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We developed stochastic time series models such as ARMA( p,q), non- seasonal
ARIMA, seasonal ARIMA (SARIMA) and MTM models to simulate and forecast hourly
averaged wind speed sequences on twenty year data ,.i.e, 1985-2004 of Quetta, Pakistan.
Stochastic Time Series Models take into account several basic features of wind speed
including autocorrelation, non-Gaussian distribution and non-stationarity. The positive
correlation between consecutive wind speed observations is taken into account by fitting
ARMA process to wind speed data. The data are normalized to make their distributions
approximately Gaussian and standardized to remove scattering of transformed data
(stationary,.i.e., without chaos).Diurnal variations has been taken into account to observe
forecasts and its dependence on lead times. We find the ARMA (p,q) model suitable for
prediction interval and probability forecasts. But the MTM model is relatively better as a
simulator compared to ARMA modeling. The suitability of ARMA (p,q) model for both
long range (1-6 hours) and short range (1-2 hours) indicates that forecast values are the
deciding components for an appropriate wind energy conversion systems, WECS. ARMA
processes work with non-stationary (chaotic) data. Non-seasonal ARIMA models and the
prediction equations for each month and indeed for each season of a twenty year wind
data are presented. The seasonal ARIMA (SARIMA) and its prediction equations for
each month of a twenty year data are also studied. With non- stationarity or chaos in data,
stochastic simulator in the ARIMA processes does not effectively work although its
prediction equations are good enough to forecast relatively short range reliable values.
Various statistical techniques are used on twenty five years, .i.e., 1980-2004 data
of average humidity, rainfall, maximum and minimum temperatures, respectively. The
relationships to regression analysis time series (RATS) are developed for determining the
overall trend of these climate parameters on the basis of which forecast models can be
corrected and modified. We followed the coefficient of determination,.i.e., a measure of
goodness of fit, to our polynomial regression analysis time series (PRATS). The
correlation to multiple linear regression (MLR) and multiple linear regression analysis
time series (MLRATS) are also developed from deciphering the interdependence of
weather parameters.
We used Spearman’s rank correlation and Goldfeld-Quandt tests to check the
uniformity or non uniformity of variances in our fit to polynomial regression (PR). The
Breusch-Pagan test was applied to MLR and MLRATS, respectively which yielded
homoscedasticity (uniformity of variances in the distribution of data). We also employed
Bartlett’s test for homogeneity of variances on a twenty five years data of rainfall and
humidity, respectively which showed that the variances in rainfall data are not
homogenous while in case of humidity, are homogenous. Our results on regression and
regression analysis time series show the best fit to prediction modeling on climatic data
of Quetta, Pakistan.
We performed design free fuzzy logic (FL) time series prediction modeling on
a twenty year wind data, .i.e., 1985-2004 for Quetta, Pakistan. We followed design free
fuzzy logic and obtained prediction of hourly wind data for spring (February, March and
April). Non-stationarity or random walk in wind data exists but it does not influence
prediction. Mackey Glass (MG) simulation of wind data indicated chaos or non
periodicity. Moreover, stable attractors are observed in MG-time series, the origin of
which is yet unknown. The attractors seen in MG simulation do not influence FL time
series prediction.
We studied singleton and non-singleton type-1 back propagation (BP) designed
sixteen rule fuzzy logic system (FLS) on hourly averaged wind data of twenty years ,.i.e.,
1985-2004. We found that the BP designed 16 rule non-singleton-type-1 FLS is relatively
a better forecaster than singleton-type-1.We find hidden or unraveled uncertainties such
as non-stationarity and stable attractors. These uncertainties make the data chaotic. The
criterion of selecting root mean square error (RMSE) for establishing comparison is not
suitable for chaotic data. Non-stationarity in the data can be properly handled with non-
singleton type-1 FLS, therefore, there appears no reason to use a type-2 FLS. The stable
attractors and non-stationarity in our data do not affect the predicted values as confirmed
by Mackey Glass simulation. The chaos can be effectively resolved through parallel
structure fuzzy system (PSFS) which exploits time-delays..
A variety of Artificial Neural Network models for prediction of hourly
wind speed (which a few hours in advance is required to ensure efficient utilization of
wind energy systems) at Quetta, Pakistan is studied and the results are compared.
Satisfactory results are obtained with Feed Forward Back Propagation Neural Networks
(FFBPNN).
An empirical relationship is developed which shows the Gaussian profile
for the number of neurons which varies with lag inputs, .i.e.,
nn = k exp(-il2)
where nn shows the number of neurons, il the lag inputs, and k the sloping ratio. Feed
Forward Neural Networks (FFNNs) can be corrected with optimization of empirical
relationship for simulators followed by back propagation technique. The disadvantages of
FFNNs comprise of heavy computational requirements, and non-existence of Artificial
Neural Network(ANN) design methodologies for deciding the value of the learning rate
and momentum. Neural Network (NN) modeling is not suitable for chaotic data
characterized by randomness and non-stationarity. |
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