the phenomenology of high explosive fireballs from … · the phenomenology of high explosive...

International Journal of High Speed Electronics and Systems Vol. 18, No. 1 (2008) 19–29 © World Scientific Publishing Company

THE PHENOMENOLOGY OF HIGH EXPLOSIVE FIREBALLS FROM FIELDED SPECTROSCOPIC AND IMAGING SENSORS FOR EVENT

CLASSIFICATION

KEVIN C. GROSS

Riverside Research Institute, 2681 Commons Blvd Beavercreek, Ohio 45431USA

[email protected]

GLEN P. PERRAM

Department of Engineering Physics, Air Force Institute of Technology, 2950 Hobson Way Wright-Patterson Air Force Base, Ohio 45433-7765 USA

[email protected]

Received (Day Month Year) Revised (Day Month Year)

Accepted (Day Month Year)

Conventional munitions emit intense radiation upon detonation which spans much of the electromagnetic spectrum. The phenomenology of time-resolved visible, near- and mid-IR spectra from these fast transient events is poorly understood. The observed spectrum is driven by many factors including the type, size and age of the chemical explosive, method of detonation, interaction with the environment, and the casing used to enclose the explosive. Midwave infrared emissions (1800–6000 cm-1, 1.67–5.56 μm) from a variety of conventional military munitions were collected with a Fourier transform spectrometer (16 cm-1, 21 Hz) to assess the possibility of event classification via remotely sensed spectra. Conventional munitions fireballs appear to be graybodies in the midwave. Modeling the spectra as a single-temperature Planckian (appropriately modified by atmospheric transmittance) provided key features for classification and substantially reduced the dimensionality of the data. The temperature cools from ~1800 K to ambient conditions in 3–5 s, often following an exponential decay with a rate near 1 s-1 second. A systematic, large residual spanning 2050–2250 cm-1 was consistently observed shortly after detonation and may be attributable to hot CO2 emission at the periphery of the fireball. For two different explosive types detonated under similar conditions, features based on the temperature, area and fit residuals could be used to distinguish between them. This paper will present the phenomenology of detonation fireballs and explore the utility of physics-based features for explosive classification.

Keywords: bomb phenomenology, detonation fireball spectra, Fourier-transform spectroscopy, classification, feature extraction.

1. Introduction

Most commercial remote sensing endeavors focus on the observation of gradual change (hours, days or months) to enhance meteorological predictions, understand climate change, and improve crop management. To effectively characterize the battle space, the military is often interested in dynamic events occurring on much shorter timescales, from

20 K. C. Gross & G. P. Perram

minutes to sub-seconds. Time-resolved infrared profiles collected from a variety of platforms have been studied for rocket plumes,1-4 missile and aircraft emissions,5-6 muzzle flashes,7-8 and to a limited extent detonation fireballs.9-14 The temporal response of band integrated intensity contains information useful in distinguishing broad classes of events. However, the munitions classification problem is particularly challenging for several reasons: (1) several factors complicate and decrease the reproducibility of detonation signatures, e.g. casing and mixture tolerances, detonation method, target interaction, and atmospheric conditions; (2) the variability in band-integrated temporal signatures within a munitions class is comparable to the variability between different classes; (3) the available data is sparse and spans multiple degrees-of-freedom with limited repetitions. To date, we are unaware of features derived from infrared temporal signatures being successfully used to discriminate between different explosives. Capturing spectral variations in the infrared may provide the information needed to distinguish one explosive type from another since absorption and emission features in this wavelength regime can often be associated with molecular species. However, the transient nature of detonation fireballs poses instrumentation challenges and trade-offs between temporal, spectral and spatial resolution common to hyperspectral platforms must be carefully considered. Moreover, extracting reproducible yet distinguishing features from time-resolved spectral data requires an understanding of the physics governing the infrared emission from high-explosives detonations. Although bomb detonation pressure waves15 and condensed matter detonation and shock kinetics are well studied,16-20 the conversion of reaction exothermicity to infrared and visible emissions is poorly documented. This research group is developing a phenomenological model for infrared emission from the detonation of high explosives to assist the munitions classification problem. We are also exploring the challenges associated with collecting time-resolved spectra of rapid infrared events via interferometry. To aid this effort, a collection of spectrometers, radiometers, and visible and infrared imagers have been deployed in several field tests to collect optical signatures from the detonation of conventional military munitions (CMMs), enhanced novel explosives, and improvised explosive devices. The model currently reproduces the CMM spectral and radiometric data with high fidelity, substantially reduces data dimensionality, provides key features for classification, and offers physical insight. Distilling the time-resolved hyperspectral data to a minimal collection of descriptive features enables pattern recognition techniques to be applied to the classification problem. The physical insight gained aids the discovery of key features that are reproducible for a munitions class and distinct from other munitions classes. This paper summarizes our spectral modeling of CMMs and the utility of derived features in discriminating two classes of ordnance.

2. Methodology

In the Fall of 1999, a set of field tests were conducted at Fallon Naval Air Station to study the optical infrared signatures arising from the detonation of conventional munitions. Three types of explosives (A, B and C) spanning several weights (extra small,

The Phenomenology of High Explosive Fireballs 21

small, medium, and large) were used for a total of 56 events. About half the events were air delivered by an F-18 aircraft and the rest were statically detonated on the ground. The detonation fireballs were observed using a Fourier-transform spectrometer (FTS) operating a 16 cm-1 resolution. Multiple spectra were collected for each event at a rate of 21 Hz. The FTS was equipped with an InSb (1800–6000 cm-1) and HgCdTe (500–6000 cm-1) detector for coverage of the mid-wave infrared (MWIR) spectrum. The background noise level for the InSb detector was about five times smaller than that of the HgCdTe detector. Calibration was performed with a blackbody at multiple temperatures resulting in data collected in intensity units (W/sr-cm-1). Absolute radiometry was verified with four 200 Hz radiometers, each with a different MWIR bandpass filter. The test range, Bravo 20, was a dry lakebed about 4000 ft above sea level. The geographical layout is detailed in Fig 1. Further details about the test setup and calibration procedure can be found in Orson’s thesis.13

Fig 1. Layout of the Radiant Brass set of field experiments conducted at the Bravo 20 test range, Fallon Naval Air Station, Nevada. An F-18 delivered munitions along three different approach vectors. Static detonations occurred at Clay Craters, Hard Sand and Rock/Rubble.

A simple phenomenological description of the fireball was developed to reduce the dimensionality of the data and extract features for classification. The observed fireball intensity Iobs was modeled by a Planckian distribution, modified by the transmittance of the atmosphere (τ), with temperature T and emissive area εA as the fit parameters, i.e.

2 3

/ ( )

2( , ) ( ) ( )1B

obs hc k T t

hcI t A te ν

νν τ ν ε=−

(1)


Since the Planckian source is a slowly-varying function of frequency, the sharp atmospheric absorption features in the observed data reveal information about the concentration of the absorbers. An iterative method based on the on-resonance off-resonance ratio of intensities at many absorption features was used to compute the concentration of atmospheric H2O, CO2, N2O, and CH4. This method does not require a model for the source intensity term and only assumes that its spectral variation with frequency is slow relative to most atmospheric absorption features. Accurate meteorological data was not available for the field test; however, reasonable agreement was found between the calculated H2O concentration and that reported by the nearest weather station. Experimental CO2, N2O and CH4 concentrations were not available, but calculated values were consistent with historical averages. Atmospheric transmission modeling was performed using the Line-by-Line Radiative-Transfer-Model.21

Fourier-transform spectroscopy is based on the Michelson interferometer and assumes the scene under analysis does not change appreciably during each mirror scan. Spectral resolution improves with total distance traveled by the mirror, but at the expense of temporal resolution. The transient nature of detonation fireballs requires that a judicious choice of spectral and temporal resolution be made to avoid corrupting the data with temporal aliasing artifacts. Assuming the Planckian fireball model above, we quantified the error associated with the Fourier transform of an interferogram acquired when the temperature decayed exponentially with a varying rate kT. The spectrum computed from an interferometer scanning at rate (ki) was compared to the true spectrum2 at zero-path difference and defined the temporal aliasing error E. The largest error at any frequency was computed for several values of ki/kT and is presented in Fig 2. As discussed below, the choice of 16 cm-1 resolution provided an acquisition rate of 21 Hz and minimized the effects of temporal aliasing.

A classification technique based on Fisher linear discrimination (FLD) was applied to features extracted from the phenomenological model just described. To illustrate how this method works, Fig 3 presents a scatter plot of two features (F2 versus F1) for several fictional events, each a member from one of three distinct classes (A, B and C). While neither feature alone provides ample separation between all three classes, a combination of these features can be found which clearly separates all classes. FLD finds the line in this feature space that maximizes between-class scatter and minimizes within-class scatter upon projection. The mean and standard deviation of each class projected onto this Fisher line can be used to define a probability distribution function (PDF). When projecting a new event onto the Fisher line, the PDF assigns a probability that it belongs to a particular class. Feature saliency and PDF stability are critical in assessing the confidence level associated with a prediction, and are thoroughly examined in Dills’dissertation.22


Fig 2. Maximum spectral error (E) attributed to temporal aliasing for an interferogram scanned at a rate ki that collects an atmospheric-attenuated Planckian source that changes in time according to an exponentially decaying temperature (kT).

Fig 3. Example data consisting of three classes (A, B & C) with two descriptors (F1 & F2) illustrates the Fisher linear discrimination technique. When the data is projected onto the Fisher line, between-class scatter (dashed arrows) is maximized and within-class scatter (solid arrows) is minimized. Gaussian curves for each class, defined by the mean and standard deviation upon projection onto the Fisher line, are also provided.


3. Results and Discussion

A typical fireball spectrum from the InSb detector is provided in Fig 4. In regions where the atmosphere is transparent, the spectra of detonation fireballs arising from both the airdropped and statically-detonated ordnance were fairly broadband in nature. Absorption from atmospheric gases such as H2O and CO2 is readily identified by characteristic spectral features. Modeling the observed spectra Iobs by a single-temperature Planckian distribution modified by the atmospheric transmittance profile accounted for most of the variation in the data. This fit is presented with the data in Fig 4 along with the residual ΔI (data minus the fit) at two different time steps. In the transmission bands (τ > 0.4), the average relative error is less than 5%. The small residuals indicate that the fireball is well-described by a single temperature and that our estimation of the atmospheric transmittance function was successful. However, a systematic underestimation of the intensity was observed near 2000–2200 cm-1 shortly after detonation and changes with time. The cause is currently being investigated and could be the result of emission from hot CO2 in the fireball. Accurate removal of the atmospheric effects is critical to interpret the fit residuals as non-Planckian behavior of the fireball. The time-dependent nature of the residual at 2152 cm-1 indicates that it is a feature of the dynamic fireball and not an artifact of incorrectly modeling atmospheric transmission.

Fig 4. Typical fit results for the static detonation of a small Type A bomb. In the top plot, the third spectrum after detonation (t = 0.14 s) is compared with the attenuation-modified Planckian fit. The difference between the observed data and model ΔI is shown at both t = 0.14 s (—) and t = 0.62 s (- - -) in the bottom plot.


Fitting the data to this simple phenomenological model affords a substantial dimensionality reduction while preserving most of the original fidelity. Each data matrix (intensity vs. frequency and time) is reduced to two vectors, namely temperature and area versus time. A representative example of the temperature and area curves are presented in Fig 5. The standard error in the area was about ten times greater than temperature, and is periodically displayed in Fig 5. Initial temperatures were 1700–2000 K and often followed an exponential decay with rates between 0.91–1.24 s-1. Examining Fig 2, we note that errors in the residuals due to temporal aliasing contribute less than 0.5% since the interferometer scanned at least 16 times faster than the temperature decay rate.

Fig 5. Temperature and area curves extracted from time-resolved spectra of statically-detonated Type A Small munitions. The periodic error bars reflect the standard error in the fit parameter.

Features based on these fit parameters and residuals can now be explored for their potential use in classifying munitions type. The most useful feature for graphically separating the events into their respective classes was the time dependent fit residual at 2152 cm-1. Figure 6a compares this feature for a set of Type A Small (AS) explosives with a set of Type B Large (BL) explosives. Both sets of munitions were air-delivered. The temperature and area curves provided a more subtle but still discernible separation between these two classes. A variety of features based on the temperature, area and fit residuals were subject to Fisher linear discrimination. The most salient features were consistently based on the fit residuals, i.e., the non-Planckian character of the fireball emissions. As an example, applying FLD to the AS, BL subset using three values taken from the 2152 cm-1 residual—the initial, maximal, and t = 0.5 s values of ΔI —indicates its utility to the classification problem. The PDFs shown in Fig 6b are well separated for the two classes. The limited number of repetitions available in the Radiant Brass field data makes assessing confidence in the PDFs’ predictive capability difficult. Dills’ work addresses this issue using bootstrapping and cross-validation techniques.14 It was found


that the initial and maximum values of ΔI were salient features, and were also useful indiscriminating static detonations from dynamic ones and identifying the explosive weight if the type was known.

Fig 6 (a) The temporal evolution of the fit residual at 2152 cm-1 of (⎯ ) air dropped Type A Small and ( ---) Type B large ordnance, (b) Probability density functions generated using FLD using three features taken from residual. namely the initial, maximal and t = 0.5 values of ΔI, with weights 0.522, 0.548, and 0.654, respectively.

4. Conclusions

Our efforts to collect, characterize, model, and derive classifiers from time-resolved infrared spectra of conventional explosives was summarized in this document. Detailed


accounts of this research can be found in the References and in several forthcoming publications. We now conclude with several important findings of these efforts. Fourier-transform spectroscopy can be used to study fast infrared events provided the selection of temporal resolution is commensurate with event timescales. For an exponentially cooling Planckian radiator, temporal aliasing of the spectra introduces a maximum error of less than 0.5% when the FTS scan rate is at least twice the temperature decay rate. Cased munitions are broadband across most of the MWIR and are well-described by a single-temperature Planckian distribution. A systematic underestimation of the observed intensity by the Planckian model is found between 2000–2200 cm-1 and is likely the result of hot CO2 emissions in the fireball. The phenomenological model provides high fidelity dimensionality reduction and offers several key, discriminating features. The time-dependent fit residual at 2152 cm-1 was the best feature for graphically separating two different explosive types, suggesting that the non-Planckian nature of detonation fireball is key to the classification problem. Accurately capturing the non-Planckian features by the fit residuals requires an accurate atmospheric transmission function. With even moderate spectral resolution (16 cm-1), the sharp absorption features in the MWIR due to atmospheric water and carbon dioxide can be used to estimate their respective concentrations assuming only that the source emission is broadband in nature. Inverting concentrations of other trace gases, namely N2O and CH4, is also possible. The substantial dimensionality reduction afforded by the current fireball model enables pattern-recognition methodologies to be applied to the classification problem. Probability density functions based on FLD were developed using non-Planckian fireball emission features and indicate strong classification potential. Additional field tests that both expand the diversity and number of repetitions will help define this potential and reduce the amount of a priori information needed to classify events. These pattern recognition techniques have also been applied to features derived from fireball imagery with promising results.10-11

A synergistic relationship exists between the modeling and classification efforts. The development of a reasonably accurate model is essential to uncovering good classifiers since the parameters offer physical interpretation and are more likely to capture real fireball characteristics. (Although dimensionality reduction is possible with an arbitrary parametric representation, the loss of feature interpretability is often accompanied by degraded classification potential.) On the other hand, the Fisher discrimination techniques unveil the most salient features and thereby guide our efforts in improving the model. We will soon include a CO2 emission term to directly model the non-Planckian behavior observed near 2150 cm-1. Physical models capable of explaining the temperature and area dynamics are also being developed, and the empirical model12 to describe time-resolved intensity curves seems well-suited to this problem. With these developments, a faithful representation of the spectral data cube will soon be expressed by a collection of 10-15 physically-interpretable fit parameters.


5. Acknowledgments

We gratefully acknowledge practical insight and constructive comments from Jim Engle and Randy Bostick. We thank Sean Miller, Tom Fitzgerald and their team for excellent work in test design and data collection under challenging field conditions.

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