Roller Bearing Fault Detection Using Ordinal Pattern-Based Methods for Acoustic and Vibration Analysis

The paper presents a method of analysis of electric motors based on acoustic measurements. Acoustic signals were measured by microphones arranged in circular shape array called acoustic camera. Measurements by acoustic camera allow localization of sound source and by that separate sounds of interests from background noise can be obtained. Typically acoustic camera measurements are accompanied by a photography associated with acoustic measurement scene which is used for mapping of sound sources on the monitored area. As a reference, acoustic analysis is compared with vibration measurements. Vibration signals were measured by piezoelectric accelerometers and data collector dedicated for condition monitoring of electric motors. As presented in the result section, acoustic analysis appears as a valuable technique for condition monitoring of electric motors even in noisy industrial environment.

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given signals (represented as time series) by considering random variables which sample from specified subsequences. In this paper, we will discuss how an entropy variant, the \textit{permutation entropy} can be used to study and classify radio frequency signals in a noisy environment. The permutation entropy is the entropy of the random variable which samples occurrences of permutation patterns from time series given a fixed window length, making it a function of the distribution of permutation patterns. Since the permutation entropy is a function of the relative order of data, it is (global) amplitude agnostic and thus allows for comparison between signals at different scales. This article is intended to describe a permutation patterns approach to a data driven problem in radio frequency communications research, and includes a primer on all non-permutation pattern specific background. An empirical analysis of the methods herein on radio frequency data is included. No prior knowledge of signals analysis is assumed, and permutation pattern specific notation will be included. This article serves as a self-contained introduction to the relationship between permutation patterns, entropy, and signals analysis for studying radio frequency signals and includes results on a classification task.

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy. Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors.Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy. Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors.

The non-contact measurement of engine speed can be realized by analyzing engine vibration frequency. However, the vibration signal is distorted by harmonics and noise in the measurement. This paper presents a novel method for the measurement of engine rotation speed by using the cross-correlation of vibration and acoustic signals. This method can enhance the same frequency components in engine vibration and acoustic signal. After cross-correlation processing, the energy centrobaric correction method is applied to estimate the accurate frequency of the engine’s vibration. This method can be implemented with a low-cost embedded system estimating the cross-correlation. Test results showed that this method outperformed the traditional vibration-based measurement method.

In a machining system, tool condition monitoring systems are required to get a high-quality product and to prevent the downtime of machine tools due to tool failures. For this purpose, tool condition monitoring systems have become very important during the years since the mechanical faults can cause high cost. This study introduces a multistage cutting tool fault diagnosis method to detect the presence and level of the involute form cutter faults on the by the cutting force and vibration signal analysis. Therefore, different fault levels (low, medium and high) were generated on the involute form cutter as a tool breakage. During the experiments, the cutting force, vibration and acoustic signals were gathered with three different feed rates for each fault level. The gathered signals were processed by a multistage signal processing algorithm developed in the MATLAB environment. As an initial step, the continuous wavelet transform of the obtained signals was taken and saved as an image by the developed algorithm. After that, a convolutional neural network model is trained and tested by using the obtained images. The developed algorithm firstly checks the presence of the cutting tool fault. Once the algorithm labels the cutting tool is damaged, it then checks the damage level of the cutting tool fault. It is observed from the results, cutting force analysis is sufficient for the detection of cutting tool fault. On the other hand, the cutting force signal analysis is insufficient to detect the damage level of the cutting tool. Therefore, the vibration signal analysis is required to detect the damage level of the cutting tool. Results prove that, by the vibration analysis, the developed algorithm could detect not only the presence of the damage on the cutting tool but also the damage level. The results of the algorithm for each stage and signal are given in the results section.

Ordinal patterns are a time-series data analysis tool used as a preliminary step to construct the permutation entropy, which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent. However, ordinal patterns store strictly more information than permutation entropy or Lyapunov exponents. We present results working with the Duffing oscillator showing that ordinal patterns reflect changes in dynamical symmetry that is invisible to other measures, even permutation entropy. We find that these changes in symmetry at given parameter values are correlated with a change in stability at neighboring parameters, which suggests a novel predictive capability for this analysis technique.

Human-machine voice interaction based on speech recognition offers an intuitive, efficient, and user-friendly interface, attracting wide attention in applications such as health monitoring, post-disaster rescue, and intelligent control. However, conventional microphone-based systems remain challenging for complex human-machine collaboration in noisy environments. Herein, an anti-noise triboelectric acoustic sensor (Anti-noise TEAS) based on flexible nanopillar structures is developed and integrated with a convolutional neural network-based deep learning model (Anti-noise TEAS-DLM). This highly synergistic system enables robust acoustic signal recognition for human-machine collaboration in complex, noisy scenarios. The Anti-noise TEAS directly captures acoustic fundamental frequency signals from laryngeal mixed-mode vibrations through contact sensing, while effectively suppressing environmental noise by optimizing device-structure buffering. The acoustic signals are subsequently processed and semantically decoded by the DLM, ensuring high-fidelity interpretation. Evaluated in both simulated virtual and real-life noisy environments, the Anti-noise TEAS-DLM demonstrates near-perfect noise immunity and reliably transmits various voice commands to guide robotic systems in executing complex post-disaster rescue tasks with high precision. The combined anti-noise robustness and execution accuracy endow this DLM-enhanced Anti-noise TEAS as a highly promising platform for next-generation human-machine collaborative systems operating in challenging noisy environments.

An improved permutation entropy (PE) algorithm named coded permutation entropy (CPE) is proposed in this paper to optimize the problems existing in PE based on the secondary partitioning. The principle of CPE algorithm is given, and the performance of it for dynamical change detection is analyzed using synthetic signal, logistic map and Lorenz map. The detection ability of CPE algorithm in different signal-to-noise ratios (SNR) is studied and the algorithm complexity is discussed. The results show that CPE can accurately capture minor feature information and amplify the detection results of dynamical changes compared with PE, weighted permutation entropy (WPE) and amplitude-aware permutation entropy (AAPE), but it has less robustness to noise and requires a higher computation cost than the others. Finally, we use the new algorithm to analyze the rolling bearing fault signals. The application of actual signals illustrates that CPE performs better in detecting abnormal pulse of the rolling bearing when the embedded dimension is small. From all the analyses in this paper, we find that CPE has a better performance for dynamical change detection compared with the other three algorithms when there is a larger repetition rate of permutation pattern in the position sequences.

International audience

Identifying complex periodic windows surrounded by chaos in the two or higher dimensional parameter space of certain dynamical systems is a challenging task for time series analysis based on complex network approaches. This holds particularly true for the case of shrimp structures, where different bifurcations occur when crossing different domain boundaries. The corresponding dynamics often exhibit either period-doubling when crossing the inner boundaries or, respectively, intermittency for outer boundaries. Numerically characterizing especially the period-doubling route to chaos is difficult for most existing complex network based time series analysis approaches. Here, we propose to use ordinal pattern transition networks (OPTNs) to characterize shrimp structures, making use of the fact that the transition behavior between ordinal patterns encodes additional dynamical information that is not captured by traditional ordinal measures such as permutation entropy. In particular, we compare three measures based on ordinal patterns: traditional permutation entropy εO, average amplitude fluctuations of ordinal patterns ⟨σ⟩, and OPTN out-link transition entropy εE. Our results demonstrate that among those three measures, εE performs best in distinguishing chaotic from periodic time series in terms of classification accuracy. Therefore, we conclude that transition frequencies between ordinal patterns encoded in the OPTN link weights provide complementary perspectives going beyond traditional methods of ordinal time series analysis that are solely based on pattern occurrence frequencies.

A new fault feature extraction method of rolling bearings based on the improved self-selection ICEEMDAN-permutation entropy

The method of spectral analysis of the envelope of high-frequency vibration signal components is used to identify defects and assess the condition of rolling bearings. The disadvantage of this approach is the high loss of useful signal as the vibration transducer moves away from the product being diagnosed. The paper presents the results of the diagnosis of rolling bearing defects using the analysis of the envelope spectrum of the acoustic pressure signal obtained using measuring microphones. The vibration and acoustic radiation of a serviceable support bearing and a bearing with a defect artificially applied to its inner race were analyzed. It is shown that the identification of rolling bearing defects by acoustic pressure signals has limitations due to the fact that sound reflection, background noise and interference can mask useful signals. The presence of random spatial noise leads to a low signal-to-noise ratio, however, microphones located close to the damaged bearing make it possible to determine the presence of a defect and its type. The obtained results can be used to improve the methods of diagnostics and monitoring of the technical condition of rolling bearings.

Wireless telephones systems are available for quite sometimes. However, wireless devices that can send and receive analog and digital data from industrial control process in a noisy industrial environment have just been introduced. Recently, Omnex Control Systems Inc. has introduced industrial friendly analog and digital wireless transceiver to reliably communicate under noisy industrial condition among sensors, transducers, final control elements, programmable logic controllers (PLCs), and similar devices and systems. This wireless digital and analog conduit is a commercialized version of the spread spectrum license free 902-928 MHz frequency hopping communication techniques used by the defense industry. Since the system is license free and maintenance free wireless conduit, it eliminates costly and time consuming cable laying for new and retrofitting of existing project. This wireless conduit is an interference free link between remote devices and control room, it is ideal for a noisy industrial environment. The subject of this paper deals with monitoring, controlling, and acquiring data continuously from an industrial process using this wireless conduit. The authors plan to demonstrate the interfacing of an industrial process, transducers, and final control elements to a remotely located computer controlled data acquisition system. The monitoring and controlling of remote process via a reliable link without sacrificing the data integrity and loss of ability to analyze the acquired data will be discussed. We are proposing to show how this wireless conduit is a two-way monitoring and controlling solutions for a variety of industrial application in heavy interference environment where other radios fail to perform.

To solve the denoising problem of ship radiated noise signal (SRNSs), a method based on successive variational mode decomposition (SVMD), amplitude-aware permutation entropy (AAPE), reverse permutation entropy (RPE), correlation coefficient (CC) and adaptive wavelet thresholding denoising (AWTD) algorithm, named SVMD-AAPE-RPE-CC-AWTD, is proposed. The algorithm integrates intrinsic mode functions (IMFs) decomposition, IMFs classification, IMFs denoising and reconstruction, and is designed in an integrated manner. In IMFs decomposition, SVMD is introduced to decompose the signal into several IMFs, which select the number of adaptive decomposition levels without the need for manual parameter presetting. In IMFs classification, AAPE and RPE are introduced to adaptively adjust the entropy threshold to discriminate between signal IMFs and non-signal IMFs. By calculating the CC between the non-signal IMFs and the original signal, the noisy IMFs and noise IMFs are further distinguished. In terms of IMFs denoising and reconstruction, an ATWD algorithm is designed based on the optimal wavelet selection method to adaptively select appropriate wavelet basis and decomposition levels, and the improved threshold selection and threshold function are introduced. Finally, comparison tests of denoising simulated signals and the measured SRNS are designed to verify the effectiveness and superiority of the proposed method.