Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression for Wind Velocity Field Estimation from Aircraft-Derived Data
Abstract
:1. Introduction
1.1. Motivation
1.2. State of the Art
2. Methods
2.1. Data Derivation and Exploratory Analysis
2.1.1. Data Source
2.1.2. ADS-B and Mode S Systems
2.1.3. Wind Velocity Derivation from ADS-B and Mode S Data
2.1.4. Exploratory Data Analysis
2.2. Gaussian Process Regression
2.3. Polynomial Chaos Expansion
2.4. Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression
2.5. Adaptation of PCE-GPR to the Wind Velocity Output
3. Results
3.1. Model Set Up
3.2. Wind Velocity Field Reconstruction
- By randomly choosing sets of individual observations, which will be referred to as data set randomly split by observation.
- By randomly selecting sets of flights, employing the individual observations gathered from them, which will be referred to as a data set randomly split by flight.
3.3. Wind Velocity Field Short-Term Prediction
3.4. Validation of the PCE-GPR Model
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Wind Speed (m/s) | Wind Direction (Deg) | |||
---|---|---|---|---|
Day 1 | Day 2 | Day 1 | Day 2 | |
Min. | 0 | 0.013 | 0.01 | 163.79 |
Max. | 56.04 | 100.75 | 359.99 | 351.55 |
Mean | 17.80 | 60.56 | 307.16 | 166.66 |
Dispersion | 11.30 | 16.67 | 19.40 (%) | 2.11 (%) |
Data Set Split by Observation | Data Set Split by Flight | ||||
---|---|---|---|---|---|
Measure of Error | Component | Day 1 | Day 2 | Day 1 | Day 2 |
RMSE (m/s) | u | 2.26 (18%) | 1.50 (21%) | 5.84 (1%) | 6.06 (−4%) |
v | 1.46 (44%) | 1.45 (22%) | 4.79 (14%) | 4.84 (1%) | |
MAE (m/s) | u | 1.17 (22%) | 0.99 (22%) | 4.46 (−1%) | 4.37 (−2%) |
v | 0.83 (43%) | 1.05 (19%) | 3.45 (13%) | 3.59 (3%) | |
MAD (m/s) | u | 0.53 (23%) | 0.64 (22%) | 3.60 (−6%) | 3.03 (−2%) |
v | 0.49 (31%) | 0.80 (15%) | 2.44 (9%) | 2.70 (5%) |
Measure of Error | Component | Day 1 | Day 2 |
---|---|---|---|
RMSE (m/s) | u | 5.28 (6%) | 6.37 (13%) |
v | 5.16 (6%) | 5.80 (8%) | |
MAE (m/s) | u | 4.00 (12%) | 4.19 (29%) |
v | 3.93 (12%) | 4.40 (15%) | |
MAD (m/s) | u | 3.00 (4%) | 3.25 (12%) |
v | 3.07 (3%) | 3.52 (4%) |
Measure | Variable | Day 1 | Day 2 |
---|---|---|---|
Bias (m/s) | Wind speed | −2.75 | −0.24 |
MAE (m/s) | Wind speed | 4.5 | 5.79 |
Bias (deg) | Wind direction | 2.06 | −1.36 |
Dispersion (%) | Wind direction | 8.5 | 0.33 |
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Marinescu, M.; Olivares, A.; Staffetti, E.; Sun, J. Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression for Wind Velocity Field Estimation from Aircraft-Derived Data. Mathematics 2023, 11, 1018. https://doi.org/10.3390/math11041018
Marinescu M, Olivares A, Staffetti E, Sun J. Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression for Wind Velocity Field Estimation from Aircraft-Derived Data. Mathematics. 2023; 11(4):1018. https://doi.org/10.3390/math11041018
Chicago/Turabian StyleMarinescu, Marius, Alberto Olivares, Ernesto Staffetti, and Junzi Sun. 2023. "Polynomial Chaos Expansion-Based Enhanced Gaussian Process Regression for Wind Velocity Field Estimation from Aircraft-Derived Data" Mathematics 11, no. 4: 1018. https://doi.org/10.3390/math11041018