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 of 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 Process Controller to efficiently analyze 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 of FRETA by the time elapsed.

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. An example of the residual turbidity graph can be found [here].
Then 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 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. For more precision in data analysis, see Ian Tse's [thesis|AGUACLARA:Tube Floc^Ian Tse MS Thesis.doc](Chapter I, data analysis). An example of the gamma PDF graph can be found [here].

Analysis Process

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

1. Go to the file containing the desired experimental data
2. Skim through the excel sheet with experimental data to check for any apparent error
3. If no apparent error is found, open the Meta file and record the appropriate information (date, directory, comments, etc.)
4. Open Process Controller on MathCad
5. Change the directory Process Controller is referring to for data**
**Reference address will be located at the top of Process Controller, and only the last portion of the directory will need to be changed
6. Run the Process Controller; this program will automatically give graphic forms of the data and calculate needed values