Two criteria for On-line Detection of Oscillations in Nuclear Fusion Experiments

Abstract

The work presented in this paper is a first approach in the application of monitoring and assessment techniques developed in the control engineering field to the diagnosis and analysis of signals in nuclear fusion experiments. Two procedures to detect oscillations in process control are explained and modified to be applied to the on-line detection of oscillations in waveforms. Steps to further research on the application of monitoring and assessment techniques from the control engineering field to the fusion are given.

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N. Duro1, J. Sánchez1, S. Dormido-Canto1, R. Dormido1, G. Farias1, H. Vargas1, J. Vega2
1 Dpto. de Informática y Automática - UNED
2 Asociación EURATOM/CIEMAT para FUSIÓN
28040 Madrid, Spain
Two criteria for On-line Detection of Oscillations in Nuclear
Fusion Experiments
As is well-known, in the diagnostic phase of every plasma experiment in nuclear fusion, thousands of
measurements of different physical magnitudes are gathered to be stored and analyze off-line by researchers.
However, due to the so huge amount of information that these data represent, there is a big problem to take
advantage of it and to extract conclusions with traditional software tools based on SQL queries. In most cases,
these queries let researchers just search and retrieve signals from the database by using name, number and date
of the pulse (in general) or identifiable time interval (in long pulse operation).
Fortunately, visual data analysis is an essential tool in plasma physics. A simple visual inspection of signals
is enough to recognize a typical plasma evolution or to distinguish the presence of interesting events. A
researcher identifies the plasma behaviour through the recognition of patterns inside wave forms: bumps,
unexpected amplitude changes, abrupt peaks, or oscillate components. Therefore, a big challenge in data access
is the creation of fast means to look for patterns within wave forms and signals.
The on-line detection of oscillations in steady-state signals should be considered as a key point. This
phenomenon is particular importance to build performance monitoring tools to detect and broadcast events as
soon as they happen in the plasma in order to take corrective control actions.
FIGURE 1: Original signal: BOL5_10141, threshold_oscil = 4, γ = 10000, N=1000. (a) presents the artificial
waveform and vertical lines to indicate the boundaries of each significant oscillation. (b) shows the variation of
the oscillation counter and it can be appreciated how the threshold is surpassed when a sustainable oscillate
behavior is presented in the waveform. Vertical lines in (c) represent the value of when it is greater
or equal than
σ ξ ⋅
This algorithm concludes that there is oscillate_behavior when the number of significant deviations
detected during a certain supervision time Tsup surpassed a certain level threshold_oscil. It can be summarized
by calling the following pseudo-code at every sampling time:
FIGURE 2: Original signal:
HALFAC3_10186,
threshold_oscil = 4,
γ = 10000, N=1000.
Examples of Application of Procedure 1
II. OSCILLATION-DETECTION PROCEDURE 1
I. INTRODUCTION
ABSTRACT
The work presented in this paper is a first approach in the application of monitoring and assessment techniques developed in the control engineering field to the diagnosis and analysis of
signals in nuclear fusion experiments. Two procedures to detect oscillations in process control are explained and modified to be applied to the on-line detection of oscillations in waveforms.
Steps to further research on the application of monitoring and assessment techniques from the control engineering field to the fusion are given.
Index terms: Diagnosis, implementation, monitoring, process control, oscillations, supervision.
∫
t
+
=
1
)(
i
i
t
i
dttY IAE
; true behavior_oscillate
oscil_
=
thresholdcounter
countercounter
; γcounter counter
T
IAE
∆

)
)
t ( YY(t)
i
i
≥
⋅=
+⋅=






⋅≥
−≠

then if
else
1 then if
then1(sign ) ( (sign if
γ
ξσ
Where:
Y(t) is the waveform after subtracting the value of the voltage offset,
and ti and ti+1 are times of successive zero crossings of Y(t).
∆ ∆ ∆ ∆Ti is the time interval between two consecutive zero crossings, σ σ σ σ is
an estimate of the root mean square (r.m.s.) value of the noise, and ξ ξ ξ ξ
is a threshold for detection.
∑
=
i
=
N
i Y
N
1
2
1
σ
σ
ξ
}Y{max
,..., 1
=
i
Ni

=
N: number of samples of the plasma waveform in steady-state
The forgetting factor γ γ γ γ is related to Tsup by the expression:
sup
T
h
−= 1
γ
i
i
IAET
∆
(a)
(b)
(c)
(a)
(b)
(c)
III. OSCILLATION-DETECTION PROCEDURE 2
In this procedure, the time instants of all zero crossings and all IAEs are computed as Fig. 3 shows it. It must be
noticed that to separate IAEs for positive errors from those of negative errors makes the criterion able to detect
asymmetric oscillations.
It can be summarized by calling the following pseudo-
code at every sampling time (Procedure 2-A):
FIGURE 3
The IAE between two zero crossing is calculated using
the expressions:
N/2 ..., 1 ,0 , ,
22
12
12
2
,idt) t (YB dt ) t (YA
i
i
i
i
t
t
i
t
t
i
===
∫∫
+
+
+
where N is a certain number of samples, and t2i, t2i+1,
t2i+2 are consecutive zero crossings.
; truebehavior _oscillate
oscil_
=
threshold counter

);B_semicycleA_semicycle(
counter counter
B
=
B
)
)
t (
ε
YY(t)
(
;A_semicycle
(sign
;A_ semicycle
else
A
A
)
)
t (YY(t)
i
i
i
i
i
i
i
i
≥
⋅
+⋅






<<∧<<
−>
=
=






<<∧<<
−<
++
++
then if

else
then
1
β
1
if
then1( sign ) elseif
0
1
then
1
β
1
if
then1(sign ) ( (sign if
11
11
γ
ε
β
α
α
δ
δ
β
α
α
Examples of Application of Procedure 2
FIGURE
threshold_oscil = 3, γ = 10000, α=0.2, β = 0.5.
(a) The original and the filtered signals, (b) presents the
positive and negative areas that fulfill the criteria
(Procedure 2-A), and (c) shows the evolution of the
oscillation counter.
4:
Original signal: BOL5_10141,
(a)
(b)
(c)
To reduce the number of false detections, the criteria in
(Procedure 2-A) have been modified to consider true
oscillations, only just positive and negative areas are
enough significant. The modification consists of taking
into account only those areas whose mean value of the
IAEi over its interval ∆Ti is greater than the r.m.s. of the
signal (Procedure 2-B): :
;truebehavior_oscillate
oscil_
=
thresholdcounter

); B_semicycleA_semicycle(
countercounter
B
=
B
)) t (
ε
YY(t)
;A_semicycle
(sign
;A_semicycle
else
A
A
)) t (YY(t)
i
i
i
i
i
i
i
i
≥
⋅
+⋅






<<∧<<
−>
=
=






<<∧<<
−<
++
++
then if

else
then
1
β
1
if
then1(sign ) (elseif
0
1
then
1
β
1
if
then1
δ
(sign ) ((sign if
11
11
γ
ε
β
α
α
δ
β
α
α
FIGURE 5: Original signal: BOL5_10141, threshold_oscil =
3, γ = 10000, α=0.2, β = 0.5, N=500, (Procedure 2-B).