Package 'DSWE'

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

trainX	a matrix or dataframe of input variable values in the training dataset.
trainY	a numeric vector for response values in the training dataset.
testX	a matrix or dataframe of test input variable values to compute predictions.
bw	a numeric vector or a character input for bandwidth. If character, bandwidth computed internally; the input should be either 'dpi' or 'dpi_gap'. Default is 'dpi_gap'. See details for more information.
nMultiCov	an integer or a character input specifying the number of multiplicative covariates in each additive term. Default is 3 (same as Lee et al., 2015). The character inputs can be: 'all' for a completely multiplicative model, or 'none' for a completely additive model. Ignored if the number of covariates is 1.
fixedCov	an integer vector specifying the fixed covariates column number(s), default value is c(1,2). Ignored if nMultiCov is set to 'all' or 'none' or if the number of covariates is less than 3.
cirCov	an integer vector specifying the circular covariates column number(s) in trainX, default value is NA.

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

data	A list of data sets to be compared, the difference in the mean function is always computed as (f(data2) - f(data1))
xCol	A numeric or vector stating column number of covariates
xCol.circ	A numeric or vector stating column number of circular covariates
yCol	A numeric value stating the column number of the response
testCol	A numeric/vector stating column number of covariates to used in generating test set. Maximum of two columns to be used.
testSet	A matrix or dataframe consisting of test points, default value NULL, if NULL computes test points internally using testCol variables. If not NULL, total number of test points must be less than or equal to 2500.
thrs	A numeric or vector representing threshold for each covariates
conflevel	A numeric between (0,1) representing the statistical significance level for constructing the band
gridSize	A numeric / vector to be used in constructing test set, should be provided when testSet is NuLL, else it is ignored. Default is c(50,50) for 2-dim input which is converted internally to a default of c(1000) for 1-dim input. Total number of test points (product of gridSize vector components) must be less than or equal to 2500.
powerbins	A numeric stating the number of power bins for computing the scaled difference, default is 15.
baseline	An integer between 0 to 2, where 1 indicates to use power curve of first dataset as the base for metric calculation, 2 indicates to use the power curve of second dataset as the base, and 0 indicates to use the average of both power curves as the base. Default is set to 1.
limitMemory	A boolean (True/False) indicating whether to limit the memory use or not. Default is true. If set to true, 5000 datapoints are randomly sampled from each dataset under comparison for inference
opt_method	A string specifying the optimization method to be used for hyperparameter estimation. Current options are: 'L-BFGS-B', 'BFGS', and 'nlminb'. Default is set to 'nlminb'.
sampleSize	A named list of two integer items: optimSize and bandSize, denoting the sample size for each dataset for hyperparameter optimization and confidence band computation, respectively, when limitMemory = TRUE. Default value is list(optimSize = 500, bandSize = 5000).
rngSeed	Random seed for sampling data when limitMemory = TRUE. Default is 1.

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

muDiff	a vector of pointwise difference between two power curves on a testset as obtained from ComparePCurve() or funGP() function.
weights	a vector of user specified weights for each element of muDiff. It can be based on any probability distribution of user's choice. The weights must sum to 1.
base	a vector of predictions from a power curve; to be used as the denominator in computing the percentage difference. It can be either mu1 or mu2 as obtained from ComparePCurve() or funGP() function.
statDiff	a boolean specifying whether to compute the statistical significant difference or not. Default is set to FALSE, i.e. statistical significant difference is not computed. If set to TRUE, confBand must be provided.
confBand	a vector of pointwise confidence band for all the points in the testset as obtained from ComparePCurve() or funGP() function, named as band. Should only be provided when statDiff is set to TRUE. Default value is NULL.

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

data	a list, consisting of data sets to match, also each of the individual data set can be dataframe or a matrix
xCol	a vector stating the column position of covariates used
xCol.circ	a vector stating the column position of circular variables
thrs	a numerical or a vector of threshold values for each covariates, against which matching happens It should be a single value or a vector of values representing threshold for each of the covariate
priority	a boolean, default value False, otherwise computes the sequence of matching

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)

---

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

data	A list of two data sets to be compared. A difference is always computed as (data2 - data1).
powercol	A numeric stating the column number of power production.
timecol	A numeric stating the column number of data time stamp. Default value is zero. A value other than zero should be provided when sync.method = 'time'.
xcol	A numeric or vector stating the column number(s) of power curve input covariates/features (environmental or weather variables are recommended).
sync.method	A string specifying data synchronization method. Default value 'minimum power'; other options include 'time' and 'random'.
imput	A boolean (TRUE/FALSE) indicating whether power imputation should be performed before calculating energy decomposition. The recommended and default value is TRUE. Change to FALSE when data have been preprocessed or imputed before.#' @param vcol A numeric stating the column number of wind speed. It is required when imput = TRUE.
vcol	A numeric stating the column number of wind speed.
vrange	A vector of cut-in, rated, and cut-out wind speed. Values should be provided when imput = TRUE.
rated.power	A numerical value stating the wind turbine rated power.
sample	A boolean (TRUE/FALSE) indicating whether to use sample or the whole data sets to train the power curve to be used for power imputation. Default value is TRUE. It is only used when imput = TRUE.
size	A numeric stating the size of sample when sample = TRUE. Default value is 2500. It is only used when imput = TRUE and sample = TRUE.
timestamp.min	A numerical value stating the resolution of the datasets in minutes. It is the difference between two consecutive time stamps at which data were recorded. Default value is 10.

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

datalist	A list of data sets to compute a function for each of them
xCol	A numeric or vector stating the column number of covariates
yCol	A numeric value stating the column number of target
confLevel	A single value representing the statistical significance level for constructing the band
testset	Test points at which the functions will be compared
limitMemory	A boolean (True/False) indicating whether to limit the memory use or not. Default is true. If set to true, 5000 datapoints are randomly sampled from each dataset under comparison for inference.
opt_method	A string specifying the optimization method to be used for hyperparameter estimation. Current options are: 'L-BFGS-B', 'BFGS', and 'nlminb'. Default is set to 'nlminb'.
sampleSize	A named list of two integer items: optimSize and bandSize, denoting the sample size for each dataset for hyperparameter optimization and confidence band computation, respectively, when limitMemory = TRUE. Default value is list(optimSize = 500, bandSize = 5000).
rngSeed	Random seed for sampling data when limitMemory = TRUE. Default is 1.

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

data	A list of two data sets that require imputation.
powercol	A numeric stating the column number of power production.
vcol	A numeric stating the column number of wind speed.
vrange	A vector of cut-in, rated, and cut-out wind speed.
rated.power	A numerical value stating the wind turbine rated power.
sample	A boolean (TRUE/FALSE) indicating whether to use sample or the whole data sets to train the power curve.
size	A numeric stating the size of sample when sample = TRUE. Default value is 2500. It is only used when sample = TRUE.

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)

---

KNN : Fit

Description

The function models the powercurve using KNN, against supplied arguments

Usage

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

Arguments

data	a dataframe or a matrix, to be used in modelling
xCol	a vector or numeric values stating the column number of features
yCol	a numerical or a vector value stating the column number of target
subsetSelection	a boolean, default value is FALSE, if TRUE returns the best feature column number as xCol

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

knnMdl	a list containing: knnMdl$data - The data set provided by user knnMdl$xCol - The column number of features provided by user or the best subset column number knnMdl$yCol - The column number of target provided by user knn$bestK - The best k nearest neighbor calculated using the function KnnFit
testData	a data frame or matrix, to compute the predictions

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

knnMdl	a list containing: knnMdl$data - The data set provided by user knnMdl$xCol - The column number of features provided by user or the best subset column number knnMdl$yCol - The column number of target provided by user knn$bestK - The best k nearest neighbor calculated using the function KnnFit
newData	a dataframe or a matrix, to be used for updating the model

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)

---

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

object	An object of class tempGP.
testX	A matrix with each column corresponding to one input variable.
testT	A vector of time indices of the test points. When NULL, only function f(x) is used for prediction. Default is NULL.
trainT	Optional argument to override the existing trainT indices of the tempGP object.
...	additional arguments for future development

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)

---

Smoothing spline Anova method

Description

Smoothing spline Anova method

Usage

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

Arguments

data	a matrix or dataframe to be used in modelling
xCol	a numeric or vector stating the column number of feature covariates
yCol	a numeric value stating the column number of target
testX	a matrix or dataframe, to be used in computing the predictions
modelFormula	default is NULL else a model formula specifying target and features.Please refer 'gss' package documentation for more details

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

trainX	a matrix or dataframe to be used in modelling
trainY	a numeric or vector as a target
testX	a matrix or dataframe, to be used in computing the predictions
kernel	default is 'radial' else can be 'linear', 'polynomial' and 'sigmoid'

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)

---

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

data	A list of two data sets to be synchronized.
powercol	A numeric stating the column number of power production.
timecol	A numeric stating the column number of data time stamp. Default value is zero. A value other than zero should be provided when method = 'time'.
xcol	A numeric or vector stating the column number(s) of power curve input covariates/features (to be used for energy decomposition).
method	A string specifying data synchronization method. Default value 'minimum power'; other options include 'time' and 'random'.

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

trainX	A matrix with each column corresponding to one input variable.
trainY	A vector with each element corresponding to the output at the corresponding row of trainX.
trainT	A vector for time indices of the data points. By default, the function assigns natural numbers starting from 1 as the time indices.
fast_computation	A Boolean that specifies whether to do exact inference or fast approximation. Default is TRUE.
limit_memory	An integer or NULL. The integer is used sample training points during prediction to limit the total memory requirement. Setting the value to NULL would result in no sampling, that is, full training data is used for prediction. Default value is 5000.
max_thinning_number	An integer specifying the max lag to compute the thinning number. If the PACF does not become insignificant till max_thinning_number, then max_thinning_number is used for thinning.
vecchia	A Boolean that specifies whether to do exact inference or vecchia approximation. Default is TRUE.
optim_control	A list parameters passed to the Adam optimizer when fast_computation is set to TRUE. The default values have been tested rigorously and tend to strike a balance between accuracy and speed. batch_size: Number of training points sampled at each iteration of Adam. learn_rate: The step size for the Adam optimizer. max_iter: The maximum number of iterations to be performed by Adam. tol: Gradient tolerance. beta1: Decay rate for the first moment of the gradient. beta2: Decay rate for the second moment of the gradient. epsilon: A small number to avoid division by zero. logfile: A string specifying a file name to store hyperparameters value for each iteration.

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

object	A model object
...	additional arguments for passing to specific methods

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

object	An object of class tempGP.
newX	A matrix with each column corresponding to one input variable.
newY	A vector with each element corresponding to the output at the corresponding row of newX.
newT	A vector with time indices of the new datapoints. If NULL, the function assigns natural numbers starting with one larger than the existing time indices in trainT.
replace	A boolean to specify whether to replace the old data with the new one, or to add the new data while still keeping all the old data. Default is TRUE, which replaces the top m rows from the old data, where m is the number of data points in the new data.
updateModelF	A boolean to specify whether to update modelF as well. If the original tempGP model is trained on a sufficiently large dataset (say one year), updating modelF regularly may not result in any significant improvement, but can be computationally expensive.
...	additional arguments for future development

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)

---

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

trainX	a matrix or dataframe to be used in modelling
trainY	a numeric or vector as a target
testX	a matrix or dataframe, to be used in computing the predictions
max.depth	maximum depth of a tree
eta	learning rate
nthread	This parameter specifies the number of CPU threads that XGBoost
nrounds	number of boosting rounds or trees to build

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)

---