Thesis

CHE 492
Chemical Engineering Project
STATISTICAL MODELING OF
TENNESSEE EASTMAN PLANT
by
Okan KİRAZ
Gökçe KUZU
Advisor : Assoc. Prof. Burak ALAKENT
Date of Submission : January 14th
, 2015
Boğaziçi University
Bebek, İstanbul

i
ABSTRACT
It is aimed to study steady-state relations between the manipulated variables and the response
variables of Tennessee Eastman Plant via statistical techniques such as the analysis of
variance and 2k
factorial design. The response variables in this project are the product flow
rate, the composition of product G and H, whereas the manipulated variables are the reactor
temperature, reactor pressure, reactor level and the rotational speed of stirrer in the reactor.
The data collection for the project was conducted via computer experiment, Simulink. The
project started with single factor experiment to observe temperature and pressure effect, and
the required sample size was calculated for temperature and pressure effect. Then, two factors
factorial experiment with the addition of center points and four factors factorial experiments
were investigated. Considering the project results, it is concluded that in order to obtain more
satisfactory outcomes, increasing the sample size and the number of repetition are preferable.

TABLE OF CONTENTS
ABSTRACT................................................................................................................................i
LIST OF TABLES ..................................................................................................................iiiii
LIST OF FIGURES...................................................................................................................iv
1. INTRODUCTION.................................................................................................................. 1
2. BASIC PRINCIPLES & BACKGROUND ........................................................................... 2
2.1. Tennessee Eastman Plant ................................................................................................ 2
2.2. The Analysis of Variance................................................................................................ 4
2.2.1. The Analysis of Variance for Single Factor Factorial Experiment.......................... 4
2.2.2. The Analysis of Variance for Two Factor Factorial Experiments ........................... 5
2.3. Determining Sample Size................................................................................................ 6
2.4. Normal Probability Plot .................................................................................................. 7
2.5. Residual Analysis and Model Checking ......................................................................... 7
2.6. 2k
Factorial Designs ........................................................................................................ 7
2.6.1. Addition of Center Points to a 2k
Design ................................................................. 8
3. SAMPLE CALCULATION & RESULTS .......................................................................... 10
3.1 Observing the Pressure Effect........................................................................................ 10
3.2 Observing the Temperature Effect ................................................................................. 12
3.3 Determining the Sample Size......................................................................................... 15
3.4 Observing Pressure Effect with 12 Experiments............................................................ 16
3.5 Observing Temperature plus Pressure Effect................................................................. 20
3.6 Observing the Effect of Temperature, Pressure, ReactorLevel and Rotation Speed of
Reactor Stirrer ...................................................................................................................... 27
4. DISCUSSION& CONCLUSION ........................................................................................ 31
REFERENCES......................................................................................................................... 34
APPENDIX .............................................................................................................................. 36
APPENDIX A: PressureEffectontheComposition of Producta G and H ............................. 36
APPENDIX B: TemperatureEffect on Composition of Products G and H.......................... 38
APPENDIX C: PressureEffectwith 12 Examples on Composition of Products G and H.... 42
APPENDIX D: TemperatureplusPressureEffectforComposition of Products G and H ...... 46
APPENDIX E:Temperature plus Pressure Effect with Five Repetitions............................. 47
APPENDIX F: Effect of Temperature, Pressure, Reactor Liquid Level and Rotation Speed
of Reactor Stirrer on Composition of Products G and H ..................................................... 52
APPENDIX G: MATLAB CODES ..................................................................................... 57

iii
LIST OF TABLES
Table 3.1 Product Flow Rate at Different Temperature Levels............................................... 12
Table 3.2Product Flow Rate at Different Pressure Levels (12 Experiments).......................... 16
Table 3.3Product Flow Rate at Different Pressure and Temperature Levels .......................... 20
Table 3.4Anova Table for Pressure & Temperature Effect on Product Flow Rate................. 23
Table 3.5Product Flow Rate at Different Pressure and Temperature Levels (with 5
repetitions)................................................................................................................................ 23
Table 3.6Anova Table for Pressure & Temperature Effect on Product Flow Rate (5
repetitions)................................................................................................................................ 24
Table 3.7Product Flow Rate at Different Pressure, Temperature, Level, Rotation Speed
Levels ....................................................................................................................................... 27
Table 3.8 Effect of Manipulated Variables ............................................................................. 28
Table 3.9 Anova Table of Model(T-P-H-Ws-TP).................................................................... 30
Table 3.10Anova Table of Model (P-H) ................................................................................. 30
Table A.1Anova Table of Temperature plus Pressure Effect for Composition of Product G. 46
Table A.2Anova Table of Temperature plus Pressure Effect for Composition of Product H. 46
Table A.3Anova Table of Temperature plus Pressure Effect with Five Repetitions on
Composition of Products G...................................................................................................... 47
Composition of Product H........................................................................................................ 49
Table A.5 Effect of Manipulated Variables on Composition of Product G ............................ 52
Table A.6Anova Table of Effect of Temperature, Pressure, Reactor Liquid Level and
Rotation Speed of Reactor Stirrer on Composition of Product G............................................ 54
Table A.7 Effect of Manipulated Variables on Composition of Product H ............................ 54
Rotation Speed of Reactor Stirrer on Composition of Product H............................................ 56

iv
LIST OF FIGURES
Figure 2.1 Tennessee Eastman Plant Diagram [1] .................................................................... 3
Figure 2.2 The analysis of variance for a single factor experiment [2]..................................... 5
Figure 2.3 The analysis of variance for a two factor experiment [2] ........................................ 6
Figure 2.4The operating characteristic curve[2] ....................................................................... 6
Figure 2.5 The 22 factorial design [2]....................................................................................... 8
Figure 2.6 2k
design with center points[2] ................................................................................ 9
Figure 3.1 Anova Table of Pressure Effect on Product Flow Rate ......................................... 10
Figure 3.2 Boxplot of Pressure Effect on Product Flow Rate................................................ 10
Figure 3.3 Data Sequence of Pressure Levels and Residuals.................................................. 11
Figure 3.4Data Sequence Plot of Mean values of Product Flow Rate and Residuals............. 11
Figure 3.5 Normal Probability Plot ......................................................................................... 12
Figure 3.6Anova Table of Temperature Effect on Product Flow Rate ................................... 13
Figure 3.7 Boxplot of Temperature Effect on Product Flow Rate .......................................... 14
Figure 3.8 Normal Probability Plot ......................................................................................... 14
Figure 3.9Anova Table of Pressure Effect on Product Flow Rate (12 Experiment)............... 18
Figure 3.10 Boxplot of Pressure Effect on Product Flow Rate (12 Experiment).................... 18
Figure 3.11 Data Sequence of Pressure Levels and Residuals (12 Experiment)..................... 19
Figure 3.12 Data Sequence Plot of Mean values of Product Flow Rate and Residuals (12
Experiment).............................................................................................................................. 19
Figure 3.13 Normal Probability Plot ....................................................................................... 20
Figure 3.14 Data Sequence of Pressure Levels and Residuals................................................ 24
Figure 3.15 Data Sequence of Temperature Levels and Residuals......................................... 25
Figure 3.16 Data Sequence Plot of Mean values of Product Flow Rate and Residuals.......... 25
Figure 3.17 Normal Probability Plot ....................................................................................... 26
Figure 3.18 Normplot of Estimated Values(Including Individual Effects)............................. 28
Figure 3.19 Normplot of Estimated Values (Individual Effects) ............................................ 29
Figure 3.20 Normplot of Estimated Values(Excluding Individual Effects)............................ 29
Figure A.1 Anova Table of Pressure Effect on Composition of Product G............................ 36
FigureA.2 Boxplot of Pressure Effect on Composition of Product G..................................... 36
Figure A.3 Anova Table of Pressure Effect on Composition of Product H............................ 36
Figure A.4 Boxplot of Pressure Effect on Composition of Product H.................................... 37
Figure A.5 Anova Table of Temperature Effect on Composition of Product G ..................... 38
Figure A.6 Boxplot of Temperature Effect on Composition of Product G............................. 38

v
Figure A.7 Data Sequence of Temperature Levels and Residuals.......................................... 39
Figure A.8 Data Sequence Plot of Mean values of Composition and Residuals .................... 39
Figure A.9 Normal Probability Plot ........................................................................................ 40
Figure A.10 Anova Table of Temperature Effect on Composition of Product H ................... 40
Figure A.11 Boxplot of Temperature Effect on Composition of Product H........................... 41
Figure A.12 Anova Table of Pressure Effect with 12 Examples on Composition of Product G
.................................................................................................................................................. 42
Figure A.13 Boxplot of Pressure Effect with 12 Examples Effect on Composition of Product
G............................................................................................................................................... 42
Figure A.14 Data Sequence of Pressure Levels and Residuals............................................... 43
Figure A.15 Data Sequence Plot of Mean values of Composition and Residuals .................. 43
Figure A.16 Normal Probability Plot ...................................................................................... 44
Figure A.17 Anova Table of Pressure Effect with 12 Examples on Composition of Product H
.................................................................................................................................................. 44
H............................................................................................................................................... 45
Figure A.20 Data Sequence of Temperature Levels and Residuals........................................ 48
FigureA.21Data Sequence Plot of Mean values of Composition and Residuals .................... 48
Figure A.24 Data Sequence of Temperature Levels and Residuals........................................ 50
Figure A.25 Data Sequence Plot of Mean values of Composition and Residuals .................. 51
Figure A.27 Normplot of Estimated Values (Including Individual Effects)........................... 53
Figure A.28 Normplot of Estimated Values (Excluding Individual Effects).......................... 53
Figure A.29 Normplot of Estimated Values (Including Individual Effects)........................... 55
Figure A30Normplot of Estimated Values (Excluding Individual Effects)............................ 55

1
1. INTRODUCTION
The main aim of the project is to investigate steady-state relations between input and response
variables of Tennessee Eastman Plant by using statistical techniques which are the analysis of
variance, in other words ANOVA test, and 2k
factorial design. The other objectives are to
check for the required sample size in order to get more accurate results and to check for
nonlinearities and interactions for factorial experiments.
The project starts with data collection via computer experiment which is conducted by using
Simulink. Set points are randomly changed in each 24 hours interval. However, the average of
12 hours is used for each interval, since the system needs to be stabilized after every change.
The response variables are the flow rate of reactor outlet stream, the composition of product G
and H, whereas the manipulated variables are reactor level, reactor pressure, reactor
temperature and the rotational speed of stirrer in the reactor.
Four main steps are followed in this project. First, the ANOVA test is applied for single factor
experiment to observe pressure effect and temperature effect, individually. While doing so,
four different levels are used for both pressure and temperature. Then, the required sample
size is determined for single factor experiment in order to get more accurate outcomes.
Afterwards, two factors factorial experiment with the addition of center points are studied via
the ANOVA test to observe interactions between temperature and pressure. This stage is
carried out with both the total number of 9 experiments and 25 experiments. In the first
situation, there are five repetitions at the zero level and one repetition at each corner. On the
other hand, for the second situation, there are five repetitions at the zero level and five
repetitions at each corner. Lastly, the ANOVA test for four factors factorial experiment is
investigated for pressure, temperature, reactor level and the rotational speed of the stirrer
without repetition.

2
2. BASIC PRINCIPLES & BACKGROUND
2.1. Tennessee Eastman Plant
This plant model has been presented by Eastman Chemical Company, but the components,
kinetics, process and operating conditions have been modified by Downs and Vogel to protect
the proprietary nature of the process.
In this process, two products are produced by using four reactants. The reactions which take
place in this process are given as follows:
𝐴(𝑔) + 𝐶(𝑔) + 𝐷(𝑔) → 𝐺(𝑙𝑖𝑞 )
𝐴(𝑔) + 𝐶(𝑔) + 𝐸(𝑔) → 𝐻(𝑙𝑖𝑞)
𝐴(𝑔) + 𝐸(𝑔) → 𝐹(𝑙𝑖𝑞 )
3𝐷(𝑔) → 2𝐹(𝑙𝑖𝑞 )
The desired products, G and H, are produced from the reactants, A, C, D, and E, which are all
in gaseous phase. D is an inert and F is produced as by-product. All the reactions are
irreversible and exothermic. Their orders are approximately first order with respect to the
reactant concentrations.The reactions giving the desired products are catalyzed by a
nonvolatile catalyst dissolved in the liquid phase. [1]
The detailed flow sheet of the process is given in Figure 1.

3
Figure 2.1Tennessee Eastman Plant Diagram [1]
As it can been seen from the figure, the process contains five major unit operations, which are
the reactor, the product condenser, a vapor-liquid separator, a recycle compressor and a
product stripper.
Since the reactions are exothermic, there is an internal cooling bundle in the reactor to remove
the heat of reaction. The reactor product stream consisting of the products and unreacted feeds
in vapor form passes through a condenser to condense the products. Then, the stream goes to
a vapor-liquid separator in order to separate the noncondensed unreacted components and the
condensed product components. Also, the inert and byproduct are purged from the system via
this separator. The unreacted components recycle back through a centrifugal compressor to
the reactor feed stream, whereas the products move to a product stripping column in which
remaining reactants is removed by stripping with the component C. After this stripping
process, the products G and H leave the stripper at the bottom.

4
2.2. The Analysis of Variance
2.2.1. The Analysis of Variance for Single Factor Factorial Experiment
The observations for single factor factorial experiments can be described by the linear
statistical model:
𝑦𝑖𝑗 = 𝜇 + 𝜏𝑖 + 𝜖𝑖𝑗 (1)
where,
𝑦𝑖𝑗 : a random variable denoting the (ij)th observation
𝜇: the overall mean effect
𝜏𝑖: parameterassociated with the ith treatment
𝜖𝑖𝑗 : random error component
The sums of squares computing formulas for the ANOVA with equal sample sizes in each
treatment are calculated as follows:
𝑆𝑆 𝑇 = 𝑦𝑖𝑗
2
𝑎
𝑗=1
𝑎
𝑖=1
−
𝑦∙∙
2
𝑁
𝑆𝑆 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 =
1
𝑛
𝑦𝑖∙
2
𝑎
𝑖=1
−
𝑦∙∙
2
𝑁
(2)
(3)
Then, the error sum of squares is obtained by,
𝑆𝑆 𝐸 = 𝑆𝑆 𝑇 − 𝑆𝑆 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 (4)
The mean square for treatments and error can be calculated by the following formula,
respectively.
𝑀𝑆 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠 = 𝑆𝑆 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠 /(𝑎 − 1) (5)
𝑀𝑆 𝐸 = 𝑆𝑆 𝐸/ 𝑎(𝑛 − 1) (6)
Then, the ratio of them gives:

5
𝐹0 =
𝑀𝑆 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡𝑠
𝑀𝑆 𝐸
(7)
The computations for this test procedure are usually summarized as shown in Figure 5.
Figure 2.2The analysis of variance for a single factor experiment [2]
2.2.2. The Analysis of Variance for Two Factor Factorial Experiments
The observations for two factor factorial experiments can be described by the linear statistical
model:
𝑦𝑖𝑗 = 𝜇 + 𝜏𝑖 + 𝜎𝑗 + 𝜏𝜎 𝑖𝑗 + 𝜖𝑖𝑗 (8)
where,
𝜇: the overall mean effect
𝜏𝑖: the effect of the ith level of factor A
𝜎𝑗 : the effect of the jth level of factor B
𝜏𝜎 𝑖𝑗 : the effect of the interaction between A and B
𝜖𝑖𝑗 : random error component
In two factor factorial experiments, in addition to the effects of A and B, there is also the
effect of the interaction between A and B. The same calculation procedure is valid for two
factor factorial experiments, as well, and the analysis of variance is summarized in Figure 6.

6
Figure 2.3 The analysis of variance for a two factor experiment [2]
2.3. Determining Sample Size
The choice of the sample or number of replicates is important in experimental design
problems to get accurate results. The number of replicates required to achieve adequate
sensitivity is determined by using the following equation and the operating curve, which is
given in Figure 2.[2]
𝜑2
=
𝑛 𝜏𝑖
2𝑎
𝑖=1
𝑎𝜎2
(9)
Figure 2.4The operating characteristic curve[2]

7
2.4. Normal Probability Plot
A normal probability plot is a graphical method for determining whether sample data conform
to a hypothesized distribution based on a subjective visual examination of the data. This
typeplots are generally more reliable than others such as histogram for small and moderate
size samples. If the hypothesized distribution sufficiently describes the data, the plotted points
will fall approximately along a straight line. On the other hand, if the plotted points deviate
significantly from a straight line, the hypothesized model is not an appropriate model. [2]
2.5. Residual Analysis and Model Checking
A residual refers to the difference between an observation and its estimated value from the
statistical model. For the completely randomized experiment design, actual observations are
equal to the corresponding estimated value. A residual is calculated as follows: [2]
𝑒𝑖𝑗 = 𝑦𝑖𝑗 − 𝑦𝑖 (10)
where,
𝑦𝑖𝑗: actual observation
𝑦𝑖: the corresponding observed treatment mean.
2.6. 2k
Factorial Designs
Factorial designs are mostly used in experiments that involve several factors. The 2k
design is
especially useful in the early stages of experimental work, when many factors are
investigated. It provides the smallest number of runs for which k factors can be studied in a
complete factorial design. The simplest type of 2k
design is the 22
which contains two factors,
A and B. This experiment design is given in the following figure.

8
Figure 2.5 The 22 factorial design [2]
According to this notation, if a letter is present, the corresponding factor is run at the high
level in that treatment combination; if it is absent, the factor is run at its low level. For
instance, treatment combination b indicates that factor B is at the high level and factor A is at
the low level. The treatment combination with both factors at the low level is shown by (1) in
the Figure 3.
While the number of factors in a factorial experiment increases, the number of effects which
can be estimated also increases. For example, a 24
experiment has 4 main effects, 6 two-factor
interactions, 4 three-factor interactions, and 1 four-factor interaction. The three-factor and
higher order interactions can be neglected. Hence, when the number of factors is large, a
common practice is to run only a single replicate of the 2k
design and then combine the higher
order interactions as an error.
2.6.1. Addition of Center Points to a 2k
Design
There is a concern in the use of two-level factorial designs which is the assumption of
linearity in the factor effects. Nevertheless, there is a method of replicating certain points in
the 2k
factorial which will provide protection against curvature as well as allow an independent
estimate error. An illustration of 2k
design with center points is given in Figure 4.

9
Figure 2.6 2k
design with center points[2]
According to the figure, there are one observation at each of the factorial points and nc
observations at the center points. A single degree of freedom sum of squares for curvature is
given by:
𝑆𝑆𝑐𝑢𝑟𝑣𝑎𝑡𝑢𝑟𝑒 =
𝑛𝑓 𝑛 𝑐 𝑦𝑓 − 𝑦𝑐
2
𝑛𝑓 + 𝑛 𝑐
(11)
where,
𝑛 𝑐: the number of observations at the center point
𝑛 𝑓:the number of factorial design points
𝑦 𝑓: the average of the four runs at the four factorial points
𝑦 𝑐
: the average of the 𝑛 𝑐run at the center point
If the difference 𝑦 𝑓 − 𝑦 𝑐 is small, the center points lie on or near the plane through the factorial
points, and there is no curvature. On the other hand, if 𝑦 𝑓 − 𝑦 𝑐 is large, curvature is present.

10
3. SAMPLE CALCULATION & RESULTS
3.1 Observing the Pressure Effect
The change in product flow rate, composition of components G and H as a result of pressure
effect is tried to be observed at four different pressure levels, -20, -10, 0, 10, and in each level,
the experiment is repeated 5 times. The sequence of the pressure levels are determined
randomly by Matlab. Anova table results of the pressure effect on product flow rate are given
below.
Figure 3.1Anova Table of Pressure Effect on Product Flow Rate
Figure 3.2 Boxplot of Pressure Effect on Product Flow Rate
Residual analysis is done by finding the mean values at each 4 different level and extracting
mean values from the corresponding flow rate values.

11
The data sequences of pressure levels versus residuals are plotted.
Figure 3.3 Data Sequence of Pressure Levels and Residuals
Then, the data sequence consists of the mean values of flow rate in each level specified at
residual values are plotted by using Matlab.
Figure 74Data Sequence Plot of Mean values of Product Flow Rate and Residuals
Also, normal probability plot based on residual analysis is obtained.

12
Figure 85 Normal Probability Plot
3.2 Observing the Temperature Effect
The effect of temperature onthe product flow rate and composition of component G and H is
observed by controlling the plant at 4 different temperature levels; -1, 0, 1 and 2. In each
level, five experiments are done, again the change in the levels are determined randomly. The
sample results are given for the analysis of change in product flow rate. P-values are obtained
by using Matlab.
Table 3.1 Product Flow Rate at Different Temperature Levels
Time(hr) Temperature level (℃) Flow Rate (m3
/hr)
0 1 22.9329
24 2 22.9262
48 -1 22.9509
72 1 22.9290
96 1 22.9276
120 0 22.9473
144 1 22.9683
168 2 22.9328
192 0 22.9727

13
216 0 22.9604
240 -1 22.9523
264 -1 22.9300
288 2 22.9228
312 1 22.9551
336 0 22.9359
360 0 22.9546
384 2 22.9714
408 -1 22.9366
432 -1 22.9519
456 2 22.9493
Figure 3.6Anova Table of Temperature Effect on Product Flow Rate

14
Figure 97 Boxplot of Temperature Effect on Product Flow Rate
Figure 3.8 Normal Probability Plot

15
3.3 Determining the Sample Size
The required number of experiments in order to find the optimum results is calculated from
equation 2.9.
𝜇 =
𝑥𝑖
𝑁
𝑖=1
𝑁
= 22.9475
Level -20 -10 0 10
Flow Rates (xi)
22.9715 22.9394 22.9316 22.9045
22.9745 22.9799 22.9276 22.9630
22.9865 22.9569 22.9232 22.9081
22.9632 22.9675 22.9602 22.8980
22.9573 22.9499 22.9426 22.9441
Mean values (𝜇𝑖) 22.9706 22.9587 22.9370 22.9235
𝜇𝑖 − 𝜇 -0.0231 -0.0112 0.0104 0.0239
𝜏𝑖
2
= 𝜇𝑖 − 𝜇 2
= −0.0231 2
+ −0.0112 2
+ 0.0104 2
+ 0.0239 2
= 0.0123
𝜎2
= (𝑥𝑖 − 𝜇)2
𝜎2
= 0.0113
𝜑2
=
𝑛 × 0.0123
4 × 0.0113
= 0.2655 × 𝑛
𝜑 = 0.515 𝑛
The number of experiments at each level was 5 in the analysis up to now. Therefore n is
accepted as 5.
𝜑 = 1.15
Degree of freedoms are:
𝑣1 = 4 − 1 = 3
𝑣2 = 5 4 − 1 = 16

16
Then, from figure 2.4 where 𝛼=0.05, probability of acceptance is
𝛽 = 0.65
Then by trial and error for n, it is sum up that for n=12;
𝜑 = 1.78
𝛽 ≅ 0.21
This 𝛽 value is within the range of accepting the experiment number as accurate. Therefore,
required sample size is found as 12.
3.4 Observing Pressure Effect with 12 Experiments
The same procedure mentioned above is followed for observing pressure effect on product
flow rate, compositions of components G and H at four different levels; -20, -10, 0, 10. The
results are given below.
Table 3.2Product Flow Rate at Different Pressure Levels (12 Experiments)
Time(hr) Pressure level (kPa) Flow Rate (m3
/hr)
0 0 22.9316
24 10 22.9045
48 -20 22.9715
72 -10 22.9393
96 0 22.9276
120 -20 22.97451
144 -10 22.9798
168 0 22.9232
192 10 22.9629
216 -20 22.9865
240 -10 22.9569
264 10 22.9081
288 10 22.8979
312 10 22.9440

17
336 -20 22.9632
360 -10 22.9674
384 0 22.9601
408 -20 22.9573
432 0 22.9425
456 -10 22.9499
480 10 22.9192
504 -20 22.9427
528 0 22.9456
552 10 22.9141
576 -10 22.9403
600 10 22.9363
624 -10 22.9798
648 0 22.9231
672 10 22.9629
696 0 22.9605
720 10 22.9318
744 0 22.9204
768 -20 22.9362
792 0 22.9564
816 -20 22.9631
840 10 22.9424
864 -10 22.9728
888 -20 22.9573
912 -10 22.9552
936 -20 22.9631
960 -10 22.9356
984 0 22.9367
1008 10 22.9727
1032 -10 22.9394
1056 -10 22.9796
1080 0 22.9698
1104 -20 22.9670
1128 -20 22.9759

18
Figure 3.910Anova Table of Pressure Effect on Product Flow Rate (12 Experiment)
Figure 3.10 11Boxplot of Pressure Effect on Product Flow Rate (12 Experiment)

19
Figure 3.11 Data Sequence of Pressure Levels and Residuals (12 Experiment)
Figure 3.12 12Data Sequence Plot of Mean values of Product Flow Rate and Residuals (12
Experiment)

20
Figure 3.13Normal Probability Plot
3.5 Observing Temperature plus Pressure Effect
The next aim is to observe the effect of both temperature and pressure on flow rate and
compositions. Three different pressure and temperature levels are determined such that one of
them is zero level. At each pressure-temperature combination one experiment is performed,
except for zero level, five experiments are done.The p-value analysis is done with hand
calculation. The sample calculation steps are given below for the change in flow rate.
Product Flow Rates for corresponding pressure and temperature levels are tabulated below.
Table 3.3Product Flow Rate at Different Pressure and Temperature Levels
Time(hr) Pressure level (kPa) Temperature level (℃) Flow Rate (m3
/hr)
0 -30 2 22.9781
24 0 0 22.9142
48 30 -2 22.9307
72 0 0 22.9288
96 30 2 22.9056

21
120 0 0 22.9460
144 0 0 22.9670
168 -30 -2 23.0095
192 0 0 22.9772
22
model of this particular case is;
P (30,-2)
(-30,-2) (-30,2)
(30,2)
-30
0
30
0-2 2
(0,0)
23.0095
22.9056
22.9781
22.9307
22.9460
22.9772
22.9670
22.9288
22.9142
T

22
𝑦𝑖𝑗 = 𝜇 + 𝜏𝑖 + 𝜎𝑗 + 𝜏𝜎 𝑖𝑗 + 𝜖𝑖𝑗
2 × 𝜏𝑖 =
22.98 − 23.01 + (22.91 − 22.93)
2
2 × 𝜏𝑖 = −0.0282
2 × 𝜏𝑖 = −0.0141
Th=-0.0141
Tl=0.0141
𝜇 =
22.91 + 22.93 + 22.97 + 23.01
4
= 22.9560
2 × 𝜎 =
22.98 − 22.91 + (23.01 − 22.93)
2
= −0.0378
𝜎 = −0.0378
Ph=-0.0378
Pl=0.0378
𝑦 = 𝜇 + 𝜏 + 𝜎
𝑦 = 22.91 − 0.0141 − 0.0378 = 22.90
𝜏𝜎 𝑇𝑃 = 𝑦 − 𝑦 = 22.91 − 22.90 = 0.0015
𝑆𝑆𝜏 = 𝑆𝑆 𝑇 = 4 × (0.014)2
= 7.95 × 10−4
𝑆𝑆 𝜎 = 𝑆𝑆 𝑃 = 4 × 0.0378 2
= 0.0057
𝑆𝑆𝜏𝜎 = 𝑆𝑆 𝑇𝑃 = 4 × (0.0015)2
= 9 × 10−6
𝜇 𝐺 =
22.90 + 22.93 + 22.98 + 23.01 + 22.91 + 22.93 + 22.95 + 22.97 + 22.98
9
𝜇 𝐺 = 22.95
𝑆𝑆 𝐸 = (22.91 − 22.95)2
+ (22.93 − 23.01)2
+ 22.95 − 22.91 2
+ (22.97 − 22.93)2
+ (22.98 − 22.93)2
= 0.0028
𝑦𝑓 =
22.98 + 23.01 + 22.91 + 22.93
4
= 22.96
𝑦𝑐 =
22.91 + 22.93 + 22.95 + 22.97 + 22.98
5
= 22.95

23
Fromequation 2.
𝑆𝑆𝑐𝑢𝑟𝑣𝑒 =
4 × 5 × (22.96 − 22.95)2
(4 + 5)
= 1.93 × 10−4
Then, anovatable is constructedbyhand as given in Table 2.4. P-
valaredeterminedbyusingcumulativedistributionfunction (fcdf) in Matlab.
Table 3.4Anova Table for Pressure &Temperature Effect on Product Flow Rate
S.S D.o.f M.S. 𝑓0 p-val
T 7.95 × 10−4 1 7.95 × 10−4 1.14 0.35
P 0.0057 1 0.0057 8.14 0.05
TP 9 × 10−6 1 9 × 10−6 0.013 0.91
Curv 1.93 × 10−4 1 1.93 × 10−4 0.26 0.63
Error 0.0028 4 0.0007
The effect of temperature and pressure is also observed by repeating the experiments at the
corner points 5 times.
Table 3.5Product Flow Rate at Different Pressure and Temperature Levels(with 5 repetitions)
Time(hr) Pressure level (kPa) Temperature level (℃) Flow Rate (m3
/hr)
0 0 0 22.9316
24 0 0 22.9474
48 0 0 22.9507
72 0 0 22.9626
96 0 0 22.9179
120 -30 -2 23.0040
144 -30 -2 23.0407
168 -30 -2 23.0191
192 -30 -2 23.0009
216 -30 -2 22.9979
240 30 -2 22.9097
264 30 -2 22.9572
288 30 -2 22.9371
312 30 -2 22.9245
336 30 -2 22.9097
360 -30 2 23.0136
384 -30 2 22.9671

24
408 -30 2 23.0094
432 -30 2 22.9755
456 -30 2 23.0136
480 30 2 22.9044
504 30 2 22.9221
528 30 2 22.9168
552 30 2 22.9044
576 30 2 22.9168
The Anova table of this model is done by following the same procedure as mentioned above.
But this time, the mean values at certain T and P values (at the corners) are taken.
Table 3.6Anova Table for Pressure &Temperature Effect on Product Flow Rate (5
repetitions)
S.S D.o.f M.S. 𝑓0 p-val
T 0.0012 1 0.0012 3.85 0.064
P 0.0352 1 0.0352 109.79 1.43 × 10−9
TP 4.76 × 10−6 1 4.76 × 10−6 0.015 0.90
Curv 0.0016 1 0.0016 5.08 0.04
Error 0.0064 20 0.0003
Figure 3.14 Data Sequence of Pressure Levels and Residuals

25
Figure 3.15 Data Sequence of Temperature Levels and Residuals
Figure 3.16 Data Sequence Plot of Mean values of Product Flow Rate and Residuals

26
Figure 3.17 Normal Probability Plot

27
3.6 Observing the Effect of Temperature, Pressure, ReactorLevel and Rotation Speed of
Reactor Stirrer
Lastly, effect of temperature, pressure, level and reactor stirrer rotation speed on product flow
rate and compositions are determined by following 24
design. The levels are -30,30; -1, 3; -8,
8; -20 20 for pressure, temperature, level and rotation speed, respectively. The change in flow
rates for corresponding levels is given in Table3.
Table 3.7Product Flow Rate at Different Pressure, Temperature, Level, Rotation Speed
Levels
Time(hr)
Pressure level
(kPa) (P)
Temperature
level (℃) (T)
Reactor Level
(m) (H)
Rotation Speed
(rpm) (Ws)
Flow Rate
(m3
/hr)
0 30 3 8 20 22.9869
24 30 3 8 -20 22.9102
48 30 3 -8 20 22.8656
72 30 3 -8 -20 22.9682
96 -30 3 8 20 22.9531
120 -30 3 8 -20 23.0570
144 -30 3 -8 20 22.8701
168 -30 3 -8 -20 22.9676
192 30 -1 8 20 22.9209
216 30 -1 8 -20 22.9490
240 30 -1 -8 20 22.7918
264 30 -1 -8 -20 22.8231
288 -30 -1 8 20 23.0450
312 -30 -1 8 -20 23.0477
336 -30 -1 -8 20 22.8670
350 -30 -1 -8 -20 22.8917
The effect of each individual parameter and interactions (including dual and triple ones,
excluding quadratic interaction) are found by using Matlab. Also, cross check is performed by
using the special functions present in Matlab.

28
Table 3.8 Effect of Manipulated Variables
Effect Name Estimated Value
T 0.0152
H 0.0515
Ws -0.0196
P -0.0302
PT 0.0156
PH -0.0118
TH 0.0089
PWs -0.0088
TWs -0.0221
HWs 0.0124
PTH -0.0019
PTWs 0.0130
PHWs 0.0104
THWs 0.0092
The normal probability plot of estimated values is plotted.
Figure 3.18Normplot of Estimated Values(Including Individual Effects)

29
Figure 3.19 Normplot of Estimated Values (Individual Effects)
Figure 3.20Normplot of Estimated Values(Excluding Individual Effects)
According to this figure, the points that are away from the plot are the interaction points that
have a changing effect on the flow rate. From Figure 3.22, temperature and pressure
interaction seems to have an effect. All of the other interaction points are considered as noise.
The effect of main factors is also important. Therefore, by including TP interaction and main
factors to the model, Anova analysis is carried on.

30
Table 3.9Anova Table of Model(T-P-H-Ws-TP)
S.S. DoF M.S. f p-Value
T 0.0036782 1 0.0036782 1.569 0.23885
P 0.014624 1 0.014624 6.2382 0.031574
H 0.042514 1 0.042514 18.135 0.0016669
Ws 0.0061671 1 0.0061671 2.6307 0.13588
TP 0.0038993 1 0.0038993 1.6633 0.22618
Error 0.023443 10 0.0023443
According to Table 3.9, it is obvious that temperature, rotation speed and temperature
pressure interaction do not have an effect on the product flow rate since the p-values are
greater than 0.05. Therefore Anova analysis is carried on one more time by accepting these
parameters as error and obtaining the exact model.
Table 3.10Anova Table of Model (P-H)
S.S. DoF M.S. f p-Value
P 0.014624 1 0.015 5.1123 0.041
H 0.042514 1 0.042 14.862 0.002
Error 0.037187 13 0.0028

31
4. DISCUSSION& CONCLUSION
The data collection which was the starting point of this project was carried out by using
computer experiment, Simulink. The manipulated variables in the Tennessee Eastman Plant,
which are reactor temperature, reactor pressure, reactor level and the rotational speed of stirrer
in the reactor, were changed randomly in each 24 hours during the data collection. But, those
changes caused some peak points at the beginning of each interval, which is against steady
state behavior. Therefore, in order to get steady state data, first 12 hours data were discarded
to get rid of unsteady state behavior.
In the project, first single factor experiments with five repetitions were carried out to observe
the effect of pressure and temperature on the product flow rate, product G and H. By using
ANOVA test, p-value of product flow rate, composition of product G and product H were
found as 0.0047, 0.3296 and 0.7746, respectively. Hence, it was understood that change in
pressure could affect only the product flow rate, because its p-value is smaller than 0.05 that
is the critical value for p-test. The same procedure was performed for temperature and it was
concluded that temperature can affect only the composition of product G. Also, the boxplot of
the models were plotted and it was observed that the results coming from the boxplots are
consistent with p-value results.
In order to investigate the adequacy of the models for single factor, residual analyses were
carried out for temperature and pressure effects. Residual vs pressure level and residual vs
treatment mean graphs were plotted using Matlab. Since there was no specific pattern, it was
checked that there is no need to change the model. Furthermore, normality assumption was
checked with normal probability plot of the residuals. Again, since there was no any pattern, it
was concluded that there is no model inadequacy.
Then, the required sample size was studied for single factor experiment in order to get more
trust worthy results. After this calculation, the required sample size was found as 12 and the
p-value of the product flow rate, composition of product G and product H were found as
0.008, 0.0206 and 0.0911, respectively, for the pressure effects. According to the p-values it
was understood that the change in pressure level can now affect both the product flow rate
and the composition of G. It was concluded with this result that increasing the sample size
provides us to observe better results. For example, the pressure effect on the composition G
cannot be observed with five repetitions, whereas the pressure effect on the composition G

32
can be observed with 12 repetitions. The boxplot of the models were plotted again and the
results of the boxplots are consistent with p-values.
In order to observe interaction between the effects of pressure and temperature, and curvature,
two factors factorial experiments with the addition center points were investigated via
ANOVA. These experiments were carried out with the total number of 9 experiments and 25
experiments. In the first case, there were five repetitions at the center where pressure and
temperature levels are zero and one repetition at each corner. The addition of center points
provides us to observe curvature. In the second case, there were five repetitions at the zero
level and five repetitions at the each corner. By doing so, the differences between one
repetition and five repetitions can be observed. In the first case, the p-value of the product
flow rate, composition of product G and product H were found as 0.05, 0.8124 and 0.1454,
respectively, for pressure. Therefore, pressure has effect only on the product flow rate. When
the p-values of temperature, interactions of temperature and pressure, and curvature are taken
into account, it can be concluded that neither of them have any effect on the response
variables. Then, the same experiment with five repetitions was carried out and it was observed
that the pressure, temperature and the interaction of pressure and temperature affects the
product flow rate, the composition of G and H. The trends of their residual analyses and
normal probability plots are consistent with the results. Thus, it can be concluded that
increasing the repetition provides better results.
Lastly, four factors factorial experiment, 24
factorial design, was studied for the pressure,
temperature, reactor level, and the rotational speed of stirrer without any repetition. Since
there are many factors in this design, it is important to choose the correct model in order to
see the effects. First, all individual variables and the interactions were plotted on the normal
probability plot. The points which are far from the normal line are assumed to have an effect.
Then, the normal probability plot was modified, which means that single factors are excluded.
By doing so, the interactions that have an effect on the response variables were observed.
Afterwards, ANOVA table was applied on the factors that were assumed to have an effect at
the beginning. If there would any factor whose p-value is bigger than 0.05, this factor was
again excluded to get right model. Then, the ANOVA table was constructed based on the
factors which can affect the response variables. In conclusion, the product flow rate is
affected by temperature and reactor level; the composition of product G is affected by
pressure, temperature, reactor level and the interaction of temperature and reactor level; the
composition of product H is affected by pressure, temperature, reactor level and the

33
interaction of temperature and the rotational speed of stirrer. Nevertheless, in order to get
more accurate results, there must be repetitions in the experiment. Also, 2k
factorial design is
not a good choice for complicated systems in which many manipulated variables exist,
because it requires a lot of experiment.

34
REFERENCES
1. Downs, J.J., Vogel E. F. ‘A Plant-wide Industrial Process Control Problem’, 1992
2. Montgomery D. C., Runger G. C., ‘Applied Statistics and Probability for Engineers’,
Fifth Edition, 2011

36
APPENDIX
APPENDIX A: PressureEffectontheComposition of Producta G and H
For Product G:
Figure A.1Anova Table of Pressure Effect on Composition of Product G
FigureA.2 Boxplot of Pressure Effect on Composition of Product G
For Product H:
Figure A.3Anova Table of Pressure Effect on Composition of Product H

37
Figure A.4 Boxplot of Pressure Effect on Composition of Product H

38
APPENDIX B: TemperatureEffect on Composition of Products G and H
For Product G:
Figure A.5Anova Table of Temperature Effect on Composition of Product G
Figure A.6 Boxplot of Temperature Effect on Composition of Product G

39
Figure A.7 Data Sequence of Temperature Levels and Residuals
Figure A.8 Data Sequence Plot of Mean values of Composition and Residuals

40
Figure A.913 Normal Probability Plot
For Product H:
Figure A.10Anova Table of Temperature Effect on Composition of Product H

41
Figure A.11 Boxplot of Temperature Effect on Composition of Product H

42
APPENDIX C: PressureEffectwith 12 Examples on Composition of Products G and H
For Product G:
Figure A.12Anova Table of Pressure Effect with 12 Examples on Composition of Product G
G

43
Figure A.14 Data Sequence of Pressure Levels and Residuals

44
For Product H:
Figure A.17Anova Table of Pressure Effect with 12 Examples on Composition of Product H

45
H

46
APPENDIX D: TemperatureplusPressureEffectforComposition of Products G and H
Table A.11Anova Table of Temperature plus Pressure Effect for Composition of Product G
S.S Dof M.S f0 p-val
T 0.2174 1 0.2174 2.6217 0.1807
P 0.0053 1 0.0053 0.0642 0.8124
TP 0.0020 1 0.0020 0.0245 0.8832
Curv 0.0593 1 0.0593 0.7155 0.4453
Error 0.3317 4 0.0829
Table A.12Anova Table of Temperature plus Pressure Effect for Composition of Product H
T 0.0010 1 0.0010 0.0685 0.8064
P 0.0455 1 0.0455 3.2578 0.1454
TP 0.0029 1 0.0029 0.2051 0.6741
Curv 0.0003 1 0.0003 0.0240 0.8844
Error 0.0558 4 0.0140

47
APPENDIX E:Temperature plus Pressure Effect with Five Repetitions
Composition of Products G
S.S Dof M.S. f0 p-val
T 1.4500 1 1.4500 171.4134 2.8725× 10−11
P 0.5463 1 0.5463 64.5837 1.0866× 10−7
TP 0.1316 1 0.1316 15.5594 8.0092× 10−4
Curv 0.0224 1 0.0224 2.6518 0.1191
Error 0.1692 20 0.0085 1

48
Figure A.20 Data Sequence of Temperature Levels and Residuals
FigureA.2116Data Sequence Plot of Mean values of Composition and Residuals

49
For Product H:
Composition of Product H
S.S Dof M.S. f0 p-val
T 0.0154 1 0.0154 4.7657 0.0411
P 0.9411 1 0.9411 290.5668 2.2282× 10−13
TP 0.1386 1 0.1386 42.7926 2.25× 10−6
Curv 0.0028 1 0.0028 0.8763 0.3604
Error 0.0648 20 0.0032 1

50
Figure A.24Data Sequence of Temperature Levels and Residuals

51

52
APPENDIX F: Effect of Temperature, Pressure, Reactor Liquid Level and Rotation
Speed of Reactor Stirrer on Composition of Products G and H
Table A.15 Effect of Manipulated Variables on Composition of Product G
T 0.24284
H -0.17192
Ws -0.021357
P 0.074735
PT -0.017339
PH 0.006595
TH 0.057548
PWs 0.020387
TWs -0.046881
HWs -0.011067
PTH -0.016037
PTWs 0.0091936
PHWs 0.035277
THWs -0.003508

53
Figure A.27Normplot of Estimated Values (Including Individual Effects)
Figure A.28Normplot of Estimated Values (Excluding Individual Effects)

54
Rotation Speed of Reactor Stirrer on Composition of Product G
T 0.94352 1 0.94352 112.59 4.0745× 10−7
P 0.089365 1 0.089365 10.664 0.0075232
H 0.47288 1 0.47288 56.431 1.1822× 10−5
TH 0.052989 1 0.052989 6.3234 0.028748
Error 0.092178 11 0.0083798
Table A.17 Effect of Manipulated Variables on Composition of Product H
T 0.066015
H 0.058555
Ws 0.010547
P -0.063173
PT 0.0024147
PH 0.0096665
TH -0.0048123
PWs 0.0014338
TWs -0.046992
HWs 0.022932
PTH 0.010802
PTWs 0.011329
PHWs 0.021167
THWs 0.016935

55
Figure A.29Normplot of Estimated Values (Including Individual Effects)
Figure A30Normplot of Estimated Values (Excluding Individual Effects)

56
Rotation Speed of Reactor Stirrer on Composition of Product H
T 0.069727 1 0.069727 18.021 0.001377
P 0.063852 1 0.063852 16.503 0.0018756
H 0.054858 1 0.054858 14.178 0.0031252
TWs 0.035331 1 0.035331 9.1315 0.011618
Error 0.042561 11 0.0038692

57
APPENDIX G: MATLAB CODES
G.1 Anova
clearall
clc
%y=[7,7,15,11,9;12,17,12,18,18;14,18,18,19,19;19,25,22,19,23;7
,10,11,15,11];
yt=y';
yi=sum(yt);
ydoubledot=sum(yi);
yidotbar=mean(y,2);
yddbar=mean(mean(y,2));
fori=1:5
for j=1:5
yij=y(i,j);
sumofsq(i,j)=(yij-yddbar)^2;
end
end
SST=sum(sum(sumofsq))
fori=1:5
for j=1:5
yij=y(i,j);
sumofsq2(i,j)=(yij-yidotbar(i,1)).^2;
end
end
G.2 ConstructrefFunction
function [U, X, Y, sY] = constructRef(xstruct, ustruct, mH,
ratio)
%
% Extract process data and partition them into U X and Y
matrices.
% mH is Number of hours over which averaging is done.

58
% ratio is the ratio of data which is going to be included in
the final
% model
%
% Assuming that Ts = 15 min
Ts = 15;
ifnargin< 3
mH = 24; % Number of hours over which
averaging is done.
ratio = 0.5; % The second half of each sampling
period is included into averaging.
elseifnargin< 4
end
x = xstruct;%.Data;
u = ustruct;%.Data;
% Remove constant agitator speed
u(:, end) = [];
% Separate manipulated, process and quality variables
Y = x(:, [17]);
U = x(:, [2 4 7:10 12 15 19 20 22]);
X = [x(:, [1 3 5 6 11 13 14 16 18 21]) u];
clearxu
% Remove the first observation
X(1, :) = [];
Y(1, :) = [];
U(1, :) = [];
[N, Mx] = size(X);
My = size(Y, 2);
Mu = size(U, 2);
Ns = 60/Ts; % Number of samples in
1 hr
nosamples = N / (mH*Ns); % Total number of samples
after averaging
X = reshape(X', [MxmH*Ns nosamples]);
X = squeeze(mean(X(:, (mH*Ns*ratio+1):end, :), 2))';
Y = reshape(Y', [My mH*Ns nosamples]);
sY = squeeze(std(Y(:, (mH*Ns*ratio+1):end, :), [], 2))';
Y = squeeze(mean(Y(:, (mH*Ns*ratio+1):end, :), 2))';

59
U = reshape(U', [Mu mH*Ns nosamples]);
U = squeeze(mean(U(:, (mH*Ns*ratio+1):end, :), 2))';
G.3FindingEffect of Pressure
[u, x, y, sy] = constructRef(X.Data, U.Data, 24, .5);
p = Psp(:, 2);
[pval, table, stats] = anova1(y(:, 1), p, 'alpha', 0.05);
plot(p, y(:, 2), '.r');
xlim([-25 15]);
holdon
plot([-20 -10 0 10], stats.means, 'ok', 'MArkerSize', 10,
'MarkerFaceColor', 'k');
meanY(find(p==-20)) = stats.means(1);
meanY(find(p==-10)) = stats.means(2);
meanY(find(p==0)) = stats.means(3);
meanY(find(p==10)) = stats.means(4);
meanY = meanY(:);
y(:, 1);
meanY;
r = y(:, 1) - meanY
% 1) Residual vs time
stem(x(:, 7));
%2) Normality?
normplot(r);
%3) r vs. ypred
stem(meanY, r);
%4) r vs level
stem(p, r)
% Residuals do not have any structure. ANOVA is OK
%%%%%%%%%%
[c, m] = multcompare(stats, 'Ctype', 'tukey-kramer', 'alpha',
0.05);

60
G.4 FindingEffect of Temperature
load(factorialT)
[u, x, y, sy] = constructRef(X.Data, U.Data, 24, .5);
t = Tsp(:, 2);
[pval, table, stats] = anova1(y(:, 2), t, 'alpha', 0.05);
plot(t, y(:, 2), '.r')
xlim([-25 15])
holdon
plot([2 -1 0 1], stats.means, 'ok', 'MArkerSize', 10,
'MarkerFaceColor', 'k')
meanY(find(t==2)) = stats.means(1);
meanY(find(t==-1)) = stats.means(2);
meanY = meanY(:);
r = y(:, 2) - meanY;
% 1) Residual vs time
stem(x(:, 7))
%2) Normality?
normplot(r)
%3) r vs. ypred
stem(meanY, r)
%4) r vs level
stem(t, r)
% Residuals do not have any structure. ANOVA is OK
%%%%%%%%%%
[c, m] = multcompare(stats, 'Ctype', 'tukey-kramer', 'alpha',
0.05);
G.5 Temperature plus Pressure Effect with Five Repetitons
function [U, X, Y, sY] = constructRef(xstruct, ustruct, mH,
ratio)

61
%
% Extract process data and partition them into U X and Y
matrices.
% mH is Number of hours over which averaging is done.
% ratio is the ratio of data which is going to be included in
the final
% model
%
% Assuming that Ts = 15 min
Ts = 15;
ifnargin< 3
mH = 24; % Number of hours over which
averaging is done.
elseifnargin< 4
end
x = xstruct;%.Data;
u = ustruct;%.Data;
% Remove constant agitator speed
u(:, end) = [];
% Separate manipulated, process and quality variables
Y = x(:, [17]);
U = x(:, [2 4 7:10 12 15 19 20 22]);
X = [x(:, [1 3 5 6 11 13 14 16 18 21]) u];
clearxu
% Remove the first observation
X(1, :) = [];
Y(1, :) = [];
U(1, :) = [];
[N, Mx] = size(X);
My = size(Y, 2);
Mu = size(U, 2);
Ns = 60/Ts; % Number of samples in
1 hr
nosamples = N / (mH*Ns); % Total number of samples
after averaging
X = reshape(X', [MxmH*Ns nosamples]);
X = squeeze(mean(X(:, (mH*Ns*ratio+1):end, :), 2))';

62
Y = reshape(Y', [My mH*Ns nosamples]);
sY = squeeze(std(Y(:, (mH*Ns*ratio+1):end, :), [], 2))';
Y = squeeze(mean(Y(:, (mH*Ns*ratio+1):end, :), 2))';
U = reshape(U', [Mu mH*Ns nosamples]);
U = squeeze(mean(U(:, (mH*Ns*ratio+1):end, :), 2))';

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