Labview Thermocouple Program

Ryan Burke

June 27, 2007

Abstract

The purpose of this program was to measure the temperature of thegas chromatography column using a thermocouple and graph the tem-perature versus time. As well as providing this graph, it is importantto have statistics for the temperature such as the average and standarddeviation to show the temperature variation. The data exhibited a sig-nificant amount of noise so our solution to this was to smooth it using anexponential moving average to clarify the graph.

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Contents

1 Operating This Program 31.1 Accessing This Program . . . . . . . . . . . . . . . . . . . . . . . 31.2 Program Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Using This Program’s Basic Functions . . . . . . . . . . . . . . . 3

2 Writing the Main Program 42.1 DAQ Assistant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Smoothing Subvi 53.1 Why Create a SubVI? . . . . . . . . . . . . . . . . . . . . . . . . 53.2 How To Create a SubVI . . . . . . . . . . . . . . . . . . . . . . . 53.3 Exponential Moving Average . . . . . . . . . . . . . . . . . . . . 53.4 Changing data types . . . . . . . . . . . . . . . . . . . . . . . . . 73.5 Manipulating the Array . . . . . . . . . . . . . . . . . . . . . . . 73.6 Combining Waveform Components . . . . . . . . . . . . . . . . . 8

4 Statistics SubVI 84.1 Case Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Making Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Min and Max Statistics . . . . . . . . . . . . . . . . . . . . . . . 94.4 Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.5 Displaying Statistic Data . . . . . . . . . . . . . . . . . . . . . . 10

5 Front Panel 10

6 Thanks 10

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1 Operating This Program

1.1 Accessing This Program

This Labview program is saved in two places as shown below:

D:\labview\standard deviation3

S:\labview\standard deviation3

The subVI’s referenced are in the same folders under the names smoothingsubVI and statistics subVI

1.2 Program Basics

This program is meant to display the raw and filtered temperature data, andshow statistics on the temperature data for the duration of the gas chromatog-raphy run[1]. It collects data from two thermocouples. One is labeled RoomTemp the other is named Column Temp. A diagram of the basic programprocess of taking statistics and applying a smoothing function to the data isshown in figure 1.

1.3 Using This Program’s Basic Functions

After this program has been opened, the Front Panel will be the only Lab-view window open. This window is shown in figure 2. To start the program,click on the Run button (labeled A in figure 2). While the program is run-ning, graphs of the two temperatures will be shown on charts. The first tablabeled Smoothed Data & Histogram (as shown in figure 2) has the chart labeledSmoothed Room and Column Temp (B in figure 2) which is the smootheddata of both thermocouples. All smoothed data in this program depends onthe smoothing constant α which can be adjusted by changing the value of N(labeled C in figure 2 and discussed in section 3.3). To see the both unsmoothedsets of data on a single chart, click on the tab labeled Both Unsmoothed (labeledD in figure 2) or for separate unsmoothed charts click on the Both Unsmoothed2 Charts tab.

When a gas chromatography run is started, click on the Take Run Statis-tics button (labeled E in figure 2). It will turn green and begin taking statistics.This button is also pressed at the end of a run to stop collecting statistics. Dur-ing and after a run, the statistics are displayed in the boxes labeled MIN,MAX, Average, and Standard Deviation. The histogram chart (labeled Fin figure 2) also depends on the Take Run Statistics button. To the right ofthe histogram are it’s controls labeled Number of Bins, Minimum Value,and Maximum Value these should be at values of 50000, 100.00, and 300.00respectively (because room temperature should be below 300K, and the columntemperature should be above 100K for this experiment[1]). Should any of thesenumbers be changed, the Number of Bins should remain at a value of about

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250 times the difference between the Minimum Value and the MaximumValue. This is to ensure that the bin sizes are not too big or too small and thehistogram displays what resembles a gaussian curve. The Number of Binsthat produce a gaussian curve depend on the deviation in data caused by noise,with too few bins, the histogram will contain only a few bins, and with toomany, it will show random spikes. To zoom in on the Histogram, use the mag-nifying glass button labeled G in figure 2. To look at the temperature graphsfor the duration of the run only, look in the tab Run Charts (labeled H in figure2). To stop this program, click on the stop button (labeled I in figure 2).

2 Writing the Main Program

2.1 DAQ Assistant

The first step in building this program is to install the software for thehardware that connects the thermocouple(s) to the computer. Our lab used thehardware NI USB-9162 . Once the software for this is installed, open up labviewand create a new VI (a VI is a set of code). Next go to the Window menu andthen select Show Block Diagram this is the window where the program is built.Then add a DAQ Assistant (this stands for Data Acquisition Assistant and islabeled A in figure 3) block to the Block Diagram by right-clicking anywhereand selecting Input then DAQ Assistant.

Once this block is added, right click on it and choose Properties, The screenshown in figure 4 will pop up, choose Analog Input then Temperature then Ther-mocouple. Next, choose a channel which corresponds to the input slots that thethermocouple is connected to on the NI USB-9162 that are used (this screenis shown in figure 5). On the following screen (shown in figure 6) choose thechannel you are using to configure from the list (shown by letter A of figure 6).In the Thermocouple Setup section (labeled B in figure 6), select the Setup taband adjust the Thermocouple Type (to T ), Signal Input Range; Max andMin (to 320 and 75 respectively), and Scaled Units (set to Kelvins). Also,CJC Source set to Constant and CJC Value set to room temperature becausethermocouples measure a difference between two temperatures, in this case be-tween that of the room and the column. In the Task Timing tab (labeled C infigure 6), the Acquisition Mode was set to Continuous, and for the ClockSettings; Samples To Read was set to 1 and Rate (Hz) was arbitrarily setto 6. The Rate should be 6 because the maximum rate for two simultaneousthermocouple readings (which this program uses) is 6. The thermocouple(s)used need to be calibrated. This is done by selecting the Calibration tab underThermocouple Setup. To calibrate the thermocouple(s), the welded end needsto be placed in something at a constant known temperature. I used both liquidnitrogen and an ice bath1for more samples. When the thermocouple is placed inthe constant temperature, take a couple of readings and tell the program what

1The ice bath was set to 273.15K as the atmosphere pressure’s deviation from 1.0 causesan insignificant freezing point change as shown in figure 7 which was obtained from [2]

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temperature it should be, the program will average the readings to calibrate thethermocouple.

2.2 Charts

On the Block Diagram, the output data of the DAQ Assistant block needsto be split if more than one thermocouple is used. This is done with a SplitSignal block (labeled B in figure 3) as this program uses two thermocouples,two outputs are needed on the Split Signal block.

The data wire before or after the split can be wired directly to a chart toshow the raw data. A chart must be used instead of a graph because a graphonly keeps the last couple of samples while a chart keeps as many samples asyou specify in the Chart History Length option. Because the frequency ofsamples is set to 6Hz in the DAQ Assistant, 1 sec corresponds to a ChartHistory Length of 6. Once the data is wired to a chart, however, the datashows a lot of noise (As shown in figure 8) and the solution to this is to use asmoothing function on the data.

3 Smoothing Subvi

3.1 Why Create a SubVI?

A subVI bundles existing code together into a smaller package, in the caseof labview, a single block. Creating a subVI necessary when certain bits of codein a program will be used over again and possibly in another program. A subVImakes the main VI easier to understand and work with as it cuts down on thenumber of crisscrossing wires by adding several components onto a single block.

3.2 How To Create a SubVI

To make a subVI, it is easiest to simply write the program you want andselect the part of the program that you want as a subVI and use Create SubVIunder the Edit menu. To change the names of the input and output terminalsof the subVI, simply right click the subVI block and rename the input andoutput boxes.

3.3 Exponential Moving Average

An exponential moving average (EMA), also known as a geometric movingaverage was chosen to smooth our data because it uses previous samples similarto a moving average but weights more heavily the recent data samples. Theexponential moving average formula used here is obtained in the following way.

X̄i is the exponential moving average value at a given index value of i, wi

is the weight given to the moving average at a given value of i. When i=N,this references the current value, and i=N-1 is the previous value. To derivean expression for the EMA, we begin by writing an expression for a general

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weighted average of N data points where wi is the weight applied to the EMAat a given index value (i)

X̄N =∑N

i=1 wiXi∑Ni=1 wi

(1)

We can expand this by separating out the last term in each sum to get:

X̄N =∑N−1

i=1 wiXi + wNXN∑Ni=1 wi

(2)

Multiplying and dividing the sum in the numerator by∑N−1

i=1 wi we get:

X̄N =

∑N−1i=1 wi(

∑N−1

i=1wiXi∑N−1

i=1wi

) + wNXN∑Ni=1 wi

(3)

Using equation 1 but adjusting the N value to N - 1, substitute in X̄N−1 for theterm in parentheses to get:

X̄N =∑N−1

i=1 wi∑Ni=1 wi

(X̄N−1) +wNXN∑N

i=1 wi

(4)

Rewriting∑N−1

i=1 wi as∑N

i=1 wi − wN we get:

X̄ =∑N

i=1 wi − wN∑Ni=1 wi

X̄N−1 +wN∑Ni=1 wN

(5)

Now we define α as a constant α ≡ wN∑N

i=1wi

and we get the usually recursive

expression for an EMA[3]

X̄N = (1− α)X̄N−1 + αXN (6)

Note that α gives the ratio of the change in the weight function to its currentvalue, or approximately the derivative over the function which is constant onlyfor an exponential function. Since α is assumed constant, we have:

α =wN∑Ni=1 wi

=wN−1∑N−1i=1 wi

(7)

From this, it is easy to derive a recurrence relation for the weights

wN (1− α) = wN−1 (8)

To apply this equation we pick a fixed number of data points (N) over which toaverage. This allows the number of data points we average over to be relatedto α as

α =2

N + 1(9)

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In this program, entering N will set the value of α using the above equationUsing the EMA from equation 6, several input values of N were used to

smooth a step function such as the plot shown in figure 9. Once this was done,the smoothed values were plotted and fitted using either an exponential growthor decay fit: y = A(1− e−bx) or y = Ae−bx, where A is the initial value and b isthe rate of exponential growth or decay. Next, each value of N was extracted andplotted against each corresponding b value. The resulting fit was an exponentialdecay. Plotting lnN vs. ln b results in a linear correlation as shown in figure10, this implies that N, and b are related by a power law relationship.

The approximate correlation between b and N is shown by the following:

b ≈ 2N − kα

(10)

Where k = α− α3 − α7 − α9 − α11 − α13 + α21 ≈ 0.26928, This correlation wasfound empirically.

3.4 Changing data types

To manipulate the data, the dynamic data wire needs to be converted towaveform. This allows for the components of the data to be separated so thatthe array portion can be extracted. (This is done by adding a Get WaveformComponents block as shown labeled A in figure 11). Four components make upthe waveform data these are t0 which is time, dt which is the time betweensamples, Y which is the array component, and attributes which says certaincharacteristics of the waveform. The Y array needs to be changed to an arrayelement (an array is composed of array elements, however, this array iscomposed of only one array element) this is done by wiring it through anIndex Array block (labeled B in figure 11).

3.5 Manipulating the Array

There are a variety of subVI’s that do a smoothing function to arrays,however, the goal of this program was to have a smoothing function that waseasy to understand and change as necessary. The first step is to create a FormulaNode (labeled C in figure 11) with three inputs as well as two outputs. Eachinput and output needs a label and these should correspond to the equationsused equation 6 and 9 in section 3.3. Refer to the help menu as necessary forhelp coding formulas in this node (or simply copy the code as well as input andoutput labels shown in figure 11).

Now, create a Shift Register (labeled C in figure 3) on the While Loop. Shiftregisters allow the previous set of data wired to them to be used in the currentiteration. The input is on the right side of the loop and the output on theleft (which would be the data that was wired into the right from the previousiteration). Wire the EMA (X̄N in equation 6 shown in section 3.3) value outputof the Formula Node to the input of the Shift Register and the output of theshift register which becomes the EMA value of the previous iteration (X̄N−1

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in equation 6 shown in section 3.3) is to be wired to an input on the formulanode to compute the next EMA. The other inputs are N (which should be wiredto a control so that it can be changed as necessary), and the array componentY (this corresponds to X in equation 6 shown in section 3.3) from the GetWaveform Components block. The second output is α which should be wiredto an Indicator.

3.6 Combining Waveform Components

To remake the waveform data to be used in a chart, the components needto be added to a Build Waveform block (labeled D in figure 11). The fourcomponents except for the Y array may simply be connected from the GetWaveform Components block to the Build Waveform block. The EMA arrayshould be taken from the output of the formula node which changes the rawdata to a compiled exponential moving average. Once in waveform data type,the data may be connected to a chart or converted to dynamic data type firstand then connected to a chart.

4 Statistics SubVI

The next portion of this program is to take statistics from the gas chromato-graph run, These statistics would be taken on command when a button startsthe run and later stops it (see section 1.3 for how to use this feature).

4.1 Case Structure

The button called a Boolean (labeled A in figure 12 and D in 3) has a truesetting and a false setting which changes by clicking the button on the FrontPanel. This Boolean is then wired to a Case Structure which has one set ofprogramming for when the Boolean is false and another for when it is true.To program the Case Structure toggle it to true at the top and box, the arrayportion of the waveform data (extracted in the smoothing subVI) needs to bewired to the Case Structure. Any outputs from the Case Structure need to beset to 0 in the false case with the exception of the minimum value output thisis shown in figure 13.

4.2 Making Statistics

The array data can then be manipulated easily to show statistics such asmode, standard deviation, and average. Start by creating a Shift Register onthe main Block Diagram (labeled E in figure 3) and wiring the array data intoan Add block (labeled B in figure 12). The output of this Add block should bewired to a Build Array node (labeled C in figure 12) then to this subVI’s shiftregister. Wire the output of the Shift Register to a Index Array block (labeledD in figure 12) within the case structure then wire the corresponding output of

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the Index Array block to the other input on the Add block. To calculate theaverage value of the temperature from these arrays, include a iteration count.This is created using an Increment block (labeled E in figure 12), which addsone to the previous iteration’s value each time. Wire the output of the Iterationblock to the Build Array block through the Shift Register to the Index Arrayblock and then back into an input node on the Increment block. These twovalues are then plugged into a Formula Node (labeled F in figure 12) and areused to find the average with the simple formula of :

x̄ =∑N

i=1 x

N(11)

next output the average value and display the it using an Indicator.The Standard Deviation is made similarly, but with a Formula Node. The

basics of this were discussed in the Smoothing subVI section, the formula usedwas

s2 ≡ 1N − 1

N∑i=1

(xi − x̄)2 (12)

Where s is the Standard Deviation[4]

s =

√√√√ 1N − 1

N∑i=1

(xi − x̄)2 (13)

4.3 Min and Max Statistics

The Max statistic is simple, inside the true portion of the statistics casestructure, use both a Select and a Greater? block (labeled G and H respecitivelyin figure 12) and wire the raw data array to the top input node on both. TheBoolean output of the Greater? block should be wired to the Boolean inputon the Select block. Finally, the Select output needs to run through the ShiftRegister and back into its own input. This selects the higher value betweenthe previous max value and the new raw data sample. The data display shouldsimply be connected to the output node of the Select block. For the false casestructure, simply make the output array value zero (as shown in figure 13).

The Min statistic is slightly trickier because once the Boolean is turnedon, the previous data point coming out of the shift register will be zero. AnotherCase Structure within the original true one is necessary. This one will dependon whether the previous minimum data point is greater than 70, because thetemperature in this experiment cannot go below the freezing point of liquidnitrogen (77k). Again, the raw data array needs to be wired in, this time tothe new Case Structure (labeled I in figure 12) and go to the top input node ofthe Less? and Select blocks within this new Case Structure’s True case. Again,the Less? node’s boolean output needs to be wired to the boolean input of theSelect block. Now the output of the Select block needs to be wired throughthe Shift Register and back to both the Less? blocks’ lower input nodes. For

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the false case of this new Case Structure, the output needs to be higher than atemperature (in Kelvins) achievable in the lab, so 4000 was chosen.

4.4 Histogram

The Labview program comes with a Histogram SubVI that should beadded into the main Case Structure with the raw dynamic data wired into itfor statistics. Once this is added in, by right clicking on it and selecting OpenFront Panel the histogram variables can be changed from the Front Panel ifyou use a Control for each input. These controls tell the Histogram SubVIhow many bins to use for the data as well as the minimum histogram value andthe maximum. 2

4.5 Displaying Statistic Data

The output of the statistics including the histogram needs to be wired intoa Case Structure. For this program, since the statistic gathering portion is ina subVI, a new Case Structure under the True tab with the same booleanwired to it needs to be made to display the statistics. If a Case Structure werenot used, the statistics would simply read zero after the button (mentioned insection 1.3) is clicked to stop running the statistics for the run.

5 Front Panel

The Front Panel needs to be edited to look pleasing to the eye. A tab con-trol can be added by right clicking anywhere on the Front Panel and selectingAll Controls then Containers then Tab Controls. This allows you to put graphdisplays in different tabs which can be renamed by right clicking on them. Themost important tab in this program is the statistic one as well as the smootheddata, so these are put into the main tab. The other graphs such as a roomtemperature one were put in separate tabs as they are somewhat important butnot as much as the statistics.

6 Thanks

I would like to thank Dr. S. Whisnant, and Dr. C. Hughes for helping me learnto operate Labview. Dr. S. Whisnant for helping me understand the derivationsin section 3.3 and general help with writing and editing this paper. Also, TravisKelley for help editing this paper.

2For details on what these values should be set to and why, see section 1.3.

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References

[1] T. D. Kelley. Chromatography with the Varian CP-3800. (2007).

[2] M. S. Silbeberg. Principles of General Chemistry. The McGraw-Hill Com-panies Inc. (2007).

[3] B. K. Ghosh, P. K. Sen. Handbook of Sequential Analysis. Vol. 118. MarcelDekker, Inc. (1991).

[4] P. R. Bevington, D. K. Robinson. Data Reduction and Error Analysis for the Physical Sciences.Second Edition. The McGraw-Hill Companies Inc. (1992).

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Raw Data

Noise Filter

Statistics

Display

Figure 1: Diagram of Basic Labview Program

A

B

D H CI

GE

F

Figure 2: Diagram of the main Front Panel, the boxed letters indicate itemsdiscussed in the text, for more features, use the tabs (two of which are shownby D and H)

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C

A

E

B

D

Figure 3: Diagram of the main Block Diagram, the boxed letters indicateitems discussed in the text. The Case Structure on the right is shown as true,when it is false, the Case Structure is empty.

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Figure 4: The Select Input screen wherethe program’s inputs are set, in this caseto thermocouple

Figure 5: The Select Channel screenwhere the input(s) channel(s) on theNI USB-9162 are selected

C

DB

A

Figure 6: Main DAQ Assistant Properties screen. The boxed letters indicateitems discussed in the text.

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Figure 7: The Phase Diagram of Water

Figure 8: The top chart displays unsmoothed temperature data over time (notethe noise). The lower chart displays data smoothed using the EMA from equa-tion 6

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Smoothed Step Function

0

0.5

1

1.5

2

2.5

1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196 209 222 235 248 261 274 287 300 313 326 339 352

Series1Series2

Figure 9: A step function which was smoothed by the EMA given in equation6 from section 3.3. For this plot, an N value of 65 was used. The fit of theexponential decay was used to find the exponential decay rate b.

N vs. b

0.01

0.1

1

10

1 10 100

N

b

Figure 10: A fitted scatter plot of: lnN vs. ln b. The relationship was linearwhich shows a power law correlation

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B

AC

D

Figure 11: This is the smoothing subVI program, the boxed letters indicateitems discussed in the text.

B

CA

D E

F

GH

I

Figure 12: This is the statistics subVI in the true case. In the true case we findthe statistics gathering programming. The false case is shown in figure 13. Theboxed letters indicate items discussed in the text

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Figure 13: This shows the statistics subVI with the Case Structure in the falsecase. Note that the output is all zero except for the minimum value output

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