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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

Member, IEEE

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.

I. INTRODUCTION

COld atmospheric plasma (CAP) sources are exceedingly

used for medical applications [1]–[3]. However, CAP

sources can suffer from unmonitored variabilities in operation.

For example, atmospheric pressure plasma jets (APPJs) exhibit

long timescale drifts [4], sharp gradients in temperature and

species concentrations [5], and high sensitivity to disturbances

such as ambient humidity and substrate impedance [6], [7].

Mode transitions are also frequently observed in CAP sources,

e.g., streamer-to-spark transitions in corona-like air discharges

[8]. Such variabilities pose a signiﬁcant challenge to CAP

research and applications, particularly where plasma interacts

with other complex systems, as in plasma medicine [9],

[10]. 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 [11], [12].

Direct quantitative diagnostics of CAP sources pose a

considerable challenge. Methods such as laser-induced ﬂuo-

rescence (LIF) [13], mass spectrometry [14], and spontaneous

Raman scattering [15], 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: mesbah@berkeley.edu

operation in plasma medicine that relies on the ﬂexibility of

hand-held treatment in the absence of plasma diagnostics [16].

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 [17], [18]. 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 [19]. 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 [20]. In contrast to the well-established

method of analyzing OES by generating and ﬁtting synthetic

spectra to measurements [18], [21], these authors note the

potential for developing correlations across large data sets for

novel applications.

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 [22] and

plasma anodizing [23]. Law et al. investigated the application

of electro-acoustic emission for process monitoring and con-

trol in a DC pulse-modulated APPJ in air [24]. 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 [25]. They utilize

wavelet transforms of electro-acoustic emission for detection

of ﬂow modes and anomalies in operation such as sparking

phenomena.

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 [26].

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 [27]. In [28], Law et al. review potential

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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 [29], [30]. Some notable

applications of ML for data analytics, among many others,

include gene discovery [31], remote sensing [32], meaning

and sentiment analysis of text [33], [34], object recognition in

images [35], as well as real-time diagnostics and modeling of

low-pressure plasma etch processes [36]–[40]. The availability

of easy-to-use software packages such as the open source

package scikit-learn [41] and Google’s Tensor Flow [42]

has made ML methods more accessible, contributing to their

popularity.

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., [29], [30], [43], [44] 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 [30]. 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 [29]. 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 [29]. 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

RMSE(Y, ˆ

Y) = 1

N

N

X

i=1 p(ˆyi−yi)2,(1)

and

Error Fraction(Y, ˆ

Y) = 1

N

N

X

i=1

1(ˆ

yi6=yi).(2)

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 [45].

In linear regression, output variables are described by a linear

combination of some (nonlinear) function of the inputs [29].

For a scalar output, a regression model can be written as

ˆy=

O

X

j=1

wjφj(x),(3)

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)

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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 [46]

min

w

||ˆy−y||2

2+α||w||1,(5)

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 [29]. 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 [44]. 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 −

N

P

i=1

(yi−ˆyi)2

N

P

i=1

(y−ˆyi)2

,(6)

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

y=1

N

N

X

i=1

yi.(7)

B. k-Means Clustering

k-means clustering is an unsupervised ML method used

to separate data into kdistinct groups or clusters [47]. 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

min

S

k

X

i=1 X

x∈Si

||x−µi||2

2,(8)

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

[44]. 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 [48]. In GP regression models, the outputs are

assumed to have a joint Gaussian distribution [30]. 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

ˆ

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∗

K>

∗K∗∗,(10)

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

2σ2||x−x0||2

2,(11)

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

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distribution are extracted using standard formulas for condi-

tioning of multivariate Gaussian distributions, based on Bayes’

rule [48]:

E(ˆ

Y|Y, Xtrain , Xtest) = K∗K−1Y, (12)

and

ˆ

Σ( ˆ

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 [48]. 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” [49], 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 [12]; 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 [49]. 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 [41].

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 [50].

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

electro-acoustic emission.

A. Determination of Rotational and Vibrational Temperatures

using OES

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 [18], [19].

The current practice is to estimate these temperatures ofﬂine

using specialized software (such as SpecAir [18]) 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

spectra.

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 [21]. 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

A.

5

(a) (b)

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 [21], 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-

variance trade-off.

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

(a)

(b)

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

R2score.

6

(a)

(b)

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

signal collection.

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 [51]. 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 [6]. 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 [52]. 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

reported.

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.

7

(a)

(b)

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-

acoustic Emission

Here, we use the hand-held battery-operated air discharge,

the Plasma Flashlight [49]. This device exempliﬁes typical

plasma medical devices, such as KINPen (neoplas tools GmbH

[53]), 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 [5]. Hence, real-time

measurement of the separation distance can be useful. Conven-

tional non-contact sensors based on infrared [54], ultrasound

[55] or time-of-ﬂight [56] 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 [24], [25], 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

[48]. 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

8

distance is outside a prescribed region that is safe for plasma

treatment.

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

treatment protocols.

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

CAP devices.

APPENDIX

A. Training Data Sets

We collect OES over varying power, ﬂow rate and in

substrate types. We ﬁt synthetic spectra using Massive OES

[21] 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.

(a)

(b)

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

operating conditions.

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.

9

ACKNOWLEDGMENT

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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