raman analysis of concentrated salt solutions using robust ... analysis of concentrated salt...

10/29/2007

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Raman Analysis of Concentrated Salt Solutions using Robust Modeling and Data Fusion

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. b Pacific Northwest National Lab

Manson/Seattle, WA Richland, WA

[email protected]

Hanford Double Shell TankHanford Double Shell Tank

• Liquid• Salt cake

10/29/2007

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Nuclear Waste Storage TanksNuclear Waste Storage Tanks

Salt cake

Composition

MonitoringStorage

Tank Farm Chemical Inventory, Hanford Site

Metric Tons

0 10000 20000 30000 40000 50000 60000

Na

NO3

OH

NO2

CO3

Al

PO4

SO4

Fe

TOC

F

others

by phase

NaNO3

Al salts

NaNO2

others

-PO4-SO4

Na-CO3-F-

BBI 3/20/03

Tank Farm Chemical InventoryTank Farm Chemical Inventory

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Raman Spectra of Ionic SpeciesRaman Spectra of Ionic Species

400 600 800 1000 1200 1400 1600 1800 2000Raman Shift (cm-1)

NO3

NO2

SO4

CO3

CrO4

H2PO4

Raman Spectrum

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Co

ncen

trati

on

(%

) 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)

Density and Conductivity

Sensors

Data and Analysis FlowchartData and Analysis Flowchart

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Estimation of Density and Conductivity from Concentrations

(1st generation models)

Estimation of Density and Conductivity from Concentrations

(1st generation models)

(dimmed and/or labeled points were not used in modeling)

50 100 150 200 250 300 3500

100

200

300

400

500

600

700

Measured Conductivity, mS/cmP

redic

ted C

onductivity,

mS

/cm

AlO2-1 AlO2-2

AlO2-3

PO4-4

SiO4-3 SiO4-4

NaOH-1 R

NaOH-2 R

NaOH-3 R

NaOH-4 R

mix-5

mix-11

mix-14

mix-15

mix-22

mix-25

mix-27

mix-29

mix-30

mix-33

mix-34

mix-35

mix-36

mix-37

mix-40

mix-43

1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.41

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

Measured Density, g/ml

Pre

dic

ted D

ensity,

g/m

l

SiO4-3

SiO4-4

Conductivity

Num. LVs: 4

RMSEC: 0.019RMSECV: 0.021

Density

Num. LVs: 3

RMSEC: 17.4132 RMSECV: 22.9085

Raman-to-Concentration Model Design Challenges

Raman-to-Concentration Model Design Challenges

• Long-Term Model

– Months-Years of Service

• Unknown Field Interferences

– Updates probably necessary

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Regression Model OptionsRegression 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

Classical Least Squares ModelClassical Least Squares Model

As concentration increases, there is a

corresponding increase in intensity as

a linear response (i.e. Beer’s law).

The typical CLS model uses a simple

response profile (spectrum) to predict

concentration of the individual species.0 200 400 600 800 1000

0 20 40 60 80 100

Species Concentration

Frequency

Pure

com

ponent

Spectr

um

pro

jection

Ram

an Inte

nsity

si

ci

T= +X CS E

C

e.g

Time

ST

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Standard CLS ModelCalibration

Standard CLS ModelCalibration

T

ions cal

†

cal

T=

= C

CS

XS

X Determine pure component spectra

(ST) from calibration samples by

ordinary least-squares regression.

leastsquares

leastsquares

least

squares

Ccal pure component spectramixtures

Standard CLS ModelPrediction

Standard CLS ModelPrediction

c1

c2

c3

c4

c5

ck

Standard “linear” CLS

Each spectrum maps to

one concentration.

… … ( )T †

ionsC = SX

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Extended Mixture ModelPrediction

Extended Mixture ModelPrediction

c1

c2

c3

ck

Add additional background

or component spectra as

needed… …cinter,2

cinter,1

Martens & Naes

( )T †

ionsC = SX

([ ])T T †

ions inter= SC SX

Stepwise RegressionPrediction

Stepwise RegressionPrediction

Use ONLY those

components which improve

the spectral residuals by a

statistically significant

amount

c1

0

c3

0

0

ck

… …

X

X

X

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Non-Linear CLS ModelNon-Linear CLS Model

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)

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.

0 200 400 600 800 1000

0 20 40 60 80 100

Total Ion Concentration

Frequency

Indiv

idual S

pecie

s

Concentr

ation

Ram

an Inte

nsity

ci,1+ci,2

ci,1

ci,2

si,1

si,2

Non-Linear CLS ModelsCalibration

Non-Linear CLS ModelsCalibration

c k

T TC MS C S X= =

' ( )T

cal

T †

ionsC SM XC = =

, ca

†

k

T

ion lcalsS XC=

,,k cal c calC MC =

Solve for Sions via ALS

(a) single factors = hard equality constraint

(b) multiple factors = soft closure constraint to species concentration

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 = [ 1 1 0 0

0 0 1 0

0 0 0 1]

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Non-Linear CLS ModelPrediction

Non-Linear CLS ModelPrediction

c1

c2

c3

c4

ck

“Non-linear” CLS

More than one pure

component spectrum

can map to an

underlying species

concentration.……

c'1,1

c'1,2

c'1,3

c'2

c'3

c'4

c'k…

0 2 4 6 8-10

-5

0

5

10

NaAl(OH)4

Na

Al(O

H)4

pre

d

0 5 10 150

5

10

Na2CO3

Na

2C

O3

p

red

0 10 20 300

10

20

30

NaNO2

Na

NO

2 p

red

0 10 20 300

10

20

30

NaNO3

Na

NO

3 p

red

0 5 10 15 200

5

10

15

Na2SO4

Na

2S

O4

p

red

0 2 4 60

2

4

6

Na2CrO4

Na

2C

rO4

p

red

0 5 10

0

5

10

Na3PO4

Na

3P

O4

p

red

0 10 20

0

10

20

Na4SiO4

Na

4S

iO4

p

red

Measured Concentration

Estim

ate

d C

on

ce

ntr

atio

n

Classical Least Squares (CLS)

Al(OH)4 in solutionwith NO3

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Example: Multiple NO3 ComponentsExample: Multiple NO3 Components

1010 1030 1050 1070 1090

Raman Shift (cm-1)

Normalized spectra at different NO3 concentrations and w/Al(OH)4

increasingionic strength

0 2 4 6 8

0

2

4

6

8

NaAl(OH)4

Na

Al(O

H)4

pre

d

0 5 10 150

5

10

Na2CO3

Na

2C

O3

p

red

0 10 20 300

10

20

30

NaNO2

Na

NO

2 p

red

0 10 20 300

10

20

30

NaNO3

Na

NO

3 p

red

0 5 10 15 200

5

10

15

20

Na2SO4

Na

2S

O4

p

red

0 2 4 60

2

4

6

Na2CrO4

Na

2C

rO4

p

red

0 5 10

0

5

10

15

Na3PO4

Na

3P

O4

p

red

0 10 20

0

10

20

Na4SiO4

Na

4S

iO4

p

red


Estim

ate

d C

on

ce

ntr

atio

n

Non-Linear Classical Least Squares (NL-CLS)

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Example: Multiple NO3 ComponentsExample: Multiple NO3 Components

Raman Shift (cm-1)

1010 1030 1050 1070 10901010 1030 1050 1070 1090

Raman Shift (cm-1)

Measured Data Recovered Spectra

Normalization of OH2nd DerivativeALS calibration

normalized

increasingionic strength

0 2 4 6 8

0

2

4

6

8

NaAl(OH)4

Na

Al(O

H)4

pre

d

0 5 10 150

5

10

Na2CO3

Na

2C

O3

p

red

0 10 20 300

10

20

30

NaNO2

Na

NO

2 p

red

0 10 20 300

10

20

30

NaNO3

Na

NO

3 p

red

0 5 10 15 200

5

10

15

20

Na2SO4

Na

2S

O4

p

red

0 2 4 60

2

4

6

Na2CrO4

Na

2C

rO4

p

red

0 5 10

0

5

10

15

Na3PO4

Na

3P

O4

p

red

0 10 20

0

10

20

Na4SiO4

Na

4S

iO4

p

red


Estim

ate

d C

on

ce

ntr

atio

n

Non-Linear Classical Least Squares (NL-CLS)

Interference of baseline/background

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0 2 4 6 8

0

2

4

6

8

NaAl(OH)4

Na

Al(O

H)4

pre

d

0 5 10 150

5

10

Na2CO3

Na

2C

O3

p

red

0 10 20 300

10

20

30

NaNO2

Na

NO

2 p

red

0 10 20 300

10

20

30

NaNO3

Na

NO

3 p

red

0 5 10 15 200

5

10

15

20

Na2SO4

Na

2S

O4

p

red

0 2 4 60

2

4

6

Na2CrO4N

a2

CrO

4 p

red

0 5 10

0

5

10

Na3PO4

Na

3P

O4

p

red

0 10 20

0

10

20

Na4SiO4

Na

4S

iO4

p

red


Estim

ate

d C

on

ce

ntr

atio

n

Non-Linear Extended Least Squares (NL-ELS)

0 2 4 6 80

2

4

6

NaAl(OH)4

Na

Al(O

H)4

pre

d

0 5 10 150

5

10

Na2CO3

Na

2C

O3

p

red

0 10 20 300

10

20

30

NaNO2

Na

NO

2 p

red

0 10 20 300

10

20

30

NaNO3

Na

NO

3 p

red

0 5 10 15 200

5

10

15

Na2SO4

Na

2S

O4

p

red

0 2 4 60

2

4

6

Na2CrO4

Na

2C

rO4

p

red

0 5 100

5

10

Na3PO4

Na

3P

O4

p

red

0 10 200

10

20

Na4SiO4

Na

4S

iO4

p

red

Non-Linear Non-Negative Extended Least Squares (NL-NNELS)


Estim

ate

d C

on

ce

ntr

atio

n

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NO3 NO2 SO4 CO3 CrO4 Al(OH) PO4 SiO4

0.18 0.19 0.36 0.11 0.04 0.43 0.53 0.78 nn

0.19 0.19 0.36 0.09 0.04 0.42 0.48 0.74 sr,nn

0.18 0.19 0.27 0.13 0.04 0.73 0.56 1.25

0.18 0.18 0.36 0.12 0.04 0.61 0.49 1.12 sr

(non-negative basis)


0.26 0.18 0.35 0.10 0.04 0.38 0.48 0.99 nn

0.26 0.18 0.35 0.09 0.04 0.39 0.45 1.04 sr,nn

0.24 0.23 0.34 0.12 0.04 0.43 0.51 0.92

0.24 0.18 0.39 0.10 0.04 0.17 0.44 0.99 sr

Calibration ResultsCalibration Results

Pure samples onlyOH Normalization2nd DerivativeALS calibration for non-linear components

Extended and Non-Linear Models Useful?Ordinary Least Squares

Extended and Non-Linear Models Useful?Ordinary Least Squares

Standard Error of Calibration (SEC)


: 0.60 0.59 0.36 0.24 0.12 3.13 2.24 2.77

B : 0.59 0.61 0.36 0.24 0.12 3.15 1.38 1.70

3: 0.57 0.54 0.31 0.21 0.11 0.61 1.50 2.33

B3: 0.57 0.54 0.31 0.21 0.11 0.67 0.67 1.68

Standard Error of Prediction (SEP)


: 0.53 0.20 0.06 0.21 0.10 2.06 2.26 2.67

B : 0.51 0.21 0.06 0.21 0.10 2.09 1.26 1.49

3: 0.48 0.19 0.12 0.17 0.09 0.55 1.56 2.03

B3: 0.46 0.18 0.13 0.17 0.09 0.58 0.26 1.55

B: Including 2 Background Factors (from NaOH)

3: Non-linear (3 components) for NO3

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Extended and Non-Linear Models Useful?Non-negative Least Squares

Extended and Non-Linear Models Useful?Non-negative Least Squares


: 0.56 0.66 0.36 0.49 0.13 2.16 4.83 2.03

BG : 0.60 0.74 0.36 0.45 0.12 1.95 1.65 2.42

NL: 0.56 0.53 0.35 0.20 0.10 0.28 1.49 2.10

BG,NL: 0.56 0.52 0.35 0.20 0.11 0.27 0.61 0.97


: 0.41 0.62 0.06 0.42 0.11 0.55 4.73 1.27

BG : 0.38 1.11 0.11 0.39 0.10 0.62 0.87 0.45

NL: 0.43 0.20 0.07 0.17 0.09 0.31 1.54 1.67

BG,NL: 0.40 0.19 0.12 0.18 0.10 0.20 0.31 0.38

BG: Including 2 Background Factors (from NaOH)

NL: Non-linear (3 components) for NO3

Standard Error of Calibration

Standard Error of Prediction


: 0.57 0.54 0.31 0.21 0.11 0.67 0.67 1.68

SR : 0.56 0.52 0.35 0.20 0.11 0.80 0.61 1.61

NN: 0.56 0.52 0.35 0.20 0.11 0.27 0.61 0.97

SR,NN: 0.56 0.51 0.35 0.19 0.11 0.26 0.53 0.79

SR: Stepwise regression

NN: Non-Negative least squares


Standard Error of PredictionNO3 NO2 SO4 CO3 CrO4 Al(OH) PO4 SiO4

: 0.46 0.18 0.13 0.17 0.09 0.58 0.26 1.55

SR : 0.45 0.17 0.13 0.17 0.09 0.55 0.55 1.32

NN: 0.40 0.19 0.12 0.18 0.10 0.20 0.31 0.38

SR,NN: 0.40 0.20 0.12 0.18 0.10 0.22 0.62 0.45

Stepwise and Non-Negative LS Useful?Background + Non-linear NO3

Stepwise and Non-Negative LS Useful?Background + Non-linear NO3

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0.53 0.20 0.06 0.21 0.10 2.06 2.26 2.67

0.40 0.19 0.12 0.18 0.10 0.20 0.31 0.38

Standard Error of Prediction

Best/Worst ResultsBest/Worst Results


0.60 0.59 0.36 0.24 0.12 3.13 2.24 2.77

0.56 0.51 0.35 0.19 0.11 0.26 0.53 0.79


OH Normalization1st derivativeNon-linear CLS modelExtended Mixture modelStepwise regressionNon-negative Least Squares

Conclusions and FutureConclusions and Future

• CLS models can be adapted to handle non-

linear single-component responses

• Updating of CLS models straightforward

• Evidence for fusion of conductivity and

Raman for correction

• On-line statistics for evaluation

raman analysis of concentrated salt solutions using robust ... analysis of concentrated salt...

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