Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra

Ashwin P. Rao; Phillip R. Jenkins; John D. Auxier; Michael B. Shattan; Anil K. Patnaik

doi:10.1364/AO.444093

Applied Optics
Vol. 61,
Issue 7,
pp. D30-D38
(2022)
•https://doi.org/10.1364/AO.444093

Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra

Ashwin P. Rao, Phillip R. Jenkins, John D. Auxier, Michael B. Shattan, and Anil K. Patnaik

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Ashwin P. Rao, Phillip R. Jenkins, John D. Auxier, Michael B. Shattan, and Anil K. Patnaik, "Development of advanced machine learning models for analysis of plutonium surrogate optical emission spectra," Appl. Opt. 61, D30-D38 (2022)

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About this Article
History
- Original Manuscript: September 24, 2021
- Revised Manuscript: November 24, 2021
- Manuscript Accepted: December 20, 2021
- Published: January 20, 2022
Virtual Issues
Applied Optics Artificial Intelligence and Machine Learning in Optical Information Processing (2022)

Abstract

This work investigates and applies machine learning paradigms seldom seen in analytical spectroscopy for quantification of gallium in cerium matrices via processing of laser-plasma spectra. Ensemble regressions, support vector machine regressions, Gaussian kernel regressions, and artificial neural network techniques are trained and tested on cerium-gallium pellet spectra. A thorough hyperparameter optimization experiment is conducted initially to determine the best design features for each model. The optimized models are evaluated for sensitivity and precision using the limit of detection (LoD) and root mean-squared error of prediction (RMSEP) metrics, respectively. Gaussian kernel regression yields the superlative predictive model with an RMSEP of 0.33% and an LoD of 0.015% for quantification of Ga in a Ce matrix. This study concludes that these machine learning methods could yield robust prediction models for rapid quality control analysis of plutonium alloys.

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References

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Year
Author
Publication

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[Crossref]
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[Crossref]
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[Crossref]
J. Sirven, A. Pailloux, Y. Baye, N. Coulon, T. Alpettaz, and S. Gosse, “Towards the determination of the geographical origin of yellow cake samples by laser-induced breakdown spectroscopy and chemometrics,” J. Anal. At. Spectrom. 24, 451–459 (2009).
[Crossref]
M. B. Shattan, D. J. Miller, M. T. Cook, A. C. Stowe, J. D. Auxier, C. Parigger, and H. L. Hall, “Detection of uranyl fluoride and sand surface contamination on metal substrates by hand-held laser-induced breakdown spectroscopy,” Appl. Opt. 56, 9868–9875 (2017).
[Crossref]
B. Bhatt, K. Hudson Angeyo, and A. Dehayem-Kamadjeu, “LIBS development methodology for forensic nuclear materials analysis,” Anal. Methods 10, 791–798 (2018).
[Crossref]
J. Klus, P. Mikysek, D. Prochazka, P. Porizka, P. Prochazková, J. Novotny, T. Trojek, K. Novotný, M. Slobodník, and J. Kaiser, “Multivariate approach to the chemical mapping of uranium in sandstone-hosted uranium ores analyzed using double pulse laser-induced breakdown spectroscopy,” Spectrochim. Acta B 123, 143–149 (2016).
[Crossref]
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B. T. Manard, M. F. Schappert, E. M. Wylie, and G. E. McMath, “Investigation of handheld laser induced breakdown spectroscopy (HH LIBS) for the analysis of beryllium on swipe surfaces,” Anal. Methods 11, 752–759 (2019).
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E. Bellou, N. Gyftokostas, D. Stefas, O. Gazeli, and S. Couris, “Laser-induced breakdown spectroscopy assisted by machine learning for olive oils classification: the effect of the experimental parameters,” Spectrochim. Acta B 163, 105746 (2020).
[Crossref]
X. Li, Z. Wang, S.-L. Lui, Y. Fu, Z. Li, J. Liu, and W. Ni, “A partial least squares based spectrum normalization method for uncertainty reduction for laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta B 88, 180–185 (2013).
[Crossref]
T. Zhang, L. Liang, K. Wang, H. Tang, X. Yang, Y. Duan, and H. Li, “A novel approach for the quantitative analysis of multiple elements in steel based on laser-induced breakdown spectroscopy (LIBS) and random forest regression (RFR),” J. Anal. At. Spectrom. 29, 2323–2329 (2014).
[Crossref]
S. M. Clegg, E. Sklute, M. D. Dyar, J. E. Barefield, and R. C. Wiens, “Multivariate analysis of remote laser-induced breakdown spectroscopy spectra using partial least squares, principal component analysis, and related techniques,” Spectrochim. Acta B 64, 79–88 (2009).
[Crossref]
R. B. Anderson, J. F. Bell, R. C. Wiens, R. V. Morris, and S. M. Clegg, “Clustering and training set selection methods for improving the accuracy of quantitative laser induced breakdown spectroscopy,” Spectrochim. Acta B 70, 24–32 (2012).
[Crossref]
P. K. Tiwari, S. Awasthi, R. Kumar, R. K. Anand, P. K. Rai, and A. K. Rai, “Rapid analysis of pharmaceutical drugs using LIBS coupled with multivariate analysis,” Lasers Med. Sci. 33, 263–270 (2018).
[Crossref]
A. P. Rao, P. R. Jenkins, J. D. Auxier, and M. B. Shattan, “Comparison of machine learning techniques to optimize the analysis of plutonium surrogate material via a portable LIBS device,” J. Anal. At. Spectrom. 36, 399–406 (2021).
[Crossref]
E. D’Andrea, S. Pagnotta, E. Grifoni, G. Lorenzetti, S. Legnaioli, V. Palleschi, and B. Lazzerini, “An artificial neural network approach to laser-induced breakdown spectroscopy quantitative analysis,” Spectrochim. Acta B 99, 52–58 (2014).
[Crossref]
T. F. Boucher, M. V. Ozanne, M. L. Carmosino, M. D. Dyar, S. Mahadevan, E. A. Breves, K. H. Lepore, and S. M. Clegg, “A study of machine learning regression methods for major elemental analysis of rocks using laser-induced breakdown spectroscopy,” Spectrochim. Acta B 107, 1–10 (2015).
[Crossref]
J. El Haddad, M. Villot-Kadri, A. Ismael, G. Gallou, K. Michel, D. Bruyère, V. Laperche, L. Canioni, and B. Bousquet, “Artificial neural network for on-site quantitative analysis of soils using laser induced breakdown spectroscopy,” Spectrochim. Acta B 78–79, 51–57 (2013).
[Crossref]
E. C. Ferreira, D. M. Milori, E. J. Ferreira, R. M. Da Silva, and L. Martin-Neto, “Artificial neural network for Cu quantitative determination in soil using a portable laser induced breakdown spectroscopy system,” Spectrochim. Acta B 63, 1216–1220 (2008).
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[Crossref]
D. Syvilay, N. Wilkie-Chancellier, B. Trichereau, A. Texier, L. Martinez, S. Serfaty, and V. Detalle, “Evaluation of the standard normal variate method for laser-induced breakdown spectroscopy data treatment applied to the discrimination of painting layers,” Spectrochim. Acta B 114, 38–45 (2015).
[Crossref]
A. Ismaël, B. Bousquet, K. M.-L. Pierrès, G. Travaillé, L. Canioni, and S. Roy, “In situ semi-quantitative analysis of polluted soils by laser-induced breakdown spectroscopy (LIBS),” Appl. Spectrosc. 65, 467–473 (2011).
[Crossref]
P. Heraud, B. R. Wood, J. Beardall, and D. McNaughton, “Effects of pre-processing of Raman spectra on in vivo classification of nutrient status of microalgal cells,” J. Chemom. 20, 193–197 (2006).
[Crossref]
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[Crossref]
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[Crossref]
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[Crossref]
W. Mo, X. Luo, Y. Zhong, and W. Jiang, “Image recognition using convolutional neural network combined with ensemble learning algorithm,” J. Phys. Conf. Ser. 1237, 022026 (2019).
[Crossref]
H. Cho, Y. Kim, E. Lee, D. Choi, Y. Lee, and W. Rhee, “Basic enhancement strategies when using Bayesian optimization for hyperparameter tuning of deep neural networks,” IEEE Access 8, 52588–52608 (2020).
[Crossref]
J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” Adv. Neural Inf. Process. Syst. 25, 2960–2968 (2012).
J. Snoek, O. Rippel, K. Swersky, R. Kiros, N. Satish, N. Sundaram, M. Patwary, M. Prabhat, and R. Adams, “Scalable Bayesian optimization using deep neural networks,” in International Conference on Machine Learning (PMLR) (2015), pp. 2171–2180.
D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503–528 (1989).
[Crossref]
G. Long and J. Winefordner, “Limit of detection. A closer look at the IUPAC definition,” Anal. Chem. 55, 712A–724A (1983).
[Crossref]
A. Rao, “Rapid analysis of plutonium surrogate metal via hand-held laser induced breakdown spectroscopy,” Master’s thesis (Air Force Institute of Technology, 2020).

2021 (2)

A. P. Rao, P. R. Jenkins, D. M. Vu, J. D. Auxier, A. K. Patnaik, and M. B. Shattan, “Rapid quantitative analysis of trace elements in plutonium alloys using a handheld laser-induced breakdown spectroscopy (LIBS) device coupled with chemometrics and machine learning,” Anal. Methods 13, 3368–3378 (2021).
[Crossref]

A. P. Rao, P. R. Jenkins, J. D. Auxier, and M. B. Shattan, “Comparison of machine learning techniques to optimize the analysis of plutonium surrogate material via a portable LIBS device,” J. Anal. At. Spectrom. 36, 399–406 (2021).
[Crossref]

2020 (2)

E. Bellou, N. Gyftokostas, D. Stefas, O. Gazeli, and S. Couris, “Laser-induced breakdown spectroscopy assisted by machine learning for olive oils classification: the effect of the experimental parameters,” Spectrochim. Acta B 163, 105746 (2020).
[Crossref]

H. Cho, Y. Kim, E. Lee, D. Choi, Y. Lee, and W. Rhee, “Basic enhancement strategies when using Bayesian optimization for hyperparameter tuning of deep neural networks,” IEEE Access 8, 52588–52608 (2020).
[Crossref]

2019 (3)

B. T. Manard, M. F. Schappert, E. M. Wylie, and G. E. McMath, “Investigation of handheld laser induced breakdown spectroscopy (HH LIBS) for the analysis of beryllium on swipe surfaces,” Anal. Methods 11, 752–759 (2019).
[Crossref]

J. Guezenoc, A. Gallet-Budynek, and B. Bousquet, “Critical review and advices on spectral-based normalization methods for LIBS quantitative analysis,” Spectrochim. Acta B 160, 105688 (2019).
[Crossref]

W. Mo, X. Luo, Y. Zhong, and W. Jiang, “Image recognition using convolutional neural network combined with ensemble learning algorithm,” J. Phys. Conf. Ser. 1237, 022026 (2019).
[Crossref]

2018 (2)

P. K. Tiwari, S. Awasthi, R. Kumar, R. K. Anand, P. K. Rai, and A. K. Rai, “Rapid analysis of pharmaceutical drugs using LIBS coupled with multivariate analysis,” Lasers Med. Sci. 33, 263–270 (2018).
[Crossref]

B. Bhatt, K. Hudson Angeyo, and A. Dehayem-Kamadjeu, “LIBS development methodology for forensic nuclear materials analysis,” Anal. Methods 10, 791–798 (2018).
[Crossref]

2017 (1)

M. B. Shattan, D. J. Miller, M. T. Cook, A. C. Stowe, J. D. Auxier, C. Parigger, and H. L. Hall, “Detection of uranyl fluoride and sand surface contamination on metal substrates by hand-held laser-induced breakdown spectroscopy,” Appl. Opt. 56, 9868–9875 (2017).
[Crossref]

2016 (2)

J. Klus, P. Mikysek, D. Prochazka, P. Porizka, P. Prochazková, J. Novotny, T. Trojek, K. Novotný, M. Slobodník, and J. Kaiser, “Multivariate approach to the chemical mapping of uranium in sandstone-hosted uranium ores analyzed using double pulse laser-induced breakdown spectroscopy,” Spectrochim. Acta B 123, 143–149 (2016).
[Crossref]

Y. Guo, Y. Ni, and S. Kokot, “Evaluation of chemical components and properties of the jujube fruit using near infrared spectroscopy and chemometrics,” Spectrochim. Acta B 153, 79–86 (2016).
[Crossref]

2015 (3)

T. F. Boucher, M. V. Ozanne, M. L. Carmosino, M. D. Dyar, S. Mahadevan, E. A. Breves, K. H. Lepore, and S. M. Clegg, “A study of machine learning regression methods for major elemental analysis of rocks using laser-induced breakdown spectroscopy,” Spectrochim. Acta B 107, 1–10 (2015).
[Crossref]

D. Syvilay, N. Wilkie-Chancellier, B. Trichereau, A. Texier, L. Martinez, S. Serfaty, and V. Detalle, “Evaluation of the standard normal variate method for laser-induced breakdown spectroscopy data treatment applied to the discrimination of painting layers,” Spectrochim. Acta B 114, 38–45 (2015).
[Crossref]

P. Söderlind, F. Zhou, A. Landa, and J. Klepeis, “Phonon and magnetic structure in δ-plutonium from density-functional theory,” Sci. Rep. 5, 15958 (2015).
[Crossref]

2014 (2)

E. D’Andrea, S. Pagnotta, E. Grifoni, G. Lorenzetti, S. Legnaioli, V. Palleschi, and B. Lazzerini, “An artificial neural network approach to laser-induced breakdown spectroscopy quantitative analysis,” Spectrochim. Acta B 99, 52–58 (2014).
[Crossref]

T. Zhang, L. Liang, K. Wang, H. Tang, X. Yang, Y. Duan, and H. Li, “A novel approach for the quantitative analysis of multiple elements in steel based on laser-induced breakdown spectroscopy (LIBS) and random forest regression (RFR),” J. Anal. At. Spectrom. 29, 2323–2329 (2014).
[Crossref]

2013 (3)

X. Li, Z. Wang, S.-L. Lui, Y. Fu, Z. Li, J. Liu, and W. Ni, “A partial least squares based spectrum normalization method for uncertainty reduction for laser-induced breakdown spectroscopy measurements,” Spectrochim. Acta B 88, 180–185 (2013).
[Crossref]

I. James, E. Barefield, E. J. Judge, J. M. Berg, S. P. Willson, L. A. Le, and L. N. Lopez, “Analysis and spectral assignments of mixed actinide oxide samples using laser-induced breakdown spectroscopy (LIBS),” Appl. Spectrosc. 67, 433–440 (2013).
[Crossref]

J. El Haddad, M. Villot-Kadri, A. Ismael, G. Gallou, K. Michel, D. Bruyère, V. Laperche, L. Canioni, and B. Bousquet, “Artificial neural network for on-site quantitative analysis of soils using laser induced breakdown spectroscopy,” Spectrochim. Acta B 78–79, 51–57 (2013).
[Crossref]

2012 (4)

R. B. Anderson, J. F. Bell, R. C. Wiens, R. V. Morris, and S. M. Clegg, “Clustering and training set selection methods for improving the accuracy of quantitative laser induced breakdown spectroscopy,” Spectrochim. Acta B 70, 24–32 (2012).
[Crossref]

D. W. Hahn and N. Omenetto, “Laser-induced breakdown spectroscopy (LIBS), part II: review of instrumental and methodological approaches to material analysis and applications to different fields,” Appl. Spectrosc. 66, 347–419 (2012).
[Crossref]

Y. Kim, B. Han, H. S. Shin, H. D. Kim, E. C. Jung, J. H. Jung, and S. H. Na, “Determination of uranium concentration in an ore sample using laser-induced breakdown spectroscopy,” Spectrochim. Acta B 75, 190–193 (2012).
[Crossref]

J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” Adv. Neural Inf. Process. Syst. 25, 2960–2968 (2012).

2011 (1)

A. Ismaël, B. Bousquet, K. M.-L. Pierrès, G. Travaillé, L. Canioni, and S. Roy, “In situ semi-quantitative analysis of polluted soils by laser-induced breakdown spectroscopy (LIBS),” Appl. Spectrosc. 65, 467–473 (2011).
[Crossref]

2010 (2)

D. Hahn and N. Omenetto, “Laser-induced breakdown spectroscopy (LIBS), part I: review of basic diagnostics and plasma-particle interactions: still-challenging issues within the analytical plasma community,” Appl. Spectrosc. 64, 335–366 (2010).
[Crossref]

R. Chinni, D. A. Cremers, and R. Multari, “Analysis of material collected on swipes using laser-induced breakdown spectroscopy,” Appl. Opt. 49, C143–C152 (2010).
[Crossref]

2009 (2)

J. Sirven, A. Pailloux, Y. Baye, N. Coulon, T. Alpettaz, and S. Gosse, “Towards the determination of the geographical origin of yellow cake samples by laser-induced breakdown spectroscopy and chemometrics,” J. Anal. At. Spectrom. 24, 451–459 (2009).
[Crossref]

S. M. Clegg, E. Sklute, M. D. Dyar, J. E. Barefield, and R. C. Wiens, “Multivariate analysis of remote laser-induced breakdown spectroscopy spectra using partial least squares, principal component analysis, and related techniques,” Spectrochim. Acta B 64, 79–88 (2009).
[Crossref]

2008 (1)

E. C. Ferreira, D. M. Milori, E. J. Ferreira, R. M. Da Silva, and L. Martin-Neto, “Artificial neural network for Cu quantitative determination in soil using a portable laser induced breakdown spectroscopy system,” Spectrochim. Acta B 63, 1216–1220 (2008).
[Crossref]

2007 (1)

H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. Image Process. 16, 349–366 (2007).
[Crossref]

2006 (1)

P. Heraud, B. R. Wood, J. Beardall, and D. McNaughton, “Effects of pre-processing of Raman spectra on in vivo classification of nutrient status of microalgal cells,” J. Chemom. 20, 193–197 (2006).
[Crossref]

2005 (1)

G. Schulze, A. Jirasek, M. M. L. Yu, A. Lim, R. F. B. Turner, and M. W. Blades, “Investigation of selected baseline removal techniques as candidates for automated implementation,” Appl. Spectrosc. 59, 545–574 (2005).
[Crossref]

2003 (1)

S. S. Hecker, “Plutonium: coping with instability,” J. Miner. Metal Mater. Soc. 55, 13–19 (2003).
[Crossref]

2000 (1)

F. E. Gibbs, D. L. Olson, and W. Hutchinson, “Identification of a physical metallurgy surrogate for the plutonium–1 wt.% gallium alloy,” AIP Conf. Proc. 532, 98–101 (2000).
[Crossref]

1999 (1)

M. Steinzig and F. H. Harlow, “Characterization of cast metals with probability distribution functions,” MRS Proc. 538, 185–190 (1999).
[Crossref]

1998 (1)

R. Blundell and A. Duncan, “Kernel regression in empirical microeconomics,” J. Human Resour. 33, 62–87 (1998).
[Crossref]

1995 (1)

K. J. Cios and I. Shin, “Image recognition neural network: IRNN,” Neurocomputing 7, 159–185 (1995).
[Crossref]

1989 (1)

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503–528 (1989).
[Crossref]

1983 (1)

G. Long and J. Winefordner, “Limit of detection. A closer look at the IUPAC definition,” Anal. Chem. 55, 712A–724A (1983).
[Crossref]

Adams, R.

J. Snoek, O. Rippel, K. Swersky, R. Kiros, N. Satish, N. Sundaram, M. Patwary, M. Prabhat, and R. Adams, “Scalable Bayesian optimization using deep neural networks,” in International Conference on Machine Learning (PMLR) (2015), pp. 2171–2180.

Adams, R. P.

J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” Adv. Neural Inf. Process. Syst. 25, 2960–2968 (2012).

Alpettaz, T.

Anand, R. K.

Anderson, R. B.

Auxier, J.

A. Rao, J. Auxier, D. Vu, and M. Shattan, “Applications of portable LIBS for actinide analysis,” in Laser Applications to Chemical, Security and Environmental Analysis (2020), paper LM1A.2.

Auxier, J. D.

Awasthi, S.

Barefield, E.

Barefield, J. E.

Baye, Y.

Beardall, J.

Bell, J. F.

Bellou, E.

Berg, J. M.

Bhatt, B.

B. Bhatt, K. Hudson Angeyo, and A. Dehayem-Kamadjeu, “LIBS development methodology for forensic nuclear materials analysis,” Anal. Methods 10, 791–798 (2018).
[Crossref]

Blades, M. W.

Blundell, R.

R. Blundell and A. Duncan, “Kernel regression in empirical microeconomics,” J. Human Resour. 33, 62–87 (1998).
[Crossref]

Boucher, T. F.

Bousquet, B.

Breves, E. A.

Bruyère, D.

Canioni, L.

Carmosino, M. L.

Cherkassky, V.

V. Cherkassky, Predictive Learning (VCtextbook, 2013).

Chinni, R.

R. Chinni, D. A. Cremers, and R. Multari, “Analysis of material collected on swipes using laser-induced breakdown spectroscopy,” Appl. Opt. 49, C143–C152 (2010).
[Crossref]

Cho, H.

Choi, D.

Cios, K. J.

K. J. Cios and I. Shin, “Image recognition neural network: IRNN,” Neurocomputing 7, 159–185 (1995).
[Crossref]

Clark, D.

D. Clark, S. Hecker, G. Jarvinen, and M. Neu, Chemistry of the Actinide and Transactinide Elements (Springer, 2008).

Clegg, S. M.

Collins, L.

P. Torrione, L. Collins, and K. Morton, “5 - multivariate analysis, chemometrics, and machine learning in laser spectroscopy,” in Laser Spectroscopy for Sensing, M. Baudelet, ed. (Woodhead, 2014), pp. 125–164.

Cook, M. T.

Coulon, N.

Couris, S.

Cremers, D. A.

R. Chinni, D. A. Cremers, and R. Multari, “Analysis of material collected on swipes using laser-induced breakdown spectroscopy,” Appl. Opt. 49, C143–C152 (2010).
[Crossref]

D’Andrea, E.

Da Silva, R. M.

Dehayem-Kamadjeu, A.

B. Bhatt, K. Hudson Angeyo, and A. Dehayem-Kamadjeu, “LIBS development methodology for forensic nuclear materials analysis,” Anal. Methods 10, 791–798 (2018).
[Crossref]

Detalle, V.

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Adv. Neural Inf. Process. Syst. (1)

J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” Adv. Neural Inf. Process. Syst. 25, 2960–2968 (2012).

AIP Conf. Proc. (1)

F. E. Gibbs, D. L. Olson, and W. Hutchinson, “Identification of a physical metallurgy surrogate for the plutonium–1 wt.% gallium alloy,” AIP Conf. Proc. 532, 98–101 (2000).
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Anal. Chem. (1)

G. Long and J. Winefordner, “Limit of detection. A closer look at the IUPAC definition,” Anal. Chem. 55, 712A–724A (1983).
[Crossref]

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B. Bhatt, K. Hudson Angeyo, and A. Dehayem-Kamadjeu, “LIBS development methodology for forensic nuclear materials analysis,” Anal. Methods 10, 791–798 (2018).
[Crossref]

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Appl. Spectrosc. (5)

IEEE Access (1)

IEEE Trans. Image Process. (1)

H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. Image Process. 16, 349–366 (2007).
[Crossref]

J. Anal. At. Spectrom. (3)

J. Chemom. (1)

J. Human Resour. (1)

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J. Miner. Metal Mater. Soc. (1)

S. S. Hecker, “Plutonium: coping with instability,” J. Miner. Metal Mater. Soc. 55, 13–19 (2003).
[Crossref]

J. Phys. Conf. Ser. (1)

W. Mo, X. Luo, Y. Zhong, and W. Jiang, “Image recognition using convolutional neural network combined with ensemble learning algorithm,” J. Phys. Conf. Ser. 1237, 022026 (2019).
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Lasers Med. Sci. (1)

Math. Program. (1)

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503–528 (1989).
[Crossref]

MRS Proc. (1)

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[Crossref]

Neurocomputing (1)

K. J. Cios and I. Shin, “Image recognition neural network: IRNN,” Neurocomputing 7, 159–185 (1995).
[Crossref]

Sci. Rep. (1)

P. Söderlind, F. Zhou, A. Landa, and J. Klepeis, “Phonon and magnetic structure in δ-plutonium from density-functional theory,” Sci. Rep. 5, 15958 (2015).
[Crossref]

Spectrochim. Acta B (13)

Other (12)

S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice Hall, 1999).

A. Rao, “Rapid analysis of plutonium surrogate metal via hand-held laser induced breakdown spectroscopy,” Master’s thesis (Air Force Institute of Technology, 2020).

D. Larose and C. Larose, Data Mining and Predictive Analysis (Wiley, 2015).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

L. Rokach and O. Maimon, Data Mining with Decision Trees (World Scientific, 2007).

V. Cherkassky, Predictive Learning (VCtextbook, 2013).

S. Garca, J. Luengo, and F. Herrera, Data Preprocessing in Data Mining (Springer, 2015), Vol. 72.

D. Clark, S. Hecker, G. Jarvinen, and M. Neu, Chemistry of the Actinide and Transactinide Elements (Springer, 2008).

A. Rao, J. Auxier, D. Vu, and M. Shattan, “Applications of portable LIBS for actinide analysis,” in Laser Applications to Chemical, Security and Environmental Analysis (2020), paper LM1A.2.

S. S. Hecker, “From atoms to microstructure,” in Plutonium and Its Alloys (2000).

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fig. 1. Pellet press die and equipment used to create samples.

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Fig. 2. Experimental LIBS setup using Everbright 1064 nm Nd:YAG laser to induce ablations. Optical emissions were collected with an

$f = + {150}\;{\rm mm}$

lens and a collimator coupled to an optical fiber. This directed light to the spectrometer (Echelle) allowing the Andor camera (CCD) to record the spectra. Timing parameters for the laser and camera were set with the digital delay generator (DG).

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Fig. 3. Flowchart describing development of predictive ML models for spectral analysis implemented in this study.

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Fig. 4. Loading values of each wavelength in the spectra from principal component 1 (PC 1). The two wavelengths corresponding to the strongest Ga I emissions load the highest and therefore contribute to most of the total variance of the data.

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Fig. 5. Application of Savitzky–Golay and noise median filters to spectra, zoomed in on the Ga I 417.2 nm peak.

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Fig. 6. Comparison of bagging and boosting ensemble methods. Squares denoted by “S” and “M” represent data subsets and individual learner models trained on those subsets, respectively.

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Fig. 7. Illustration of the support vector regression method.

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Fig. 8. ANN architecture diagram; each circular node represents a single neuron, and each arrow represents the connection of the output of one neuron to the input of another.

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Fig. 9. Ensemble test regressions using (a) bagging and (b) boosting algorithms.

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Fig. 10. Test regressions of the (a) SVR, (b) GKR, and (c) ANN models.

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Tables (2)

Table 1. Hyperparameter Optimization Options for All Models

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Table 2. Regression Model Error and Sensitivity Results

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Equations (5)

Equations on this page are rendered with MathJax. Learn more.

I_{k}^{s n v} = \frac{I_{k} - μ_{I}}{σ_{I}}, \forall k .

{\hat{y}}_{s} = \frac{\sum_{i = 1}^{n} K_{h} (x_{s}, x_{i}) y_{i}}{\sum_{i = 1}^{n} K_{h} (x_{s}, x_{i})} .

K_{h} (x_{s}, x_{i}) = \exp (- \frac{‖ x_{s} - x_{i} ‖^{2}}{h}) .

R M S E P = \sqrt{\frac{\sum_{i}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}{n}},

L o D = \frac{3 σ_{a}}{b} .

Model	Hyperparameters	Range	Tuned Value
Bagging	Min. leaf size	1–144	10
Bagging	Num. learning cycles	10–500	495
Boost	Max. num. splits	1–100	34
	Num. learning cycles	10–500	180
	Learning rate	0.001–1	0.095
SVR	Kernel function	Linear; Gaussian; polynomial	Linear
	Slack ( $ξ$ )	0.001–1000	200.2
	Bandwidth ( $h$ )	0.001–1000	454.7
	Error ( $ϵ$ )	1.48e-3–148	0.362
GKR	Bandwidth ( $h$ )	0.001–1000	51.14
	Regularization ( $λ$ )	4.99e-7–0.499	1.72e-5
	Error ( $ϵ$ )	1.48e-3–148	1.51e-3
ANN	Layer size	Narrow; medium; wide; bilayer; trilayer	Trilayer
	Number of neurons	2–50	[20;10;10]
	Activation function	ReLU; sigmoid, tanh	Sigmoid
	Iteration limit	1e2–1e4	1000
	Regularization ( $λ$ )	4.99e-7–0.499	4.96e-5

Model	Bagging	Boost	SVR	GKR	ANN
RMSEP	0.394%	0.422%	0.611%	0.329%	0.399%
LoD	0.025%	0.256%	0.098%	0.015%	0.017%

Model	Hyperparameters	Range	Tuned Value
Bagging	Min. leaf size	1–144	10
Bagging	Num. learning cycles	10–500	495
Boost	Max. num. splits	1–100	34
	Num. learning cycles	10–500	180
	Learning rate	0.001–1	0.095
SVR	Kernel function	Linear; Gaussian; polynomial	Linear
	Slack ( $ξ$ )	0.001–1000	200.2
	Bandwidth ( $h$ )	0.001–1000	454.7
	Error ( $ϵ$ )	1.48e-3–148	0.362
GKR	Bandwidth ( $h$ )	0.001–1000	51.14
	Regularization ( $λ$ )	4.99e-7–0.499	1.72e-5
	Error ( $ϵ$ )	1.48e-3–148	1.51e-3
ANN	Layer size	Narrow; medium; wide; bilayer; trilayer	Trilayer
	Number of neurons	2–50	[20;10;10]
	Activation function	ReLU; sigmoid, tanh	Sigmoid
	Iteration limit	1e2–1e4	1000
	Regularization ( $λ$ )	4.99e-7–0.499	4.96e-5

Model	Bagging	Boost	SVR	GKR	ANN
RMSEP	0.394%	0.422%	0.611%	0.329%	0.399%
LoD	0.025%	0.256%	0.098%	0.015%	0.017%