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Fault detection and isolation

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118:, wavelet transform, short term Fourier transform, Gabor Expansion, Wigner-Ville distribution (WVD), cepstrum, bispectrum, correlation method, high resolution spectral analysis, waveform analysis (in the time domain, because spectral analysis usually concerns only frequency distribution and not phase information) and others. The results of this analysis are used in a root cause failure analysis in order to determine the original cause of the fault. For example, if a bearing fault is diagnosed, then it is likely that the bearing was not itself damaged at installation, but rather as the consequence of another installation error (e.g., misalignment) which then led to bearing damage. Diagnosing the bearing's damaged state is not enough for precision maintenance purposes. The root cause needs to be identified and remedied. If this is not done, the replacement bearing will soon wear out for the same reason and the machine will suffer more damage, remaining dangerous. Of course, the cause may also be visible as a result of the spectral analysis undertaken at the data-collection stage, but this may not always be the case. 353: 125:), is not a constant, especially not during the start-up and shutdown stages of the machine. Even if the machine is running in the steady state, the rotational speed will vary around a steady-state mean value, and this variation depends on load and other factors. Since sound and vibration signals obtained from a rotating machine are strongly related to its rotational speed, it can be said that they are time-variant signals in nature. These time-variant features carry the machine fault signatures. Consequently, how these features are extracted and interpreted is important to research and industrial applications. 181:, then quadratic time frequency analysis would be the power spectrum counterpart. Quadratic algorithms include the Gabor spectrogram, Cohen's class and the adaptive spectrogram. The main advantage of time frequency analysis is discovering the patterns of frequency changes, which usually represent the nature of the signal. As long as this pattern is identified the machine fault associated with this pattern can be identified. Another important use of time frequency analysis is the ability to filter out a particular frequency component using a time-varying filter. 72:
switches between the different modes of operation (passive, active, standby, off, and isolated) of each actuator. For example, if a fault is detected in hydraulic system 1, then the truth table sends an event to the state chart that the left inner actuator should be turned off. One of the benefits of this model-based FDI technique is that this reactive controller can also be connected to a continuous-time model of the actuator hydraulics, allowing the study of switching transients.
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reduction and time-varying filtering. Although the quadratic method describes the energy distribution of a signal in the joint time frequency domain, which is useful for analysis, classification, and detection of signal features, phase information is lost in the quadratic time-frequency representation; also, the time histories cannot be reconstructed with this method.
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The example shown in the figure on the right illustrates a model-based FDI technique for an aircraft elevator reactive controller through the use of a truth table and a state chart. The truth table defines how the controller reacts to detected faults, and the state chart defines how the controller
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where a signal is sent down a cable or electrical line and the reflected signal is compared mathematically to original signal to identify faults. Spread Spectrum Time Domain Reflectometry, for instance, involves sending down a spread spectrum signal down a wire line to detect wire faults. Several
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has occurred, and pinpointing the type of fault and its location. Two approaches can be distinguished: A direct pattern recognition of sensor readings that indicate a fault and an analysis of the discrepancy between the sensor readings and expected values, derived from some model. In the latter
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or knowledge based. Some of the model-based FDI techniques include observer-based approach, parity-space approach, and parameter identification based methods. There is another trend of model-based FDI schemes, which is called set-membership methods. These methods guarantee the detection of fault
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in fault detection and diagnosis. ANNs are well-known for their efficient self-learning capabilities of the complex relations (which generally exist inherently in fault detection and diagnosis problems) and are easy to operate. Another advantage of ANNs is that they perform automatic feature
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The time frequency approach for machine fault diagnosis can be divided into two broad categories: linear methods and the quadratic methods. The difference is that linear transforms can be inverted to construct the time signal, thus, they are more suitable for signal processing, such as noise
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concerned with finding faults arising in machines. A particularly well developed part of it applies specifically to rotating machinery, one of the most common types encountered. To identify the most probable faults leading to failure, many methods are used for data collection, including
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As a result, using fault diagnostics to meet industrial needs in a cost-effective way, and to reduce maintenance costs without requiring more investments than the cost of what is to be avoided in the first place, requires an effective scheme of applying them. This is the subject of
648:"Pieter J. Mosterman and Jason Ghidella, "Model Reuse for the Training of Fault Scenarios in Aerospace," in Proceedings of the AIAA Modeling and Simulation Technologies Conference, CD-ROM, paper 2004-4931, August 16 - 19, Rhode Island Convention Center, Providence, RI, 2004" 161:
of a machine is increasing or decreasing during its startup or shutdown period, its bandwidth in the FFT spectrum will become much wider than it would be simply for the steady state. Hence, in such a case, the harmonics are not so distinguishable in the spectrum.
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can be directly classified to normal and faulty classes. Such a technique avoids omitting any important fault message and results in a better performance of fault detection and diagnosis. In addition, by transforming signals to image constructions, 2D
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is only suitable for signals whose frequency contents do not change over time; however, as mentioned above, the frequency contents of the sound and vibration signals obtained from a rotating machine are very much time-dependent. For this reason,
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Jason R. Ghidella and Pieter J. Mosterman, "Requirements-Based Testing in Aircraft Control Design," Paper ID AIAA 2005-5886 in AIAA Modeling and Simulations Technologies Conference and Exhibit 2005, August 15-18, San Francisco, California,
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and achieve higher performance. Moreover, properly determining the size of the hidden layer needs an exhaustive parameter tuning, to avoid poor approximation and generalization capabilities. In general, different SVMs and ANNs models (i.e.
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Tian, Jing; Morillo, Carlos; Azarian, Michael H.; Pecht, Michael (March 2016). "Motor Bearing Fault Detection Using Spectral Kurtosis-Based Feature Extraction Coupled With K-Nearest Neighbor Distance Analysis".
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In signal processing based FDI, some mathematical or statistical operations are performed on the measurements, or some neural network is trained using measurements to extract the information about the fault.
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Ahmadimanesh, Alireza, and Seyyed Mohammad Shahrtash. "Time–time-transform-based fault location algorithm for three-terminal transmission lines." IET Generation, Transmission & Distribution 7.5 (2013):
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Ahmadimanesh, A., and S. M. Shahrtash. "Employing S-transform for fault location in three terminal lines." Environment and Electrical Engineering (EEEIC), 2011 10th International Conference on. IEEE, 2011.
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NN) is one of the oldest techniques which has been used to solve fault detection and diagnosis problems. Despite the simple logic that this instance-based algorithm has, there are some problems with large
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Jia, Feng; Lei, Yaguo; Lin, Jing; Zhou, Xin; Lu, Na (May 2016). "Deep neural networks: A promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data".
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Saravanan, N.; Siddabattuni, V.N.S. Kumar; Ramachandran, K.I. (January 2010). "Fault diagnosis of spur bevel gear box using artificial neural network (ANN), and proximal support vector machine (PSVM)".
349:, a parameter tuning process is required to be conducted first. Therefore, the low speed of the training phase is a limitation of SVMs when it comes to its usage in fault detection and diagnosis cases. 372:
the training set, which will have consequences of having poor validation accuracy on the validation set. Hence, often, some regularization terms and prior knowledge are added to the ANN model to avoid
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Ahmadimanesh, Alireza, and S. Mohammad Shahrtash. "Transient-based fault-location method for multiterminal lines employing S-transform." IEEE transactions on power delivery 28.3 (2013): 1373-1380.
136:-based spectrum of a time signal shows us the existence of its frequency contents. By studying these and their magnitude or phase relations, we can obtain various types of information, such as 1437:
Lei, Yaguo; Jia, Feng; Lin, Jing; Xing, Saibo; Ding, Steven X. (May 2016). "An Intelligent Fault Diagnosis Method Using Unsupervised Feature Learning Towards Mechanical Big Data".
330:, SVMs have an impressive performance in generalization, even with small training data. However, general SVMs do not have automatic feature extraction themselves and just like 1154:
Qi, Guanqiu; Zhu, Zhiqin; Erqinhu, Ke; Chen, Yinong; Chai, Yi; Sun, Jian (January 2018). "Fault-diagnosis for reciprocating compressors using big data and machine learning".
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Verdier, Ghislain; Ferreira, Ariane (February 2011). "Adaptive Mahalanobis Distance and $ k$ -Nearest Neighbor Rule for Fault Detection in Semiconductor Manufacturing".
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Fault Recovery in FDIR is the action taken after a failure has been detected and isolated to return the system to a stable state. Some examples of fault recoveries are:
132:, or Fourier transform. The Fourier transform and its inverse counterpart offer two perspectives to study a signal: via the time domain or via the frequency domain. The 121:
The most common technique for detecting faults is the time-frequency analysis technique. For a rotating machine, the rotational speed of the machine (often known as the
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Wong, Pak Kin; Yang, Zhixin; Vong, Chi Man; Zhong, Jianhua (March 2014). "Real-time fault diagnosis for gas turbine generator systems using extreme learning machine".
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Safizadeh, M.S.; Latifi, S.K. (July 2014). "Using multi-sensor data fusion for vibration fault diagnosis of rolling element bearings by accelerometer and load cell".
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under certain conditions. The main difference is that instead of finding the most likely model, these techniques omit the models, which are not compatible with data.
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extraction by allocating negligible weights to the irrelevant features, helping the system to avoid dealing with another feature extractor. However, ANNs tend to
605:"Model Invalidation for Switched Affine Systems with Applications to Fault and Anomaly Detection**This work is supported in part by DARPA grant N66001-14-1-4045" 769:
Bahrampour, Soheil; Moshiri, Behzad; Salahshour, Karim. "Weighted and constrained possibilistic C-means clustering for online fault detection and isolation
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are two algorithms commonly used as linear time-frequency methods. If we consider linear time-frequency analysis to be the evolution of the conventional
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Shao, Haidong; Jiang, Hongkai; Zhang, Xun; Niu, Maogui (1 November 2015). "Rolling bearing fault diagnosis using an optimization deep belief network".
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Liu, Ruonan; Yang, Boyuan; Zio, Enrico; Chen, Xuefeng (August 2018). "Artificial intelligence for fault diagnosis of rotating machinery: A review".
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goes above a certain threshold. It is then the task of fault isolation to categorize the type of fault and its location in the machinery.
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Farshad Harirchi and Necmiye Ozay, "Guaranteed Model-Based Fault Detection in Cyber-Physical Systems: A Model Invalidation Approach", arXiv
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Hoang, Duy-Tang; Kang, Hee-Jun (2019). "Rolling element bearing fault diagnosis using convolutional neural network and vibration image".
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Liu, Jie; Zio, Enrico (December 2016). "Feature vector regression with efficient hyperparameters tuning and geometric interpretation".
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Kotsiantis, S.B.; Zaharakis, I.D.; Pintelas, P.E. (2006). "Machine learning: a review of classification and combining techniques".
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clustering methods have also been proposed to identify the novel fault and segment a given signal into normal and faulty segments.
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technique. Another drawback of SVMs is that their performance is highly sensitive to the initial parameters, particularly to the
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In model-based FDI techniques some model of the system is used to decide about the occurrence of fault. The system model may be
1319: 1077: 47:) techniques can be broadly classified into two categories. These include model-based FDI and signal processing based FDI. 672:
Liu, Jie (2012). "Shannon wavelet spectrum analysis on truncated vibration signals for machine incipient fault detection".
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Tian, Yang; Fu, Mengyu; Wu, Fang (March 2015). "Steel plates fault diagnosis on the basis of support vector machines".
799:"Fault detection, classification and location for transmission lines and distribution systems: a review on the methods" 194: 542: 260:
to accurately identify the redundancies, faults and anomalous samples. During the past decades, there are different
352: 157:-based spectra are unable to detect how the frequency contents develop over time. To be more specific, if the 331: 316: 289: 269: 1558: 478: 468: 460: 456: 308: 304: 170: 1302:
Lv, Feiya; Wen, Chenglin; Bao, Zejing; Liu, Meiqin (July 2016). "Fault diagnosis based on deep learning".
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In practice, model uncertainties and measurement noise can complicate fault detection and isolation.
85: 517: 1553: 532: 315:(CCA) accompany it to reach a better performance. In many industrial cases, the effectiveness of 296: 385:) have shown successful performances in the fault detection and diagnosis in industries such as 326:(SVMs), which is widely used in this field. Thanks to their appropriate nonlinear mapping using 322:
has been compared with other methods, specially with more complex classification models such as
1345:"A Novel Fault Diagnosis Method for Rotating Machinery Based on a Convolutional Neural Network" 552: 323: 216: 211: 178: 158: 154: 149: 133: 129: 122: 98: 1189:
Santos, Pedro; Villa, Luisa; Reñones, Aníbal; Bustillo, Andres; Maudes, Jesús (9 March 2015).
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Genton, Marc G. (2001). "Classes of Kernels for Machine Learning: A Statistics Perspective".
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architectures which have been successfully used in this field of research. In comparison to
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Hui, Kar Hoou; Ooi, Ching Sheng; Lim, Meng Hee; Leong, Mohd Salman (15 November 2016).
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Example of model-based FDI logic for an actuator in an aircraft elevator control system
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Change of state of the complete system into a Safe Mode with limited functionalities
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case, it is typical that a fault is said to be detected if the discrepancy or
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Business intelligence : data mining and optimization for decision making
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can be implemented to identify faulty signals from vibration image features.
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have been developed to cope with fault detection and diagnosis. Most of the
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models that have been developed and proposed in this research area.
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which concerns itself with monitoring a system, identifying when a
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is not able to automatically extract the features to overcome the
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Ding, S.X., Model-based fault diagnosis techniques, Springer 2008
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Time domain waveform (top) and CWTS (bottom) of a normal signal
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Machine learning techniques for fault detection and diagnosis
1191:"An SVM-Based Solution for Fault Detection in Wind Turbines" 447:
models extract a few feature values from signals, causing a
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Guo, Sheng; Yang, Tao; Gao, Wei; Zhang, Chen (4 May 2018).
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Fault detection and diagnosis using artificial intelligence
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Chen, Kunjin; Huang, Caowei; He, Jinliang (1 April 2016).
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Deep learning techniques for fault detection and diagnosis
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models are able to learn more complex structures from
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Typical architecture of a Convolutional Neural Network
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The most common method used in signal analysis is the
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With the research advances in ANNs and the advent of
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Hoboken, N.J.: Wiley. p. 436. 363:(ANNs) are among the most mature and widely used 84:A good example of signal processing based FDI is 1545: 1153: 832:IEEE Transactions on Semiconductor Manufacturing 439:algorithms using deep and complex layers, novel 1342: 900: 829: 774:Applied Intelligence, Vol 35, pp. 269-284, 2011 1120: 959: 75: 1514: 1436: 284:and processing time when it is used on large 602: 1439:IEEE Transactions on Industrial Electronics 1301: 868:IEEE Transactions on Industrial Electronics 796: 92: 1401: 1378: 1368: 1224: 1214: 1138: 1067: 955: 953: 951: 814: 620: 603:Harirchi, Farshad; Ozay, Necmiye (2015). 558:Spread-spectrum time-domain reflectometry 516:Switch-over from a faulty equipment to a 184: 1518:Mechanical Systems and Signal Processing 1274: 1156:Simulation Modelling Practice and Theory 962:Mechanical Systems and Signal Processing 758:Structural Control and Health Monitoring 420: 351: 54: 20:Fault detection, isolation, and recovery 1546: 1304:2016 American Control Conference (ACC) 1028: 1026: 1002: 948: 927: 365:mathematical classification algorithms 97:Machine fault diagnosis is a field of 1005:Journal of Machine Learning Research 223:Integrated vehicle health management 197:; the different strategies include: 1023: 671: 13: 1474:Measurement Science and Technology 674:Measurement Science and Technology 493:, due to their deep architecture, 246:mathematical classification models 244:In fault detection and diagnosis, 195:maintenance, repair and operations 169:The short-term Fourier transform ( 50: 14: 1570: 543:Failure mode and effects analysis 504: 513:Switch-off of a faulty equipment 379:Back-Propagation Neural Networks 1508: 1465: 1430: 1395: 1336: 1295: 1268: 1241: 1182: 1147: 1114: 1086: 1061: 996: 921: 894: 858: 823: 790: 779: 763: 736: 16:Subfield of control engineering 1494:10.1088/0957-0233/26/11/115002 1035:Artificial Intelligence Review 727: 717: 708: 665: 640: 629: 596: 587: 575: 313:Canonical correlation analysis 207:Planned preventive maintenance 1: 694:10.1088/0957-0233/23/5/055604 568: 479:Restricted Boltzmann machines 469:Convolutional neural networks 457:Convolutional neural networks 41:Fault detection and isolation 1416:10.1016/j.cogsys.2018.03.002 1289:10.1016/j.neucom.2014.09.036 1262:10.1016/j.neucom.2013.03.059 1168:10.1016/j.simpat.2017.10.005 942:10.1016/j.neucom.2016.08.093 915:10.1016/j.inffus.2013.10.002 622:10.1016/j.ifacol.2015.11.185 491:traditional machine learning 461:continuous wavelet transform 451:reduction from the original 309:Linear discriminant analysis 305:Principal component analysis 273:-nearest-neighbors algorithm 252:methods, are trained on the 7: 1534:10.1016/j.ymssp.2015.10.025 1127:Journal of Vibroengineering 982:10.1016/j.ymssp.2018.02.016 526: 337:, are often coupled with a 202:Condition-based maintenance 76:Signal processing based FDI 10: 1575: 1404:Cognitive Systems Research 1108:10.1016/j.asoc.2009.08.006 428: 361:Artificial Neural Networks 237: 219:(does not use diagnostics) 1068:Vercellis, Carlo (2008). 1047:10.1007/s10462-007-9052-3 1017:10.1162/15324430260185646 86:time domain reflectometry 1451:10.1109/TIE.2016.2519325 1312:10.1109/ACC.2016.7526751 880:10.1109/TIE.2015.2509913 844:10.1109/TSM.2010.2065531 248:which in fact belong to 1140:10.21595/jve.2016.17024 756:on Live Wire Networks" 533:Control reconfiguration 324:Support Vector Machines 297:curse of dimensionality 93:Machine fault diagnosis 1306:. pp. 6851–6856. 1096:Applied Soft Computing 553:Predictive maintenance 426: 383:Multi-Layer Perceptron 357: 217:Corrective maintenance 212:Preventive maintenance 185:Robust fault diagnosis 99:mechanical engineering 60: 816:10.1049/hve.2016.0005 563:System identification 548:Fault-tolerant system 441:classification models 424: 355: 58: 487:deep neural networks 475:Deep belief networks 345:, so in each signal 1559:Systems engineering 1526:2016MSSP...72..303J 1486:2015MeScT..26k5002S 1361:2018Senso..18.1429G 1207:2015Senso..15.5627S 974:2018MSSP..108...33L 686:2012MeScT..23e5604L 518:redundant equipment 395:mechanical bearings 339:data pre-processing 250:supervised learning 28:control engineering 26:) is a subfield of 1520:. 72–73: 303–315. 1216:10.3390/s150305627 903:Information Fusion 427: 358: 301:data preprocessing 61: 1370:10.3390/s18051429 1321:978-1-4673-8682-1 1079:978-0-470-51138-1 609:IFAC-PapersOnLine 112:spectral analysis 1566: 1538: 1537: 1512: 1506: 1505: 1469: 1463: 1462: 1445:(5): 3137–3147. 1434: 1428: 1427: 1399: 1393: 1392: 1382: 1372: 1340: 1334: 1333: 1299: 1293: 1292: 1272: 1266: 1265: 1245: 1239: 1238: 1228: 1218: 1201:(3): 5627–5648. 1186: 1180: 1179: 1151: 1145: 1144: 1142: 1133:(7): 4409–4418. 1118: 1112: 1111: 1090: 1084: 1083: 1065: 1059: 1058: 1030: 1021: 1020: 1000: 994: 993: 957: 946: 945: 925: 919: 918: 898: 892: 891: 874:(3): 1793–1803. 862: 856: 855: 827: 821: 820: 818: 794: 788: 783: 777: 767: 761: 740: 734: 731: 725: 721: 715: 712: 706: 705: 669: 663: 662: 660: 659: 650:. Archived from 644: 638: 633: 627: 626: 624: 600: 594: 591: 585: 579: 445:shallow learning 303:techniques like 299:, so often some 240:Machine learning 116:wavelet analysis 1574: 1573: 1569: 1568: 1567: 1565: 1564: 1563: 1544: 1543: 1542: 1541: 1513: 1509: 1470: 1466: 1435: 1431: 1400: 1396: 1341: 1337: 1322: 1300: 1296: 1273: 1269: 1246: 1242: 1187: 1183: 1152: 1148: 1119: 1115: 1091: 1087: 1080: 1066: 1062: 1031: 1024: 1001: 997: 958: 949: 926: 922: 899: 895: 863: 859: 828: 824: 795: 791: 784: 780: 776:June 6th, 2005. 768: 764: 741: 737: 732: 728: 722: 718: 713: 709: 670: 666: 657: 655: 646: 645: 641: 634: 630: 615:(27): 260–266. 601: 597: 592: 588: 580: 576: 571: 529: 507: 433: 419: 242: 236: 231: 187: 175:Gabor transform 108:thermal imaging 95: 78: 53: 51:Model-based FDI 17: 12: 11: 5: 1572: 1562: 1561: 1556: 1554:Control theory 1540: 1539: 1507: 1480:(11): 115002. 1464: 1429: 1394: 1335: 1320: 1294: 1277:Neurocomputing 1267: 1250:Neurocomputing 1240: 1181: 1146: 1113: 1102:(1): 344–360. 1085: 1078: 1060: 1041:(3): 159–190. 1022: 995: 947: 930:Neurocomputing 920: 893: 857: 822: 789: 778: 762: 752:2010-05-01 at 747:Fault Location 743:Furse, Cynthia 735: 726: 716: 707: 664: 639: 628: 595: 586: 573: 572: 570: 567: 566: 565: 560: 555: 550: 545: 540: 538:Control theory 535: 528: 525: 524: 523: 520: 514: 506: 505:Fault recovery 503: 449:dimensionality 418: 415: 343:kernel methods 328:kernel methods 282:dimensionality 262:classification 235: 232: 230: 227: 226: 225: 220: 214: 209: 204: 186: 183: 146:beat frequency 94: 91: 77: 74: 52: 49: 15: 9: 6: 4: 3: 2: 1571: 1560: 1557: 1555: 1552: 1551: 1549: 1535: 1531: 1527: 1523: 1519: 1511: 1503: 1499: 1495: 1491: 1487: 1483: 1479: 1475: 1468: 1460: 1456: 1452: 1448: 1444: 1440: 1433: 1425: 1421: 1417: 1413: 1409: 1405: 1398: 1390: 1386: 1381: 1376: 1371: 1366: 1362: 1358: 1354: 1350: 1346: 1339: 1331: 1327: 1323: 1317: 1313: 1309: 1305: 1298: 1290: 1286: 1282: 1278: 1271: 1263: 1259: 1255: 1251: 1244: 1236: 1232: 1227: 1222: 1217: 1212: 1208: 1204: 1200: 1196: 1192: 1185: 1177: 1173: 1169: 1165: 1161: 1157: 1150: 1141: 1136: 1132: 1128: 1124: 1117: 1109: 1105: 1101: 1097: 1089: 1081: 1075: 1071: 1064: 1056: 1052: 1048: 1044: 1040: 1036: 1029: 1027: 1018: 1014: 1010: 1006: 999: 991: 987: 983: 979: 975: 971: 967: 963: 956: 954: 952: 943: 939: 935: 931: 924: 916: 912: 908: 904: 897: 889: 885: 881: 877: 873: 869: 861: 853: 849: 845: 841: 837: 833: 826: 817: 812: 808: 804: 800: 793: 787: 782: 775: 771: 766: 760:June 6, 2005. 759: 755: 754:archive.today 751: 748: 744: 739: 730: 720: 711: 703: 699: 695: 691: 687: 683: 679: 675: 668: 654:on 2013-01-28 653: 649: 643: 637: 632: 623: 618: 614: 610: 606: 599: 590: 584: 578: 574: 564: 561: 559: 556: 554: 551: 549: 546: 544: 541: 539: 536: 534: 531: 530: 521: 519: 515: 512: 511: 510: 502: 500: 496: 495:deep learning 492: 488: 484: 480: 476: 472: 470: 465: 462: 458: 454: 450: 446: 442: 438: 437:deep learning 432: 431:Deep learning 423: 414: 412: 408: 404: 400: 396: 392: 388: 384: 380: 375: 371: 366: 362: 354: 350: 348: 344: 340: 336: 334: 329: 325: 321: 319: 314: 310: 306: 302: 298: 294: 292: 287: 283: 278: 274: 272: 267: 266:preprocessing 263: 259: 256:of a labeled 255: 251: 247: 241: 224: 221: 218: 215: 213: 210: 208: 205: 203: 200: 199: 198: 196: 190: 182: 180: 176: 172: 167: 163: 160: 156: 151: 147: 143: 139: 135: 131: 126: 124: 119: 117: 113: 109: 105: 100: 90: 87: 82: 73: 69: 66: 57: 48: 46: 42: 38: 33: 29: 25: 21: 1517: 1510: 1477: 1473: 1467: 1442: 1438: 1432: 1407: 1403: 1397: 1352: 1348: 1338: 1303: 1297: 1280: 1276: 1270: 1253: 1249: 1243: 1198: 1194: 1184: 1159: 1155: 1149: 1130: 1126: 1116: 1099: 1095: 1088: 1069: 1063: 1038: 1034: 1008: 1004: 998: 965: 961: 933: 929: 923: 906: 902: 896: 871: 867: 860: 838:(1): 59–68. 835: 831: 825: 809:(1): 25–33. 806: 803:High Voltage 802: 792: 781: 773: 765: 757: 738: 729: 719: 710: 677: 673: 667: 656:. 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Index

control engineering
fault

mathematical
time domain reflectometry
mechanical engineering
vibration
thermal imaging
spectral analysis
wavelet analysis
RPM
FFT
FFT
harmonics
sidebands
beat frequency
FFT
FFT
RPM
STFT
Gabor transform
FFT
maintenance, repair and operations
Condition-based maintenance
Planned preventive maintenance
Preventive maintenance
Corrective maintenance
Integrated vehicle health management
Machine learning
mathematical classification models

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