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    Experiments, Tests, and Data

    Massachusetts Institute of Technology, Subject 2.017

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    Purpose of Experiments and Tests

    Prove or Support a Hypothesis The Earths diameter is 6500km.

    Multiple propellers on a single shaft can reduce cavitation (Turbinia).

    The archaea prokaryotes in the ocean fix carbon and consume other organisms,

    and the balance has profound impact on ocean uptake of CO2. (Ed Delong, AnnPearson, etc.)

    Outriggers provide better roll stability than does a single hull in random beamseas, when wavelength is much larger than the beam.

    Prove a Capability, Support Design Manned flight to the upper atmosphere can be achieved bi-weekly with a

    specialized aircraft (X-Prize).

    Characteristic of lift force as a function of elevator aspect ratio and inflow angle.

    Delay calculation in pulsed 20kHz acoustic signals is possible with the TattleTaleModel 8, and the performance obtained is XX.

    Massachusetts Institute of Technology, Subject 2.017

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    Does the work

    stand up to

    scrutiny?

    Use of controls

    Calibration

    Data qualityData processing

    Documentation and

    record-keeping!

    Massachusetts Institute of Technology, Subject 2.017

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    Controls

    Did you really measure what you thought?

    Rat Maze: Is the maze acoustically navigable?(R. Feynman)

    Mass Spectroscopy: When you put in a sampleof known composition, are the other bins clean?

    When measuring electrical resistance, touch theprobes together. Check a precision resistor too.

    Resonance in load measurement rigs?

    When measuring hull resistance, does zero speed give zero force?

    Massachusetts Institute of Technology, Subject 2.017

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    Calibration

    More time can be spent on calibration than the rest of the experiment!

    Sensors should be calibrated and re-checked using independent references, such as:

    Manufacturers specifications

    Another sensor with very well-known calibration A tape measure, protractor, calipers, weights & balance, stopwatch, etc..

    Calibration range should include the expected range in the experiment. Some statistics of the calibration:

    Precision of fit (r-value orV)

    Linearity (if applicable)

    Understand special properties of the sensor, e.g., drift, PWM

    Massachusetts Institute of Technology, Subject 2.017

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    Data and Sensor Quality

    Signal-to-Noise Ratio

    (SNR): compares Vto the signal you want

    Repeatability/Precision: If

    we run the same test again,

    how close is the answer?

    Accuracy: Take the average

    of a large number of tests

    is it the right value?

    Massachusetts Institute of Technology, Subject 2.017

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    Time and Frequency Domain

    Fourier series/transforms establish an exactcorrespondence between these domains, e.g.,

    X = VTcos( 2Sm t / T ) z(t) dt * 2 / T, m = 0,1,2,m 0Y = V

    Tsin( 2Sm t / T ) z(t) dt * 2 / T

    m 0

    z(t) = X0 / 2 + 6Xm cos( 2Sm t / T ) + 6Ym sin( 2Sm t / T )

    Massachusetts Institute of Technology, Subject 2.017

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    Time Resolution in

    Sampled Systems

    The Sampling Theorom shows that the highestfrequency that can be detected by sampling at frequencyZ = 2S't is the Nyquist rate: ZN = Zs / 2.s

    Higher frequencies than this are aliased to the range

    below the Nyquist rate, through frequency folding. Thisincludes sensor noise!

    The required rate for visual analysis of the signal, andphase and magnitude calculation is much higher, say tensamples per cycle.

    Massachusetts Institute of Technology, Subject 2.017

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    Sample Statistics

    Sample mean m:

    Sample standard dev. V:V= sqrt [ ( (x1-m)2 + (x2-m)2 + + (xn-m)2 ) / (n-1) ]

    Error budgets for multiplication and addition

    (VA is standard deviation of A):

    (A + VA)(B + VB) ~ AB + AVB + BVA

    Example: (1.0 + V0.2)(3.0 + V0.3) ~ 3.0 + V0.9

    (A + VA) + (B + VB) = A + B + V(A+B)

    Example: (1.0 + s0.2) + (3.0 + s0.3) = 4.0 + V0.5

    Massachusetts Institute of Technology, Subject 2.017

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    Gaussian (Normal) Distribution

    Probability Density Function f(x) ~ Histogramf(x) = exp [ - (x-m)2 / 2V2 ] / sqrt(2S) / V

    This is the most common

    distribution encountered in sensors and systems.

    +/- 1Vcovers 68.3% +/- 2Vcovers 95.4%+/- 3Vcovers 99.7%Area under f(x) is 1!

    Massachusetts Institute of Technology, Subject 2.017

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    Filtering of Signals

    Filterx xf

    Use good judgement!

    filtering brings out trends, reduces noise

    filtering obscures dynamic responseCausal filtering: xf(t) depends only on past

    measurements appropriate for real-time implementation

    Example: xf(t) = (1-H)xf(t-1) + Hx(t-1)Acausal filtering: xf(t) depends on all

    measurements appropriate for post-processing

    Example: xf(t) = [ x(t+1) + x(t) + x(t-1) ] / 3

    Massachusetts Institute of Technology, Subject 2.017

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    A first-order filter transferfunction in the freq. domain:

    xf(jZ) / x(jZ) = O/ (jw + O)

    At low Z, this is approximately1 (OO)

    At highZ

    , this goes to 0magnitude, with 90 degreesphase lag (O/jZ= -jOZ)Time domain equivalent:

    dxf/dt = O(x xf)In discrete time, try

    xf(k) = (1-O't) xf(k-1) +O't x(k-1)

    Massachusetts Institute of Technology, Subject 2.017

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    BUT linear filters will not handle outliers very well!

    First defense against outliers: find out their originand eliminate them at the beginning!

    Detection: Exceeding a known, fixed bound, or animpossible deviation from previous values. Example:vehicle speed >> the possible value given thrust leveland prior tests.

    Second defense: set data to NaN (or equivalent), soit wont be used in calculations.

    Third defense: try to fill in.

    Example:

    ifabs(x(k)

    x(k

    1))

    >MX,

    x(k)=x(k1);end;

    Limited usefulness!Massachusetts Institute of Technology, Subject 2.017

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    Presentations: Written

    and Spoken

    or

    People will pay more attention to you if you communicate well!

    Massachusetts Institute of Technology, Subject 2.017

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    Sources and Ethics

    Somebody has almost certainly thought aboutwhat you are doing, and parts of it have almostcertainly been solved.

    For specific items, you must give an original

    source and cite it properly. Refereed publications vs. flashy Internet

    postings.

    Plagiarism: Consider it ILLEGAL.If there is any question about whether a phrase(or even a particular word) should be cited,protect yourself! and the associated noise is

    systematically coupled to the

    underlying process [13].

    Massachusetts Institute of Technology, Subject 2.017

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    Linearity

    Start at the beginning

    and go to the end!

    Antithesis: Michael

    Ondaatji (The

    English Patient)

    Flowchart or detailed

    outline may help

    Omit needless

    words*.

    * Strunk, Jr., W. and E.B. White, 1972.The elements of style. Allyn and

    Bacon: Boston.

    Massachusetts Institute of Technology, Subject 2.017

    Introduction:

    Approach:

    Discussion:

    Bring reader from general to specific

    State hypothesis or objective

    Indicate why work is important

    Review prior work that applies

    etc

    How the experiment or test was designed

    Details of the apparatus or system

    Accuracy and precision issues etc

    Results:

    Major Result A, with figures and description

    Major Result B

    etc

    Do results support hypothesis?

    Impact of findings

    Future work

    etc

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    Pointers on Speaking

    The audience is here to see YOU, not

    just your materials.

    Smile and engage them!

    Write out your talk so it is

    clean from start to end.

    Dont lose anyone!

    Practice your talk so you

    are confident up there.

    Get feedback on your talk,

    because it will help.

    distribution of expertise

    level in the audience

    layman expert

    cumulative

    average YOU average YOU

    Prepare for questions.student (student) professional (professional)

    90% of the talk accessible to

    90% of the audience

    Massachusetts Institute of Technology, Subject 2.017

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    A GOOD FIGURE > 1000 WORDSA bad figure is worth a few bad words

    Massachusetts Institute of Technology, Subject 2.017

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    Vehicle trajectory: one

    hidden independent

    variable; five dependent

    variables

    Wind speed and direction as a

    function of time. Top two plots

    are combined into the bottom

    plot: one independent

    variable, three dependentvariables.

    Massachusetts Institute of Technology, Subject 2.017

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    Figure from Principles of Naval Architecture, E. Lewis, ed.,

    SNAME: New York, 1988. Original reference: Vossers, G., and

    W.A. Swaan 1960. Some seakeeping tests with a Victory model.

    Int. Shipbuilding Progress.

    Image removed for copyright reasons.Figure and its caption from above-mentioned source.

    Shows two independent

    and one dependent

    variable. Style shows the

    effects of varying phase and period.

    Caption injured, and y-axis label missing; gives

    three independent variables (length ratio, Froude

    number, and heading to waves) and one

    dependent variable (added power coefficient).Massachusetts Institute of Technology, Subject 2.017