered vibration data associated with each accelerometer axis.These fifteen features were subsequently employed as input variables for the ANN model.In Scenario S2, the ReliefF ranking method was implemented on the feature set extracted from Scenario S1.This approach aimed to reduce the input feature dimensionality of the ANN model from fifteen to three.This reduction was accomplished by selecting the top-ranked features for each accelerometer axis based on their ReliefF scores.
The application of the ReliefF ranking method in this research demonstrated that the three highest-ranked features extracted were the root mean square values of the X, Y, and Z axes.Furthermore, the findings indicated that the filtering procedure resulted in the mean value becoming uniformly zero, leading to the RMS and STD features possessing identical values and, consequently, equivalent rankings.As a result, only the RMS feature was selected for further analysis.Figure 8 depicts the ranking and selection process of the extracted features.
The evaluation of a fault diagnosis system's performance can be accomplished by employing various performance indicators, including Classification Accuracy (CA), F1-Score, Precision (P), Recall (R), and Specificity [54].These indicators offer a comprehensive system performance assessment by considering multiple aspects of the diagnosis process.The calculation of these performance indicators can be carried out using the following equations:  Furthermore, the findings underscore the potential for ongoing exploration and refinement of feature selection methods, coupled with the integration of sophisticated machine learning algorithms.The proposal to explore diverse sensor modalities and employ data fusion techniques in conjunction with filtered vibration signals represents an additional avenue for enriching the comprehensiveness of crack detection assessments.
Fundamentally, this study not only contributes to the understanding of crack detection in rotating machinery but also sets a standard for engineers and researchers seeking to improve proactive maintenance strategies and operational efficiency.The showcased advancements create opportunities for subsequent investigations, laying the foundation for ongoing innovation in the field of reliability within rotating machinery.
In conclusion, the developed ANN model holds significant practical implications across industries.Its application promises enhanced equipment reliability through proactive maintenance, contributing to improved safety and optimized performance.The model's adaptability and automated crack detection capabilities offer cost-effective solutions by reducing manual inspection efforts, saving time, and conserving resources.Ultimately, this research provides a valuable tool for pre-emptive maintenance, ensuring the longevity and efficiency of rotating machinery in diverse industrial contexts.

Number of hidden layers 4
Neurons in the input layer 15 Neurons in the first hidden layer 60 Neurons in the second hidden layer 40 Neurons in the third hidden layer 40 Neurons in the fourth hidden layer 40 Neurons in the output layer 10

Figure 7 .Figure 8
Figure 7. Data Processing Flow of ANN Model in Orange Data Mining