Engineering and Models: Hint - Real Engineers Use More than Just Equations

Engineering & Models:Hint: Real Engineers Use More than Just Equations

David E. GoldbergIllinois Foundry for Innovation in Engineering Education University of Illinois at Urbana-ChampaignUrbana, Illinois 61801 [email protected]

Engineering Modeling: Education vs. Practice• Math-science march in first two years of

engineering education is misleading.• Imples: Meaningful models come from math &

science alone.• Young engineers confused on first jobs.• 2 problems:

– Don’t use appropriate models.– Don’t think they’re doing engineering.

• Need better understanding of types & breadth of engineering modeling.

Roadmap

• What is a model?• Legacy of Newton: equations versus words & images.• Matching models to problems.• What are models used for.• Tech visionaries as broad spectrum modelers.• Toulmin’s model of arguments as unifying approach.• Return to flour physics.

What is a Model?

• A model is a system that represents one or more facets of some other system.

• Typical model facet combinations:– Drawing or solid model geometry.– Prototype geometry & operation.– Graph variation of variable with independent variable(s)

(time, space, etc.).– Equilibrium equation select state variables at steady

state.– Dynamic equation variation of select state variables with

time.– Computer simulation similar to equations.

Models & Engineering Knowledge• Models capture what engineers

know about what exists or could exist.– Study of knowledge: Epistemology.– Study of existence: Ontology.

• What engineers know and how they know it?

• Walter Vincenti’s book takes examples from aeronautical history.

• Discusses distinctions between engineering knowledge and scientific-mathematical knowledge.

Newton & Engineering Models

• Invented calculus (so did Leibniz).• In 1687 published Philosophiae

Naturalis Principia Mathematica.• Changed world.• Remarkable agreement between

equations & measurements.• Many engineering models use his

equations (F=ma) directly.• Represents an ideal of scientific

knowledge that others attempt to emulate.

• Highest status accorded to those who use these kinds of models.

• Does status = efficacy? Sir Isaac Newton (1643-1727)

Words, Language and Engineering Models

• Newton-style models dominate engineering equation.• Engineers often use natural language in modeling.• Many first models are verbal.• Types of verbal models:

– Single word or noun phrase.– Description of an object/process.– Feature list.– Dimension list.– Set of engineering specifications, standards, or

claims.

Images and Engineering Modeling

• History of drawings and visual representations of engineered objects is long.

• Downgrading of engineering visualization and drawing since Cold War.

• Ferguson’s book argues this was/is educational mistake.

Connection to the Napkin

• Diagrams can be models.

• Drawings can be models.

• The Back of the Napkin connects visual thinking and verbal thinking in important way.

How to Match Models to Engin Problems

• What characterizes an appropriate model in engineering?

• What do you think?• Take out a piece of paper

and write down 3 attributes that suggest you have a good model.

• 2 minutes.

An Economy of Models

• Engineers think in terms of models.• Have many models with different precision-

accuracy and different costs.• Can we distinguish appropriate engineering

model usage from that of scientist?• The economics of modeling. • Engineers use models in economic context

model usage must support objectives within available resources.

Fundamental Modeling Tradeoff • Error versus cost of modeling

ε, Error

C, Cost of Modeling

Engineer/Inventor

Scientist/Mathematician

Spectrum of Models

Low Cost/High Error

High Cost/Low Error

Unarticulated Wisdom

Articulated QualitativeModel

DimensionalModels

FacetwiseModels

Equations of Motion

What Are Models Good For?

• Many uses for models:– Description: describe the ways things are

(were).– Prediction: describe the ways things will be.– Prescription: describe the way things should

be. • Key variables: time and change.• Usually assumes have extant object to model.

Research on Tech Visionaries as Clue

• Helpful to look at extreme exemplars of success.

• Price, Vojak, & Griffin have done work on tech visionaries (TVs).

• TV creates bottom line revenue from new products & services.

• TVs are consummate broad-spectrum modelers.

• Use qualitative-quantitative models as necessary to bring monster products/services to market. Ray Price

Key Distinction: Imagined vs. Existing

• Modeling of imagined or desired objects versus extant objects (recall category creatory vs. enhancer).

• To model imagined or desired objects, what can we draw upon?– Existing objects that fail in some regard.– Similar or related objects.– Analogically related objects.– Creatively concocted objects.

• Problem of the tabula rasa: How to model that which does not exist.

• In category creation, more modeling will be to the left (qualitative versus quantitative).

• Category enhancement: improvements require more precision. More modeling to the right (quant over qual).

• How can we model the burnt-flour-as-mold problem?

• Newton’s laws?• Need framework to tie

different models together.

Back to the Tortilla Factory 17

Help from Argumentation Theory

• 1958 book by philosopher Stephen Toulmin formed basis of argumentation theory.

• How do people really make arguments?

• How do people give reasons for what they think or do?

• Form of reasoning ties together formal and informal engineering reasoning.

Formal Reasoning: Logic

• Modus ponens (modus ponendo ponens: mode that affirms by affirming): – if p then q– p is true– therefore q is true

• Method of mathematical logic & formal reasoning.

• Note: Once premises and rules in place, formal logic derives conclusions mechanistically.

Aristotle (384-322 BCE)

Toulmin: Elements of a Human Argument

• Like modus ponens:– Claim. A single statement advanced for the adherence of

others.– Grounds. A statement about persons, conditions, events, or

things that says support is available to provide a reason for a claim.

– Warrant. A general statement that justifies using the grounds as a basis for the claim

– Backing. Any support (specific instance, statistics, testimony, values, or credibility) that provides more specific data for the grounds or warrant.

– Qualifier. A statement that indicates the force of the argument (words such as certainly, possibly, probably, usually, or somewhat).

• Warrants can be generalizations, cause, sign, analogy, authority.• Backing can be anecdote, stats, testimony, credibility, and values.

Rieke, R. D & Sillars, M. O. (1997). Argumentation and critical decision making. New York: Longman.

€

G → C↑

B

↑

W

↑

Q↑

B

Back to the Tortillas: Burnt Flour Model

Grounds. Dusting flour is spread onto the moving dough on a continuous tortilla line.

Warrant. Excess flour can become airborne and burn in the oven, deposit on tortilla.

Claim. Burnt black flour deposits is mistaken for mold, resulting in quality complaints

Qualifier. Sometimes

Backing. Client story & increased flour results in increased spot problem.

Tradeoff: Improve Backing or Solve Problem

• In resource limited environment, often face decision:– Should you improve warrant and backing?– Or should you work on solving the problem?

• Difficult choice: If you assume correctness of warrant/backing & you are wrong, will it prevent you from solving problem.

• In tortilla problem students took explanation as true because it didn’t affect investigation.

Summary

• Engineering students are convinced that math and physics are the main (only?) tools of engineering.

• Real engineers use a spectrum of models from qualitative to quantitative.

• Economy of modeling separates engineering from scientific practice.

• Toulmin’s model of arguments introduced & example from flour physics given.

Bottom Line

• Modeling is critical engineering activity, but don’t let emphasis on math-science mislead you.

• Great engineers and tech visionaries are broad-spectrum modelers.

• Use simplest models that will advance design objectives (economy of modeling).

• Unify models by using Toulmin’s model of arguments & use explicitly to tradeoff model improvement vs. design.