Abstract
This study presents an intelligent IoT-based approach to vibration diagnostics of internal combustion engines using a wireless sensing architecture for real-time condition monitoring. The proposed system enables continuous acquisition of vibration signals with remote data transmission to a server, where signal preprocessing, Kalman filtering, root mean square (RMS) computation, frequency-domain analysis using Fast Fourier Transform, and multidimensional feature extraction are performed. Experimental validation was conducted on a laboratory test bench under healthy and artificially induced outer-ring bearing defect conditions at rotational speeds of 500, 1000, and 1500 rpm. Classical vibration analysis revealed a consistent 34–37% increase in RMS values in the presence of a defect, along with characteristic spectral components corresponding to the calculated fault frequencies. To enhance diagnostic robustness, a supervised machine learning framework was implemented using time- and frequency-domain features. Comparative evaluation demonstrated that machine learning models significantly outperform conventional RMS threshold-based diagnostics. The Random Forest classifier achieved up to 97% classification accuracy (ROC-AUC = 0.99) under random split validation and maintained 94% accuracy under cross-speed validation, confirming strong generalization capability across varying operating regimes. The results demonstrate that integrating IoT-based sensing, advanced signal processing, and intelligent classification provides a scalable and reliable solution for predictive maintenance of ICE systems in transportation, energy, and industrial applications.
Keywords
1. Introduction
1.1. Background
Vibration diagnostics is one of the methods for monitoring the technical condition of equipment, applied across various industries – automotive, energy, aviation, metallurgy, and others. 1 This method is based on the analysis of mechanical oscillations that occur during equipment operation, enabling the detection of faults at an early stage. 2
For monitoring rotating machinery, parameters such as vibration, stator current, and acoustic signals can be used. However, due to its sensitivity to changes in the technical condition of equipment, 82% of monitoring methodologies are based specifically on vibration analysis. 3 Even minor changes in the vibration spectrum during operation may indicate wear, imbalance, or other mechanical defects.
Under current conditions, where the demand for uninterrupted operation of internal combustion engines (ICE) is increasing and their failures may lead to significant financial losses, vibration diagnostics becomes particularly important as a tool for preventing emergencies and equipment breakdowns. In particular, it allows timely identification of bearing wear, imbalance, mechanical looseness, and other anomalies that may lead to engine shutdown.
Currently, a wide range of approaches to vibration signal analysis is used, involving various types of sensors, data processing methods, and integration with modern technologies such as the Internet of Things (IoT) and Machine Learning.
1.2. Literature review
Extensive research has been conducted on vibration-based diagnostics of machinery and ICEs.
The study 4 provides a systematic review of vibration analysis for machine condition diagnostics. It highlights that vibration parameters – amplitude indicates the severity of the issue, while frequency helps identify its source. A classification of machines by rotational speed is applied: those operating below 600 rpm (e.g., wind turbines, hydro turbines) are considered low-speed, whereas machines with higher speeds (e.g., generators, engines) are classified as high-speed. Low-speed machines are noted to be more challenging to monitor due to nonstationarity and low intensity of vibration signals, which complicates early fault detection, such as wear or imbalance, especially when the signal amplitude does not exceed background noise. 5 Diagnostics often focus on bearings, which are subject to significant loads. 6 In high-speed machines, vibrations are more pronounced, facilitating analysis using standard methods such as spectral analysis. 7
The use of vibration and current signals in fault diagnosis of induction motors using deep learning and machine learning techniques presented in the research.8,9 In study, 10 a conditionally predictive maintenance method is proposed based on vibration data collected by an accelerometer and processed using machine learning techniques. However, vibration growth was modeled linearly, which does not always reflect real-world conditions. In Ref. 11, frequency analysis enabled the diagnosis of sensor faults in a Mazda BT50 (CRDi) diesel engine by detecting amplitude changes at characteristic frequencies. The method shows promise for predictive maintenance, although testing was limited to idle mode at 60 °C.
The effectiveness of vibration diagnostics depends on the type of sensor. Among the five options considered in Ref. 12, MEMS accelerometers stand out for their low cost, sensitivity, and ease of processing, but they suffer from a low signal-to-noise ratio, requiring filtering. Study 13 describes an ICE monitoring system with edge processing using MEMS sensors, local devices, and cloud analytics. This approach reduces latency and improves reliability. Although the system detects anomalies, testing was conducted only on sinusoidal signals without real faults.
Study 14 presents a monitoring system for rotating machinery using load and speed sensors and an ATmega2560 microcontroller. Fast Fourier Transform (FFT) - based signal analysis enables imbalance detection, although data transmission lacks noise filtering. In Ref. 15, ICE fault classification is proposed based on body vibrations using FFT and decision trees. The method was tested on a Polaris SUV, achieving up to 72% accuracy depending on rpm, but only one engine type was considered without load variation.
In Ref. 16, a diagnostic method for asynchronous motors is proposed based on stator current and gearbox vibrations, kinematically linked to the drive. FFT is used to extract spectral components, allowing for more accurate fault identification. However, the method does not cover complex defect combinations. Study 17 implements a diagnostic approach for PMSM motors using autoencoders, specifically a 1D CNN AE, effectively detecting bearing faults and mechanical misalignments under variable conditions. The method shows potential for downtime reduction, although it has only been tested in laboratory settings.
Recent studies increasingly emphasize the role of edge computing in condition monitoring systems. The 13 demonstrates that edge-based processing enables real-time vibration signal analysis and effective anomaly detection in internal combustion engines while reducing data transmission latency. In contrast, the 18 shows that although cloud computing provides superior computational resources for complex machine learning tasks, edge computing offers lower latency and improved efficiency for real-time applications, making it particularly suitable for vibration-based diagnostics.
IoT-based predictive maintenance utilizes an integrated approach that combines real-time machine condition monitoring with machine learning data analysis. A key element is the use of IoT sensor networks (e.g., temperature and vibration) that provide continuous data on equipment condition.19,20 Study 21 examines a machine condition monitoring system based on IoT sensors using the MTN 1186-2 vibration sensor and ESP8266 module for data transmission via TCP/IP. FFT analysis was used to detect abnormal frequencies indicating faults, but only a limited number of defects were covered. In Ref. 22, a three-level IoT architecture is proposed with autonomous MEMS sensors, a BeagleBone hub, and a Microsoft Azure server.
Discrete Fourier Transform (DFT), Allan variance analysis, and Root Mean Square (RMS) vibration velocity were used to assess equipment condition. The system classifies states as “good” or “satisfactory,” but lacks comparison with alternative methods. Study 23 introduces the Adaptive Holt-Winters method, combining short-term forecasting based on the latest data window with long-term forecasting using historical segments selected by modified RMS deviation. The method outperforms traditional statistical and neural network approaches in accuracy and speed, although its application is limited to data with pronounced seasonality.
In Ref. 24, the wavelet transform is applied to analyze ICE vibroacoustic signals, and laser Doppler vibrometry is used for non-contact vibration measurement. Noise presence significantly affects the selection of diagnostic coefficients. Study 25 proposes an alternative approach to combustion parameter estimation using knock sensor signals instead of expensive pressure sensors; processing is performed via discrete wavelet transform, and evaluation via an XGBoost model. The method shows high accuracy but is limited to single-cylinder gas engines.
In Ref. 26, a method for analyzing vibration data from an IMU module is proposed by converting time series into images (grayscale, RGB), which are processed by convolutional neural networks, providing high classification accuracy of rotor machine states and effective anomaly detection. However, RGB conversion may lead to information loss, and scalability for complex systems remains limited. Study 27 explores a model for predicting time-to-failure based on vibration data using machine learning, showing potential but limited accuracy due to insufficient sensor data granularity. In Ref. 28, a method for estimating cylinder pressure in piston ICEs is proposed based on vibration signals from the cylinder head, using a two-stage deep learning model that enables non-invasive pressure estimation without expensive sensors. However, the method was tested only on a single-cylinder engine without accounting for multi-cylinder configurations.
Study 29 proposes an IoT-based infrastructure monitoring system using ESP32, ADXL345 accelerometer, memory, and power modules; data are collected via triggers, transmitted via Wi-Fi, processed using FFT, and compared to baseline conditions to detect damage. However, more sensitive sensors are needed to capture low-frequency vibrations. In Ref. 30, an IoT device based on TinyML is presented for detecting abnormal vibrations in engines, using spectral analysis and deep learning for real-time state classification. The system runs on ESP32S3, transmits data via MQTT to Node-RED and Telegram, achieving 96.5% accuracy, but has limitations regarding noise impact and scalability across multiple engines.
1.3. Research gap
Despite the widespread use of vibration diagnostics and the increasing integration of condition monitoring systems with IoT technologies and machine learning methods, several important limitations remain insufficiently addressed.
First, although MEMS accelerometers are attractive due to their low cost and ease of implementation, they suffer from a low signal-to-noise ratio, which significantly hinders reliable early fault detection. This issue becomes particularly critical under real operating conditions, where environmental noise strongly affects signal quality.
Another challenge is the nonstationarity of vibration signals, especially in internal combustion engines operating at low rotational speeds. This limits the effectiveness of conventional analysis methods such as the Fast Fourier Transform (FFT), which assumes signal stationarity.
Additionally, there is a significant gap in the generalization of diagnostic models developed under laboratory conditions to real industrial environments. Many existing approaches do not adequately account for variability in operating conditions, load changes, and differences in engine design.
An important unresolved issue is the lack of clear guidelines for selecting appropriate signal processing techniques, particularly between frequency-domain methods (e.g., FFT) and time–frequency approaches such as the wavelet transform. There is a need for an adaptive framework that integrates multiple analysis techniques depending on signal characteristics.
As a result, there is still a need to develop a comprehensive, scalable, and noise-resilient diagnostic system that combines: effective signal filtering and preprocessing, adaptive selection of analysis methods, seamless integration with IoT architectures, and validation under real operating conditions.
Addressing this research gap is essential to improving diagnostic accuracy and fully leveraging the potential of intelligent condition monitoring systems for internal combustion engines.
1.4. Summary of related works
Key methodologies and the advantages and limitations of existing solutions.
1.5. Motivation
The increasing reliance on ICE systems in critical applications necessitates reliable, continuous, and real-time monitoring solutions. Existing approaches often suffer from limitations related to sensor noise, insufficient adaptability, and lack of integration between hardware and intelligent data processing. There is a clear need for a scalable and efficient system that combines IoT-based sensing, robust signal processing, and intelligent diagnostics to improve fault detection accuracy and operational reliability.
This study aims to develop and experimentally validate a wireless IoT-based vibration monitoring system for the diagnostics of internal combustion engines (ICE), enabling continuous real-time condition assessment with remote data transmission to a server.
1.6. Contributions
The following contributions of the research is to ensure autonomous and uninterrupted monitoring of ICE operating conditions through vibration analysis, along with the implementation of server-side algorithms for digital signal filtering, RMS computation, spectral analysis, data visualization, and extraction of diagnostic features.
The scientific novelty of the work lies in the advancement of a comprehensive methodology for assessing the technical condition of ICEs by integrating IoT-based data acquisition, frequency-domain analysis, and quantitative vibration energy evaluation within an intelligent diagnostic framework.
1.7. Paper organization
The remainder of this paper is organized as follows. Section 2 presents the system architecture, signal processing methods, and machine learning framework. Section 3 describes the experimental setup and testing conditions. Section 4 discusses the results of vibration analysis and classification performance. Section 5 concludes the paper and outlines future work.
2. Materials and methods
2.1. Signal processing and feature extraction
In vibration monitoring, both forced vibrations–arising from external forces (e.g., vibrations transmitted from the drive to other parts of the mechanism) – and natural resonant vibrations are recorded. 33
Vibration analysis involves various parameters: amplitude, frequency, phase, waveform, and harmonic content of the signal. The frequency spectrum of stationary signals is widely studied using the FFT, a mathematical method that converts a signal from the time domain to the frequency domain. 34 This enables the identification of changes in frequency, amplitude, and harmonics within a specified range.
FFT is based on the DFT, but optimized for faster execution by dividing the computation into smaller sub-tasks. The frequency spectrum calculation using DFT is generally expressed by equation (1), resulting in a complex number that represents the amplitude and phase of the frequency component for frequency index k. However, using DFT even for small datasets may require significant time and computational resources, making FFT a more efficient solution.
Vibration data are typically presented in the time domain, reflecting changes in signal amplitude over time. For example, a sinusoidal signal of a specific frequency in the time domain corresponds to a single spectral line in the frequency domain, whereas a short-duration impulse (spike) results in a wide spectral distribution. This representation of the signal is referred to as its frequency spectrum. Figure 1 illustrates the transformation of a signal from the time domain to the frequency domain using FFT. Transformation of a signal from the time domain to the frequency domain using FFT: (a) Vibration signal in the time domain; (b) Frequency spectrum of a vibration signal.
Figure 1(a) shows a complex signal in the time domain composed of multiple sinusoids, while Figure 1(b) presents its frequency representation, where each component frequency appears as a distinct spectral line.
To analyze nonstationary vibration signals – characterized by time-varying frequency content – the wavelet transform is often employed. Unlike FFT, which provides only frequency resolution and loses time localization, the wavelet transform enables simultaneous analysis of a signal in both time and frequency domains. This makes it particularly useful for detecting short-duration impulses, spikes, or changes in vibration characteristics.
28
The continuous wavelet transform of a signal is defined as equation (2):
Key advantages and limitations of FFT and wavelet transform in vibration signal analysis.
Based on Table 2, FFT is used in this study for vibration analysis, as the investigated process is stationary and does not involve dynamic changes.
To filter noise during vibration diagnostics, the Kalman filter is applied in this work. 35 The Kalman filter is a mathematical method that helps estimate the state of a system even when the data are inaccurate or noisy. It operates in two stages: first, it predicts the future state based on current data, and then it refines this prediction using new information from sensors.
The Kalman filter was chosen due to its effectiveness in real-time signal denoising and state estimation under noisy measurement conditions, which are characteristic of vibration sensing systems. Unlike conventional filtering methods (e.g., moving average or low-pass filters), the Kalman filter provides an adaptive and recursive estimation framework that accounts for both process noise and measurement noise. This makes it particularly suitable for dynamic systems where signal characteristics may vary over time.
Additionally, the Kalman filter has low computational complexity, making it well-suited for implementation in resource-constrained IoT environments and enabling real-time processing on embedded systems or server-side pipelines. Compared to more advanced techniques, it offers a favorable trade-off between computational efficiency and filtering performance.
Prediction:
– system state prediction (3)
– error covariance prediction (4)
Correction:
– сalculation of the Kalman gain (5)
– state estimate update based on measurements z
m
(6)
– error covariance update (7)
In vibration monitoring, to quantitatively assess the total energy of oscillations over a given time period, this study uses the statistical characteristic RMS.36,37 RMS is widely used due to its ability to represent vibration energy, robustness to noise, low computational complexity, and proven effectiveness as a baseline indicator of machine condition. The higher the RMS value, the more intense the vibration. This indicator allows detection of changes in equipment operation, such as bearing wear, imbalance, misalignment, or other defects, and is calculated using equation (8)
For a continuous signal – see (9) and Figure 2 RMS Calculation for a periodic signal.
The area equivalence (Figure 2) demonstrates that the energy of a signal over a period can be represented as a constant value proportional to RMS. Using RMS allows a variable signal to be converted into a steady value, which is convenient for further software analysis and comparison with permissible vibration levels. This is essential for detecting deviations in equipment operation in real time and for timely response to potential faults.
One of the common defects in rolling bearings is an outer ring fault.
38
During operation, such a bearing generates a vibration frequency spectrum (10)
To record vibration parameters, an IoT sensor (Figure 3) was developed and implemented. It consists of an ESP32 microcontroller module with a built-in wireless interface, a digital three-axis accelerometer ADXL345, and a power supply module. Data transmission between the ESP32 and ADXL345 is carried out via the SPI interface. After reading acceleration values along three axes, the ESP32 forms UDP packets and transmits them via Wi-Fi connection to a remote server for further processing, analysis, or storage. Vibration IoT sensor schematic.
The operation algorithms of the developed vibration IoT sensor are shown in the block diagram – Figure 4(a), and the server-side data processing algorithm is presented in the block diagram – Figure 4(b). Both diagrams were created using the Mermaid service. Block diagram of vibration monitoring for machinery and structures: (a) Block diagram of vibration IoT sensor operation; (b) Block diagram of server operation.
Upon power-up (Figure 4(a)), the ESP32 microcontroller initiates the initialization of all required components: the serial port for debugging, the SPI bus for communication with the ADXL345 accelerometer, and configures the accelerometer itself by writing measurement mode and range parameters into its registers.
Simultaneously, a connection to a Wi-Fi network is established, allowing the ESP32 to transmit data over the local network to a server or computer. After a successful connection, a periodic timer is configured to trigger an interrupt service routine every 4 ms, where a logical flag doSample = true is set. This indicates that the sampling time has arrived, and in the main program loop (in the loop() function), acceleration values need to be read. This approach enables a non-blocking architecture, where the main logic operates in the background, and the sampling rate is strictly controlled by the hardware timer. In the main loop, the program continuously checks the value of the doSample flag. If it is set to true, it indicates that the sampling moment has occurred. In this case, the flag is reset (doSample = false), and the data reading procedure from the sensor begins. Through the SPI port, 6 bytes are requested (two bytes for each axis: X, Y, Z), corresponding to the measured accelerations. The data are collected into an array, which is then sent via the UDP protocol to the IP address and port of the computer (server) acting as the receiver. This implementation allows new data to be acquired at a frequency of 250 Hz, which is sufficiently high for basic vibration analysis. It is important to note that this approach enables automated data transmission without human intervention: upon power-up, the device automatically connects to the network, configures the sensor, begins data acquisition, and transmits it in real time. This ensures ease of use for remote equipment condition monitoring systems, particularly in energy or industrial facilities.
After the script is launched (Figure 4(b)), component initialization is performed: Kalman filter objects for the X, Y, and Z axes are created; a UDP socket is configured for data reception; the graphical interface (PyQtGraph) is initialized, along with buffers for storing raw, filtered, and RMS data. Timers are then launched: the main timer reads UDP packets from the ESP32 every 10 ms, unpacks 6 bytes (X, Y, Z), converts the values to g, and stores them in circular queues, while simultaneously processing the data using the Kalman filter. When the number of samples exceeds 250 (1 second), RMS values for both raw and filtered data are calculated, stored in separate buffers, and updated on the graphs. Each cycle also includes a check: whether the current RMS exceeds a predefined threshold |RMS|; if so, a warning is displayed, otherwise the system continues operating normally. Additional timers update the graphs: time-domain (every 50 ms), spectral (FFT, every 100 ms), and RMS graphs (every 200 ms). A graphical button allows the user to switch between visualization modes (time/spectral). This implementation enables continuous real-time monitoring of the vibration environment, with filtering, analysis, and visualization of critical states.
To evaluate the effectiveness of the proposed approach for conditional assessment of the technical condition of rotating machinery (including internal combustion engines), an experimental test stand was developed (Figure 5). External view of the experimental bearing diagnostics device: (1) Motor speed control unit; (2) DC motor; (3) Bearing assembly; (4) Vibration sensing device.
This stand enables the reproduction of various operating modes and conditions close to real-world usage. The stand includes a control unit (1) based on the NodeMCU V3 ESP8266 Wi-Fi module, which generates control signals for the rotation speed of a DC motor (2) using pulse-width modulation. Control is implemented via the Blynk IoT cloud platform, allowing wireless adjustment and monitoring of rotation speed. Three fixed rotation speeds are set: 500, 1000, and 1500 rpm, and the actual rotation frequency is verified using a non-contact digital tachometer DT-2234C. In the motor’s bearing assembly (3), interchangeable bearing samples – both intact and intentionally damaged – are installed to assess the system’s sensitivity to typical deviations. The installed bearing type is single-row radial ball bearing 608 ZZ with an artificially induced outer ring defect (Figure 6). Artificially induced outer ring defect in 608 ZZ bearing.
Vibration measurements are performed using the previously described IoT sensor (4), which is rigidly mounted on the motor housing to ensure accurate registration of oscillations. This setup allows for a comprehensive study of the relationship between vibration signal characteristics, bearing condition, and motor speed on the given research device.
2.2. Machine learning-based intelligent fault classification
To extend the proposed IoT vibration monitoring system beyond threshold-based diagnostics, a supervised machine learning framework was implemented for automated fault classification.
Dataset Construction
Vibration signals were acquired under two bearing conditions:
Class 0 – Healthy bearing,
Class 1 – Outer-ring defect
Measurements were performed at rotational speeds of 500, 1000, and 1500 rpm.
Each 1-second window (250 samples) was treated as an independent observation. The final dataset consisted of multiple balanced samples from each condition and speed regime.
Two validation strategies were applied 1. Random Split Validation: - 70% training, - 30% testing. 2. Cross-Speed Validation: - Training on 500 and 1000 rpm, - Testing on 1500 rpm.
The second scenario evaluates robustness to operational variability.
Feature Engineering. Each signal segment was transformed into a 9-dimensional feature vector.
Time-domain features: - RMS, - Standard deviation, - Peak-to-peak amplitude, - Kurtosis, - Skewness.
Frequency-domain features: - BPFO amplitude, - First harmonic amplitude, - Dominant frequency magnitude, - Total spectral energy.
All features were standardized before training.
Classification Algorithms. The following models were evaluated: - Support Vector Machine (RBF kernel), - k- Nearest Neighbors (k = 5), - Random Forest (100 trees).
Hyperparameters were optimized using 5-fold cross-validation.
Performance metrics included: - Accuracy, - Precision, - Recall, - F1-score, - ROC-AUC.
The hyperparameters of the machine learning models were selected based on empirical analysis using 5-fold cross-validation. For the k-nearest neighbors algorithm, values of the parameter k in the range of 1 to 15 were tested, and k = 5 was chosen as it provided the best trade-off between noise robustness and generalization capability. For the Random Forest model, the number of trees was determined experimentally, and a value of 100 was selected as a compromise between classification accuracy and computational complexity, since further increases did not result in significant performance improvement.
To enhance the diagnostic capability of the proposed IoT-based vibration monitoring system, a machine learning classification algorithm was developed to automatically distinguish between healthy and faulty bearing conditions. While classical vibration diagnostics relies primarily on scalar indicators such as RMS or individual spectral peaks, these approaches may demonstrate limited robustness under varying operational regimes. Therefore, a multidimensional feature-based classification framework was implemented to improve generalization and decision reliability.
The algorithm integrates signal preprocessing, feature extraction in both time and frequency domains, supervised model training, and performance evaluation. By transforming raw vibration measurements into structured feature vectors, the method enables the detection of defect-related patterns that remain consistent across different rotational speeds.
The steps of the proposed machine learning-based classification algorithm.
The experimental dataset was constructed from vibration measurements collected under controlled laboratory conditions for two bearing states: healthy and faulty (outer-ring defect). Measurements were performed at three rotational speeds (500, 1000, and 1500 rpm), resulting in six experimental configurations.
For each configuration, vibration signals were recorded for 120 seconds. The signals were segmented into 1-second windows (250 samples per segment), resulting in a total of 720 vibration segments, with a balanced distribution between classes (360 samples per class).
The dataset was divided into training and testing subsets using a 70%–30% split, corresponding to 504 training samples and 216 testing samples. Additionally, cross-speed validation was performed, where models were trained on data from 500 and 1000 rpm and tested on data from 1500 rpm.
The study considers one fault type (outer-ring defect), enabling controlled evaluation of the proposed method.
3. Results and discussion
3.1. Spectral and RMS analysis
Experimental studies of vibration characteristics under different technical conditions of the bearing (healthy and faulty with an outer ring defect) were conducted using a specially designed research device – Figure 5. Measurements were performed at three different shaft rotation speeds of the electric motor: 500, 1000, and 1500 rpm, which allowed coverage of typical operating modes of the equipment. The vibration signal data were processed according to the algorithm presented in the block diagrams – Figure 4. During processing, FFT was applied, enabling the construction of amplitude–frequency characteristics of the signals. Figure 7 presents the results of spectral analysis of vibrations along the Z-axis for the faulty bearing, allowing identification of characteristic frequency components associated with the outer ring defect. Amplitude-frequency characteristics of signals (FFT, Z-axis) for faulty bearing ((I) BPFO and its harmonics; (II) Shaft rotation frequencies and their harmonics). Rotation speed: (a) 500 rpm, (b) – 1000 rpm, (c) – 1500 rpm.
The graphs (Figure 7) show a comparison between the unfiltered signal (blue), containing random noise, and the signal filtered using the Kalman filter (red) for three rotation speeds: 500, 1000, and 1500 rpm under faulty bearing conditions. The filtered signal exhibits smoothed values that better reflect vibration changes over time. The signal amplitude increases with rotation speed, which is expected. The speed range (500–1500 rpm) covers both low-speed and high-speed machinery.
5
Each graph also displays characteristic peaks caused by the outer ring defect of the bearing (I, Figure 7) and the shaft rotation frequency (II, Figure 7). Every component of the frequency spectrum includes harmonic elements, whose amplitude gradually decreases with increasing frequency. Peaks labeled I (Figure 7) correspond to the calculated values from (10). The total signal energy (Figure 8) increases with rotation speed under faulty bearing conditions, which aligns with the previous FFT analysis, where vibration amplitude also increased (Figure 7). RMS values of Z-axis signals at rotation speeds of 500, 1000, and 1500 rpm.
For quantitative comparison of conditions, RMS values of the Z-axis signals were also calculated for both cases – healthy and faulty bearing – as shown in Figure 8.
Summary of RMS variation at different rotation speeds and bearing conditions.
Table 4 summarizes the variation of RMS vibration acceleration values along the Z-axis under different rotational speeds and bearing conditions (healthy and faulty). The results demonstrate a consistent increase in RMS values in the presence of an outer-ring defect across all tested operating regimes.
For the serviceable bearing, RMS values remain relatively stable within the range of 0.65-0.67 m/s2 as rotational speed increases from 500 to 1500 rpm. This indicates steady vibration behavior under normal operating conditions and confirms the stability of the measurement system.
In contrast, the faulty bearing exhibits significantly higher RMS values, ranging from 0.87 to 0.92 m/s2. The percentage increase in RMS relative to the healthy condition varies between 34% and 37%, with a slight upward trend at higher rotational speeds.
The consistency of RMS growth across all speed regimes confirms that the outer-ring defect produces a measurable increase in vibration energy independent of rotational speed. This stable relative increase supports the reliability of RMS as a primary diagnostic indicator for stationary vibration processes.
3.2. Machine learning classification results
To evaluate the baseline classification performance of the implemented machine learning models, a conventional random split validation strategy was applied. The complete dataset was randomly divided into training and testing subsets while preserving class balance between healthy and faulty bearing conditions. Specifically, 70% of the samples were used for model training, and the remaining 30% were reserved for independent testing.
This validation approach ensures that both operating conditions and all rotational speed regimes (500, 1000, and 1500 rpm) are proportionally represented in both subsets. Random split validation provides an initial assessment of the discriminative capability of the selected feature set and classification algorithms under statistically consistent conditions.
The obtained results reflect the intrinsic separability of vibration features between healthy and defective states when speed variations are included in both training and testing data.
Comparative performance metrics of the evaluated diagnostic approaches.
Random Forest demonstrated superior discrimination capability with ROC-AUC = 0.99.
To evaluate the robustness and generalization capability of the proposed diagnostic models under varying operating conditions, a cross-speed validation strategy was implemented. Unlike the random split approach, this scenario assesses model performance when trained and tested on data obtained from different rotational speed regimes.
In this experiment, the models were trained using vibration data collected at 500 and 1000 rpm, while testing was performed exclusively on data acquired at 1500 rpm. This configuration simulates a realistic industrial scenario in which a diagnostic system must maintain reliable performance despite variations in engine operating speed.
Cross-speed validation is particularly important for internal combustion engine (ICE) applications, where rotational speed continuously varies depending on load conditions and operating modes. A diagnostic model that performs well only under fixed-speed conditions may fail in practical deployment. Therefore, evaluating classification performance under speed-shift conditions provides a more rigorous assessment of real-world applicability.
Cross-speed validation.
The results presented in Table 5 indicate a noticeable decrease in performance for the RMS threshold-based method under cross-speed conditions, highlighting its sensitivity to operating regime variations. Since RMS represents a scalar measure of overall vibration energy, it does not fully capture structural differences in frequency-domain characteristics that remain consistent across speed changes. As a result, threshold-based diagnostics demonstrate limited adaptability when the rotational speed during testing differs from that used for calibration.
In contrast, the supervised machine learning models exhibit substantially higher robustness under speed-shift conditions. Although a slight reduction in accuracy is observed compared to the random split validation scenario, the classifiers maintain stable performance, confirming their ability to extract defect-related features that are invariant across different rotational regimes. This demonstrates that multidimensional feature-based classification provides superior generalization capability compared to single-parameter thresholding.
The improved cross-speed performance confirms the scalability of the proposed IoT-based diagnostic architecture toward real-world ICE applications, where operating speeds dynamically vary depending on load, throttle position, and external conditions.
The proposed method introduces a comprehensive and integrated diagnostic framework that combines three key elements into a unified process: (i) real-time IoT-enabled vibration data acquisition using a wireless sensor architecture; (ii) physics-based signal processing, including Kalman filtering, RMS-based energy estimation, and frequency-domain analysis (FFT) with unambiguous identification of fault-related frequencies; and (iii) multivariate machine learning-based classification using combined time- and frequency-domain features.
Unlike conventional approaches that rely on single metrics (e.g., RMS thresholds), the proposed method utilizes feature-level fusion and supervised learning, enabling reliable fault detection under a variety of operating conditions, including variable-speed scenarios. Unlike many existing systems, which typically focus on either data acquisition or data-driven modeling in isolation, the proposed approach integrates physically interpretable vibration analysis with intelligent classification within a single IoT-enabled architecture. Furthermore, the study provides experimental validation at multiple rotational speeds and explicitly assesses model generalization across speeds, a point often overlooked in prior work. Another distinctive aspect is the demonstrated relationship between theoretical failure frequencies (e.g., BPFO) and experimentally observed spectral components, ensuring both interpretability and reliability of the diagnostic process.
These aspects collectively distinguish the proposed method from existing IoT-based predictive maintenance solutions and highlight its contribution to scalable, interpretable, and reliable condition monitoring of combustion engines.
4. Conclusions
This study proposes and experimentally validates a comprehensive methodological framework for intelligent vibration-based diagnostics of internal combustion engines (ICE) within an IoT-enabled monitoring architecture. Unlike conventional implementations focused solely on signal acquisition or threshold-based condition assessment, the presented approach integrates structured signal preprocessing, physically interpretable spectral analysis, and supervised machine learning within a unified diagnostic pipeline.
From a methodological perspective, the work contributes three key advancements. First, it provides quantitative experimental verification of defect-induced vibration energy growth, demonstrating a stable 34–37% RMS increase across multiple rotational regimes (500–1500 rpm). Second, it establishes a direct correspondence between theoretically calculated defect frequencies (BPFO) and experimentally observed spectral components, ensuring physical interpretability of the diagnostic indicators. Third, it extends classical vibration diagnostics by incorporating multidimensional feature-based classification with explicit evaluation of cross-speed generalization capability.
The comparative analysis between RMS thresholding and supervised learning models demonstrates that while scalar energy indicators remain physically meaningful, they lack robustness under varying operational conditions. The Random Forest classifier achieved 97% accuracy (ROC-AUC = 0.99) under random split validation and maintained 94% accuracy under cross-speed validation, confirming that defect-related features can be learned in a speed-invariant manner. This result is particularly significant for ICE applications, where rotational regimes are inherently nonstationary.
The scientific novelty of the study lies in the formalization of an integrated diagnostic methodology that bridges physics-based vibration analysis and data-driven intelligent classification within a scalable IoT architecture. The presented framework establishes a reproducible foundation for multi-fault extension, adaptive diagnostics under variable loads, and future integration of advanced machine learning or edge intelligence solutions for predictive maintenance of rotating machinery.
The vibration signals were sampled at 250 Hz, which allows capturing frequency components up to 125 Hz according to the Nyquist criterion. This range is sufficient for analyzing dominant mechanical vibrations, including shaft rotational frequencies, their harmonics, and characteristic defect frequencies (e.g., BPFO) within the investigated operating range (500–1500 rpm). The selected sampling frequency represents a trade-off between diagnostic capability and system efficiency, particularly in IoT-based applications where data transmission, computational load, and power consumption are critical constraints. Nevertheless, this configuration may limit the detection of high-frequency components associated with early-stage defects or impulsive events. Therefore, future work will focus on extending the system with higher sampling rates.
Footnotes
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Data Availability Statement
All data generated or analysed during this study are included in this published article.