1188
Energy & Fuels 1997, 11, 1188-1193
Asphalt Study by Neuronal Networks. Correlation between Chemical and Rheological Properties Laurent Michon and Bernard Hanquet Laboratoire de Synthe` se et d'Electrosynthe` se Organome´ talliques, L.S.E.O. UMR CNRS 5632, Universite´ de Bourgogne, BP 138, 21000 Dijon Cedex 04, France
Boubakar Diawara* Ecole Nationale Supe´ rieure de Chimie de Paris, 11, Rue Pierre et Marie Curie, 75005 Paris, France
Didier Martin and Jean-Pascal Planche Centre de Recherche Elf Solaize, BP 22, 69360 Solaize Cedex, France Received March 11, 1997X
In this paper we investigate the prediction of rheological properties of bitumens using some structural parameters calculated from 13C NMR data. This study was carried out using methods of quantitative structure properties relationships (QSPR) and more particularly neural networks (NN). Such a mathematical tool can find out non linear relations between descriptors and properties. Two asphalt rheological properties, m (creep slope at low temperature) and G*/sin δ (stiffness at high temperature) were selected, whereas the descriptors are the average molecular parameters which characterize the hydrocarbon skeleton of bitumens. This work permitted to prove that the skeleton information contained in the average molecular parameters could be correlated to the m value but not to the G*/sin δ. Thus, the low-temperature rheological behavior appears to be highly dependent on the aliphatic part of the bitumens.
Introduction antiquity1
and The bitumens have been known since they are considered as very technical materials.2 A great deal of effort has been devoted lately to better understand their physical and chemical properties.3,4 Their chemistry and structure are still being investigated by lots of researchers with respect to colloidal structure5-7 and functions.8,9 Studies carried out in this field pointed out that asphalt cements (AC) are complex mixtures of a wide variety of molecules: paraffinics, naphthenics, and aromatics including heteroatoms. This complexity makes the prediction of the properties of bitumens particularly difficult. An alternative is to use methods of quantitative structure properties relationships (QSPR) to predict bitumens properties from macroscopic measurements and more particularly spectroscopic data. In a recent work, Pieri et al.10 used * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, October 15, 1997. (1) Connan, J.; Deschesne, O. La Recherche 1991, 229, 152-159. (2) Rondelez, F.; King, G. N. La Recherche 1989, 208, Suppl. 2931. (3) Brule, B.; Raymond, G.; Such, C. Bull. Liaison Labo. Ponts Chausse´ es 1987, 148, 69-81. (4) Soury, M.-P. Rev. Ge´ n. Routes Ae´ rodromes 1994, 714, 52-53. (5) Yen, T. F. Symposium on Chemistry and Characterization of Asphalts; Am. Chem. Soc.: Washington, D.C., 1990; pp 314-317. (6) Storm, D. A.; Edwards, J. C.; DeCanio, S. J.; Sheu, E. Y. Energy Fuels 1994, 8, 561-566. (7) Christopher, J.; Sarpal, A. S.; Kapur, G. S.; Krishna, A.; Tyagi, B. R.; Jain, M. C.; Jain, S. K.; Bhatnagar, A. K. Fuel 1996, 75, 9991008. (8) Huggins, F. E.; Vaidya, S. V.; Huffman, G. P.; Mill, T.; Youtcheff, J. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1992, 37, 1376-1382. (9) Michon, L.; Siri, O.; Hanquet, B.; Martin, D. Energy Fuels 1996, 10, 1142-1146.
S0887-0624(97)00038-8 CCC: $14.00
statistical methods such as the principal component analysis (PCA) to link some rheological properties of AC’s to chemical indexes obtained from Fourier transform infra-red (FT-IR) and synchronous ultraviolet fluorescence (SF) spectroscopy data. In a previous paper11 we reported a new set of chemical parameters to characterize the skeleton of AC’s. In contrast to earlier studies,12-15 our method is based only on the carbon-13 nuclear magnetic resonance (13C NMR) data and gives 14 independent average molecular parameters. The purpose of this study was to determine if these new parameters could be correlated to the rheological properties of bitumens using neural networks (NN) which can perform nonlinear multiregression. Artificial neural networks are mathematical methods inspired by a simplified model of the human brain.16 The basis of the model is a formal neuron, an automaton which receives inputs from other neurons. A weight, (10) Pieri, N.; Planche, J.-P.; Martin, D.; Germanaud, L.; Kister, J. In Ve` me Symposium Eurobitume, Strasbourg, Proc. Eurasphalt Eurobitume, 7-10 May 1996. 1996, 5.120, 01-13. (11) Michon, L.; Martin, D.; Planche, J.-P.; Hanquet, B. Fuel 1997, 76, 9-15. (12) Dickinson, E. M. Fuel 1980, 59, 290-294. (13) Gillet, S.; Delpuech, J.-J.; Valentin, P.; Escalier, J.-C. Anal. Chem. 1980, 52, 813-817. (14) Gupta, P. L.; Dogra, P. V.; Kuchhal, R. K.; Kumar, P. Fuel 1986, 65, 515-519. (15) Rafenomanantsoa, A.; Nicole, D.; Rubini, P.; Lauer, J.-C. Energy Fuels 1994, 8, 618-628. (16) Zupan, J.; Gasteiger, J. Neural Networks for Chemists. An Introduction; VCH: New York, 1993.
© 1997 American Chemical Society
Asphalt Study by Neuronal Networks
Figure 1. Formal neuron.
Figure 2. Layered neural network.
representing the connection strength, is associated to each input. The neuron processes the sum of the weighed inputs via an activation function and generates an output transmitted to other neurons (see Figure 1). Individual neurons can be connected with different topologies: layered networks, fully or partially connected networks, recurrent networks, etc. Layered networks are the most frequently used in the fields of QSPR. They are made of neurons arranged in layers. The neurons of the same layer are not connected together. They receive inputs only from the neurons of the former layer and they transmit their output only to the neurons of the next layer. Three layers are sufficient in most cases. The number of neurons of the first layer (input layer) is the same as the number of descriptors. The last layer (output layer) contains the same number of neurons as the number of properties to be predicted (usually one neuron). The number of neurons of the second layer (hidden layer) is variable (see Figure 2). A neural network study is based on two steps: training and generalization. During the training, the network learns to predict the property for known prototypes. In this step, the weights are modified in such a way that, for each prototype, the difference between predicted and known values is as small as possible. In the generalization phase, the predictive ability of the network is evaluated using prototypes with known values and which were not used during the training. Experimental Section Samples. In this study, 34 different samples of bitumens from the Strategic Highway Research ProgramsReference Materials Library (SHRP-RML) were investigated. These bitumens were supplied by Elf-Antar France Co. and noted as AAA, AAB, AAB2, AAC, AAD, AAD2, AAE, AAF, AAF2, AAG, AAH, AAJ, AAK, AAL, AAM, AAN, AAO, AAP, AAQ, AAR, AAS, AAS2, AAT, AAU, AAV, AAW, AAX, AAY, AAZ, ABD, ABF, ABG, ABH, and ABK.
Energy & Fuels, Vol. 11, No. 6, 1997 1189 Properties. These AC’s are from different origins and grades. Two rheological properties (m measured at -10 °C and G*/sin δ measured at +58 °C) were evaluated and are listed in Table 1 (SHRP-RML source). The value of m corresponds to the slope in a three-point bending mode of the creep stiffness S(t) as a function of the loading time t. The creep experiment is carried out at low temperature (between 0 and -40 °C) using a bending beam rheometer. The AC specimen was aged prior to testing by rolling thin film oven test (RTFOT) and pressure aging vessel (PAV). This aging protocol is meant to duplicate the actual aging of the material in the field (handling and service life). m and δ characterize the fragility of the bitumen at low temperature. G*/sin δ is the dynamic shear rheometer stiffness of the AC’s after RTFOT.17 The relative error on the two rheological properties are about 15%. This parameter was found to correlate with the rutting resistance of the bitumen-mineral aggregate mixture for a given mixture design. Descriptors: Average Molecular Parameters Calculation. The calculation of the average molecular parameters is made using our method described in a previous paper.11 NMR Spectroscopy: Inverse Gated Decoupling Spectra. Samples were prepared by dissolving about 100 mg of AC in 0.5 mL of CDCl3. Accurately weighed dioxan (about 100 mg) was use as a standard. Cr(acac)3 (chromium[III] tris[acetylacetonato]) was added as a relaxation reagent (10-2 mol/L as final concentration). The inverse gated decoupling sequence (Bruker Library) was used to obtain quantitative spectrum with a pulse delay of 5 s and a flip angle of 30° (3 µs at -2 dB). 32K data points were acquired during 0.65 s over a 25 kHz sweep width. The total number of scans was about 8000 giving an experiment time of 12 h. The FIDs were zero-filled to 64 K and exponentially weighed with a 4 Hz line broadening. Molecular Weight Determinations. Molecular weights were measured with a Knauer vapor pressure osmometer (ASTM D2503-92). Squalane was used as a reference. Reference and samples were dissolved in dry toluene, and the measurements were taken at 51 °C after 4 min of stabilization. Three determinations were done on solutions with the following concentrations: 2, 5, and 8 g/L. Assignment of the Different Types of Carbon Atoms. The assignments of the different carbon atoms in the aliphatic and aromatic parts are given in Table 2. The calculation of the different number of carbon atoms was established using the following formula: Cb ) 4(Ib/Id)(md/mb)(Mb/Md). The subscript b stands for bitumen and d for dioxan. I refers to the integration values, M corresponds to the molecular weight, and m is the mass of each compound. Calculation of the Average Molecular Parameters. The equations for calculating the average molecular parameters are given in Table 3. The results of these calculations for the 34 AC’s are listed in Table 4. The relative errors on these values are from 6 to 12% according to the different equations. Neural Networks. We used Neuralchemist18 a NN simulator designed for use by chemists. The training of the NN was done by back-propagation algorithm. The input parameters are scaled beetween 0.1 and 0.9, the transfer function being the usual logistic function. The weights are initialized to small random value between -0.05 and + 0.05, revised after each presentation of a prototype. To compare the predictive ability of the regression analysis and of the neural network, the cross-validation technique (leave-one-out method) was used. Each bitumen is removed one after the other from the database and predicted with a neural network trained with the other samples or with a regression equation obtained from the other samples. The quality of the prediction is assessed by the overall standard (17) Anderson, D. Rev. Ge´ n. Routes Ae´ rodromes 1994, 714, 48-52. (18) Diawara, B.; Roullet, G.; Cense, J. M.; Legendre, J. J. Proc. 4th Int. Conf. Neural Networks Their Applications. 1991, 777-781.
1190 Energy & Fuels, Vol. 11, No. 6, 1997
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Table 1. Main Characteristics of the AC’s %C m G*/sin δ
AAA
AAB
AAB-2
AAC
AAD
AAD-2
AAE
AAF
AAF-2
AAG
AAH
AAJ
AAK
AAL
AAM
AAN
AAO
83.9 0.41 1.0
82.3 0.34 1.9
85.7 0.36 0.8
86.5 0.30 1.1
81.6 0.38 1.5
81.9 0.43 0.7
83.8 0.31 4.5
84.5 0.27 2.6
84.8 0.32 1.4
85.6 0.43 3.0
86.3 0.31 1.7
86.5 0.32 2.6
83.7 0.35 3.8
83.4 0.41 1.1
86.8 0.29 2.4
84.5 0.30 1.9
83.8 0.35 1.9
AAP
AAQ
AAR
AAS
AAS-2
AAT
AAU
AAV
AAW
AAX
AAY
AAZ
ABD
ABF
ABG
ABH
ABK
85.9 0.32 3.5
85.5 0.34 1.4
84.1 0.35 2.3
84.0 0.35 2.2
83.1 0.38 2.1
83.9 0.29 3.7
84.4 0.30 2.7
86.4 0.39 0.8
84.5 0.30 3.1
86.6 0.30 2.2
83.7 0.33 3.0
85.0 0.34 2.4
86.8 0.28 2.7
85.5 0.39 2.7
83.7 0.41 2.4
89.8 0.33 1.0
85.0 0.31 2.6
%C m G*/sin δ
Table 2. Chemical Shift and Nomenclature Correlation Chart of the Carbon Atoms C type
δ (ppm)
symbol
assignment
aliphatic
10.0-55.0 10.0-18.6
Cali CH3
18.6-23.0
CH3R
23.0-32.5
CH2
32.5-34.6 34.6-42.7
CH CH2R
42.7-55.0 115.0-145.0 115.0-129.3 129.3-137.1 137.1-145.0
CHR Caro CHaro Cqp Cqs
aliphatic carbon atoms terminal methyl groups in aliphatic chain (except the case where two methyl groups are terminal) methyl groups branched to an aliphatic chain (except the case where they are branched in R or β position on a alkyl chain from a ring) methyl groups branched to an aromatic or naphthenic rings case where two methyl groups are terminal methyl groups branched in R or β position on a alkyl chain from a ring methylene groups of alkyl chains (except the case where they are branched in R or β position from an aromatic ring or in R position from a naphthenic ring) methylene groups of naphthenic rings methine groups in aliphatic chainsa methylene groups branched in R or β position from an aromatic ring or in R position from a naphthenic ring methine groups of naphthenic rings aromatic carbon atoms aromatic protonated carbon atoms aromatic bridgehead quaternary carbon atoms aromatic substituted quaternary carbon atoms
aromatic
a
In this part the methylene groups were determined by deconvolution and added to the CH2R for the next calculations. Table 3. Equation and Description Chart of the Molecular Parameters11
notation
equation
description
Ct % Cs Rs n f r Rn Ca % Ca fa Ra Canb % Canb %S
Cali + Caro 100(Cali/Ct) Cqs Cali/Cqs (12Cali)/[3(CH3 + CH3R) + 2(CH2 + CH2R) + (CH + CHR)] n(1 - 6/f) + 0.5 rCqs Caro 100(Caro/Ct) Caro/Ct 0.25(Caro - 1) CHaro + Cqs 100(Canb/Ct) 100(Cqs/Ct)
no. of total carbon atoms percentage of saturated carbon atoms no. of alkyl substituents no. of carbon atoms per alkyl substituent carbon-hydrogen weight ratio of alkyl substituents no. of naphthenic rings per alkyl substituent no. of naphthenic rings no. of aromatic carbon atoms percentage of aromatic carbon atoms aromaticity no. of aromatic rings no. of nonbridge aromatic ring carbon atoms percentage of aromatic carbon atoms percentage of substitued aromatic carbon atoms
error of prediction (SEP) and the cross-validated r2:
∑ (y
SEP ) [ r2 ) 1 -
∑(y
obs
obs
- ypred)2/N]1/2
∑(y
- ypred)2/
obs
- ymean)2
where N represents the number of samples, yobs, ymean, and ypred, respectively, represent the experimental, the mean, and the predicted values of the property.
Results and Discussion Prediction of m Value. Preliminary Study. Preliminary tests were done using all 34 bitumens and all 14 descriptors with a three-layer neural network denoted as 14B-XB-1 (14 neurons on the first layer with a bias B, a variable number X of neurons in the hidden layer, and 1 neuron in the output layer). With a 14B-2B-1 network, learning was satisfactory with a r value of 0.86 and a SEP of 0.043 but generalization was particularly poor (r ) 0). The mean error for generalization (10%) was of the same order of
magnitude as the experimental error but the dispersion of the values was very wide. Some bitumens had an error inferior to 1% while others had an error superior to 30%. Figure 3, showing predicted values versus experimental values, illustrates the range of the dispersion. The too small number of bitumens (34) compared to the number of descriptors (14) can partially explain the poor results of the generalization. It is well-known that a model with too many parameters will correctly fit the database but will poorly predict the new prototypes. Additionally, the presence in the database of bitumens out of the domain of validity of the model (called outliers) can also contribute to the poor results. Further investigations were carried out in order to select the most pertinent descriptors and identify bitumens which cannot be well predicted by the model. Selection of Pertinent Descriptors. To detect the most pertinent combinations of descriptors, an evolutionary search was performed within the descriptors space using the cross-validated r2 and F values (Fischer’s ratio).19
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Energy & Fuels, Vol. 11, No. 6, 1997 1191
Table 4. Average Molecular Parameters for the 12 Bitumens Ct % Cs Rs n f r Rn Ca % Ca fa Ra Canb % Canb %S
Ct % Cs Rs n f r Rn Ca % Ca fa Ra Canb % Canb %S
AAA
AAB
AAB-2
AAC
AAD
AAD-2
AAE
AAF
AAF-2
AAG
AAH
AAJ
AAK
AAL
AAM
AAN
AAO
54.2 73.8 4.0 10.0 6.2 0.9 3.4 14.2 26.2 0.3 3.3 10.8 19.9 28.2
59.0 69.7 3.3 12.5 6.0 0.6 1.9 17.9 30.3 0.3 4.2 13.3 22.5 18.4
58.2 73.2 3.0 14.2 6.2 1.0 3.0 15.6 26.8 0.3 3.7 11.6 19.9 19.2
63.2 71.8 4.1 11.1 6.1 0.7 2.7 17.8 28.2 0.3 4.2 13.8 21.8 23.0
47.1 74.3 2.8 12.5 6.3 1.2 3.3 12.1 25.7 0.3 2.8 9.0 19.1 23.1
49.7 74.0 2.9 12.7 6.0 0.4 1.2 12.9 26.0 0.3 3.0 9.5 19.1 22.5
54.6 69.4 3.7 10.2 6.0 0.5 1.8 16.7 30.6 0.3 3.9 12.6 23.1 22.2
58.4 68.8 3.6 11.2 6.2 0.8 2.9 18.2 31.2 0.3 4.3 13.7 23.5 19.8
59.6 67.1 3.2 12.5 6.2 0.9 2.8 19.6 32.9 0.3 4.7 15.2 25.5 16.3
48.5 71.1 2.9 11.9 6.4 1.2 3.5 14.0 28.9 0.3 3.3 11.1 22.9 20.7
57.3 67.0 4.1 9.4 5.9 0.4 1.5 18.9 33.0 0.3 4.5 14.3 25.0 21.7
71.0 72.1 4.1 12.5 6.0 0.5 2.0 19.8 27.9 0.3 4.7 15.0 21.1 20.7
54.3 72.2 2.7 14.5 6.0 0.6 1.6 15.1 27.8 0.3 3.5 10.8 19.9 17.9
50.1 70.3 2.9 12.1 6.1 0.7 2.2 14.9 29.7 0.3 3.5 10.9 21.8 19.5
90.7 75.0 4.8 14.2 6.2 0.9 4.6 22.7 25.0 0.3 5.4 17.5 19.3 21.1
60.1 69.6 4.0 10.5 6.1 0.6 2.6 18.3 30.4 0.3 4.3 13.4 22.3 21.9
63.8 69.7 4.2 10.6 6.2 0.8 3.6 19.3 30.3 0.3 4.6 14.2 22.3 21.8
AAP
AAQ
AAR
AAS
AAS2
AAT
AAU
AAV
AAW
AAX
AAY
AAZ
ABD
ABF
ABG
ABH
ABK
82.6 75.9 3.8 16.5 6.3 1.2 4.7 19.9 24.1 0.2 4.7 16.0 19.4 19.1
57.3 68.1 3.4 11.5 6.1 0.7 2.3 18.3 31.9 0.3 4.3 13.6 23.7 18.6
62.0 66.6 4.1 10.1 6.1 0.7 3.0 20.7 33.4 0.3 4.9 15.3 24.7 19.8
68.7 68.1 5.6 8.4 5.8 0.2 1.3 21.9 31.9 0.3 5.2 15.8 23.0 25.6
61.3 70.0 3.8 11.3 6.1 0.8 2.9 18.4 30.0 0.3 4.4 13.6 22.2 20.7
59.0 71.0 2.0 21.0 6.0 0.6 1.2 17.1 29.0 0.3 4.0 13.0 22.0 11.7
60.3 71.5 3.4 12.7 6.1 0.6 2.2 17.2 28.5 0.3 4.1 12.9 21.4 19.8
61.3 70.3 3.8 11.3 6.0 0.5 2.0 18.2 29.7 0.3 4.3 13.8 22.5 20.9
58.7 66.3 5.0 7.8 5.9 0.4 1.9 19.8 33.7 0.3 4.7 14.7 25.0 25.3
68.8 69.5 4.5 10.6 6.0 0.4 2.0 21.0 30.5 0.3 5.0 15.9 23.1 21.4
58.8 67.0 5.3 7.4 6.0 0.5 2.7 19.4 33.0 0.3 4.6 14.5 24.7 27.3
68.5 69.1 4.2 11.3 6.1 0.7 2.8 21.2 30.9 0.3 5.1 15.5 22.6 19.8
49.4 71.5 3.0 11.8 6.1 0.6 1.9 14.1 28.5 0.3 3.3 11.1 22.5 21.3
58.5 70.6 3.1 13.3 6.1 0.8 2.6 17.2 29.4 0.3 4.1 13.0 22.2 18.0
57.9 69.8 2.8 14.4 6.2 0.9 2.4 17.5 30.2 0.3 4.1 13.4 23.1 16.0
81.9 63.1 4.7 11.0 6.1 0.6 2.9 30.2 36.9 0.4 7.3 23.6 28.8 15.6
53.5 74.0 2.0 19.8 6.0 0.6 1.3 13.9 26.0 0.3 3.2 10.5 19.6 14.4
Table 5. Results of the Evolutionary Search no. of parameters
r value for training
14 8 6 4
0.85 0.87 0.88 0.67
r value for generalization
0.21
SEP
av error (%)
0.045 0.047 0.043 0.050
10.0 10.4 9.7 11.3
Table 6. Weight of Each Parameter in the Prediction parameter r n f Ct Canb
Figure 3. Correlation between the measured and the predicted m values with 34 AC’s and 14 average molecular parameters.
The F value measures the importance of a parameter in a multilinear regression. It is the ratio beetween the error of prediction with a complete model (using all the parameters) and the error of prediction with a reduced model (without the parameter wich importance is to be measured).
F ) (n - p - 1)(Qr - Qc)/Qc where Qc ) ∑(yobs - ypred)2 is the error with the complete model, Qr ) ∑(yobs - ypred)2 the error with the reduced model, n the number of observations, and p the number of parameters. Starting from the pool of 14 parameters, a multilinear regression was performed. The eight parameters with a value of F greater than 1 are selected. Similarly, this (19) Nefati, H.; Cense, J. M.; Legendre, J. J. J. Chem Inf. Comput. Sci. 1996, 36, 804-810.
% Canb
designation no. of naphthenic rings per alkyl substituent no. of carbon atoms per alkyl substituent carbon-hydrogen weight ratio of alkyl substituents no. of total carbon atoms no. of nonbridge aromatic ring carbon atoms percentage of substituted aromatic carbon atoms
wt in the prediction (%) 41.0 32.4 10.2 9.4 3.9 3.1
new pool leads successively to six and four parameters models. As seen in Table 5, the six-parameter model gives the best prediction. Further reduction of the number of the parameters decresases the prediction quality. The six parameters which give the best result are listed in Table 6. In the last column are reported the weight of each parameters in the prediction. The most important ones are r and n with a total weight around 73%. Discarding Outliers. Despite the increase of the prediction quality by selecting more pertinent parameters, the properties of some bitumens are still erroneously predicted. A bad prediction can be explained by two factors: either the bitumens have no or few neighbors in the descriptors space or they are not compatible with some other bitumens. To identify the outliers, we first proceed by discarding the worst predicted bitumen after cross validation with
1192 Energy & Fuels, Vol. 11, No. 6, 1997
Michon et al.
Figure 4. Correlation between the measured and the predicted m values with 28 AC’s and six average molecular parameters.
all samples. Second, the worst predicted bitumen is discarded after performing a new cross validation with the remaining samples. This process is repeated until the predictability is satisfactory, which is reached after discarding six bitumens: AAC, AAD2, AAF, AAF2, AAV, and ABD. Evaluation of the cleaned database (28 bitumens and six descriptors) with a 6B-2B-1 network gives as results r ) 0.83 and SEP ) 0.040. The mean error was 5.7% with a small dispersion as shown in Figure 4. Building of Predictive Neural Network. The crossvalidation technique is well adapted to the evaluation of the predictive ability of a set of descriptors and the identification of the outliers. But this technique leads to n networks (n is the number of prototypes) which cannot be merged to build an unique network for further prediction. For this, it is necessary to train a unique network with all the prototypes split into three sets: one for the learning, one for the generalization, and one for the tests. Each set must be representative of the diversity of the prototypes. This process requires a criterion for classification of the prototypes. For all the investigated bitumens, the aromatic ring condensation mode (i.e., the number of cycles and the number of substituents) seems to be the most reliable structural characteristic. The Ra values calculated for the bitumens were plotted against the Caro (see Figure 5). This representation allows to define three different groups located around the four-aromatic-ring family. That is the reason why the number of aromatic rings was used as a criterion for sharing out each bitumen in the three partitions.11 But it is still necessary to verify that the neural network processing takes into account this classification: an encoding-decoding neural network was used for this purpose. This kind of NN has the same number of neurons in the input as in the output layers (Figure 6).20 The encoding-decoding neural network is trained to generate the same information in the output layer as in the input layer. Outputs of neurons in the middle layer performed a reduction of the dimension of the descriptor space. A NN with a 6-3-2-3-6 architecture gives the results represented in Figure 7. (20) Cense, J. M.; Diawara, B.; Legendre, J. J.; Roulet, G. Chemom. Intell. Lab. Syst. 1994, 23, 301-308.
Figure 5. Correlation between the number of aromatic rings and average number of aromatic carbon atoms for the 34 AC’s.
Figure 6. Scheme of the encoding-decoding neural network.
Figure 7. Two dimensional representation of the six molecluar parameters.
Bitumens of the same family (according to the number of aromatic rings) are in a same area of the representation (only AAT is misclassified). This result validates the use of the classification according to the number of aromatic rings as a criterion for the partition of the database. Using such a criterion, the database is partitionedsas usually doneswith 70% of the AC’s in
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Energy & Fuels, Vol. 11, No. 6, 1997 1193
Table 7. Composition of the Three Partitions and Results partition
composition
r
training
AAM, AAS, AAZ, ABH, AAE, AAH, AAN, AAO, 0.93 AAP, AAS2, AAT, AAU, AAW, ABG, AAD, AAG, AAL, and ABK generalization AAR, AAB, AAQ, AAY, and AAA 0.86 test AAX, AAJ, ABF, and AAK 0.87
the training set, 20% in the generalization set, and 10% in the testing set. For each set, bitumen from each family are selected in order to cover as homogeneously as possible the space specific to this family in the two dimensionnal representation (Figure 7). The composition of the sets and the results of the simulation with an 6B-2B-1 network are summarized in Table 7. These results are homogeneous in the three sets and therefore the partition criterion is validated afterwards. For this property (m value) the neural network gives better results than the multilinear regression (r ) 0.76 for training). Prediction of G*/sin δ Values. This property was tested by cross validation with different architectures of neuronal networks, and in all cases, the predictions were of bad quality, the best result being obtained with an average error around 25%. Interpretation. Contrary to the m value, G*/sin δ was not well predicted. Such a difference can be related to the experimental conditions in which these properties are obtained. The m value is measured at -10 °C, temperature at which the bitumens are near the glassy state. This physical property may be dependent on the hydrocarbon skeleton characteristics which are well described by the average NMR molecular parameters. When the temperature is increased up to +58 °C (where G*/sin δ is measured) the bitumen becomes more fluid. Different functional groups may be involved in such a behavior. The average NMR molecular parameters do
not contain any functional information. Consequently, these parameters are not relevant enough to give a good prediction of G*/sin δ. Concerning the m value, the selection of pertinent parameters pointed out the importance of two parameters (r and n) relative to the aliphatic part of the AC’s. This result goes in the same direction as those described by Claudy et al.21 These authors demonstrated that the association rate is bitumen dependent and closely related to the presence and the nature of aliphatic hydrocarbons. Conclusions Neuronal networks appearseven with a small number of bitumen samplessto be a well-adapted tool to establish relationships between the structure and properties of the bitumens. This work permitted to prove that the hydrocarbon skeleton informations contained in the average molecular parameters are correlated to the m value, an important physical property of AC’s at low temperature. More particularly, we proved that the m value is very dependent on the aliphatic part of the bitumens. On the other hand, the aliphatics appear to play very little role in the rheological properties at higher temperature. Acknowledgment. The authors gratefully acknowledge the Conseil Re´gional de Bourgogne and Elf-Antar France for their financial support. We thanks Dr. Cense (ENSCP) for providing additional tools for computation of multilinear regression and encoding-decoding neural network and F. Hartmann (Centre de Recherche Elf Solaize) for his advice. EF9700386 (21) Claudy, P.; Letoffe, J. M.; Germanaud, L.; Planche, J. P.; King, G. Eurobitumes 1993, 61-65.
