slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Chanyoung Park Raphael T. Haftka PowerPoint Presentation
Download Presentation
Chanyoung Park Raphael T. Haftka

Loading in 2 Seconds...

play fullscreen
1 / 28

Chanyoung Park Raphael T. Haftka - PowerPoint PPT Presentation


  • 87 Views
  • Uploaded on

Paper Helicopter Project. Chanyoung Park Raphael T. Haftka. Problem1: Conservative estimate of the fall time. Estimating the 5 th percentile of the fall time of one helicopter Estimating the 5 th percentile to compensate the variability in the fall time ( aleatory uncertainty)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Chanyoung Park Raphael T. Haftka' - liseli


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Paper Helicopter Project

Chanyoung Park

Raphael T. Haftka

problem1 conservative estimate of the fall time
Problem1: Conservative estimate of the fall time
  • Estimating the 5th percentile of the fall time of one helicopter
    • Estimating the 5th percentile to compensate the variability in the fall time(aleatory uncertainty)
    • The sampling error (epistemic uncertainty)
    • Estimating the sampling uncertaintyin the mean and the STD
    • Obtaining a distribution of the 5th percentile
    • Taking the 5th percentile of the 5thpercentile distribution to compensatethe sampling error

mt,P

st,P

Sampling

tP

Sampling

t0.05,P

problem1 conservative estimate of the fall time1
Problem1: Conservative estimate of the fall time
  • Estimating the 5th percentile of the fall time of first helicopter (mean 3.78, std 0.37)
    • 100,000 5th percentiles of fall time
    • Helicopter 1 of the dataset 3
    • Height: 148.5 in
    • 2.88 (sec) is the 5th percentile of the histogram(a conservative estimate ofthe 5th percentile of the fall time for 95% confidence)
problem2 predicted variability using prior
Problem2: Predicted variability using prior
  • Calculating predicted variability in the fall time
    • We assume that the variability in the fall time is caused by the variability in the CD
    • The variability in the fall time is predicted using the computational model (quadratic model) and the distribution of the CD
    • The prior distribution represents our initial guess for the distribution of the CD

Height at time t

where

Steady state speed

problem2 comparing predicted variability and observed variability using prior
Problem2: Comparing predicted variability and observed variability using prior
  • Area metric with the prior
    • Data set 3
problem3 calibration posterior distribution of mean and standard deviation
Problem3: Calibration: Posterior distribution of mean and standard deviation
  • Estimating parameters of the CD distribution
    • We assume that CD of each helicopter follows the normal distribution
    • The parameters, CD and σtest are estimated using 10 data
    • Posterior distribution is obtained based on 10 fall time data
    • Non informative distribution is used for the standard deviation

After 1 update

After 5 updates

After 10 updates

problem3 comparing predicted variability using posterior and observed variability
Problem3: Comparing predicted variability using posterior and observed variability
  • Comparing MLE and sampling statistics
  • MCMC sampling
    • 10,000 pairs of the CD and the STD of CD are generated using Metropolis-Hastings algorithm
    • An independent bivariate normal distribution is used as a proposal distribution
    • MLE of the posterior distribution is used as a starting point
problem3 comparing predicted variability using posterior and observed variability1
Problem3: Comparing predicted variability using posterior and observed variability
  • Handling the epistemic uncertainty due to finite sample
    • How to handle epistemic uncertainty in the CD and the test standard deviation estimates?
    • Comparing the posterior predictive distribution of the fall time and the empirical CDF of tests (combining epistemic and aleatory uncertainties)
    • Using p-box with 95% confidence interval of epistemic uncertainty (separating epistemic and alreatory uncertainties)
problem3 comparing predicted variability using posterior and observed variability2
Problem3: Comparing predicted variability using posterior and observed variability
  • Area metric of the posterior predictive distribution of CD
problem3 comparing predicted variability using posterior and observed variability3
Problem3: Comparing predicted variability using posterior and observed variability
  • Area metric of the posterior predictive distribution of CD
problem4 predictive validation for the same height and different weight
Problem4: Predictive validation for the same height and different weight
  • Area metric of the posterior predictive distribution of CD
problem4 predictive validation for the same height and different weight1
Problem4: Predictive validation for the same height and different weight
  • Area metric of the distribution of CD with p-box
problem6 predictive validation for different height and the same weight
Problem6: Predictive validation for different height and the same weight
  • Area metric of the posterior predictive distribution of CD
problem6 predictive validation for different height and the same weight1
Problem6: Predictive validation for different height and the same weight
  • Area metric of the distribution of CD with p-box
problem5 l inear model
Problem5: Linear model
  • Area metric with the prior
    • Data set 3
comparison to predictive validation
Comparison to predictive validation
  • Area metric of the posterior predictive distribution of CD
    • The predictive validation with the linear model is not as successful as that with the quadratic model
  • Area metric with p-box
    • Area metric with p-box tries to capture the extreme discrepancy between the predicted variability and the observed variability
problem5 l inear model1
Problem5: Linear model
  • Area metric of the posterior predictive distribution of CD
problem5 linear model
Problem5: Linear model
  • Area metric of the distribution of CD with p-box
problem5 linear model with one clip
Problem5: Linear model with one clip
  • Area metric of the posterior predictive distribution of CD
problem5 linear model with one clip1
Problem5: Linear model with one clip
  • Area metric of the distribution of CD with p-box
comparison between quadratic and linear models
Comparison between quadratic and linear models
  • Area metric of the posterior predictive distribution of CD
  • Area metric of the distribution of CD with p-box
concluding remarks
Concluding remarks
  • Predictive validation for both quadratic and linear models
    • The predictive validation for different mass is a partially success
    • The predictive validation for different height is a success but the assumption of constant CD is not clearly proven
  • Comparison between models
    • Cannot conclude
  • Overall
    • Reason for the differences in the area metric is not clear
    • The effect of the manufacturing uncertainty is significant (i.e. very different area metrics for the same test condition)
slide23

Kaitlin Harris, VVUQ Fall 2013

  • Comments:
  • Chose to maintain uniform distribution for calibration parameter based on histogram results (vs normal)
  • Conclusions:
  • Best models: calibrated quadratic at both heights and calibrated linear with 2 paper clips
  • Worst models: un-calibrated linear with 2 paper clips and un-calibrated linear with 1 clip for data set 1
validation of analytical m odel used to predict fall time for paper helicopter by nikhil londhe

Validation of analytical model used to predict fall time for Paper HelicopterBy Nikhil Londhe

*Calibrated Analytical Model is validated to represent experimental data

*Quadratic dependence is valid assumption between drag force and speed

*For given difference in fall height, Cd can be assumed to be constant

slide25

Course Project: Validation of Drag Coefficient -Yiming Zhang

Validation based on 1 set of data:

Validation based on 3 set of data:

Quadratic Dependence

2 clips

Prior VS. Posterior Dist.

Prior Area Metric:0.4920

Prior Area Metric:0.4042

Post Area Metric:0.2

Post Area Metric:0.1695

95% Confidence 0.77

95% Confidence 0.83

Quadratic Dependence

1 clip

Predictive Validation.

Validation Area Metric:0.1267

Validation Area Metric:0.1923

If just use this set to calculate posterior.95% Confidence 0.86

If just use this set to calculate posterior.95% Confidence 0.82

Linear Dependence

2 clips & 1clip

Prior VS. Posterior Dist.

Summary:

2 clips:

1 clip:

2 clips:

Summary:

1 clip:

Posterior Area Metric:0.1987

Validation Area Metric:0.1960

Validation Area Metric: 0.1253

Posterior Area Metric:0.1729

Seems reasonable, but not accurate

Two confi. interval of Cd don’t coincide. Linear dependence seems inaccurate.

95% Confidence 0.8

95% Confidence 0.88

95% Confidence 0.8

95% Confidence 0.91

Quadratic Dependence

2 clips

Different height.

Validation Area Metric:0.1394

Validation Area Metric:0.0970

If just use this set to calculate posterior.95% Confidence 0.76

If just use this set to calculate posterior.95% Confidence 0.79

Summary: (1) Quadratic dependence seems accurate using one set; Quadratic and linear dependence both don’t match well using 3 sets;

(2) SRQ is required to be fall time. If use Cd as SRQ, comparison could be more consistent and clear;

(3) 0.8 seems a reasonable estimation of Cd. This estimation would be more accurate while introducing more sets of data.

problems
Problems
  • Problem1: Conservative estimate of the fall time
  • Problem2: Comparing predicted variability and observed variability using prior
  • Problem3: Comparing predicted variability and observed variability using posterior
  • Problem4: Predictive validation for the same height and different weight
  • Problem5: Comparing the quadratic and linear models
  • Problem6: Predictive validation for different height and the same weight (proving the assumption of constant CD)
problem1 conservative estimate of the fall time2
Problem1: Conservative estimate of the fall time
  • Estimating the 5th percentile of the fall time of one helicopter
    • Since fall time follows a normal distribution, estimating the 5th percentile is based on estimating the mean and standard deviation (STD) of the fall time distribution
    • The mean and STD are estimated based on 10 samples
    • There is epistemic uncertainty in the estimated mean and STD due to a finite number of samples
    • To compensate the epistemic uncertainty, a conservative measure to compensate the epistemic uncertainty is required
    • Estimating the 5th percentile with 95% confidence level