Data Analysis

Overview

During each experiment,data are automatically recorded in an Excel file (see example). The address for the excel file is recorded into the Meta file which is a spreadsheet with all the directories of the experimental data that will be/has been analyzed. Process Controller will be referring to the Meta file in order to acquire appropriate information on the experiment being analyzed; the Meta file will be an address book for Data Processor to efficiently access data.

The first graphs produced by the Mathcad file are the plots of the raw turbidity data vs. time and raw turbidity vs. settling velocity. The settling velocity (Vs) is calculated by dividing the distance between the ball valve and the zone illuminated by the infrared LED (z) of FRETA by the time elapsed(t).

For experiments involving varying alum dosage, another graph was produced to obtain the residual turbidity vs. settling velocity. Residual turbidity is the turbidity resulting from the flocs that failed to reach the capture velocity, which is 0.12 mm/s for the sedimentation tanks of the AguaClara plants. From this, we can get the mean residual turbidity for each variation of alum dose. The mean residual turbidity is the mean of all the raw turbidity measured after a time of approximatively 22 min till the end of the sedimentation state. It correspond to a range of sedimentation velocities from 0.12 mm/s to ???. See example of the residual turbidity graph: Analysis Alum Dose Experiment.
TThen data smoothing and normalization are performed on the raw turbidity data. The smoothing allows us to exclude outlying data points caused by really large flocs passing in front of the light sensor of FRETA, which create turbidity fluctuations. The normalization allows us to compare data sets with varying influent turbidities. The plot of normalized turbidity vs. Vs (settling velocity) can be interpreted as a cumulative distribution function (CFD) of turbidity with respect to Vs. A CFD describes the probability that a variable is less than or equal to some value.
To make the analysis more robust, the experimental data was fit to a gamma distribution. Then a derivative of the CFD of the gamma distribution gives a probability distribution of the particle population with respect to Vs. From the fitted data, the data processor retrieves the mean sedimentation velocity for each alum dose as well as the coefficient of variation of the distribution. The coefficient of variation is the standard deviation of the distribution divided by the mean. It is an indication of the width of the sedimentation velocity distribution.

For more discussion of the data analysis, see Ian Tse's [thesis|AGUACLARA:Tube Floc^Ian Tse MS Thesis.doc](Chapter I, data analysis). See an example of the gamma PDF graph: Example of Analysis Alum Dose Experiment.

Analysis Process

The data analysis process of the current project emphasizes organization and accuracy. The following is a step-by-step guide for the analysis process.

1. Go to the file containing the desired experimental data
2. Skim through the datalog (excel sheet with experimental data) to check for any apparent error. (Wrong influent turbidity, no variation in alum dose...)
3. If no apparent error is found, open the Meta file and record the appropriate information**
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**Meta File Information
-The Meta File is like as an address book for the datalogs. It is important to update this file after an experiment for the Data Processor to access. The steps following will show how information is recorded into the Meta File:
a. Put the appropriate ID Tag number in the A column
b. If the duration of the experiment was three days, put the first day in the B column, the second day in the C column, and the third day in the D column; if the experiment only lasted for 2 days, C column will be left as zero, and the following will be applied for an experiment with a one day duration-only the B column will be filled.
c. Record the appropriate directory and flocculator length in column F and G
d. Column J will be adjusted according to the datalog; it will be the first row in the datalog where the settle state has been activated. **Note, for most experiments, start row is not adjusted
e. Comment on the experiment the datalog is referring to (eg. influent turbidity, alum dose, etc.)

Remember to save the Meta file. If not, the Data Processor won't be able to access the data!
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4. Open Data Processor on MathCad
5. Change the directory Data Processor is referring to for data (Enter the ID tag) **
**Reference address will be located at the top of Data Processor, and only the last portion of the directory will need to be changed-which is the ID tag appearing on the Meta file.
6. Run the Data Processor; this program will automatically give graphic forms of the data and calculate needed values.
7. In the data processor you will need to change a value. FirstFittedcolumn.
The Data processor cannot fit the data for alum dose too low. This will enable you to eliminate the data that would not be fitted from the data vector.