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Special Issue "Entropy-Based Fault Diagnosis"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 May 2019

Special Issue Editor

Guest Editor
Prof. Dr. Spyros G. Tzafestas

School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
Website | E-Mail
Interests: intelligent control; intelligent robotics; intelligent automation; fault detection/diagnosis; roboethics/robophilosophy; infoethics/infophilosophy

Special Issue Information

Dear Colleagues,

Modern systems (chemical processes, power plants, robotic systems, manufacturing systems, automotive systems, etc.) are complex and large scale systems that are subject to faults, failures and malfunctions which degrade their operational performance, and may cause instability and safety problems, sometimes catastrophic. Thus, over the years, engineers have attempted to develop and apply proper techniques and fast algorithms for detecting, isolating, and diagnosing such faults and failures as quickly and accurately as possible. Typically, these techniques require information from several measurable or non-measurable system variables. In general, fault detection and diagnosis (FDD) techniques are distinguished in: (i) data techniques (PCA, spectrum techniques, pattern recognition techniques), (ii) model-based techniques (parity technique, parameter estimation, state estimation), and (iii) model-free techniques (expert systems, fuzzy logic methods, neural network methods, Hybrid methods, etc.). A recent development in the system FDD field is the use of information theoretic methods, and in particular entropy-based methods. The purpose of this Special Issue is exactly to include high quality theoretical and application papers that treat various FDD problems using the entropy-based approach or its combination with other approaches.

Specifically, the Special Issue will consider research and review papers using the following (non-inclusive) entropy-based FDD methods:

  • Maximum entropy methods.
  • Sample entropy methods.
  • Approximate entropy methods.
  • Single-scale and multi-scale entropy methods.
  • Permutation entropy methods.
  • Wavelet entropy methods.
  • Fuzzy entropy methods.
  • Singular entropy methods.
  • Neural network entropy methods.
  • Entropy-based complexity measures methods.
  • Combinations of the above methods (hybrid methods).

Case study papers treating FDD problems of real-life practical systems, and presenting respective experimental/simulation results are mostly welcome.

Prof. Dr. Spyros G. Tzafestas
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fault detection
  • fault diagnosis
  • fault isolation
  • entropy
  • parameter estimation
  • state estimation
  • pattern recognition
  • model-based fault diagnosis
  • model-free fault diagnosis
  • approximate entropy
  • fuzzy entropy
  • sample entropy

Published Papers (20 papers)

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Open AccessArticle
Negentropy Spectrum Decomposition and Its Application in Compound Fault Diagnosis of Rolling Bearing
Entropy 2019, 21(5), 490; https://doi.org/10.3390/e21050490
Received: 24 April 2019 / Revised: 6 May 2019 / Accepted: 11 May 2019 / Published: 13 May 2019
PDF Full-text (754 KB)
Abstract
The rolling bearings often suffer from compound fault in practice. Compared with single fault, compound fault contains multiple fault features that are coupled together and make it difficult to detect and extract all fault features by traditional methods such as Hilbert envelope demodulation, [...] Read more.
The rolling bearings often suffer from compound fault in practice. Compared with single fault, compound fault contains multiple fault features that are coupled together and make it difficult to detect and extract all fault features by traditional methods such as Hilbert envelope demodulation, wavelet transform and empirical node decomposition (EMD). In order to realize the compound fault diagnosis of rolling bearings and improve the diagnostic accuracy, we developed negentropy spectrum decomposition (NSD), which is based on fast empirical wavelet transform (FEWT) and spectral negentropy, with cyclic extraction as the extraction method. The infogram is constructed by FEWT combined with spectral negentropy to select the best band center and bandwidth for band-pass filtering. The filtered signal is used as a new measured signal, and the fast empirical wavelet transform combined with spectral negentropy is used to filter the new measured signal again. This operation is repeated to achieve cyclic extraction, until the signal no longer contains obvious fault features. After obtaining the envelope of all extracted components, compound fault diagnosis of rolling bearings can be realized. The analysis of the simulation signal and the experimental signal shows that the method can realize the compound fault diagnosis of rolling bearings, which verifies the feasibility and effectiveness of the method. The method proposed in this paper can detect and extract all the fault features of compound fault completely, and it is more reliable for the diagnosis of compound fault. Therefore, the method has practical significance in rolling bearing compound fault diagnosis. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
Open AccessArticle
Fault Feature Extraction of Hydraulic Pumps Based on Symplectic Geometry Mode Decomposition and Power Spectral Entropy
Entropy 2019, 21(5), 476; https://doi.org/10.3390/e21050476
Received: 14 February 2019 / Revised: 22 April 2019 / Accepted: 28 April 2019 / Published: 7 May 2019
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Abstract
Aiming at fault feature extraction of a hydraulic pump signal, a new method based on symplectic geometry mode decomposition (SGMD) and power spectral entropy (PSE) is proposed. First, the SGMD is applied to decompose a multi-component fault signal, then the N symplectic geometry [...] Read more.
Aiming at fault feature extraction of a hydraulic pump signal, a new method based on symplectic geometry mode decomposition (SGMD) and power spectral entropy (PSE) is proposed. First, the SGMD is applied to decompose a multi-component fault signal, then the N symplectic geometry components (SGCs) can be obtained. Second, the N SGCs are reconstructed as a signal of interest and, consequently, the power spectral entropy of each constructed signal is computed to quantify the complexity and uncertainty of their spectra. Finally, the difference value (D-value) between the adjacent entropies is used as a SGCs criterion, whose turning point indicates the most information of reconstructed signal. Hydraulic pump signals are tested and verified, and results demonstrate that the proposed method can extract the richest fault feature information of hydraulic pump signals effectively. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
A Novel Signal Separation Method Based on Improved Sparse Non-Negative Matrix Factorization
Entropy 2019, 21(5), 445; https://doi.org/10.3390/e21050445
Received: 5 March 2019 / Revised: 7 April 2019 / Accepted: 26 April 2019 / Published: 28 April 2019
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Abstract
In order to separate and extract compound fault features of a vibration signal from a single channel, a novel signal separation method is proposed based on improved sparse non-negative matrix factorization (SNMF). In view of the traditional SNMF failure to perform well in [...] Read more.
In order to separate and extract compound fault features of a vibration signal from a single channel, a novel signal separation method is proposed based on improved sparse non-negative matrix factorization (SNMF). In view of the traditional SNMF failure to perform well in the underdetermined blind source separation, a constraint reference vector is introduced in the SNMF algorithm, which can be generated by the pulse method. The square wave sequences are constructed as the constraint reference vector. The output separated signal is constrained by the vector, and the vector will update according to the feedback of the separated signal. The redundancy of the mixture signal will be reduced during the constantly updating of the vector. The time–frequency distribution is firstly applied to capture the local fault features of the vibration signal. Then the high dimension feature matrix of time–frequency distribution is factorized to select local fault features with the improved SNMF method. Meanwhile, the compound fault features can be separated and extracted automatically by using the sparse property of the improved SNMF method. Finally, envelope analysis is used to identify the feature of the output separated signal and realize compound faults diagnosis. The simulation and test results show that the proposed method can effectively solve the separation of compound faults for rotating machinery, which can reduce the dimension and improve the efficiency of algorithm. It is also confirmed that the feature extraction and separation capability of proposed method is superior to the traditional SNMF algorithm. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
An Entropy-Based Car Failure Detection Method Based on Data Acquisition Pipeline
Entropy 2019, 21(4), 426; https://doi.org/10.3390/e21040426
Received: 11 March 2019 / Revised: 18 April 2019 / Accepted: 18 April 2019 / Published: 22 April 2019
PDF Full-text (630 KB) | HTML Full-text | XML Full-text
Abstract
Modern cars are equipped with plenty of electronic devices called Electronic Control Units (ECU). ECUs collect diagnostic data from a car’s components such as the engine, brakes etc. These data are then processed, and the appropriate information is communicated to the driver. From [...] Read more.
Modern cars are equipped with plenty of electronic devices called Electronic Control Units (ECU). ECUs collect diagnostic data from a car’s components such as the engine, brakes etc. These data are then processed, and the appropriate information is communicated to the driver. From the point of view of safety of the driver and the passengers, the information about the car faults is vital. Regardless of the development of on-board computers, only a small amount of information is passed on to the driver. With the data mining approach, it is possible to obtain much more information from the data than it is provided by standard car equipment. This paper describes the environment built by the authors for data collection from ECUs. The collected data have been processed using parameterized entropies and data mining algorithms. Finally, we built a classifier able to detect a malfunctioning thermostat even if the car equipment does not indicate it. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Bearing Fault Diagnosis Considering the Effect of Imbalance Training Sample
Entropy 2019, 21(4), 386; https://doi.org/10.3390/e21040386
Received: 4 March 2019 / Revised: 29 March 2019 / Accepted: 8 April 2019 / Published: 10 April 2019
PDF Full-text (2233 KB) | HTML Full-text | XML Full-text
Abstract
To improve the accuracy of the recognition of complicated mechanical faults in bearings, a large number of features containing fault information need to be extracted. In most studies regarding bearing fault diagnosis, the influence of the limitation of fault training samples has not [...] Read more.
To improve the accuracy of the recognition of complicated mechanical faults in bearings, a large number of features containing fault information need to be extracted. In most studies regarding bearing fault diagnosis, the influence of the limitation of fault training samples has not been considered. Furthermore, commonly used multi-classifiers could misidentify the type or severity of faults without using normal samples as training samples. Therefore, a novel bearing fault diagnosis method based on the one-class classification concept and random forest is proposed for reducing the impact of the limitations of the fault training sample. First, the bearing vibration signals are decomposed into numerous intrinsic mode functions using empirical wavelet transform. Then, 284 features including multiple entropy are extracted from the original signal and intrinsic mode functions to construct the initial feature set. Lastly, a hybrid classifier based on one-class support vector machine trained by normal samples and a random forest trained by imbalanced fault data without some specific severities is set up to accurately identify the mechanical state and specific fault type of the bearings. The experimental results show that the proposed method can significantly improve the classification accuracy compared with traditional methods in different diagnostic target. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
An Integrated Approach Based on Swarm Decomposition, Morphology Envelope Dispersion Entropy, and Random Forest for Multi-Fault Recognition of Rolling Bearing
Entropy 2019, 21(4), 354; https://doi.org/10.3390/e21040354
Received: 4 March 2019 / Revised: 19 March 2019 / Accepted: 28 March 2019 / Published: 1 April 2019
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Abstract
Aiming at the problem that the weak faults of rolling bearing are difficult to recognize accurately, an approach on the basis of swarm decomposition (SWD), morphology envelope dispersion entropy (MEDE), and random forest (RF) is proposed to realize effective detection and intelligent recognition [...] Read more.
Aiming at the problem that the weak faults of rolling bearing are difficult to recognize accurately, an approach on the basis of swarm decomposition (SWD), morphology envelope dispersion entropy (MEDE), and random forest (RF) is proposed to realize effective detection and intelligent recognition of weak faults in rolling bearings. The proposed approach is based on the idea of signal denoising, feature extraction and pattern classification. Firstly, the raw signal is divided into a group of oscillatory components through SWD algorithm. The first component has the richest fault information and perceived as the principal oscillatory component (POC). Secondly, the MEDE value of the POC is calculated and used to describe the characteristics of signal. Ultimately, the obtained MEDE values of various states are trained and recognized by being input as the feature vectors into the RF classifier to achieve the automatic identification of rolling bearing fault under different operation states. The dataset of Case Western Reserve University is conducted, the proposed approach achieves recognition accuracy rate of 100%. In summary, the proposed approach is efficient and robust, which can be used as a supplement to the rolling bearing fault diagnosis methods. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Composite Interpolation-Based Multiscale Fuzzy Entropy and Its Application to Fault Diagnosis of Rolling Bearing
Entropy 2019, 21(3), 292; https://doi.org/10.3390/e21030292
Received: 16 February 2019 / Revised: 8 March 2019 / Accepted: 15 March 2019 / Published: 18 March 2019
PDF Full-text (2513 KB) | HTML Full-text | XML Full-text
Abstract
Multiscale fuzzy entropy (MFE), as an enhanced multiscale sample entropy (MSE) method, is an effective nonlinear method for measuring the complexity of time series. In this paper, an improved MFE algorithm termed composite interpolation-based multiscale fuzzy entropy (CIMFE) is proposed by using cubic [...] Read more.
Multiscale fuzzy entropy (MFE), as an enhanced multiscale sample entropy (MSE) method, is an effective nonlinear method for measuring the complexity of time series. In this paper, an improved MFE algorithm termed composite interpolation-based multiscale fuzzy entropy (CIMFE) is proposed by using cubic spline interpolation of the time series over different scales to overcome the drawbacks of the coarse-grained MFE process. The proposed CIMFE method is compared with MSE and MFE by analyzing simulation signals and the result indicates that CIMFE is more robust than MSE and MFE in analyzing short time series. Taking this into account, a new fault diagnosis method for rolling bearing is presented by combining CIMFE for feature extraction with Laplacian support vector machine for fault feature classification. Finally, the proposed fault diagnosis method is applied to the experiment data of rolling bearing by comparing with the MSE, MFE and other existing methods, and the recognition rate of the proposed method is 98.71%, 98.71%, 98.71%, 98.71% and 100% under different training samples (5, 10, 15, 20 and 25), which is higher than that of the existing methods. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
An Intuitionistic Evidential Method for Weight Determination in FMEA Based on Belief Entropy
Entropy 2019, 21(2), 211; https://doi.org/10.3390/e21020211
Received: 23 January 2019 / Revised: 14 February 2019 / Accepted: 20 February 2019 / Published: 22 February 2019
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Abstract
Failure Mode and Effects Analysis (FMEA) has been regarded as an effective analysis approach to identify and rank the potential failure modes in many applications. However, how to determine the weights of team members appropriately, with the impact factor of domain experts’ uncertainty [...] Read more.
Failure Mode and Effects Analysis (FMEA) has been regarded as an effective analysis approach to identify and rank the potential failure modes in many applications. However, how to determine the weights of team members appropriately, with the impact factor of domain experts’ uncertainty in decision-making of FMEA, is still an open issue. In this paper, a new method to determine the weights of team members, which combines evidence theory, intuitionistic fuzzy sets (IFSs) and belief entropy, is proposed to analyze the failure modes. One of the advantages of the presented model is that the uncertainty of experts in the decision-making process is taken into consideration. The proposed method is data driven with objective and reasonable properties, which considers the risk of weights more completely. A numerical example is shown to illustrate the feasibility and availability of the proposed method. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Improving the Performance of Storage Tank Fault Diagnosis by Removing Unwanted Components and Utilizing Wavelet-Based Features
Entropy 2019, 21(2), 145; https://doi.org/10.3390/e21020145
Received: 10 January 2019 / Revised: 24 January 2019 / Accepted: 3 February 2019 / Published: 4 February 2019
Cited by 1 | PDF Full-text (4171 KB) | HTML Full-text | XML Full-text
Abstract
This paper proposes a reliable fault diagnosis model for a spherical storage tank. The proposed method first used a blind source separation (BSS) technique to de-noise the input signals so that the signals acquired from a spherical tank under two types of conditions [...] Read more.
This paper proposes a reliable fault diagnosis model for a spherical storage tank. The proposed method first used a blind source separation (BSS) technique to de-noise the input signals so that the signals acquired from a spherical tank under two types of conditions (i.e., normal and crack conditions) were easily distinguishable. BSS split the signals into different sources that provided information about the noise and useful components of the signals. Therefore, an unimpaired signal could be restored from the useful components. From the de-noised signals, wavelet-based fault features, i.e., the relative energy (REWPN) and entropy (EWPN) of a wavelet packet node, were extracted. Finally, these features were used to train one-against-all multiclass support vector machines (OAA MCSVMs), which classified the instances of normal and faulty states of the tank. The efficiency of the proposed fault diagnosis model was examined by visualizing the de-noised signals obtained from the BSS method and its classification performance. The proposed fault diagnostic model was also compared to existing techniques. Experimental results showed that the proposed method outperformed conventional techniques, yielding average classification accuracies of 97.25% and 98.48% for the two datasets used in this study. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
A Method for Detecting Dynamic Mutation of Complex Systems Using Improved Information Entropy
Entropy 2019, 21(2), 115; https://doi.org/10.3390/e21020115
Received: 18 December 2018 / Revised: 12 January 2019 / Accepted: 22 January 2019 / Published: 27 January 2019
Cited by 1 | PDF Full-text (4918 KB) | HTML Full-text | XML Full-text
Abstract
In this study, a nonlinear analysis method called improved information entropy (IIE) is proposed on the basis of constructing a special probability mass function for the normalized analysis of Shannon entropy for a time series. The definition is directly applied to several typical [...] Read more.
In this study, a nonlinear analysis method called improved information entropy (IIE) is proposed on the basis of constructing a special probability mass function for the normalized analysis of Shannon entropy for a time series. The definition is directly applied to several typical time series, and the characteristic of IIE is analyzed. This method can distinguish different kinds of signals and reflects the complexity of one-dimensional time series of high sensitivity to the changes in signal. Thus, the method is applied to the fault diagnosis of a rolling bearing. Experimental results show that the method can effectively extract the sensitive characteristics of the bearing running state and has fast operation time and minimal parameter requirements. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Rolling Element Bearing Fault Diagnosis under Impulsive Noise Environment Based on Cyclic Correntropy Spectrum
Entropy 2019, 21(1), 50; https://doi.org/10.3390/e21010050
Received: 7 December 2018 / Revised: 2 January 2019 / Accepted: 4 January 2019 / Published: 10 January 2019
Cited by 1 | PDF Full-text (3388 KB) | HTML Full-text | XML Full-text
Abstract
Rolling element bearings are widely used in various industrial machines. Fault diagnosis of rolling element bearings is a necessary tool to prevent any unexpected accidents and improve industrial efficiency. Although proved to be a powerful method in detecting the resonance band excited by [...] Read more.
Rolling element bearings are widely used in various industrial machines. Fault diagnosis of rolling element bearings is a necessary tool to prevent any unexpected accidents and improve industrial efficiency. Although proved to be a powerful method in detecting the resonance band excited by faults, the spectral kurtosis (SK) exposes an obvious weakness in the case of impulsive background noise. To well process the bearing fault signal in the presence of impulsive noise, this paper proposes a fault diagnosis method based on the cyclic correntropy (CCE) function and its spectrum. Furthermore, an important parameter of CCE function, namely kernel size, is analyzed to emphasize its critical influence on the fault diagnosis performance. Finally, comparisons with the SK-based Fast Kurtogram are conducted to highlight the superiority of the proposed method. The experimental results show that the proposed method not only largely suppresses the impulsive noise, but also has a robust self-adaptation ability. The application of the proposed method is validated on a simulated signal and real data, including rolling element bearing data of a train axle. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Entropy Churn Metrics for Fault Prediction in Software Systems
Entropy 2018, 20(12), 963; https://doi.org/10.3390/e20120963
Received: 5 November 2018 / Revised: 11 December 2018 / Accepted: 11 December 2018 / Published: 13 December 2018
PDF Full-text (1712 KB) | HTML Full-text | XML Full-text
Abstract
Fault prediction is an important research area that aids software development and the maintenance process. It is a field that has been continuously improving its approaches in order to reduce the fault resolution time and effort. With an aim to contribute towards building [...] Read more.
Fault prediction is an important research area that aids software development and the maintenance process. It is a field that has been continuously improving its approaches in order to reduce the fault resolution time and effort. With an aim to contribute towards building new approaches for fault prediction, this paper proposes Entropy Churn Metrics (ECM) based on History Complexity Metrics (HCM) and Churn of Source Code Metrics (CHU). The study also compares performance of ECM with that of HCM. The performance of both these metrics is compared for 14 subsystems of 5different software projects: Android, Eclipse, Apache Http Server, Eclipse C/C++ Development Tooling (CDT), and Mozilla Firefox. The study also analyses the software subsystems on three parameters: (i) distribution of faults, (ii) subsystem size, and (iii) programming language, to determine which characteristics of software systems make HCM or ECM more preferred over others. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Bearing Remaining Useful Life Prediction Based on Naive Bayes and Weibull Distributions
Entropy 2018, 20(12), 944; https://doi.org/10.3390/e20120944
Received: 12 November 2018 / Revised: 3 December 2018 / Accepted: 5 December 2018 / Published: 8 December 2018
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Abstract
Bearing plays an important role in mechanical equipment, and its remaining useful life (RUL) prediction is an important research topic of mechanical equipment. To accurately predict the RUL of bearing, this paper proposes a data-driven RUL prediction method. First, the statistical method is [...] Read more.
Bearing plays an important role in mechanical equipment, and its remaining useful life (RUL) prediction is an important research topic of mechanical equipment. To accurately predict the RUL of bearing, this paper proposes a data-driven RUL prediction method. First, the statistical method is used to extract the features of the signal, and the root mean square (RMS) is regarded as the main performance degradation index. Second, the correlation coefficient is used to select the statistical characteristics that have high correlation with the RMS. Then, In order to avoid the fluctuation of the statistical feature, the improved Weibull distributions (WD) algorithm is used to fit the fluctuation feature of bearing at different recession stages, which is used as input of Naive Bayes (NB) training stage. During the testing stage, the true fluctuation feature of the bearings are used as the input of NB. After the NB testing, five classes are obtained: health states and four states for bearing degradation. Finally, the exponential smoothing algorithm is used to smooth the five classes, and to predict the RUL of bearing. The experimental results show that the proposed method is effective for RUL prediction of bearing. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Rotor Fault Diagnosis Based on Characteristic Frequency Band Energy Entropy and Support Vector Machine
Entropy 2018, 20(12), 932; https://doi.org/10.3390/e20120932
Received: 21 November 2018 / Revised: 2 December 2018 / Accepted: 5 December 2018 / Published: 5 December 2018
Cited by 2 | PDF Full-text (9605 KB) | HTML Full-text | XML Full-text
Abstract
Rotor is a widely used and easily defected mechanical component. Thus, it is significant to develop effective techniques for rotor fault diagnosis. Fault signature extraction and state classification of the extracted signatures are two key steps for diagnosing rotor faults. To complete the [...] Read more.
Rotor is a widely used and easily defected mechanical component. Thus, it is significant to develop effective techniques for rotor fault diagnosis. Fault signature extraction and state classification of the extracted signatures are two key steps for diagnosing rotor faults. To complete the accurate recognition of rotor states, a novel evaluation index named characteristic frequency band energy entropy (CFBEE) was proposed to extract the defective features of rotors, and support vector machine (SVM) was employed to automatically identify the rotor fault types. Specifically, the raw vibration signal of rotor was first analyzed by a joint time–frequency method based on improved singular spectrum decomposition (ISSD) and Hilbert transform (HT) to derive its time–frequency spectrum (TFS), which is named ISSD-HT TFS in this paper. Then, the CFBEE of the ISSD-HT TFS was calculated as the fault feature vector. Finally, SVM was used to complete the automatic identification of rotor faults. Simulated processing results indicate that ISSD improves the end effects of singular spectrum decomposition (SSD) and is superior to empirical mode decomposition (EMD) in extracting the sub-components of rotor vibration signal. The ISSD-HT TFS can more accurately reflect the time–frequency information compared to the EMD-HT TFS. Experimental verification demonstrates that the proposed method can accurately identify rotor defect types and outperform some other methods. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Rolling Element Bearing Fault Diagnosis by Combining Adaptive Local Iterative Filtering, Modified Fuzzy Entropy and Support Vector Machine
Entropy 2018, 20(12), 926; https://doi.org/10.3390/e20120926
Received: 11 November 2018 / Revised: 29 November 2018 / Accepted: 1 December 2018 / Published: 4 December 2018
Cited by 1 | PDF Full-text (1794 KB) | HTML Full-text | XML Full-text
Abstract
A new fault feature extraction method for rolling element bearing is put forward in this paper based on the adaptive local iterative filtering (ALIF) algorithm and the modified fuzzy entropy. Due to the bearing vibration signals’ non-stationary and nonlinear characteristics, the ALIF method, [...] Read more.
A new fault feature extraction method for rolling element bearing is put forward in this paper based on the adaptive local iterative filtering (ALIF) algorithm and the modified fuzzy entropy. Due to the bearing vibration signals’ non-stationary and nonlinear characteristics, the ALIF method, which is a new approach for the analysis of the non-stationary signals, is used to decompose the original vibration signals into a series of mode components. Fuzzy entropy (FuzzyEn) is a nonlinear dynamic parameter for measuring the signals’ complexity. However, it only emphasizes the signals’ local characteristics while neglecting its global fluctuation. Considering the global fluctuation of bearing vibration signals will change with the bearing working condition varying, we modified the FuzzyEn. The modified FuzzyEn (MFuzzyEn) of the first few modes obtained by the ALIF is utilized to form the fault feature vectors. Subsequently, the corresponding feature vectors are input into the multi-class SVM classifier to accomplish the bearing fault identification automatically. The experimental analysis demonstrates that the presented ALIF-MFuzzyEn-SVM approach can effectively recognize the different fault categories and different levels of bearing fault severity. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
A Bayesian Failure Prediction Network Based on Text Sequence Mining and Clustering
Entropy 2018, 20(12), 923; https://doi.org/10.3390/e20120923
Received: 23 October 2018 / Revised: 27 November 2018 / Accepted: 30 November 2018 / Published: 3 December 2018
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Abstract
The purpose of this paper is to predict failures based on textual sequence data. The current failure prediction is mainly based on structured data. However, there are many unstructured data in aircraft maintenance. The failure mentioned here refers to failure types, such as [...] Read more.
The purpose of this paper is to predict failures based on textual sequence data. The current failure prediction is mainly based on structured data. However, there are many unstructured data in aircraft maintenance. The failure mentioned here refers to failure types, such as transmitter failure and signal failure, which are classified by the clustering algorithm based on the failure text. For the failure text, this paper uses the natural language processing technology. Firstly, segmentation and the removal of stop words for Chinese failure text data is performed. The study applies the word2vec moving distance model to obtain the failure occurrence sequence for failure texts collected in a fixed period of time. According to the distance, a clustering algorithm is used to obtain a typical number of fault types. Secondly, the failure occurrence sequence is mined using sequence mining algorithms, such as-PrefixSpan. Finally, the above failure sequence is used to train the Bayesian failure network model. The final experimental results show that the Bayesian failure network has higher accuracy for failure prediction. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Optimized Adaptive Local Iterative Filtering Algorithm Based on Permutation Entropy for Rolling Bearing Fault Diagnosis
Entropy 2018, 20(12), 920; https://doi.org/10.3390/e20120920
Received: 16 October 2018 / Revised: 26 November 2018 / Accepted: 27 November 2018 / Published: 1 December 2018
Cited by 2 | PDF Full-text (3925 KB) | HTML Full-text | XML Full-text
Abstract
The characteristics of the early fault signal of the rolling bearing are weak and this leads to difficulties in feature extraction. In order to diagnose and identify the fault feature from the bearing vibration signal, an adaptive local iterative filter decomposition method based [...] Read more.
The characteristics of the early fault signal of the rolling bearing are weak and this leads to difficulties in feature extraction. In order to diagnose and identify the fault feature from the bearing vibration signal, an adaptive local iterative filter decomposition method based on permutation entropy is proposed in this paper. As a new time-frequency analysis method, the adaptive local iterative filtering overcomes two main problems of mode decomposition, comparing traditional methods: modal aliasing and the number of components is uncertain. However, there are still some problems in adaptive local iterative filtering, mainly the selection of threshold parameters and the number of components. In this paper, an improved adaptive local iterative filtering algorithm based on particle swarm optimization and permutation entropy is proposed. Firstly, particle swarm optimization is applied to select threshold parameters and the number of components in ALIF. Then, permutation entropy is used to evaluate the mode components we desire. In order to verify the effectiveness of the proposed method, the numerical simulation and experimental data of bearing failure are analyzed. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Modeling and Fusing the Uncertainty of FMEA Experts Using an Entropy-Like Measure with an Application in Fault Evaluation of Aircraft Turbine Rotor Blades
Entropy 2018, 20(11), 864; https://doi.org/10.3390/e20110864
Received: 14 October 2018 / Revised: 3 November 2018 / Accepted: 7 November 2018 / Published: 9 November 2018
PDF Full-text (354 KB) | HTML Full-text | XML Full-text
Abstract
As a typical tool of risk analysis in practical engineering, failure mode and effects analysis (FMEA) theory is a well known method for risk prediction and prevention. However, how to quantify the uncertainty of the subjective assessments from FMEA experts and aggregate the [...] Read more.
As a typical tool of risk analysis in practical engineering, failure mode and effects analysis (FMEA) theory is a well known method for risk prediction and prevention. However, how to quantify the uncertainty of the subjective assessments from FMEA experts and aggregate the corresponding uncertainty to the classical FMEA approach still needs further study. In this paper, we argue that the subjective assessments of FMEA experts can be adopted to model the weight of each FMEA expert, which can be regarded as a data-driven method for ambiguity information modeling in FMEA method. Based on this new perspective, a modified FMEA approach is proposed, where the subjective uncertainty of FMEA experts is handled in the framework of Dempster–Shafer evidence theory (DST). In the improved FMEA approach, the ambiguity measure (AM) which is an entropy-like uncertainty measure in DST framework is applied to quantify the uncertainty degree of each FMEA expert. Then, the classical risk priority number (RPN) model is improved by aggregating an AM-based weight factor into the RPN function. A case study based on the new RPN model in aircraft turbine rotor blades verifies the applicable and useful of the proposed FMEA approach. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Open AccessArticle
Mechanical Fault Diagnosis of HVCBs Based on Multi-Feature Entropy Fusion and Hybrid Classifier
Entropy 2018, 20(11), 847; https://doi.org/10.3390/e20110847
Received: 17 October 2018 / Revised: 2 November 2018 / Accepted: 3 November 2018 / Published: 5 November 2018
Cited by 3 | PDF Full-text (7895 KB) | HTML Full-text | XML Full-text
Abstract
As high-voltage circuit breakers (HVCBs) are directly related to the safety and the stability of a power grid, it is of great significance to carry out fault diagnoses of HVCBs. To accurately identify operating states of HVCBs, a novel mechanical fault diagnosis method [...] Read more.
As high-voltage circuit breakers (HVCBs) are directly related to the safety and the stability of a power grid, it is of great significance to carry out fault diagnoses of HVCBs. To accurately identify operating states of HVCBs, a novel mechanical fault diagnosis method of HVCBs based on multi-feature entropy fusion (MFEF) and a hybrid classifier is proposed. MFEF involves the decomposition of vibration signals of HVCBs into several intrinsic mode functions using variational mode decomposition (VMD) and the calculation of multi-feature entropy by the integration of three Shannon entropies. Principle component analysis (PCA) is then used to reduce the dimension of the multi-feature entropy to achieve an effective fusion of features for selecting the feature vector. The detection of an unknown fault in HVCBs is achieved using support vector data description (SVDD) trained by normal-state samples and specific fault samples. On this basis, the identification and classification of the known states are realized by the support vector machine (SVM). Three faults (i.e., closing spring force decrease fault, buffer spring invalid fault, opening spring force decrease fault) are simulated on a real SF6 HVCB to test the feasibility of the proposed method. The detection accuracies of the unknown fault are 100%, 87.5%, and 100% respectively when each of the three faults is assumed to be the unknown fault. The comparative experiments show that SVM has no ability to detect the unknown fault, and that one-class support vector machine (OCSVM) has a weaker ability to detect the unknown fault than SVDD. For known-state classification, the adoption of the MFEF method achieved an accuracy of 100%, while the use of a single-feature method only achieved an accuracy of 75%. These results indicate that the proposed method combining MFEF with hybrid classifier is thus more efficient and robust than traditional methods. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Review

Jump to: Research

Open AccessReview
A Review of Early Fault Diagnosis Approaches and Their Applications in Rotating Machinery
Entropy 2019, 21(4), 409; https://doi.org/10.3390/e21040409
Received: 14 February 2019 / Revised: 12 March 2019 / Accepted: 12 April 2019 / Published: 17 April 2019
PDF Full-text (2004 KB) | HTML Full-text | XML Full-text
Abstract
Rotating machinery is widely applied in various types of industrial applications. As a promising field for reliability of modern industrial systems, early fault diagnosis (EFD) techniques have attracted increasing attention from both academia and industry. EFD is critical to provide appropriate information for [...] Read more.
Rotating machinery is widely applied in various types of industrial applications. As a promising field for reliability of modern industrial systems, early fault diagnosis (EFD) techniques have attracted increasing attention from both academia and industry. EFD is critical to provide appropriate information for taking necessary maintenance actions and thereby prevent severe failures and reduce financial losses. A massive amounts of research work has been conducted in last two decades to develop EFD techniques. This paper reviews and summarizes the research works on EFD of gears, rotors, and bearings. The main purpose of this paper is to serve as a guidemap for researchers in the field of early fault diagnosis. After a brief introduction of early fault diagnosis techniques, the applications of EFD of rotating machine are reviewed in two aspects: fault frequency-based methods and artificial intelligence-based methods. Finally, a summary and some new research prospects are discussed. Full article
(This article belongs to the Special Issue Entropy-Based Fault Diagnosis)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Author: Prof. Spyros G. Tzafestas
Title: Overview of Fault Detection and Diagnosis: The Entropy-Based Approach
Abstract: Fault detection and diagnosis (FDD) is a system theory branch of primary importance for the successful, efficient, and safe operation of technological systems. The aim of this paper is to provide an overview of FDD with focus on the entropy-based methodology. The paper starts with background material on information, Shannon entropy, approximate entropy (ApEn), and sample entropy (SampEn), including a brief review of the literature on ApEn and SampEn. Then, it provides an outline of the FDD concept, including a tour to FDD methods for dynamic systems. The general procedure for model-based FDD that involves the signal processing approach, to which the entropy-based methods belong, is then described. Next, an overview of the entropy-based FDD literature is given and the associated general FDD procedure is described. Finally, three entropy-based FDD examples, selected from the above reviewed literature, are outlined at some more detail to illustrate how the entropy-based feature extraction can be implemented and combined with available classifiers to complete the fault diagnosis. 
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