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TRANSCRIPT
Ricardo BessaINESC TEC, Portugal
Feature Engineering to Improve Time Series Forecasting
EES-UETP: Advanced Data Analytics for Energy Systems
September 3-5, 2018Porto, Portugal
Course Module Outline
1 Feature Engineering Concept
2 Manual and Automated Feature Engineering
3 Case Study: Solar and Wind Power Forecasting
4 Case Study: Electricity Price Forecasting
5 Other Use Cases and Concluding Remarks
Feature Engineering Concept
Feature Engineering
Motivation
Improve forecasting skill by extracting
additional information from raw data
(case studies ahead…)
Explain data and uncover relevant
information from unsupervised learning
(one example in this tutorial…)
Process information from
continuous streaming data
internet-of-things
➢ Aggregate information from
multiple sensors
➢ Explore multilevel information
(hierarchical features)
Feature Engineering
Concept
CRoss Industry Standard Process for
Data MiningCRISP-DM
Feature engineering area of the process
OPTIONS
➢ Manual creation of features with domain knowledge
➢ Automatic extraction of features, e.g. deep learning techniques
Feature Engineering
Toy Example
Predicting the life time of a specific component within the car or the equipment → forecast horizon is longer-term (days, weeks or months)
Sensors will produce data every second (atomic level)
Data needs to be aggregated over time to understand meaningful trends and changes that will signify an impending failure (aggregated level)
features feeding the statistical learning model
Example later on electricity price forecasting
Manual and Automated Feature Engineering
Manual Feature Engineering
Temporal Aggregation
Temporal aggregation of data
Overlapping windowOne may use various definitions of creating the time windows and then naturally these windows will overlap
Fixed time windowAggregation is performed over a specific, uniform time interval, e.g. 15-min
Variable time windowVarious measures can be used to generate variable time windows. In most cases, a specific number of occurrences of events are used to determine the window size
Exponentially expanding or exponentially contracting time windowsAggregate the near-term data across more granular time windows, while data that is further off, may be aggregated across a wider window [exponentially expanding windows]
The opposite is referred to as exponentially contracting window
1
Manual Feature Engineering
Basic Features
Creation of basic features2
Simple features involving one type of signal▪ Change over time: Cm+1 = (Xm+1 – Xm)/(tm+1 – tm)▪ Rate of change over time: RTm= (Cm+1 – Cm)/(tm+1 – tm)▪ Growth or decay: Gm+1 = (Xm+1 – Xm)/Xm
▪ Rate of growth or decay: RGm= (Gm+1 – Gm)/(tm+1 – tm)▪ Count of values above or below a threshold value▪ Moving average = Average of (Xm-p to Xm)▪ Moving standard deviation = Standard deviation of (Xm-p to Xm)▪ Relative average = Moving average / Global average▪ Relatives standard deviation = Moving standard deviation / Global standard deviation▪ Ratio of changes, growth rate etc. with standard deviation▪ Features involving trend of values across various aggregation windows: change and rate of change in
average, standard deviation etc. across windows
Manual Feature Engineering
Basic Features
Creation of basic features2
Using multiple time series to create large number of combined features▪ Simple ratio between the two series▪ Ratio of changes, rate of change and growth between the two series▪ Ratio of moving average and moving standard deviation▪ Ratio of relative averages and relative standard deviation▪ Relative first difference: RV1m+1 = (XAm+1 – XAm)/(XBm+1 – XBm)▪ Relative second difference: RV2m+1 = (GAm+1 – GAm)/(GBm+1 – GBm)▪ Count of cases where Growth of both series is positive or negative▪ Count of cases where Growth of both series is in opposite direction▪ Count of cases where the first series is above a threshold and the second below a threshold and vice-a-versa
Manual Feature Engineering
Advanced Features
Features based on higher order statistics3
▪ Moments (mean, variance, skewness and kurtosis etc.) are calculated within the aggregation window▪ In non-Gaussian time series, cumulants are used rather than the moments for obtaining information
about the nature of the distribution within the window
Features based on series transformation4
Mathematical transformations can be used to decompose the time series into a set of simpler functions. Usually the following transformations are attempted:▪ Fast Fourier Transform▪ Hilbert Huang Transform▪ Wigner Ville Distribution▪ Wavelet Transformation
Automated Feature Engineering
Available Software
➢ Automatically create features from a set of related tables
➢ Method known as Deep Feature Synthesis (Kanter and Veeramachaneni, 2015)➢ Deep feature synthesis stacks multiple
transformation and aggregation operations (which are called feature primitives **analogues to basic features in previous slides) to create features from data spread across many tables
Source: Kanter, J. M., & Veeramachaneni, K. (2015, October). Deep feature synthesis: Towards automating data science endeavors. In Data Science and Advanced Analytics (DSAA), 2015. 36678 2015. IEEE International Conference on (pp. 1-10). IEEE.
Automated Feature Engineering
Representation Learning Framework
CLASSICALPrincipal Components Analysis (PCA)(+) simplicity(-) linear (non-linear versions require parameter tuning)
Source: Angermueller, C., Pärnamaa, T., Parts, L., & Stegle, O. (2016). Deep learning for computational biology. Molecular systems biology, 12(7), 878.
Automated Feature Engineering
Convolutional Extraction
Source: Angermueller, C., Pärnamaa, T., Parts, L., & Stegle, O. (2016). Deep learning for computational biology. Molecular systems biology, 12(7), 878.
Input Image
Automated Feature Engineering
Stack of Restricted Boltzmann Machines(RBM)
Source: Testolin, A., Stoianov, I., De Filippo De Grazia, M., & Zorzi, M. (2013). Deep unsupervised learning on a desktop PC: a primer for cognitive scientists. Frontiers in psychology, 4, 251..
Source: Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. science, 313(5786), 504-507.
Case Study: Solar and Wind Power Forecasting
Case-Study
PV Installation in INESC TEC Building & Sotavento Wind Farm in Spain
Data available upon request
Raw NWP dataset: 2704 variables for the wind power plant and 1014 variables for the PV site
Clear case for feature engineering: how much information can be extracted from this raw data?
Local NWP Information
PV Forecasting
Clear SkyPartially Cloud Cover OvercastLo
cal N
WP
info
rmat
ion
Tem
po
ral Varian
ce
Local NWP Information
PV Forecasting
Clear SkyPartially Cloud Cover Overcast
Loca
l NW
P in
form
atio
n
Grid NWP Information
PV Forecasting
Clear SkyPartially Cloud Cover OvercastSp
atia
l Gri
d N
WP
info
rmat
ion
List of Created Features
PV Forecasting
PV Forecasting Framework
Model Chain
NWP for the client location
Grid of NWP
Gradient Boosting Trees
PV Power Forecasts
(point & probabilistic)
Temporal Features+ Point Forecasts Spatial Features
Forecast Example
PV Forecasting
Probabilistic forecasts• Uncertainty better modeled around the observed values• Some of the abnormal high uncertainty verified for clear-sky days is removed
Point forecasts• Some of the over/underestimation situations are resolved• Improvements on the power peak forecasts for some clear-sky days
Temporal Information Temporal & Spatial Information
Numerical Results
PV Forecasting
Local Temporal Information
Grid Spatial Information
Combination temporal & spatial
inputs
(best overall model)
24h Forecast Horizon
𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 = 1 −𝑚𝑒𝑡𝑟𝑖𝑐𝑚𝑜𝑑𝑒𝑙
𝑚𝑒𝑡𝑟𝑖𝑐𝑏𝑎𝑠𝑒∙ 100%
Local NWP Information
Wind Power Forecasting
Local NWP Information
Wind Power Forecasting
Spatial NWP Information
Wind Power Forecasting
Power and Spatial NWP Grid Comparison
List of Created Features
Wind Power Forecasting
Lo
ca
l In
form
ati
on
Do
ma
in K
no
wle
dg
e
Automated Features from NWP Grid
Wind Power Forecasting
Without considering the spatial relationbetween the variables
extractedfeatures
extractedfeatures
with the spatial relationbetween the variables
Automated Features from NWP Grid
Wind Power Forecasting
Lo
ca
l In
form
ati
on
Au
to-E
nc
od
ers
Numerical Results
Wind Power Forecasting
24h Forecast Time Horizon
𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 = 1 −𝑚𝑒𝑡𝑟𝑖𝑐𝑚𝑜𝑑𝑒𝑙
𝑚𝑒𝑡𝑟𝑖𝑐𝑏𝑎𝑠𝑒∙ 100%
Numerical Results
Wind Power Forecasting
Forecast Example
Wind Power Forecasting
Base model
Model spatial & temporal data
The Impact of Feature Engineering
In Contrast to Probabilistic Forecasts Generated with Weather Ensembles
Probabilistic forecast generated with a weather ensemble model
Probabilistic forecast generated with a feature engineering + GBT
Case Study: Electricity Price Forecasting
Electricity Price Forecasting
Motivation
Statistical learning methods heavily dependent onthe availability of sufficient historical data withhigh (or low) price regimes
highest prices during thistwo years period
Feature Engineering Approach
Electricity Price Forecasting
combine additional (in addition to exogenous variables) information with the statistical model
forecast the daily average price including information from daily futures contracts
(proxy forecast of spot price)
Feature Engineering Approach
Statistical Models
Linear Median Regression
➢ Day of the week, month of the year➢ Past daily average prices➢ Daily futures contracts➢ D-1 generation: coal, wind and PV
Forecast Daily Average Price
Gradient Boosting Trees
➢ Day of the week, hour of the day, month of the year➢ Past daily average prices➢ D-1 generation: coal, hydro w/reservoir➢ Forecasts: load, wind power penetration, PV, solar thermal
Forecast Day-ahead Price
The analysis of cross-effects between variables needs to be analyzed within the model (model-specific)
Feature Engineering Approach
The Impact of the Average Price Feature in the Forecasting Skill
without rescaling
with rescaling
➢ Low price regime
Feature Engineering Approach
The Impact of the Average Price Feature in the Forecasting Skill
without rescaling
with rescaling
➢ High price regime
Day-ahead Price Forecasting
Results
without rescaling with rescaling
Features for Intraday Price Forecasting
Data Analysis
All intraday sessions are strongly influenced by the day-ahead prices
Each intraday session is highly correlated with the previous one
Features for Intraday Price Forecasting
Model
Linear Quantile Regression
i-th intraday session
𝑆𝑖 𝜏 = ൞
𝑐 + 𝛽7 × 𝑃𝐷𝐴, 𝑖𝑓 𝑖 = 1
𝑐 + 𝛽7 × 𝑃𝐷𝐴 +𝑗=1
𝑖−1
𝛽8+𝑗−1 × 𝐼𝐷 𝑗 , 𝑖𝑓 𝑖 > 1
where c comprises calendar variables
𝑐 = 𝛽0 + 𝛽1 × 𝐶𝐻,𝑐𝑜𝑠 + 𝛽2 × 𝐶𝐻,𝑠𝑖𝑛+ 𝛽3 × 𝐶𝑊𝑑,𝑐𝑜𝑠+ 𝛽4 × 𝐶𝑊𝑑,𝑠𝑖𝑛+ 𝛽5 × 𝐶𝑀,𝑐𝑜𝑠 + 𝛽6 × 𝐶𝑀,𝑠𝑖𝑛
Intraday Price Forecasting
Results
Deep Learning for Electricity Markets
Curve Forecasting
CONCEPT
GOALForecast the 24 residual demand curves from the day-ahead market
Demand
Supply Residual demand
Type of Features
Curve Forecasting
Long Short Term Memory networks
1-Dimensional input vector
-0.49446
-0.407376
-0.407376
…
…
0.39716
0.420512
0.731689
Type of Features
Curve Forecasting
Long Short Term Memory networks
2-Dimensional input vector
Automatic Feature Extraction with LSTM
1-D and 2-D Approaches
1-D 2-D
Exogenous variables(solar, load, windforecast, wind andsolar penetration).
Illustrative Results (1-D)
Iberian Electricity Market
Illustrative Results (2-D)
Iberian Electricity Market
Other Use Cases and Concluding Remarks
Distribution Grids
Visualization of Low Voltage Grid Operation
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Distributed Stochastic Neighbor Embedding (t-SNE)
2125 belief states
PCA (no information!)
Classify Events in Transmission Networks
Using Data Collected by Phasor Measurement Units (PMU)
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Generator tripping Load shedding
Line tripping Oscillation
❑ Events collected at several PMUs simultaneously in Brazil (MedFasee project)❑ Frequency data collected at the rate of 1 measurement per 1/60 second
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59.5 Hz
60 Hz
Classify Events in Transmission Networks
Results
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model error in event recognition
Deeper Feedforward ANN 1,5 %
Deep Belief Networks 8,5 %
Convolutional NN 30x40 0 %
Look: can you see?
Layer 1 Layer 2 Layer 32D image
• Feature engineering can result in significant improvements for renewable energy forecasting
• #personal opinion# more important than the choice of the statistical learning model
• Deep learning (frame representation) and manual feature construction can be combined to extract meaningful information from the raw NWP dataset
• Several business cases exist for feature engineering, including data-driven optimization (e.g. reinforcement learning)
• Additional information is very critical when producing uncertainty forecasts
• Feature engineering can also be used for machine learning model interpretation and big data visualization
Concluding Remarks
J.R. Andrade, R.J. Bessa, “Improving renewable energy forecasting with a grid of numericalweather predictions”, IEEE Transactions on Sustainable Energy, vol. 8, no. 4, pp. 1571-1580,Oct. 2017.
J.R. Andrade, J.M. Filipe, M. Reis, R.J. Bessa, “Probabilistic price forecasting for day-ahead andintraday markets: Beyond the statistical model,” Sustainability, vol. 9, no. 11, pp. 1990, 2017.
R.J. Bessa, C. Möhrlen, V. Fundel, M. Siefert, J. Browell, S. Haglund El Gaidi, Bri-Mathias Hodge,U. Cali, and G. Kariniotakis, “Towards improved understanding of the applicability ofuncertainty forecasts in the electric power industry,” Energies, vol. 10, no. 9, pp. 1402, 2017.
L. Cavalcante, R. J. Bessa, M. Reis, J. Dowell, “LASSO vector autoregression structures for veryshort-term wind power forecasting,” Wind Energy, vol. 20, no. 4, pp. 657-675, April 2017.
V. Miranda, P. Cardoso, R.J. Bessa, “Through the looking glass: seeing events in power systemsdynamics,” working paper, 2018.
M. Pereira, R.J. Bessa, C. Gouveia Moura, “Low voltage grid data visualization with abiologically inspired cognitive architecture,” working paper, 2018.
References
INESC TEC Work