Team Helios (a) The God Helios (b) Our sun Dr. Thomai Tsiftsi & - - PowerPoint PPT Presentation

Team Helios

(a) The God Helios (b) Our sun

• Dr. Thomai Tsiftsi & Dr. James Edwards

UNAM - UMICH SpaceApps Challenge 2017

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Accessible year round with very little variation in weather This allows longer-duration isolated and confined environment studies The Mars-like environment provides for high-fidelity analog tasks, such as geological field work

Team Helios

Challenge: You are my sunshine

How low is low? Can we predict it? (YES!)

Team Helios

Challenge: You are my sunshine

The data: several parameters such as solar radiation, humidity, temperature Measured every 5 minutes Calculate: daily energy output knowing the area and solar radiation

Team Helios

Challenge: You are my sunshine

Use Extreme Value Analysis to model extremely small daily energy

• utput

These can be due to severe weather conditions This will provide the researchers to prepare themselves for such phenomena Help them tackle the problem by storing more energy to be used on such days

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

P(Mi ≤ z) ≃ G(z|µ, σ, ξ) ≡ exp

• −
• 1 + ξ

z − µ σ − 1

ξ

µ σ ξ Estimate −2.6 × 104 48.3 × 103 3.9 × 10−2 Std Err 2.3 × 103 2.8 × 103 4.6 × 10−1

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

PROBLEM!!!! ξ close to 0!

Team Helios

Challenge: You are my sunshine

Take lim ξ → 0 and fit Gumbel P(Mi ≤ z) ≃ exp

• −e− z−µ

σ

• µ

σ Estimate −2.6 × 104 8.3 × 103 Std Err 2.1 × 103 1.8 × 103

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Compare the two models? Which of the two gives substantially more information? Likelihood-ratio Test data: dfweek Likelihood-ratio = 0.016038, chi-square critical value = 3.8415, alpha = 0.0500, Degrees of Freedom = 1.0000, p-value = 0.8992

Choose Gumbel!

Team Helios

Challenge: You are my sunshine

Estimate Lower confidence interval Upper confidence interval 2 years 22.7kJ 17.9 kJ 27.9kJ 3 years 18.1kJ 12.2kJ 24.0kJ 4 years 15.2kJ 8.4kJ 22.0kJ 5 years 13.1kJ 5.6kJ 20.6kJ As an example, once every 4 years, we expect to see a weekly maximum total daily flux of 8.4kJ or less.

Team Helios

Challenge: You are my sunshine

Extreme waste of data. Many values are extreme yet are discarded Try a different approach Set a threshold and include all values that exceed the threshold as extreme

Team Helios

Challenge: You are my sunshine How do we choose the threshold??

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

H(y ≡ x − u) = 1 −

• 1 + ξy

˜ σ − 1

ξ

µ σ Estimate 1.7 × 104 4.8 × 10−1 Std Err 3.2 × 103 1.7 × 10−1

Team Helios

Challenge: You are my sunshine

Team Helios

Challenge: You are my sunshine

Estimate 2 years 19.3kJ 3 years 15kJ 4 years 12kJ 5 years 11kJ As an example, once every 4 years, we expect to see a total daily flux of 12kJ or less.

Team Helios

Challenge: You are my sunshine Problems

Not enough data Not enough time

Future considerations

The analysis was performed on stationary data Include covariates that affect the data e.g. humidity Allow the estimated parameters to vary with time Inspect for dependencies within the data

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THANK YOU FOR YOUR ATTENTION!

Team Helios