On-line crystallinity measurement using laser Raman spectrometer and neural network

On-line crystallinity measurement using laser Ramanspectrometer and neural network

Celal Batur a, *, Mohamad Hanif Vhoraa, Miko Cakmakb,Toprak Serhatkulub

aDepartment of Mechanical Engineering, University of Akron, Akron, OH 44325-3903, USAbDepartment of Polymer Engineering, University of Akron, Akron, OH 44325-0301, USA

Abstract

A neural network is con®gured and trained to measure the polymer crytallinity in real time and non-intrusive man-ner. After the training, input to the neural network becomes the laser Raman spectrum at selected ferquencies and theoutput from the network is the current crystallinity of polymer. In order to train the neural network, a training data set

is constructed where the crystallinities corresponding to a given set of Raman spectra are pre-determined by the smallangle light scattering (SALS) methodology. The technique is applied to measure the crystallinity of low-density thinpolyethylene (LDPE) ®lm. A typical sampling period for the determination of the crystallinity is around 12 s. The

technique is compared to the principal component analysis that uses the same input data for calibration. # 1999Elsevier Science Ltd. All rights reserved.

Keywords: Polymer crystallinity; Raman signal; Neural network

1. Introduction

Real time, non-intrusive measurement of poly-mer crystallinity is an essential step towards animplementation of a structural control system thatcan regulate the structure development duringpolymer processing [1]. Crystallinity developmentfollows a complex function of temperature history,which can be described by the generalized Avramiequation

� � 1ÿ eÿ� t

0K T�� dr �1�

where � is the crystallinity and the nonlinearfunction K�T� represents the temperature depen-dency. If cooling follows a ®xed gradient i.e.dT=d� � C, the crystallinity can be written as afunction of temperature and cooling rate as

� � 1ÿ eÿ 1�dT=d��

� T

0K�T�dT �2�

A qualitative on-line observation of crystallinityvia measurement of the birefringence is demon-strated by Bansal and Shambaugh [2]. In thisstudy, we present an on-line and non-intrusive,

ISATRANSACTIONS

1

ISA Transactions 38 (1999) 139±148

0019-0578/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0019-0578(99)00012-9

* Corresponding author. Tel: +1-330-972-7367; fax: +1-

330-972-6027.

E-mail addresses: [email protected] (Celal Batur); cakmak

@uakron.edu (Miko Cakmak); [email protected] (Toprak

Serhatkulu)

crystallinity measurement technique that can esti-mate the crystallinity while the material is coolingwith a ®xed gradient. This technique is based on aneural network that uses the spectrum of theRaman signal. Basically the neural network istrained to learn the expression (2). However, as wewill see later, it also successfully learns the generalexpression (1). The use of laser Raman signal fordetermination of some structural parameters iswell established. For example Everall et al. [3]have calibrated the Raman signal in terms of thedensity of poly(ethylene terephthalate) in an o�-line fashion. We use a laser Raman spectrometermade by Kaiser Optics [4] to capture the Ramansignal from the surface of low-density thin poly-ethylene (LDPE) ®lm. Selected regions of theRaman spectrum are used to estimate the crystal-linity. In order to train the neural network, atraining data set is constructed where the crystal-linities corresponding to a given set of Ramanspectra are pre-determined by an independentcrystallinity measurement technique. This inde-pendent technique is the small angle light scatter-ing (SALS) methodology [5]. Using SALS, wedetermine the crystallinity corresponding to atemperature while the material is cooled followinga speci®c cooling rate. This crystallinity value isthen used as the true crystallinity corresponding tothe Raman spectrum, which is captured from the®lm at the same temperature. The SALS techni-que, in turn, also needs to be calibrated. In orderto perform this calibration, we use the di�erentialscanning calorimetry (DSC) technique. The pro-posed technique in this study, which we will referto as the Raman neural network (RANN) techni-que, is compared with a technique that uses theRaman signal in connection with the principalcomponent analysis, (RAPCA). Table 1 presentsgeneral properties of four di�erent techniquesconsidered in this study.

This paper is organized as follows. In Section 1,we provide brief descriptions of the DSC and theSALS techniques. The Raman spectrum followedby the principal component analysis, RAPCA, isdescribed in Section 2. The Raman neural net-work technique, RANN, is presented in Section3. Finally, the experimental results are given inSection 4.

2. Crystallinity measurement using DSC andSALS

2.1. Di�erential scanning calorimetry (DSC)

The DSC measures the heat ¯ow and the tem-peratures associated with transitions. Exothermicand endothermic heat exchanges of a polymersample and a base line Indium sample are con-tinuously measured during crystallization. Bymeasuring the di�erence in heat ¯ows between thepolymer sample and the base line sample, a char-acteristic heating pro®le shown in Fig. 1 isobtained. The two samples are heated at a con-stant heating rate from a room temperature untilthe polymer sample becomes an amorphous melt.

The ®rst characteristic point is observed whenthe polymer is above the glass transition point, Tg.Following this temperature, polymer chains canalign themselves to crystallize. An exothermic heat¯ow shown in region I is due to crystallization.The area between the curve and the base linearound this region determines the exothermic heat¯ow due to crystallization. Further heat ¯ow fol-lowing crystallization causes an endothermic heat¯ow since the polymer becomes an amorphousmelt. This is shown as region II in the same ®gure.The degree of crystallinity is determined from thedi�erence between the endothermic heat ¯ow dueto melting, �Hmelt, and the exothermic heat ¯owdue to crystallinity, �Hcry, i.e.

� � �Hmelt ÿ�Hcry

�H1�3�

where �H1 is the heat of fusion for 100% crys-talline material.

2.2. Small angle light scattering (SALS)

Fig. 2 shows a typical set-up for small anglescattering (SALS) measurement device. A laserlight passes through a thin ®lm of polymer. If thematerial is amorphous, light scattering is ran-domly oriented. If the material is partially crystal-line, the spherullitic form of crystals scatters thelight in speci®c directions. In order to capture thescattered light, a polarizer and an analyzer are

140 C. Batur et al. / ISA Transactions 38 (1999) 139±148

placed before and after the thin ®lm of polymer.The laser light ®rst passes the polarizer, whichremoves one orthogonal component of the light.The other component of light passes through thepolymer ®lm with resulting scattering due to crys-tallinity. The analyzer removes the second com-ponent since it is placed 90� out of phase withrespect to the analyzer. Therefore, any light thatcomes out of the analyzer is entirely due to thescattering within the ®lm. The average size of thespherules of the crystalline structure, therefore, theamount of crystallinity can be determined usingthe scattering pattern. In our experiments thedepolarized intensity of light that passes throughthe polarizer, crystallizing sample and analyzer isrecorded and related to the volume fraction ofcrystallizing polymer. Both transmitted and scat-tered light are used. Calibration of the light inten-sity in terms of the crystallinity is made by thedi�erential scanning calorimetry measurement.Here we assume that there is a linear relationbetween the total intensity (transmitted and scat-tered light intensity) and the crystallinity. The fol-lowing steps are used in the calibration process.

(a) The thin polymer ®lm is heated to 120�Cuntil it reaches a complete amorphous state.

(b) The ®lm is then put into a hot stage andcooled to 45�C following a constant coolingrate. A CCD camera captures the imageand the total intensity of the image isdetermined in every 6 s.

(c) The total intensity is assumed proportionalto crystallinity. If the intensity is plotted

with respect to time (or equivalently withrespect to temperature) it follows a sigmoi-dal curve such as the one given by Eq. (2)where the minimum point on this curvecorresponds to zero crystallinity and themaximum point corresponds to the ®nalcrystallinity.

(d) The ®lm is taken to the DSC in order todetermine ®nal crystallinity of the material.

(e) The amplitudes of the sigmoidal curve ismultiplied by the ®nal crystallinity in orderto calibrate it in terms of crystallinity.

3. Raman spectroscopy with principal componentanalysis

Fig. 3 shows how the Raman signal is captured.A monochromatic light from a laser source strikesthe polymer ®lm. Almost all light is scattered

Table 1

Comparison among four di�erent crystallinity measurement systems

Technique Raw signal Calibration procedure Non-intrusive Real time

Di�erential scanning

calorimetry (DSC)

Heat ¯ow di�erence

versus temperature

Use of an Indium sample

which melts at 156.65�CNo No

Small angle light

scattering (SALS)

Normalized light

intensity

versus temperature

Use of DCS data Yes, but it can work only

on thin transparent ®lms

Sampling period

is 6±10 s

Raman spectrometry

and principal component

analysis (RAPCA)

Raman signal Principal component analysis

and least squares using

SALS data

Yes Min 10±15 s sampling

period

Raman spectrometry

and neural network

(RANN)

Raman signal Training a neural network

using SALS data

Yes Min 10±15 s sampling

period

Fig. 1. Characteristic thermal pro®le for DSC.

C. Batur et al. / ISA Transactions 38 (1999) 139±148 141

elastically, i.e. with no change in energy (or fre-quency). A very small part, approximately 1 in107, is scattered with a change in frequency. Thedi�erence between the incident and the scatteredfrequencies corresponds to an excitation of themolecular system, most often an excitation of avibrational nature. By measuring the intensity ofthe scattered photons as a function of the fre-quency di�erence, we obtain the Raman signalspectrum. This spectrum can be considered as thesignature of the molecular structure.

The purpose of the principal component analy-sis is to determine a linear regression modelbetween the crystallinity and the observed Ramanspectrum. It is accomplished through the follow-ing steps.

3.1. Step 1. Determination of a regression model

We assume that each column of the followingmatrix represents the intensities of one observedRaman spectrum at the selected waveshifts,

Fig. 3. Generation of the laser Raman signal.

Fig. 2. A typical set-up for SALS.


D �d1;1 d1;2 � d1;nd2;1 d2;2 � s2;n� � � �

dm;1 dm;2 � dm;n

26643775;D 2 Rm�m �4�

Therefore, each spectrum is represented by (m)number of spectral intensities and a total of (n)spectrum exist. The dispersion matrix Z thatrepresents the variation in the data is computed as

Z � DTD; Z 2 Rm�m �5�

An important step in the principal componentanalysis is to express the data matrix D in terms ofthe eigenvectors of the dispersion matrix Z. Tothis end, we ®rst use the singular value decom-position and express the dispersion matrix interms of its eigenvalues and eigenvectors, i.e.

Z � LlLT �6�

where L and l matrices contain the eigenvectors(li) and the eigenvalues (li) of Z as

L � l1l2 . . . ln� �; l �l1 0 0 00 l2 0 00 0 : 00 0 0 ln

26643775 �7�

Since the eigenvectors are orthonormal, i.e.

LT � LLT � I �8�

we can trivially write the data matrix as

D � DLLT � FLT �9�

where F � DL 2 Rm�n is known as the factormatrix. The kth spectrum of the data matrix D cannow be written as a linear combination of the col-umns of the factor matrix as

spectrum�k� �d1;kd2;k�

dm;k

26643775 �

f1;1f1;2�

f1;m

26643775:l1k � . . .�

fn;1fn;2�

fn;m

26643775�lnk�10�

The coe�cients (lik) in this linear expression comefrom the eigenvectors and they are referred to asfactor loadings. A geometric description of thisexpression is shown in Fig. 4. One can interpreteach column of the F matrix as an abstract spec-trum.

Elimination of negligible factors can simplifythe expression above. Let us assume that only (nf)number of factors are signi®cant, then the spec-trum (k) can be approximated as

spectrum�k� �

d1;k

d2;k

�dm;k

2666437775 �

f1;1

f1;2

�f1;m

2666437775�ll;k � . . .

�

fnf;1

fnf;2

�fnf;m

2666437775�lnf;k �

fnf�1;1fnf�1;2�

fnf�1;m

2666437775�lnf�1;k . . .

�

fn;1

fn;2

�fn;m

2666437775:ln;k �

f1;1

f1;2

�f1;m

2666437775:ll;k � ::�

fnf;1

fnf;2

�fnf;m

2666437775:lnf;k�11�

Fig. 4. Geometric interpretation of factor loading.


The basic idea of the principal component analysisis to express the crystallinity using a linear regres-sion model with the number of factor loadingsthat correspond to the number of signi®cant fac-tors i.e.

�i � �1l1;i � �2l2;i � . . . �nflnf;i � ei; i � 1; 2; . . . nf

�12�

where (�i; i � 1; 2::nf) are the linear regressioncoe�cients, (lj;i; j � 1; 2::nf) are the factor loadingsand (ei) is the equation error term. It may benoticed that the factor loadings act like datapoints for this regression. The linear regressioncoe�cients are obtained by minimizing the sum ofsquares of equation errors for (nf) number ofsample spectra and their corresponding crystal-linities. This leads to the solution

�̂ ��̂1�̂2��̂nf

26643775 � LT

nf

�1�2��nf

26643775 � LT

nf�;Lnf 2 Rm�nf �13�

where the matrix Lnf is obtained by taking the ®rst(nf) columns of matrix L. In step 2 we will describehow this regression model can be used to estimatethe crystallinity for a new sample spectrum.

3.2. Step 2. Estimation of crystallinity

Suppose that we obtained a new spectrum as

dnew � new spectrum �d1;new

d2;new

�dm;new

26643775 �14�

In order to use the regression model above, weneed to determine the factor loadings that corre-spond to this new spectrum. Writing the datamatrix from Eq. (9) as D � FLT we express thisnew spectrum as

dnew � Flnew �15�where lnew contains the factor loadings corre-sponding to this new data. The least squares solu-tion for the new factor loading is obtained as

lnew � lÿ1FTdnew �16�

In this derivation, we use the fact thatFTF � LTZL � l. Using the regression model Eq.(12), the crystallinity corresponding to this spec-trum can now be estimated as

�new � �̂1l1;new � �̂2l2;new � . . . �̂nflnf;new �17�

Further details of the techniques can be found inFrederics et al. [6].

4. Raman spectroscopy with neural network(RANN)

The structure of the neural network is shown inFig. 5. The network receives the selected portionof the Raman spectrum on its input neurons. Fig.6a shows the regions of the spectra that are usedto train the network. For uniformity of compar-ison, the same regions are also used in the princi-pal component analysis. The output of the neuralnetwork is the estimated crystallinity. The ®naloptimized structure of the network has two hiddenlayers with ten neurons in each layer. The inputlayer has 307 neurons, which receive the spectrumat selected Raman waveshifts. These wavelengthsare determined by observing the changes in spec-trum during crystallization by and picking thewavelength regions where the most signi®cantchanges take place. The changes are detected byplotting the spectra on top of each other andlooking for the regions where signi®cant changestake place. We determined that the followingRaman waveshifts produce the largest changes inthe intensities during crystallization: 1045±1140,1163±1175, 1270±1376 and 1400±1490 cmÿ1. Dur-ing the training phase, we input the spectrum for agiven temperature and compare the output of theneural network with the crystallinity valueobtained by SALS at the same temperature. Typi-cal training data are shown in Figs. 6a±b.

The di�erence between the estimated crystal-linity and the crystallinity obtained by SALS isused as the error signal in the back propagation-training algorithm. The performance index of


training is the sum of squares of the estimationerror for a total of N training samples, i.e.

V � 1

2

XNk�1

e2k �18�

The estimation error (ek) is the di�erence betweenthe true crystallinity, which is obtained throughthe SALS experiment and the estimated crystal-linity by the neural network, i.e.

ek � true crystallinity ÿ estimated crystallinity

�tk ÿ f d1k; . . . ; dmk;W�1�;B�1�;W�2�;B�2�;W�3�;B�3�

ÿ ��19�

The weights (W) and biases (B) can be expressedin a vector-matrix form as

W�1� � w1ij; i � 1; . . .m; j � 1; . . . J

n o;

B�1� � b1i ; i � 1; . . .m�

W�2� � w2js; j � 1; . . . J; s � 1; . . .S

n o;

B�2� � b2j ; i � 1; . . . Jn o

W�3� � w3s ; s � 1; . . .S

� ;

B�3� � b3s s � 1; . . .S�

�20�

The transfer function of a typical neuron is chosenas a sigmoid function. For example, for a neuronon the ®rst hidden layer, the neuron output isgiven as

yj � fXi�mi�1

wijxi � bi

!; j � 1; 2; . . . J;

and f�:� � 1

1� eÿ�:�

�21�

Fig. 5. Structure of the neural network used.


The weights and biases of the network are updatedusing an adaptive gradient descent algorithm as

w�k� 1� � w�k� ÿ ��k� @V@wjk;

b�k� 1� � b�k� ÿ ��k� @V@bjk

�22�

where w�k� is the weight and b�k� is the bias atiteration k and � is the adaptive learning rate.Further details of the algorithm can be found in[7,8]. The subroutine TRAINGDX of the Matlabneural network toolbox is used to implement thetraining algorithm.

5. Results

The neural network shown in Fig. 5 is trainedusing the experimental data, which is based on2�C/min cooling rate. The total number of datapairs can be represented as

spectrum; crystallinity� ��d1;kd2;k::dm;k�; �k; k � 1; . . .N

where m � 307 and N � 188. The training data isdivided into two halves and the even numbereddata pairs (i.e. k even), are used for training andthe odd numbered data pairs are used for evalu-ating the performance of the trained neural net-work. The neural network is optimized by plottingthe performance index V of Eq. (18) as a functionof the number of neurons in two hidden layers.The performance index, in general, decreases asthe number of hidden layer neurons increases. Wefound that increasing the number of hidden layerneurons to more than 10 does not signi®cantlyreduce V, therefore we used 10 neurons in eachhidden layer. We also observed that using toomany neurons such as 15 neurons in each hiddenlayer encourages a situation that the neural net-work simply memorizes the training data insteadof trying to capture the basic non-linear relation.We also added 2% noise to the training data inorder to minimize the memorization tendency.Training is stopped once the square of the estima-tion error reached 0.001. The initial learningparameter � is chosen as 0.01. The variable learn-ing rate algorithm adjusts the learning ratedepending on the ratio between the old error andthe new error. The details of the variable learningrate algorithm can be found in [9]. For the ®rst layerand the following two hidden layers a sigmoidalnonlinear function is used in each neuron. Theneuron at the output layer has a linear function.The initial weights and biases are picked ran-domly. The training data is normalized betweenzero and one in order to avoid saturation in sig-moidal functions used by neurons.

Figs. 7 and 8 show how crystallinities are esti-mated for cooling rates of 3 and 0.3�C/min. Sincethese cooling rates are di�erent than the ones that

Fig. 6. a. Changes in light intensity and laser Raman spectrum

as functions of temperature. b. Changes in crystallinity during

cooling with a gradient of 2�C/min.


generate the training data, it follows that these®gures are actually representing the performanceof RAPCA and RANN for data sets that theyhave not seen before. The performance in the caseof the training data of 2�C/min is predictably verygood, therefore, these results are not presentedhere. Each ®gure shows how crystallinities areestimated by SALS, RAPCA and RANN. Sincethe exact value of crystallinity is unknown, com-parison among these techniques can be based onhow close the RAPCA and RANN are to theSALS. We also present the DSC results in order toillustrate the consistency of di�erent techniques.However, the DSC results are obtained o�-line

and only used to calibrate the SALS data. Weobserve the following patterns in the results.

(a) Crystallization is very fast in the early phaseof the cooling period. Following the glasstransition temperature, almost 60% ofcrystallinity development is completedwithin the ®rst 10�C of cooling.

(b) In general, both RAPCA and RANN per-form equally well to estimate crystallinitiesin transition and they eventually approachthe ®nal crystallinity measured by the DSCtechnique.

(c) When the cooling rate is close to the onethat is used in the training data, as in thecase of 3�C/min, estimated crystallinities arecloser to those of SALS particularly in theearly stages of crystallinity development.This can be observed in Fig. 7. On the otherhand, as Fig. 8 shows, when the cooling rateis signi®cantly di�erent from that of thetraining data, as in the case of 0.3�C/min,estimated crystallinities signi®cantly di�erin the initial transitional phase.

(d) Increasing the number of sample spectra inthe data matrix D of the RAPCA does notsigni®cantly improve the results. In ourstudy we found that the properly selected 16spectra provide a satisfactory performance.On the other hand increasing the number oftraining spectra used in RANN alwaysimproves the performance.

From an implementation point of view, the fol-lowing observations can be made.

1. Once trained, the neural network based esti-mator RANN does not require further cal-culations in order to determine thecrystallinity. In the case of RAPCA, how-ever, one needs to determine the factor load-ings corresponding to the new spectrum, asoutlined in Eqs. (15±17).

2. The Kaiser Optic spectrometer operatingwith 532 nm Nd:YAG laser needs a mini-mum of 10 s in order to secure a reasonablynoise and ¯uorescence free Raman spectrum.Therefore, for both RAPCA and RANN the

Fig. 7. Performance of SALS, RAPCA, DSC and RANN for

3�C/min cooling rate.

Fig. 8. Performance of SALS, RAPCA, DSC and RANN for

0.3�C/min cooling rate.


sampling period is about 10 s. Using ashorter wavelength laser can reduce thesampling time at the expense of increased¯uorescent noise.

6. Conclusion

We presented a new technique that can be usedto measure crystallinity on-line and non-intru-sively while the material is cooling with a ®xedcooling rate. The technique is based on calibrationof Raman spectrum in terms of crystallinity usinga neural network. Only selected regions of thespectrum are used to train the neural network. Ithas been demonstrated that the neural networkcan capture the basic crystallinity dynamics sinceit works equally well on data sets with di�erentcooling rates than those of the training data. Thetechnique is compared with the one that is basedon the Raman signal in connection with the prin-cipal component analysis. It is shown that theproposed technique is easier to implement andprovides more ¯exibility approximating the non-linear relation between the crystallinity and thecorresponding spectrum.

We collected our training data set while thematerial was cooling with a ®xed cooling ratestarting with an amorphous state. The ®xed cool-ing rate constraint was convenient in order todetermine the true crystallinity corresponding to agiven temperature. In real life processing condi-tions the cooling rate and the initial state may notbe exactly known. Since the crystallinity develop-ment follows a function of the temperature historyas indicated by Eq. (1), it will be necessary to trainthe neural network under a set of expected coolinghistories, which are speci®c to the actual proces-sing conditions. The following procedure can beused in order to generate a training data set cor-responding to the actual operating conditions.First, the cooling history can be determined bymeasuring the temperature of material with an

infrared camera at more than one location,including the location of the Raman probe. Oncethe cooling history is known, the DSC, or theSALS as implemented in this study, can evaluatethe corresponding true crystallinity at the locationwhere the Raman probe is. Given the true crys-tallinity and the Raman spectrum, one set oftraining data can be prepared. Repeating thisprocess for other expected processing conditionsor equivalently other cooling histories, we cangenerate a series of data sets in order to properlytrain a neural network. To this end, our results arestrongly encouraging since the neural networktrained on one cooling rate such as 2�C/min cansuccessfully estimate crystallinities at other coolingrates such as 0.3 and 3�C/min.

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On-line crystallinity measurement using laser Raman spectrometer and neural network

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