Experiments, Tests, and DataPurpose of Experiments and TestsSlide Number 3Controls CalibrationData and Sensor QualitySample StatisticsGaussian (Normal) DistributionSlide Number 9Massachusetts Institute of Techology 2.017Experiments, Tests, and DataMassachusetts Institute of Techology 2.017Purpose of Experiments and Tests• Prove or Support a Hypothesis– The Earth’s diameter is 6500km.– Multiple propellers on a single shaft can reduce cavitation (Turbinia).– Prokaryotes in the ocean fix carbon and consume other organisms, and the balance has profound impact on ocean uptake of CO2 . (Ed Delong, Ann Pearson, etc.)– Outriggers provide better roll stability than does a single hull in random beam seas, 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 TattleTale Model 8, and the performance obtained is XX.Massachusetts Institute of Techology 2.017• Does the work stand up to scrutiny?– Use of controls– Calibration– Data quality– Data processing– Documentation and record-keeping!Massachusetts Institute of Techology 2.017Controls • Did you really measure what you thought?• Rat Maze: Is the maze acoustically navigable? (R. Feynman)• Mass Spectroscopy: When you put in a sample of known composition, are the other bins clean?• When measuring electrical resistance, touch the probes together. Check a precision resistor too. • Resonance in load measurement rigs?• When measuring hull resistance, does zero speed give zero force?DUH!Massachusetts Institute of Techology 2.017Calibration• 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:– Manufacturer’s 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 or )– Linearity (if applicable)• Understand special properties of the sensor, e.g., drift, PWMMassachusetts Institute of Techology 2.017Data and Sensor Quality• Signal-to-Noise Ratio (SNR): compares to 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 Techology 2.017Sample Statistics• Sample mean m:• Sample standard dev. : = sqrt [ ( (x1 -m)2 + (x2 -m)2 + … + (xn -m)2 ) / (n-1) ] • Error budgets for multiplication and addition (A is standard deviation of A):(A + A)(B + B) ~ AB + AB+ BAExample: (1.0 + 0.2)(3.0 + 0.3) ~ 3.0 + 0.9(A + A) + (B + B) = A + B + (A+B)Example: (1.0 + s0.2) + (3.0 + s0.3) = 4.0 + 0.5Massachusetts Institute of Techology 2.017Gaussian (Normal) DistributionProbability Density Function f(x) ~ Histogramf(x) = exp [ - (x-m)2 / 22 ] / sqrt(2) / This is the most common distribution encountered in sensors and systems.+/- 1 covers 68.3% +/- 2 covers 95.4%+/- 3 covers 99.7%Area under f(x) is 1!Massachusetts Institute of Techology 2.017MIT OpenCourseWarehttp://ocw.mit.edu 2.017J Design of Electromechanical Robotic SystemsFall 2009 For information about citing these materials or our Terms of Use, visit:
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