quickest change detection with applications on wind turbine … · 2018-12-14 · analysis,...

Quickest Change Detection with Applications on Wind Turbine Fault Detections

Dr. Jingxian WuDepartment of Electrical Engineering

University of ArkansasU.S.A.

Forum for Electromagnetic Research Methods and Application Technologies (FERMAT)

Copyright

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© The use of this work is restricted solely for academic purposes. The author of this work owns the copyright and no reproduction in any form is permitted without written permission by the author.

Abstract

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Quickest change detection (QCD) aims to minimize the detection delay of an abrupt change inprobability distributions of a random process, subject to certain performance constraints such as theprobability of false alarm (PFA). It has a wide range of applications, such as wireless network dataanalysis, intrusion detection, anomaly detection, quality control, financial market analysis and medicaldiagnosis, etc. In this talk I will first give an overview of existing quickest change detection algorithmsand discuss some of our recent results. Then I will present the application of QCD on the detection ofbearing faults of wind turbines (WT). The QCD algorithm is developed by analyzing the statisticalbehaviors of stator currents generated by the WTs. It is discovered that, at a given frequency, theamplitude of stator current follows the Gamma distribution, and the presence of fault will affect theparameters of the Gamma distribution. Since the signature of a fault can appear in one of multiplepossible frequencies, we need to monitor the signals on multiple frequencies simultaneously, and eachpossible frequency is denoted as a candidate. Based on the unique properties of WT bearing faults, wepropose a new multi-candidate QCD (MC-QCD) algorithm that can combine the statistics of signalsfrom multiple candidate frequencies. The new algorithm does not require a separate training phase, andit can be directly applied to the stator current data and perform online detection of various possiblebearing faults. The theoretical performance of the proposed algorithm is analytically identified in theform of upper bounds of the PFA and average detection delay (ADD).

Index Terms: Quickest change detection (QCD), wind turbines (WT), Change point detection

Biography

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Jingxian Wu received the B.S. degree in Electrical Engineering from Beijing University of Aeronautics and Astronautics, Beijing, China, in 1998, the M.S. degree in Electrical Engineering from Tsinghua University, Beijing, China, in 2001, and the Ph.D. degree in Electrical Engineering from the University of Missouri, Columbia, in 2005. He is currently an Associate Professor with the Department of Electrical Engineering, University of Arkansas. His research interests mainly focus on statistical signal processing, large scale data analytics, and wireless communications. He served as a symposium or track cochair for various international conferences, including the 2012 IEEE International Conference on Communication, the 2009, 2015, and 2017 IEEE Global Telecommunications Conference, etc. He is an Associate Editor of the IEEE ACCESS, and served as an Editor of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 2011 to 2016, and an Associate Editor of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY from 2007 to 2011.

UNIVERSITY OF ARKANSAS

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UNIVERSITY OF ARKANSAS

• Established in 1871• The flagship university in the state of Arkansas• Student population: ~30,000• Academic staff: 1,000+, administrative staff: 2,900+• Colleges and Schools

– Arts and Sciences, Agriculture, Architecture, Business, Engineering, Education & Health Professions, Food and Life Science, Law

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COLLEGE OF ENGINEERING

• The only comprehensive engineering program in the state• 2,500+ undergraduate students and ~1,000 graduate students• 100+ tenured/tenure track faculty members• Departments

– Biomedical, biology, chemistry, civil, computer science and computer engineering, electrical, industrial, mechanical

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ELECTRICAL ENGINEERING

• Over 100 years in history• 16 tenured/tenure track faculty

– 3 IEEE Fellows, 1 NAI Fellow

• Undergraduates: 250+; graduates: 120+

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INTELLIGENT INFORMATION PROCESSING LAB• Director: Jingxian Wu

– 5 Ph.D., 1 M.S., • Sponsor: NSF, NIH, DoD, DoE, NASA, AT&T, DoEd, TI, …• Selected Research Projects

– Low latency anomaly Detection (funded by NSF 2017)– Terahertz imaging for margin assessment of three dimensional breast cancer

tumors (funded by NIH 2017)– Cyber Security for Energy Delivery Systems (funded by DOE 2015)– Energy Aware Sparse Sensing (Funded by NSF 2014)– EEG Sensors for Brain Signal Processing (Funded by ABI 2014)– Distortion Tolerant Communications (Funded by NSF 2012)

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OUTLINE

• Change point detection– Introduction– Bayesian change detection– Minmax change detection– Impact of model mismatch of post-change distribution

• Quickest detection of wind turbine bearing faults– Data collection– Feature extraction– Statistical analysis of feature vector– Quickest fault detection– Simulation and Experiment Results

• Conclusions

CHANGE POINT DETECTION

• Change detection (or, change point detection，CPD)– Detect an abrupt change in a stochastic process

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Change point

The change can be due to a change in amplitude, mean, variance, or distribution, etc.

time

CHANGE POINT DETECTON

12change point


• Applications:– Finance

• stock market change from a bull market to a bear market– Wireless network

• User behavior and traffic statistics change over time– Surveillance

• target detection (change from no target to the presence of target)

– Intrusion detection • before intrusion, the data follows a certain probability

distribution• After intrusion, the data follows a different distribution

– Fault detection or anomaly detection• Normal data follows a certain distribution• Abnormal data follows a different distribution

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• Two types of change point detection– Offline detection

• A sequence of data has been collected before hand• Find the change point somewhere in the data sequence

– Online detection• The data are collected sequentially as time goes on.• New data are used to update certain test statistics• Use test statistics to determine whether a change has occurred

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• Tradeoff in online change detection– Probability of false alarm (PFA): the probability that the true

change point occurs after the detected change point

– Detection delay (DD): once the change point happens, how much longer it takes to identify the change point

– E.g. if we never detect the change point, then PFA = 0 and DD is infinity

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• Preliminaries– Consider a random process:– There is an unknown change point:

– The change point is random• Prior distribution of the change point

16Change point


• Metrics: for a given detection procedure

– Probability of false alarm (PFA)

– Average detection delay (ADD)

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• Problem formulation– Find the detection procedure

• Minimize:

Subject to:

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• Cumulative sum (CUSUM) Procedure

– Where

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E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, pp. 100-115, 1954.


• Shiryaev-Roberts Procedure

– Where

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S. W. Roberts, “A comparison of some control chart procedures,” Technometrics, vol. 8, pp. 411-430, 1966.


• Performance comparisons– Shiryaev procedure (Bayesian detection)

– CUSUM and Shiryaev-Roberts Procedure (Minmax criterion)

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A. G. Tartakovsky, and V. V. Veeravalli, “General asymptotic Bayesian theory of quickest change detection,” Theory Probab. Appl., vol. 49, pp. 458-497, 2005.


• Mismatched post-change model– It is usually difficult to get an accurate estimate of the post-change

distribution– Assume:

true model after change: estimated model after change:

– The Kullback-Leibler divergence between true and estimated models:

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• CUSUM Procedure with mismatched post-change model

– where

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• Lemma 1– The PFA of the CUSUM procedure with mismatched model is

upper bounded by

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The mismatched post-change model will not affect the PFA upper bound!


• Theorem 1– If , let As

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• Theorem 2– If . Let , then

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Data: two-dimensional multivariate Gaussian with zero-mean and covariance matrix

Before change:After change:

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OUTLINE

• Change point detection– Introduction– Bayesian change detection– Minmax change detection– Impact of model mismatch of post-change distribution

• Quickest detection of wind turbine bearing faults– Data collection– Feature extraction– Statistical analysis of feature vector– Quickest fault detection– Simulation and Experiment Results

• Conclusions

WIND TURBINE BEARING FAULT

• Direct drive wind turbine

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B. Courtice, “Rare earth magnets: not all new turbines areusing them.”, http://yes2renewables.org/2012/03/06/rare-earth-magnets-not-all-new-turbines-are-using-them/, 2012. Online;


• Bearing faults– Bearing: the part that connects the blade shaft and generator– Outer bearing fault:

– Inner bearing fault:

30X. Gong and W. Qiao, “Current-based mechanical fault detection for direct-drive wind tur-

bines via synchronous sampling and impulse detection,” IEEE Trans. Industrial Electron.vol. 62, no. 3, pp. 1693-1702, 2015


• Bearing faults– Ball fault

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WIND TURBINE BEARING FAULTS

• Bearing faults feature frequencies– Bearing faults introduce harmonics at different frequencies in the

stator currents– Frequencies due to various types of bearing faults

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• Experiment setup

33Wind tunnel with wind turbine under testing Data acquisition system


• Experiment setup– Lubricant on bearing was removed to accelerate degradation– One of the two bearings was removed to simulate eccentricity– Wind speed: 0 – 10 m/s– Sampling frequency: 10 KHz– Stator current was recorded in 100 second bursts every 20 minutes– Wind turbine stops rotating after 25 hours

34Bearing before and after the testing


• Data preprocessing:– 1. Synchronous resampling– 2. Frequency domain feature extraction– 3. Energy normalization

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• Preprocessing: Synchronous resampling

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Spectrogram before and after synchronous resampling


• Feature vector in the frequency domain

– The time is divided into frames, n is the index of frame– Each element in the feature vector is the amplitude of the stator

current at a given frequency.

– E.g. is the amplitude of the current on the j-th frequency and in the n-th frame

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STATISTICAL ANALYSIS

• Statistical modeling– It is found that the distribution of samples on a given frequency,

can be modeled by the Gamma distribution

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STATISTICAL ANALYSIS• Parameter estimation

– Use a sliding window to estimate the parameters of the j-th element at the n-th frame

– Assumption: when fault is NOT present, the data at different frequencies are i.i.d.

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HYPOTHESIS FORMULATION

• Hypothesis

– Since the power is normalized,

• Parameter estimation before change point

– Since the fault will be at one frequency at most. Even if the fault is present, it will have very small impact on the estimation of

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QUICKEST FAULT DETECTION

• Challenge:– The feature vector has dimension

w– Each dimension represents a frequency– The fault will happen in only one frequency– Each frequency is a candidate for faults, and there are multiple

candidates

• Solution: Multi-candidate quickest detection

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• Definition: Multi-candidate quickest detection– The detection procedure is

• Where

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• Theorem 1– Assume the elements in the feature vector are independent. The

probability of false alarm of the multi-candidate test procedure is upper bounded by

• Where is the prior mean of the change point

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• Theorem 2– Assume the elements in the feature vector are independent, and the

frames are independent in time. Let PFA < As

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EXPERIMENT RESULTS

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EXPERIMENT RESULTS

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EXPERIMENT RESULTS

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CONCLUSIONS

• Quickest change detection aims at minimizing the detection delay subject to certain contstraints, such as PFA.– Bayesian detection: Shiryaev procedure– Minmax detection: CUSUM procedure, Shiryaev-Roberts

procedure

• Identified the performance of CUSUM with mismatched post-change modes– The PFA upper bound is not affected .– The asymptotic ADD upper bound becomes larger.

• Quickest detection of bearing fault of wind turbine– Proposed a new multi-candidate quickest change detection (MC-

QCD) procedure

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REFERENCES – contd.[12] W. Yang, P. J. Tavner, and M. Wilkinson, “Condition monitoring and fault diagnosis of a wind turbine synchronous generatordrive train,” Renewable Power Generation, IET, vol. 3, no. 1, pp. 1–11, 2009.[13] F. Immovilli, A. Bellini, R. Rubini, and C. Tassoni, “Diagnosis of bearing faults in induction machines by vibration or currentsignals: A critical comparison,” Industry Applications, IEEE Transactions on, vol. 46, no. 4, pp. 1350–1359, 2010.[14] X. Gong and W. Qiao, “Current-based mechanical fault detection for direct-drive wind turbines via synchronous sampling andimpulse detection,” Industrial Electronics, IEEE Transactions on, vol. 62, no. 3, pp. 1693–1702, 2015.[15] X. Gong, W. Qiao, and W. Zhou, “Incipient bearing fault detection via wind generator stator current and wavelet filter,” inIECON 2010-36th Annual Conference on IEEE Industrial Electronics Society. IEEE, 2010, pp. 2615–2620.[16] I. S. Bozchalooi and M. Liang, “Parameter-free bearing fault detection based on maximum likelihood estimation anddifferentiation,” Measurement Science and Technology, vol. 20, no. 6, p. 065102, 2009.[17] H. Ocak and K. A. Loparo, “A new bearing fault detection and diagnosis scheme based on hidden markov modeling of vibrationsignals,” in Acoustics, Speech, and Signal Processing, 2001. Proceedings.(ICASSP’01). 2001 IEEE International Conference on, vol.5. IEEE, 2001, pp. 3141– 3144.[18] X. Zhang, R. Xu, C. Kwan, S. Y. Liang, Q. Xie, and L. Haynes, “An integrated approach to bearing fault diagnostics andprognostics,” in American Control Conference, 2005. Proceedings of the 2005. IEEE, 2005, pp. 2750–2755.[19] X. An, D. Jiang, and S. Li, “Application of back propagation neural network to fault diagnosis of direct-drive wind turbine,” inWorld NonGrid-Connected Wind Power and Energy Conference (WNWEC), 2010. IEEE, 2010, pp. 1–5. [20] Y. Wang and D. Infield,“Neural network modelling with autoregressive inputs for wind turbine condition monitoring,” in Sustainable Power Generation andSupply (SUPERGEN 2012), International Conference on. IET, 2012, pp. 1–6.[21] M.-S. An, S.-J. Park, J.-S. Shin, H.-Y. Lim, and D.-S. Kang, “Implementation of automatic failure diagnosis for wind turbinemonitoring system based on neural network,” in Multimedia and Ubiquitous Engineering. Springer, 2013, pp. 1181–1188.[22] A. G. Tartakovsky and G. V. Moustakides, “State-of-the-art in bayesian changepoint detection,” Sequential Analysis, vol. 29, no.2, pp. 125–145, 2010. [23] J. Wu and J. Yang, “Quickest change detection with mismatched postchange models,” arXiv preprintarXiv:1601.06868, 2016.

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quickest change detection with applications on wind turbine … · 2018-12-14 · analysis,...

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