Fault Detection of Rotating Machines Using poly-Coherent Composite Spectrum of Measured Vibration Responses with Machine Learning

Abstract

This study presents an efficient vibration-based fault detection method for rotating machines utilising the poly-coherent composite spectrum (pCCS) and machine learning techniques. pCCS combines vibration measurements from multiple bearing locations into a single spectrum, retaining amplitude and phase information while reducing background noise. The use of pCCS significantly reduces the number of extracted parameters in the frequency domain compared to using individual spectra at each measurement location. This reduction in parameters is crucial, especially for large industrial rotating machines, as processing and analysing extensive datasets demand significant computational resources, increasing the time and cost of fault detection. An artificial neural network (ANN)-based machine learning model is then employed for fault detection using these reduced extracted parameters. The methodology is developed and validated on an experimental rotating machine at three different speeds: below the first critical speed, between the first and second critical speeds, and above the second critical speed. This range of speeds represents the diverse dynamic conditions commonly encountered in industrial settings. This study examines both healthy machine conditions and various simulated fault conditions, including misalignment, rotor-to-stator rub, shaft cracks, and bearing faults. By combining the pCCS technique with machine learning, this study enhances the reliability, efficiency, and practical applicability of fault detection in rotating machines under varying dynamic conditions and different machine conditions.

1. Introduction

Rotating machines are the cornerstone of many power plants and industries around the world. Therefore, their reliability and availability are very imperative to these industries [1]. However, rotor faults often occur, preventing these machines from meeting reliability goals [2,3,4,5]. Given the critical role of these machines in industrial operations, it is essential to continually enhance methods for the early detection and diagnosis of rotating machine malfunctions early in their occurrence.

The vibration response of rotating machinery is highly sensitive to any changes in its structural parameters. Additionally, the vibration behaviour due to malfunctions in rotating machinery varies depending on the nature of the fault that is present [6]. Hence, the mechanical failures can be indicated early by analysing the vibration signals. Therefore, vibration-based condition monitoring (VCM) has become a well-accepted method for detecting and diagnosing faults in rotating machinery. The implementation of VCM has many advantages, such as ensuring operational safety, minimising machine downtime, and reducing maintenance costs [7,8,9]. Over the past few decades, numerous vibration-based rotor fault diagnosis techniques have been developed [10,11,12,13,14]. Generally, VCM is performed through the installation of several vibration sensors at individual bearing locations of the monitored machine [15].

However, large and complex rotating systems with multiple shafts and bearings, such as turbo-generator sets, present significant challenges in analysing vibration data from numerous bearing locations [16,17,18]. Typically, vibration measurements from individual bearing pedestals are analysed independently, which can complicate the diagnosis process and potentially lead to inconsistencies in fault identification [19,20,21]. To address these challenges, researchers have explored data fusion techniques that combine vibration data from multiple sensors [22,23,24,25]. Elbahabah et al. [26] proposed using one accelerometer per bearing pedestal for vibration measurements in rotating machines. They also introduced the use of a single composite spectrum to include the entire machine’s dynamics. This method proved to be helpful for fault detection. Additionally, they employed cross-power spectral density to merge vibration data from all bearing pedestals. Still, a notable limitation of this method was its inability to incorporate phase information from the vibration measurements in different bearing housings.

Yunusa-Kaltungo, Sinha, and Elbabhah [27] suggested using a poly-coherent composite spectrum (pCCS) for rotating machines, extending the concept of cross-spectral density (CSD) to include multiple signals. This method retains both the amplitude and phase information for all vibration data. By integrating data from various vibration accelerometers into one spectrum, their approach simplifies rotor fault identification and diagnosis. They enhanced fault detection by incorporating both the amplitudes and phases of pCCS components, providing a more comprehensive representation of machine behaviour.

Recently, machine learning algorithms, particularly artificial neural networks (ANNs), have shown significant potential in vibration-based fault diagnosis [28,29]. Liu et al. [30] provided a comprehensive review of recent AI research and development in rotating machinery fault diagnosis, covering both theoretical and practical aspects. Khalid and Sinha [31] built upon earlier work [32], both of which employed the vibration-based machine learning (VML) method with ANN models. While [32] focused on rotor-related faults, [31] expanded the application of this method to detect faults in both rotors and anti-friction bearings. The authors extended the analysed frequency range up to 5000 Hz for certain extracted vibration parameters to capture bearing resonance responses and accommodate bearing fault characteristics alongside rotor fault detection. The improved VML model was experimentally validated on a lab rig, demonstrating very high accuracy in identifying intact machines as well as faulty rotors and bearings. Nevertheless, the model’s dependence on vibration parameters from all bearing locations across time and frequency domains adds complexity to diagnosing large or complicated machinery. This could be overwhelming and lead to significant reliance on experience and engineering judgement during data analysis.

While the authors of [31] demonstrated high performance, they did not explore the integration of the poly-coherent composite spectrum (pCCS) technique with machine learning for detecting rotor and bearing faults in rotating machines. By combining the pCCS and vibration-based machine learning (VML) techniques, this study merges vibration signals from multiple bearing locations into a single composite spectrum, preserving amplitude and phase information, and significantly reducing the required frequency domain parameters. This enhancement reduces the noise content and also improves the correlation among the signals through the use of coherence [33]. The reduction in the parameters also helps to reduce the computational efficiency for the VML, which is crucial for large industrial rotating machines that generate extensive datasets. The current study investigates rotating machine faults, including misalignment, shaft cracks, rotor–stator rub, and bearing faults, using an experimental setup that simulates various fault scenarios at three operating speeds: below the first critical speed, between the first and second critical speeds, and above the second critical speed. The extracted reduced vibration parameters from the pCCS analysis are then fed into a supervised feed-forward artificial neural network (ANN) for fault detection. This approach not only enhances the accuracy and efficiency of fault detection, but also offers a practical solution for industrial applications, potentially reducing downtime and maintenance costs in complex rotating systems.

2. Methodology

The proposed methodology combines the poly-coherent composite spectrum (pCCS) technique and machine learning for the vibration-based fault detection of rotor and bearing faults in rotating machinery. Raw vibration signals are acquired from accelerometers installed at multiple bearing locations on the rotating machine. These signals are then fused into a single composite spectrum using the pCCS method, which combines both amplitudes and phases, comprehensively representing the machine’s dynamics in a spectrum. Relevant vibration parameters are extracted from both time-domain signals and the pCCS frequency-domain spectrum to detect rotor and bearing faults in the rotating machine. These extracted vibration parameters serve as inputs to an artificial neural network (ANN) model, which is trained to classify the machine’s condition and detect various faults. The use of pCCS will reduce the number of vibration parameters compared to the use of spectra from all measurement locations. Figure 1 illustrates the step-by-step process of the poly-coherent composite spectrum (pCCS) analysis methodology, integrated with machine learning, for fault detection in rotating machines.

2.1. Poly-Coherent Composite Spectrum (pCCS)

The poly-coherent composite spectrum (pCCS) is a data fusion technique for vibration-based condition monitoring and fault diagnosis in rotating machines [1,27]. It combines vibration measurements from multiple bearing locations into a single composite spectrum while retaining amplitude and phase information from all measurement points. The pCCS calculation, as shown in Equation (1), involves multiplying the Fourier transforms (FT) of vibration signals from consecutive bearing locations with their corresponding coherence values. This process is repeated for all bearing locations, and the results are then averaged over the number of segments ($n_s$).

$$\begin{array}{c}{S}_{pCCS}\left(f_k\right)=\\ \end{array}{\left({\displaystyle \frac{\sum _{r=1}^{n_s} X_1^r\left(f_k\right){\gamma }_{12}^2{X}_2^r\left(f_k\right){\gamma }_{23}^2{X}_3^r\left(f_k\right){\gamma }_{34}^2{X}_4^r\left(f_k\right)\dots X_{(b-1)}^r\left(f_k\right){\gamma }_{(b-1)b}^2{X}_b^r\left(f_k\right)}{n_s}}\right)}^{(1/b)}$$

(1)

The components of the above equation are defined as follows:

$n_s$ is the number of equal segments into which the measured time-domain vibration data are divided for Fourier transformation.

$X_m^r\left(f_k\right)$ is the Fourier transform of the rth segment of the vibration signal measured at the mth bearing location at frequency $f_k$.

${\gamma }_{mq}^2\left(f_k\right)$ is the coherence between the vibration signals measured at bearing locations m and q at frequency $f_k$.

b is the total number of bearing locations or measurement points used in the pCCS calculation.

The coherence function, represented by ${\gamma }_{mq}^2\left(f_k\right)$, measures the linear relationship between two signals at a given frequency [33] by removing the noise and also based on the system dynamic behaviour at a frequency. It is used in the pCCS calculation to suppress the effects of background noise and other unrelated signals, thereby enhancing the signal-to-noise ratio, and also represents the correlated dynamic behaviour of the machine. By retaining the phase information, the pCCS method provides a more accurate representation of the machine’s dynamics, which can potentially improve fault detection capabilities. This is particularly important for rotating machines, where phase information can identify and characterise faults.

The amplitude spectrum of pCCS$,A_{pCCS}\left(f_k\right)$ for acceleration or $V_{pCCS}\left(f_k\right)$ for velocity can be used for further analysis and vibration parameter extraction. Relevant parameters or features, such as the amplitudes at specific frequencies or the spectral energy within certain frequency bands, can be extracted from the pCCS and used as inputs for machine learning algorithms or other fault detection techniques. It is important to note that the pCCS method requires vibration measurements from multiple locations on the rotating machine. This can be achieved by installing accelerometers or other vibration sensors at various bearing locations or other strategic points on the machine.

2.2. Vibration Parameters Extraction

Time and frequency domain analyses are used to extract vibration parameters from the vibration data for fault detection. Here, the pCCS is used in the frequency domain to extract the vibration parameters. The pCCS will reduce the number of parameters compared to the use of many spectra. The filtered kurtosis ($K$) of acceleration is used as a time-domain feature for fault detection. Kurtosis is a statistical measure that characterises data distribution and is effective in detecting bearing faults, as these faults often cause impulsive events that lead to heavy-tailed distributions, thereby increasing the kurtosis value [1,34]. $K$ is computed using Equation (2) from the vibration acceleration data after applying a band-pass filter between 2000 Hz and 5000 Hz. This frequency range is chosen to focus on the bearing-related defects, as bearing resonances are likely to occur within this range [35], and the bearing defects’ related frequencies are generally modulated with the bearing housing and assembly resonance frequency [1]. Hence, the frequency band of 2000–5000 Hz is likely to contain only bearing-related dynamic behaviour.

$$K={\displaystyle \frac{\frac{1}{N}\sum _{j=1}^N {\left(a_j-\overline{a}\right)}^4}{{\left(\frac{1}{N}\sum _{j=1}^N {\left(a_j-\overline{a}\right)}^2\right)}^2}}$$

(2)

where $N$ is the number of data points, $a_j$ is the acceleration value at the jth data point, and $\overline{a}$ is the mean value of the acceleration dataset.

From the pCCS velocity amplitude spectrum $\left(V_{pCCS}\left(f_k\right)\right)$, the extracted vibration parameters are ${1X}_{pCCS}$, ${2X}_{pCCS}$, ${3X}_{pCCS}$, and a spectrum energy of pCCS (${SE}_{pCCS}$). ${SE}_{pCCS}$is defined as the energy content of the pCCS spectrum within a specific frequency band and computed using Equation (3):

$${SE}_{pCCS}={\displaystyle \sum _{k=k_0}^{k_m}}{V}_{pCCS}\left(f_k\right).df$$

(3)

where $V_{pCCS}\left(f_k\right)$ is the pCCS velocity amplitude at frequency $f_k$, and $df$ is the frequency resolution. For the computation of spectrum energy from 0.3X to 5 kHz, $k_0$ is the frequency index corresponding to the 0.3X component, and $k_m$ denotes the frequency index of 5 kHz. In total, eight vibration parameters are selected for fault detection, as shown in

Table 1. Extracted vibration parameters (features) for fault detection of rotor/bearing faults of rotating machine.

Vibration Parameters	Frequency Range	Amplitude	Domain
Filtered kurtosis ($K$)	2–5 kHz	Acceleration	Time domain
${1X}_{pCCS}$	1X Shaft Rotational Speed	Velocity	Frequency domain (pCCS)
${2X}_{pCCS}$	2X Shaft Rotational Speed
${3X}_{pCCS}$	3X Shaft Rotational Speed
${SE}_{pCCS}$	0.3X Shaft Rotational Speed to 5 kHz

: four K values from the time domain (one for each bearing channel) and four pCCS-based vibration parameters (${1X}_{pCCS}$, ${2X}_{pCCS}$, ${3X}_{pCCS}$, and ${SE}_{pCCS}$). These parameters are exactly based on earlier studies [31,32]. Earlier studies [31,32] optimised the rotor-related parameters as 1X–3X components and the spectrum energy to cover a frequency range related to sub-harmonics and their higher harmonics due to different rotor-related defects. The study [31] confirms that filtered kurtosis is useful for bearing defect detection. Therefore, the use of pCCS reduces the parameters to 8 from 20 when using 4 accelerometer data separately.

2.3. Artificial Neural Network (ANN) Model

Here, again, the artificial neural network (ANN)-based machine learning (ML) model developed by Espinoza-Sepulveda and Sinha [32] is used for this study. Hence, there is no change in the ML model. The multi-layered perceptron (MLP) with four hidden layers is used for classifying multiple health conditions based on the input data. The MLP is a classical type of ANN that has been used for fitting nonlinear functions in a wide range of classification or regression tasks from pattern recognition to prediction [36]. Specifically, the structure of the implemented ANN-based ML model is summarised in Figure 2, which takes the vibration parameters as the inputs and then generates the condition classifications as the outputs. Between the input and output layers, four hidden layers with a decreasing number of neurons are utilised, adapting to the dimensionality of the vibration parameters and output conditions. Each hidden neuron is activated by the hyperbolic tangent sigmoid function [37] to approximate the nonlinear relationship. As each output neuron represents a different class, the normalised exponential function (SoftMax) [38] is employed for the activation of the output layer to provide probability estimates under various health conditions. For the training of the ANN model, the optimising algorithm based on the scaled conjugate gradient (SCG) is used for error back-propagation with cross-entropy as the performance measure.

To obtain an ANN-based ML model with reliable performance, the measured vibration data for each machine condition at different tested speeds are separated by a ratio of (70%–15%–15%) into three subsets, including a training set, a validation set, and a testing set. The training set with a large portion of data samples is used to fit the ANN model by updating the weights and biases through back-propagation toward a low classification error. The validation set, consisting of the samples unused during training, is utilised to validate the classification performance of the trained ANN-based ML model on the training set. The validation process is beneficial for the evaluation and the selection of the ANN model by tuning the network parameters, where the training stage can be stopped to avoid overfitting by monitoring the classification performance on the validation set [39]. As for the testing set, the remaining data samples are used for assessing the generalisation capability of the ANN-based ML model on unseen and distinct data, which verifies the robustness and the reliability of the trained ANN-based ML model for fault detection on new data.

3. Experimental Setup and Data Collection

The experiment involves a laboratory-scale rotating machine test rig to study vibration-based fault detection rotor and bearing defects. As in Figure 3, the test rig is made up of two steel shafts of 20 mm in diameter connected by a rigid flanged sleeve coupler. The longer one of the two shafts is 1000 mm in length, denoted by Sh1, while the shorter one is 500 mm, denoted by Sh2. Each shaft of the rotor is support through 2 ball bearings installed within the flange housings. The bearings are lubricated with grease and their housings are safely attached to the baseplate (steel frame) using four springs on each bearing. Two balancing discs are mounted using lock nuts on the longer shaft, Sh1, each with a dimension of 125 $\times$ 14 mm in diameter and thickness. For Sh2, only one identical balancing disc is mounted. For the drive of the test rig, an induction motor with 0.75 kW rated power is connected to Sh1 with a flexible coupler, providing a maximum shaft speed of 3000 RPM. The experimental rig is enclosed within a safety cage to protect the operators and researchers from potential hazards, such as high-speed rotating components or debris that may be ejected in the event of failure during the simulated fault conditions.

Vibration data are acquired using four accelerometers (CH1-CH4) [39]. The accelerometers are mounted on the bearing housings at a 45-degree angle to the horizontal axis (Figure 4). The sensitivity and the linear frequency range of the accelerometer are 100 mV/g and 10 kHz, respectively. The accelerometer used at a 45-degree angle is expected to have vibration responses from both vertical and horizontal directions. Hence, the 2 accelerometers (vertical and horizontal directions) are not required. The accelerometers are connected to a data acquisition system with anti-aliasing filters. Vibration data are collected from all bearings with a sampling rate of 10 kHz, and the sample duration is 10 s [40]. A sampling frequency of 10 kHz is selected to cover both rotor- and bearing-related defect frequencies [1].

Five experimentally simulated cases are tested at each speed: healthy (H) (with residual unbalance and misalignment), misalignment (MS), shaft crack (SC), rotor-to-stator rub (RSR), and a defective bearing at location B2 (BF). The faults’ descriptions and locations are displayed in Figure 5 and Figure 6, and

Table 2. Data samples under different machine conditions at the tested speed of the experimental rig.

Machine Condition	Number of Runs (Samples)			Description
	450 RPM	900 RPM	1350 RPM
Healthy (H)	40	40	40	Residual unbalance and misalignment.
Misalignment (MS)	40	40	40	Parallel misalignment, induced by a vertical displacement of B1 of 0.8 mm.
Shaft crack (SC)	80	80	80	A notch of 0.34 $\times$ 4 mm (width by depth) with the 0.33 mm shim glued.
Rotor-to-stator rub (RSR)	40	40	40	Perspex blade on the shaft next to D1.
Faulty bearing (BF)	40	40	40	Seeded bearing defect at the cage of B2.

.

The experimental rig is operated at three selected speeds: 450 RPM (7.5 Hz), 900 RPM (15 Hz), and 1350 RPM (22.5 Hz). These speeds were chosen based on the rotor system’s first two bending critical speeds, identified through modal tests as 11.52 Hz and 18.62 Hz to avoid any resonance at any operating speeds [40]. The impulse-response method is used in the modal tests [1,33] to identify the natural frequencies and mode shapes. Figure 7 illustrates the experimental mode shapes of the rotor system at these two natural frequencies, spanning from the coupling location (C1) to the end of the shaft. The deformation on the y-axis in the mode shapes shown in Figure 7 only represents the relative deformation shape at each mode within the machine. The selected operating speeds represent conditions below, between, and above the critical speeds, allowing for a comprehensive analysis of the rotor system’s dynamics. As evident from the mode shapes, the test rig exhibits significantly different dynamic behaviours at the 2 natural frequencies. Hence, the machine dynamics are expected to be significantly different at the three speeds, enabling the study of fault detection under various operating conditions.

4. Experimental Results and Analysis

4.1. Poly-Coherent Composite Spectrum (pCCS) Analysis

Vibration data were collected from all the bearing channels for all the experimentally simulated cases (misalignment, shaft crack, rotor-to-stator rub, faulty bearing) at a speed of 450 RPM. Hence, the averaged spectra for all cases were computed using a sampling frequency (fs) of 10,000 Hz, a number of data points of $\left(N\right)=2^{15}$, a frequency resolution ($df$) of 0.305 Hz, 99.5% overlap, and 410 averages.

The acceleration amplitude spectra for the rotor fault cases, including misalignment (Figure 8a–c), shaft crack (Figure 9a–c), and rubbing (Figure 10a–c), are characterised by visible peaks at several harmonics of the rotational speed, such as 1X, 2X, 3X, and others. The x-axis scale was chosen such that the figures show the 1X to 3X components clearly. These harmonic components are commonly used as indicators of rotor-related faults [1]. However, it is challenging to distinguish between specific rotor fault types solely based on these harmonic patterns, as expertise in the field of vibration analysis is often required. In the case of the rubbing fault (Figure 10a–c), an increase in the energy content around the 1X harmonic of the rotational speed is observed in addition to the harmonic components.

pCCS analysis is a valuable tool for enhancing the vibration parameters of rotor faults in rotating machines. As shown in Figure 8e–g, Figure 9e–g and Figure 10e–g, the coherence across neighbouring channels exhibits high correlation at the locations of the 1X, 2X, and 3X harmonics of the rotational speed. This high coherence effectively amplifies these harmonic features (vibration parameters) in the resulting pCCS, as demonstrated in Figure 8h, Figure 9h and Figure 10h.

In addition to the harmonic components of the rubbing in Figure 10h, an increase in the energy content around the 1X harmonic of the rotational speed is observed. This increase in energy content is attributed to the rubbing phenomenon, which generates additional vibration at the rotational frequency [41]. Consequently, the spectrum energy, calculated over a specific frequency range, is considered one of the pCCS vibration parameters for fault detection.

While pCCS and harmonic analysis provide valuable insights into the presence of rotor faults, it is difficult to distinguish between specific fault types based on these features alone. Therefore, incorporating machine learning (ML) techniques with carefully selected vibration parameters becomes necessary to achieve accurate fault detection, especially when dealing with larger samples or fault scenarios.

4.2. Input Data and Vibration Parameter Matrices for ML-Based Fault Detection

The input data for the machine learning model are organised into matrices representing fault detection for rotating machinery. The ANN is used to classify the condition of the machine into one of the following categories: healthy (H), misalignment (MS), shaft crack (SC), rubbing (RSR), or bearing defect (BF). The input matrix, A, represents the extracted vibration parameters across various bearings and conditions. Each row in the matrix stands for an individual sample run, while each column represents a vibration parameter for each of the four bearings (B1, B2, B3, and B4). The vibration parameters used are the filtered kurtosis (K) of acceleration from the time domain and pCCS velocity peaks at ${1X}_{pCCS}$, ${2X}_{pCCS}$, ${3X}_{pCCS}$, and ${SE}_{pCCS}$ from the frequency domain. Matrix A is represented as:

$$A=[H, MS,SC , RSR, BF]$$

(4)

where $H=[h_1,h_2,h_3,...,h_{\mathrm{x}}]{ }^{\mathrm{T}}$ is the databank for the healthy condition, $MS=[m{s}_1,m{s}_2,m{s}_3,...,m{s}_{\mathrm{x}}]{ }^{\mathrm{T}}$ is for a misalignment fault, $SC=[s{c}_1,s{c}_2,s{c}_3,...,s{c}_{\mathrm{x}}]{ }^{\mathrm{T}}$ is for a cracked shaft, $RSR=[rs{r}_1,rs{r}_2,rs{r}_3,...,rs{r}_{\mathrm{x}}]{ }^{\mathrm{T}}$ is for a rotor rub fault, and $BF=[b{f}_1,b{f}_2,b{f}_3,...,b{f}_{\mathrm{x}}]{ }^{\mathrm{T}}$ is for a bearing fault.

Each databank contains the extracted vibration parameters from individual experimental runs, organised as follows:

$$h_i=\left[K_{B1}{ K}_{B2}{ K}_{B2}{ K}_{B4}{1x}_{pCCS}{2x}_{pCCS}{3x}_{pCCS}{ SE}_{pCCS}\right]$$

(5)

and $i=1, 2, 3, ..., x$ represents the run number for each condition.

4.3. Fault Detection of Rotor and Bearing of Rotating Machinery

The machine learning model based on ANN was developed and evaluated for fault detection. The model’s performance was assessed through confusion matrices, which provide a comprehensive overview of the actual machine condition and identified machine condition detected by the model. The confusion matrices presented represent the model’s overall performance, encompassing the results from the training, validation, and testing phases.

4.3.1. Model Development and Testing (450 RPM)

The initial model development and testing stage was conducted at a rotational speed of 450 RPM. The overall performance results obtained at this speed are presented as a confusion matrix, as shown in

Table 3. The overall performance of the ANN model in fault detection at a rotating speed of 450 RPM (below the first critical speed).

		Identified Machine Condition
		H	MS	SC	RSR	BF
Actual Machine Condition	H	100	0	0	0	0
	MS	0	100	0	0	0
	SC	0	0	100	0	0
	RSR	0	0	0	100	0
	BF	0	0	0	0	100

.

The overall performance results in Table 3 demonstrate the model’s remarkable ability to achieve 100% accuracy in detecting different fault conditions of the rotor and bearing. This performance underscores the effectiveness of the extracted vibration parameters from both the time-domain and pCCS analyses in capturing distinct fault signatures. The model’s high precision and recall in identifying normal operation conditions, as well as various fault states, highlight the discriminative power of these carefully selected features. Moreover, minimising false positives is crucial to avoid unnecessary maintenance actions and associated costs [8,42].

4.3.2. Model Validation (900 RPM and 1350 RPM)

Additional testing was conducted at rotational speeds of 900 RPM and 1350 RPM to validate the proposed methodology and assess the model’s fault detection capabilities using the extracted pCCS vibration parameters. These speeds represent different operating conditions, as they are above the first and second critical speeds, respectively, resulting in varying dynamics and vibration characteristics.

The collected vibration data were analysed, and the computed pCCS plots for both speeds are represented in Figure 11 and Figure 12. Similar to the speed of 450 RPM, the training, validation, and testing were performed for the ANN-based machine learning model for each speed separately to further test the proposed methodology. The overall performance of the ANN model in fault detection, presented in

Table 4. Overall performance of the ANN model in fault detection at a rotating speed of 900 RPM (above first critical speed).

		Identified Machine Condition
		H	MS	SC	RSR	BF
Actual Machine Condition	H	100	0	0	0	0
	MS	0	100	0	0	0
	SC	0	0	100	0	0
	RSR	0	0	0	100	0
	BF	0	0	0	0	100

and

Table 5. The overall performance of the ANN model in fault detection at a rotating speed of 1350 RPM (above the second critical speed).

		Identified Machine Condition
		H	MS	SC	RSR	BF
Actual Machine Condition	H	100	0	0	0	0
	MS	0	100	0	0	0
	SC	0	0	100	0	0
	RSR	0	0	0	100	0
	BF	0	0	0	0	100

, demonstrates the model’s remarkable robustness and ability to achieve 100% accuracy in detecting faults of rotors and bearings, including healthy conditions, at different rotational speeds. The successful validation at multiple rotational speeds, despite the varying dynamics and vibration patterns, highlights the potential of the developed model for practical applications in condition monitoring and predictive maintenance [43].

4.3.3. Observations and Discussion

The fault detections are observed to be 100% accurate even with a significantly reduced number of parameters and at different machine operation speeds where the dynamics are expected to be significantly different.

Earlier studies [31,32] have optimised the vibration-based parameters for both rotor and bearing defect detection when parameters are used separately for each measured piece of vibration data from an accelerometer. However, it is further demonstrated that the same parameters are still valid when using the pCCS. This simply indicates the following:

(i)

The coherence between the sensors data eliminates the noise but retains the dynamic correlations.

(ii)

The amplitude values used at 1X, 2X, 3X and the SE from the pCCS are only used but it is clearly observed that the phases and amplitudes at each frequency during the pCCS computation retain the difference in the machine dynamics between the different faults.

5. Concluding Remarks

This study introduces an efficient and robust methodology for vibration-based fault detection in rotating machines, combining the poly-coherent composite spectrum (pCCS) technique with machine learning. This approach effectively addresses the challenges of complex rotating systems by reducing data dimensionality while preserving critical fault signatures.

The pCCS method successfully fuses vibration measurements from multiple bearing locations into a single spectrum. This data fusion technique significantly reduces the number of parameters in the frequency domain compared to individual spectrum analysis, a crucial advantage for large industrial rotating machines where extensive datasets can strain computational resources.

The artificial neural network (ANN) model, trained on carefully selected vibration parameters from both pCCS and time-domain data, demonstrated remarkable performance in fault detection. This methodology achieved 100% accuracy in detecting various conditions, including a healthy state, misalignment, shaft cracks, rotor-to-stator rub, and bearing faults. Most notably, this high level of accuracy was maintained across three different rotational speeds: 450 RPM (below the first critical speed), 900 RPM (between the first and second critical speeds), and 1350 RPM (above the second critical speed). This speed-invariant performance underscores this methodology’s robustness and adaptability to the diverse dynamic conditions commonly encountered in industrial settings.

By successfully detecting and differentiating between various fault types across a range of operating speeds, the proposed approach demonstrates its potential for practical implementation in condition monitoring and predictive maintenance systems.