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A Disruption Predictor Based on Fuzzy Logic Applied to JET Database Guido Vagliasindi, Student Member, IEEE, Andrea Murari, Paolo Arena, Senior Member, IEEE, Luigi Fortuna, Fellow Member, IEEE, Mike Johnson, David Howell, and JET-EFDA Contributors

Abstract—Disruptions remain a serious issue for International Thermonuclear Experimental Reactor (ITER) and the commercial reactor. In the past years, significant efforts have been devoted to the development of reliable disruption predictors. In this paper, the potential of fuzzy logic in this field is explored. A new disruption predictor for Joint European Torus (JET), which is based on fuzzy logic, was tested off-line using data collected during several JET campaigns, covering a very wide range of scenarios and plasma parameters. In the standard configuration, it was able to predict 92% of disruptions with about 18% of false alarms (FAs). The flexibility of the approach, which is to provide a different tradeoff between missed and FAs, depending on the desired results in terms of safety, is demonstrated. The potential of the technique to help quantifying the risks that are associated with the operation outside the already explored parameter space is also discussed. Index Terms—Disruption prediction, fuzzy logic, tokamak.

I. I NTRODUCTION

O

NE OF THE main open issues of the tokamak configuration, in the perspective of building an economically viable fusion reactor, is certainly the occurrence of uncontrolled and irreversible sudden losses of magnetic confinement, which are called disruptions [1]. During these fast and unforeseen events, on a time scale of a few milliseconds, the energy stored in the plasma is quickly lost to the wall, generating large heat fluxes to the plasma-facing components, which can significantly contribute to their erosion and can also induce more severe damage. In elongated plasmas, which are intrinsically unstable, the plasma vertical position control can be lost during a disruption, and the consequent vertical movement of the plasma, together with the fast decay of the current, can produce high electromechanical stresses on the tokamak structures, particularly the vacuum vessel. Moreover, the voltage peak, which occurs during the fast current decay, may generate runaway electrons that, interacting with the plasma-facing structures,

Manuscript received March 19, 2007; revised October 28, 2007. This work was supported in part by the Italian Embassy in London. G. Vagliasindi and P. Arena are with the Department of Electric and Electronic Systems Engineering, University of Catania, 95125 Catania, Italy (e-mail: [email protected]). A. Murari is with Consorzio RFX—Associazione EURATOM ENEA per la Fusione, 35127 Padua, Italy. L. Fortuna is with the School of Engineering, University of Catania, 95125 Catania, Italy. M. Johnson and D. Howell are with Euratom/United Kingdom Atomic Energy Authority Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB, U.K. See the Appendix of M.L.Watkins et al., Fusion Energy 2006 (Proc. 21st Int. Conf. Chengdu, 2006) IAEA, (2006). Digital Object Identifier 10.1109/TPS.2007.914067

can lead to localized damage. Therefore, disruptions, which could have catastrophic consequences in ITER, are already potentially very hazardous in Joint European Torus (JET). On the other hand, the objective of developing plasma scenarios for ITER imposes the necessity of exploring the operational space and pushing the boundaries, in order to identify higher performance configurations. This of course obliges one to take significant risks in terms of disruption probability. In this framework, reliable prediction methods for disruptions would be extremely useful from the design of a plasma configuration to the actual carrying out of the experiments. In the preparation phase of a discharge, such a prediction capability would allow one to make conscious decisions, evaluating in advance the level of risk associated with a certain experiment. During an actual shot, forecasting sufficiently in advance the beginning of a disruption could give the opportunity to interrupt the experiment or to intervene with disruption mitigation systems [2] in order to avoid potential damage to the vacuum vessel and to the internal components that a disruption can lead to. For all these reasons, disruption prediction has been an important area of study for many years. On the other hand, the very significant efforts devoted to this issue have not lead to completely reliable prediction approaches, given the high complexity of the physics behind the problem. Disruptions can indeed be due to different causes, which can interact nonlinearly in complicated ways, making the diagnosis of the real trigger even during the off-line analyses of a discharge very difficult. This complex and nonlinear nature of the problem has motivated in the last few years a lot of research in the field of nonalgorithmic approaches, principally neural networks. In Wroblewski [3], neural networks were used to predict the disruption boundary for high-β disruptions in DIII-D. The network, a three-layer feedforward perceptron, used as input 33 diagnostic signals and produced as output the value of βN = βt (aB)/Ip at the time of disruption for each discharge. The ratio of the actual value of βN to the predicted one was used as the detection parameter. In this way, it was possible to predict a disruption about 100 ms before its occurrence with a probability of disruption detection higher than 90% and with less than 20% probability of false alarms (FAs). The main limitations of this approach are the attention to a specific disruption type (high-β variety) and the use of a high number of diagnostic signals and its dependence on the specific machine for which it was devised. Pautasso [4] developed a neural network for predicting the time to disruption (ttd) in the Axially Symmetric Divertor

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Experiment (ASDEX) Upgrade tokamak. The data used for training the network were as follows: the safety factor q95 , the plasma internal inductance li , the plasma density divided by the Greenwald limit, the radiated fraction of the input power, the energy confinement time normalized to the time predicted by a scaling law, a multifaceted asymmetric radiation from the edge [5] indicator, using two divertor bolometer channels, a locked-mode signal, using the measurement from the saddle coils, βN and the time derivatives of some of the aforementioned quantities. The inputs were chosen to be dimensionless in order to improve the portability of the network and were, also, normalized and time averaged. When the output of the neural network, which is the ttd, had a value smaller than 50 ms and it remains below 50 ms for at least 7.5 ms, the disruption alarm was triggered. The network was able to identify up to 85% of disruptive pulses, with a percentage of FAs of about 1%. The predictable disruptions, however, were limited to lower X-point configuration in flat-top states, and the use of time-averaged inputs reduced also the possibility to detect fast disruptions. Further improvements were obtained by Morabito [6] by adopting a fuzzy approach to classify data sets selected from the ASDEX Upgrade into four nonoverlapping subsets. Starting from these subsets, four different artificial neural networks (ANNs) were trained, and a radial basis function network decided which of them had to be used. The performance obtained on the test set was pretty good, 95% of correctly activated alarms with a 2% of FA, but it was tested on a very limited number of pulses (46 test and 62 training pulses). At JET, the first work was published by Milani [7], who developed a disruption alarm trained to distinguish between predisruptive plasmas and stable plasmas using a two-layer feedforward perceptron model. The best performance (90% of disruptive pulse detected and 5% of FA) was obtained using the following seven input parameters: locked-mode amplitude, density, input power, radiated power, the safety factor (q95 ), the internal inductance (li ), the poloidal beta (βp ), and the derivative of the stored energy. Further works in this direction is reported in Cannas [8] where an ANN was used to estimate the risk of disruption. An ANN was trained using both disrupted and safe pulses with the following characteristics: Ipla > 1.5 MA, X-point configuration and flat-top plasma-current profile. The database was constructed taking into account the range [tD − 440 ms, tD − 40 ms] for the disruptive pulses and a randomly selected window of 400 ms in the range where the criteria are satisfied for the safe pulses. The output of the network was the risk of disruption; therefore, a pulse was considered disruptive if the value of the output exceeded a defined threshold. The threshold was selected minimizing the detection error and using a weight factor in order to reduce the misclassification of safe pulses. The performance, which was evaluated considering the output of the network at 100 ms before the disruption, was about 84% of the correct alarms produced over a test set of 62 pulses. This neural-networks predictor was also tested online as reported in [9]. The prediction performance were tested for over 86 disruptive pulses and 102 nondisruptive presenting to the network all the samples of each pulse sampled every 20 ms. The

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missed-alarm (MA) rate and the FA rate of the predictor, which is up to 100 ms prior to the disruption time, were 23% and 1%, respectively. As most of the MA were due to different plasma configurations in comparison with those used for training the network, a novelty detector was integrated in the predictor leading to an improvement in the performance, reducing the MA rate to 7% but reducing the discrimination capability of the system from a prediction success rate of 87.23% to 84.57%. This was because the novelty detector reported some of the disruption pulses correctly detected by the multilayer perceptron predictor as novel. In Morabito and Versaci [10], a fuzzy neural approach for plasma-disruption prediction was proposed. The use of fuzzy logic has the advantage of embodying the expert knowledge included in the rules of the fuzzy inference system. The devised fuzzy system was used in combination with a neural network for predicting the ttd achieving a root mean square error, which is averaged on the total number of shots, of 0.0191. In Versaci and Morabito [11], a fuzzy time-series approach was proposed. In addition, in this case, the output was the ttd, and the achieved probability of predicting the onset of a disruption in the range from 400 to 0.5 ms before the disruption was in the order of 93% with very limited FAs. In Windsor [12], a disruption-prediction approach based on a neural network trained on another tokamak is reported. A neural network was trained using seven normalized plasma parameters using the data from ASDEX-U and JET. When the network is trained using the data from ASDEX-U and is tested on JET, it correctly anticipated 69% of the disruptions in advance of 0.04 s, whereas, in the opposite case, it correctly predicted 67% of the disruptions at 0.1 s from disruption. Testing the network on the same tokamak used for training, the prediction performance rises to 86% for JET and 90% for ASDEX-U. In this paper, a new disruption predictor for JET, which is based on fuzzy logic, is presented. The traditional set of input signals, which is already used in the past for different estimators at JET [14], is evaluated by a series of fuzzy logic inference rules to provide the final probability of a disruption. The motivations behind the decision to adopt a fuzzy logic approach has a number of different aspects. First of all, in general conceptual terms, fuzzy logic looks like a quite natural candidate for the prediction of disruptions, since it is often very difficult even for the experts to attribute a clear-cut cause to a specific disruption, which very often seems to be due to the interplay of many parameters. Therefore, a fuzzy logic approach looks more appropriate to model these phenomena than the typical Boolean logic, implicitly assumed in the more traditional methods. Moreover, contrary to ANNs, which are black boxes that can only be used as transfer functions, the fuzzy logic approach is fully algorithmic and therefore allows one to draw a direct link between any inference rule and its effects on the prediction accuracy. This is therefore potentially much more useful in the perspective of understanding the physical phenomena leading to a disruption, because various interpretations could be in principle tested investigating their effects on the predictor performance. From the operational point of view, the present approach could also be very useful in the design of pulses outside of the already investigated operational space, because it is naturally suited

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The complement of a fuzzy set is the fuzzy set F defined by the membership function

to providing information about the additional risk implicit in pushing the boundaries of the discharge parameters. This risk assessment is indeed what is normally performed at JET, even if in a less formalized way, when new configurations have to be prepared. With regard to the structure of this paper, for the convenience of the general reader in the next section, the basic elements of fuzzy logic are briefly reviewed with particular attention to the aspects relevant to this paper. The criteria behind the selection of the signal databases, which are prepared for the identification of the selection rules and for the test of the method final performance, are the subject of Section III. Section IV describes the design, implementation, and performance of the final fuzzy logic identifier. Some conclusions are drawn in Section V.

Since fuzzy logic can be considered a superset of standard Boolean or crisp logic, it is possible to extend the basic logical operations AND and OR. Given two fuzzy sets A and B, the union of the two fuzzy sets, A OR B, is a fuzzy set defined by the membership function

II. B RIEF O VERVIEW OF F UZZY L OGIC

µA and B = min (µA (u), µB (u)) .

The term “fuzzy logic” was introduced in 1965 by Zadeh [15]. The basic notion of fuzzy logic is a fuzzy set. A fuzzy set is an alternative to the traditional notion of set membership and logic that has its origin in ancient Greek philosophy. Aristotle formulated the so-called “Law of the Excluded Middle,” which states that a proposition must either be true or false or, considering a set, an element X must either be in set A or in set not-A. Therefore, a classical Boolean or “crisp” set is a container that includes or excludes totally any given element. On the other hand, in the real world, it is frequently necessary to deal with unsharp phenomena, in which it is not always easy to attribute the membership of an element to a set or its complementary in such a drastic form. The fuzzy logic is an alternative and fully coherent formal logic to handle sets with less sharp degrees of membership. A fuzzy set F defined on U (called the universe of discourse) is a set [15]

µF (u) = 1 − µF (u).

µA or B = max (µA (u), µB (u)) .

(4)

(5)

The intersection of two fuzzy sets, A AND B, is the fuzzy set defined by the membership function (6)

A fuzzy system is a nonlinear system formed by a set of fuzzy rules and an appropriate inference mechanism. The set of rules represents the knowledge base of the fuzzy system, and the inference mechanism numerically processes the knowledge base to yield the results. Fuzzy rules are used to formulate the conditional statements that allow a fuzzy system to process data by mimicking human decision making [13]. Usually, a fuzzy rule is in the form of an if-then rule like if x is A then y is B

(7)

In other words, for each u ∈ U , the membership function attributes the degree of membership of u to the fuzzy set F . The degree varies in a continuous way from zero (no membership) to one (full membership) according to the particular fuzzy set shape chosen. Usually, the most common membership functions have a triangular or trapezoidal shape, which reduces the computational burden, but more sophisticated shapes, like Gaussian or bell, can be used depending on the application. Fuzzy sets, which were originally devised to implement verbal knowledge, are usually identified by linguistic labels. It is possible to define some quantities and properties of the fuzzy sets. The support of a fuzzy set F is the Boolean set S(F ) composed by the elements which have a nonzero degree of membership to the fuzzy set F

where A and B are two fuzzy sets defined in the universes of discourse X and Y , with x ∈ X and y ∈ Y . The if part of the rule is called antecedent, whereas the then part is called consequent. A typical fuzzy system is a system that maps a set of scalar inputs to one scalar output. In this case, considering a typical fuzzy set with N inputs u1 , . . . , uN , one output variable v0 , and M fuzzy rules, it can be written in this way 1) Rule 1. IF (u1 , F1,1 ) AND (u2 , F2,1 ) AND . . . AND (uN , FN,1 ) THEN (v0 , G1 ) . . .; 2) Rule j. IF (u1 , F1,j ) AND (u2 , F2,j ) AND . . . AND (uN , FN,j ) THEN (v0 , Gj ) . . .; 3) Rule M . IF (u1 , F1,M ) AND (u2 , F2,M ) AND . . . AND (uN , FN,M ) THEN (v0 , GM ). Fi,j identifies the fuzzy set associated with the ith input variable in the jth rule, and Gj is the consequent fuzzy set associated with the output variable in the same rule. Evaluating an if-then rule implies the following two different steps: first evaluating the antecedent, i.e., fuzzifying the input and applying the necessary fuzzy operators recalled in the antecedent clause, then applying the result to the consequent, which is the so-called implication or inference. Evaluating the antecedent implies the calculation of the degree of activation of the rule. Referring to the typical fuzzy set reported before, when the operation among the input in the antecedent clause is an AND, the degree of activation λj for the jth rule is evaluated as follows:

S(F ) = {u ∈ U |µF (u) > 0} .

λj = min {µF i,j (ui )} .

F = {(u, µF (u)) |u ∈ U }

(1)

where µF (u) is the membership function, which is a curve that defines how each element of U is mapped to the real interval [0, 1], i.e., µF (u) : U → [0, 1].

(2)

(3)

i

(8)

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The resulting consequent can be considered a new fuzzy set defined by the membership function as follows:

Gj

µGj (u) = λj µGj (u).

TABLE I SETS OF PULSES USED DURING THE DEVELOPMENT AND TESTING PHASE OF THE FUZZY PREDICTOR

(9)

Once the rules are evaluated, the consequent fuzzy sets are aggregated together to produce a single fuzzy set. The output of the aggregation is then subject to the process of defuzzification, though which a crisp value, representing the final output of the fuzzy inference system, is evaluated. There are different methods that could be used during the defuzzification process. The most common is the centroid method which calculates the output as the centroid of the area delimited by the aggregated fuzzy set. The fuzzy inference system described so far is known as the Mamdani fuzzy model. Another fuzzy inference system was introduced in 1985 by Takagi and Sugeno [18]. Unlike the Mamdani model, which uses linguistic rules to generate a fuzzy output set from fuzzy inputs, the Sugeno-type of fuzzy implication is of the general form

TABLE II LIST OF SIGNALS INCLUDED IN THE DATABASES

IF(u1 , F1,1 ) AND (u2 , F2,1 ) AND . . . AND (uN , FN,1 ) THEN V0 = f (u1 , u2 , . . . , uN ) where f (u1 , u2 , . . . , uN ) is a mathematical function of the input variable which is generally a zero-order or first-order polynomial with constant coefficients. This last model is more computationally efficient and works well with optimization and adaptive techniques. On the other hand, the Mamdani model is widely accepted for capturing the expert knowledge as it allows to describe the expertise in a more intuitive human-like manner. III. D ATABASE AND D IAGNOSTIC S IGNALS At JET, a disruption database was created in order to monitor the disruptability (the ratio among disruptive and safe discharges) and the force each disruption produces on the machine. This database groups all the disruptions since discharge 27 000 [19]. A subset of this database contains all disruptions since year 2000 with reliable vessel force data. It contains 1344 disruptions (disruptability of 10%). The database used for this paper (Table I) was extracted from this subset. In particular, the same criteria exposed in previous works done at JET [8] were used, i.e., plasma current above 1.5 MA, X-point configuration, and flat-top plasma-current profile. Moreover, the disruptions classified as due to vertical displacement events were discarded as they are principally triggered by the control system itself. These criteria resulted in a subset of 814 disruptive pulses. To refine the selection during the developing phase of the new fuzzy logic predictor, a deeper understanding of the reasons leading to the various disruptions was deemed necessary. In the database, some of the disruptive pulses had been studied by experts at JET to provide a classification of the disruption causes. Knowing the cause which leads to a disruption can help in understanding the time evolution of a discharge and in devising the correct fuzzy rules to predict the incipience of

a disruptive event. Using only discharges for which the cause of the disruption had been clearly identified by the experts, the selected ones reduced to 180 (164 after data availability evaluation). These discharges belong to campaigns C1 to C9, and the resulting database is called “Disruptive.” Other databases were created including temporal windows which do not present disruption and that can be considered safe. A database was selected choosing the same disruptive pulses as for the “Disruptive” one but 2 s before the disruption takes place. This is considered a reasonable interval to guarantee the absence of any precursors. This database is called “Predisruptive Safe.” Moreover, it was deemed important to test the approach also with pulses, which were carried out successfully to the end without any disruptions. In this case, the time window was selected, adding 7 s to the time when the plasma reaches the X-point configuration. This is called, instead, “Safe” database in the following. Finally, two other sets of pulses were prepared for testing the performance of the predictor whose pulses were not used for developing the fuzzy inference system. They are called, respectively, “Disruptive Test” and “Safe test.” Altogether, five sets of pulses were used to design and to test the fuzzy predictor. They are summarized in Table I together with the number of pulses that each set contains. For the discharges in all the previously described data sets, the same diagnostic signals were chosen as the ones considered in the other predictors described in the literature [3], [5], [6]. For the discharges in all the previously described data sets, the same diagnostic signals were chosen as the ones considered in the other predictors described in the literature [3], [5], [6]. This choice was due to profit from previous experience and to make the comparison easier between the different methods. The

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Fig. 1.

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Schematic representation of the fuzzy system.

chosen quantities (see Table II) present the following properties that make them suitable for a disruption-predictor input. 1) They are all none postprocessed signals, which are available in real time at JET. 2) They refer to global measurements of the plasma parameters. 3) They could be normalized to obtain machine-independent parameters, as they are calculated and measured in almost every tokamak. After a careful observation of the signals from the various pulses, both disruptive and safe, it was noticed that the useful information can also be obtained from the derivative that some of the diagnostic signals have during the time window. These signals are the poloidal beta, the safety factor, and the internal inductance. Moreover, the radiated power is a useful indicator when it overcomes the total input power; therefore, instead of using its absolute value, it was preferred to use it in relation to the input power. The difference among the two signals was used, obtaining what was called net power Pnet = Pinput − Prad . It was found at the end the selection process inputs converged to the list of 12 signals reported in Table II. Only a reduced time window of the whole pulse duration has been taken into account. As the aim of this paper is to predict the disruption in order to permit the intervention of disruption mitigation systems or a shutdown of the pulse itself, it is useless to consider the last milliseconds before the disruption took place, when it is too late to undertake any remedial action. Therefore, calling tD as the disruption time as reported in

the database, the time window considered for each pulse is [tD − 440 ms; tD − 40 ms]. The sampling period chosen is 20 ms as it is the slowest sampling rate of the diagnostics considered. Since the signals do not have all the same time basis, they were resampled in order to synchronize them. IV. F UZZY I DENTIFIER A fuzzy inference system [20] was devised for accomplishing the task of predicting the proximity of a disruption. The system, shown schematically in Fig. 1, has 12 inputs, which are the ones described in the previous section, and one output which represents the probability of a disruption, in the range [0, 1], where 1 represents a 100% probability of an incipient disruption. The inference model chosen is the Mamdani type [17] as it allows to define the consequent in a more intuitive way (see previous chapter on fuzzy logic). The fuzzy system uses the minimum as the implication method, as defined in Section II, the maximum as the aggregation method, and the centroid as the defuzzification method. A. Membership Functions For every input to the fuzzy inference system, three, four, or five membership functions have been selected according to the experimental observation of the trend of this input signal. In Table III, the membership functions for every input variable are listed. In particular, the name of the membership

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TABLE III MEMBERSHIP FUNCTIONS

functions together with the type and the parameters needed to reproduce the functions themselves in the MATLAB Fuzzy Logic Toolbox [20] are reported. In Figs. 2 and 3, the membership functions for two variables are displayed in a graphical way. B. Rules On the basis of careful observation of the trends shown by the selected signals in disruptive and nondisruptive pulses contained in the database, 36 if-then rules have been devised.

Fig. 2.

Membership functions devised for the dWdia /dt input signal.

Fig. 3.

Membership function devised for the Loca input signal.

Table IV reports all these rules in detail. In the following, some of the criteria used in determining the basic rules are described. Some of the rules have been developed considering the strong predictive nature of some signals. For instance, the lockedmode signal (Loca) is a good indicator of an incipient disruption, as the presence of a locked-mode amplitude very often leads to a disruption. Typically, at JET, when the Loca signal rises above the 10−3 T threshold, while the current remains above 2 MA in absolute value, the disruption probability is very high (see Fig. 4 for an example of a typical disruption due to a mode-locked). From these considerations, the membership functions shown in Fig. 2 and the first rule of Table III were chosen. Other rules derive strictly from the observation of the signal trends with respect to the general behavior of the discharge, like rule 4. In this case, the presence of a very negative value of the Diamagnetic Energy derivative (dWdia /dt) while the total input power is high, the density is high, and the current is at the flat-top value, like the case of the discharge shown in Fig. 5,

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TABLE IV FUZZY INFERENCE SYSTEM RULES

Fig. 4. Trend of some signals from the database for shot #50772. It presents a mode-lock class disruption occurring at 22.052 s.

Fig. 5. Trend of the database signals in Table II for shot #52105. It presents a density-limit class disruption occurring at 23.978 s.

is a distinct disruption precursor. Using the same strategy, the rules to identify safe pulses were developed. Subsequently, several trial and error tests were performed on the data of the training databases, both disruptive and safe, in order to optimize the rules already devised or to develop new rules to reach an acceptable performance. In particular, the refining of the rules and membership was performed using the rule viewer of the MATLAB Fuzzy Logic Toolbox [20]. Using the outputs of the already devised predictor, the input signals, at the time instant when it failed in producing the correct output, were introduced in the rule viewer to determine directly the influence of the various rules on the output produced. In this way, it was easier to decide whether it was necessary to modify a membership of the input signal, change the rules, or introduce new rules.

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TABLE V PERFORMANCE IN TERMS OF MA WITH A THRESHOLD VALUE OF 0.51, 0.47, AND 0.45

TABLE VI PERFORMANCE IN TERMS OF FA WITH A THRESHOLD VALUE OF 0.51, 0.47, AND 0.45

It is worth pointing out that the contribution of the physics and expert knowledge to the selection of the rules has been limited so far. Therefore, the present predictor is mainly the result of a simple statistical investigation of the database performed manually. Indeed, the objective of this paper consists of evaluating the potential of using the fuzzy networks to the problem of disruption prediction in tokamak machines not of presenting a final optimized predictor. C. Performance In order to evaluate the performance of the devised predictor, a rule for discriminating between the correct and wrong predictions was needed. Since the output of the fuzzy network is the probability of a specific configuration (in terms of input signals) to be disruptive, a shot can be considered disruptive if the output is above a certain threshold. For the purpose of this paper, this threshold has been chosen to be around 0.5 (see later) but this numerical value can be changed in order to reflect the “risk aversion” of the experimental team with regard to a certain plasma configuration. In order to prevent false detection in cases of spurious transients in the plasma that can look similar to a predisruption phase, the condition of having the value above the threshold for at least two consecutives steps or, in other words, at least 40 ms was added. Evaluating in this way the output of the devised fuzzy predictor, the resulting performance are shown in Tables V and VI for the disruptive and the safe pulses, respectively. In particular, the number of MAs for the disruptive pulses and the number of FA for the safe ones are reported at 100 ms. Varying the value of this threshold gives the opportunity to impose more or less stringent conditions and strike a different balance between the number of missed disruptions and FA. For example, reducing the threshold from 0.51 to 0.47 can reduce significantly the number of MAs at the expense of an increase

TABLE VII TOTAL MAs AT DIFFERENT TIME STEP WITH THE A T HRESHOLD V ALUE OF 0.51

in the FAs. This is shown again in Tables V and VI and proves the great flexibility of the method and its potential to assist in the various phases of a scenario development program, from the design to the execution of the pulses. Tables VII and VIII report the number of MA at a different time step, using a threshold value of 0.51 and 0.45, respectively. Since, at JET, a normalized mode-lock indicator (Loca/ Ipla > 3 × 10−10 TA−1 ) is presently used in the on-line disruption protection system, several tests were also performed in order to use this quantity as input signal for the network instead of the absolute mode-lock amplitude. Overall, the performance of the predictor decreased significantly. In particular, even if at some times the modified network presented a slight decrease in the number of FA, this was more than compensated by the increase in the number of MA. Moreover, in order to increase the number of adimensional quantities used by the predictor, the same attempt was done to replace the Pnet with the adimensional quantity Pfraction = Prad /Pinput . In addition, in this case, the modified network presented worst performance in terms of number of MAs. These results seem to indicate that, even if normalized parameters can be useful to obtain an intuitive understanding of the physics, important information resides also in the absolute values of certain quantities, and therefore, the predictor performs better with the more informative inputs. V. C ONCLUSION AND P ERSPECTIVE A disruption is an event that should be avoided, in particular in future large tokamaks where such event could produce significant damage. In this paper, a disruption predictor based on fuzzy logic has been devised, in order to provide an alarm when the monitored signals enter a region of the operational space that can be ascribed to a predisruptive phase. The predictor has been tested on a total of 292 disruptive pulses and 385 safe pulses with a 7.87% of MAs and 17.66% of FAs. Although, as already mentioned, the contribution of the physics and the experts knowledge is limited, the results of the presented approach compare quite well with the previous work in the field as reported in Table IX. Introducing the expertise from the physicists can increase considerably the capability of such a fuzzy logic predictor. Moreover, the explicit formulation of the fuzzy rules constitutes an additional method to understand the physical mechanisms behind the occurrence of disruptions. For example, given a candidate explanation for a certain class of disruptions, the hypotheses behind the model can be verified by altering the corresponding rules in the fuzzy logic predictor to see if the final output changes as logically expected on the

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TABLE VIII TOTAL MAs AT DIFFERENT TIME STEP WITH THE A T HRESHOLD V ALUE OF 0.45

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ACKNOWLEDGMENT The authors would also like to thank M. K. Zedda, S. Pinches, and R. Koslowski for their useful discussions. R EFERENCES

TABLE IX COMPARISON WITH THE OTHER TECHNIQUES

basis of the original assumptions. It is planned to explicitly test this aspect, in particular in the analysis of JET future ITER-like configurations. The flexibility provided by the direct control of the rules would also allow to estimate the probability of a disruption for discharges outside the already explored range of parameters. This can be particularly useful in the development of plasma scenarios and in the phase of pushing the boundaries to improve the performance of the plasma. The use of the fuzzy tools in this way would therefore help significantly in estimating the risk of a configuration because it would provide the probability of the disruptions, whereas the potential hazard to the device can normally be easily determined by the main plasma parameters (like current, magnetic field elongation, etc.). Further work in this direction is also planned. In the actual experiments, a critical issue could be the realtime availability and reliability of the signals which are given as input to the fuzzy predictor. It would be therefore important to reduce to a minimum the diagnostics used, without affecting the predicting power of the approach. In order to reach a conscious decision on this matter, a correlation analysis is under way to assess the real incremental value brought by any individual signal and to see if some of them are superfluous and can be eliminated.

[1] F. C. Schuller, “Disruptions in tokamaks,” Plasma Phys. Control. Fusion, vol. 37, no. 11A, pp. A135–A162, Nov. 1995. [2] M. Watkins, “Overview of JET results,” in Proc. 21st IAEA Fusion Energy Conf., Chengdu, China, Oct. 16–22, 2006. [3] D. Wroblewski et al., “Tokamak disruption alarm based on a neural network model of the high-β limit,” Nucl. Fusion, vol. 37, no. 6, pp. 725– 740, Jun. 1997. [4] G. Pautasso et al., “On-line prediction and mitigation of disruptions in ASDEX upgrade,” Nucl. Fusion, vol. 42, no. 1, pp. 100–108, Jan. 2002. [5] B. Lipschultz, E. S. Marmar, M. M. Pickerell, J. L. Terry, R. Watterson, and S. M. Wolfe, “MARFE: An edge plasma phenomenon,” Nucl. Fusion, vol. 24, no. 8, pp. 977–989, Aug. 1984. [6] F. C. Morabito et al., “Fuzzy-neural approaches to the prediction of disruptions in ASDEX upgrade,” Nucl. Fusion, vol. 41, no. 11, pp. 1715– 1723, Nov. 2001. [7] F. Milani, “Disruption prediction in JET,” Ph.D. dissertation, Univ. Aston, Birmingham, U.K., 1998. [8] B. Cannas et al., “Disruption forecasting at JET using neural networks,” Nucl. Fusion, vol. 44, no. 1, pp. 68–76, Jan. 2004. [9] B. Cannas et al. “A prediction tool for real-time application in the disruption protection system at JET”, Nucl. Fusion vol. 47, no. 11, pp. 1559–1569, Nov. 2007. [10] F. C. Morabito and M. Versaci, “A fuzzy neural approach to plasma disruption prediction in tokamak reactors,” in Proc. Int. Joint Conf. Neural Netw., Washington, DC, 1999, pp. 3463–3467. [11] M. Versaci and F. C. Morabito, “Fuzzy time series approach for disruption prediction in tokamak reactors,” IEEE Trans. Magn., vol. 39, no. 3, pp. 1503–1506, May 2003. [12] C. G. Windsor et al., “A cross-tokamak neural network disruption predictor for the JET and ASDEX upgrade tokamaks,” Nucl. Fusion, vol. 45, no. 5, pp. 337–350, May 2005. [13] R. G. Kleva and J. F. Drake, “Density limit disruptions in tokamaks,” Phys. Fluids B, vol. 3, no. 2, pp. 372–383, Feb. 1991. [14] A. Murari, G. Vagliasindi, M. K. Zedda, R. Felton, C. Sammon, L. Fortuna, and P. Arena, “Fuzzy logic and support vector machine approaches to regime identification in JET,” IEEE Trans. Plasma Sci., vol. 34, no. 3, pt. 3, pp. 1013–1020, Jun. 2006. [15] L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, Jun. 1965. [16] B. Kosko, Neural Network and Fuzzy Systems. Englewood Cliffs, NJ: Prentice-Hall, 1992. [17] E. H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” Int. J. Man-Mach. Stud., vol. 7, no. 1, pp. 1–13, 1975. [18] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116–132, Jan. 1985. [19] JET’s Disruption Database. [Online]. Available: http://users.jet.efda.org/ pages/plasma-ops/disruptions.htm [20] Fuzzy Logic Toolbox User’s Guide, The Mathworks Inc., Natick, MA, 2002. Version 2.

Guido Vagliasindi (S’04) was born in Catania, Italy, in 1979. He received the M.S. degree in electrical engineering and the Ph.D. degree in electronic and automation engineering from the University of Catania, Catania, in 2003 and 2007, respectively. Currently, he holds a postdoctoral position with the Department of Electrical, Electronic and System Engineering, University of Catania. His scientific interests are focused on cellular nonlinear networks, image, and signal processing applied to nuclear fusion experiments.

262

Andrea Murari was born in Verona, Italy, on August 19, 1963. He received the B.A. degree in applied electronics, the M.S. degree in plasma engineering, and the Ph.D. degree in nuclear power plants, in 1989, 1991, and 1993, respectively from the University of Padova. He has mainly worked in the field of measurements for nuclear fusion experiments. He has installed various diagnostic systems on several European experiments, and between 1998 and 2002, he was responsible for the support to all the diagnostics on the Reverse Field eXperiment (RFX) in Padova. Since 2002, he has been the Task Force Leader for Diagnostics at the Joint European Torus (JET). Dr. Murari has been a member of the Euroforum working group on measurements, since 2003. He is now the Scientific Coordinator of all JET diagnostic upgrades for the next framework program.

Paolo Arena (S’93–M’97–SM’01) received the degree in electronic engineering and the Ph.D. degree in electrical engineering from the University of Catania, Catania, Italy, in 1990 and in 1994, respectively. He is currently an Associate Professor of System Theory, Optimization theory, Biorobotics, and Bioengineering with the Department of Electrical, Electronic and System Engineering, University of Catania. He is the coauthor of more than 200 technical papers, five books, and several industrial patents. His research interests include adaptive and learning systems, neural networks and optimization algorithms, cellular nonlinear networks, and collective behaviors in living and artificial neural systems for locomotion and perception. Dr. Arena is the Chair of the IEEE CAS Chapter, Central and South Italy, and served as a Distinguished Lecturer for the IEEE CAS in 2006–2007 and as an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS— PART I (2002–2003 and 2005).

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 1, FEBRUARY 2008

Luigi Fortuna (M’90–SM’99–F’00) received the Bachelor’s degree in electrical engineering from the University of Catania, Catania, Italy, in 1977. Until 1987, he was a Researcher in electronics with the University of Catania, where he later became an Associate Professor of automatic control, has been a Full Professor of system theory since 1994, and is currently the Dean of the School of Engineering. He has coordinated research projects that are supported by public institutions and a consortium of private companies. He is the coauthor of six books, among which is Cellular Neural Networks (Springer, 1999). He is the holder of several U.S. patents. His research interests include nonlinear science and complexity, chaos, and cellular neural networks, with applications in bioengineering.

Mike Johnson received the degree in mathematics from Open University, Milton Keynes, U.K., in 1978 (credits in Linear Mathematics and Pure Maths). In 1985, he was with the Joint European Torus (JET) as a Contractor, and in 1986, he took over the management of the JET disruption. In 1990, he created a new JET disruption database applying fast sampled magnetic data to calculate disruption parameters. He contributed to various papers and publications on plasma disruptions during the last 22 years at JET. He is currently semiretired though still employed with the United Kingdom Atomic Energy Authority, Culham Science Centre, Abingdon, Oxon, U.K., as Plasma Operations Database Manager. He is also active in providing disruption data for International Thermonuclear Experimental Reactor (ITER).

David Howell, photograph and biography not available at the time of publication.

A Disruption Predictor Based on Fuzzy Logic Applied to ...

Electronic Systems Engineering, University of Catania, 95125 Catania, Italy. (e-mail: .... This neural-networks predictor was also tested online as re- ported in [9]. ...... Bachelor's degree in electrical engineering from the. University of Catania ...

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