Anal. Chem. 2003, 75, 2018-2026
Robust Classifier for the Automated Detection of Ammonia in Heated Plumes by Passive Fourier Transform Infrared Spectrometry Mukire J. Wabomba† and Gary W. Small*
Center for Intelligent Chemical Instrumentation, Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701
An automated classification algorithm is implemented for the detection of ammonia vapor in heated plumes by passive Fourier transform infrared (FT-IR) spectrometry. This classification methodology allows the real-time detection of chemical signatures in gaseous effluents such as those generated from industrial processes. The characteristics of real-time implementation and excellent robustness are achieved by an analysis strategy based on the application of band-pass digital filters to short segments of the interferogram data collected by the FT-IR spectrometer, followed by the use of piecewise linear discriminant analysis to obtain a yes/no classification regarding the presence of the analyte signature in the filtered data. The optimal classifier developed through this work is based on only 110 interferogram points and employs a single band-pass filter centered at 945 cm-1 with a pass-band full width at half-maximum of 93 cm-1. The average stopband attenuation of the optimal filter is 42.1 dB. The robustness of the algorithm is tested by exposing it to chemical releases of sulfur hexafluoride, ethanol, methanol, sulfur dioxide, and hydrogen chloride that were not included in the development of the classifier. Excellent classification performance is demonstrated, with missed ammonia detections occurring at a rate of ∼1%. The occurrence of false detections is less than 0.1% for SF6 and less than 0.02% for the other interferences tested. Passive Fourier transform infrared (FT-IR) spectrometry is being given increased attention for a variety of environmental monitoring applications.1-4 These applications include both airborne and ground-based measurements of heated effluent plumes from industrial stacks. Specific measurement scenarios include regulatory monitoring of pollutants and quality control/assurance of industrial processes. * To whom correspondence should be addressed. E-mail:
[email protected]. † Present address: Millennium Pharmaceuticals, Inc., 256 E. Grand Ave., South San Francisco, CA 94080. (1) Combs, R. J.; Kroutil, R. T.; Small, G. W. In Handbook of Vibrational Spectroscopy; Chalmers, J. M., Ed.; John Wiley & Sons Ltd.: Chichester, U.K., 2002; Vol. 4, pp 2842-2856. (2) Gruber, T. C.; Grim, L. B.; Ditillo, J. T. Proc. SPIE-Int. Soc. Opt. Eng. 1998, 3383, 2-22. (3) Harig, R.; Matz, G.; Rusch, P. Proc. SPIE-Int. Soc. Opt. Eng. 2002, 4574, 83-94. (4) Theriault, J.-M. Proc. SPIE-Int. Soc. Opt. Eng. 2001, 4168, 211-220.
2018 Analytical Chemistry, Vol. 75, No. 9, May 1, 2003
For the stack monitoring application, the passive infrared experiment employs an emission FT-IR spectrometer configured with telescope entrance optics that allow the acquisition of naturally occurring IR radiance within a small field of view (FOV). For a ground-based measurement, this allows the radiance from the region of the stack exit flue to be obtained. Hot gases exiting the stack will emit at their characteristic vibrational frequencies, and this radiance will be observed with excellent contrast against the cold background of the sky. Similarly, a downward-looking spectrometer mounted on an airborne platform can observe the radiance of the hot plume from above. In addition, the airborne measurement can observe the plume downwind from the stack as it absorbs ground radiance. In either ground-based or airborne implementations, the passive FT-IR experiment has the advantage of completely remote operation and no requirements for retroreflectors or other external optical components not included in the spectrometer package. In many of the monitoring scenarios that are applicable to passive FT-IR measurements, the need exists for automated data reduction and classification. For example, the occurrence of a particular chemical species in the effluent plume may signal a quality control problem in an industrial process. In this scenario, it is desired to monitor the stack emission continuously and to implement an automated classifier for detecting the IR signature of the target species. This automated monitoring task is made difficult by both the nature of the passive IR experiment and the complexity of the industrial environment. Because the passive measurement employs no controlled high-temperature IR source, the measured data are sensitive to even small changes in the background radiance. Changes in the IR background may arise from variation in meteorological conditions, changes in the temperature (and hence the self-emission) of the spectrometer components, or changes in the atmospheric composition within the FOV. The latter issue is particularly problematic in industrial settings where a variety of chemical effluents may be present. In the work reported here, a robust classification strategy is demonstrated for application to the automated detection of chemical signatures from passive FT-IR measurements of heated plumes. Through a combination of digital filtering and pattern recognition methodology, an automated classifier is developed for direct application to the interferogram data collected by the FTIR spectrometer. This approach is demonstrated for use in the 10.1021/ac026105x CCC: $25.00
© 2003 American Chemical Society Published on Web 04/02/2003
detection of controlled releases of heated plumes of ammonia from a portable emission stack. The classifier is then evaluated for its ability to operate correctly in the presence of other chemical species that were not included in the classifier development. EXPERIMENTAL SECTION Data used in this work were collected with a Midac passive FT-IR spectrometer (model M2401-SR, Unit 258, Midac Corp., Irvine, CA). The spectrometer was furnished with a narrow-band liquid nitrogen-cooled mercury cadmium telluride (MCT) detector operating over the 800-1200-cm-1 atmospheric transmission window. The ∼6° FOV of the instrument was limited to 0.3° by use of a 25.4-cm-aperture Newtonian telescope (Midac Corp.). The interferometer mirror velocity was 0.6576 ( 0.0004 cm/s. Interferograms (1024 points) were sampled at every eighth zero-crossing of the HeNe reference laser. The maximum digitized frequency was 1974.75 cm-1, and the transformed spectra had a nominal point spacing of 4 cm-1 (8-cm-1 resolution). Each collected interferogram was a single scan; i.e., no signal averaging was performed. Data acquisition was performed with an IBM/ PC-compatible computer and employed the MIDCOL software package.5 The scan rate was 4.3 interferograms/s. Heated plumes were generated from a 4.5-m portable stack with an exit diameter of 0.4 m (Aerosurvey, Inc., Manhattan, KS). Details regarding the design and operation of this stack have been presented previously.6 For the data reported here, the stack output temperatures ranged from 175 to 300 °C. The spectrometer monitored the atmosphere just above the stack exit flue from ground level at two locations with distances of between 311 and 334 m from the stack. These distances specified that the stack emission was viewed against a low-angle sky background. The data collection spanned four days in December. Within each day, data were collected in morning and afternoon sessions. Recorded minimum and maximum wind speeds at the release site for days 1-4 were 1.9-4.5, 0.4-2.0, 2.6-5.6, and 2.5-6.9 m/s, respectively. Recorded minimum and maximum air temperatures were -3.0 to 6.8, -1.0 to 8.6, 1.0 to 13.4, and 0.4 to 12.6 °C for days 1-4, respectively. Three categories of data were collected corresponding to (1) the release of chemical plumes, (2) various open-air background interferograms, and (3) interferograms collected with a blackbody source filling the FOV of the spectrometer. The open-air background interferograms included various sky, terrain, and horizon backgrounds. In addition, some interferograms were collected above the stack with only hot air or water vapor being released. The blackbody interferograms were collected with a 12 in. × 12 in. extended blackbody source (model 11-140M, Infrared Systems, Inc., Milford, CT). Temperature settings ranged from 10 to 100 °C at increments of 10 °C and with an accuracy of (3 °C. For the generation of the chemical plumes, anhydrous NH3 (99.99%, Matheson Gas Products, Joliet, IL), absolute ethanol (AAPER Alcohol and Chemical Co., Shelbyville, KY), methanol (AAPER Alcohol and Chemical Co.), sulfur hexafluoride (99.8%, Matheson Gas Products), sulfur dioxide (99.98%, Matheson Gas Products), and hydrogen chloride (99%, Matheson Gas Products) were released from the plume generator. The methodology for (5) Kroutil, R. T.; Housky, M.; Small, G. W. Spectroscopy 1994, 9, 41-47. (6) Chaffin, C. T., Jr.; Marshall, T. L. Proc. SPIE-Int. Soc. Opt. Eng. 1998, 3383, 113.
estimating plume concentrations was based on the use of gravimetrically calibrated flow tubes. This allowed the emission rate of each compound to be estimated for a given flow tube setting. Concentrations were subsequently computed by converting the emission rates to volume flow rates (assuming ideal gas behavior and complete vaporization of the liquids) and dividing by the volumetric air flow rate of the stack. Air flow rates were measured with a Pitot tube placed in the center of the stack. Path-averaged concentrations in ppm‚m were then obtained by estimating the optical path length of the plume as 0.4 m, the diameter of the stack. Table 1 summarizes the data collection conditions. For subsequent analysis, the interferograms were transferred to Silicon Graphics Indigo2 IMPACT 10000 workstations (Silicon Graphics, Inc., Mountain View, CA) operating under IRIX (version 6.5, Silicon Graphics, Inc.). All computations were performed on these systems with original software written in FORTRAN 77. Some calculations used subroutines from the IMSL library (IMSL, Inc., Houston, TX). Any single-beam spectra reported in this work were Fourier processed with triangular apodization and Mertz phase correction. RESULTS AND DISCUSSION Overview of Data Processing. Figure 1 plots the single-beam spectrum generated from an interferogram collected during an NH3 release (run 1 in Table 1). This plot illustrates the characteristic spectral features encountered when a heated plume is viewed against a low-angle sky background. The overall spectral profile incorporates the spectrum of the IR radiance within the FOV, the self-emission from the spectrometer, the responsivity of the optical system and detector, and the instrumental line shape. As indicated by the arrow, two prominent emission bands are superimposed on the spectral background. These bands correspond to the symmetric H-N-H deformation band of NH3 (ν2), observed as a doublet with peaks at 968 and 932 cm-1.7 The remaining small features in the spectrum arise from a complex pattern of emission and absorption bands produced by the contributions of atmospheric species (e.g., water vapor, ozone) viewed over a long path length. The rotational fine structure associated with the doublet NH3 emission band also contributes to this complex spectral pattern. The research described here focused on the development of a robust classification algorithm capable of implementing a continuous monitoring system for the presence of NH3 in the stack emission. As illustrated in Figure 1, the key to the development of such a classifier is the ability to extract the characteristic NH3 signature from the complex spectral background. As the NH3 concentration decreases, this becomes increasingly difficult. The methodology employed in this work was based on the application of signal processing and pattern recognition techniques directly to short segments of the interferogram data collected by the spectrometer. We have demonstrated this approach previously with data from heated plumes.8,9 This work extends the methodol(7) Herzberg, G. Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1945. (8) Koehler, F. W., IV; Small, G. W.; Combs, R. J.; Knapp, R. B.; Kroutil, R. T. Vib. Spectrosc. 2001, 27, 97-107. (9) Idwasi, P. O.; Small, G. W.; Combs, R. J.; Knapp, R. B.; Kroutil, R. T. Appl. Spectrosc. 2001, 55, 1544-1552.
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Table 1. Data Set Description stack temp (°C)
composition
1 1 1 2 2 3 4
202-206 173-175 n/aa 297-302 n/a 301-306 301-305
NH3 NH3 NH3 NH3 NH3 NH3 NH3
1 1 2 2 2 2 3 3 3 3 4 4
197-201
SF6 backgroundb SF6 ethanol ethanol backgroundb HCl methanol methanol backgroundb SO2 backgroundb
run
day
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 a
299-301 189-208 173-176 -202-204 197-203 174-178 301-310
concentration (ppm‚m)
training set
Analyte-Active Data 456-1519 898-1258 n/a 1042-1389 n/a 692-991 852-1036 Analyte-Inactive Data 303-316 294-297 739-3125 2061-2571 844-846 788-3172 788-3150 5796-6581
monitoring set
prediction set I
prediction set II
1282 530 432 1748 66 2291 1151
2670 571 429 1555 39 2962 1774
3986 409 322 1695 552 6342 10961
0 0 0 0 0 0 0
0 49 0 0 0 5920 0 0 0 8795 0 5436
0 18 0 0 0 3831 0 0 0 3657 0 5494
0 2528 0 0 0 1924 0 0 0 36075 0 41640
6391 0 5868 1788 5621 0 5067 6000 3638 0 18500 0
n/a, not available. b Includes blackbody and various open-air backgrounds.
Figure 1. Single-beam spectrum computed from an interferogram collected during a release of NH3 (estimated concentration 1517 ppm‚ m with stack temperature of 203 °C). The arrow indicates the H-N-H emission bands of NH3 superimposed on the infrared background radiance.
ogy by evaluating the robustness of the algorithm to the presence of chemical species not included in the development of the classifier. Direct use of the interferogram data to implement the classifier offers two advantages. First, this approach takes advantage of the inverse relationship between the width of the representation of a spectral band in the time and frequency domains. The spectral bands of target analytes such as NH3 are narrower than the broad spectral profile of the background radiance. There exists a location, tstart, in the interferogram displaced from the centerburst or point of zero path difference (ZPD) at which the narrow time domain representation of the broad spectral background has effectively damped to zero. For example, the broad background signature in Figure 1 has a full width at half-maximum (fwhm) of 2020 Analytical Chemistry, Vol. 75, No. 9, May 1, 2003
∼450 cm-1. At the sampling rate used in this work, the interferogram representation of a Gaussian-shaped band with fwhm of 450 cm-1 has damped to 0.0002% of its maximum value by point 30 (ZPD ) 1). Similarly, the interferogram representation of a Gaussian with fwhm of 5 cm-1 (analogous to the peaks in the NH3 doublet in Figure 1) retains greater than 99% of its maximum at point 30 and 88% of its maximum at point 140. Thus, restricting the analyis to a section of the interferogram located after tstart can effectively eliminate the background signal while retaining information about the narrower features. The second advantage of this strategy is realized if the ending point of the interferogram section, tend, can be selected such that the total segment length is short (e.g., 100 points). If a short interferogram segment is used for the analysis, the time required to collect each interferogram scan can be decreased significantly. This increase in scan speed can be especially valuable when the spectrometer is operated from a moving platform such as an aircraft. This approach also makes possible the use of specialized interferometer designs that could be adapted to collect only a short segment.10 While the information corresponding to broad spectral features has been significantly suppressed by the windowing step described above, the contributions of all the narrow spectral features remain in the selected interferogram segment. This is particularly problematic in applications such as the current work in which the analyte spectral band is very narrow and a sky background is used in which many narrow bands are present. In this case, selectivity for the target analyte can be enhanced by applying one or more band-pass digital filters to the interferogram segment to suppress frequencies outside of the region of the analyte vibrations. In this work, finite impulse response (FIR) digital filters with time-dependent coefficients were used. In previous work, a (10) Hariharan, P. Basics of Interferometry; Academic Press: San Diego, 1992; pp 15-23.
Figure 2. Frequency responses (attenuation in dB) of timedependent FIR filters positioned at 945 cm-1 and with pass-band fwhm values of 93 cm-1. The solid line (s) plots the frequency response for a filter whose average attenuation over the range of 200-700 cm-1 is 42.1 dB, while the dashed line (- - -) plots the corresponding trace for a filter with average attenuation of 23.9 dB.
design method was developed to tailor these filters specifically to interferogram data.11 In effect, a different set of filter coefficients is applied to each interferogram point. This time-dependent nature of the coefficients allows a favorable compromise to be made between the performance characteristics of the filters and the number of coefficients.11 The filters are applied by a convolution sum of the filter coefficients and interferogram intensities in a window that encompasses the point being filtered. The frequency responses of two such filters with different attenuation characteristics are shown in Figure 2. The pass-bands of both filters are centered at 945 cm-1, roughly at the midpoint between the two NH3 emission bands discussed above. For both filters, the fwhm of the pass-band is 93 cm-1. The attenuation of each filter is plotted in decibel units. The dB scale is logarithmic, with attenuation values of 20, 40, and 60 dB corresponding to 10-, 100-, and 1000-fold reductions in signal intensity, respectively. Over the range of 200-700 cm-1, the average stop-band attenuation values of the solid and dashed traces in Figure 2 are 42.1 and 23.9 dB, respectively. The more highly attenuating filter also has essentially zero attenuation in the pass-band, whereas the less attenuating filter has a pass-band attenuation of ∼6 dB. Figure 3 plots the product of each filter frequency response shown in Figure 2 (after conversion to transmittance units) with the single-beam spectrum displayed in Figure 1. These traces reflect the frequency content of the interferogram after application of each filter. The solid line shows the results obtained with the highly attenuating filter, while the dotted line corresponds to the filter with low attenuation. The filter with high attenuation passes significantly more signal through its pass-band while suppressing more signal in the stop-bands. The average numbers of coefficients required to implement the filters corresponding to the solid and dashed traces in Figure 2 are 115 and 38, respectively. For the two filters, these coefficients are applied to selected interferogram points in the windows of [-150, 50] and [-100, 0], respectively, where the point specifica(11) Small, G. W.; Harms, A. C.; Kroutil, R. T.; Ditillo, J. T.; Loerop, W. R. Anal. Chem. 1990, 62, 1769-1777.
Figure 3. Products of the filter frequency responses in Figure 2 (transmittance units) with the single-beam spectrum displayed in Figure 1. These traces reflect the frequency content of the interferogram after application of each filter. The solid and dotted lines correspond to the high- and low-attenuation filters, respectively.
tions are relative to the point being filtered. For example, 0 denotes the point being filtered and -100 indicates a location 100 points behind the point being filtered. In this designation, the interferogram is treated as a circular sequence in which the last point of the sequence (i.e., point 1024) is considered to be the point before point 1. For the coefficients used to filter a given interferogram point, the filter design method identifies which points within the window are statistically significant for use in implementing the convolution at that point.11 Improved attenuation is thus obtained at the cost of increased computational overhead (i.e., more multiplications and additions in the convolution sum) and the requirement for a longer interferogram segment. For example, applying the filter based on an average of 115 coefficients in the [-150, 50] window to a 100point interferogram segment requires a total segment length of 300 points (i.e., 150 points behind the first point of the segment and 50 points after the last point). By comparison, application of the [-100, 0] window to a 100-point segment requires a total segment length of only 200 points. While both cases represent significant reductions relative to the full interferogram length of 1024 points (factors of 3.4 and 5.1, respectively, for the [-150, 50] and [-100, 0] windows), there is clearly no benefit to using a longer segment than necessary. To address this issue, the impact of the filter pass-band position, width, and attenuation characteristics on the robustness of the NH3 classifier will be explored in this work. If the windowing and filtering steps are effective, interferograms containing the NH3 signature will be distinct. Stated differently, these interferograms will form a cluster in the n-dimensional data space defined by the n points of the filtered interferogram segment. Numerical pattern recognition methods can then be used to implement an automated classifier for detecting the NH3 signature in the filtered interferogram (pattern).12 In this work, piecewise linear discriminant analysis (PLDA) was used to implement the NH3 classifier.13,14 (12) Duda, R. O.; Hart, P. E. Pattern Classification and Scene Analysis; Wiley: New York, 1973. (13) Kaltenbach, T. F.; Small, G. W. Anal. Chem. 1991, 63, 936-944.
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The PLDA method constructs a piecewise linear boundary in the data space to separate two classes of data. In the application discussed here, the two classes correspond to those interferograms with and without the NH3 signature. These will be termed analyte-active and analyte-inactive patterns, respectively. The boundary is formed by the joint action of several linear discriminant functions. Together, they trace a piecewise linear approximation to a nonlinear classification boundary. A training set of data with known classification is used in conjunction with simplex optimization to position the discriminants.13,14 In placing the discriminant boundaries, a bias is introduced against false detections by assigning a large penalty to misclassified analyte-inactive patterns (i.e., patterns mistakenly judged to contain the analyte signature).14 After the discriminants are computed, a pattern with unknown classification can be evaluated by computing its distance to the separating boundary and the side of the boundary on which it lies. This information is encoded in a discriminant score, d. The magnitude of d specifies the distance to the nearest piecewise linear portion of the boundary, and the sign of d indicates its orientation relative to the boundary. In this work, positive values of d denote locations on the analyte-active side of the classification boundary. Implementing a continuous monitoring system thus involves the serial collection of interferogram data, followed by calculation of d as a function of time. Data Partitioning. As described above, development of the NH3 classifier requires a training set of data of known classification. In addition, separate test data must be available to evaluate the performance of the computed piecewise linear discriminant. To calculate accurate classification statistics, this performance evaluation also requires knowledge of the correct classification of the interferograms. Establishing the correct classification of each interferogram is complicated by the nature of the open-air experiments performed here. Even though a known amount of chemical is being released from the stack, there is no guarantee that the chemical plume will be in the small FOV of the spectrometer at a given time or that the chemical signature will be intense enough to be detected. For this reason, the correct classifications of the interferograms were established by visual inspection of the corresponding spectral data. Interferograms were Fourier processed to single-beam spectra, normalized to unit area, and a similarly processed background single-beam spectrum was subtracted. The background spectrum used corresponded to a FOV above the stack during the same data collection session but at a time when only hot air was being released. To establish the classification of each interferogram, the corresponding difference spectrum was inspected for the characteristic emission bands of the released compound (e.g., the H-N-H doublet of NH3 at 932 and 968 cm-1). If the presence of the compound signature was indeterminate, the interferogram was removed from further use because its true classification could not be established. This procedure had to be modified for the data acquired during the HCl releases because HCl has no bands within the 0-1974.75-cm-1 bandwidth used here. In this case, all interferograms acquired during the release were assigned to the HCl group.
Through this procedure, six pools of interferograms were assembled from data acquired during the chemical releases, corresponding to NH3, SF6, ethanol, methanol, SO2, and HCl. The interferograms corresponding to the various blackbody and openair backgrounds constituted a seventh pool. These data were subsequently organized into a training set and three test sets (termed the monitoring set and prediction sets I and II). The interferograms assigned to each of these sets are indicated in Table 1. Three replicate training sets were formed from data in the NH3 and blackbody/background pools only. No interferograms collected during the release of other compounds were used in training the classifier. The subset selection algorithm of Carpenter and Small15 was employed to select three sets of 2500 analyteactive patterns from the 41 747 interferograms in the NH3 pool. This selection procedure was applied to interferogram points 25136, where point 1 denotes the ZPD location. Similarly, three sets of 7500 blackbody/background interferograms were selected from the pool of 132 667 to form the analyte-inactive data class. Three training sets of 10 000 interferograms were thus assembled by pairing the individual sets of 2500 analyte-active and 7500 analyteinactive patterns. The monitoring set and prediction set I were formed in a similar manner from the remaining 34 247 and 110 167 interferograms in the NH3 and blackbody/background pools, respectively. The monitoring set contained 10 000 and 13 000 interferograms in the analyte-active and analyte-inactive classes, respectively. The remaining 24 247 and 97 167 interferograms in the NH3 and blackbody/background pools, respectively, formed prediction set I. Prediction set II was formed by simply combining the pools of 12 259 SF6, 16 409 ethanol, 9638 methanol, 18 500 SO2, and 5067 HCl interferograms. The monitoring set was used as a test set in the optimization of the interferogram segment and filter pass-band parameters. Prediction set I was withheld from all training and optimization studies and used subsequently to test the classifier with data similar in character to the training and monitoring sets. Prediction set II was used in a similar manner to test the robustness of the classifier to potential interferences not present during training or optimization. Characterization of Signal Strengths. A study was performed to characterize the signal strengths present in the collected data. This characterization was made on the basis of the spectral signalto-noise (S/N) ratio. For the interferograms in the NH3, SF6, ethanol, methanol, and SO2 pools, single-beam spectra were computed. Scaled difference spectra were then obtained as
(14) Shaffer, R. E.; Small, G. W. Chemom. Intell. Lab. Syst. 1996, 32, 95-109.
(15) Carpenter, S. E.; Small, G. W. Anal. Chim. Acta 1991, 249, 305-321.
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Di ) Is,i - (b0 + b1Ir,i)
(1)
where Di is the computed intensity difference at resolution element i, Is,i is the corresponding intensity in the sample single-beam spectrum, Ir,i is the intensity in a background single-beam spectrum collected over the stack when only air was being released, and b0 and b1 are obtained by a two-parameter linear least-squares fit of the sample and background spectra. In this calculation, the p points in the sample spectrum form the observations in the dependent variable and the corresponding p
Table 2. Spectral S/N Ratiosa S/N ratio compd
minimum
maximum
median
NH3b SF6 ethanol methanol SO2
5.7 9.4 5.4 11.4 111.8
1023.0 541.1 162.1 343.5 447.5
219.8 137.4 55.5 146.6 268.3
a Values reported correspond to the maximum S/N ratio in the 8001200-cm-1 range. b Results are presented for the pooled interferograms from the training set, monitoring set, and prediction set I.
points in the background spectrum comprise the independent variable for the regression. Use of the scaling parameters helps to correct for variability in the infrared background between the two spectra. The noise level in the difference spectrum, sd, was estimated as the standard deviation of Di over the range of 400-600 cm-1, a region outside of the detector response envelope. An estimate for the corresponding noise level in the sample spectrum, ss, can be obtained by applying the principles of error propagation to eq 1. If the errors in b0 and b1 are neglected and if the errors in Is and Ir are assumed to be equal, the following relationship is obtained.
ss ) xsd2/(1 + b12)
(2)
The S/N value was then computed as the ratio of the difference between the maximum and minimum Di over the region of 8001200 cm-1 to ss. Use of the range in Di as the signal estimate in the S/N calculation requires a good match between the background and sample spectra in terms of the FOV of the spectrometer and the meteorological conditions at the time of the data collection. In this regard, care was taken to select the best background spectrum available for the calculation. Table 2 lists the minimum, maximum, and median spectral S/N values for NH3, SF6, ethanol, methanol, and SO2 computed over the total pool of interferograms for each compound. These results indicate that the signal strengths span a representative range for each compound and are roughly equal for NH3, SF6, methanol, and SO2. The ethanol signals are somewhat smaller than the others. Figure 4 plots the scaled difference spectra corresponding to the median S/N values over the range of 800-1300 cm-1. The S-F stretching band of SF6 at ∼945 cm-1 (plot C) exhibits the greatest overlap with the NH3 spectrum (plot E). The methanol and ethanol C-O stretching bands near 1038 and 1066 cm-1, respectively, and the symmetric S-O stretch of SO2 near 1151 cm-1 do not overlap extensively with NH3 but may provide interference in situations in which the NH3 signal is low while that of the interfering species is high. Optimization of NH3 Classifier. Previous work in our laboratory has shown that the starting point of the interferogram segment, the filter pass-band width, and pass-band position are important optimization parameters that must be studied together.16 This previous study also determined that the interferogram
Figure 4. Scaled difference spectra computed by use of eq 1 and plotted over the range of 800-1300 cm-1: (A) 5796 ppm‚m SO2 with a stack temperature of 300 °C, (B) 2527 ppm‚m ethanol with a stack temperature of 173 °C, (C) 297 ppm‚m SF6 with a stack temperature of 301 °C, (D) 2010 ppm‚m methanol with a stack temperature of 198 °C, and (E) 743 ppm‚m NH3 with a stack temperature of 304 °C. These spectra correspond to the median spectral S/N ratios computed for the release of each compound.
segment length can be optimized independently. In the current work, an initial optimization was performed in which a full factorial experimental design was applied to eight segment starting positions (26, 50, 75, 100, 125, 150, 175, and 200, where ZPD ) 1), 10 levels of the filter pass-band position from 930 to 975 cm-1 in steps of 5 cm-1, and three levels of filter pass-band fwhm (104, 117, 131 cm-1). These filters had average stop-band attenuation values of ∼25 dB, computed over the range of 200-700 cm-1. The interferogram segment length was fixed at 100 points. Piecewise linear discriminants consisting of three individual discriminant functions were computed with each of the three replicate training sets. Subsequent evaluation of the discriminant performance revealed that no significant improvement was obtained with the second and third discriminant functions. For this reason, all results reported here were obtained with the first discriminant function only. The computed discriminants were tested by applying them to predict the classifications of the interferograms in the monitoring set. The average of the missed detection and false detection percentages obtained with the three replicate discriminants was used to select the best-performing combinations. The false (16) Shaffer, R. E.; Small, G. W.; Combs, R. J.; Knapp, R. B.; Kroutil, R. T. Chemom. Intell. Lab. Syst. 1995, 29, 89-108.
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Table 3. Performance of Low-Attenuation Filters filter width (cm-1)a stop-band attenuation (dB)b pass-band attenuation (dB)c average no. coefficients backgrounds false detection (%)d,e HCl false detection (%)d,f methanol false detection (%)d,f SO2 false detection (%)d,f
62 21.2 6.6 39 0.01 0.05 0 0
93g 23.9 5.6 38 0.04 0.03 0.33 0
104 23.0 5.5 35 0.03 0.09 0 0
117 25.0 6.2 33 0.02 0.05 0 0
131 22.8 5.4 32 0.03 0.02 0.02 0
a Width reported as the fwhm of the filter pass-band. b Attenuation reported as the average over the region of 200-700 cm-1. c Minimum attenuation in the filter pass-band. d False detection percentages are reported as the average over the three replicate discriminants. e Blackbody/background interferograms from prediction set I. f Interferograms in prediction set II derived from releases of potentially interfering compounds. g The frequency response of this filter is plotted as the dashed trace in Figure 2.
Table 4. Performance of High-Attenuation Filters filter width (cm-1)a stop-band attenuation (dB)b pass-band attenuation (dB)c average no. coefficients backgrounds false detection (%)d,e HCl false detection (%)d,f methanol false detection (%)d,f SO2 false detection (%)d,f
77 39.0 1.0 114 0.03 0.01 0 0.41
85 40.3 0.8 115 0.01 0.01 0 0
93g 42.1 0.6 115 0.02 0 0.01 0
100 44.1 0.4 114 0.05 0 0.01 0
108 46.2 0.3 113 0.02 0 0 0
a Width reported as the fwhm of the filter pass-band. b Attenuation reported as the average over the region of 200-700 cm-1. c Minimum attenuation in the filter pass-band. d False detection percentages are reported as the average over the three replicate discriminants. e Blackbody/background interferograms from prediction set I. f Interferograms in prediction set II derived from releases of potentially interfering compounds. g The frequency response of this filter is plotted as the solid trace in Figure 2.
detection percentage describes the occurrence of analyte-inactive patterns being classified as analyte-active. Similarly, the missed detection percentage describes the classification of analyte-active patterns as analyte-inactive. This optimization resulted in the selection of starting point 26 and a filter pass-band position of 945 cm-1. The filter width was not observed to affect the classification performance across the three levels studied. For the monitoring set, the best result obtained produced missed detection and false detection percentages of 1.07 and 0.01%, respectively. A study of segment length was performed next in conjunction with an expanded investigation of the filter width parameter and an evaluation of the effect of filter stop-band attenuation. Two sets of filters were designed corresponding to “low” and “high” attenuation. For the low- and high-attenuation filters, respectively, the top three lines in Tables 3 and 4 specify the fwhm of the passband, the average stop-band attenuation over 200-700 cm-1, and the average number of filter coefficients. The filter widths in the two groups are similar but not identical. An inspection of Tables 3 and 4 reveals that, on average, the cost of increasing the stopband attenuation by a factor of ∼6 (26 to 41 on the logarithmic dB scale) is a corresponding increase in the number of filter coefficients by a factor of ∼3 (35 to 114). The low-attenuation filters were investigated first. New discriminants were generated with each of the three training sets and all combinations of segment lengths of 100-150 points in 2024 Analytical Chemistry, Vol. 75, No. 9, May 1, 2003
Figure 5. Missed detection percentages for NH3-active interferograms in the training set (solid bars) and prediction set I (open bars) as a function of filter pass-band fwhm. Results are presented for (A) low- and (B) high-attenuation filters. Error bars are computed as the upper 95% confidence limits based on the classification results obtained with three replicate discriminants.
steps of 10 points and filter pass-band fwhm values of 62, 93, 104, 117, and 131 cm-1. The starting point and filter position were fixed at the previously determined values of 26 and 945 cm-1, respectively. The calculated discriminants were applied to the monitoring set, and the average of the missed detection and false detection percentages was computed. These results revealed that the best segment length was 110 points. For each of the five filters, the replicate discriminants based on 110 points were next applied to prediction sets I and II. The classification results will be considered separately for analyte-active and analyte-inactive interferograms. For the data in the first training set (solid bars) and prediction set I (open bars), Figure 5A plots the average missed detection percentages for the analyteactive interferograms across the five filter widths. Error bars are plotted as the upper 95% confidence limits computed from the results obtained with the three replicate discriminants. The general trend in Figure 5A is an improvement in the ammonia detection performance as the filter width increases, with the performance stabilizing when the pass-band fwhm reaches ∼100 cm-1. At this value, missed detections occur at a rate of less than 5% for both training and prediction data. Inspection of Figure 5A also reveals that the prediction results are consistently better than the training results. This can be explained on the basis of the spectral S/N ratios discussed previously. The median spectral S/N ratio for the 7500 analyteactive training interferograms is 142.3. The corresponding median
Figure 6. False detection percentages for interferograms collected during the release of ethanol (solid bars) and SF6 (open bars) as a function of filter pass-band fwhm. Results are presented for (A) lowand (B) high-attenuation filters. Error bars are computed as the upper 95% confidence limits based on the classification results obtained with three replicate discriminants. To improve the display, the large error bar in (A) (93 cm-1 fwhm) is truncated.
S/N ratio for the 24 247 analyte-active interferograms in prediction set I is 243.2. This increased signal is reflected in the lower rate of missed detections for the prediction data. The prediction results for the analyte-inactive interferograms can be divided into two groups corresponding to (1) negligible and (2) significant false detection rates. The negligible cases are summarized in Table 3. The blackbody/background interferograms in prediction set I produced false detection percentages of less than 0.05%, regardless of filter width. This is reasonable, given that the training set and prediction set I were designed to be consistent in terms of the experimental conditions. Similarly, the interferograms corresponding to the releases of HCl, methanol, and SO2 produced negligible rates of false detections. This can be rationalized by consideration of the difference spectra plotted in Figure 4. Very little spectral overlap exists between these compounds and ammonia. After application of the band-pass filter, these interferograms will have a spectral character similar to the blackbody/background interferograms in the training set. The interferograms acquired during the releases of SF6 and ethanol produced quite different results, however. Figure 6A plots the average false detection percentages for ethanol (solid bars) and SF6 (open bars). The error bars are again computed as the upper 95% confidence limits based on the results of the three replicate discriminants. It is clear from an inspection of the figure that the classifiers based on the low-attenuation filters are unable
to discriminate ethanol and SF6 from NH3 to an acceptable degree. The classifier based on the narrowest filter (pass-band fwhm ) 62) performs best, although the false detection rate for SF6 approaches 5%. As discussed previously, however, this filter is not optimal for detecting ammonia. Figure 6A shows that, overall, SF6 is more problematic than ethanol. This can be explained by inspection of the difference spectra in Figure 4. The SF6 band is much stronger in the median spectrum and is positioned between the two ammonia bands. Furthermore, the band location coincides almost exactly with the previously optimized filter pass-band position of 945 cm-1. The SF6 signal will thus pass through the filter. This band is also sufficiently narrow to possess an interferogram representation with a low rate of damping. The windowing step will thus not eliminate much of the SF6 signal. These results also illustrate a further difficulty in handling unknown interferences. The training set contained no interferograms collected during the SF6 releases. Thus, the optimization procedures had no knowledge of the potential SF6 interference. The optimal pass-band position for the NH3 detection coincided exactly with the SF6 band location. If the training set had included interferograms with SF6 signatures, a different filter pass-band would most likely have been chosen (e.g., moving the filter toward one or the other of the peaks in the NH3 doublet rather than a location between them). The high-attenuation filters described in Table 4 were investigated next based on the hypothesis that greater stop-band attenuation may improve the robustness of the classifier to the presence of unknown interferences. The same joint study of segment length and pass-band width described above was performed with these filters. A segment of length of 110 points was again judged to be optimal on the basis of the results obtained with the training and monitoring sets. As before, the classifiers based on the 110-point segment were then applied to prediction sets I and II. Figure 5B plots the missed detection percentages as a function of pass-band fwhm for the NH3-active interferograms in the first training set and prediction set I. Comparison of the results in Figure 5A and B reveals essentially equivalent performance between the high- and low-attenuation filters. As before, better performance is obtained with the wider filters and the performance is slightly improved with the data in prediction set I relative to the training data. False detection percentages for the blackbody/background interferograms in prediction set I and the HCl, methanol, and SO2 interferograms in prediction set II are reported in Table 4. As observed previously with the low-attenuation filters, very low rates of false detections are obtained for these groups of interferograms. Comparison of Tables 3 and 4 reveals essentially equivalent performance between the two sets of filters. Figure 6B plots the false detection percentages for the ethanol (solid bar) and SF6 (open bar) interferograms as a function of pass-band fwhm. The results displayed in this figure are greatly improved relative to those obtained with the low-attenuation filters (Figure 6A). The filter with pass-band fwhm of 93 cm-1 appears optimal. The classifiers based on this filter have few missed detections (∼1% for data in the prediction set) and exhibit a low rate of false detections (
