Evaluation of Spectra in Chemistry and Physics. with Kohonen's Selforganizing Feature Map. Lehrstuhl fuer technische Informatik

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1 Evaluation of Spectra in Chemistry and Physics with Kohonen's Selforganizing Feature Map J. Goppert 1, H. Speckmann 1, W. Rosenstiel 1, W. Kessler 2, G. Kraus 3, G. Gauglitz 3 1 Lehrstuhl fuer technische Informatik University of Tubingen 7400 Tubingen, Sand 13, Germany 2 Institut fuer Angewandte Forschung FH Reutlingen 7410 Reutlingen, Altenburg. 150, Germany 3 Institut fur Physikalische und Theoretische Chemie University of Tubingen 7400 Tubingen, Auf der Morgenstelle 8, Germany Abstract In this paper we present a method for analyzing optical data with Kohonen's selforganizing feature map (SOM). Two applications are considered, the determination of presence and concentration of organic gases and solvants and the prediction of corrosion resistance of car body steels. Both applications use a similar method based on optical measurement. The goal is to extract correlations of the spectral data and to classify unknown spectra. Keywords self-organizing map, analyzing optical data, determination of gas concentration, prediction of corrosion restistance of car body steels In Proceedings of NeuroNimes 92, p , EC2, Nanterre, Nov

2 1 Motivation Evaluation of spectral data with a lot of components are an important problem in physics and chemistry. But traditional analytic and statistic methods fails, because of noisy and complex data. Self organizing maps (SOM) seem to be able to oer a solution. The SOM can classify data sets and nd correlations between vector components of the data. The map is fault tolerant covering noisy data. In contrast to many classical evaluation methods, where the calculation time raises exponentially with numbers of components, Kohonen's SOM time increases linearly. Relationships of data can be unknown. If once the map is trained, no further calculation is necessary. 2 Short description of Kohonen's selforganizing feature map algorithm For our implementations we use a modied version of Kohonen's algorithm [9, 13]. The self-organizing feature map consists of a two-dimensional array of identical processor units P E ij with each processor unit storing a single vector w ij with the components w ijk, i and j denote the position of the processor unit in the array. When the map is trained, each processor unit computes the euclidian distance D ij of the input vector S = (s1,..,s n ) and the stored vector w ij according to (1). k=n X D ij = k=1 (w ijk? s k ) 2 (1) After computing the distance for all P E ij, the map searches the processor unit which stores the most similar vector with the minimum distance D ijmin to the input vector of the array, and then the processor unit and its neighbourhood are made more similar to the input vector according to (2). w ijk (t + 1) = (1? e ij (t)) w ijk (t) + e ij (t) s k (2) where e ij (t) is the adaptation function which indicates the degree of adaptation of the processor units towards the input vector (0 e ij (t) 1, e ij (t)! 0 towards the training time t). For the adaptation function e ij we use the Gaussian function, which decreases linearly during training time in width and height. For the presentation of the learning results we use the vector position map and the component card. For the rst method we determine the position where the input vectors are stored by searching the minimum distance D ij (w ij, s k ) for each input vector s and plotting the number at the position (i min, j min ). For drawing the component card we choose one component k and draw the value of each P E ij (w ijk ) in greyscales on a two dimensional grid. 3 Recognition of solvents by interference spectra For chemical processes, as well as for security reason, fast and non destructive methods are needed for determining presence, and concentration of organic gases and solvents. One of these methods were developed at the \Institut fur Physikalische Chemie" of the \Universitat Tubingen". Specic gases change the thickness of polymerical membranes and are measured by interference spectra. The work shows that the SOM is able to detect specic gases and its concentrations in spectra. [1, 5].

3 3.1 Physical Background Polymer/solvent interaction Organic solvents, like hydrocarbons, interact with certain polymers. These solvents coming out of a gaseous stream, cause a change of volume especially of thickness of polymer membranes. As shown in [1] the relative change of thickness by absorption of dierent gases varies in big scale. Furthermore the dependency of gas concentration and membrane thickness is a linear calibration curve. The limit of determination of n-heptane in air corresponds to a relative change of %. In the same way swelling of thickness in membranes is perfectly reversible and reproducable. The typical response time for nonpolar solvent vapors in air is below 1 s [1]. Similar eects are obtained using liquids instead of gases, as addition of ethanol to distilled water Observation of spectral interferences A common and very sensitive tool to measure changes in thickness is the interferometry. But monochromatic interference produces neither absolute values of optical pathlength in the layer, nor a distinction between surface and volume eects. One solution is to use spectral interferometry. It was successfully used in the solution for similar problems. It was considered as an interesting approach to detect sensitively and rapidly any changes of optical pathlength in thin polymer lms. Spectral interferometry also allows the calculation of the refractive indices as function of the wavelength. These patterns depend on refractive indices at the interfaces of the analyzed material. All in all spectral interferometry seems to be a method to characterize physical and chemical properties of polymer lms and interaction with organic solvents Optical detection system Thermostatised sensor head for reflectance measurements Gas out Polymer film substrate Gas in diode array spectrometer and data acquisition light source (Xenon) Figure 1: Optical system. The optical detection system [1] consists of a new type of chemical and biochemical sensors, consisting of an silica and single or double [5] polymer layer xed on substrate like glass or silica. The optical part (gure 1) consists of a ber, placed perpendicularly to the polymer lm which provides light in the range of 300 to 720 nm by a XENON light source. The reected light is analyzed by a diode array spectrometer (C. Zeiss Oberkochen) with 512 spectral diodes. Hardware allows a repetition rate of 75 Hz.

4 3.1.4 Theoretical principles Chromatic light enters by a ber optic sensor and penetrates the dierent layers or is reected or absorbed by the dierent surfaces (gure 2). I I Ref I 1 I 2 n 1 n n 2 3 silica polimer n 1 Figure 2: Diagram of silica and polymer layer and lightpaths. At the rst layer, the silica plate, some percent of the light is reected. This intensity is used as reference signal I Ref which allows the normalization of the reecture measurement. The greater part penetrates the silica plate and is spliced once more at each surface of the polymer membrane (I1 and I2). If the polymer does not absorb, the partial beams just depend on the incident intensity and the refractive indices (n1 and n2) (perpendicular penetration supposed) according to Fresnel's equation [11]: R12 = ( n 1? n2 n1 + n2 )2 (3) The reected light beam I2 can be calculated by: I2 = R12 (I? (I Ref + I1)) (4) If the conditions of coherence between I1 and I2 are perfectly fullled (phase constant), the intensity of the two beams depends on the wavelength [11]: I() = I1 + I2 + 2 q I1I2 cos 2 As the refractive index of the polymer is a function of wavelength (n()) the phase () isn't constant. And if the material absorbs light, a supplement phase shift () is produced. The phase is calculated by: = 2dn() (6) The chromatic intensity can be expressed by: I = I1 + I2 + 2 qi1i2 cos 2dn() 2 + The multiple dependence of intensity from wavelength is the reason why monochromatic measurements can't be calculated by monochromatic methods. 3.2 Data processing with the SOM The most important factor is to choose the right parameters. In the following sections, the whole network is described and data - processing is shown.! (5) (7)

5 3.2.1 Preprocessing of the spectral data The intensity of reected light varies only in small scales, and length of spectral vector, as well as it's Fourier Transformation is nearly constant. For this normalization is not required. One of the most important properties of the SOM is its ability to conserve data topology of data space and to project this properties in network organization. The SOM tries to conserve the relations of neighborhood and resemblance. This is exactly what is needed for gas recognition [10]. The shape of cos 1 shows a lot of redundancy in input data. The data needs a lot of disk space and central memory to store the raw data and processor weights. Even more important is the fact that the learning time and calculation of the winning element increase with dimension, so that the reduction of dimension seems to be necessary SOM layer Network size for beginning was chosen to be 32x32 processing units (PUs). Beginning size of neighborhood is about 3 2 of network width. The number of iterations was chosen to be Initialization of unit-weights was randomly realized. Further experimentation showed that most of these parameters could be reduced one order of magnitude Association in Output Layer The SOM has no output layer. During training the map is organized in a specic way. The second part of training is to nd associations between the active unit and the desired output. The architecture of the SOM can be extended by addition of an association layer (gure 3). This can be done by adding some units to generate the output value. These units can be trained by several methods as delta rule, outstar procedure [4]. Gas A Gas B Gas C Figure 3: Simple output layer for a SOM. The easiest output layer is formed by one simple neuron which is trained to associate the presence of the concentration of specic gases to the winning neuron. In this case only the winning SOM unit has an output of 1, all other units have an output value of 0. The network output in this case is exactly the weight of the connection between winning SOM unit and output neuron. The number of output values in this case is limited to the number of SOM units. To produce also output for intermediate input values, two or more units can be used as described in [3]. In this case two units win and output is interpolated corresponding to its similarity to the input vector.

6 3.3 Recognition of simple gas The rst step was to learn one simple gas and to verify the results. This gas represented concentration jumps with increasing amplitude and was formed by 1200 input spectra. To see the quality of learning results, two methods are used. The clustering organisation is regarded and the concentration calculated by the output layer is compared with the real concentration Clustering of the map In the case of single gas the clustering was continuous as illustrated by gure 4. All of the 512 components have similar forms like this example component. Figure 4: Clustering result of rst spectral component. It can be noted that the network seems to preserve global relationship in data by projecting it onto the map. Neigboored PUs on the map represents similar gas concentration. Secondly concentration data was learned additionally as 513th component with spectral data. This component card shows where the dierent concentrations were learned (gure 5). Figure 5: Clustering of concentration-component. The vector position map in gure 6 shows that the 1200 learned input vectors are distributed nearly equally on the map. The whole map is used and dierent regions on the map respond to dierent concentrations of the gas. It is important to see that in the border area between zero and high gas concentration no input vector hits Recognition of concentration The network was trained with 125 concentration spectra of one gas and validated with a bigger set of 1200 vectors of spectral data of the same gas. These data are composed by

7 Figure 6: Number of winners per unit. by 50 concentration jumps with increasing amplitude as shown in gure 7. The answer of the network is shown in gure 8. Figure 7: Real gas concentration of sample date. Figure 8: Output for 32x32 network with 512 components. The network as described in chapter has learned spectral relation and is able to determine the gas concentration. In fact measuring error in the area with concentration lower than 0.2 are due to problems in gas mixture. Analytic methods show the same measuring errors. The next step was to reduce input and network size to minimize learning time. A network with 12x12 processing units and training steps turned out to be ecient without loss of precision. Also a reduction of input spectra components is quite interesting. Smaller input vectors reduce the learning parameters and the need of memory. The measuring error increases with decreasing number of components used for recognizing gas concentration. A reduction to less than 4 components can't deliver correct results, as described in chapter The network size has been reduced to 12x12 PUs with training steps and only 32 spectral components were learned. With this modications the learning time (Unix

8 Workstation) was reduced from 4 hours to about 2 minutes. Need of disk space and central memory for processor weights could be reduced from 4 MByte to 36 kbytes (gure 9). Figure 9: Output for 12x12 network with 32 components. 3.4 Multiple gases If concentration of known gases can be determined, the next step is to train the map with dierent gases and to recognize the type and the concentration of each gas. This is much more dicult as the characteristic eect of gases to membrane and interference spectra are not known. For simple gases, analytic methods and calibration of the membrane can be used to calculate concentration, but for multiple gases no deterministic method exists. The main problem is that every gas changes thickness as a main eect. The network must learn the characteristics of each gas and nd dierences between several gases. In the following example two gases (toluene and tetrachloroetene) are used and learning was done with 120 spectra of dierent concentrations of the rst gas and 120 spectra of the second gas Clustering of the map The clustering of the spectral components in this case is quite dierent. Some of the components begin to form two clusters (see gure 10) others are looking quite like the components shown in gure 4. Figure 10: Clustering result of one spectral component. The following gures show that the network is able to distinguish between the two gases. Figure 11 shows the area of recognition of the rst gas (toluene). As illustrated by gure 12 this region is completely separated from the area of recognition of the second gas (tetrachloroetene).

9 Figure 11: Clustering of rst gas. Figure 12: Clustering of second gas. Additionally learning of the gas concentration helps the network to come to separated clusters for the dierent gases more quickly. In the recognition period the concentration is not known and only the spectral components are used to calculate the winning element Recognition of gases The validation of network with another set of input vectors shows the learning results. The recognition of the rst gas (toluene) as well as the second gas (tetrachloroetene) is veried. As an example, gures 13 and 14 show the result. Figure 13: Real Output concentration of verication data. In 95.5 % the SOM recognizes the gas with an error of less than 5 %, in 2.4 % the wrong gas even if it was not presented during the measuring period. If the other gas is used for validation, 95.4 % of input is recognized with an error less than 5 %. For this example a network of 20x20 units was used with training steps.

10 3.5 Conclusions Figure 14: Output of network. This work showed the use of the SOM to evaluate interference spectra. The SOM turned out to be able not only to determine gas concentration, but also to distinguish between dierent gases. In the case of two gases, the concentration could be determined with a rate of 95%. The network turned out to be able to distinguish between dierent gases, next step will be to recognize gases in mixtures. Future extensions will be to test the use of Fourier Transformation for preprocessing. This transformation should make an input vector more distinctive and help the network to recognize characteristic patterns of dierent gases. Another objective is to study use of another output layer for increasing precision of the output value. The use of multiple winning elements of the SOM Layer and of completely dierent association architectures will be tested. 4 Using the self-organizing feature map for material classication 4.1 Theoretical background Traditional methods for quality control in the case of corrosion resistance of metals are often time consuming and not very reliable. These methods are restricted to principal investigations of new materials but not for a standardized quality control on a production line. For an online control optical methods are preferable, since they oer the possibility of fast and reliable measurements. In [6] it was shown that the corrosion properties of low carbon steel (car body steel) can be determined by diuse reectance spectroscopy. An optical on line system was developed to predict the corrosion tendency of car body steels [7]. The surface of a metal is always covered by a thin oxide lm. This lm contains all information which inuences the corrosion. The reectance spectrum is inuenced by the lm thickness, inhomogenities and distortions in the lm (e. g. number and size of corrosion pits on the surface) as well as the distribution of Fe(II)- or Fe(III)-ions within the lm. However, the nal spectrum consists of the superposition of these eects with dierent contributions of each factor. In previous studies it was shown, that a corrosion index can be calculated from the spectrum, which correlates with the corrosion under paint by r > 0:9 [7]. For a future more general and broader application of the spectral information it is necessary to extract the independent components of the spectrum [2]. 4.2 SOM To derive more detailed information about corrosion behaviour the spectral data are analysed by a SOM. The applied network and the details of the network are described in

11 Figure 15: Diuse reectance spectra of car body steel samples with dierent corrosion resistance Figure 16: Vector position map of low carbon steel samples characterized by their diuse reectance spectra. chapter 2. For this specic application the network is reduced to 25 x 25 PUs. The SOM is trained with a set of 81 dierent car body steel samples characterized by their diuse reectance spectra. The learning rate is iterations. The spectra consist of 512 data points. Preexaminations of the spectra using the component card showed that training the network with 26 data points in the 450 nm region as well as in the 650 nm region is sucient for a mapping of the samples in 5 clusters as shown in Figure 15 (spectra) and Figure 16 (vector position map). The data are also characterized by the traditional corrosion index [7, 8]. 4.3 Results Examples of spectra of low carbon steel (car body steel) measured by diuse reectance spectroscopy and detected by a diode array spectrometer are shown in gure 15 [8]. These examples represent 5 dierent corrosion tendencies. Spectrum (A) exemplies a low corrosion resistance with increasing corrosion resistance of the sample with spectrum (B), (C) and (D). Spectrum (E) typies as well a low corrosion resistance if calculated according to the methods as described in [8]. The clustering of the 81 steel samples by the neural network is shown in Figure 16.

12 Cluster (A) represents samples of the lowest corrosion resistance. Cluster (B) and (C) illustrate samples of higher corrosion resistance as compared to (A). Samples in cluster (D) show very high corrosion resistance and are therefore best quality steel. These results are comparable to results derived so far by the corrosion index. Samples in cluster (E) are dierently qualied by the neural net and by the corrosion index method. Samples in cluster (E) qualied by the corrosion index are attributed to a low corrosion resistance similar to samples of cluster (A). Classication by the neural net indicates a higher corrosion resistance comparable to samples in cluster (C) and (D). The true corrosion behaviour can only be obtained by eld tests of the corrosion under paint, which take at minimum 1 1/2 years. Short term characterization methods [7] tend to conrm the result obtained by the neural net. 4.4 Conclusion The results validate that a SOM can successfully be applied to the qualication of materials. It oers a tool for the classication of complex data like diuse reectance spectra of car body steel samples. The result of the net helps to dierentiate the individual samples to a higher degree. It also gives hints to optimize the optical set up of the spectroscopic sensor for a better discrimination of the independent factors. 5 Resume Kohonen's self organizing feature map is a good solution for evaluation of spectral data concerning the problems of exibility quality and perfomance. Spectral data can be recognized in real time by a learned SOM. The network validates noisy data. This is an important fact because every measurement for one gas concentration can vary in several parameters. Additionally we achieve a great reduction of data, which is important for ecient calculation and minimize the need of memory. Furthermore the gas sensors can be connected to a hardware implementation of Kohonen SOM, which has been develloped at \Lehrstuhl fur Technische Informatik, University of Tubingen" described in [12]. This would decrease the training time and increase the performance once more. References [1] A. Brecht, G. Gauglitz, und W. Nahm. Interferometric measurements used in chemical and biochemical sensors. Analusis, 20, [2] D. Ende, B. Quint, W. Kessler, D. Oelkrug, und R. Fuchs. Application of Factor Analysis for the Interpretation of Corrosion Results. Fresenius Z. Anal. Chem., [3] J. A. Freeman. Neural networks for machine vision applications: The spacecraft orientation demonstration. Ford Aerospace Technical Journal, Spring [4] J. A. Freeman und D. M. Skapura. Neural Networks Algorithms, Applications and Programming Techniques. Addison Wesley Publishing Company. [5] G. Gauglitz und W. Nahm. Observation of spectral interferences for the determination of volume and surface eects of thin lms. Fresenius Z. Anal. Chem., Seite 279 pp., [6] R. W. Kessler, E. Bottcher, R. Fullemann, und D. Oelkrug. In situ Characterization of Electrochemically-formed Oxide Films on Low Carbon Steel by Diuse Reectance Spectroscopy. Fresenius Z. Anal. Chem, Seite 695 pp., 1984.

13 [7] R. W. Kessler, M. Brogeler, M. Tubach, W. Degen, und W. Zwick. Determination of the Corrosion Behaviour of Car-body Steel by optical Methods. Werkstoe und Korrosion, Seite 539 pp., [8] R. W. Kessler, W. Degen, und W. Zwick. Optisches Verfahren zur online Kontrolle der Korrosionsneigung von Automobilfeinblechen. In Conference on Materials Testing, Bad Nauheim, Germany, Seite 329 pp., [9] T. Kohonen. Self-Organization and Associative Memory. Springer Verlag Heidelberg New York Tokyo, [10] T. Kohonen. The Neural Phonetic Typewriter. IEEE Computer, Seiten 11{22, March [11] G. Kraus und G. Gauglitz. Application and Comparison of Algorithms for the Evaluation of Interferograms. Fresenius Z. Anal. Chem., September [12] H. Speckmann, P. Thole, und W. Rosenstiel. Hardware Implementations of Kohonen's Selforganizing feature Map. In Proceedings of ICANN 92, Brighton, [13] V. Tryba, H. Speckmann, und K. Goser. A Digital Hardware-Implementation of a Self-Organizing Feature Map as a Neural Coprocessor to a Von-Neumann Computer. In Proceedings of the rst International Workshop on Microelectronics for Neural Networks, 1990.