Quantifying Design Aesthetics – My TEDxUND talk

A few years ago I started watching TED talks over the internet, mostly during lunch time.  The talks’ topics that I watched were mostly design, engineering, and art related.  When I learned that The University of Notre Dame was going to hold a TEDx event I applied to be a speaker, to share my research with the TEDx community.  After the selection process, I was one of the 19 speakers chosen!

The email read:

“We were very impressed with your ideas and your passion, and as such, we are officially inviting you to perform at TEDxUND 2014, to be held on January 21st, 2014, at the DeBartolo Performing Arts Center…”

Then the preparation process started.  I had to explain my research in 12 minutes!  I’m just going to comment that once I understood that the purpose of the TEDx talks is to share ideas, it enabled me to focus only on the essential information needed. The organizers were very supportive giving speakers the tools needed to present on stage, which help me gain the confidence to stand in front of the TEDx audience.  The talk was streamed real-time and last week a recording of the presentation was posted on the TEDx Talks YouTube channel.  Here is my presentation:

httpvh://www.youtube.com/watch?v=kABcNKa7Dk0

After the talk, I had a good time talking to people and answering questions.  The most common question was: Where was the “beauty” number of each wheel rim? For each of the wheel rims I only presented three quantified Gestalt principles but there were more. Nevertheless, they weren’t shown for simplicity; remember the goal was to share an idea, not to present years of research in 12 minutes.  To summarize the “beauty” number is a unit vector and its dimensions are equal to the number of quantified Gestalt principles.  With that said, if you really want a scalar number, then is just a matter of taking the Euclidean norm of the vector.

The second comment was regarding the complexity of the wheel rims and now looking at the video it seems like I passed these slides quickly so here you can see the two examples of wheel rims with similar complexity that were not shown in the youtube video (at 8:26).

Wheel rims with similar complexity

Wheel rims with similar complexity.

People didn’t ask me about the equations to quantify the Gestalt principles. I don’t know if it was because they were shown briefly; this was on purpose as time was limited.  I think that here it is appropriate to share that slide.

Summary Slide of Gestalt Principles Equations

This is just a summary and more information regarding the equations can be found at my webpage.

Lastly, I want to thank all the people from the University of Notre Dame that helped me prepare for the talk.  Also, I want to thank everyone from academia, industry and friends that have guided me through this research journey questioning, challenging and inspiring myself to do good research.

When we solve problems together, we don’t only solve them, we also create new knowledge together…

Pugh Method: How to decide between different designs?

How can engineers decide systematically between different designs? How can engineers do a concept evaluation and selection?

One method, called Pugh method, helps engineers in design decisions by establishing a procedure to choose the best design from the considered designs.  This method is also known as Decision-Matrix Method or Pugh Concept Selection.  There are variations of the method however I’m going to explain here how I use it.

Step 1:  Make a list of the criteria that you want to compare between different designs.  Each criterion should be an objectively quantifiable measure.

Criteria
Criterion 1
Criterion 2
Criterion M

 

Step 2: Establish weights factors for each criterion.  A number between 1 and 10 can be chosen for each criteria, the bigger the scale the more experienced you should be to impose the weights.  Other approach can be to distribute a number of points (e.g. 100) between all criterions.  This step can be challenging for novice engineers, one way to overcome this is to just classify them in a 3-point scale where 1 is important, 2 is very important and 3 is extremely important.  The last option is to omit the use of the weights; this would mean that all criterions are equally important.  Whatever weight approach you choose I have to warn that the design selected is influenced by the selection of the weights.  The last issue before passing to the next step is that the order matters when you use this method, establish the weights factor before any analysis is made!  Otherwise you will be unconsciously biased toward one design and assign weights that benefit the strong criterions of that particular design.

Criteria Weights
Criterion 1

3

Criterion 2

2

Criterion M

3

 

Step 3:  Generation of different designs.  The designs can be generated with Brainstorming, or TRIZ just to mention two examples.  However the way to generate the designs is not the focus here.  The number of designs to evaluate will depend on the complexity of the product being designed.  That being said I would advice not to do a Pugh matrix for just 2 designs, in practice something between 3 to 7 designs could be compared.  At first generate as many designs as possible but then filter them to a manageable quantity.

Criteria Weights Design 1 Design 2 Design N
Criterion 1

3

Criterion 2

2

Criterion M

3

 

 

Step 4: Analysis of designs.  This is the step were the classical engineering takes place.  You will quantify mass, energy lost, stress, flow, etc.  All the criterions will need an analysis to quantify it, thus those numbers will have units.

Criteria Weights Design 1 Design 2 Design N
Criterion 1 Analysis

3

#.## [Kg]

#.## [Kg]

#.## [Kg]

Criterion 2Analysis

2

#.## %

#.## %

#.## %

Criterion MAnalysis

3

#.## [MPa]

#.## [MPa]

#.## [MPa]

 

Step 5: Fill the matrix.  Now for each design a number has to be calculated to fill its criterion cell.

Criteria Weights Design 1 Design 2 Design N
Criterion 1

3

?

?

?

Criterion 2

2

?

?

?

Criterion M

3

?

?

?

Again, there is more than one way to do this.  A common way is to establish one of the designs as the Datum design, and compare the other designs criterion analysis numbers (from Step 4) against the Datum design.  A scale is established beforehand, a common one goes from -3 to 3.  If the design is better than the Datum it will get a positive number and the magnitude of the number depends on how much better it is.

After using this approach, I started to modify it in order to have a minimal number of decisions based on the designer assessment of the analysis numbers.  So instead of choosing a number between -3 and 3, I calculated one.  The procedure starts by calculating the average across designs for the criterions.   Then that average is subtracted to each design criterion and that is the number that is input into the decision matrix.

Criteria Weights Design 1 Design 2 Design N
Criterion 1

3

±#.##

±#.##

±#.##

Criterion 2

2

±#.##

±#.##

±#.##

Criterion M

3

±#.##

±#.##

±#.##

 

Step 6: Calculate each design score.  This is done by multiplying each criterion weight by the design cell value (±#.##) and summing all the values for the design.  This procedure is repeated for all designs.  Then the design with the higher score is the best design and the decision was made taken into consideration all of the criterions and designs in an objective manner.

Criteria Weights Design 1 Design 2 Design N
Criterion 1

3

±#.##

±#.##

±#.##

Criterion 2

2

±#.##

±#.##

±#.##

Criterion M

3

±#.##

±#.##

±#.##

Total:

#.##

#.##

#.##

 

 

Now that the steps are explained, we can go over a specific example.  Since a previous post already discussed Baja and Formula SAE Frame Design we are going to use a frame / chassis as the example for the Pugh Method (decision-matrix method).

 

Step 1: Make a list of the criteria that you want to compare between different designs.

  • Torsional Stiffness
  • Torsional Stiffness to Weight ratio
  • Frontal Impact (Max Stress)
  • Roll Over (Max Stress)
  • CG height
  • Weight

Step 2: Establish weight factors for each criterion.  In this case choose a number between 1 and 10.

Criteria Weight (1-10)
Torsional Stiffness 9
Torsional Stiffness to weight ratio 10
Frontal Impact 7
Roll Over 8
CG height 8

 

Step 3: Generate Different Designs.

 

Step 4: Analysis of designs.

Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6
Torsional Stiffness [lbf-deg] 857.81 1057.3 1128.5 1444.9 1009.26 1430.8
Torsional Stiffness to weight ratio 14.767 17.595 18.761 32.293 16.877 23.141
Frontal Impact [psi] 53,011 47,775 38,961 24,444 36,791 26,238
Roll Over [psi] 33,929 28,835 30,995 28,174 36,176 32,705
CG height [in.] 9.64 9.47 9.94 9.78 9.77 9.60

 

Step 5: Fill in the matrix.  In this case each criteria was averaged across designs.  Then each criteria average was subtracted from each design criterion.  This is known as to center the values.  See the example below.

Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Average
Torsional Stiffness [lbf-deg]

857.81

1,057.3

1,128.5

1,444.9

1,009.26

1,430.8

1,154.76 (Average of all designs TS)

= Criterion-Average

857.81-1,154.76 =

 -296.95

 

Then the procedure is repeated for the whole table.

Criteria Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Average
Torsional Stiffness [lbf-deg]

8,57.81

1,057.3

1,128.5

1,444.9

1,009.26

1,430.8

1,154.76

= Criterion-Average

-296.95

-97.46

-26.26

290.13

-145.50

276.04

Torsional Stiffness to weight ratio

14.767

17.595

18.761

32.293

16.877

23.141

20.57

= Criterion-Average

-5.80

-2.98

-1.81

11.72

-3.69

2.56

Frontal Impact [psi]

53,011

47,775

38,961

24,444

36,791

26238

37,870

= Criterion-Average

15,141

9,905

1,091

-13,426

-1,079

-11632

Roll Over [psi]

33,929

28,835

30,995

28,174

36,176

32705

31,802.33

= Criterion-Average

2,127

-2,967

-807

-3,628

4,374

902.67

CG height [in.]

9.64

9.47

9.94

9.78

9.77

9.6

9.7

= Criterion-Average

-0.06

-0.23

0.24

0.08

0.07

-0.1

The only problem now is that each criterion is on different scales, we want to  have all in the same scale.  This can be accomplished by dividing each centered value by the biggest value for that criterion.  The resulting table should look like this:

Criteria Weight Design 1 Design 2 Design 3 Design 4 Design 5 Design 6
Torsional Stiffness [lbf-deg]

9

-1.0234

-0.3359

-0.0905

1

-0.5014

0.9514

Torsional Stiffness to weight ratio

10

-0.4953

-0.2540

-0.1545

1

-0.3152

0.2191

Frontal Impact [psi]

7

1

0.6541

0.0720

-0.8867

-0.0712

-0.7682

Roll Over [psi]

8

0.4862

-0.6784

-0.1845

-0.8295

1

0.2063

CG height [in.]

8

-0.25

-0.9583

1

0.3333

0.2916

-0.4166

 

Step 6: Calculate each design score. See the example for Design 1

Criteria Weight Design 1
Torsional Stiffness [lbf-deg]

9

-1.0234

Torsional Stiffness to weight ratio

10

-0.4953

Frontal Impact [psi]

7

1

Roll Over [psi]

8

0.4862

CG height [in.]

8

-0.25

Totals

9 x (-1.02) +10 x ( -0.49) + 7 x 1 +8 x 0.48 + 8 x (-0.25) = -5.2744

 

This is the final Pugh Decision Matrix

Criteria Weight Design 1 Design 2 Design 3 Design 4 Design 5 Design 6
Torsional Stiffness [lbf-deg]

9

-1.0234

-0.3359

-0.0905

1

-0.5014

0.9514

Torsional Stiffness to weight ratio

10

-0.4953

-0.2540

-0.1545

1

-0.3152

0.2191

Frontal Impact [psi]

7

1

0.6541

0.0720

-0.8867

-0.0712

-0.7682

Roll Over [psi]

8

0.4862

-0.6784

-0.1845

-0.8295

1

0.2063

CG height [in.]

8

-0.25

-0.9583

1

0.3333

0.2916

-0.4166

Totals

-5.2744

-14.0784

4.6676

8.8228

2.1682

3.6942

 

Design 4 is the design that the decision matrix chose based in the analysis and weight factors.  With the specific procedure carried here, once the designer establish the criterion weights, all other numbers are calculated without need of the designer to interpret or assign ratings to the designs.

As was mentioned in the description of the general steps there are many variations to the Pugh method.  This is the version that I ended up using, after using it over the years for Formula SAE design decision-making.