Modeling with Poisson's Posse

Kristoph KleinerAlice Lou

Nathan stokes

Data Collected

Measured the vibrations of a Thin beam caused by surface-mounted PZT patches

Repeated the measurements ten times

Spring Model

Initial approach: to understand modeling vibrations, we first considered the underdamped spring model, my’’+By’+ky=Fnet

However, this model was a poor fit forthe beam data.

First model using raw data

0 0.5 1 1.5 2 2.5 3 3.5-1

0

1x 10

-4

Time (s)

Dis

pla

cem

ent

(m)

Model

Data

Descriptive Statistics

Standard deviation

C= 0.1118K= 6.8544

C K

0.9 1.510e+003

0.7 1.556e+003

0.5 1.5595e+003

0.6 1.5546e+003

0.8 1.5454e+003

0.6 1.5376e+003

0.5 1.5501e+003

0.6 1.5474e+003

0.6 1.5474e+003

0.8 1.5565e+003

1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Index of data

Est

imat

ion

of C

C

meanmean+sd

mean+2sd

1 2 3 4 5 6 7 8 9

1535

1540

1545

1550

1555

1560

Index of data

Est

imat

ion

of K

K

meanmean-sd

mean-2sd

The Optimized q0

0 0.5 1 1.5 2 2.5 3 3.5-1

0

1x 10

-4

Time (s)

Dis

plac

emen

t (m

)

Model

Data

Side-by-Side Comparison

500 1000 1500 2000 2500 3000 3500

-5

0

5

x 10-5

Dat

a

500 1000 1500 2000 2500 3000 3500

-5

0

5

x 10-5

Mod

el

500 1000 1500 2000 2500 3000 3500

-5

0

5

x 10-5

Res

idua

l

Residual plot

500 1000 1500 2000 2500 3000 3500

-6

-4

-2

0

2

4

6

x 10-5

Res

idua

l

Time

Comparison with normal PDF

-4 -3 -2 -1 0 1 2 3 4-1.5

-1

-0.5

0

0.5

1

1.5x 10

-4

Standard Normal Quantiles

Quantile

s o

f In

put

Sam

ple

QQ Plot of Sample Data versus Standard Normal

Thank You !