DoE applied on visual appearance of materials

Implementation of Statistical Design

of Experiments (DoE) in Evaluating

the Visual Appearance of Materials

Fco M. Martínez-Verdú

Color & Vision Group: http://web.ua.es/en/gvc

University of Alicante (Spain)

[email protected]

http://web.ua.es/en/gvc

mailto:[email protected]

http://www.ua.es/es/index.html

http://web.ua.es/es/gvc

Visual appearance of materials in automotive sector Color & Texture: ColTAS MSc course

Challenges for its optimal and efficient management Multi-scale approach (bottom-up vs. top-down)

Feasible solution: DoE + regression models

Examples: sparkle detection, color matching & 3D printing

Conclusions

OUTLINE


Color & Texture

Reflection & Transmission

Goniochromatism: BRDF

Sparkle & Graininess

VISUAL APPEARANCE OF MATERIALS

® Wikipedia


MSc degree in Color Technology for the Automotive Sector

VISUAL APPEARANCE OF MATERIALS


• Bottom – up:

• Many variables

• Impracticable

• Top – down:

• Feasible

• How?

CHALLENGES: MULTI-SCALE APPROACH

Color, Texture

Radiative

transfer theory

Particles

interaction

Light – matter

interaction

particle models

Light sources tech.,

Pigments, dyes

Gloss, sparkle, etc.

Color differences

Visual appearance

Emission S(l)

Reflection r(l)

Transmission t(l)

Coefficients:

Absorption K

Scattering S

Substrate

Cross

sections:

QA(D, l)

QS(D, l)

D size

Phys. + Chem.

particles:

Size (D), Shape,

Refraction index,

Extinction index,

Roughness, etc.

TH

EO

RE

TIC

AL

AP

PR

OA

CH

EX

PE

RIM

EN

TA

L A

PP

RO

AC

H


• But, in this case (empirical approach = top – down), the

typical challenge is how we can understand and manage

by a pro-active way the relevance and interplay of

nano/micro (structural) parameters, and other ones

(coloration application processes, optical, etc.), on final

visual appearance attributes (color, texture, etc.).

• HOW?

• Metrology, Visual Psychophysics, and Statistics

• inter and multi-disciplinary (hybrid) approach

CHALLENGES: MULTI-SCALE APPROACH


1- Statistical Design of Experiments (DoE)• Statistical technique used in quality control for planning,

conducting, analyzing, and interpreting sets of experiments

aimed at making sound decisions without incurring a too high

cost or taking too much time• Qualitative and quantitative variables optimization objective

• Selection of the minimal number of samples

2- Non-linear / linear multidimensional regression models• Increasing sampling for an optimal prediction model

• even combining qualitative and quantitative (measureable) variables

FEASIBLE SOLUTION


• Problem formulation• Aim (reproducible and measurable)

• Relevant factors (qualitative and quantitative)

• Screening design• Selection of levels for each factor

• Experiments (no. of samples)

• Analysis of the raw data

• Data analysis (Pareto, regression, etc.)

• Optimization & Robustness studies

DoE: FUNDAMENTALS


1 – Sparkle detection distance vs. metallic pigment size & shape

2 – Sparkle detection distance vs. concentration, achromatic

background, illuminance level & pigment type

3 – Sparkle detection distance vs. colored background

4 – Color matching vs. silver finishing process

5 – Gonio-appearance of 3D printed parts vs. 3D printing technology

and its sub-processes

FIVE EXAMPLES


• Aim: maximize the sparkle detection distance

• ASTM definition: the aspect of the appearance of a material that

seems to emit or reveal tiny bright points of light that are

strikingly brighter than their immediate surround and are made

more apparent when a minimum of one contributors (observer,

specimen, light source) is moved.

SPARKLE DETECTION DISTANCE


• Key factors for the “problem formulation”:

• Instruments for measuring structural and visual parameters

• Directional lighting booths for assessing visually sparkle



• Unknown multidimensional surface function for understanding the

interplay among variables for the detection distance of sparkle

• distance = f (C*, L*, hab , E(lx), Tc , pigment size, pigment shape, thickness,

geometry, concentration, application process, etc.)

• What variables are more important on the sparkle detection?

• Structural: pigment size, shape & type, concentration, layer thickness, …

• Environmental: Tc , measurement geometry, illuminance level, …

• Colorimetric: black vs. white background, colored background, …

• Engineering: coating application process (SB, WB, powder, etc.), …



• DoE strategy: fixate some variables, and give free others

• 1st Example: distance = f(metallic pigment size & shape)

• Only free pigment size (D50) and shape (silver dollar vs.

cornflake)

• Light intensity (E in lx), geometry, SPD, Tc , are fixed now

• Challenge:

• manage quantitative (D50) and qualitative (shape) variables

SPARKLE DETECTION DISTANCE 1


• After DoE analysis for 22 factorial table:

• Small (-1) vs. Big (1);

• Cornflake (-1) vs. Dollar (1)

• Pareto chart, interaction diagram, etc.


ExperimentPigment

Size (A)

Pigment

Type (B)

1 1 1

2 1 -1

3 -1 1

4 -1 -1

p = 0,05

Strong effects!!



0

50

100

150

200

250

300

0 10 20 30 40Sp

ark

le d

ete

cti

on

dis

tan

ce

(c

m)

Size D50 (mm)

Size & Shape Interaction:d = 0,214·(D50)

2 - 3,347·D50·Shape , R2 = 94,88 %

Silver dollar (0) Cornflake (1)


• Prediction models by instrumental data (Sg)


Sg = 0,313·D50 - 1,777R² = 0,9784

Sg = 0,133·D50 - 0,933R² = 0,95700

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40

Sp

ark

leg

rad

e (

Sg)

Size D50 (mm)

Silver dollar Cornflake

d = 20.44e0.29·S

g

R2 = 0.8754

Sparkle grade (Sg)

0 2 4 6 8 10D

ete

cti

on

dis

tan

ce

(cm

)

0

50

100

150

200

250

300

d = 4.01e0.97·S

g

R2 = 0.9664

Sparkle grade (Sg)

0 1 2 3 4

Dete

cti

on

dis

tan

ce

(cm

)

0

50

100

150

200

250

300

d = a·exp(b·Sg), a and b fitting parameters


• Variable concentration: from 1 % to 26 % , 6 levels

• Pigment type: Hydrolan®, Iriodin®, Xirallic®

• Achromatic background

• Black vs. White

• Geometry:

• 15as15 vs. 45as45

• Light intensity:

• 800 vs. 5000 lx


Fixed D50 and coating thickness


• Pareto chart for a multi-level factorial table

• Xirallic® better


p = 0,05

quadratic

interaction

LOWER

concentration,

LONGER sparkle

detection distance

BETTER


• Longer for:

• Black backg.

• Low PMC (%)

• Xirallic®

• 45as45

• Model for

Bk background


d = a·(PMC)-b


• Relevance and interplay of colored backgrounds by CIE-L*C*abhab

• Fixed structural and environmental data (factors)• Color mix: variable solid pigment + fixed effect pigment

• L*: 3 levels• C*ab: 3 levels• hab: 4 levels


Complete multi-level factorial table of experiments (samples)

Sample no. C L h Sample description [Hue / Lightness / Chroma]

1 0 1 1,00 RED / LIGHT / MEDIUM

2 1 -1 1,00 RED / DARK / STRONG

… … … … …

13 -1 1 -1,00 GREEN / LIGHT / WEAK

14 -1 -1 0,33 BLUE / DARK/ WEAK

… …

23 0 1 0,33 BLUE / LIGHT / MEDIUM

24 0 -1 -0,33 YELLOW / DARK / MEDIUM

… … … … …

34 1 0 1,00 RED / GRAY / STRONG

35 0 0 0,33 BLUE / GRAY / MEDIUM

36 -1 1 1,00 RED / LIGHT / WEAK


• Goal: color matching (DEab = 0), L* = 82 , & maximum transparency

• Initial DoE proposal: Taguchi L16 (215-11) Matrix, before analysis

COLOR MATCH vs. SILVER FINISHING

Worksheet MEASURED RESPONSES

Nº experim. MaterialPVD

Thickness

PVD

Conc.Topcoat

Topcoat

RobotBasecoat

Basecoat

Robot DEab L* Transparency (T)

1 Metal A

Low

Low Low

translucent

white

Low Low Low

2Metal B

HighHigh High

3High

Low

4 Metal AHigh Low Low

5 Metal CLow

High

translucent

white

6Metal D

LowHigh High

7High

High

8 Metal CLow Low

Low

9 Metal A

High

LowHigh

10Metal B

HighHigh Low

11High

Low

12 Metal AHigh Low High

13 Metal CLow Low

translucent

white

14Metal D

LowHigh Low

15High

High

16 Metal C Low Low High


• Can 3D printed parts for cars (body or interior) equal or better

color & texture without losing phys-chem performance?

• DoE goals: high sparkle, gloss, flop, chroma, colorfastness, etc.

• Factors:

• Qualitative:

• Technologies: FFF, MultiJet Fusion, ColorJet, Powder-bed, living AM, etc.

• Materials: (bio)polymers, pigments, additives, composites, etc.

• Quantitative:

• Temperature, irradiation, speed, layer height, infill, head size, etc.

GONIO-APPEARANCE IN 3D PRINTED PARTS


• FFF experiment table (Taguchi L9): PLA fixed, simple interactions

• Head size (mm): 3 levels

• 100, 200 & 300

• Speed (mm/s): 3 levels

• 20, 40 & 60

• Infill (%): 3 levels

• 0, 20 & 100

• Color: 3 levels

• Without pigment

• Solid or special-effect pigment


Sample no. HEAD SPEED INFILL COLOR

1 1 3 2 3

2 3 2 2 1

3 1 2 3 2

4 3 1 3 3

5 3 3 1 2

6 2 1 2 2

7 2 3 3 1

8 1 1 1 1

9 2 2 1 3

Plane printed samples for measuring flop


• FFF experiment tables:

• Complete multi-level factorial:

• All previous factors with 2 levels, except color set = 24, all possible interactions

• Multi-level factorial + D – optimal design

• Only speed with 2 levels complete set = 54, but optimally reduced to 21

• Multi-level factorial + D – optimal design:

• All factors with 3 levels + new factor (polymer: ABS or PLA) complete set = 162, but

optimally reduced to 21, and simple interactions well detected

• Multi-level V2 factorial + D – optimal design:

• Only speed and polymer with 2 levels from 108 to 21, quadratic interactions



The statistical design of experiments (DoE), successfully

implemented in other engineering topics, can be used in coatings, as

well as in visual appearance of materials.

Both for car body and car interior (dashboard, etc.), this multi-scale

hybrid knowledge can be very interesting for the automotive sector.

Inspired examples: sparkle detection, color matching, and 3D printed parts

Future applications for the automotive sector?

CONCLUSIONS


This research initiative is indirectly supported by the European Union and

Spanish Ministry of Economy and Competitiveness under the grants DPI2011-

30090-C02 & DPI2015-65814-R with European Regional Development Funds

(ERDF) support.

This research was also done within the EMRP IND52 Project

xD-Reflect “Multidimensional reflectometry for industry”.

The EMRP is jointly funded by the EMRP

participating countries within EURAMET

and the European Union.

ACKNOWLEDGEMENTS


Rössler, A. (2014): Design of Experiments for Coatings. Hanover: Vincent

Network.

Gómez, O., et al. (2016): “Analysis of the interplay of the pigment shape and

size on sparkle detection distance by design of experiments”. CIE x043, 345.

Micó-Vicent, B., et al. (2017): “A combination of three surface modifiers for the

optimal generation and application of natural hybrid nanopigments in a

biodegradable resin”. J. Mater. Sci., 52(2), 889.

Micó-Vicent, B., et al. (2017): “Optimum multilayer-graphene-montmorillonite

composites from sugar for thermosolar coatings formulations”. J. Sol. Energy

Eng., 139(3), 031005.

REFERENCES


Implementation of Statistical Design

of Experiments (DoE) in Evaluating

the Visual Appearance of Materials

Fco M. Martínez-Verdú

Color & Vision Group: http://web.ua.es/en/gvc

University of Alicante (Spain)

[email protected]

http://web.ua.es/en/gvc

mailto:[email protected]


http://web.ua.es/es/gvc