Week 1 Lecture: (1) Course Introduction (2) Data Analysis and Processing

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Aer E 322: Aerospace Structures Laboratory

Week 1 Lecture:

(1) Course Introduction

(2) Data Analysis and Processing

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Aer E 322: Aerospace Structures Laboratory

Welcome, Class!

Instructor:

C. Thomas Chiou, [email protected]

Teaching assistant:

Jared Taylor, [email protected]

Website:

http://thermal.cnde.iastate.edu/aere322

• Please sound off all electronic devices and no eating in lecture • No eating and drinking in lab

• Prefix subject line of all your e-mails with “AerE322-”

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Aer E 322: Aerospace Structures Laboratory 3 Source: http://people.rit.edu/~ pnveme/EMEM671/Ima ges/skybolt_cutaway_w hite_truss.jpg

Aircraft Structures

Conventional manufacturing:

beam, bar, column, truss, plate, etc. connected by screws, rivets, wield, etc. subjected to bending, torsion, etc.

Modern advances:

plastic+metal+ceramic composites, honeycomb

sandwich, etc. via bonding, etc.

Additive manufacturing

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A New Home!

Moved in 0257 Howe Fall 2014

renovation continues!

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Renovation: a Working Progress



Throughput increased 300-500% by the addition of

new Instron load stations and other equipment



Lab topics largely revised/re-designed (near half are

new)



Fully computerized and multi-media driven



Instruction videos made for all lab topics

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Lab Topics

 Practice experiment and data analysis: lab 1, HW 1  Stress concentration-photoelasticity: lab 2

 Column buckling testing and analysis: lab 3  Composite laminate design: lab 4

 Strain gage applications: lab 5

 Beam deflection and analysis: lab 6, HW 2  Thin-walled section and shear center: lab 7

 Riveted joint design, fabrication and testing: lab 8  2D frame testing and analysis: lab 9, HW 3

 Structural vibration analysis: lab 10  3D structure model building: lab 10

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Class Web Site

 Full download of

all lecture notes, lab assignments and related

documents

 Online submission of lab reports and homework

 Online composite calculator

 Peer evaluations

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Lab Activity Highlights

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Rapid Structure Design, Prototyping and Learning



PASCO tool kits: “Lego”-like

building blocks specially designed

for structure model construction



Various load cells, motion sensors,

vibration generator, etc.

plug-and-play with centralized interface



Fully monitored and controlled by

PC via user-friendly software



Fast turnaround



Cost effective

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Rapid Structure Design and Prototyping:

S14 Student Term Project Examples

Unbalanced propeller Wing structure vibration

Underwing fuel tank

Impact loading of landing gear

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F14 Student Term Project Examples

Wing structure vibration (flutter)

Force analysis of landing gear

FEM (ANSYS) Stress analysis

Vibration of quad-copter

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S15 Student Term Project Examples

Stress analysis of wing structure with payload

Vibration (resonance) analysis of cantilever beam

more

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Improving Computational Skills:

A Gradual Approach



Structural analysis via matrix method emphasized



Concept introduced gently from early 4-DOF beam to

later 6-DOF frame



Smooth learning curve toward finite element method

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Lab 1 and homework 1:

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Data Analysis: Basic Concepts

…..

x x x x _{x x}

…..

So m e m ea su re m en t operator True value (often unknown) Suppose you and your classmates are tasked to measure something …

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Data Analysis: Basic Concepts

(cont’d)

Random error

Random error, often called “noise” and “fluctuation”, is almost always incurred in measurement, causing the data to spread around a central average value (hopefully the true value) in a unpredictable way

There are a variety of random error types and sources:

thermal noise, electronic noise, human interpretation error, quantization/truncation/rounding error, etc.

….. ….. x x x x _{x x} ….. me as ur eme nt operator True value measurement occur re nce histogram

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Data Analysis: Basic Concepts

(cont’d)

Systematic error (bias)

…..

x x x x _{x x}

…..

So m e m ea su re m en t operator True value

Say you and your classmates use the same ruler which is inaccurate with a constant offset or bias …

Caused by imperfect measurement methods and/or calibrations, environmental interferences, etc. in a predictable way

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Data Analysis: Basic Concepts

(cont’d)

Level of Accuracy, Precision, Resolution

The accuracy of measurement is often dictated by measuring device’s resolution. E.g. your ruler’s smallest marking is only 1/8 inch (so don’t bother to take data in 1/64 inch).

Sometimes the environment (e.g. vibration) limits the data accuracy, even your measuring device has high precision

Sampling, Population, Sampling Rate

Sampling describes the process of data collection from a sample group, organization or population. Sampling rate

determines how the data are collected in time (frequency) or in space (spacing)

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Data Analysis: Basic Concepts

(cont’d)

Identification of Outlier

…..

x x x x x x

…..

So m e m ea su re m en t operator

Reproducibility

Is your Nobel-prize-winning discovery a one-time deal? Can you repeat the same measurement with the same accuracy?

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Statistics 101: Quantifications of Data

….. ….. x x x x _x x ….. m ea su rem en t operator True value measurement occur re nce histogram measurement occur re nce distribution

Mean (central tendency)

Arithmetic mean

Standard Deviation (variability)

𝜇𝜇 = 𝑥𝑥1 + 𝑥𝑥2 + 𝑥𝑥_𝑛𝑛 3 + ⋯ = _{𝑛𝑛 �}1 𝑖𝑖=1 𝑛𝑛 𝑥𝑥_𝑖𝑖 𝜎𝜎 = _{𝑛𝑛 �}1 𝑖𝑖=1 𝑛𝑛 𝑥𝑥_𝑖𝑖 − 𝜇𝜇 2 _{Variance =}_σ₂

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Data Processing: Smoothing

Smoothing operations are commonly applied to the data for suppressing interference or noise while preserving important features. Popular algorithms include running average and Savitzky-Golay filter

Running average (or moving average) works by continuously

taking average of neighboring data on the run

(x,y) data equal spaced in x

y(n-2)

…

y(n-1)

…

y(n) y(n+1) y(n+2) y(n+3) ( 2) ( 1) ( ) ( 1) ( 2 '( ) ), 5 y n y n y n y n y n y n = − + − + + + + + ( 1) ( ) ( 1) ( 2) ( 3) 1 5 '( ) , . y n+ = y n− + y n + y n+ + y n+ + y n+ etc

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Data Processing: Smoothing

(cont’d)

A priori information is important! Your prior knowledge about the data dictate how you will process the data.

Short span to preserve feature span = 5 span = 51 long span to maximize smoothing Raw data edge effect!

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Data Processing: Smoothing

(cont’d)

Often the running average is applied iteratively using multiple passes with different average spans - output of previous run become the new data for next run

span combinations of 11,31,51,71,31,21,11,5 Raw data

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Data Processing: Outlier Removal

Brute force approach: remove them “by hand” if you can guess where the data suppose to be located

…..

x x x x x x

…..

So m e m ea su re m en t operator x

Or you can continue using running average in multiple passes to smooth out the outliers. But don’t overdo it – otherwise you may ruin the underlying trend you wish to preserve

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Data Processing: Outlier Removal

(cont’d)

2 1 1 1 2 1 ( ) y y y y x x x x − = + − −

For more elaborate data, the following simple formula allows you to remove a “hump” from a slope by using “good” neighboring data

(x₁,y₁) (x2,y2)

Raw data _{5,11 smoothing} Hump removed

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Data Processing: Curve Fitting

As mentioned, A priori information is important. Your knowledge about the data will help you to decide how you will fit the data: the choice of the fitting functions and the parameters within, e.g. straight line vs. polynomials, first order vs. second order, etc.

Once you have done enough data smoothing, you may want to continue fitting the smoothed data to a model for gaining more insight to the underlying trend of the data and even backing out key parameters of the trend

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Data Processing: Curve Fitting

(cont’d)

Least squares fit

A popular and robust method for general functional fit: linear or non-linear. Suppose you wish to fit your (x,y) data to a model function f with parameters a:

2

1 2 3

y a a x a x

= +

+

( ; )

y f a x= _e.g.

You can use a minimization software to obtain the best-fit parameters a by minimizing the least squares sum

[

]

2 1 ˆ ( ; ) N i i i y f a x = −

∑

Min. best-fit parameters

a

ˆ

_i

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Data Processing: Curve Fitting

(cont’d)

Data after 5,11 smoothing

and hump removed (page 24) _{Fitted with linear line}

Original underlying baseline: Best-fit baseline:

2 5

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Data Processing: Outlier Removal Revisited

Warning! Once again, your prior knowledge about the data dictate how you should process the data. Suppose your data actually came from a communication channel in which some non-zero signals were transmitted. Then those non-zero

outliers are the features you need to keep and the random noise and the baseline are the ones you should remove!

Raw data _{5,11 smoothing} _{baseline removed}

The “hump” you actually want to keep!

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Homework 1: Data Processing

Height-distance trajectory of a projectile fired at

an angle

Noisy corrupted raw data

Smoothed data & Best-fit curve ?

Homework assignment and practice data file received from e-mail (also available from class web site)

Due 11:59pm, Wednesday, January 27

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Data Processing: Useful Matlab Functions

Polynomial Curve Evaluation:

y = polyval(p,x)

p = array of polynomial’s coefficients x = array of x-data

y = array of polynomial’s y-data General Curve Fitting:

Matlab function: lsqcurvefit

x = lsqcurvefit(fun,x0,xdata,ydata) fun = function format

x0 = original guess of the coefficients xdata = x-array of data

ydata = y-array of data

x = coefficients of the curve example of fun and x0:

fun = @(x,t) x(1)+x(2)*t+x(3)*t.*t x0 = [1,5,10]

Running Average:

Matlab function: smooth yy = smooth(y,span) y = original data

span = running average span yy = output of smoothed data The default span is 5.

Polynomial Curve Fitting:

Matlab function: polyfit p = polyfit(x,y,n)

x = original x-array y = original y-array

n = degree of polynomial

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!!! Remember to apply what you learned

today in data analysis and processing to all

other labs in this course (and your future

measurement work as well) !!!

http://thermal.cnde.iastate.edu/aere322

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