Volume 55, Number 11, 2001 APPLIED SPECTROSCOPY 15530003-7028 / 01 / 5511-1553$2.00 / 0q 2001 Society for Applied Spectroscopy

Calibration Transfer of Chemometric Models Based onProcess Nuclear Magnetic Resonance Spectroscopy

JASON GISLASON, HING CHAN,* and MAZIAR SARDASHTI†Phillips Petroleum Company, 150 PL, PRC, Bartlesville, Oklahoma 74004

This paper establishes the protocol for calibration transfer of par-tial least-squares (PLS) regression models between process nuclearmagnetic resonance (NMR) spectrometers. The ability to transfercalibration models between instruments allows the addition of newinstruments and the upgrade of old instruments with little � nancialor manpower investment. It will also allow development of calibra-tion for an on-line system on a lab system, which will require lessmanpower and no down time for the on-line measurements. Thiscapability will result in great cost savings for a production facilitywhere even a minor interruption in the plant operations would re-sult in great loss of production and loss of income.

Index Headings: Calibration transfer; Nuclear magnetic resonance;Chemometrics; Partial least-squares.

INTRODUCTION

Process nuclear magnetic resonance (NMR) spectros-copy has been used successfully to measure chemicalconcentrations of monomers in copolymers,1 hydrogencontent in fuels,2 and physical properties of polymerssuch as density and high load melt index.3 For most ofthese cases, extraction of chemical information from theNMR free induction decay (FID) data is done throughthe application of multivariate analysis (i.e., chemome-trics).4 In these applications, a regression method such asprincipal components regression (PCR) or partial least-squares (PLS) regression5–8 is applied to a set of FIDsfrom known samples to develop a calibration model, con-sisting of a regression vector and numerous test statistics.The FID from an unknown sample is then multiplied bythe regression vector to yield a quantitative value for thephysical or chemical property of interest.

A signi� cant limitation of chemometrics when appliedto all forms of spectroscopy is the inability of a calibra-tion model to be directly transferred between instruments.In the case of NMR spectroscopy, this limitation iscaused by small differences in instrumental response, re-sulting in differences in the FIDs between two instru-ments on identical samples. These differences in FIDscan cause a signi� cant discrepancy in the reported resultsbetween the two instruments for the property of interest.Similarly, a calibration model built by using chemome-trics is absolutely valid only at the time it is constructed.If there are any changes in the instrument’s operatingconditions or hardware from maintenance or normal wearand tear on the spectrometer, the calibration model canbecome unreliable. Rebuilding a large calibration modelto compensate for changes in the instrument over time or

Received 2 November 2000; accepted 25 June 2001.* Present address: Chevron-Phillips Chemical Company, Pasadena, TX

77504.† Author to whom correspondence should be sent.

for the purchase of a new instrument can be costly andtime consuming.

There are three basic approaches to model update orcalibration transfer. The � rst approach is the transfer ofthe actual calibration model from the original instrumentto the new instrument by adding FIDs from the new in-strument, with their corresponding reference propertymeasurements, to the original training set and recalculat-ing the regression vector. This approach is known as hy-brid calibration (HC).9 The second approach involves themapping of the response of one instrument onto the re-sponse of the new instrument via a � nite impulse re-sponse (FIR) � lter.10 The third and most successful ap-proach to calibration transfer is the direct transfer of theFIDs from the new instrument to the original instrument.This third type of transfer is usually accomplishedthrough direct standardization (DS) or piece-wise directstandardization (PDS) with additive background correc-tion.11–14

In this research, calibration models were developed ona set of FIDs with the use of PLS. The FIDs were thensystematically altered to simulate variations between twoinstruments. We then applied the hybrid calibration, di-rect standardization, and piece-wise direct standardizationmethods to transfer the models to the ‘‘new’’ instrument.To our knowledge, this is the � rst report on the abilityof any of these methods to effect calibration transfer withprocess NMR spectroscopy.

THEORY

Direct Standardization with Additive BackgroundCorrection. Direct standardization is accomplished byrelating a set of FIDs generated on the new instrumentto a set of FIDs generated on the original instrumentwhere each set of FIDs is generated from exactly thesame set of samples. This correlation is given by the fol-lowing equation:‡

S1 5 S2Fb 1 T1bs (1)

where S1 and S2 are the n 3 w matrices of variables fromthe FIDs. Fb is the w 3 w transformation matrix (TM),and is the transpose of the background correction vec-Tbs

tor (BCV).An n 3 n centering matrix is de� ned by Cn 5 In 2

‡ The following discussion of direct standardization uses standard linearalgebra nomenclature. Any bold face type represents a matrix or avector and any normal type represents a scalar. The superscript ‘‘T’’is used to represent the vector or matrix transpose. I and 1 are theidentity matrix and the ones vector, respectively. Any character witha bar over the top indicates the mean of that variable. Similarly, asuperscript ‘‘1’’ indicates the pseudo-inverse of the matrix.

1554 Volume 55, Number 11, 2001

(1/n)11T. The centering matrix has the property that CnX5 X 2 x̄1. Multiplying both sides of Eq. 1 by Cn gives

CnS1 5 CnS2Fb 1 TC 1bn s (2)

Because has identical rows, 5 0. Therefore,T T1b C 1bs n s

S̄1 5 S̄2Fb (3)

where S̄ i51,2 is the S i51,2 matrix with the mean of eachcolumn subtracted from each component in the respectivecolumn (i.e., the matrix is mean centered).

By least-squares,

Fb 5 S̄11S̄2 (4)

This equation can be solved by using a singular valuedecomposition (SVD),15,16 where any real matrix X canbe decomposed into three matrices U , S , and V to give

X 5 U S VT (5)

where U and V are orthonormal and S is a matrix of thesingular values, which are equal to the square roots ofthe eigenvalues of XTX . The pseudo-inverse of X is cal-culated from the SVD as

X1 5 V S 21UT (6)

The primary advantage in solving the least-squares prob-lem in this manner is one of noise reduction. It frequentlyhappens that a number of the singular values in S aresmall and represent noise in the FID. Therefore, thesesingular values can be set equal to zero, which reducesthe random error in X .

The additive background correction vector can be cal-culated by multiplying Eq. 1 by (1/n)1T,

1 1 1T T T T1 S 5 1 S F 1 1 b (7)1 2 b sn n n

Therefore,

s 5 s Fb 1 bT T T1m 2m s (8)

where s and s are vectors of column means of ma-T T1m 2m

trices S1 and S2, respectively. Rearranging Eq. 8 gives

bs 5 s1m 2 F s2mTb (9)

Piece-wise Direct Standardization with AdditiveBackground Correction. Piece-wise direct standardiza-tion is a modi� cation of DS, which uses only the localvariation in the FID between the two instruments to trans-fer the FIDs from the new instrument to the original in-strument. PDS is simply the application of DS to a localregion de� ned by a calibration window. In DS, the FIDtransfer was optimized with regard to the number of sam-ples used to develop the TM and BCV. This optimizationis also performed in PDS. However, the width of thewindow used for PDS affects the FID transfer by chang-ing the relative amount of global and local variation be-tween the instruments that is incorporated into the esti-mated FIDs. Therefore, PDS is optimized by adjustingthe number of samples and the window width, k, used tocreate the TM and BCV. The points in the S matrix be-tween i 2 k /2 and i 1 k /2 are put into a matrix as follows:

x i 5 [s2,i2 (k/2), s2,i2 (k /2)11, . . . , s2 ,i1 (k/2)21, s2 ,i1 (k/2)] (10)

where s2,i is the column vector of FID magnitudes at point

i in the FID for the new instrument. Then a multivariateregression in the form of

r1 ,i 5 X ib i (11)

is performed by using PLS regression by a singular valuedecomposition. This method yields a transformation ma-trix of

F 5 diag(b , b , . . . , b , . . . , b )T T T T1 2 i p (12)

where p is the number of points in the FID included inthe transfer. The effect of building the F matrix this wayis to zero the majority of the off-diagonal terms and cre-ate an F matrix that is banded.

Hybrid Calibration. This method of calibration trans-fer is simply the construction of a new PLS model withboth the calibration set from the original instrument andthe calibration set from the new instrument. However, ithas been previously shown for NIR calibration transfer13

that the full set of samples from the new instrument doesnot need to be included in the combined model to get anaccurate transfer of the model to the new instrument.Therefore, 62 PLS models were created by sequentiallyadding FIDs from the new instrument calibration set tothe calibration set of the original instrument. The 62 PLSmodels each had 62 FIDs from the original instrumentand between 1 and 62 FIDs from the new instrument.The FIDs from the new instrument were added into eachof the combined models in the order from highest lever-age to lowest leverage. Therefore, the � rst combinedmodel’s calibration set contained 63 FIDs, where 62 werefrom the original instrument and one (the one of highestleverage) was from the new instrument. Similarly, theseventh combined model contained 62 FIDs from theoriginal model and the 7 FIDs with the highest leveragesfrom the new instrument. Adding the samples to the com-bined models on the basis of highest leverage adds thesamples with the greatest in� uence on the model � rst.Therefore, the most improvement in the model should beseen early in the calibration transfer.

Sample Selection. Appropriate selection of the set ofsamples to be used for calibration transfer is very im-portant. The samples should be selected so that the trans-fer occurs with the fewest number of samples. One com-mon method used for sample selection is to select thesamples in order of highest to lowest leverage. The sam-ples with highest leverage should have the greatest effecton the calibration transfer. Alternatively, the samplescould be selected by maximizing the Euclidean distancein scores space between each sample. This approachwould ensure the most representative set of transfer sam-ples for the model. This method is the Kennard and Stone(KS) algorithm.17 Finally, a combination of the two pub-lished methods could be used. In this method, the scoresof each sample are � rst multiplied by the leverage for thesample to give leverage-weighted scores. Then the sam-ples are selected to maximize the Euclidean distance inscores space for subsequently selected samples. Each ofthese methods of sample selection was tested below. Theresults from the best selection method are given.

EXPERIMENT

Process Nuclear Magnetic Resonance Spectroscopy.An Oxford/Auburn MagStation laboratory NMR system

APPLIED SPECTROSCOPY 1555

FIG. 1. RMSECV and RMSEC for the model developed on VORIG, theoriginal instrument.

FIG. 2. RMSECV and RMSEC for the model developed on the VPRD

instrument (5 ms shift).

operating at 20 MHz for H-1 frequency was used. Theinstrument uses GRAMS 3218 software from Galactic,Inc., running on a Pentium-based IBM PC as the mainoperating software, and the Auburn Counterpoint19 pro-gram for data collection and processing. Fluff samples ofpolymer were loaded into an autosampler that placedthem sequentially in the NMR instrument. After an initial2 min preheating in the instrument at 72 8C, a tuningsequence is applied to adjust the magnetic � eld, and thena single pulse sequence is used to obtain the FID curvefor each sample. The FID curves are stored and usedeither in producing a PLS model or in measuring thephysical or chemical property in question. The total ex-periment time for each sample is approximately 6 min.

Simulated FIDs. A set of simulated data was gener-ated by � tting FIDs of 77 polymer samples to two ex-ponential functions and a Weibull function using theNelder–Mead simplex method to minimize the sum ofsquares maximum likelihood estimator.16

FID 5 Ae Bx 1 CeDx 1 EE21 2 (x /F )(E /F )(x /F ) e (13)

where the � rst two terms are the exponential functionsand the third term is the Weibull function. No physicalmeaning is implied by the values of the coef� cients orthe functional forms of the terms in Eq. 13. This func-tional form was simply the easiest form to use for thisstudy. This was done to permit selective alteration of theFID parameters to simulate instrumental response varia-tions due to probe ring-down, changes in pulse length,differences in magnetic susceptibility, temperature � uc-tuations, and sample packing in the probe. Thus, each ofthese instrumental variations could be applied to the dataeither singularly or in combination with others to test theeffect of the variation(s) on model transfer.

A representative FID was � rst � tted manually to givethe initial guess for the simplex routine. Then the simplexroutine was used to minimize the sum of squares betweenthe � tted FID and the real FID. The simplex routine wasstopped when the sum of squares reached a value of 0.05.After all the FIDs were � t by using the simplex method,the FIDs were normalized by dividing each FID point-

by-point by the amplitude of the � rst point in that FID.The y-block was generated by multiplying the knownHLMI (high load melt index) values for each sample bya factor that gave a new y-block range from 0 to 100.This data set forms the basis for all of the transfer testsdescribed below and can be viewed as originating froma ‘‘virtual’’ instrument, designated VORIG.

Transfer Tests. Once the simulated data set was cre-ated, it was selectively altered to simulate changes in thedata that might be induced by physical or electronic dif-ferences between instruments. Thus, each altered data setcan be viewed as originating from a separate virtual in-strument that is different from the basis instrument, VORIG.Each of the model transfer methods can then be testedon its ability to compensate for selected instrumental var-iations by simply transferring the basis model from VORIG

to each of the new virtual instruments. In this report, datafrom � ve additional virtual instruments were created totest the effects of longer probe ring-down, shorter pulse-width, and temperature � uctuations on model transfer.These tests are described below.

Probe Ring-Down. To simulate an instrument with alonger probe ring-down time, we added a 5 ms shift inthe time of acquisition to the FIDs. This was done byremoving the � rst 50 points of each 4000 point FID andthen adding 50 points to the end of each FID, whichwould represent further decay of the part of the samplewith a long T2. The modi� ed FIDs were then assigned toa new virtual instrument to which the calibration modelwas being transferred. A PLS model was developed, withthe use of the NIPLS algorithm, for both the originalinstrument, VORIG, and the new instrument, VPRD, whichhad a longer ring-down. The maximum number of latentvariables for each model was selected by choosing thenumber of latent variables to coincide with the � rst dra-matic break in the prediction residual error sum ofsquares (PRESS) plot. The VORIG model and the VPRD

model were selected to have four and three latent vari-ables, respectively (Figs. 1 and 2). A validation set wasselected for each model by removing every � fth samplefrom the original data sets of 77 FIDs. This approach

1556 Volume 55, Number 11, 2001

FIG. 3. Hybrid calibration model RMSEP for the combined modelswith added samples from the VPRD instrument (5 ms shift).

Table I. Results from the hybrid calibration method transfer.

VPRD : probering-down

VSPW,1: shorter pulsewidth (part 1)

VSPW,2: shorter pulsewidth (part 2)

VTEMP,1:temperatureoffset (part 1)

VTEMP,2: temperatureoffset (part 2)

Original model RMSEP 8.59 8.59 8.59 8.59 8.59New model RMSEP 8.60 8.77 8.73 8.52 8.73Combined-calibration

model RMSEP9.16 9.42 9.63 9.42 16.81

Percent difference 6.6% 9.7% 12.1% 9.7% 92.6%Number of samples needed

for transfera

14 27 N/Ab 56 N/Ab

a The transfer was considered complete after the percent difference between the original model and the combined-calibration model was below10%.

b N/A indicates that this level of calibration transfer was never achieved.

created a training set of 62 FIDs and a validation set of15 FIDs for each instrument. The training set and vali-dation sets were from exactly the same samples for bothmodels. The two models gave RMSEP values of 8.59 and8.60 for the VORIG instrument and the VPRD instrument,respectively.

Shorter Pulse Width. The effects of a shorter pulsewidth were simulated by changing the FIDs in two dif-ferent ways. In the � rst test, the amplitudes of the � rstexponential functions in the � tted FIDs were increasedby 20%. This increase gives signi� cantly larger ampli-tude at the beginning of the FID while keeping the restof the FID relatively unchanged. After the amplitudechange, the FIDs were normalized so that the initial am-plitude was set equal to 1. The overall effect of increasingthe initial amplitude of the FID is then to decrease theamplitude of the middle and tail end of the normalizedFID. This data set was then assigned to virtual instrumentVSPW,1. In the second test, a change in the pulse lengthwas simulated by increasing the initial amplitude by 20%and the amplitude of the Weibull function by 10%. Thisdata set was assigned to virtual instrument VSPW,2.

Temperature Offset. The FID shape can also bechanged by differences in the temperature or susceptibil-ity of the sample. Changing either of these physical pa-rameters has the effect of altering the spin–spin relaxationtime, T2. For the � rst temperature offset test, the FIDswere modi� ed by decreasing the T2 of the fast decaying

exponential function. Decreasing the T2 is equivalent todecreasing the temperature of the system. The exponentof the fast decaying exponential term was increased by5%. A model was built on the new virtual instrument,VTEM P,1, with the use of just the new instrument calibrationset. The root mean square error of prediction (RMSEP)value for this model was 8.52 at four latent variables. Inthe second temperature offset test, the FIDs were con-structed by increasing the exponent of the slow decayingexponential by 10%, simulating a temperature increase.A model was built with data from this new virtual in-strument, VTEM P,2. The RMSEP for this model was 8.73,which is only slightly higher than the 8.59 RMSEP ofthe calibration on the original VORIG instrument.

RESULTS AND DISCUSSION

Method of Hybrid Calibration. The PLS model fromthe instrument, VORIG, was transferred to instrument VPRD,which had a longer probe ring-down, through the methodof hybrid calibration. Each of the combined models wasselected to have four latent variables because this numberof latent variables was coincident with the break on thePRESS plot, as shown above. A plot of the number ofVPRD instrument samples added vs. the RMSEP§ for thevalidation set developed on the VPRD instrument is shownin Fig. 3. Similarly to what was previously observed withNIR calibration transfer, the combined model improvesover the original model with addition of FIDs from theVPRD instrument.13 The majority of the improvement seenin the calibration transfer is observed in the � rst 10 sam-ples. By the tenth sample, the combined calibration mod-el RMSEP was within 11% of the VORIG instrument modelRMSEP. The RMSEP values of these samples and theRMSEP of the VPRD instrument validation set predictedby the original model are shown in Table I. The RMSEPvalue for the addition of a single sample from the newVPRD instrument to the original model decreases by107.68, which is the largest decrease for the addition of

§ A test statistic used for the determination of the accuracy of a partialleast-squares model is the root mean square error of prediction. TheRMSEP is given by the following equation:

N

2(x 2 y )O i ii51ÎRMSEP 5

N

where N is the total number of FIDs and x i and y i are the extrusionplastometer and NMR HLMI values for the ith sample, respectively.The RMSEP value is interpreted as the expected error (1s) in NMRmeasurement of future samples.

APPLIED SPECTROSCOPY 1557

FIG. 4. Hybrid calibration model RMSEP for the combined modelswith added samples from the V SPW,1 instrument (20% initial amplitudeincrease).

FIG. 5. Hybrid calibration model RMSEP for the combined modelswith added samples from the V SPW,2 instrument (20% initial amplitudeincrease and a 10% Weibull amplitude increase).

any sample. This large decrease in the RMSEP is due toPLS using the least-squares maximum likelihood esti-mator, which gives grossly high weighting to sampleswith large deviations from the � tted line and gives higherweighting to samples close to the mean. Since the FIDthat was added from the VPRD instrument is by far themost different of all the VORIG FIDs, it is given the highestweighting.

In addition to shifts in the delay time between the pulseand acquisition, different instruments could also have dif-ferent pulse lengths and coil con� gurations. To simulatethese differences and determine how they affect calibra-tion transfer, we modi� ed the original VORIG data as de-scribed above in the � rst part of the shorter pulse widthtest to give virtual instrument VSPW,1. The model createdon the original instrument gave an RMSEP value of33.66 for the validation set from the new VSPW,1 instru-ment. Therefore, the calibration curve from the VORIG in-strument could not be used on the VSPW,1 instrument di-rectly because the error in the measurement would beapproximately four times the error of the original cali-bration on VORIG. It is interesting to note that the errorfor using the original VORIG calibration on the VPRD (5 mspulse delay) instrument is four times greater than that forthe VSPW,1 instrument (20% increase in the initial FID am-plitude). This observation indicates that changes in thedelay time of the instrument have a much greater effecton calibration transfer than changes in the initial ampli-tude of the FID. As was the case in the previous example,a PLS model could be created by using all 62 samplesfrom the VSPW,1 instrument, but this approach would beextremely time consuming and in some instances impos-sible. The PLS model created from the VSPW,1 instrumentFIDs gives an RMSEP value of 8.77.

A plot of the change in RMSEP with respect to thenumber of samples added to the model from the VSPW,1

instrument is shown in Fig. 4. Unlike the calibrationtransfer for instrument VPRD, the calibration transfer forVSPW,1 occurs immediately after samples are added intothe combined calibration model. After the � rst sample isadded into the combined calibration model, the RMSEP

drops by a factor of 2.4. This is not as dramatic a changeas seen for the VPRD longer probe ring-down test, but thecalibration transfer converges faster for the VSPW,1 modelthan for the VPRD model. The continuous decrease inRMSEP as samples are added is indicative of how PLSusually behaves under hybrid calibration model transfer.Normally the PLS model continues to improve as moresamples from the new instrument are put into the model.It would be foolish to repeat the measurement of all 62samples on the new instrument and then add them intothe original calibration curve. The combined model withall 124 samples gives an RMSEP of 8.97, which ap-proaches the RMSEP of 8.77 for the model built solelyon the VSPW,1 instrument.

The second test for shorter pulse width was simulatedas described above. When the new VSPW,2 instrument val-idation set with a 20% increase in initial amplitude anda 10% increase in the Weibull function was predicted onthe original VORIG calibration model, the RMSEP valuewas 13.17, a factor of 1.5 higher than the RMSEP forthe original instrument. A plot of the RMSEP vs. thenumber of VSPW,2 instrument samples added to the cali-bration model is shown in Fig. 5. The RMSEP for theaddition of a single VSPW,2 instrument sample into the cal-ibration model gives a decrease of only a factor of 1.1 inthe RMSEP from 13.17 to 12.08. This transfer methodtook 30 added samples from the VSPW,2 instrument beforethe majority of the change in the RMSEP was captured.

Two tests were performed to simulate differences intemperature and susceptibility. The simulated FIDs weremodi� ed as described in the � rst part of the temperatureoffset test and assigned to virtual instrument VTEM P,1. Theoriginal VORIG instrument calibration model was used topredict the validation set from the VTEM P,1 instrument. TheRMSEP of this prediction was 13.57. This RMSEP issigni� cantly lower than those seen for either the VPRD

(probe ring-down) or the VSPW,1 and VSPW,2 (short pulsewidth) tests. A plot of the variation of the RMSEP for acombined instrument model vs. the number of samplesadded to the combined calibration set is shown in Fig. 6.

When the FIDs were modi� ed as described in the sec-

1558 Volume 55, Number 11, 2001

FIG. 6. Hybrid calibration model RMSEP for the combined modelswith added samples from the VTEMP,1 instrument (5% increase in theexponent for the fast decaying exponential function).

FIG. 7. Hybrid calibration model RMSEP for the combined modelswith added samples from the VTEMP,2 instrument (10% increase in theexponent for the slow decaying exponential function).

FIG. 8. RMSEP for direct standardization transferred VPRD (5 ms shift)FIDs predicted by the original VORIG calibration model.

ond part of the temperature offset test, the RMSEP forthe validation set of the new VTEMP,2 instrument predictedby the original calibration model was 37.86. This resultindicates that a change in the exponent of the slow de-caying exponential (i.e., VTEMP,2) has a much greater effecton the predictability of a calibration model than the samechange in the fast decaying exponential (i.e., VTEMP,1). Thecalibration transfer had a very slow convergence with achange in the slow decaying exponential exponent, andthe combined calibration model never approached theRMSEP values of either the new VTEMP,2 instrument orthe original VORIG instrument models (Fig. 7).

In summary, the hybrid calibration method requiredtoo many samples for calibration transfer and rarely suc-cessfully transferred the calibration. The original model,new instrument model, and best combined-calibrationmodel RMSEP values are shown in Table I. The hybridcalibration model transfer method required at least 14samples to transfer the model to the virtual instrument.In this case, a successful transfer is considered to occurwhen the RMSEP of the combined-calibration model iswithin 10% of the original VORIG model RMSEP. How-ever, the method was not able to compensate for changesin the amplitude of the � rst exponential and Weibull(model VSPW,2) or changes in the exponent of the secondexponential (model VTEMP,2) effectively. For hybrid cali-bration, the method of FID selection did not appear tomake any difference in the rate of convergence of thecalibrated model.

Direct Standardization. Direct standardization withadditive background correction has been shown to ac-curately transfer NIR spectra from a new instrument toan original instrument.15,16 These transferred spectra wereused successfully in the prediction of chemical concen-trations present in new samples run on the new instru-ment using the original NIR calibration model. Therefore,DS was explored as a possible calibration transfer tech-nique for process NMR models. Because the DS calcu-lations were prohibitively long, the 4000 point FIDs weredecreased in size to 400 points by taking every tenthpoint starting with 1 and ending with 3991. This size

decrease increased the RMSEP of the original model byless than 2% from 8.59 to 8.73.

The VPRD (probe ring-down) test was performed bytransferring a validation set that included a 5 ms delay inthe acquisition start time to the original VORIG instrumentand predicted with the use of the original calibrationmodel. The DS was performed sequentially with increas-ing numbers of FIDs between 2 and 62. The FIDs usedto develop the transformation matrix and the backgroundcorrection vector were FIDs from the VORIG instrument’scalibration set and were used in the order described inthe section on transfer FID selection. The DS methodconverged rapidly to a minimum in the RMSEP with re-spect to the number of samples used to generate the TMand the BCV (Fig. 8). This plot of number of transfersamples vs. RSMEP for the VPRD instrument is represen-tative of all the DS transfer plots. The optimum numberof transfer samples for this DS calculation is 9, and themethod of choice for selecting the order of the samplesis the leverage method. The RMSEP value at this point

APPLIED SPECTROSCOPY 1559

Table II. Results from the direct standardization transfer.

VPRD : probering-down

VSPW,1: shorterpulse width (part 1)

VSPW,2: shorterpulse width (part 2)

VTEMP,1 : temperatureoffset (part 1)

VTEMP,2 : temperatureoffset (part 2)

Original model RMSEP 8.73 8.73 8.73 8.73 8.73New model RMSEP 8.60 8.77 8.73 8.52 8.73DS transfer 8.41 8.26 8.24 7.76 8.38Number of samples needed

for transfer a9 8 8 4 8

a The transfer was considered complete when the minimum in the RMSEP plot was observed.

FIG. 9. PDS on VPRD data (5 ms shift in initial acquisition time). (Min-imum at two samples and a window width of 59.)

is 8.41 (Table II). An intermediate minimum in theRMSEP surface occurs with four transfer samples. TheRMSEP at this point is 9.56. This is a trend that occurswith all of the DS transfers to follow. The transfer canbe performed with four samples, but the optimal transfer(i.e., minimum RMSEP) usually takes more samples.

Decreased pulse widths were simulated as described inthe shorter pulse width test section above. The VSPW,1 in-strument data set with a 20% increase in initial amplitudewas used in a DS transfer of the FIDs from the VSPW,1

instrument to the VORIG instrument. The optimum FIDtransfer occurred with eight transfer FIDs and the KS FIDselection method. The RMSEP value was 8.26 for thetransferred VSPW,1 instrument validation set predicted onthe original calibration model. The VSPW,2 shorter pulsewidth test resulted in an RMSEP of the transferred vali-dation set for the original calibration model of 8.24.

Changes in temperature were simulated as described inthe temperature offset test. When the FIDs were alteredas described for instrument VTEMP,1, optimal transfer oc-curred with four transfer FIDs and the KS FID selectionroutine. The RMSEP for the VTEMP,1 instrument validationset after transfer from the new instrument predicted withthe original model was 7.76. The data set for the VTEM P,2

part of the temperature offset test gave a minimumRMSEP value of 8.38 with eight transfer samples and theleverage-weighted KS FID selection method.

Direct standardization transfers the models successful-ly from the old instrument to the new instrument for anyof the simulated FID changes. The calibration transferrequires between four and nine samples for calibration

transfer with the minimum RMSEP (Fig. 8). The optimalmethod for sample selection was the KS method.

Piece-Wise Direct Standardization. The VPRD (probering-down) test was performed with PDS as described inthe Experimental section. The FID set with 400 pointswas used to increase the rate of transfer between the twoinstruments. The number of samples used to create theTM and BCV was stepped between 2 and 14 with incre-ments of 1. Similarly, the window width was increasedfrom 3 to 67 points with increments of 4 points. Thelowest RMSEP coincided with two transfer samples anda window width of 59 (Fig. 9). The RMSEP at this pointwas 7.44 (Table III). Similarly to DS, the RMSEP of theFID transfer steadily increased upon the addition of moresamples for the development of the TM and BCV. Theoptimum transfer for the VPRD FID set was KS FID se-lection.

Changes in the pulse width of the instrument were sim-ulated in the manner described above. The VSPW,1 instru-ment FIDs used for PDS was the set with the � rst ex-ponential function amplitude increased by 20%. The op-timum transfer of these FIDs occurred with two samplesto construct the TM and BCV and with a window widthof 23. The RMSEP for this transfer was 6.07. The VSPW,2

instrument FID set with a 20% increase in initial ampli-tude and a 10% increase in the amplitude of the Weibullfunction was also used for PDS. The FIDs transferredwith an optimum RMSEP of 6.27, which coincided withtwo transfer samples and a window width of 23.

The VTEM P,1 part of the temperature offset test gave anRMSEP for the optimally transferred FID set of 6.20.This optimal transfer occurred with four samples to createthe TM and BCV and a window width of 55 points. TheVTEM P,2 part of the temperature offset test gave an RMSEPof 6.08. This transfer was performed with � ve samplesand a window width of 63 points.

In summary, PDS successfully transferred all the mod-els from the original VORIG instrument to each of the newvirtual instruments and appears to be the transfer methodof choice. The RMSEP values for the transferred modelswere all signi� cantly lower than the RMSEP values forthe DS method. Optimal calibration transfer usually oc-curred with two samples but sometimes required up to� ve samples. Therefore, PDS transfers the calibrationmodels more effectively than either DS or HC, and thetransfer occurs with less work. Similarly to the DS re-sults, the KS method of sample selection gave a fastercalibration transfer.

CONCLUSIONThe main conclusion from this work is that PLS re-

gression models developed from process NMR free in-

1560 Volume 55, Number 11, 2001

Table III. Results from the PDS transfer.

VPRD: probering-down

V SPW,1: shorterpulse width (part 1)

V SPW,2: shorterpulse width (part 2)

VTEMP,1: temperatureoffset (part 1)

VTEMP,2: temperatureoffset (part 2)

Original model RMSEP 8.59 8.59 8.59 8.59 8.59New model RMSEP 8.60 8.77 8.73 8.52 8.73PDS transfer 7.44 6.07 6.27 6.20 6.08Optimal window width 59 23 23 55 63Number of samples needed

for transfer a

2 2 2 4 5

a The transfer was considered complete when the minimum in the RMSEP plot was observed.

duction decays can be ef� ciently transferred between dif-ferent NMR spectrometers. The most accurate modeltransfer between NMR spectrometers with different pro-cesses can be achieved through piece-wise direct stan-dardization. Other model transfer methods (direct stan-dardization and hybrid calibration) were found to be lesssatisfactory under the conditions used here. Furthermore,piece-wise direct standardization transfer tends to transferoptimally with only two to � ve samples, whereas the oth-er methods require more samples for model transfer.These methods will be tested on real applications, andthe results will be published in the future.

ACKNOWLEDGMENTS

The authors thank Dr. Dan O’Donnell and Dr. Joe Cross for infor-mative suggestions and support of this project.

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