Estimating Wind Turbine Failure Quantiles via Non-Integer Bootstrap Methodology

Statistical Reliability Meets Wind EnergySemester 2 PresentationPresenter: Michael S. CzahorPhD Candidate: WESEP &StatisticsMajor Professor: Dr. William Q. Meeker

Presentation Date: April 17th 2014

1Quick Review from Semester 1Prevent unplanned maintenance via the use of statistical analysisBig DataFailure Modes/DetectionBegin Analysis Non-Parametrically

2Benefits of Early DetectionLimit downtower repairsEliminate expedited crane chargesMinimize downtime and optimize planning for low wind repairs

3Semester 2 OverviewStatistics 533 (Reliability) in relation to researchStrategy for Data Analysis, Modeling and InferenceBootstrapping with Non- Integer Weights Relate small simulation study to Wind Energy through estimation of quantiles.Model-free graphical data analysis. Model fitting (parametric, including possible use of prior information). Inference: estimation or prediction (e.g., statistical intervals to reflect statistical uncertainty/variability). Graphical display of model-fitting results. Graphical and analytical diagnostics and assessment of as- sumptions. Sensitivity Analysis. Conclusions.

4Reasons for Collecting Reliability DataAssessing characteristics of materialsPredict product reliability in design stageAssessing the effect of a proposed design changeComparing 2 or more different manufacturers Assess product reliability in fieldChecking the veracity of an advertising claimPredict product warranty costs

Slide: 1-5 From Dr. Meekers Statistics 533 at Iowa State5Probability Plotting

Slide 6-10 from Dr. Meeker Stat 533 at Iowa StateProbability plots are used to: Assess the adequacy of a particular distributional model. To detect multiple failure modes or mixture of different populations. Displaying the results of a parametric maximum likelihood fit along with the data. Obtain, by drawing a smooth curve through the points, a semiparametric estimate of failure probabilities and distri- butional quantiles. Obtain graphical estimates of model parameters (e.g., by fitting a straight line through the points on a probability plot).

6Functions of the Parameters Cumulative distribution function (cdf) of T F(t;)=Pr(T t), t>0. The p quantile of T is the smallest value tp such that F(tp;) p.

Estimating quantiles (fraction failing as a function of time) The estimation will provide the corresponding time scale value

Standard convention Bullet point 2

Questions:Hazard function at a certain time propensity of failure in the next small interval of time given survival to time tProbability of Failing before a certain time.Proportion of units failing within a certain amount of timeTime to first failure

Example: t.20 time at which 20% will fail tp=F^-1(p)

7Reliability in Wind TurbinesHigh repair costAnalyze stresses affecting the critical componentsUse of sensors to send data to centralized locationsSystem Retirement Detect unsafe operating conditionsPrognostic Purposeswould be to prevent in-service failures, unplanned maintenance, and especially system failures that could cause serious loss of property or lives. There are also needs to plan for system retirement and predictions of future financial needs and obligations (e.g., warranty costs). This section describes some of the particular applications of field data and explains how and why modern SOE data will be able to do a much better job.

prognostic purposes to provide short-term predictions about the remaining life of a system.

8Component Reliability I

Wind energy statistics in Finland: http://www.vtt.fi/proj/windenergystatistics/?lang=en [accessed 06/11/2013].

Downtime and failure frequency for each component in a wind turbine

Production1992 Failure199672 Wind Turbines Overall 116Disturbance time of difference components as a function of lifetime of turbines

Develop Systematic Methodologies for preventative maintenance 147 MW By 2009

73 MW from 600KW 1MW 2.3MW1014 KW/WT Average of 175-200 hours/year/turbine

Technical Failures= 60% 152428/253789Minor Disturbance=29%Maintenance=4%Network=2%

9Component Reliability II

Wind energy statistics in Finland: http://www.vtt.fi/proj/windenergystatistics/?lang=en [accessed 06/11/2013].

Component Downtime

-Gear Failure- Largest amount of time---Long repair time-Generator-Changing of slip rings due to wear and tear-Rotor Blade/Pitch Mechanism- 51 out of 72 turbines 16 used active stallpitching is often related to failures in hydraulic system-Electrical System- Small in size cheap so can keep spare parts.burned cables-Brakes- Mechanical Brake 2500 hours- adjustment and replacement of breaking pads(easy to predict) Aero/Tip Brake 13500 hours- rare- as pitching is used this problem will fade awayHyrdraulic SystemPumps/oil leakages

10Converting Data Into Information

Reliability ManagementReactive: Trending, Analysis, TroubleshootingProactive: Failure predictors, Reliability Centered Maintenance Data: Provided byShell Corporation11

Data: Provided byShell CorporationConverting Data Into Information12Brief Statistics ReviewWhen estimating something the estimate will have uncertainty due to limited amounts of data.The estimate will be within some amount of the true parameter value. Crude approximation via normal intervalMore sophisticated methods through simulation (e.g. bootstrapping) Datamustbefromarandomsamplefromlargepopulation Observationsinthesamplemustbeindependentofeachother nsmall,populationdistributionmustbeapproximatelynormal nlarge,populationneednotbeapproximatelynormal(CLTkicksin)Astatisticalprocedureissaidtoberobustiftheresultsoftheprocedurearenotaffectedverymuchwhentheconditionsforvalidityareviolated.13Brief Statistics ReviewCoverage probability: This term refers to the probability that a procedure for constructing random regions will produce an interval containing, or covering, the true value. It is a property of the interval producing procedure, and is independent of the particular sample to which such a procedure is applied. We can think of this quantity as the chance that the interval constructed by such a procedure will contain the parameter of interest.Confidence level: The interval produced for any particular sample, using a procedure with coverage probability p, is said to have a confidence level of p; hence the term confidence interval. Note that, by this definition, the confidence level and coverage probability are equivalent before we have obtained our sample. After, of course, the parameter is either in or not in the interval, and hence the chance that the interval contains the parameter is either 0 or 1.

Actual Coverage Probability- probability that the procedure will result in an interval containing the quantity of interest

Level of Confidence- Expresses ones confidence (not probability) that a specific interval contains the quantity of interest

14Background on BootstrappingStep 1: When given n data objects, how can we estimate the parameter of the population?Step 2: Resampling the data B times with replacement. From here we can get many resampling data.Step 3: Regard X1, X2,., Xn as the new population and resample it B times with replacement, X1*,X2*,.. Xn*~Fn(x). We can then calculate statistics.

When exact statistical interval procedures are not readily available, one generally has to use an approximatemethod resulting in a procedure that will have actual coverage probability approximate to the nominal coverage probability.

In practice we cant repeat the sampling process over and over. We can simulate the process and use the info from the distribution of the appropriate statistics. Reduce reliance on crude large sample approximations.

Nonparametricallytheta is directly from the dataNo assumptions about underlying distribution of data

Integer Weights---some are 0 completely ignored

Continuous Weights---Each has a contribution Data are censored and few noncensored observations Logistic regression where probability of a response tends to have high or low success Analysis of data from designed experiments where # of parameters is close to number of observational units

15BCa Percentile MethodThe bootstrap bias-corrected accelerated (BCa) interval is a modification of the percentile method that adjusts the percentiles to correct for bias and skewness.Transform follows a normal distribution with median equal to transformed median of boot distribution of quantity of interestand a variance that does not depend on QOI

Adjusts for both bias and variance dependency

b^ is fraction of B values less than theta^z(b^) corrects for median biasa^ is acceleration constant and corrects for dependence of variance

16BCa Percentile Method(Reference Material)

17BCa Percentile Method(Reference Material)

18BCa Percentile Method(Reference Material)

19BCa Percentile Method(Reference Material)

20BCa Percentile Method

Smooth- Create and approximating function that attempts to capture important patterns in the data while leaving out noise.

Being able to extract more info from data as long as the assumption of smoothing is reasonableBeing able to provide analyses that are both flexible and robust

21Warnings on Non-Parametric Bootstrap MethodsDoes not require on to assume a statistical distribution underlying observed data.Observations come from a distribution with a finite variance.Observations are independent.Number of observations in the dataset is sufficiently large.

STATISTICAL INTERVALSA Guide for PractitionersSecond EditionCopyright 2014 G. J. Hahn, W. Q. Meeker, and L. A. Escobar.To be published by John Wiley & Sons Inc. in 2015.A key advantage of using nonparametric bootstrap methods to construct statistical intervals, as compared, for example, tothe parametric bootstrap methods (to be discussed subsequently in this chapter) is that they do not require one to assume astatistical distribution underlying the observed data.

The statistical theory that justifies the use of the nonparametric bootstrap,however, does depend on several other conditions. These include that.22ConclusionNeed to:Review more papersKeep working in RAcquire DataSummer PlansMasters written ExamResearchPrepare for PhD Qualifier 23

24ReferencesG. J. Hahn, W. Q. Meeker, and L. A. Escobar. STATISTICAL INTERVALS A Guide for Practitioners Second Edition Copyright 2014.To be published by John Wiley & Sons Inc. in 2015.PAGANO, M., and GAUVREAU, K. (1993) Principles of Biostatistics. Wadsworth Belmont California, USA.Shell Corporation: 2013 Sandia National Laboratories Wind Plant Reliability Workshop Wind energy statistics in Finland: http://www.vtt.fi/proj/windenergystatistics/?lang=en [accessed 06/11/2013].

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