Additive Multiplicative Kernel Regression

Description

An additive multiplicative kernel regression based on Lee et al. (2015).

Usage

AMK(
  trainX,
  trainY,
  testX,
  bw = "dpi_gap",
  nMultiCov = 3,
  fixedCov = c(1, 2),
  cirCov = NA
)

Arguments

Details

This function is based on Lee et al. (2015). Main features are:

• Flexible number of multiplicative covariates in each additive term, which can be set using nMultiCov.

• Flexible number and columns for fixed covariates, which can be set using fixedCov. The default option c(1,2) sets the first two columns as fixed covariates in each additive term.

• Handling the data with gaps when the direct plug-in estimator used in Lee et al. fails to return a finite bandwidth. This is set using the option bw = 'dpi_gap' for bandwidth estimation.

Value

a numeric vector for predictions at the data points in testX.

References

Lee, Ding, Genton, and Xie, 2015, “Power curve estimation with multivariate environmental factors for inland and offshore wind farms,” Journal of the American Statistical Association, Vol. 110, pp. 56-67, doi:10.1080/01621459.2014.977385.

Examples

data = data1
trainX = as.matrix(data[c(1:100),2])
trainY = data[c(1:100),7]
testX = as.matrix(data[c(101:110),2])
AMK_prediction = AMK(trainX, trainY, testX, bw = 'dpi_gap', cirCov = NA)

Power curve comparison

Description

Power curve comparison

Usage

ComparePCurve(
  data,
  xCol,
  xCol.circ = NULL,
  yCol,
  testCol,
  testSet = NULL,
  thrs = 0.2,
  conflevel = 0.95,
  gridSize = c(50, 50),
  powerbins = 15,
  baseline = 1,
  limitMemory = TRUE,
  opt_method = "nlminb",
  sampleSize = list(optimSize = 500, bandSize = 5000),
  rngSeed = 1
)

Arguments

Value

a list containing :

• weightedDiff - a numeric, % difference between the functions weighted using the density of the covariates

• weightedStatDiff - a numeric, % statistically significant difference between the functions weighted using the density of the covariates

• scaledDiff - a numeric, % difference between the functions scaled to the orginal data

• scaledStatDiff - a numeric, % statistically significant difference between the functions scaled to the orginal data

• unweightedDiff - a numeric, % difference between the functions unweighted

• unweightedStatDiff - a numeric, % statistically significant difference between the functions unweighted

• reductionRatio - a list consisting of shrinkage ratio of features used in testSet

• mu1 - a vector of prediction on testset using the first data set

• mu2 - a vector of prediction on testset using the second data set

• muDiff - a vector of the difference in prediction (mu2 - mu1) for each test point

• band - a vector for the confidence band at all the testpoints for the two functions to be the same at a given cofidence level.

• confLevel - a numeric representing the statistical significance level for constructing the band

• testSet - a vector/matrix of the test points either provided by user, or generated internally

• estimatedParams - a list of estimated hyperaparameters for the Gaussian process model

• matchedData - a list of two matched datasets as generated by covariate matching

References

For details, see Ding et al. (2021) available doi:10.1016/j.renene.2021.02.136.

Examples

data1 = data1[1:100, ]
data2 = data2[1:100, ]
data = list(data1, data2)
xCol = 2
xCol.circ = NULL
yCol = 7
testCol = 2
testSet = NULL
thrs = 0.2
confLevel = 0.95
gridSize = 20
function_comparison = ComparePCurve(data, xCol, xCol.circ, yCol,
testCol, testSet, thrs, confLevel, gridSize)

Percentage weighted difference between power curves

Description

Computes percentage weighted difference between power curves based on user provided weights instead of the weights computed from the data. Please see details for more information.

Usage

ComputeWeightedDifference(
  muDiff,
  weights,
  base,
  statDiff = FALSE,
  confBand = NULL
)

Arguments

Details

The function is a modification to the percentage weighted difference defined in Ding et al. (2021). It computes a weighted difference between power curves on a testset, where the weights have to be provided by the user based on any probability distribution of their choice rather than the weights being computed from the data. The weights must sum to 1 to be valid.

Value

a numeric percentage weighted difference or statistical significant percetage weighted difference based on whether statDiff is set to FALSE or TRUE.

References

For details, see Ding et al. (2021) available at doi:10.1016/j.renene.2021.02.136.

Examples

ws_test = as.matrix(seq(4.5,8.5,length.out = 10))

userweights = dweibull(ws_test, shape = 2.25, scale = 6.5) 
userweights = userweights/sum(userweights) 
data1 = data1[1:100, ]
data2 = data2[1:100, ]
datalist = list(data1, data2)
xCol = 2
xCol.circ = NULL
yCol = 7
testCol = 2
output = ComparePCurve(data = datalist, xCol = xCol, yCol = yCol, 
testCol = testCol, testSet = ws_test) 
weightedDiff = ComputeWeightedDifference(output$muDiff, userweights, output$mu1)
weightedStatDiff = ComputeWeightedDifference(output$muDiff, userweights, output$mu1, 
statDiff = TRUE, confBand = output$band)

Covariate Matching

Description

The function aims to take list of two data sets and returns the after matched data sets using user specified covariates and threshold

Usage

CovMatch(data, xCol, xCol.circ, thrs, priority)

Arguments

Value

a list containing :

• originalData - The data sets provided for matching

• matchedData - The data sets after matching

• MinMaxOriginal - The minimum and maximum value in original data for each covariate used in matching

• MinMaxMatched - The minimum and maximum value in matched data for each covariates used in matching

References

Ding, Y. (2019). Data Science for Wind Energy. Chapman & Hall, Boca Raton, FL.

Examples

data1 = data1[1:100, ]
data2 = data2[1:100, ]
data = list(data1, data2)
xCol = 2
xCol.circ = NULL
thrs = 0.1
priority = FALSE
matched_data = CovMatch(data, xCol, xCol.circ, thrs, priority)

KNN : Fit

Description

The function models the powercurve using KNN, against supplied arguments

Usage

KnnPCFit(data, xCol, yCol, subsetSelection = FALSE)

Arguments

Value

a list containing :

• data - The data set provided by user

• xCol - The column number of features provided by user or the best subset column number

• yCol - The column number of target provided by user

• bestK - The best k nearest neighbor calculated using the function

• RMSE - The RMSE calculated using the function for provided data using user defined features and best obtained K

• MAE - The MAE calculated using the function for provided data using user defined features and best obtained K

Examples

data = data1[c(1:100),]
xCol = 2
yCol = 7
subsetSelection = FALSE

knn_model = KnnPCFit(data, xCol, yCol, subsetSelection)

KNN : Predict

Description

The function can be used to make prediction on test data using trained model

Usage

KnnPredict(knnMdl, testData)

Arguments

Value

a numeric / vector with prediction on test data using model generated by KnnFit

Examples

data = data1[c(1:100),]
xCol = 2
yCol = 7
subsetSelection = FALSE

knn_model = KnnPCFit(data, xCol, yCol, subsetSelection)
testData = data1[c(101:110), ]

prediction = KnnPredict(knn_model, testData)

KNN : Update

Description

The function can be used to update KNN model when new data is provided

Usage

KnnUpdate(knnMdl, newData)

Arguments

Value

a list containing :

• data - The updated data using old data set and new data

• xCol - The column number of features provided by user or the best subset column number

• yCol - The column number of target provided by user

• bestK - The best k nearest neighbor calculated for the new data using user specified features and target

Examples

data = data1[c(1:100),]
xCol = 2
yCol = 7
subsetSelection = FALSE

knn_model = KnnPCFit(data, xCol, yCol, subsetSelection)
newData = data1[c(101:110), ]

knn_newmodel = KnnUpdate(knn_model, newData)

Smoothing spline Anova method

Description

Smoothing spline Anova method

Usage

SplinePCFit(data, xCol, yCol, testX, modelFormula = NULL)

Arguments

Value

a vector or numeric predictions on user provided test data

Examples

data = data1[c(1:100),]
xCol = 2
yCol = 7
testX = data1[c(101:110), ]
Spline_prediction = SplinePCFit(data, xCol, yCol, testX)

SVM based power curve modelling

Description

SVM based power curve modelling

Usage

SvmPCFit(trainX, trainY, testX, kernel = "radial")

Arguments

Value

a vector or numeric predictions on user provided test data

Examples

data = data1
trainX = as.matrix(data[c(1:100),2])
trainY = data[c(1:100),7]
testX = as.matrix(data[c(101:110),2])

Svm_prediction = SvmPCFit(trainX, trainY, testX)

xgboost based power curve modelling

Description

xgboost based power curve modelling

Usage

XgbPCFit(
  trainX,
  trainY,
  testX,
  max.depth = 8,
  eta = 0.25,
  nthread = 2,
  nrounds = 5
)

Arguments

Value

a vector or numeric predictions on user provided test data

References

Chen, T., & Guestrin, C. (2016). "XGBoost: A Scalable Tree Boosting System." Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785-794. doi:10.1145/2939672.2939785.

Examples

data = data1
trainX = as.matrix(data[c(1:100),2])
trainY = data[c(1:100),7]
testX = as.matrix(data[c(101:110),2])

Xgb_prediction = XgbPCFit(trainX, trainY, testX)

Wind Energy data set containing 47,542 data points

Description

A dataset containing the power produced and other attributes of almost 47,542 records.

Usage

data(data1)

Format

A data frame with 47,542 rows and 7 variables

Details

• Data.point - sequence of integers displaying each record

• V - wind speed

• D - wind direction

• air.density - air density

• I - turbulence intensity

• S_b - wind shear

• Y - wind power

Wind Energy data set containing 48,068 data points

Description

A dataset containing the power produced and other attributes of almost 48,068 records.

Usage

data(data2)

Format

A data frame with 48,068 rows and 7 variables

Details

• Data.point - sequence of integers displaying each record

• V - wind speed

• D - wind direction

• air.density - air density

• I - turbulence intensity

• S_b - wind shear

• Y - wind power

Energy decomposition for wind turbine performance comparison

Description

Energy decomposition compares energy production from two datasets and separates it into turbine effects (deltaE.turb) and weather/environment effects (deltaE.weather).

Usage

deltaEnergy(
  data,
  powercol,
  timecol = 0,
  xcol,
  sync.method = "minimum power",
  imput = TRUE,
  vcol = NULL,
  vrange = NULL,
  rated.power = NULL,
  sample = TRUE,
  size = 2500,
  timestamp.min = 10
)

Arguments

Value

a list containing :

• deltaE.turb - A numeric,

• deltaE.weather - A numeric,

• deltaE.hat - A numeric,

• deltaE.obs - A numeric,

• estimated.energy - A numeric vector of the total energy calculated from each of f1(x2), f1(x1), f2(x2), f1(x2). If power is in kW, these values will be in kWh.

• data - A list of two datasets used to calculate energy decomposition, i.e. synchronized. When imput = TRUE, the power column is the result from imputation.

References

Latiffianti, E, Ding, Y, Sheng, S, Williams, L, Morshedizadeh, M, Rodgers, M (2022). "Analysis of leading edge protection application on wind turbine performance through energy and power decomposition approaches". Wind Energy. 2022; 1-19. doi:10.1002/we.2722.

Examples

data = list(data1[1:50,], data2[1:60,])
powercol = 7
timecol = 1
xcol = c(2:6)
sync.method = 'time'
imput = TRUE
vcol = 2
vrange = c(5,12,25)
rated.power = 100
sample = FALSE
Decomposition = deltaEnergy(data, powercol, timecol, xcol, sync.method, imput,
vcol, vrange, rated.power, sample)

Function comparison using Gaussian Process and Hypothesis testing

Description

Function comparison using Gaussian Process and Hypothesis testing

Usage

funGP(
  datalist,
  xCol,
  yCol,
  confLevel = 0.95,
  testset,
  limitMemory = TRUE,
  opt_method = "nlminb",
  sampleSize = list(optimSize = 500, bandSize = 5000),
  rngSeed = 1
)

Arguments

Value

a list containing :

• muDiff - A vector of pointwise difference between the predictions from the two datasets (mu2- mu1)

• mu1 - A vector of test prediction for first data set

• mu2 - A vector of test prediction for second data set

• band - A vector of the allowed statistical difference between functions at testpoints in testset

• confLevel - A numeric representing the statistical significance level for constructing the band

• testset - A matrix of test points to compare the functions

• estimatedParams - A list of estimated hyperparameters for GP

References

Prakash, A., Tuo, R., & Ding, Y. (2022). "Gaussian process aided function comparison using noisy scattered data," Technometrics, Vol. 64, No. 1, pp. 92-102, doi:10.1080/00401706.2021.1905073.

Examples

datalist = list(data1[1:50,], data2[1:50, ])
xCol = 2
yCol = 7
confLevel = 0.95
testset = seq(4,10,length.out = 10)
function_diff = funGP(datalist, xCol, yCol, confLevel, testset)

Power imputation

Description

Good power curve modeling requires valid power values in the region between cut-in and cut-out wind speed. However, when turbine is not operating, the power production will be recorded as zero or negative. This function replaces those values with predicted values obtained from the estimated tempGP power curve model using one input variable - the wind speed.

Usage

imptPower(
  data,
  powercol,
  vcol,
  vrange,
  rated.power = NULL,
  sample = TRUE,
  size = 2500
)

Arguments

Value

a list containing datasets with the imputed power.

References

Latiffianti, E, Ding, Y, Sheng, S, Williams, L, Morshedizadeh, M, Rodgers, M (2022). "Analysis of leading edge protection application on wind turbine performance through energy and power decomposition approaches". Wind Energy. 2022; 1-19. doi:10.1002/we.2722.

Examples

data = list(data1[1:100,], data2[1:120, ])
powercol = 7
vcol = 2
vrange = c(5,12,25)
rated.power = 100
sample = FALSE

imputed.dat = imptPower(data, powercol, vcol, vrange, rated.power, sample)

predict from temporal Gaussian process

Description

predict function for tempGP objects. This function computes the prediction f(x) or f(x) + g(t) depending on the temporal distance between training and test points and whether the time indices for the test points are provided.

Usage

## S3 method for class 'tempGP'
predict(object, testX, testT = NULL, trainT = NULL, ...)

Arguments

Value

A vector of predictions at the testpoints in testX.

Examples

   data = DSWE::data1
   trainindex = 1:50 #using the first 50 data points to train the model
   traindata = data[trainindex,]
   xCol = 2 #input variable columns
   yCol = 7 #response column
   trainX = as.matrix(traindata[,xCol])
   trainY = as.numeric(traindata[,yCol])
   tempGPObject = tempGP(trainX, trainY)
   testdata = DSWE::data1[101:110,] # defining test data 
   testX = as.matrix(testdata[,xCol, drop = FALSE])
   predF = predict(tempGPObject, testX)

Data synchronization

Description

Data synchronization is meant to make a pair of data to have the same size. It is performed by removing some data points from the larger dataset. This step is important when comparing energy production between two data sets because energy production is time-based.

Usage

syncSize(data, powercol, timecol = 0, xcol, method = "minimum power")

Arguments

Value

a list containing the synchronized datasets.

References

Latiffianti, E, Ding, Y, Sheng, S, Williams, L, Morshedizadeh, M, Rodgers, M (2022). "Analysis of leading edge protection application on wind turbine performance through energy and power decomposition approaches". Wind Energy. 2022; 1-19. doi:10.1002/we.2722.

Examples

data = list(data1[1:200,], data2[1:180, ])
powercol = 7
timecol = 1
xcol = c(2:6)
method = 'random'
sync.dat = syncSize(data, powercol, timecol, xcol, method)

data = list(data1[500:700,], data2[600:750, ])
powercol = 7
timecol = 1
xcol = c(2:6)
method = 'time'
sync.dat = syncSize(data, powercol, timecol, xcol, method)

temporal Gaussian process

Description

A Gaussian process based power curve model which explicitly models the temporal aspect of the power curve. The model consists of two parts: f(x) and g(t).

Usage

tempGP(
  trainX,
  trainY,
  trainT = NULL,
  fast_computation = TRUE,
  limit_memory = 5000L,
  max_thinning_number = 20L,
  vecchia = TRUE,
  optim_control = list(batch_size = 100L, learn_rate = 0.05, max_iter = 5000L, tol =
    1e-06, beta1 = 0.9, beta2 = 0.999, epsilon = 1e-08, logfile = NULL)
)

Arguments

Value

An object of class tempGP with the following attributes:

• trainX - same as the input matrix trainX.

• trainY - same as the input vector trainY.

• thinningNumber - the thinning number computed by the algorithm.

• modelF - A list containing the details of the model for predicting function f(x):

  • X - The input variable matrix for computing the cross-covariance for predictions, same as trainX unless the model is updated. See updateData.tempGP method for details on updating the model.

  • y - The response vector, again same as trainY unless the model is updated.

  • weightedY - The weighted response, that is, the response left multiplied by the inverse of the covariance matrix.

• modelG - A list containing the details of the model for predicting function g(t):

  • residuals - The residuals after subtracting function f(x) from the response. Used to predict g(t). See updateData.tempGP method for updating the residuals.

  • time_index - The time indices of the residuals, same as trainT.

• estimatedParams - Estimated hyperparameters for function f(x).

• llval - log-likelihood value of the hyperparameter optimization for f(x).

• gradval - gradient vector at the optimal log-likelihood value.

References

Prakash, A., Tuo, R., & Ding, Y. (2022). "The temporal overfitting problem with applications in wind power curve modeling." Technometrics. doi:10.1080/00401706.2022.2069158.

Katzfuss, M., & Guinness, J. (2021). "A General Framework for Vecchia Approximations of Gaussian Processes." Statistical Science. doi:10.1214/19-STS755.

Guinness, J. (2018). "Permutation and Grouping Methods for Sharpening Gaussian Process Approximations." Technometrics. doi:10.1080/00401706.2018.1437476.

See Also

predict.tempGP for computing predictions and updateData.tempGP for updating data in a tempGP object.

Examples

    data = DSWE::data1
    trainindex = 1:50 #using the first 50 data points to train the model
    traindata = data[trainindex,]
    xCol = 2 #input variable columns
    yCol = 7 #response column
    trainX = as.matrix(traindata[,xCol])
    trainY = as.numeric(traindata[,yCol])
    tempGPObject = tempGP(trainX, trainY)

Updating data in a model

Description

updateData is a generic function to update data in a model.

Usage

updateData(object, ...)

Arguments

Value

The returned value would depend on the class of its argument object.

See Also

updateData.tempGP

Update the data in a tempGP object

Description

This function updates trainX, trainY, and trainT in a tempGP object. By default, if the new data has m data points, the function removes top m data points from the tempGP object and appends the new data at the bottom, thus keeping the total number of data points the same. This can be overwritten by setting replace = FALSE to keep all the data points (old and new). The method also updates modelG by computing and updating residuals at the new data points. modelF can be also be updated by setting the argument updateModelF to TRUE, though not required generally (see comments in the Arguments.)

Usage

## S3 method for class 'tempGP'
updateData(
  object,
  newX,
  newY,
  newT = NULL,
  replace = TRUE,
  updateModelF = FALSE,
  ...
)

Arguments

Value

An updated object of class tempGP.

Examples

   data = DSWE::data1
   trainindex = 1:50 #using the first 50 data points to train the model
   traindata = data[trainindex,]
   xCol = 2 #input variable columns
   yCol = 7 #response column
   trainX = as.matrix(traindata[,xCol])
   trainY = as.numeric(traindata[,yCol])
   tempGPObject = tempGP(trainX, trainY)
   newdata = DSWE::data1[101:110,] # defining new data  
   newX = as.matrix(newdata[,xCol, drop = FALSE])
   newY = as.numeric(newdata[,yCol])
   tempGPupdated = updateData(tempGPObject, newX, newY)