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Session 3 – Central composite designs, second order models, ANOVA, blocking, qualitative factors An intensive practical course mainly for PhD-students on the use of designs of experiments (DOE) and response surface methodology (RSM) for optimization problems. The course covers relevant background, nomenclature and general theory of DOE and RSM modelling for factorial and optimisation designs in addition to practical exercises in Matlab. Due to time limitations, the course concentrates on linear and quadratic models on the k≤3 design dimension. This course is an ideal starting point for every experimental engineering wanting to work effectively, extract maximal information and predict the future behaviour of their system. Mikko Mäkelä (DSc, Tech) is a postdoctoral fellow at the Swedish University of Agricultural Sciences in Umeå, Sweden and is currently visiting the Department of Chemical Engineering at the University of Alicante. He is working in close cooperation with Paul Geladi, Professor of Chemometrics, and using DOE and RSM for process optimization mainly for the valorization of industrial wastes in laboratory and pilot scales.” Schedule and details: The course took place at the University of Alicante and would not had been possible without the support of the Instituto Universitario de Ingeniería de Procesos Químicos.
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Process/product optimization using design of experiments and response surface methodology
Mikko Mäkelä
Sveriges landbruksuniversitetSwedish University of Agricultural Sciences
Department of Forest Biomaterials and TechnologyDivision of Biomass Technology and ChemistryUmeå, Sweden
Contents
Practical course, arranged in 4 individual sessions:
Session 1 – Introduction, factorial design, first order models
Session 2 – Matlab exercise: factorial design
Session 3 – Central composite designs, second order models, ANOVA,
blocking, qualitative factors
Session 4 – Matlab exercise: practical optimization example on given
data
Session 1
Introduction
Why experimental design
Factorial design
Design matrix
Model equation = coefficients
Residual
Response contour
Session 2
Factorial design
Research problem
Design matrix
Model equation = coefficients
Degrees of freedom
Predicted response
Residual
ANOVA
R2
Response contour
Session 3
Central composite designs
Design variance
Common designs
Second order models
Stationary points
ANOVA
Blocking
Confounding
Qualitative factors
Session 4Uncontrolled factors
Factor coding
Realized vs. planned
Response transformation
Coefficients
Observed vs. predicted
Residuals
ANOVA
Contour
Estimated prediction variance
Confidence interval
Research problem
A cuboidal (α=1, nc=3) central composite design to
study the effect of three factors on a response
Inlet air temperature, T: 0-90 °C
Slit height, S: 70-150 mm
Sludge feeding, F: 275-775 kg/h
Ambient RH (%) included as an uncontrolled
factor
Cuboidal designα = 1
Research problem
Research problem
Factor coding?
Uncontrolled factors?
Research problemN:o T S F RH
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Research problem
Research problem
Research problem
Research problem
Research problem
Parameter df Sum of squares (SS)
Meansquare (MS) F-value p-value
Total corrected
Regression
Residual
Lack of fit
Pure error
Research problem
Research problem
′ where
⋯ , ⋮ and
/2 ⋯ /2⋯ /2⋱ ⋮
sym.
→ 0
→
Research problem
Session 4Uncontrolled factors
Factor coding
Realized vs. planned
Response transformation
Coefficients
Observed vs. predicted
Residuals
ANOVA
Contour
Estimated prediction variance
Confidence interval
How to continue?
Literature Myers RH, Montgomery DC, Anderson-Cook CM, Response Surface Methodology,
Process and Product Optimization Using Designed Experiments, 3rd ed., John Wiley &
Sons, Hoboken, New Jersey, 2009 (recommended)
Eriksson L, Johansson E, Kettaneh-Wold N, Wikström C, Wold S, Design of
Experiments, Principles and Applications, 3rd ed., Umetrics, Umeå,2008 (useful for
beginners)
Software Matlab (The MathWorks, Inc.), Modde (Umetrics), Design Expert® (Stat-Ease, Inc.),
JMP (SAS Institute Inc.), Minitab (Minitab Inc.)
Thank you for participating!
You can contact me via
E-mail ([email protected])
ResearchGate (https://www.researchgate.net/profile/Mikko_Maekelae)
LinkedIn (https://www.linkedin.com/in/mikkomaekelae)
