ARIMA-Based Frequency-Decomposed Modeling of Wind Speed Time Series
2016-12-01 22:06:56 3 举报AI智能生成
The Processon file about a scientific paper, ARIMA-Based Frequency-Decomposed Modeling of Wind Speed Time Series
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Introduction
Characteristics of Wind-speed data
Time correlation
Probability distribution
Diurnal and seasonal periodical property
Different ways of modeling wind-speed data
Weibull Distribution
Only capture probability distribution
Not temporal correlation
Power Spectral Density (PSD)
Capture frequency components of wind-speed data
Not consider temporal correlation
Discrete Markov Model
Capture probability distribution
Consider the time correlation
Quantization error
Too many model parameters
Large set of tme-series data is needed
ARIMA
Advantage
Probability distribution
Time correlation
No quantization error
Low number of parameters
Small set of data
Shortage
ARIMA is designed for first-/second-order moments of a linear stationary time series
Wind-speed data is nonlinear, nonstationary time series
The ARIMA method need to be modified
Standard ARIMA Modeling Procedure
A. Standard ARIMA Model
ARIMA (p, d, q)
the BoxCox's power transformation, used to stabilize the variance
B. Model Identification and Diagnostic Check
Model Identification
Analyze the observed time-series data and determine the required type of transformation
Identify the corresponding ARIMA model structure (compare estimated ACC and PACC with theoretical ACC and PACC)
The way to calculate the estimated ACC
The way to calculate the estimated PACC
Determine the deterministic trend term so that the mean of the simulated time-series data is equal to the mean of the observed time-series data
Diagnostic Check
ACC and PACC of the residual have to be within the critical limits for the lags different from 0
Critical limits of ACC and PACC
C. Verification and Final Diagnostic Check
Compare the simulated time-series data with measurement
If not same, parameters have to be uploaded in the above way
ARIMA-Based Wind-speed Model
The measured wind-speed data is highly nonstationary and requires proper transform
Standard ARIMA does not produce an acceptable match in time correlation (ACC) and probability distribution (Q-Q plot) compared with the measurement
Require a modification of the standard ARIMA modeling procedure
Modified ARIMA Modeling Procedure
A. Limiting the wind-speed data before modeling
Why limit wind-speed data
Mismatch of simulated data and measurement at lower or higher speed
Lower or higher speed wind occurs little
Limit the wind-speed in a proper range
The ARIMA fails to capture the time correlation and periodic characteristics
Concept of frequency decomposition is introduced
B. Frequency Decomposition
Why conduct frequency decomposition
The unstationary characteristics are mainly contributed by LF components
To decrease the unstationary feature, split the data into HF & LF components
Procedure to conduct frequency decomposition
1. Determine the cutoff frequency
For a time-series data to be stationary, the ACC and PACC
of the residual data need to have the characteristics of a
white noise
of the residual data need to have the characteristics of a
white noise
HF component is the stationary part of wind-speed data
According to this feature, the HF component can be selected out
2. Model the HF components of wind-speed data
Using the modeling procedure described in PART 2 to model the HF component
3. Model the LF components of wind-speed data
the LF component can be determined by subtracting the HF component
from the observed wind-speed data
from the observed wind-speed data
Resample the LF component
Using the modeling procedure described in PART 2 to model the LF component
4. Combine the simulation results from the HF & LF models and compare it with the observed wind-speed data
Fig. 7
Fig. 7 shows that the proposed method produces better results
The match in Q-Q plot is not tight at higher wind speed
Because there is little information about the wind speed higher than 20m/s
Extreme wind conditions can be handled separately
Fig. 8
The characteristics of the ACC of the observed & simulated wind-speed data at larger time lags
The model capture the pattern of observed ACC at largee time lags
Fig. 9
The periodogram of the observed wind-speed data & the simulated wind-speed data
The model can capture general periodic characteristics of the observed wind-speed data
C. Shifting the wind-speed data
Shifting ( adding a constant offset value to the signal) the observed time-series data before transformation can improve results
D. Flowchart of the modified ARIMA-Based wind-speed modeling procedure
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