1803-DataScienceOverview.pdf presentatino slides

Multivariate Multiple Regression
Devin Gordon

SDLE Research Center, VUV-Lab, Materials Science & Engineering Department, Roger H. French © 2016 http://sdle.case.edu August 6, 2017, VuGraph 2
Degradation Science “Data Block” For Statistical Analytics
Using a < Stress | Mechanism | Response > Framework
Evaluation
s
Multiple Datatypes
• “Point” values
• Spectra
• Images
• Hyper-spectral Images
Basis in Physics and Chemistry
• Stressors: Heat, Moisture, Irradiance,
etc.
• Responses: Yellowness Index, Gloss,
Haze, Power output, etc.
Statistically Informed Study
• Large Volume of Samples
• Diverse Exposures
• Real-world & Lab Base
• Accelerated & Real-time
• Many Evaluations
• Mechanistic & Performance

Data Block
Consistent naming structure
Sample number - step of exposure - measurement step - meas. number - meas. type
Retain Samples through exposure for additional analysis
Large enough data set for statistical significance
● Number steps
● Number of samples
Measure step 0 samples at every evaluation

Weathering Driven Degradation
Degradation yields performance loss
Mechanisms
• Photolysis: light induced degradation
• Hydrolysis: moisture induced degradation
• Thermolysis: heat induced degradation
Results in:
• Decreased molecular weight
• Increase in crystallinity
• Embrittlement
• Increase in reactive end groups
Poly(ethylene-terephthalate)

Cross-Correlation: Accelerated and Real-World Exposures
Samples - Clear PET
• 3 types (proprietary)
• Unstabilized vs. UV Stabilized
Exposures
• Accelerated (different temperatures)
• Full Spectrum-Dry
• Full Spectrum-Humid
• Ultraviolet-Dry
• Ultraviolet-Humid
• Real-World
• Florida (Open and Glass-Covered)
• Arizona (Open and Glass-Covered)
Evaluations
• Color (L*, a*, b*, ΔE)
• Percent Haze
• Gloss
Cross-correlate between
• Accelerated
• Real-world
What Accelerated Exposure
• Best Mimics the Real-world?
• Comparable Dose Basis
Evaluations

<Stress|Response> Modeling
Variable Definition
• Stress: UVA<360
photodose, moisture, temperature (Z)
• Response: ΔE, ΔGloss, ΔHaze (Y)
• Indicator variables (1 or 0) used for categorical factors (material type, exposure type) (Z)
Variable Selection
• Rank-ordered predictors selected through a forward step-wise selection process
• Begin with null model (Y = 1) and add variables to minimize Akaike Information Criterion (AIC)
Model type Selection
Multivariate Multiple Regression (MMR): Applied for data with multiple responses
Ynxm
= znx(r+1)
𝜷(r+1)xm
+ 𝛜nxm

<Stress|Response> Modeling
Functional Form Selection
Linear
Linear-Linear Change Point
Polynomial
Exponential
Logarithmic
Splines - Natural Splines:
• Smoothly varying functions to capture nonlinear behavior
• Knot positions optimized to minimize model error (root mean square error)
Boundary knot (y’’ = 0): linear
Boundary knot (y’’ = 0): linear
https://en.wikipedia.org/wiki/Spline_interpolation#/media/File:Cubic_splines_three_points.svg

Multivariate Multiple Regression Model: Example Outdoor Clear PET

Change in Percent Haze: Clear PET
● Moisture increases degradation rate of clear PET
○ AZ vs. FL, Wet vs. Dry
● Direct water contact (Open) causes more rapid degradation
○ than moisture from humidity
● UV stabilizer doesn’t seem to mitigate degradation (C3 is UV Stabilized)

<Stress|Mechanism|Response> Modeling
Identify the strength of relationships between all variables
Identify the degradation pathway
● based on individual stressors
● or a combination of stressors
Stressors
● Irradiance, water, temperature, etc.
Mechanisms generally from non-destructive analysis
● FTIR
● Acoustic spectroscopy
● Fluorescence
● UV-VIS
● Raman
Responses
● Performance parameters
● Gloss-loss (roughness)
● Color changes
● Cracking (Optical profilometry)

SDLE Research Center, Materials Science & Engineering Department, Roger H. French © 2017 http://sdle.case.edu January 25, 2018, VuGraph 13
Compare Pathways in the Models
Direct pathway (Stressor to Response)
● dy
→ Pmp
○ Equation/model:
○ Calculate RMSE
Indirect pathway (one mechanism)
● dy
→ Rs
→ Pmp
○ Equations :
○ Calculate RMSE
Determine the pathways that are happening in a model
Compare to the <Stress|Response> Model

Example: Indoor Time Series Data

P/P/E Backsheet Exposed to Damp Heat Condition
● Two types of degradation reactions
○ Hydrolysis
■ New peaks appear
■ at 2800-3400 cm-1
○ Oxidation
■ New peaks appear
■ 1654, 1552 cm-1
● Accompany with increases
crystallinity
● The new formed conjugation
structure causes discoloration
○ Lower energy gap
○ Absorbing blue light
Cut
off
R2
<0.3 0.3<R2
<0.6
0.6<R2
<0.8
R2
>0.8
line
type
Very
thin
thin thick thickes
t

P/P/E Backsheet Exposed to Dry, Full Spectrum Irradiance Condition
● Photooxidation
○ Chain scission
■ Ethylene
■ Ester
○ Oxidation
■ Form carboxylic acid
■ Form conjugated structure
○ All mechanism variables
■ Show strong relation with
■ Discoloration
Cut
off
R2
<0.3 0.3<R2
<0.6
0.6<R2
<0.8
R2
>0.8
line
type
Very
thin
thin thick thickes
t

Outdoor/Indoor Spatio-temporal modeling:
Cross Correlation Scale Factor (CCSF)
and Cross Correlation Coefficients (CCC)
JiQi Liu

Brief Introduction
● Cross correlation scale factor is a scale factor
to define the relationship between the time of
indoor accelerated tests and real-world
outdoor exposure time.
● In order to distinguish from another widely
used scale factor which is accelerated factor
(AF), we name our scale factor as cross
correlation scale factor, the abbreviation is
CCSF.
● Eq1: Indoor Time × AF = Outdoor Time
● Eq2: Indoor Time / CCSF = Outdoor Time
● Deduce from Eq1 & Eq 2: Eq3: AF = 1 / CCSF
● Eg: If the indoor accelerated test is 2 times
faster than the outdoor exposure test which
means 3000h indoor exposure is equal to
6000h outdoor exposure. In this case, the
accelerated factor(AF) is equal to 2, and the
cross correlation scale factor is equal to 0.5
The ccsf between the outdoor system
GCF and indoor system TCB is 0.101

Indoor Models (dy → Pmp
)
Summary
● All models are the
<S|R> path from dy to
Pmp
extracted from the
netSEM model
● Four model types
were obtained for
accelerated tests:
Exp, CP, Quad, SL.
● DHA, DHB, DHE, TCB,
TCD are always
decreasing;
DHC is first increasing
and then decreasing;
DHD, TCA, TCC, TCE
are first decreasing
and then increasing.
19
Exposure
Type
Bran
d
Equation Coefficient
β0
β1
β2
𝜏
DH A Pmp
= β0
+ β1
*exp(dy) 301.10 -39.04
DH B Pmp
= β0
+ β1
*dy + β2
*(dy-𝜏)+
291.97 -87.98 -979.97 0.3
DH C Pmp
= β0
+ β1
*dy + β2
*(dy-𝜏)+
289.413 11.40 -2316.72 0.3
DH D Pmp
= β0
+ β1
*dy + β2
*dy2
264.12 -49.99 83.86
DH E Pmp
= β0
+ β1
*dy + β2
*(dy-𝜏)+
314.14 -78.12 -2219.68 0.3
TC A Pmp
= β0
+ β1
*dy + β2
*dy2
263.75 -66.70 111.75
TC B Pmp
= β0
+ β1
*dy 290.15 -19.20
TC C Pmp
= β0
+ β1
*dy + β2
*dy2
295.23 -71.09 119.45
TC D Pmp
= β0
+ β1
*dy + β2
*dy2
263.96 -48.68 43.16
TC E Pmp
= β0
+ β1
*dy + β2
*(dy-𝜏)+
317.94 -46.33 77.40 0.3
where (dy-𝜏)+
= (dy-𝜏)*Ⅰ(dy > 𝜏), 𝜏 is the break point, and Ⅰ(⠂) is the indicator function equal to one if dy > 𝜏

Outdoor Models (dy → Pmp
)
Summary:
● All models are the path from dy to Pmp extracted from the netSEM model
● The system Age is from Month-by-Month result, not raw data.
● 2 types of models were obtained from the outdoor data: CP and Quad.
● GC_F1 and GC_F2 are always decreasing; NEG_F and NEG_G decrease in the first three years
and then increase; UFS_G increases in the first 1.5 years and then decreases. 20
Location Climate
Zone
Brand System Age
(year)
Equations Coefficient
β0
β1
β2
𝜏
GC BWh F 6.83 Pmp
= β0
+ β1
*dy + β2
*dy2
272.39 -2.60 0.30
GC BWh F 6.25 Pmp
= β0
+ β1
*dy + β2
*(dy-𝜏)+
168.22 -0.56 -1.94 3.2
NEG BSh F 5.17 Pmp
= β0
+ β1
*dy + β2
*dy2
188.02 28.03 4.55
NEG BSh G 5.17 Pmp
= β0
+ β1
*dy + β2
*dy2
101.67 3.40 -0.70
UFS ET G 4.83 Pmp
= β0
+ β1
*dy + β2
*dy2
117.88 13.78 -4.69
where (dy-𝜏)+
= (dy-𝜏)*Ⅰ(dy > 𝜏), 𝜏 is the break point, and Ⅰ(⠂) is the indicator function equal to one if dy > 𝜏

Cross Correlation Scale Factor (CCSF) - Method
Denote the indoor model and outdoor model to be
● where f1
& f2
are unknown functions of and
respectively, and ε is the error term.
We scale to
● through the cross-correlation scale factor c.
● The x range is limited to common real data.
Based on the ordinary least square method,
● we want to minimize:
● where
Then we obtain the least square estimate of c, called c* ,
Indoor scaled 1
Indoor Scaled 2
Outdoor Original

Cross Correlation Coefficients (CCC)
Correlation Coefficients (R):
● A correlation coefficient is a numerical measure
of some type of correlation, meaning a statistical
relationship between two variables. The range is
[-1,1].
● More positive relationship -> Biased towards 1
● More negative relationship -> Biased towards -1
● Eq:
xi
-> yindoor,i
yi
-> youtdoor,i
Eq:
Correlation Coefficients Plot

Cross Correlation Coefficients (CCC)
Applied CCSF to calculate the overlapping
time range of two model.
Generate outdoor time (x) sequence and
calculate indoor time sequence (x × CCSF)
Input the two x sequence to their own indoor
and outdoor model and obtain yindoor
and
youtdoor
sequence.
Using the two y sequence to calculate Cross
Correlation Coefficients
Outdoor Indoor CCSF RMSE Cross Correlation Coefficients
GCF TCB 0.101 0.0025 0.97
GCF TCB 0.085 0.0043 0.93
GCF TCE 0.044 0.0071 0.95
GCF TCE 0.040 0.0098 0.70
GCF DHE 0.041 0.0143 0.95
GCF DHC 0.041 0.0221 -0.38
NEGG DHC 0.054 0.0248 0.24
GCF DHE 0.038 0.0251 0.62
GCF DHB 0.046 0.0270 0.95
GCF DHC 0.046 0.0293 0.27
GCF DHB 0.042 0.0362 0.68

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