1. Objectives Uncertainty analysis Quality control Regression analysis

2. Example: Convective heat transfer calculation h = q/(Tsurface – Tair) …….

3. How about measurement variation or time or spatial averaging ? Sometimes quantities of interest fluctuate Sometimes we are interested in slopes of lines/regression equations Often appropriate to use standard deviation or standard error Be careful and acknowledge when you are doing so

4. Example of uncertainty reporting 4

5. Repetition of experiments 5

6. 6 General procedure Expend substantial effort on uncertainty Consider all sources of error State best guess of reasonable “best guess” Always say something about uncertainty Clearly state your procedure in your Methodology

7. Experimental Design Huge topic (we will talk about this during whole course) Questions: What do you need to know? How well (i.e. with what confidence) do you need to know it? How much do you expect it to vary? What factors are likely to influence/confound your results? Always find fundamental parameters

8. 8 Some Approaches Bench-scale experiments in laboratory, followed by large-scale laboratory tests, followed by field tests Field tests followed by controlled laboratory investigation Larger field studies 65

9. Example 1 What is the average efficiency of AC units in Austin (average COP) ?

10. 10 Quality Assurance (QA) Quality Control (QC) How to incorporated QA/QC into your experimental study? Experiment Design Phase: Define objective - What question are you trying to answer? - How will you know you are finished? Choose -Factors of interest -Parameters to measure -Experiments control method(s) -The data analysis techniques

11. 11 How to incorporated QA/QC into your experimental study? Experiment Design Phase: For measured parameters consider: - Range - Number of points - Number of repetitions Create an experimental matrix

12. 12 How to incorporated QA/QC into your experimental study? Experimental matrix Be real: - Consider available time and funding - Predict potential for failure - predict more experiments than minimum - predict extra time for repetition - Preliminary experiments help

13. 13 How to incorporated QA/QC into your experimental study? Measuring Phase: - Use measuring techniques that will meet the needs of your experiment - Collect sufficient data (including repetition) to adequately characterize the measured parameter - Record all available conditions/parameters (even those that are not in your matrix) - Use experiment control methods

14. 14 How to incorporated QA/QC into your experimental study? Data Analysis Phase: Graphs & descriptive statistics first Hypothesis testing Regression next Interpret the results Draw conclusions

15. 15 How to incorporated QA/QC into your experimental study? Be ready to modify and/or go back and forth between phases Example…..

16. Example from convection correlation development study Repetition and multiple measurements of important variables Repetition of experiments Independent development of data processing templates Comparison with previous research Energy balance check Large number of experiments Graphing to identify discrepancy ….. 16

17. Regression analysis 17 Single variable: Minimum number of points depends on number of variable in the function (3 for the function above). Using the data we can set the system of equation to find the coefficients.

18. Lagrange interpolation 18 Rewrite: Find coefficients: General form:

19. Model of complex system based on experimental data 19 Example: chiller model T OA water Building users (cooling coil in AHU) T CWR = 11 o C T CWS =5 o C T Condensation

20. Chiller model 20 Impact of temperatures: Impact of capacity:

21. Two variable function fitting

22. What do you think Does correlation where R 2 =0.82 represent a good data modeling? Mean: Total sum of squares: Sum of squares of residuals : Coefficient of determination

23. Anscombe's quartet Example of statistical misinterpretation of data - all data have the same Mean (for x and y), Variance (for x and y) - correlation R 2 : 0.816, linear regression: y=3.00+0.500·x

24. Anscombe's quartet Example of statistical misinterpretation of data - all curves have the same Mean (x, y), Variance (x, y) - correlation R 2 : 0.816, linear regression

25. Moral of the story Francis Anscombe (in 1973) demonstrated the importance of graphing data before analyzing it the effect of outliers on statistical properties 25