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

Transcription

1 Week 1 Lecture: (1) Course Introduction (2) Data Analysis and Processing January 11, 2016

2 Welcome, Class! Instructor: C. Thomas Chiou, Teaching assistant: Jared Taylor, Website: Please sound off all electronic devices and no eating in lecture No eating and drinking in lab Prefi subject line of all your s with AerE322-2

3 Aircraft Structures Conventional manufacturing: beam, bar, column, truss, plate, etc. connected by screws, rivets, wield, etc. subjected to bending, torsion, etc. Source: pnveme/emem671/ima ges/skybolt_cutaway_w hite_truss.jpg Source: CNDE.iastate.edu Modern advances: plastic+metal+ceramic composites, honeycomb sandwich, etc. via bonding, etc. Additive manufacturing 3

4 Course Renovation 4

5 A New Home! Moved in 0257 Howe Fall 2014 renovation continues! 5

6 Renovation: a Working Progress Throughput increased % 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 6

7 Lab Topics Practice eperiment 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 7

8 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 8

9 Lab Activity Highlights 9

10 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-andplay with centralized interface Fully monitored and controlled by PC via user-friendly software Fast turnaround Cost effective 10

11 Rapid Structure Design and Prototyping: S14 Student Term Project Eamples Wing structure vibration Unbalanced propeller Underwing fuel tank Truss force distribution Impact loading of landing gear 11

12 Rapid Structure Design and Prototyping: F14 Student Term Project Eamples Wing structure vibration (flutter) Vibration of quad-copter FEM (ANSYS) Stress analysis Force analysis of landing gear Missile payload under wing 12

13 Rapid Structure Design and Prototyping: S15 Student Term Project Eamples Stress analysis of wing structure with payload more quantitative! Vibration (resonance) analysis of cantilever beam 13

14 Improving Computational Skills: A Gradual Approach Structural analysis via matri method emphasized Concept introduced gently from early 4-DOF beam to later 6-DOF frame Smooth learning curve toward finite element method (covered in AerE 421, etc.) 14

15 More Coverage of Vibration Analysis 15

16 Vibration Analysis: Fun Stuff 16

17 Lab 1 and homework 1: Data Analysis and Processing 17

18 Data Analysis: Basic Concepts Suppose you and your classmates are tasked to measure something Some measurement True value (often unknown) operator Data (Measurements) = true value + error 18

19 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. histogram measurement True value operator occurrence measurement 19

20 Data Analysis: Basic Concepts (cont d) Systematic error (bias) Caused by imperfect measurement methods and/or calibrations, environmental interferences, etc. in a predictable way Say you and your classmates use the same ruler which is inaccurate with a constant offset or bias Some measurement True value operator 20

21 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) 21

22 Data Analysis: Basic Concepts (cont d) Reproducibility Is your Nobel-prize-winning discovery a one-time deal? Can you repeat the same measurement with the same accuracy? Identification of Outlier Some measurement operator 22

23 Statistics 101: Quantifications of Data measurement True value operator occurrence histogram occurrence distribution measurement measurement Mean (central tendency) Arithmetic mean μμ = nn Standard Deviation (variability) nn = 1 nn ii=1 ii σσ = nn 1 nn ii=1 ii μμ 2 Variance = σ 2 23

24 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 yn ( 2) + yn ( 1) + yn ( ) + yn ( + 1) + yn ( + 2) y' ( n) =, 5 y(n-1) y(n-2) y(n) y(n+2) y(n+1) here average span = 5 (,y) data equal spaced in y(n+3) yn ( 1) + yn ( ) + yn ( + 1) + yn ( + 2) + yn ( + 3) y '( n + 1) =, etc. 5 24

25 Data Processing: Smoothing (cont d) A priori information is important! Your prior knowledge about the data dictate how you will process the data. span = 5 Raw data Short span to preserve feature span = 51 edge effect! long span to maimize smoothing 25

26 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 net run Raw data span combinations of 11,31,51,71,31,21,11,5 26

27 Data Processing: Outlier Removal Brute force approach: remove them by hand if you can guess where the data suppose to be located Some measurement operator 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 27

28 Data Processing: Outlier Removal (cont d) For more elaborate data, the following simple formula allows you to remove a hump from a slope by using good neighboring data 1 ( 1) y y = y + y ( 1,y 1 ) ( 2,y 2 ) Raw data 5,11 smoothing Hump removed 28

29 Data Processing: Curve Fitting 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 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. 29

30 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 (,y) data to a model function f with parameters a: y = f( a ; ) e.g. y= a+ a+ a You can use a minimization software to obtain the best-fit parameters a by minimizing the least squares sum Min. N i= 1 [ yˆ f( a ; )] 2 i i best-fit parameters a y ˆi : measured data 30

31 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: y = 2+ 5 y =

32 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! 32

33 Homework 1: Data Processing Homework assignment and practice data file received from (also available from class web site) θ Height-distance trajectory of a projectile fired at an angle Smoothed data & Best-fit curve? Noisy corrupted raw data Due 11:59pm, Wednesday, January 27 33

34 Data Processing: Useful Matlab Functions 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(,y,n) = original -array y = original y-array n = degree of polynomial p = array of the polynomial s coefficients Polynomial Curve Evaluation: y = polyval(p,) p = array of polynomial s coefficients = array of -data y = array of polynomial s y-data General Curve Fitting: Matlab function: lsqcurvefit = lsqcurvefit(fun,0,data,ydata) fun = function format 0 = original guess of the coefficients data = -array of data ydata = y-array of data = coefficients of the curve eample of fun and 0: fun (1)+(2)*t+(3)*t.*t 0 = [1,5,10] 34

35 Lab 1: Practice Eperiment (starting this Thursday) 35

36 !!! 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)!!! 36