Vibration-Response-Based Damage Detection For Wind Turbine Blades Under Varying Environmental Conditions

Transcription

1 Vibration-Response-Based Damage Detection For Wind Turbine Blades Under Varying Environmental Conditions Ana Gómez González Spilios D. Fassois Stochastic Mechanical Systems & Automation (SMSA) Laboratory University of Patras. Web: Contact: Ruzgem 2013, Ankara October 3rd-4th Vu Pham Damage detection in wind turbine blades

2 Outline 1. Introduction 2. Methodology Baseline Inspection 3. Experimental set-up 4. Results 5. Conclusions

3 1 Introduction Need for Structural Health Monitoring. Real structures are subject to changes in environmental and operational conditions. This limitation of several damage detection methodologies restricts their applicability. Different approaches are available to take into account this effects: normalization techniques (Sohn 2007). In general a big bank of data under normal condition is needed. Two main groups can be distinguished.

4 1 Introduction Model the dependence of the environmental and/or operating conditions on the dynamics Multi-model approaches (Sohn et al 1999, Worden et al 2002). Global-model approaches (Hios et al 2009). Look for a characteristic insensitive to environmental variations but still sensitive to damage Outlier analysis (Manson et al 2002). Discriminant analysis (Manson et al 2004). Principal component analysis (Yan et al 2005, Bellino et al 2010, Manson et al 2002). Factor analysis (Deraemaecker et al 2008). Cointegration (Cross et al 2011).

5 1 Introduction Our contribution will be on a method from the second class based on Principal Component Analysis. The main difference with existing methods relies on the specific selection of certain components more sensitive to damage. The presented method belongs to the category of vibration response based (output-only) methods. Application field: wind turbines blades (Ganeriwala et al 2011, Rumsey et al 2008).

6 2 Methodology - baseline Selection of components non containing variability with respect to environment but sensitive to damage. Feature vector: θ Welch PSD estimate at n selected frequencies. Two sets of feature vectors are used in the baseline phase, a healthy set Θ 0 composed of ρ 0 data records (from the healthy structure at different environmental conditions), and a damaged set Θ d consisting of ρ d data records (also at different environmental conditions).

7 2 Methodology - baseline Step 1: Estimation of the feature covariance matrix. (set Θ 0 ) θ = 1 ρ 0 θ, P = θ Θ 0 θ θ (θ θ) T θ Θ 0 ρ 0 1 R n n. Step 2: Principal Component Analysis. (Jollife, 2010). P = U Λ U T, Λ = diag λ 1,, λ n R n n, U = u 1 u n R n n. Transformation into principal components for any feature vector θ: s = U T θ θ R n, For elements in Θ 0 warrants a sample mean of 0 and diagonal covariance matrix Λ.

8 2 Methodology - baseline Step 3: Dimensionality reduction. Look for components with the desired behavior. The first n components are discarded and n 0 components are to be kept from the set {s n+1,, s n } with indexes b 1,, b(n 0 ). The selection of the specific components will be based on computation of Mahalanobis distance D j 2 (θ). Step 3a: Selection of n: Given 0 < δ < 1, n is chosen as the minimum value verifying: n j=1 λ j n j=1 λ j δ.

9 2 Methodology - baseline Steps 3b-3d: Selection of specific components. Based on the two sets Θ 0 and Θ d and the following ratio: where: R j = min θ Θ d D j 2 (θ) max θ Θ0 D j 2 (θ), D 2 j (θ) = s T j Λ 1 j s j s j = U T j θ θ R j Λ j = diag λ b 1,, λ b j R j j U j = u b 1 u b j R n j An increase of the ratio for the addition of a new component implies a better performance.

10 2 Methodology - inspection Given a new θ u in an unknown state: is computed. s n0 = U T n0 θ u θ R n 0, U n0 = u b 1 u b n0 R n n 0 The squared Mahalanobis distance with respecto to set Θ 0 is: D 2 n0 θ u = s T n0 Λ 1 n0 s n0, Λ n0 = diag λ b 1,, λ b n0 R n 0 n 0. Each principal component is a linear combination of random variables normality may be assumed. The squared Mahalanobis distance is then χ 2 (n 0 ) (sum of n 0 squared N(0,1) and mutually independent random variables).

11 2 Methodology - inspection Hypothesis test: H 0 : D n0 (θ u ) = 0 (null hypothesis healthy) H 1 : Else (alternative hypothesis damaged) Since D 2 n0 ~χ 2 n 0 for a selected α risk level, the quantity D 2 2 n0 (θ u ) should be in the range 0, χ 1 α n 0 so: D 2 n0 (θ u ) χ 1 α (n 0 ) Healthy structure Else Damaged structure 2 where χ 1 α (n 0 ) denotes the critical point of the χ 2 distribution with n 0 degrees of freedom at level 1 α.

12 3 Experimental set-up The blade Length 0.77 m Max width m Mass kg The damages D1: 2.5 mm radius D2: 2.5 mm depth 1.5 cm long

13 3 Experimental set-up The experiments Blade Health State Temperature step Number of cases (Temperature range: ºC) Number of experiments (per temperature) Baseline Inspection Total number of experiments (data records) Baseline Inspection Healthy Step 2ºC 21 cases Healthy with water Step 4ºC 11 cases Damage 1 Step 4ºC 11 cases Damage 2 Step 2ºC 21 cases Damage 2 with water Step 4ºC 11 cases Sampling frequency f s = Hz Bandwidth Hz Signal length N = samples (6.4 s)

14 4 Results Determination of n Inclusion of new components

15 4 Results n 0 = 1 n 0 = 22 n 0 = 11

16 4 Results Output 1

17 4 Results Output 2

18 4 Results Output 3

19 4 Results Output 4

20 4 Results Detailed SHM results for each sensor position distinguishing the two levels of damage severity (inspection data records only). Sensor False False alarm Undetected damages Detection rate alarms rate D1 D2 D1 D2 1 35/ % 0/385 1/ % 99.9% 2 73/ % 0/385 3/ % 99.7% 3 34/ % 0/385 21/ % 98.1% 4 22/ % 0/385 0/ % 100.0% The number of false alarms is quite high for some outputs, by different methods for selecting the specific n 0 components, this can be improved.

21 5 Conclusions A vibration-response-based statistical time series type damage detection methodology, capable of operating under varying environmental and operational conditions, has been postulated based on PSD and PCA. The methodology is characterized by conceptual and computational simplicity. The methodology proved effective, exhibiting a detection rate over 98% and a corresponding false alarm rate below 7%.

22 Acknowledgement The support of this work by the EU FP7 ITN project SYSWIND (Grant ) is gratefully acknowledged.

23 Questions? Thank you for your attention