1 / 15

Vibrating Beam Inverse Problem

Vibrating Beam Inverse Problem. Team K.E.Y Scott Clark ● Asya Monds ● Hanh Pham SAMSI Undergraduate Workshop 2007. Outline. First Model (spring) Potential Problems How to improve Second Model (beam) Results. The first model: Spring Model.

sol
Download Presentation

Vibrating Beam Inverse Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Vibrating Beam Inverse Problem Team K.E.Y Scott Clark ● Asya Monds ● Hanh Pham SAMSI Undergraduate Workshop 2007

  2. Outline • First Model (spring) • Potential Problems • How to improve • Second Model (beam) • Results

  3. The first model:Spring Model • We have observations : (t1; y1); … ; (tm; ym). • The goal is to estimate the unknown parameters C and K.

  4. Our cost function: Now we need to minimize the cost function. After running the script, we get: C=0.7284; K=1537.8

  5. Checking the assumptions • Homoscedasticity Assumption:

  6. Normality assumption

  7. Independence Assumption

  8. Beam Model

  9. Cost Function • Minimize it. How? • 7 parameters, YI, CI, ρ, etc • Extremum may be dense in parameter space • Find “reasonable” values • Set beam to same as patch, search near given data, try to minimize a new cost function

  10. A new cost function • Needs to take into account spatial variations as well as frequency variations from the model and the data • So we use a weighted least squares cost function minimized a simplex method (fminsearch). • This doesn’t work. Phase change too much to overcome.

  11. What now then? • Limit the search. Fewer parameters, smaller variations. • And then, it works! (kind of)

  12. The data

  13. The parameters found • gamma 0.17916724273807 air damping • YI_beam ** 0.00000669769791 beam -- Young's modulus • CI_beam 0.01013780051727 beam -- internal damping • Kp 0.00036441688104 Kp for beam • rho_patch ** 0.08291057427864 linear density of patch • YI_patch ** 0.20912090251615 patch -- Young's modulus • CI_patch 0.00009783931434 patch -- internal damping

  14. Thank You Any Questions?

More Related