For a certain short interval of a TG scan, the correlation between mass and time is linear. A smoothing and filtering routine based on use of linear regression and error analysis was developed and successfully applied in the TG data processing. This method provides a filter to smooth the noise fluctuations and, at the same time, to introduce no distortions into the TGA experimental data. The computer program required is quite simple and effective. The method used in the program promises auto-convergence

Calkins, W. H.

Huang, He

Klein, M. T.

Wang, Keyu

Wang, Shaojie

UNT Digital Library

* APPENDIX 7 UNIVERSITY OF DELAWARE PAPERS (Presented at the 211th National Meeting of the American Chemical Society, March 24-28, 1996, New Orleans, LA) . .  H u U  -W,ang, K.: Wang, S .; .KMR;-$dFE.~E%tkirrs;-W. H. 'm- Y Thermogravimetry" Wang, K; Wang, S.; Huang, H; Klein, M. T.; Catkins, W. H. "A Novel Smoothing Routine for the Data Processing in Thermogravimetric Analysis. Huang, H.; Wang, K.; Wang, S.; K l e i n ~ ~ ~ ~ ~ C ~ ~ ~ ~ n ~ W ~ ~ : ~ ~ p ~ l i ~ t i o n s  of the Thermogravimetric Ana #&pfT%TS- A7- 1 DISCLAIMER This report was prepared as an account of work sporrsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal tiabili- ty or responsibility for the accuracy, completeness, or usefulness of any information, appa- ram product, or process disdosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, madktum, or otherwise does not necessarily mnsth& or imply its end-ent, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not neetsar- ily state or reflect those of the United States Government or any agency thereof. Portions of this document may be illegible in electronic image products. Images are produced from the best available original document, A NOVEL SMOOTHING ROLTINE FOR THE DATA PROCESSING IN THERMOGRAVIMETRIC ANALYSIS Keyu Wang. Shaojie Wang. He Huang. ,M. T Klein and W H. Calkins' Dept ot' Chemical Engineering, University of Delaware. Newark. DE 19716 Key words: smoothing, differentiation. thermogravimetric anaIysis INTRODL'CTION Thermogravimetric (TG) techniques have been used in characterizing fossil hels (1- 4) and in studying coal liquefaction kinetics, mechanisms. and processes (5 .6 ) .  The TG techniques have been providing sensitive. rapid, and reproducible measurements for those purposes. The primary Output of thermogravimetric analysis (TGX) is in the form of a three- column matrix of time. remperanrre, and mass (or mass%). The first derivative of the TG i i .2.  DTG) is capable of revealing fine details of the processes occurring more clearly for sample characterization (2.7) and/or as an  input variable for further analysis. for example. in the SimDis (Simulated Distillation) TG technique (8). There always is a limitation on the sensitivity of the TGA instrument. This is particularly true for those analyses run at either very low heating rates or veri slow DTG decay experiments. where small changes in mass occur. Therefore, smoothing and filtering of these large data sets to obtain noise-free DTG curves are crucial in those TGA applications. Several methods have k e n  developed for smoothing and differentiation of experimental data (9-15). The objective of this paper is to present a novel and specific method for smoothing and differentiation of thermogravimetric data. The principle of the method is based on the characteristics of the TG data (e.& time vs. mass). Linear regression and error analysis are used in the smoothing and filtering routine. The computer program required is simple and effective. The method used in the program promises auto- convergence. The reported technique in this paper could also be applied to other analytical instrumentation. EXPEIUhIENTAL The thermogravimetric analyzer (TGA) was a Model 51 TGA (TA Instruments, New Castle, Delaware). The program of manipulation of the TG variables, such as heating rate, type of purge gas and its flow rate, and final (or step) temperature. was determined by the objectives of the particular experiment. The output matrix of a TG scan ( K i m ,  temperature, mass) was recorded by computer. The digitized data were then transferred into DOS (ASCII) format using a program provided by TA Instruments. The ASCII format data were loaded into MATLAB (The Mathworks, Inc.) and processed using a MATLAB routine. METHOD OF ShfOOTHNG ATID DIFFERENTIATION The Generat Problem. The random errors which, regardless of their source, are characterized as noise are always present in the TGA measurements. This background noise reduces signal-to-noise ratio, resulting in decreasing sensitivity. This is particularly true when the DTG is the objective result of a TG scan. Figures 1 and 2 show the DTG plots for TG scans run at a very low heating rate (1"Cimin) and a very slow DTG decay, respectively. These DTG plots were obtained from numerical differentiation of the original TG data. As shown in Figures 1 and 2, it is necessary for the investigator to remove the noise as much as possible without, at the same time, distorting the experimental data. especially for those processes where small changes in mass occur. Smoothing and filtering of these thermogravimetric data to obtain the noise-free differentiation (DTG curve), therefore, are required in the TGA applications. The Characteristics of the TG Data (time vs. mass). A TG curve of the Illinois #6 coal at a heating rate of 1 "C:min in 100 cm'(STP)imin nitrogen is shown in Figure 3.  Thirty one data points of (t,w) taken from Figure 3 are ploaed in Figure 4. The plqt shows 3 very zood linearity between the mass and time. In general. this is always true for a certain shofl time interval of a TG scan. It is this characteristic that is used to develop a method for smoothing and differentiation of the TG data. Snioothing and Differentiation by Linear Regression and Error Analysis. One of the simplest ways to smooth fluctuating data is by a n-point (n=2k+ 1; k= 1.2.3 .... Moving average procedure. In this method. a fixed odd number (2k+ 1) of data points are taken to obtain the average for the center point. (k+l)th point, of the group. To move on. the first point in the group is dropped, the next point at the end of the group added. and the process is repeated. In statistics. noises in the data file are not filtered by this simple average procedure. 27 Consider a group of n (for example, n = 11) points of (1. m) taken from a TG file and plotted in Figure 5 .  Based on the characteristics of the TG data discussed in the previous section, a linear regression can be performed in this group by m = a + b x r  (9 and represented by the solid line in Figure 5. The obtained linear regression parameters (i.e..a and b) can be used to estimate the m (mass) at each f (time) in the group. The errors (e) between the linear regression (m,,, (i)) and experimental data (mexp,(i)) in the group are defined as The statistical parameters of the errors for this group, e.g. mean (e,.) and standard derivation (esld) of the errors. are calculated by: E-" di) e- = - (e.g. n = 11) ,=I  n (3) To eliminate the noise from this group, standard deviation of the errors can be used as a criterion to define the filter range. This is plotted as dashed-lines in Figure 5 .  In detail, if the experimental data point locates outside the filter range, i.e. e, > e&. it is considered as 3 noise in the group. To filter this noisy point, it is replaced by an estimated value of q J i >  using the linear regression. This filter procedure can be used- on each point in the group and a new data set can be formed. This new data set is plotted in Figure 6. The points with "x"in Figure 6 represent the filtered data. Linear regression can be again carried out in this new data group, followed with upgraded error analysis and filtering process. The linear regression, error analysis and the filter procedure are repeated until the standard deviation of the errors is below a predetermined value of ertd. 0. In this smdy, a relative standard deviation of the errors, re,, rather than ea, has been used for evaluating the calculations. This relative standard deviation of the errors is defmed as e, times the absolute value of the slope (DTG) of the linear regression, Le., red = awb)  x ed (4) This relative standard deviation of the errors used as a criterion to evaluate calculations can insure the precision of very slow process (i.e., very low DTG scan). It has been found that The final regression results are used to estimate the smoothed mass and differentiation for the center point of tcr+,,. Le.. set at io5 gives very satisfactory results. mi., = a + b x ti+] (5) Since the standard deviation of the errors constantly decreases with iterations, the computation method used in the program promises auto-convergence. For a TG analysis. the n-point smoothing, filtering and differentiation routine has been moved in the data file similarly as the moving average method which has been described earlier. A scheme of the computation routine is illustrated in Figure 7. For the "end-points" (i.e..either the initial or the final k points in the data file), a different method has to be used to evaluate them. One of the simplest ways to handle this "end-points" problem is to rhrow them away. since these end-points usually are not important or not of interest. In this srudy, the end-points have been simply assigned by their original values. If the "end-points" become important, a much more sophisticated method developed by Leach et at. (10) could be used. APPLICATIONS SimDis TGA. A SimDis TGA method for determining the boiling point distribution of liquid fuels is reponed elsewhere (8). Original DTG plot for a petroleum sample,light paraffinic vacuum distillate,is shown in Figure 2. To transfer the DTG decay into boiling point distribution. it is necessary to smooth the noisy DTG data. The results of n = 0- (ix. ,  original). 3-. 5-.  7-. 9-, and 11-point smoothing and filtering are illustrated in Figure 8. The 28 more the data points used for smoothing and filtering. the smoother the DTG curve. However. at the same time. the more CPU or the longer computing time are required. More importantly. a large data number n used in smoothing increases the risk of distorting the experimental data. Eleven-point smoothing and filtering has been found to give the optimized results for the cases studied thus far. Figures 9a and 9b show the comparison plot (i.e.,  a plot including both smoothed results and original experimental data) and I 1-point smoothing plot, respectively. The results indicate the smoothing and filtering method used in this study is very effective. Characterization of coal structure. A representative TG scan on the Argonne Premium Illinois #6 bituminous coal, which was dried in a vacuum oven with a nitrogen purge at 105 "Cfor 18 hours before use, is shown in Figure 10. The two phases. i.e.. 1) the heating rate to 950°C in nitrogen and hold for 7 min; and 2 )  the oxidation at 950°C. provided measures of VM. FC. and Ash. respectively. The differential of the weight loss (DTG) curve highlights the various TG processes more clearly. This becomes even more distinct and zompiex if the heating rate is slowed down to about 1 ' C h i n  (3. However. the original DTG plot for this low heating rate shown in Figure I is so noisy that the processes involved in the TG scan could not be distinguished. The comparison plot and the 1 1-point smoothing results for this low heating rate scan are shown in Figures 113 and I Ib. respectively. The processes involved in the TG pyrolysis of the coal at this low heating rate. as shown in Figure I lb .  are very clearly distinguished. The low temperature peak represents the loss of residual moisture below 200 "C. The main Volatile Matter peak starts at 350-400 "Cand actually consists of three or perhaps four individual weight loss processes. The large peak is broad and probably consists of a number of pyrolysis processes. The well defined peak at 571 "Cis tentatively identified as due to pyrite decomposition to pyrrhotite and sulfur because this peak is absent in coals containing little or no pyrite. Also. the decomposition temperature corresponds closely to that reported for pyrite (16). Two other small peaks are not yet identified but are fairly broad. They disappear gradually during coal liquefaction (5).  With this smoothing and filtered method. the sole function of the computation is to act as a filter to smmth the noise fluctuations and hopefully to introduce no distortions into the experimental data. The problem of distortion is quite difficult to assess. In Figures 1 and 2. there are small fluctuations in the raw data. Are these fluctuations real. or, as is more likely, are they just noise? The question can not be simply answered by raking just the data from a single run. However. if two or k e  NIIS were taken, they gave the same results or, more characteristically, in same patterns. These indicated that the fluctuations are due to the noise, since the random errors will not recur in the same place in different runs. The results of duplicate tests on all samples inspected in this study suggest that the fluctuations are truly due to noise. CONCLUSION For a certain short interval of a TG scan. the correlation between the mass and time is linear. A smoothing and filtering routine based on the use of linear regression and error analysis has been developed and successfully applied in the thermogravimemc data processing. This method provides a filter to smooth the noise fluctuations and. at the same time, to introduce no distortions into the TGA experimental data. The computer program required is quite simple and effective. The method used in the program promises auto- convergence. - ACKNOWLEDGEMENTS The support of this work by the subcontract from CONSOL under DOE Contract DE-AC22-94PC93054 and by the Department of Energy under DE22-93PC93205 is acknowledged. Additional funds for purchase of thermal analysis equipment was provided by the University of Delaware. REFERENCES 1. Ottaway, M. FUEL. 1982.61.713. 2. He Huang, Keyu Wang. M.T. Klein, and W.H. Calkins ACS Fuel Chem Div Preprinrs 40 (3). 465 (1995). 3. He Huang, Keyu Wang, W.H. Calkins and M.T. Klein ACS Fuel Chem Div Preprints 4. He Huang. W.H. Calkins and M.T. Klein f&EC Research 33. 2272-2279 (1994). 5. He Huang, Keyu Wang. M.T. Klein, and W.H. Calkins ACS Fuel Chem Div Preprints40 (3 ) .  550 (1995). 6. He Huang. Keyu Wang. M.T. Klein, and W.H. Calkins Coal Science and Technology 24: Coal Science. Eds J.A. Pajares and J.M.D. Tascon, Vol. 11, p. 1207 (1995). 7. He Huang. D.M. Bodily, and V.J. Huch  Proceedings I993 Inrernarional Conference 39 (3). 741 - 746 (1994). 29 8.  9. 10. 11. 12. 13. 14. 15. 16. on cool science pp 411-414. He HWK, Kcyu Wang. M.T. Klein. and W.H. Calkins ACS Fuel Chem Div Preprinrs 40 (3). 485 (1995). Whitaker, S.:Pigford, R.L. Ind. Eng. Chem. 52, 185 (1960). Leach, R.A.; Caner, C.A.;Har~is. J.M. AM^. Chem. 56, pp. 2304-2307 (1984) Baedecker, P.A.  AM^. Chem. 57, pp. 1477-1479 (1985) Khan. A. Anal. Chem. 60, pp. 369-371 (1988) Guest, P.G. Numerical Merho& of Curve Fining University Press, Cambridge, England (1961). Hamming R.W. Numerical Methodc for Sciemisrs and Engineers McGraw-Hill Book Co..  New York (1962). Ralston. A. A Firsr Course in Numerical Analysis McGraw-Hill Book Co., New York (1965). Luganov. V.A.; Schebalin. V.I. Can. Merall. Q. 1982.21. 157. ;-i " I a a a a d ..'-*I 3 I 30 muping n (n=Zk+I) dur poinu using thc moving m c W  Liacu tcgreuion of Using the cst i lcd  v a l u  N O  Figure 7 Flow-sheet of the n-point smoothing and tiliming procedure " UI ..* : i  ' f  E Figure 8 The results of n a 0-. 3-. 5-. 7-. 9-. 1 I-point smoothing and filteriog 31 7- - h- e.¶ Figwe 9 Viudiution of n-point m t h i i n g  and Filtering of the DTG at very slow heating rate shown in Figure 1: a). comparison plot; b). 1 I-point smoothing and filtering plot -2.0 W -  Boo- - - $ '  -$.a g e m -  ; \ \ \ 7-0- ; I -0 . l  3 \ \ \ . -- 5 1" L '  r 4- L / \ri: --- 0.0 M- / / 11.94s 0 4  / I--0.1 2Q 4 €4 80 1W 120 I40 71. 1.1") Figure IO A TG scan of Illinois H6 coal at 10 Umin m- Figure I I Visualization of n-point smoothing and fiItcnng of the DTG decay shown in Figure 2: a). comparison plot; b). 11-point smoothing and filtering plot 32 

A novel smoothing routine for the data processing in thermogravimetric analysis

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A novel smoothing routine for the data processing in thermogravimetric analysis

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