10/29/2007
Raman Analysis of Concentrated
Salt Solutions using Robust
Modeling and Data Fusion
Jeremy M. Shaver a, Samuel A. Bryan b,
Tatiana G. Levitskaia b, Serguei I. Sinkov b
a Eigenvector
Research, Inc.
Manson/Seattle, WA
b
Pacific Northwest National Lab
Richland, WA
[email protected]
Hanford Double Shell Tank
• Liquid
• Salt cake
1
10/29/2007
Nuclear Waste Storage Tanks
Composition
Monitoring
Storage
Salt cake
Tank Farm
Chemical
Inventory, Hanford
Site
Tank
Farm
Chemical
Inventory
NO3
Na
OH
by phase
NO2
CO3
Al salts
Al
NaNO2
PO4
SO4
Na-CO3-F-PO4-SO4
Fe
TOC
NaNO3
F
others
others
0
BBI 3/20/03
10000
20000
30000
40000
50000
60000
Metric Tons
2
10/29/2007
Raman Spectra of Ionic Species
NO3
CrO4
SO4
H2PO4
400
600
800
CO3
NO2
1000
1200
1400
Raman Shift (cm-1)
1600
1800
2000
Raman Spectrum
Density and Conductivity
Sensors
Concentration (%)
Data and Analysis Flowchart
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Ion Concentrations
Expected
Density
Expected
Conductivity
Measured
Density
Measured
Conductivity
Density Discrepancy
Particulates in Solution
(Volume of Particulates)
Conductivity Discrepancy
New Species or Interactions
(Refinement of Raman Model)
3
10/29/2007
Estimation of Density and Conductivity
from Concentrations
(1st generation models)
700
Density
1.4
Num. LVs: 3
RMSEC: 17.4132
1.35 RMSECV: 22.9085
Conductivity
Predicted Conductivity, mS/cm
Predicted Density, g/ml
1.45
1.3
1.25
1.2
1.15
SiO4-3
1.1
1.05
AlO2-1
AlO2-2
600 Num. LVs: 4
RMSEC: 0.019
RMSECV: 0.021
NaOH-1 R
500
NaOH-2 R
400
NaOH-3 R
AlO2-3
300
mix-33
mix-15
NaOH-4 R
mix-43
mix-5
mix-37
200
mix-30
mix-36
mix-35
mix-27
mix-40
mix-11
mix-14
100
mix-22
SiO4-4
mix-25
mix-29
mix-34
PO4-4
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
0
Measured Density, g/ml
SiO4-3
50
100
150
200
SiO4-4
250
300
350
Measured Conductivity, mS/cm
(dimmed and/or labeled points were not used in modeling)
Raman-to-Concentration Model
Design Challenges
• Long-Term Model
– Months-Years of Service
• Unknown Field Interferences
– Updates probably necessary
4
10/29/2007
Regression Model Options
• ILS – Inverse Least Squares (PLS, PCR, MLR)
+ Nonlinearities often easily included
- Model updating a challenge
• CLS – Classical Least Squares
+ Model updating straightforward
- Does not typically allow for nonlinearities
Raman Intensity
Classical Least Squares Model
As concentration increases, there is a
corresponding increase in intensity as
a linear response (i.e. Beer’s law).
si
0
200
400
600
800
1000
The typical CLS model uses a simple
response profile (spectrum) to predict
concentration of the individual species.
Pure component
Spectrum projection
Frequency
ST
e.g
Time
ci
0
20
C
40
60
Species Concentration
80
100
X = CST + E
5
10/29/2007
Standard CLS Model
Calibration
CS T = X
T
†
Sions
= Ccal
X cal
mixtures
Determine pure component spectra
(ST) from calibration samples by
ordinary least-squares regression.
Ccal
pure component spectra
least
least
squares
squares
Standard CLS Model
Prediction
c1
c2
c3
Standard “linear” CLS
Each spectrum maps to
one concentration.
c4
c5
T
C = X ( Sions
)†
…
…
ck
6
10/29/2007
Extended Mixture Model
Prediction
c1
c2
c3
Add additional background
or component spectra as
needed
…
…
T
C = X ( Sions
)†
ck
T
T
C = X ([ Sions
Sinter
])†
cinter,1
cinter,2
Martens & Naes
Stepwise Regression
Prediction
c1
X
0
c3
X
X
0
Use ONLY those
components which improve
the spectral residuals by a
statistically significant
amount
0
…
…
ck
7
10/29/2007
Raman Intensity
Non-Linear CLS Model
si,2
si,1
0
200
400
600
800
1000
Individual Species
Concentration
Frequency
The typical CLS model expects only a
change in intensity and no change in
spectral profile. The non-linear CLS
model allows for multiple spectral
profiles as concentration changes.
ci,1+ci,2
ci,1
ci,2
0
20
40
60
80
As concentration increases, there is
an increase in intensity as well as,
eventually, a shift of the peak
position (due to molecular
interactions such as hydrogen
bonding)
100
Total Ion Concentration
Non-Linear CLS Models
Calibration
Cc MS T = Ck S T = X
T
†
Sion
=
C
s
k ,cal X cal
Ck ,cal = Cc ,cal M
If M is diagonal, this is CLS
Otherwise, M imposes closure between
underlying factors to known concentration.
e.g. Two factors for first component
M=
[ 1100
0010
0 0 0 1]
Solve for Sions via ALS
(a) single factors = hard equality constraint
(b) multiple factors = soft closure constraint to species concentration
T
CM T = C ' = X cal ( Sions
)†
8
10/29/2007
Non-Linear CLS Model
Prediction
c'1,1
c'1,2
c1
c'1,3
c2
c'3
c3
c'4
c4
…
…
c'2
…
“Non-linear” CLS
More than one pure
component spectrum
can map to an
underlying species
concentration.
c'k
ck
20
10
0
0
10
20
NaNO3
30
0
10
5
0
10
20
NaNO2
6
4
2
10
Na2CO3
10
5
0
0
15
0
Na4SiO4 pred
5
5
10
Na3PO4
2
4
Na2CrO4
6
20
15
10
5
0
30
0
0
Na3PO4 pred
Na2SO4 pred
10
30
NaAl(OH)4pred
Na2CO3 pred
NaNO2
20
0
Estimated Concentration
pred
30
Na2CrO4 pred
NaNO3
pred
Classical Least Squares (CLS)
0
5
10
15
Na2SO4
20
10
5
0
-5
-10
0
2
4
6
NaAl(OH)4
8
Al(OH)4 in solution
10
with NO3
0
0
10
20
Na4SiO4
Measured Concentration
9
10/29/2007
Example: Multiple NO3 Components
Normalized spectra at different NO3
concentrations and w/Al(OH)4
increasing
ionic strength
1010
1030
1050
1070
1090
Raman Shift (cm-1)
10
20
NaNO3
30
5
0
5
10
Na2CO3
0
10
20
NaNO2
15
10
4
2
0
2
4
Na2CrO4
6
5
0
30
6
0
15
Na2SO4 pred
10
0
10
0
20
Na2CrO4 pred
Na2CO3 pred
0
20
30
NaAl(OH)4pred
10
0
0
5
0
2
10
15
Na2SO4
20
8
6
4
2
0
4
6
NaAl(OH)4
8
Na4SiO4 pred
15
Na3PO4 pred
Estimated Concentration
pred
20
NaNO2
pred
30
NaNO3
Non-Linear Classical Least Squares (NL-CLS)
10
5
0
0
5
10
Na3PO4
20
10
0
0
10
20
Na4SiO4
Measured Concentration
10
10/29/2007
Example: Multiple NO3 Components
Measured Data
Recovered Spectra
normalized
Normalization of OH
2nd Derivative
ALS calibration
increasing
ionic strength
1010
1030
1050
1070
1090
1010
1030
Raman Shift (cm-1)
1050
1070
1090
Raman Shift (cm-1)
10
20
NaNO3
30
5
0
5
10
Na2CO3
0
10
20
NaNO2
15
10
4
2
0
2
4
Na2CrO4
6
5
0
30
6
0
15
Na2SO4 pred
10
0
10
0
20
Na2CrO4 pred
Na2CO3 pred
0
20
30
NaAl(OH)4pred
10
0
0
5
0
2
10
15
Na2SO4
20
8
6
4
2
0
4
6
NaAl(OH)4
8
Na4SiO4 pred
15
Na3PO4 pred
Estimated Concentration
pred
20
NaNO2
pred
30
NaNO3
Non-Linear Classical Least Squares (NL-CLS)
10
5
0
0
5
10
Na3PO4
20
Interference of
baseline/background
10
0
0
10
20
Na4SiO4
Measured Concentration
11
10/29/2007
10
20
NaNO3
10
0
30
10
5
0
5
10
Na2CO3
10
5
10
20
NaNO2
15
10
5
0
30
4
2
0
2
4
Na2CrO4
0
5
0
2
10
15
Na2SO4
20
8
6
4
2
0
6
4
6
NaAl(OH)4
8
20
10
0
0
0
0
6
0
15
Na4SiO4 pred
Na3PO4 pred
0
Na2SO4 pred
20
Na2CrO4 pred
Na2CO3 pred
0
20
30
NaAl(OH)4pred
10
0
Estimated Concentration
pred
20
NaNO2
pred
30
NaNO3
Non-Linear Extended Least Squares (NL-ELS)
5
10
Na3PO4
0
10
20
Na4SiO4
Measured Concentration
10
20
NaNO3
30
5
5
10
Na2CO3
10
5
0
0
5
10
Na3PO4
0
10
20
NaNO2
15
10
4
2
0
2
4
Na2CrO4
6
5
0
30
6
0
15
Na2SO4 pred
10
0
10
0
20
Na2CrO4 pred
Na2CO3 pred
0
30
NaAl(OH)4pred
10
0
Na3PO4 pred
NaNO2
20
0
Estimated Concentration
pred
30
Na4SiO4 pred
NaNO3
pred
Non-Linear Non-Negative Extended Least Squares (NL-NNELS)
0
5
0
2
10
15
Na2SO4
20
6
4
2
0
4
6
NaAl(OH)4
8
20
10
0
0
10
20
Na4SiO4
Measured Concentration
12
10/29/2007
Calibration Results
NO3
0.18
0.19
0.18
0.18
NO2
0.19
0.19
0.19
0.18
SO4
0.36
0.36
0.27
0.36
CO3
0.11
0.09
0.13
0.12
CrO4
0.04
0.04
0.04
0.04
Al(OH)
0.43
0.42
0.73
0.61
PO4
0.53
0.48
0.56
0.49
SiO4
0.78 nn
0.74 sr,nn
1.25
1.12 sr
(non-negative basis)
NO3
NO2
SO4
0.26
0.18
0.35
0.26
0.18
0.35
0.24
0.23
0.34
0.24
0.18
0.39
CO3
0.10
0.09
0.12
0.10
CrO4
0.04
0.04
0.04
0.04
Al(OH)
0.38
0.39
0.43
0.17
PO4
0.48
0.45
0.51
0.44
SiO4
0.99 nn
1.04 sr,nn
0.92
0.99 sr
Pure samples only
OH Normalization
2nd Derivative
ALS calibration for non-linear components
Extended and Non-Linear Models Useful?
Ordinary Least Squares
Standard Error of Calibration (SEC)
NO3
NO2
SO4
CO3
: 0.60
0.59
0.36
0.24
B : 0.59
0.61
0.36
0.24
3: 0.57
0.54
0.31
0.21
B3: 0.57
0.54
0.31
0.21
CrO4
0.12
0.12
0.11
0.11
Al(OH)
3.13
3.15
0.61
0.67
PO4
2.24
1.38
1.50
0.67
SiO4
2.77
1.70
2.33
1.68
Standard Error of Prediction (SEP)
NO3
NO2
SO4
CO3
: 0.53
0.20
0.06
0.21
B : 0.51
0.21
0.06
0.21
3: 0.48
0.19
0.12
0.17
B3: 0.46
0.18
0.13
0.17
CrO4
0.10
0.10
0.09
0.09
Al(OH)
2.06
2.09
0.55
0.58
PO4
2.26
1.26
1.56
0.26
SiO4
2.67
1.49
2.03
1.55
B: Including 2 Background Factors (from NaOH)
3: Non-linear (3 components) for NO3
13
10/29/2007
Extended and Non-Linear Models Useful?
Non-negative Least Squares
Standard Error of Calibration
:
BG
:
NL:
BG,NL:
NO3
0.56
0.60
0.56
0.56
NO2
0.66
0.74
0.53
0.52
:
BG
:
NL:
BG,NL:
NO3
0.41
0.38
0.43
0.40
NO2
0.62
1.11
0.20
0.19
SO4
0.36
0.36
0.35
0.35
CO3
0.49
0.45
0.20
0.20
CrO4
0.13
0.12
0.10
0.11
Al(OH)
2.16
1.95
0.28
0.27
PO4
4.83
1.65
1.49
0.61
SiO4
2.03
2.42
2.10
0.97
PO4
4.73
0.87
1.54
0.31
SiO4
1.27
0.45
1.67
0.38
Standard Error of Prediction
SO4
0.06
0.11
0.07
0.12
CO3
0.42
0.39
0.17
0.18
CrO4
0.11
0.10
0.09
0.10
Al(OH)
0.55
0.62
0.31
0.20
BG: Including 2 Background Factors (from NaOH)
NL: Non-linear (3 components) for NO3
Stepwise and Non-Negative LS Useful?
Background + Non-linear NO3
Standard Error of Calibration
:
SR
:
NN:
SR,NN:
NO3
0.57
0.56
0.56
0.56
NO2
0.54
0.52
0.52
0.51
:
SR
:
NN:
SR,NN:
NO3
0.46
0.45
0.40
0.40
NO2
0.18
0.17
0.19
0.20
SO4
0.31
0.35
0.35
0.35
CO3
0.21
0.20
0.20
0.19
CrO4
0.11
0.11
0.11
0.11
Al(OH)
0.67
0.80
0.27
0.26
PO4
0.67
0.61
0.61
0.53
SiO4
1.68
1.61
0.97
0.79
PO4
0.26
0.55
0.31
0.62
SiO4
1.55
1.32
0.38
0.45
Standard Error of Prediction
SO4
0.13
0.13
0.12
0.12
CO3
0.17
0.17
0.18
0.18
CrO4
0.09
0.09
0.10
0.10
Al(OH)
0.58
0.55
0.20
0.22
SR: Stepwise regression
NN: Non-Negative least squares
14
10/29/2007
Best/Worst Results
Standard Error of Calibration
NO3
0.60
0.56
NO2
0.59
0.51
SO4
0.36
0.35
CO3
0.24
0.19
CrO4
0.12
0.11
Al(OH)
3.13
0.26
PO4
2.24
0.53
SiO4
2.77
0.79
PO4
2.26
0.31
SiO4
2.67
0.38
Standard Error of Prediction
NO3
0.53
0.40
NO2
0.20
0.19
SO4
0.06
0.12
CO3
0.21
0.18
CrO4
0.10
0.10
Al(OH)
2.06
0.20
OH Normalization
1st derivative
Non-linear CLS model
Extended Mixture model
Stepwise regression
Non-negative Least Squares
Conclusions and Future
• CLS models can be adapted to handle nonlinear single-component responses
• Updating of CLS models straightforward
• Evidence for fusion of conductivity and
Raman for correction
• On-line statistics for evaluation
15