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Class:MAE 2381 - EXPERIMENTAL METHODS AND MEASUREMENTS
Subject:Mechanical and Aerospace Engineering
University:University of Texas - Arlington
Term:Fall 2014
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Linear Trend-line A linear trend-line is a best-fit straight line that is used with simple linear data sets. A linear trend-line usually shows that something is increasing or decreasing at a steady rate.
Polynomial Trend-line A polynomial trend-line is a curved line that is used when data fluctuates. It is useful, for example, for analyzing gains and losses over a large data set. The order of the polynomial can be determined by the number of fluctuations in the data or by how many bends (hills and valleys) appear in the curve. An Order 2 polynomial trend-line generally has only one hill or valley. Order 3 generally has one or two hills or valleys. Order 4 generally has up to three.
Power Trend-line power trend-line is a curved line that is best used with data sets that compare measurements that increase at a specific rate — for example, the acceleration of a race car at one-second intervals. You cannot create a power trend-line if your data contains zero or negative values.
Trend-line Exponential


An exponential trend-line is a curved line that is most useful when data values rise or fall at increasingly higher rates. You cannot create an exponential trend-line if your data contains zero or negative values.

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Why is Plagiarism Bad?
  1. Constitutes Academic Theft and Fraud
  2. bad study and homework habits
  3. Misrepresentation of abilities
Unintentional Plagiarism

  1. Paraphrasing without giving citation
  2. Summarizing without citation
  3. Giving inappropriate, improper, or incorrect information about the source
  4. improper citation of a source
intentional Plag.
  1. Copying words, sentences, or paragraphs from previously published articles
  2. Quoting only a part of a quotation and claiming the rest as your own
  3. paste of material from sources without giving full citation,quotation, or attribution
  4. Buying ready made material from internet vendors
Infamous Plagiarism Scandals
  1. Joe Biden: Plagiarism in Law School
  2. Plagiarized substantial portions of a law review article in Law School
  3. Failed course, later caused substantial damage to presidential bid
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When in Doubt Cite teh source
cheating
  1. Plagiarism
  2. Collusion:
    1. Giving work to or taking it from another student for the purposes of helping one of them improve their work
To avoid cheating allegations:
  1. Summarize, paraphrase, and cite
  2. Ask for help if you need it
  3. Do your own work
What Does Not Constitute Cheating ?
  1. Two or more students working together at the same time Must each produce their own work
  2. Getting assistance with proofreading or editing
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Measurement
  1. the act of assigning a specific value to a specific variable
Measurement system (1) sensor–transducer stage, (2) signal-conditioning
stage, (3) output stage, and (4) feedback-control stage. These stages form the bridge between the
input to the measurement system and the system output, a quantity that is used to infer the value of
the physical variable measured

Stage 1: Sensor A physical element that employs a natural phenomenon to sense’ the variable being measured.
Stage 2:Transducer
  1. Converts sensed information into a detectable signal
  1. This can be a change in voltage, resistance, current, etc. or a mechanical signal like the mercury level in thermometer
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Stage 3: Signal Conditioner
  1. Takes transducer signal and modifies it to a desired magnitude range.
  2. A portion of the signal may be removed with a filter (to be explained later).
Stage 4: Output Stage
Feedback Control
  1. Measurement tool coupled to another device that can affect the value of the measured parameter.
Experimental Test Plan Variables and parameters
What question needs to be answered?
What needs to be measured
What variables affect the results? Often the most troublesome question
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Variables
  1. Independent variable:Can be changed independently of other variables
  2. Dependent variable: Affected by changes in other variables “y = y(x)”
  3. Extraneous variables: Can’t be controlled in the experiment  and Differences in results with same conditions
Parameters Functional groups’ of variables.Parameter = combination of properties
Contrast to “property”: physical characteristic of system
2) Tolerance Design Plan How can measurements be made?
Highly accurate/precise experiments can become expensive.

Noise and Interference Two types of extraneous variables: Noise and Interference
Two types of extraneous variables
Noise: Random variable in the measured signal. Increases scatter of data but it can be accounted for with statistics (filtering, averaging, etc.) Interference: Imposes a trend on the signal which can be more difficult to account for
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3) Data Reduction Plan How will the data collected answer the question?
What trend is being looked for?
If there are anticipated results, how will they be analyzed?
Replication
  1. repeat measurements in another test with similar operating conditions
Repetition repeat the same measurement during a single test Helps to see if there is any variation in the variable being measured
Concomitant Methods
  1. Get two or more estimates of a measurement based on different methods that can be compared
  2. Helps to validate results so people believe them
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Calibration definition
  1. Apply a known input value to a measurement system to observe the output
  2. Known input value’ is very important and must be accurate It is called a standard: best estimate of the ‘true value’Weights, voltage, force profile, etc.
Static Calibration Values are held constant and you make a calibration curve
Dynamic Calibration
  1. Variables that change in time and space have magnitude and frequency
Static sensitivity:
  1. slope of calibration curve between input and output
  2. Constant for a linear relationship
  3. Most devices that can be purchased are linear for simplicity
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Resolution:
  1. Smallest increment of the value that can be measured (i.e., tick marks on a ruler or dial gauge)
Accuracy
  1. Accuracy: closeness of agreement between measured value and true value Do we ever know the true value?  (Hint: no, almost never)
Error
  1. Quantitative measurement
  2. Difference between measured value and true value
Uncertainty:
  1. if the true value is not known, then this is an estimate of the interval around the measurement where the true value is
We should usually say “the uncertainty is...” instead of “the error
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Types of Errors & Causes
  1. Precision errors: not repeatable Scatter about a mean Quoted as mean and an indication of deviation,
Experimental ‘noise’ is a big factor in precision errors
Finite quantized values in measurement system can’t be 100% precise
Bias (or systematic) errors (accuracy)
These are repeatable and may be due to multiple factors
 Bias in instrument, Bias in instrument,  In many instances, systematic errors can be removed by calibrating the instrument This is only true if you know you have a systematic error
Hysteresis Error
  1. The output of the system is dependent on the value that was previously measured
Linearity Error A linear static calibration curve has the equation
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Zero error:
  1. Drift in output for the condition of zero input May occur over time in some devices
Amplitude: magnitude of the input
Frequency how the input changes with time
order of a system (zero, first, second) Describes behavior of system response to input
  1. Information can consist of multiple magnitudes with associated frequencies
  2. it is common to view data as amplitude vs. time,Time domain. Amplitude vs. frequency is just as important. Frequency domain
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A/D Conversion
where M is the number of bits of the register
2 M is number of quantized values available that the converted signal can have in the range. Called “counts”
The converter compares the analog signal and finds the
closest digital value of voltage to it
Truncates: always rounds down
Waveform Classifications
  1. Analog: continuous in time (most things in nature)
  2. Discrete time: only information at certain points in time (but quantity measured still varies continuously)
  3. Discrete time: only information at certain points in time but quantity measured still varies continuously)
Signal Amplification
  1. Amplification involves an increase in the overall magnitude of a signal; usually voltage
Aliasing

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Nyquist rate and frequency
Folding
  1. Frequencies in the original signal above, fN are folded back into the sampled signal as lower frequencies below, fN
Practical issues
Types of Waveforms
  1. varies in a way that is predictable
  2. Simple periodic: only one frequency
  3. Complex periodic: more than 1 frequency
  4. A periodic: does not repeat at regular intervals
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Non deterministic
  1. cannot be predicted, must be
  2. described by statistical characteristics: Noise, turbulence
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List View: Terms & Definitions

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 Linear Trend-lineA linear trend-line is a best-fit straight line that is used with simple linear data sets. A linear trend-line usually shows that something is increasing or decreasing at a steady rate.
 Polynomial Trend-lineA polynomial trend-line is a curved line that is used when data fluctuates. It is useful, for example, for analyzing gains and losses over a large data set. The order of the polynomial can be determined by the number of fluctuations in the data or by how many bends (hills and valleys) appear in the curve. An Order 2 polynomial trend-line generally has only one hill or valley. Order 3 generally has one or two hills or valleys. Order 4 generally has up to three.
 Power Trend-linepower trend-line is a curved line that is best used with data sets that compare measurements that increase at a specific rate — for example, the acceleration of a race car at one-second intervals. You cannot create a power trend-line if your data contains zero or negative values.
 Trend-line Exponential


An exponential trend-line is a curved line that is most useful when data values rise or fall at increasingly higher rates. You cannot create an exponential trend-line if your data contains zero or negative values.

 Why is Plagiarism Bad?
  1. Constitutes Academic Theft and Fraud
  2. bad study and homework habits
  3. Misrepresentation of abilities
 Unintentional Plagiarism

  1. Paraphrasing without giving citation
  2. Summarizing without citation
  3. Giving inappropriate, improper, or incorrect information about the source
  4. improper citation of a source
 intentional Plag.
  1. Copying words, sentences, or paragraphs from previously published articles
  2. Quoting only a part of a quotation and claiming the rest as your own
  3. paste of material from sources without giving full citation,quotation, or attribution
  4. Buying ready made material from internet vendors
 Infamous Plagiarism Scandals
  1. Joe Biden: Plagiarism in Law School
  2. Plagiarized substantial portions of a law review article in Law School
  3. Failed course, later caused substantial damage to presidential bid
 When in DoubtCite teh source
 cheating
  1. Plagiarism
  2. Collusion:
    1. Giving work to or taking it from another student for the purposes of helping one of them improve their work
 To avoid cheating allegations:
  1. Summarize, paraphrase, and cite
  2. Ask for help if you need it
  3. Do your own work
 What Does Not Constitute Cheating ?
  1. Two or more students working together at the same time Must each produce their own work
  2. Getting assistance with proofreading or editing
 Measurement
  1. the act of assigning a specific value to a specific variable
 Measurement system(1) sensor–transducer stage, (2) signal-conditioning
stage, (3) output stage, and (4) feedback-control stage. These stages form the bridge between the
input to the measurement system and the system output, a quantity that is used to infer the value of
the physical variable measured

 Stage 1: SensorA physical element that employs a natural phenomenon to sense’ the variable being measured.
 Stage 2:Transducer
  1. Converts sensed information into a detectable signal
  1. This can be a change in voltage, resistance, current, etc. or a mechanical signal like the mercury level in thermometer
 Stage 3: Signal Conditioner
  1. Takes transducer signal and modifies it to a desired magnitude range.
  2. A portion of the signal may be removed with a filter (to be explained later).
 Stage 4: Output Stage 
 Feedback Control
  1. Measurement tool coupled to another device that can affect the value of the measured parameter.
 Experimental Test PlanVariables and parameters
What question needs to be answered?
What needs to be measured
What variables affect the results? Often the most troublesome question
 Variables
  1. Independent variable:Can be changed independently of other variables
  2. Dependent variable: Affected by changes in other variables “y = y(x)”
  3. Extraneous variables: Can’t be controlled in the experiment  and Differences in results with same conditions
 ParametersFunctional groups’ of variables.Parameter = combination of properties
Contrast to “property”: physical characteristic of system
 2) Tolerance Design PlanHow can measurements be made?
Highly accurate/precise experiments can become expensive.

 Noise and InterferenceTwo types of extraneous variables: Noise and Interference
Two types of extraneous variables
Noise: Random variable in the measured signal. Increases scatter of data but it can be accounted for with statistics (filtering, averaging, etc.) Interference: Imposes a trend on the signal which can be more difficult to account for
 3) Data Reduction PlanHow will the data collected answer the question?
What trend is being looked for?
If there are anticipated results, how will they be analyzed?
 Replication
  1. repeat measurements in another test with similar operating conditions
 Repetitionrepeat the same measurement during a single test Helps to see if there is any variation in the variable being measured
 Concomitant Methods
  1. Get two or more estimates of a measurement based on different methods that can be compared
  2. Helps to validate results so people believe them
 Calibration definition
  1. Apply a known input value to a measurement system to observe the output
  2. Known input value’ is very important and must be accurate It is called a standard: best estimate of the ‘true value’Weights, voltage, force profile, etc.
 Static CalibrationValues are held constant and you make a calibration curve
 Dynamic Calibration
  1. Variables that change in time and space have magnitude and frequency
 Static sensitivity:
  1. slope of calibration curve between input and output
  2. Constant for a linear relationship
  3. Most devices that can be purchased are linear for simplicity
 Resolution:
  1. Smallest increment of the value that can be measured (i.e., tick marks on a ruler or dial gauge)
 Accuracy
  1. Accuracy: closeness of agreement between measured value and true value Do we ever know the true value?  (Hint: no, almost never)
 Error
  1. Quantitative measurement
  2. Difference between measured value and true value
 Uncertainty:
  1. if the true value is not known, then this is an estimate of the interval around the measurement where the true value is
We should usually say “the uncertainty is...” instead of “the error
 Types of Errors & Causes
  1. Precision errors: not repeatable Scatter about a mean Quoted as mean and an indication of deviation,
Experimental ‘noise’ is a big factor in precision errors
Finite quantized values in measurement system can’t be 100% precise
 Bias(or systematic) errors (accuracy)
These are repeatable and may be due to multiple factors
 Bias in instrument, Bias in instrument,  In many instances, systematic errors can be removed by calibrating the instrument This is only true if you know you have a systematic error
 Hysteresis Error
  1. The output of the system is dependent on the value that was previously measured
 Linearity ErrorA linear static calibration curve has the equation
 Zero error:
  1. Drift in output for the condition of zero input May occur over time in some devices
 Amplitude:magnitude of the input
 Frequencyhow the input changes with time
 order of a system (zero, first, second)Describes behavior of system response to input
  1. Information can consist of multiple magnitudes with associated frequencies
  2. it is common to view data as amplitude vs. time,Time domain. Amplitude vs. frequency is just as important. Frequency domain
 A/D Conversion
where M is the number of bits of the register
2 M is number of quantized values available that the converted signal can have in the range. Called “counts”
The converter compares the analog signal and finds the
closest digital value of voltage to it
Truncates: always rounds down
 Waveform Classifications
  1. Analog: continuous in time (most things in nature)
  2. Discrete time: only information at certain points in time (but quantity measured still varies continuously)
  3. Discrete time: only information at certain points in time but quantity measured still varies continuously)
 Signal Amplification
  1. Amplification involves an increase in the overall magnitude of a signal; usually voltage
 Aliasing

 Nyquist rate and frequency 
 Folding
  1. Frequencies in the original signal above, fN are folded back into the sampled signal as lower frequencies below, fN
 Practical issues 
 Types of Waveforms
  1. varies in a way that is predictable
  2. Simple periodic: only one frequency
  3. Complex periodic: more than 1 frequency
  4. A periodic: does not repeat at regular intervals
 Non deterministic
  1. cannot be predicted, must be
  2. described by statistical characteristics: Noise, turbulence
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