Machine Learning for Real-time Diagnostics of
Cold Atmospheric Plasma Sources
Dogan Gidon, Xuekai Pei, Angelo D. Bonzanini, David B. Graves, Member, IEEE, and Ali Mesbah, Senior
Abstract—Real-time diagnostics of cold atmospheric plasma
(CAP) sources can be challenging due to the requirement for
expensive equipment and complicated analysis. Data analytics
that rely on machine learning methods can help address this
challenge. In this work, we demonstrate the application of several
machine learning methods for real-time diagnosis of CAPs using
information-rich optical emission spectra and electro-acoustic
emission. We show that data analytics based on machine learning
can provide a simple and effective means for estimation of
operation-relevant parameters such as rotational and vibrational
temperature and substrate characteristic in real time. Our
ﬁndings indicate a great potential promise for machine learning
for real-time diagnostics of CAPs.
Index Terms—Cold atmospheric plasma, real-time diagnostics,
optical emission spectrum, electro-acousitc signal, machine learn-
ing, linear regression, k-means clustering, Gaussian process.
COld atmospheric plasma (CAP) sources are exceedingly
used for medical applications –. However, CAP
sources can suffer from unmonitored variabilities in operation.
For example, atmospheric pressure plasma jets (APPJs) exhibit
long timescale drifts , sharp gradients in temperature and
species concentrations , and high sensitivity to disturbances
such as ambient humidity and substrate impedance , .
Mode transitions are also frequently observed in CAP sources,
e.g., streamer-to-spark transitions in corona-like air discharges
. Such variabilities pose a signiﬁcant challenge to CAP
research and applications, particularly where plasma interacts
with other complex systems, as in plasma medicine ,
. Thus, monitoring variabilities in plasma characteristics
in real time can be especially useful for both understand-
ing and minimizing irreproducible plasma effects. Real-time
diagnostics can allow detection of abnormal or undesirable
operating conditions and drifts in key plasma characteristics.
Furthermore, real-time plasma diagnostics are indispensable
for advanced process control in order to (partly) mitigate
variabilities of CAP sources and improve their operational
reliability , .
Direct quantitative diagnostics of CAP sources pose a
considerable challenge. Methods such as laser-induced ﬂuo-
rescence (LIF) , mass spectrometry , and spontaneous
Raman scattering , for example, rely on sophisticated
instrumentation and specially designed experimental setups.
This is in stark contrast with the current practice of CAP
Department of Chemical and Biomolecular Engineering, University of
California, Berkeley, CA 94720 USA.
Corresponding author: email@example.com
operation in plasma medicine that relies on the ﬂexibility of
hand-held treatment in the absence of plasma diagnostics .
Spectral information from various sources such as optical and
electro-acoustic emission can be used for plasma diagnostics.
Emission signals are often easy to acquire and typically
contain a wealth of implicit information about the plasma
characteristics , . However, this information is often
indirect and requires computationally expensive analysis to ex-
tract physical quantities such as gas and electron temperatures
or reactive species concentrations . This can make the use
of spectral information for real-time diagnostics impractical.
Investigation of spectral information for real-time diag-
nostics of CAP sources has received some attention in the
literature. Most notably, O’Connor et al. reported on a mul-
tivariate method based on principle component analysis for
correlating various optical emission spectrum (OES) peaks to
electrical properties and electron density for a dielectric barrier
discharge in helium . In contrast to the well-established
method of analyzing OES by generating and ﬁtting synthetic
spectra to measurements , , these authors note the
potential for developing correlations across large data sets for
Electro-acoustic emission also contains useful informa-
tion on plasma characteristics. Diagnostics based on electro-
acoustic emission is commonly used in high-temperature ma-
terials processing applications such as arc welding  and
plasma anodizing . Law et al. investigated the application
of electro-acoustic emission for process monitoring and con-
trol in a DC pulse-modulated APPJ in air . These authors
point to the usefulness of spectrally-resolved electro-acoustic
emission as a diagnostic tool for various plasma characteristics
including surface properties, dissipated power, and separation
distance between jet nozzle and substrate. O’Connor et al.
investigated the electro-acoustic emission of a non-thermal
helium plasma jet for process monitoring . They utilize
wavelet transforms of electro-acoustic emission for detection
of ﬂow modes and anomalies in operation such as sparking
In addition, the voltage-current signal is easily available in
most plasma setups. Utilization of these signals for diagnostics
has been investigated by Walsh et al. in the context of mode
behavior of a non-thermal kHz-excited APPJ in helium .
These authors demonstrate that phase-space representations of
current signals can help distinguish between the three identi-
ﬁed modes, although later work by Liu and Kong indicates the
detection of mode behavior may be more complicated in the
presence of humidity . In , Law et al. review potential
application of electro-acoustic emission and current signals for
real-time diagnostics and process control.
Data analytics can present an alternative to the commonly
used purely physics-based approaches for extracting informa-
tion from spectra. With the increasing size of available data
sets, automated algorithms for discovering patterns in data,
broadly referred to as Machine Learning (ML) methods, have
found success as data analytics tools , . Some notable
applications of ML for data analytics, among many others,
include gene discovery , remote sensing , meaning
and sentiment analysis of text , , object recognition in
images , as well as real-time diagnostics and modeling of
low-pressure plasma etch processes –. The availability
of easy-to-use software packages such as the open source
package scikit-learn  and Google’s Tensor Flow 
has made ML methods more accessible, contributing to their
In this paper, we demonstrate the potential of data analytics
for real-time diagnostics of CAP sources. Through use of
ML methods, physical quantities, which are otherwise difﬁcult
to obtain in real-time due to limitations of instrumentation
(e.g., optical setup required for LIF) or time required for
analysis (e.g., ﬁtting OES spectra), can be inferred by utilizing
the raw spectral information. We present three case studies
demonstrating the application of data analytics tools for real-
time CAP diagnostics: (i) determination of rotational and
vibrational temperature from OES; (ii) discrimination between
a conductive and an insulating substrate from OES; and
(iii) determination of discharge gap distance from electro-
acoustic emission. In the rest of the paper, we ﬁrst present an
overview of selected machine learning methods, then describe
the utilized experimental setup, and ﬁnally present results
pertaining to each of the three investigated cases.
II. MAC HI NE LEARNING ME TH OD S
In this section, we review the ML methods used in this work
(see, e.g., , , ,  for a detailed description).
The selection of a suitable ML method relies on two
principal considerations related to the output data: (i) whether
the output variables are continuous or discrete, and (ii) whether
they are used for training a model. When a ML method uses
the output data for training, it is known as supervised learning,
where the goal is to predict continuous (e.g., regression) or
discrete (e.g., classiﬁcation) output variables. On the other
hand, unsupervised learning only uses the input data to dis-
cover patterns in the data. For example, clustering methods
are used to separate data into discrete bins.
Data sets used for ML consist of inputs denoted by X∈
RN×nand, where applicable, outputs denoted by Y∈ RN×m.
Here, nand mare the dimensions of the inputs and outputs,
respectively, and Nis the number of samples in the data
set. We denote one sample of inputs by x∈ Rnand one
sample of outputs by y∈ Rm. We further denote predictions
of a ML model by ˆ
Y∈ RN×mand a single instance of
prediction by ˆy ∈ Rm. Data are typically divided into training,
validation, and test sets. In general, the majority of the data
set (50-90%) is used for training and validation . During
training, mathematical descriptions of the relationships among
the data are inferred. Training typically involves a parametric
or non-parametric ﬁtting process. In order to systematically
assess the quality of inferences made by an ML model, a
validation procedure is employed. A common approach is
k-fold cross-validation procedure in which the training data
are partitioned into kcomplementary training and validation
subsets or folds . k−1of the subsets are used for training
and the remaining subset is used for validation. To overcome
the inherent randomness of arbitrarily partitioning a data set,
this process is systematically repeated for different partitioned
sets . Furthermore, ML models often have some hyper-
parameters, whose values cannot be directly estimated from
data and thus are ﬁxed prior to training. The models are
often trained using different values of hyperparameters and
subsequently the appropriate values are selected based on the
model performance in the validation step. Finally, in the testing
stage, the capability of the ML model is assessed against an
independent data set. In this work, the performance of the
ML model is quantiﬁed in terms of some error metrics such
as root mean squared error (RMSE) and error fraction when
the output variables are continuous and discrete, respectively.
These error metrics are deﬁned as
Y) = 1
Error Fraction(Y, ˆ
Y) = 1
In expression (2), the indicator function 1takes the value 1
when the condition ˆ
yi6=yiis met and 0 otherwise.
In Section IV, we explore the use of supervised methods
for determination of rotational and vibrational temperatures
(linear regression) and discharge gap distance (Gaussian pro-
cess regression), and unsupervised learning for discrimination
between glass and metal substrates (k-means clustering). An
overview of the adopted ML methods is presented in the
remainder of this section.
A. Linear Regression
Linear regression is widely used in statistical analysis .
In linear regression, output variables are described by a linear
combination of some (nonlinear) function of the inputs .
For a scalar output, a regression model can be written as
where w= [w1, . . . , wO]is the vector of weights, xis the
vector of inputs, and φj(x)denotes basis functions. Note that
expression (3) readily generalizes to higher output dimensions.
A common choice for the basis functions, which is utilized in
this work, is powers of the inputs deﬁned as
φj(x) = xj.(4)
In this case, O, the highest order of the polynomial basis
functions in (4), comprises the order of the regression model.
We treat Oas a hyperparameter.
In linear regression, the weights ware determined by
solving a least-squares minimization problem. A key challenge
in regression is over-ﬁtting. In particular, when a large model
order Oin (3) is selected, a large number of weights should be
ﬁtted. This can lead to a regression model that describes the
data too closely, even describing the random noise in the data.
To avoid over ﬁtting, regularized least-squares estimation is
commonly used. Here, we utilize the least absolute shrinkage
and selection operator (LASSO) method, where the regression
problem for a scalar output is expressed as 
with αbeing the regularization hyperparameter. In classic
linear regression, αis set to 0, leaving only the ﬁrst term in
the least squares problem (5). The selection of αgoverns what
is known as the bias-variance tradeoff . An excessively
large value of αgives rise to under-ﬁtting of the data, therefore
leading to predictions with a large bias and a small variance.
On the other hand, excessively small values of αcause over-
ﬁtting of the data, yielding predictions with small bias but high
variance, since the regression model also captures the noise of
the data . In this work, we select the appropriate value of
αduring the validation step, as described in Section IV-A.
The RMSE metric (1) provides a measure of the average
error between true values and predictions; however, this metric
is not sufﬁciently sensitive to noise in the measurement. We
therefore also use the R2score, which indicates the capability
of the regression model in capturing the variability in the
output variables. The R2score is deﬁned by
R2= 1 −
where Nis the total number of samples, ˆyis computed from
(3), yiis the ith measured sample of the scalar output y, and
yis the mean of the true values of the scalar output
B. k-Means Clustering
k-means clustering is an unsupervised ML method used
to separate data into kdistinct groups or clusters . The
clusters are characterized in terms of their center points or
centroids. In k-means clustering, the centroids of the clusters
are initialized at random points and the distance between each
input in a cluster to the corresponding centroid is evaluated
in terms of some distance metric such as the Euclidean norm.
The clusters are then iteratively updated and input clustering
is reﬁned by minimizing the sum of distances between the
centroids and the inputs in each cluster. k-means clustering
relies on the minimization problem
where Siis the set corresponding to the ith cluster, S∈ Rn
is the set of sets Si, and µi∈ Rndenotes the centroid of
the cluster i. The user-deﬁned hyperparameter in k-means
clustering is the value of k. The choice of kcan depend
on some prior knowledge of data, or can rely on heuristics.
In the case study presented in Section IV-B, we utilize prior
knowledge of data for selection of k.
Note that since k-means clustering is an unsupervised
learning method it does not predict clusters of new samples
. Nevertheless, new samples can be assigned to a cluster
either by pre-computing the relevant groups and dividing the
space into regions, or by retraining the k-means clustering
model when new data becomes available.
C. Gaussian Process Regression
Gaussian process (GP) regression is a non-parametric super-
vised ML method that relies on a probabilistic interpretation
of the data . In GP regression models, the outputs are
assumed to have a joint Gaussian distribution . Thus,
the GP regression problem is formulated as estimation of the
probability distribution of the predicted variables conditional
on the training data. The joint prior probability distribution of
the outputs is expressed as
Y∼ N 0,Σ,(9)
where Nrepresents a Gaussian distribution with mean 0and
covariance matrix Σ. Without loss of generality, the mean of
the joint distribution can be assumed to be zero. Even if the
outputs are distributed around some non-zero mean, this value
can be subtracted from the joint distribution to satisfy the zero-
mean assumption. The covariance matrix Σis deﬁned by
Σ = K K∗
where K,K∗, and K∗∗ denote the individual covariance
matrices corresponding to combinations of training and test
data sets: K=K(Xtrain, Xtrain ),K∗=K(Xtrain, Xtest ), and
K∗∗ =K(Xtest, Xtest ). The covariance matrices Kcan be
deﬁned in terms of a positive deﬁnite kernel function:
K(x,x0) = −λexp 1
where xand x0are inputs pairs belonging to appropriate
data sets, and σand λare the model hyperparameters. The
kernel function Kdescribes a measure of distance or similarity
between the input pairs. Given the prior Gaussian distribution
(9), the goal in GP regression is to predict the posterior
distribution of the test data conditional on the training data.
Then, the expected value Eand covariance ˆ
Σof this posterior
distribution are extracted using standard formulas for condi-
tioning of multivariate Gaussian distributions, based on Bayes’
Y|Y, Xtrain , Xtest) = K∗K−1Y, (12)
Y|Y, Xtrain , Xtest) = K∗∗ −K∗K−1K∗.(13)
Expressions (12) and (13) fully deﬁne the distribution of
outputs predicted by GP.
A key difference between GP and linear regression is that a
GP model does not have a parametric functional form. Instead,
GP explicitly uses the provided training data when making
predictions. The hyperparameters of the kernel function (11)
can be obtained a priori, for example, by maximizing the log
marginal likelihood function with respect to the hyperparame-
ters . The non-parametric nature of GP is advantageous in
predicting arbitrarily nonlinear behaviors. Another important
feature of GP regression is that it predicts a variance associated
with the expected value of the prediction, which provides
conﬁdence bounds on the model predictions.
III. EXP ER IM EN TAL MET HO DS
We utilize two different CAP sources to demonstrate the
applicability of ML to different types of discharges; a kHz-
range APPJ in helium and the “Plasma Flashlight” , a
hand-held corona-like discharge in air. The kHz-range APPJ
has the advantage of being a very stable discharge with easily-
obtainable OES spectra. On the other hand, the corona-like
discharge produces clearly audible electro-acoustic emission.
The schematic representations of the two setups are pre-
sented in Figure 1. The speciﬁcations of the APPJ (Figure
1a) are similar to those presented in ; a quartz tube
(ID= 3 mm and OD= 4 mm) serves the dual purpose of ﬂow
channel and dielectric barrier. Plasma is ignited by applying a
sinusoidal voltage at a frequency of 20 kHz on a copper ring
electrode wrapped around the tube. An aluminum plate at a
ﬁxed distance of 4mm from the tube nozzle acts as ground
and, as the conductive substrate. A borosilicate microscope
cover slip is placed under the APPJ to be used as the dielectric
substrate. The corona-like discharge (Figure 1b) is identical
to the Plasma Flashlight device reported in . The device
consists of a needle-type electrode situated in a plastic nozzle.
The plasma is ignited by DC voltage ampliﬁed by booster
circuit and exhibits self-pulsing behavior.
Fitting accurate ML models generally requires large
amounts of data which are both labor and time intensive
to collect manually. Therefore, automation of the data ac-
quisition and processing is a key requirement for effective
implementation of ML strategies. To this end, both setups
are equipped with automated data acquisition and actuation
systems based on the the open-source micro controller Arduino
UNO. A single board computer (Raspberry Pi 3) is used to
coordinate actuation and data acquisition from various sources.
Automated data collection and actuation is implemented in
Python and the ML methods are implemented using scikit-
learn package .
In the APPJ setup (Figure 1a) power and ﬂow can be
actuated within ranges of 1.5-5 W and 1-3 slm, respec-
tively. The applied power is maintained via a proportional-
integral (PI) controller, based on instantaneous measurements
of current (via an 830 Ωresistor) and voltage (via Tektronix
P6015A high voltage probe) signals, and ﬂow is manipulated
through a mass ﬂow controller (UNIT UFC-1660) interfaced to
Arduino UNO. The OES signal is collected with a spectrom-
eter (OceanOptics USB2000+, 0.375 nm resolution). In the
Plasma Flashlight setup (Figure 1b) the separation distance is
manipulated through a linear actuator based on a stepper motor
controlled by the Arduino UNO. The electro-acoustic emission
is collected in the range of 0.5-25 kHz with a resolution of
200 Hz using an adjustable gain microphone (MAX4466). The
fast Fourier transform (FFT) of the signal is implemented via
the Open Music library .
IV. RES ULT S AN D DISCUSSION
We now discuss the application of the ML methods of
Section 2 for real-time diagnostics of CAP operation using
three case studies: (i) determination of rotational and vibra-
tional temperatures of APPJ using OES, (ii) discrimination
between a conductive and an insulating substrate using OES,
and (iii) determination of the discharge gap distance using
A. Determination of Rotational and Vibrational Temperatures
Rotational (Trot) and vibrational (Tvib ) temperatures contain
vital information about gas temperature and energy transport
processes within the discharge. Different OES peaks such as
OH (A 2Σ+→X2Πat 306-328 nm) and N2(C3Πu→
B3Πgat 365-390 nm) transitions are commonly used to
estimate rotational and vibrational temperatures , .
The current practice is to estimate these temperatures ofﬂine
using specialized software (such as SpecAir ) to achieve
a ﬁt between generated synthetic spectra and measured OES
spectra. Due to the presence of a large number of ﬁtting
parameters, this approach can be computationally expensive
for real-time diagnostics, taking several seconds to a few
minutes. Here, we propose a data-driven diagnostics tool based
on linear regression (see Section II-A) for real-time inference
of the rotational and vibrational temperatures from the OES
The regression model is trained using 1500 samples of
the normalized peaks of N2second positive system between
365-385 nm (input) and estimated rotational and vibrational
temperatures (outputs). A typical OES spectrum over the
wavelengths corresponding to N2(C3Πu→B3Πg) transition
and the ﬁt of the synthetic spectrum is shown in Figure 2.
The training data for values Trot and Tvib are determined via
ﬁtting synthetic spectra in Massive OES . The data set
is collected over a range of operating conditions: varying He
ﬂow, applied power, and substrate type (i.e., insulating and
conductive). The data are split into 80%training and 20%
testing segments. The training data are presented in Appendix
Figure 1 The experimental setup for (a) the kHz-range APPJ in helium and (b) the Plasma Flashlight. Dashed lines indicate
the ﬂow of information, where blue represents actuation and red represents measurements.
Figure 2 An example OES spectrum of N2(C3Πu→B
3Πg) second positive transition and corresponding ﬁt from
Massive OES , used to estimate rotational and vibrational
temperatures of the APPJ operated at P= 3 W and q= 1.5
slm over glass substrate.
We considered two hyperparameters for linear regression:
the model order as deﬁned by the choice of basis functions
(4) and the choice of the regularization parameter αin (5).
The model is validated using 10-fold cross-validation. Figures
3a and 3b show the average R2score of the model predictions
over 10 folds as a function of the model order and as a function
of the regularization parameter α, respectively. We observe
that the R2score increases with model order and appears to
plateau at an order of four (Figure 3a). Above this model
order, increasing the complexity of the model does not provide
further improvement in the predictive capability of the model.
In contrast, we observe that R2score is low for low values
of α, possibly causing the model to over-ﬁt (Figure 3b). In
this case the model is unnecessarily complex due to ﬁtting
the noise in the output data. When αis increased beyond α
= 0.7×10−5, the model tends to under-ﬁt. Thus, we choose
the model order O= 3 in (3) and regularization parameter α
= 0.7×10−5in (5) in order to strike a balance in the bias-
Figure 4 depicts the predictions of the linear regression
model against the test data. The operating conditions under
which the test data are obtained are shown in Figure 4b.
The predictive capability of the linear regression model is
quantiﬁed separately for the two outputs Trot and Tvib. The
RMSE values, calculated using (1), are 30.2 K and 141.0 K,
respectively, and R2scores are computed as 0.79 for both
outputs. Figure 4a suggests that the regression model can
describe the ﬁtted Trot and Tvib fairly well. A notably poor
performance is observed between sampling instances 210 -
250, where the ﬂow rate is decreased and power is increased
Figure 3 Determination of rotational and vibrational temper-
ature using linear regression. Effect of (a) the order of the
linear regression model and (b) the regularization parameter
αon the predictive capability of the model as quantiﬁed by
Figure 4 Determination of rotational and vibrational tem-
perature using linear regression. (a) Predictions of the linear
regression model for Trot and Tvib compared against the ﬁtted
values from Massive OES using the test data and (b) operating
conditions (applied power, He ﬂow rate, and substrate type)
under which the test data are obtained.
on the metal substrate. Under these conditions, the ﬁtted
temperatures are subject to more noise. This can be attributed
to the fact that the plasma jet under these conditions moves
rapidly from point to point on the surface, disrupting the OES
The results illustrated in Figure 4 indicate that the pre-
dictions of the linear regression model are comparable to the
ﬁtted values from Massive OES under a range of operating
conditions. Further testing also revealed that linear regression
model retains its accuracy even under additional variations
which may be expected to signiﬁcantly impact the emission
from the second positive transition of N2such as jet-tip-to-
substrate separation distance and O2admixture in the work-
ing gas (results not reported). The robustness of the linear
regression model can be attributed, in part, to the inherent
repeatability of underlying physical phenomena in this type
of discharges . Thus, the linear regression model can
provide an effective tool for real-time inference of Trot and
Tvib. This type of regression model relating OES to physical
quantities can be a powerful diagnostic tool even beyond the
determination of temperatures. When additional quantitative
measurements such as LIF and picosecond second harmonic
generation are available for training, supervised regression
models might be developed using OES data to provide real-
time estimates of other process variables such as such as
chemical species concentrations and electric ﬁeld strength.
B. Substrate Discrimination using OES
APPJ characteristics can signiﬁcantly change as a function
of the substrate properties such as the conductive or insulating
nature of the substrate . However, it is often impractical to
directly measure the substrate properties in real time. Changes
in the optical emission of the discharge can provide an
indication of changing substrate properties and allow detection
of distinct substrates such as tumorous tissues as compared to
healthy tissue . Here, we develop a real-time diagnostics
tool based on k-means clustering to detect the substrate type
based on OES measurements. We utilize the same data set
as in the previous section for training (see Appendix A). The
data set consists of 1500 samples, 1000 of which are collected
over a glass substrate and 500 are collected over a metal
substrate. The inputs are the raw OES spectra of the second
positive transition of N2as in the previous section. Labels
of the substrate types are the outputs. However, as k-means
is an unsupervised method, the output labels are not used for
training. Using k-means clustering, we aim to cluster the OES
spectra in two distinct groups (k= 2). We use 10-fold cross-
validation to validate the ability of the k-means method to
assign data to appropriate classes. We ﬁnd that the k-means
model is able to classify the glass and metal substrates with
an error fraction (2) of 0.01. This means that the clustering
model misclassiﬁes the substrate only 1% of the time.
The centroids, or the average spectra, corresponding to the
two clusters are shown in Figure 5a. The k-means method
clusters the OES spectra into two classes coinciding with glass
and metal substrates. We further veriﬁed the clustering with
respect to the two substrate types by plotting the Trot and Tvib
values ﬁtted from Massive OES. As shown in Figure 5b, the
temperatures over glass and metal are clearly separated by the
dashed diagonal line. This clustering of temperatures is not
particularly surprising given the sensitivity of the discharge to
electrical properties of the substrate. However, to the authors’
knowledge, this clustering behavior has not been previously
We further test this clustering model for substrate discrimi-
nation in real-time. In this scenario, the glass cover slip used
as the insulating substrate (see Figure 1a) is removed from
under the jet after 30 seconds of operation and is re-inserted
after another 30 seconds. The jet is operated with 3 W of
applied power and He ﬂow of 1.5 slm. Under these conditions,
we observed perfect identiﬁcation of the substrate type (an
error fraction of 0), indicating the promising potential for
the real-time use of k-means clustering. We note that the
case we examine here is fairly simple, since the transition
between a purely conductive and a purely insulating substrate
is fairly drastic. Nevertheless, this case study demonstrates the
promise of unsupervised clustering for real-time diagnostics
of discrete phenomena. Knowledge of discrete phenomena,
such as substrate type or discharge modes can greatly increase
the ﬂexibility of operation, for example, for treatment of
electrically heterogeneous substrates.
Figure 5 Substrate discrimination using k-means. (a) Cen-
troids of the clusters that correspond to glass and metal sub-
strates and (b) the rotational temperature Trot and vibrational
temperature Tvib in the training data, ﬁtted using Massive OES.
Figure 6 Fast Fourier Transform of the electro-acoustic emis-
sion of the Plasma Flashlight, recorded at two different inter-
electrode separation distances of d= 2 mm and d= 5 mm.
C. Determination of Separation Distance using Electro-
Here, we use the hand-held battery-operated air discharge,
the Plasma Flashlight . This device exempliﬁes typical
plasma medical devices, such as KINPen (neoplas tools GmbH
), in the sense that it is hand-held and relies on the exper-
tise of the user for reliable operation. In these devices, changes
in the electrode-to-substrate distance can generate signiﬁcant
variability in operation, caused by the sharp gradients and
drastic changes in discharge properties . Hence, real-time
measurement of the separation distance can be useful. Conven-
tional non-contact sensors based on infrared , ultrasound
 or time-of-ﬂight  may not be able to readily address
this issue as the desired measurement range is particularly
small, and the discharge interference with electronics limit
their use. Here, we aim to use the information provided by
the discharge to extract information about separation distance.
The Plasma Flashlight has audible electro-acoustic emis-
sion, which noticeably changes with variations in the sep-
aration distance. Based on the literature , , we use
fast Fourier Transform to analyze the effect of the separation
distance on the sound signal in the frequency domain. Figure
6 shows an example of fast Fourier Transforms of the electro-
acoustic emission collected under two separation distances at 2
mm and 5 mm. We use GP regression to describe the complex
relationship between the fast Fourier Transform of the electro-
acoustic emission and the separation distance. The data set for
training and testing the GP regression model consists of 2500
samples collected over a range of labeled separation distances
dsep, which is also the output. 60%of the data are used for
training and validation while the rest is reserved for testing.
The GP regression model is trained as described in Section
II-C. The training data are given in Appendix A.
Figure 7 Determination of separation distance using GP
regression. Comparison of predictions of the GP regression
model against the test data. The conﬁdence interval of in
the GP predictions, quantiﬁed within one standard deviation
shown with solid gray lines.
In the GP regression model, the hyperparameters in (11)
are systematically chosen by maximizing the log marginal
likelihood of predictions with respect to the hyperparameters
. This results in λ= 1.73 and σ= 0.08. After training and
validation of the GP model, its performance is evaluated with
respect to the test data, as shown in Figure 7. The performance
of the GP model is quantiﬁed with an R2score of 0.98 and
RMSE of 0.34 mm. Figure 7 suggests that the GP model
reliably predicts the true value of the separation distance. The
noisy nature of the prediction is attributed to the high noise
level of the raw electro-acoustic emission data. Notably, the
standard deviation predicted by the GP prediction is smaller
for larger separation distances, as indicated by the dashed lines
in Figure 7. Overall, the GP regression model is capable of
predicting the separation distance based on electro-acoustic
emission with reasonable accuracy. Thus, the GP regression
model provides a real-time diagnostic for determination of the
separation distance, for example, to monitor if the separation
distance is outside a prescribed region that is safe for plasma
V. CONCLUSIONS AND FUTURE WORK
In this paper we demonstrate three examples of data an-
alytics applications to real-time diagnostics of atmospheric
pressure plasma devices: (i) determination of Trot and Tvib
from OES using linear regression, (ii) discrimination of glass
and metal substrates from OES using k-means clustering, and
(iii) determination of separation distance from electro-acoustic
emission using GP. A common feature of all the investigated
examples is that difﬁcult-to-obtain information is extracted
from data which are available in real time. The caveat is that
large quantities of data have to be collected and processed off-
line in order to be able to draw accurate inferences. Where
possible, we made use of this off-line processing and external
measurements (as in determination of Trot,Tvib and separation
distance) in conjunction with supervisory methods. In addition,
we demonstrated the use of unsupervised methods to obtain
insight on physical characteristics (e.g., the clustering of Trot,
Tvib based on substrate types) from patterns in the data. Our
results indicate that, despite the simplicity of the utilized
methods, the performance of the ML inferences is more than
adequate in the context of the respective examples. This serves
to show the potential promise of ML methods in the context of
CAPs. In particular, ML methods can create vast opportunities
in plasma medicine for modeling the end effects (i.e., dosage)
of plasma treatment and enabling development of personalized
A key challenge in applying data analytics to real-time
diagnostics is the choice of appropriate sources of spectral
information and ML methods. For example, in the third case
we examine, we choose electro-acoustic signal due to its ease
of collection. The GP methods was chosen since simpler
regression methods like linear regression did not produce ade-
quate results. It may not be possible to readily extend the same
approach in all circumstances; for example, in radio frequency
discharges, the excitation frequency considerably exceeds the
audible range. Discovering the appropriate combinations of
methods and measurements, then, largely relies on heuristics.
In future research, we will focus on investigating data
analytics tools for building accurate data-driven models of
the plasma. Such models, have the capacity to be combined
with the real-time diagnostic tools presented in this work to
achieve high-performance automation and process control on
A. Training Data Sets
We collect OES over varying power, ﬂow rate and in
substrate types. We ﬁt synthetic spectra using Massive OES
 to obtain corresponding values of the outputs Trot and
Tvib for each condition. The operating conditions as well as
the output variables used for training are shown in Figure 8.
We use this training data for both determination of temperature
Trot and Tvib and substrate discrimination.
Figure 8 Training data set collected from the APPJ set-up,
used in linear regression and k-means classiﬁcation. (a) Trot
and Tvib estimates from Massive OES and (b) corresponding
Figure 9 Training data set collected from the Plasma Flash-
light set-up used in GP regression.
For the separation distance estimation, electro-acoustic
emission from the Plasma Flashlight is collected over a
range of separation distances for which the discharge remains
coupled to the ground plate. The conditions over which the
training data are collected is presented in Figure 9.
The authors thank Mahima Parashar for her help with data
processing. This material is based upon work supported by the
National Science Foundation under Grant No. 1839527.
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