Evaluation of Fertility Data Collected from Population Censuses

This content discusses the evaluation of fertility data collected from population censuses, focusing on measures like Crude Birth Rate (CBR) and methods for deriving fertility estimates. It highlights the advantages and disadvantages of using CBR as a measure of fertility and emphasizes the need for standardized fertility measures for accurate assessments.

• Fertility
• Data Evaluation
• Population Census
• Measures
• Crude Birth Rate

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1. Parameter/State Estimation and Trajectory Planning of the Skysails flying kite system Jesus Lago, Adrian B rger, Florian Messerer, Michael Erhard Systems control and optimization laboratory- IMTEK University of Freiburg, Germany

2. Overview System Model State estimation Importance of wind direction estimation Results Parameter estimation Introduction to PECas Parameter estimation results Planning of optimal trajectories - 2 - 12.06.2015 Jesus lago

3. Flying kite model dynamics State space: : angle tether-x axis (wind direction) : angle tether projected XZ plane and z axis : angle roll axis and wind direction l: tether length Inputs: : steering deflection vwinch: winch speed Parameters E: glide ratio of the kite gk: proportional gain vw: wind speed at kite altitude Others: va: air path speed - 3 - 12.06.2015 Jesus lago

4. Kite model dynamics Motivation: Simplified dynamics Symmetric w.r.t wind direction (x-axis) Accurate for state prediction Fast for online estimation Probably suitable for NMPC - 4 - 12.06.2015 Jesus lago

5. State Estimation Main Motivation Wind importance in the model Model referenced respect to wind direction ? Wind speed included in the model ? Wind direction and speed measured at ground differs from flight altitude ? ? Some estimation needed ? - 5 - 12.06.2015 Jesus lago

6. State Estimation Wind Speed Results Ground unit data useless for wind estimation at flight altitudes Current estimation: variability power vs. retraction phase EKF based on model: better estimation with lower variability - 6 - 12.06.2015 Jesus lago

7. Introduction to PECas Easy-to-apply parameter estimation software for application within the HIGHWIND project Uses a direct collocation approach using IPOPT from CasADi Provides possibilities for comfortable results interpretation Main developer: Adrian B rger (Still under development) Tutorial, documentation and more: syscop.de/pecas - 7 - 12.06.2015 Jesus lago

8. Parameter Estimation Motivation Change in parameters shows changes or problems in flying conditions Online estimation of parameters desired Challenges Fast estimation for real time implementation Simplified dynamical model not every assumption holds constantly Model sensitive to wind direction Unknown variance of measurement errors weighting matrix problem - 8 - 12.06.2015 Jesus lago

9. Parameter Estimation Main results Setup of best trade off accuracy vs speed T = 0.4 s - f = 2.5 Hz Collocation structure - 3rdorder polynomial 5 minutes horizon 40 minutes of data analyzed 70 s. simulation time E = 4.1 0.23 gk = 0.087 0.002 R2= 99 % - 9 - 12.06.2015 Jesus lago

10. Parameter Estimation Trade off Study of horizon length: Eand estimation time as critical parameter Trade off accuracy vs. speed: 5 minutes - 10 - 12.06.2015 Jesus lago

11. Parameter Estimation Trade off Study of sampling frequency: Elow variability, mostly estimation time critical Trade off accuracy vs. speed: 2.5 Hz - 11 - 12.06.2015 Jesus lago

12. Parameter Estimation Trade off Study of polynomial order: No influence on E, almost no influence on estimation time - 12 - 12.06.2015 Jesus lago

13. Optimal trajectory planning Experimental cycles M. Erhard, H. Strauch, Flight control of tehered kites in autonomous pumping cycles for airborne wind energy, Control Engineering Practice (2015), http://dx.doi.org/10.1016/j.conengprac.2015.03.001 But, are they optimal? - 13 - 12.06.2015 Jesus lago

14. Optimal trajectory planning - Video Problem Video Algorithm Casadi implementation Multiple shooting 250 states - 14 - 12.06.2015 Jesus lago

15. Conclusion Different ongoing work: State / Parameter estimation Trajectory Planning Several obstacles / constrains: Computing speed Accuracy Future plan Use current work to implement NMPC for trajectory control and test NMPC controller with real SkySails Power prototype - 15 - 12.06.2015 Jesus lago

16. Thank you for your attention. Questions/suggestions are welcome! - 16 - 12.06.2015 Jesus lago