Fault Detection and Prediction in Off-shore Wind Turbines
Jürgen Herp
1, Esmaeil S. Nadimi
2†, John Hallam
3†Mærsk Mc-Kinney Møller Institute, Syddansk University, DK-5000, Odense
1 herp@mmmi.sdu.dk, 2 esi@mmmi.sdu.dk, 3 john@mmmi.sdu.dk
† Supervisor
1. Motivation
I Wind Turbines (WT) are one of the fastest growing renewable energy sources. However to make wind power competitive with other sources of energy, availability, reliability and the life of turbines will all need to be improved, especially in harsh off-shore environments [1]. Condition monitoring is a tool commonly employed for the early detection of faults & failures so as to minimise downtime and maximize productivity [2].
I Of course, some WT components fail earlier than expected and, because unscheduled down- time can be costly, condition monitoring systems are employed to improve WT availability and reduce the operations and maintenance costs. However there is a degree of uncertainty about
the appropriateness of applying specific maintenance policies to WT components. [1, 2] Figure: World wide overall and annual installed wind energy capacity. Global Wind Statistics 2011
2. Maintenance Theory & Conditioned Monitoring
Fault detection
Fault
location Dismantle Repair/Replace Assembly
Test Varification
Dismantle Repair/Replace Assembly Test Varification
Figure: [top] Corrective and [bottom] preventive maintenance.
I Classical theory sees maintenance as either corrective or preventive. The former is carried out when turbines break down and when faults are detected or failures occur in any of the components. [1]
I By contrast, the objective behind preventive maintenance is to either repair or replace components before they fail [1]. But reducing failures in this way comes at the cost of completing maintenance tasks more frequently than absolutely necessary and not exhausting the full life of the various components already in service. An alternative is to mitigate against major component failure and system breakdown with condi- tion based maintenance in which continuous monitoring and inspection techniques are employed to detect incipient faults early, and to determine any necessary maintenance tasks ahead of failure.
I Condition monitoring systems (CMS) comprise combinations of sensors and signal processing equipment that provide continuous indications of component condition based on techniques including vibration analysis, acoustics, oil analysis, strain measurement and thermography.
I Regardless of the technique, the capability of a CMS relies upon two basic elements: the number and type of sensors, and the associated signal processing and simplification methods utilized to extract important information from the various signals (statistical models, FFT, trend analysis, time-domain analysis, etc.).
I With good data acquisition and appropriate signal processing, faults can thus be detected while components are operational and appropriate actions can be planned in time to prevent damage or failure of components.
Figure: One-to-many relationship of condition mon- itoring techniques and their applications to turbine components. Kusiak et al.
3. Problem Formulation
I To verify the quality level of a WT in a very short time, tests are conducted and the recorded data are provided for this project.
I The scope of this Ph.D. project is to develop a novel method capable of detecting and predicting WT faults at an early stage during test or operations to prevent the occurrence of faults (i) in both foreseen and unforeseen events, (ii) in both test platform and the device under the test, and (iii) at both component and system level.
I The strategy and challenge for handling the task is to find meaningful parameters for fault indication, adopted and develop methods for signal-analysis and pattern recognition, as well as handling the huge amount of data.
I Due to the inherent complexity of characterizing the normal WT behaviour, the problem of fault detection (FD) can be approached from many angles such as random matrix theory, statistical analysis, machine learning, etc.
4. Statistical Analysis
Figure: Effect of using the T 2 and Q statis- tics as fault detection indices. Penha et al.
0 200 400 600 800 0
0.5 1 1.5 2
overservation number
GLRdecisionfunction
h(α)
Figure: GLR testing on pseudo generated data.
I In the absence of a process model, principal component analysis has been suc- cessfully used as a data-based FD technique for highly correlated process variables [4]. Common statistical measurements are T 2 and Q statistics, however, given the nature of falls alarms one could consider generalized likelihood ratio (GLR) testing of hypothesis.
I The sample matrix X can be expressed using singular value decomposition X = TP0, where T contains the principal components (PC).
I In the case of collinear process variables a smaller number l of PC are needed to capture most of the variations in the data, the rest is considered noise. Various method exists to determine l. [4]
I The residuals e are supposed to satisfy either H0 = e ∼ N (0, σ2In) or H1 = e ∼ N (θ 6= 0, σ2In), depending on a minimum false alarm probability h(α), such that
δ(e) =
H0 if L(e) < h(α)
H1 else.
(1)
Here L(e) is the maximum likelihood estimation
L(e) = likelyhood to observe e when H1
likelyhood to observe e when H0.
(2)
5. Random Matrix Theory
I Let fault free data be X ∈ Rn×m with n observations, m variable, E[xij] = 0, E[xij2] = 1, limited fourth-order moments.
The correlation matrix C ≡ Corr(X) = XX0 can then be decomposed. For identical independent distributed entries xij as n, m → ∞ with n/m → c ∈ (0, ∞) the empirical spectral distribution converges almost surely to
ρ(λ) = (1 − c−1)+δ(λ) + 1 2πc
p(λ+ − λ)+(λ − λ−)+
λ ,
(3)
where λ± = (1 ± √
c)2 for the limited ratio c. Eq. (3) is known as Marˇcenko-Pastur law.
I Consider now data apart from just containing noise, it is believed that extreme empirical eigenvalues leave the support of eq. (3), and thus indicates a fault or abnormal behaviour. [3]
I In this project, the properties of the extreme eigenvalues of the correlation matrix collected from extensive WT data will be used to provide FD tests.
I For failure localization, information on the eigenvalue position can be used to reduce the number of hypotheses.
I However, tests only based on the limiting properties of the eigenvalues, will almost surely, turn out to be inefficient for which novel results on the eigenspaces and eigenvectors associated with these eigenvalues should be developed.
0 1 2 3 4
0 0.5 1
−4 −2 0 2
0 0.2 0.4
−4 −2 0 2 4
0 0.2 0.4
Figure: [left] Marˇcenko-Pastur law with 20000 × 2000 data X, [center] comparison of the empirical distribution of largest eigenvalue in the support of eq. (1) with the Tracy-Widom density, and [rigth] comparison of the empirical distribution of largest eigenvalue outside the support of eq. (1) with the Tracy-Widom density.
6. References
[1] M. Wilkinson, F. Spianto, and M. Knowles. Towards the zero maintenance wind turbine. In Universities Power Engineering Conference, 2006. UPEC ’06. Proceedings of the 41st International, volume 1, pages 74–78, 2006.
[2] Fausto Pedro García Márquez, Andrew Mark Tobias, Jesús María Pinar Pérez, and Mayorkinos Papaelias. Condition monitoring of wind turbines: Techniques and methods. Renewable Energy, 46(0):169 – 178, 2012.
[3] Alan Edelman and Yuyang Wang. Random matrix theory and its innovative applications. In Advances in Applied Mathematics, Modeling, and Computational Science 66, pages 91–116, 2013.
[4] I.T. Jolliffe. Principal Component Analysis. Springer Series in Statistics. Springer, 2002.
Acknowledgements
This work is partially supported by LORC and SIEMENS Wind Power.
