# June 2007: Modelling

## Introduction

The term modelling is ubiquitous in engineering. More commonly these days it refers to a computer simulation of some type. This highlight article will take a basic view of modelling then try to answer more probing questions such as what exactly a model is and what is it used for. Frequently in engineering modelling has to be justified in which case we can add 'why' to these questions as well.

Fig 1. Models may take many forms

## What is a model?

A model may be viewed as a simplified representation of an object, a system or an ideas, which is in some form other than the entity we wish to model. This could be:

- something that already exists,
- something you have a design or idea for,
- an environment, or
- any interaction that may occur between these entities.

There are a number of reasons why we should wish to do this. More commonly we want to know what a new design will look like or what its behaviour will be. In such scenarios we are attempting to see if an artefact will work to our expectations. In some cases we want to model natural phenomenon, such as turbulent flow (for example the weather). In these cases a modelling approach may be suitable because we cannot apply analytical laws to determine a complex systems' behaviour. Instead we give the system a number of rules, some starting conditions then let the model run and wait to see what emerges from this.

## How do models exist?

Having briefly described what models are, we next turn to how a model may exist. This may seem trivial, but a model must exist within some accessible medium to be of practical use. Although most engineering models are now expected to exist in the form of computer programs they were of course widely used prior to the advent of computers. Indeed valid mediums for models may vary enormously. For example they can exist:

- in your mind as an idea,
- as a scale model,
- on paper (drawing etc.),
- mathematical (symbolic relationships between properties),
- in an abstract modelling language such as UML, or
- as a computer program.

There is no practical limit to how models may be expressed.

## What are models for?

Modelling can be used to predict behaviour and generate data ...

As we know models can be used for a wide range of reasons. This includes for example the validation of design decisions, where you may wish to prove that an idea works or not. Modelling can be used to predict behaviour and generate data, which can be used either for validation or to help with a decision making process. To do this may require further techniques such as MCDM and Genetic Algorithms, which can be used to optimise results towards a favourable outcome.

## Modelling uncertainty

Since we have already stated that a model is just a representation of some artefact we need to know more about, we have already implied an assumption that our model will incorporate some uncertainty.

All models include uncertainty; this can take many forms and be derived from a number of sources. For instance:

- the underlying theory of the model may be subject to debate,
- interpretation of data may vary depending upon expert opinion,
- input data cannot be assumed to be perfect, and
- the size and availability of input data sets will already contribute to overall uncertainty.

Two common forms are variability and input uncertainty:

**Variability** is often described as aleatory or stochastic
uncertainty and describes natural differences that may occur
in population say, or in general data variation that cannot
be explained from an analytical point of view.

**Input uncertainty** may occur as a result of general subjective
(or approximate) knowledge of something. This is often termed
epistemic uncertainty. Examples of this may occur as a result
of differing levels of knowledge about a subject, or general
use of defined constants (i.e. using PI = 3.14 instead of a more
accurate figure).

Another form more directly associated with the model itself is fidelity, or model resolution, which stems from the level of detail associated with a model. Tied in again with how close to reality a model should be, models are by definition a simplification of the real world (Figure 2).

If the underlying mathematics describing something is complex and involves non-linear equations then often a modeller will decide to represent a subset of that domain. This can mean the difference between a model running in a few seconds and one that may take many days to reach a solution, not to mention the model development time!

Fig 2. An abstract view of modelling fidelity

Without a complete knowledge of the problem domain good representation depends on the modellers experience and expertise. Often a quick model can be achieved, which gives adequate results; sometimes a more precise set of solutions is required.

A good example is the often used (Barlow) calculation of stress in a pressurised cylinder:

Fig 3. An approximation of stress

This simplification assumes the wall thickness is negligible compared with the diameter and only yields an approximation. Nevertheless this is frequently deemed sufficient because it results in a conservative value for stress in comparison with more accurate versions such as the Lamé formula:

Fig 4. A more 'accurate' approximation

In practice any differences in the value of stress are most likely to be within material tolerances and are as such acceptable for most purposes.

Other aspects of uncertainty that relate to research activities is how they can be visualised. Graphical representation is one approach, which can aid and highlight areas where uncertainty can be a problem. Another is that of dynamic uncertainty, which varies depending on domain conditions.

## Integrated modelling

A more abstract view of modelling involves the integration of modelling. This simply means using a variety of available models to model at a higher level. The technique of modelling of models in this way is often referred to as meta-modelling and is a useful approach in the representation of complex systems. Modelling can be integrated in this way using specialist applications such as Modelling Frameworks (see Figure 5).

Fig 5. Conceptual view of a modelling framework

Implementations like these allow for more efficient and effective use of modelling capability. This can provide an insight into the functioning of complex systems as well as generating emerging properties. The use of modelling frameworks or most other modelling integration techniques is considered a useful and practical means of designing and developing systems.

### Author: John Dalton

Contact: john.dalton@ncl.ac.uk