Engineering & Models:Hint: Real Engineers Use More than Just EquationsDavid E. GoldbergIllinois Foundry for Innovation in Engineering Education University of Illinois at Urbana-ChampaignUrbana, Illinois 61801 USAdeg@illinois.edu

Engineering Modeling: Education vs. PracticeMath-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.

RoadmapWhat 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 KnowledgeModels 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’sbook takes examples from aeronautical history.Discusses distinctions between engineering knowledge and scientific-mathematical knowledge.

Newton & Engineering ModelsInvented calculus (so did Leibniz).In 1687 published PhilosophiaeNaturalis 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 ModelsNewton-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 ModelingHistory 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 NapkinDiagrams 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 ProblemsWhat 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 ModelsEngineers 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 TradeoffEngineer/Inventorε, ErrorScientist/MathematicianC, Cost of ModelingError versus cost of modeling

Spectrum of Models

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 ClueHelpful 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. ExistingModeling 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 Theory1958 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: LogicModus ponens (modus ponendo ponens: mode that affirms by affirming): if pthen qpis truethereforeqis trueMethod 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 ArgumentLike 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 claimBacking. 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.

Back to the Tortillas: Burnt Flour ModelGrounds. Dusting flour is spread onto the moving dough on a continuous tortilla line.Claim. Burnt black flour deposits is mistaken for mold, resulting in quality complaintsWarrant. Excess flour can become airborne and burn in the oven, deposit on tortilla.Qualifier. SometimesBacking. Client story & increased flour results in increased spot problem.

Tradeoff: Improve Backing or Solve ProblemIn 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.

SummaryEngineering 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 LineModeling 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.