Empirical+Modelling+FB+2015

Empirical+Modelling+FB+2015 - Empirical Modelling ES1050...

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“Empirical Modelling” ES1050 Prof. Franco Berruti Director, Institute for Chemicals and Fuels from Alternative Resources (ICFAR) Professor, Department of Chemical and Biochemical Engineering 2015 1
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What will we learn? Systems can be empirically modelled To develop empirical models we need data Data are obtained with appropriate instruments Data can be regressed in different ways Data sets and regressions need to make sense (need to be tested for statistical significance)
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• Types of Mathematical Models Measurements and Measurement Errors • Empirical Modelling • Simple Regression • Use of Statistics to determine the statistical significance ’ of a ‘ factor ’ on the system ‘ response • Optimization and Examples OUTLINE of the LECTURES 3
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Every SYSTEM has INPUT(S) and OUTPUT(S) SYSTEM Inputs Causes Factors Independent variables Outputs Effects Responses Dependent variables 4
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A mathematical expression that defines the RELATIONSHIP between the OUTPUT and the INPUT variables of a system is referred to as the system’s “MATHEMATICAL MODEL” If this relationship changes with time, the model is DYNAMIC or TRANSIENT If this relationship does not change with time, it is STEADY-STATE or STATIC 5
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6 A mathematical model is the representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in a usable form
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7 Remember that all models are wrong, but some are useful. The practical question is how wrong do they have to be to not be useful. George Edward Pelham Box Professor Emeritus of Statistics at the University of Wisconsin,
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The RELATIONSHIP between the OUTPUT and the INPUT variables, or the MATHEMATICAL MODEL can be developed theoretically , empirically , or semi-empirically . 8
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EMPIRICAL MODELS are developed based on the experimental observation and statistical manipulation of the experimental data to fit a given equation Example: Fitting the input ( x ) - output ( y ) data to a polynomial equation: 2 0 1 2 y a a x a x = + + 9
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Question 1 10 What is a mathematical models?: a) Academic mathematical exercise b) Mathematical expression to define relationship between input and output parameters c) Mathematical expression which defines the optimal operating conditions of a process d) A mathematical formula which simplifies the understanding of an instrument or process
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Question 1 11 What is a mathematical models?: a) Academic mathematical exercise b) Mathematical expression to define relationship between input and output parameters c) Mathematical expression which defines the optimal operating conditions of a process d) A mathematical formula which simplifies the understanding of an instrument or process
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Question 2 12 Do you need to know how the system works to develop its empirical model?: a) YES b) NO
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Question 2 13 Do you need to know how the system works to develop its empirical model?: a) YES b) NO
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Empirical Modeling Controllable factors “x” Noise factors “z” Responses “y” System 1) DEFINE
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