ME 392Chapter 6

Data Processing

March 12, 2012week 9

Joseph Vignola

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

For now we can use the voltage to represent what ever physical quantity we might be interested in.

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

For now we can use the voltage to represent what ever physical quantity we might be interested in.

We use a sensitivity to relate the voltage to the thing we want

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

For now we can use the voltage to represent what ever physical quantity we might be interested in.

We use a sensitivity to relate the voltage to the thing we want for the accelerates

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

For now we can use the voltage to represent what ever physical quantity we might be interested in.

We use a sensitivity to relate the voltage to the thing we want for the accelerates

for the speaker

Experimental Error

There is always an assumption that what you measure is the sum, or some combination of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

For now we can use the voltage to represent what ever physical quantity we might be interested in.

We use a sensitivity to relate the voltage to the thing we want for the accelerates

for the speaker

Experimental Error

The error can be broke down into two categories

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Examples of systematic error

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Examples of systematic error 1) Bad calibration

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Examples of systematic error 1) Bad calibration2) Non-linearity

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Examples of systematic error 1) Bad calibration2) Non-linearity3) Digitizer noise (bit noise)

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Systematic error is error that occurs the say way every time an experiment is run.

Examples of systematic error 1) Bad calibration2) Non-linearity3) Digitizer noise (bit noise)4) Saturating the digitizer

(hitting the rail)

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Random error is error that is different every time you run your experiment.

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Random error is error that is different every time you run your experiment.

Examples of random error

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Random error is error that is different every time you run your experiment.

Examples of random error 1)Electronic noise

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Random error is error that is different every time you run your experiment.

Examples of random error 1) Electronic noise2) You lab partner

Experimental Error

The error can be broke down into two categories 1) Systematic error (a.k.a. bias)2) Random error (a.k.a. noise)

Random error is error that is different every time you run your experiment.

Examples of random error 1) Electronic noise2) You lab partner3) Environmental effect

(room temperature, humidity…)

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

And we make the measurement many times

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

Typically we measure a voltage that represents a physical quantity like temperature or velocity and then multiply or divide by some constant (the sensitivity)

And we make the measurement many times

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

For this plot we can think of this as finding the “best” horizontal line that represents the data

Aggregate Comparisons

There is always an assumption that what you measure is the sum of the real phenomena plus some error

For this plot we can think of this as finding the “best” horizontal line that represents the data

But what if we don’t expect the data to remain the same with each measurement and we want to know something about the trend?

Curve Fitting

If we have reason to expect that the data will follow some functional form

But what if we don’t expect the data to remain the same with each measurement and we want to know something about the trend?

Curve Fitting

If we have reason to expect that the data will follow some functional form

But what if we don’t expect the data to remain the same with each measurement and we want to know something about the trend?

Curve Fitting

If we have reason to expect that the data will follow some functional form

But what if we don’t expect the data to remain the same with each measurement and we want to know something about the trend?

Curve Fitting

We use the polyfit command in Matlab to find the closest polynomial to a set of data

The polynomial might be a

Horizontal line (average)

Curve Fitting

We use the polyfit command in Matlab to find the closest polynomial to a set of data

The polynomial might be a

Sloping line (linear fit)

Curve Fitting

We use the polyfit command in Matlab to find the closest polynomial to a set of data

The polynomial might be a

Curve Fitting

We use the polyfit command in Matlab to find the closest polynomial to a set of data

The polynomial might be a

Any polynomial (linear fit)

Curve Fitting

We use the polyfit command in Matlab to find the closest polynomial to a set of data

The polynomial might be a

Maybe a parabola

Ultimately we would like to make a plot where we can compare data to some predictive model

Using “polyfit.m” for Curve Fitting

So in Matlab we can make these fits by first reading in the datainfile = 'height_data.mat';

load(infile) % this file has a pair of vector t & height (same length) N = length(t);

Using “polyfit.m” for Curve Fitting

… using “polyfit.m”

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,1); % p is a vector of the coefficients of the polynomial

The first two inputs are your x – y data pair

The third input is the order of the fit, 1 for a straight line

Using “polyfit.m” for Curve Fitting

… using “polyfit.m”

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,2); % p is a vector of the coefficients of the polynomial

The first two inputs are your x – y data pair

The third input is the order of the fit, 2 for a parabola

Using “polyfit.m” for Curve Fitting

… using “polyfit.m”

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,6); % p is a vector of the coefficients of the polynomial

The first two inputs are your x – y data pair

The third input is the order of the fit, 6 for a …

Using “polyfit.m” for Curve Fitting

..and then evaluate the polynomial using “polyval.m”

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,2); % p is a vector of the coefficients of the polynomial[y_fit] = polyval(p,t); % polyval evaluates the polynomial

Using “polyfit.m” for Curve Fitting

…and plotting as we have earlier.

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,2); % p is a vector of the coefficients of the polynomial[y_fit] = polyval(p,t); % polyval evaluates the polynomial

zf(5) = figure(5);clfza(1) = axes;zp = plot(t,height,'o’,t,y_fit);gridxlabel('time (months)’)ylabel('childs height (in)’) ss0 = ['data'];ss1 = ['fit = ' num2str(p2(1)) 'x^2 + ' num2str(p2(2)) 'x +' num2str(p2(3))];zl = legend(ss0,ss1);

Using “polyfit.m” for Curve Fitting

infile = 'height_data.mat';load(infile) % this file has a pair of vector t & height (same length) N = length(t); p = polyfit(t,height,2); % p is a vector of the coefficients of the polynomial[y_fit] = polyval(p,t); % polyval evaluates the polynomial

zf(5) = figure(5);clfza(1) = axes;zp = plot(t,height,'o’,t,y_fit);gridxlabel('time (months)’)ylabel('childs height (in)’) ss0 = ['data'];ss1 = ['fit = ' num2str(p2(1)) 'x^2 + ' num2str(p2(2)) 'x +' num2str(p2(3))];zl = legend(ss0,ss1);

Today’s Assignment

There are notes on the web page for fitting to a function of your choosing

Today's Assignment

The current assignment is to put an accelerometer on the tip of the shaker and shake it

Today's Assignment

The current assignment is to put an accelerometer on the tip of the shaker and shake it

At something like 10 amplitudes

Today's Assignment

The current assignment is to put an accelerometer on the tip of the shaker and shake it

At something like 10 amplitudes

And something like 3 frequenciesmaybe10Hz, 100Hz, 1kHz

Today's Assignment

Then for each frequencies

Today's Assignment

Then for each frequencies

Determine the displacement amplitude per input voltage to the shaker using a linear curve fit.

Today's Assignment

Then for each frequencies

Determine the displacement amplitude per input voltage to the shaker using a linear curve fit.

You will need the amplifier gain for this.

Today's Assignment

Then for each frequencies

Determine the displacement amplitude per input voltage to the shaker using a linear curve fit.

You will need the amplifier gain for this.

Please measure it with something like a 0.1 V sinusoid at about 500Hz.

Non-Linearity

There is one other thing I would like you to look at that is not on the assignment sheet

Non-linearity

Both the amplifier and the shaker will start producing harmonic responses when the their inputs exceed some level