Selection Strategies

Making selections

• Let’s attempt to remove the emotional and intangibles from this discussion:

• It’s cool

• Johnny has one

• I love the color

Logical Approach

• Assemble data for the characteristics of the thing you want to select; make a database, mental or physical

• Formulate the characteristics that the thing must have to satisfy your requirements; list the constraints.

• Decide on the ranking criterion you will use to decide which is best; choose and apply the objective

• Research top ranked candidates more fully to satisfy yourself nothing has been overlooked; seek documentation.

Example: New Car

• Need a new car, mid-sized, 4 doors, gasoline engine, at least 150 HP.

• Want to minimize the cost to own and operate

Constraints

• Simple Constraints - MUST have these to be a candidate:

• 4 doors & gasoline powered

• Limit Constraints - fits in a range

• At LEAST 150 HP (more than this is OK)

Objective

• Objective: a criterion of acceptance

• Minimize cost to own/operate

• Oh, and we should probably look at carbon footprint too!

Desired featuresexpressed asConstraintsObjective

Desired featuresexpressed asConstraintsObjective

Car DataPerformance

EconomyWhat car? rating

Car DataPerformance

EconomyWhat car? rating

Selection EngineScreeningRanking

Documentation

Selection EngineScreeningRanking

Documentation

Final SelectionFinal Selection

Mid-sized family sedan4 door

Gasoline fuel150+ HP

Lowest cost of ownership

Lowest CO2 footprint

MakeModelPrice

DimensionsFuel Type

Fuel ConsumptionCO2 rating

Cost of ownershipetc.

Objectives

• When we have more than one objective things get complicated.

• We have lowest cost and lowest CO2 profile.

• Plus there might still be some “other” aspects - so don’t just list one result - keep a couple for comparison

• The lowest cost car might not be the most carbon efficient car.

Trade-Offs

• We need to handle trade-offs.

• Suppose we have two objectives and we look at different cars and plot out their performance for each objective.

High

HighLowLow

Low cost, high carbon Unacceptable

Low carbon, high costLow carbon, low cost

Storage Shed for Bikes

• Need properties like weather resistance, UV resistance, sufficient stiffness and strength, low weight, low cost

• The material properties associated with these are things like density, price, stiffness, strength, etc.

Design Requirementsexpressed asConstraintsObjective

Design Requirementsexpressed asConstraintsObjective

Materials DataMaterial attributesProcess Attributes

Documentation

Materials DataMaterial attributesProcess Attributes

Documentation

Selection EngineScreeningRanking

Documentation

Selection EngineScreeningRanking

Documentation

Final SelectionFinal Selection

Able to be moldedWater and UV

resistantModulus > 40 GPaStrength > 80 MPaAs light as possible

As cheap as possible

DensityPrice

ModulusStrength

Thermal PropertiesElectrical Properties

DurabilityProcess Compatibility

Etc.

A bit more complicated

• The properties we are seeking are not as obviously presented as in the case of a car.

• We have to translate the design requirements into materials related constraints and objectives.

• The screening process works similarly.

Translate Design Requirementsexpress as function, constraints,

objectives and free variables

Screen using constraintseliminate materials that

cannot do the job

Rank using objectivesfind the screened materials

that do the best job

Seek Documentationresearch the family history of

top ranked candidates

FINAL MATERIAL CHOICE

ALL MATERIALS

Translation

• Engineered components have functions

• This is achieved through constraints:

• certain dimensions are fixed,

• component must carry design load w/o failure

• transfer or insulate heat, electricity

• must function in given temperature range

Translation

• Designer has one or more objectives

• Certain parameters can be adjusted to optimize the objective. These are called free variables.

Functions, Constraints, Objectives & Free Variables

Function What does the component do?

ConstraintsWhat non-negotiable conditions must be

met?

Objective What is to be maximized/minimized?

Free variables

What parameters is the designer free to change?

Common Constraints Common ObjectiveMust be: Minimize:

Electically conductive CostOptically transparent MassCorrosion Resistant Volume

Nontoxic Thermal lossesNon-restricted substance Resource depletion

Recyclable Energy consumptionCarbon Emissions

Must meet target: WasteStiffness Environmental ImpactStrength

Fracture toughnessThermal ConductivityService temperature

Screening

• Constraints are gates - keeps out concepts that will fail.

• Screening is the process of using the constraints to identify candidate solutions.

Ranking

• To rank the materials that pass screening, we need a criteria: objectives

• Performance is sometimes limited by a single property, sometimes by a combination of them.

• If we want to minimize heat losses, we look for materials with the smallest thermal conductivity (at least those that have passed the screening evaluation and meet other criteria).

• Sometimes we are combining things - for a light weight high stiffness tie-rod, we actually want to maximize stiffness divided by weight. This combines both properties into a single ranking element.

Rankings: Material Indices

• Sometimes the actual parameter to be ranked can be complex.

• For example, in our light stiff tie rod application, we can minimize

• But for a strong beam with low embodied energy, we would minimize

ρ / E

Hmρ / σ y2 /3

Material Indices

• These complex terms are identified during engineering analysis. There are some standard terms that we can accept from other peoples’ work.

• Ultimately it depends on what we are trying to do.

Stiffness and Strength indicesConfigurati

on and objective

Configuration

Minimize volume

Minimize mass

Minimize embod. energy

Minimize material

cost

Stiffness Limited

Tie

Beam

Panel

Strength limited

Tie

Beam

Panel

Above values should be minimized to meet goals

1 / E ρ / E Hmρ / E Cmρ / E

1 / E ρ / E Hmρ / E Cmρ / E

ρ / E3 Hmρ / E3 Cmρ / E31 / E3

1 /σ 0 ρ / σ 0 Hmρ / σ 0 Cmρ / σ 0

1 /σ 2 /30 ρ / σ 0

2 /3Hmρ / σ 0

2 /3 Cmρ / σ 02 /3

ρ / σ 0 Hmρ / σ 0 Cmρ / σ 01 / σ 0

Thermal property indices

• Minimum steady state heat loss: λ

• Minimum thermal inertia: Cp ρ

• Minimum heat loss in thermal cycle: √(λ Cp ρ)

Stiffness design Tie Rod

Material

E ρ Hm Cm

Aluminum 80 2.7 200 2

Steel 200 7.9 35 1

CFRP 170 1.6 280 40

GFRP 28 1.8 112 20

Volume MassEnergy

Cost

0.01250.033

86.75 0.068

0.00500.039

51.38 0.040

0.00590.009

42.64 0.376

0.03570.064

37.20 1.286

MInimum volume design

Minimum mass design

MInimum energy design

Minimum cost design

Resolving Conflicts

• In most real design applications, a compromise is needed because different design parameters have different optimal material choices.

• Some methods are Weighting and Tradeoff Strategies

Weight Factors

• This is an attempt to quantify judgement.

• Key properties are identified and there values are listed

• Then they are combined, but not in equal amounts.

• the “weights” are the importance factors associated with each characteristic

Weighting functions

• First we identify all parameters and their values.

• Mi represents the value of the ith parameter of interest, and Mi,max is the largest value of all being considered.

• The weights are a set of numbers wi between 0 and 1 that indicate the importance of parameter i.

Weighting Functions

Wi =wi

M i

M i,max

Weighting FUnctions

• Some parameters don’t have experimental numerical values. These are usually rated something like 5=good, to 1= bad.

• Sometimes a property has a good low value, then we use the reciprocal of the property so that in all cases a large number is a good thing for the calculation.

Weighting Function

• Then we can calculated the weighted value of the material by simply summing everything up

W = Wi∑

Example with our Plate• Suppose we want to have low mass, energy and cost.

Material Mass Energy Cost

Aluminum 0.627 125.32 1.25

Steel 1.351 47.28 1.35

CFRP 0.289 80.87 11.55

GFRP 0.593 66.39 11.86

Best Plate

• Because we want to minimize all three values, we can either take reciprocals of each value and do the normal weighting process, or we can do the normal weighting and look for the smallest value.

• Let’s take the reciprocals to get the feel for the process.

Best Plate

Material 1/Mass 1/Energy 1/Cost

Aluminum 1.596 0.008 0.798

Steel 0.740 0.021 0.740

CFRP 3.462 0.012 0.087

GFRP 1.687 0.015 0.084

MAXIMUM 3.462 0.021 0.798

Best Plate• Now we come up with the weighted values.

• We could make them equally weighted (case 1):

• w1=1/3; w2=1/3; w3 = 1/3

• Or we could use some other combination, say where mass is most important, followed by cost then energy (case 2):

• w1 = 0.5; w2=0.2; w3=0.3

• First we renormalize all the data by taking each materials value and dividing it my the maximum value for the characteristic.

Best Plate

Material M1/M1,max M2/M2,max M3/M3,max

Aluminum 0.46 0.38 1.00

Steel 0.21 1.00 0.93

CFRP 1.00 0.58 0.11

GFRP 0.49 0.71 0.11

Weighted Values

Material Case 1 Case 2

Aluminum 0.613 0.606

Steel 0.714 0.585

CFRP 0.564 0.649

GFRP 0.435 0.418

Weighting

• So, although weighting reduces the problem to a simple numerical calculation, the choice of the weights can affect the results.

Systematic tradeoff strategies

• We define a solution as a viable choice of material that meets all the constraints but is not necessarily optimal for the objectives.

• Consider some data where we are to minimize cost and mass (while meeting some other constraints). Let’s say P1 is the cost and P2 is the mass.

• The next slide shows some material choices.

P1: Cost

P2:

M

ass

Cheap Expensive

Light

Heavy

Dominated Solutions

• A solution is said to be dominated if there are better solutions on either parametric axis.

• We can draw a box towards the axis and see if there are any solutions contained in that region. If there are, then the solution is dominated.

P1: Cost

P2:

M

ass

Cheap Expensive

Light

Heavy

Dominated Solution

Tradeoff Surface

• If we can make a curve out of all of the non-dominated solutions (by connecting the dots) we call this the trade-off surface.

• Points on the trade-off surface offer the best compromises.

• This can create our shortlist from which we choose a solution.

P1: Cost

P2:

M

ass

Cheap Expensive

Light

Heavy

Penalty Function

• Suppose we want to minimze the cost (C) and the mass (m).

• We create a simple equation:

• Z = C + α m

• The term α is the change in Z associated with a increase in m (mass) so has units of cost/mass ($/kg, for example).

• It is called the exchange constant.

Penalty Function

• If we think of our data as a plot of mass vs. cost, we can re-write our penalty function to look like y = mx + b.

• m = -(1/α) C + (Z/α)

• Our choice of alpha describes the shape of the penalty function.

• We can plot these lines for different values of Z and find the solution corresponding to the smallest Z value.

P1: Cost

P2:

M

ass

Cheap Expensive

Light

Heavy

Decreasing values of Z

P1: Cost

P2:

M

ass

Cheap Expensive

Light

Heavy

Decreasing values of Z

Different values of α can result in different choices

Exchange constants

• The exchange constant must be chosen appropriate to the problem. In our case, comparing mass and cost, our exchange constant is the cost of a kilogram of mass.

• So for a family car, this might be a relatively small value. But for a spaceship this would be some very high value.

• For many engineering applications this exchange constant can actually be calculated based on the life cost of the system being designed.

Exchange Constants

System Basis of estimateExchange constant

($/kg)

Family car Fuel savings 1-2

Truck Payload 5-20

Civil aircraft Payload 100-500

Military aircraft

Payload/performance

500-1,000

Space vehicle

Payload 3,000-10,000

Exercise

• You are designing a disposable fork for a fast-food restaurant.

• identify the objective and constraints you think are important for this application.

Exercise

• A maker of polypropylene patio furniture hires you to evaluate his product. The competition makes cast-iron patio furniture and claims their product is much “greener” than the PP.

• The PP chair weighs about 1 kg and the cast iron about 11 kg.

• Considering energy and carbon as the metrics, which chair is greener?

• Does the projected life of the chairs matter? If so, how long before the answer changes?