ENG246 Outline

Introduction to modeling in engineering

What is a model?

Figure from: https://www.flickr.com/photos/creative_tools/4325785556

What is a modelIt is an idea or concept that represents the physical world.

ModelRepresents the physical world

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Model

It includes only the important aspects of the phenomena

“All models are wrong, but some are useful”

Models

Assumptions define the context in where the model is used.

¿Does the model predict the behaviour of the system at the level that is required?

A model is ONLY valid in the context and under the assumptions made during its development.

Using a model to calculate some behaviour far from its assumptions is wrong.

A model needs to be always verified.

There are a lot of models that can be use to describe a system. Each of these models show different aspects of the system.

Important details of modelling

Why do we use models?

Frequently to

• Design• Training• Take decisions …

To predict and understand the behaviour of the system

• What actually happens during the process?• What would happen if?• How can the process be optimum?

Develop control systems

• How to keep the system close to a desired value?

Classification of Models• They are:

• Heuristic• Intuitive• Not too accurate

Mental model

• They are:• Linguistic => they describe the process• QualitativeSymbolic

• They are:• A set of equations that shows the relationship

between process’ variables

Mathematical models

• They are:• Expensive,• Complicated to build up and use

Physical models

Mathematical modelsDiscreet and continuous

• Discrete: particulate system, system made of states

• Continuous: fluid flow, vector fieldTime dependent

• Dynamic: it accounts for time dependent changes in the system.

• Static: the system is at the equilibrium and it is time invariant.Spatial distribution

• Lumped parameters: • Distributed parameters

Linear and non linear

• Linear• Non linear

Theoretical and empirical

• Theoretical:• Empirical

General info click here

Physical models

Physical models

Static models,.. Dynamic

Electrical PrototypesPilot plant

Discrete and continuous models

Continuous models• Variables change with time and can have any value. • Example: Temperature• These models are described from transport phenomena, momentum,

mass and energy balances.

Discrete models• Variables change in discrete manner and they have a limited number of

values• These modes describe processes that follow sequences of steps.

Static and dynamic models

• Variables are at the equilibrium state

Static models:

• Variables change with time

Dynamic models:

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Lumped and distributed parameters models

Lumped parameters)• A variable is a function of time but no position

• Stirred tank (Ordinary differential equations)

Distributed parameters• A variable is a function of time and at least one space variable (Partial

differential equations).• Tubular reactor [CA = f(L, r, t)]• Heat exchangers

Linear and non linear models

• They are represented by linear differential equations (Superposition principle)

Linear models:

• They are represented by non linear differential equations. – Chaos Theory -

Non linear models:

𝑥1(𝑡) System 𝑦 1(𝑡)𝑥2(𝑡) System 𝑦 2(𝑡)

𝑎𝑥 1(𝑡)+𝑏𝑥2(𝑡) System 𝑎𝑦 1(𝑡)+𝑏𝑦 2(𝑡 )

Theoretical and empirical models

Theoretical model• Physical insight of the process behaviour.• Applicable in a wide range of conditions.• Good understanding of the process.• Expensive and time consuming to develop.• Include some information difficult to obtain.

Empirical models• Inexpensive to develop.• Easy to develop.• Do not extrapolate well.

What does it make a good model?

Accuracy

• The most accurate model some time is not the best

Applicability

• Range of application• Conditions of use

Complexity

• Simple (macroscopic)• Detailed (microscopic)

Easy to use

Accurate

Occam’s Razor

• The principle states that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. http://en.wikipedia.org/wiki/Occam%27s_razor

Workshop 1

Now you have 30 min to solve this questions

1. Search on the web for three models that are usually use in your engineering field. You need to A. Describe de models. If it is a mathematical model you need to develop

mental model that describes it. B. Indicate the assumptions and limitations of the model.C. Classify the models according to the classifications given in class.