Method for detecting presence of arc and associated apparatus

Abstract

The invention relates to a computer-implemented method for detecting the presence of an arc on a power line (L1) using a machine learning algorithm, the method is carried out using time-dependent measurements of the arc voltage Varc, the current I and the source voltage Vsource and a knowledge model for linking the arc voltage Varc and the current I together with constants dependent on the knowledge model implemented after a learning phase comprising adjusting the learning model, the learning model adopts a current I and a source voltage Vsource at an input position and provides a voltage Varc and a constant of the knowledge model at an output position; the method includes continuously detecting the presence of the arc using a decision function dependent on a cost function used in the learning phase.

Description

Technical Field

[0001] The technical field of this invention is the use of machine learning methods to detect the presence of electric arcs.

[0002] This invention relates to a process and apparatus for detecting the presence of an electric arc using a learning method, and more particularly to a method that combines a learning model and a knowledge model. Background Technology

[0003] For many years, the civil aviation industry has been committed to contributing to the fight against climate change.

[0004] Technological research has led to significant improvements in the environmental performance of aircraft. This application comprehensively considers factors affecting all stages of design and development in order to obtain aviation components and products that consume less energy, are more environmentally friendly, and have a smaller environmental impact when integrated and used in civil aviation, with the aim of improving the energy efficiency of aircraft.

[0005] In other words, this invention is the result of ongoing research focused on reducing the climate impact of civil aviation through various methods and the utilization of sound development and manufacturing processes, minimizing greenhouse gas emissions as much as possible, thereby reducing the environmental footprint of civil aviation activities. As this invention illustrates, this ongoing research and development work focuses particularly on the development of electric propulsion technology. Within this context, the ability to detect the formation of electric arcs is of paramount importance.

[0006] It is important to note that an electric arc is a self-sustaining high-current discharge. There are two main types of arcs that occur in aviation environments: interrupted current arcs (which occur in contactors when a circuit is opened or closed) and fault arcs (which can occur unexpectedly on all components of an electrical system). Fault arcs can cause serious damage to equipment, systems, and even aircraft structures. Therefore, extreme caution is required.

[0007] Depending on the location of the fault arc in the electrical circuit, there are two types of fault arcs: parallel arcs and series arcs. Series arcs typically occur at the terminals of intermediate interfaces (connection terminals, connectors) after connection problems occur during maintenance / installation or when interfaces show signs of performance degradation due to natural aging or premature aging caused by chemical, electrical, or mechanical interactions.

[0008] In power distribution networks, series arcs are always more difficult to detect than parallel arcs. In fact, from an electrical characteristic perspective, parallel arcs generate high current demands, allowing real-time diagnostic systems to quickly and effectively identify them, thus issuing commands to the disconnect system to protect the lines. In contrast, in the case of a series arc, the impact on the current is minimal. This is because an arc is a low-impedance fault. As a result, when a series arc is present in an electrical system, the current will only experience slight fluctuations, more precisely, a small percentage drop in its nominal value. This is the main reason why series arcs are more difficult to detect with standard control devices compared to parallel arcs. Furthermore, the waveform of the electrical signals from the network also complicates detection. Regarding AC networks, the moment when the voltage is 0V during a half-cycle is when the arc can no longer continue. When a series arc occurs on this type of network, this moment may cause a brief open circuit, resulting in a short period of 0A current in the line (this phenomenon forms a current shoulder), which can be used to diagnose series arc faults. Conversely, when the waveform is DC (DC network), this phenomenon no longer exists, and the arc continues without an open circuit, thus eliminating one of the possibilities for diagnosing the fault.

[0009] In the current network, the incidence of arcing is low due to the relatively moderate power allocation, as the maximum voltage level allocated in aviation is 230 / 400V. Furthermore, for these voltage levels (maximum 230 / 400V), the allocation is in the form of an alternating current (AC) waveform, which facilitates the self-extinguishing of arcs within each half-cycle of the voltage passing 0V. Additionally, the allocated direct current (DC) voltage is primarily limited to 28V. To limit the environmental impact of fault arcing, the effects are limited by using passive protection (selecting "arc-resistant" materials and defining isolation distances) and active protection (detection and line disconnection) in the event of an overcurrent fault observed by a current sensor. This has the advantage of providing detection for most parallel arcs, but not for series arcs, as active protection against series arcs has not yet been deployed.

[0010] Current work on aircraft electrification / hybridization considers distributing direct current (DC) waveforms at voltage levels up to 1,000 volts. This approach challenges the passive strategies for arc faults just discussed. Therefore, series arcs must be considered in the same way as parallel arcs, because damage associated with high-power faults generated at DC voltages could damage the aircraft and endanger the safety of passengers and crew.

[0011] One way to mitigate series arcing faults is to identify (detect) the fault so that the faulty line can be isolated if necessary.

[0012] The main challenge in detecting electrical arcs in aviation lies in meeting high-performance expectations. More specifically, the first requirement is reliability—the system's ability to systematically detect hazardous electrical phenomena in all situations. This refers to its ability to achieve a true positive rate as close as possible to 100%. The second requirement is robustness—the system's ability to withstand events other than those programmed into its system. In other words, it's the ability to achieve a false alarm rate as close as possible to 0%. Therefore, the system must be able to cope with diverse aircraft load characteristics (which behave similarly to electrical arcs) and all environmental parameters associated with aircraft flight and its lifecycle.

[0013] To date, existing solutions for arc detection have consistently demonstrated weaknesses in reliability or robustness. There are many reasons for this, but it is worth noting that inaccuracies in the fault arc models used to calibrate the system, a lack of understanding (or simplification) of the target electrical architecture, or even environmental limitations encountered, all of these degrade the performance of the offered technologies.

[0014] To meet these high demands, people are seeking new methods. Among them, machine learning methods are gaining increasing use. They offer new alternative solutions. These methods are mainly categorized into unsupervised learning, semi-supervised learning, supervised learning, and even reinforcement learning.

[0015] The most commonly applied branch of electrical fault detection is supervised learning. This type of learning is a set of methods designed to generate functions that correlate an input set with its output, using a library of examples and sophisticated mathematical methods. The model derives this function from labeled data consisting of a set of learning examples. Detection methods using models obtained through supervised learning are classified into regression methods and classification methods.

[0016] The goal of classification is to predict discrete values ​​that allow any data to be assigned to a category called a class. Therefore, the decision function obtained through classification methods can separate existing classes. The goal of regression is to predict continuous quantities. Therefore, the decision function obtained through regression will be able to represent the behavior of the system under study by continuously representing the quantity of interest (rather than discretely as in classification).

[0017] In existing technologies, arc detection (including arc detection in aviation environments) is typically performed based on electrical measurements using supervised machine learning. However, these technologies either do not specify the labeling method used, or, while specifying a method, fail to correctly identify all phenomena. For example, in existing technologies, arc voltage measurement can be used for labeling. The paper titled "AC Series Arc-Fault Detection With A Transformer Neural Network" (A Chabert et al., June 2022) provides an AC series arc detection method using supervised learning and offers a fully automated labeling algorithm using arc voltage.

[0018] However, known solutions using machine learning tools designed for arc detection (such as fault arcs) are sometimes unrepresentative. Often, their labeling methods (crucial to this method) are not described and / or are not precise enough regarding the unstable nature of arcs. However, if the labeling step is not performed correctly, the learning step will be biased by including all the phenomena presupposed in the detection step, resulting in detection tools that perform poorly in real-world environments.

[0019] To detect the formation of fault arcs, document EP3695476 A1 proposes a machine learning-based detection method using recurrent neural networks. This is a detection method that uses only mathematical information provided by machine learning tools. Specifically, in the proposed method, the learning phase does not use the physical arc equations. The document "Physics-Informed Learning for High Impedance Faults Detection" (WentingLi, Deepjyoti Deka, 2021 IEEE Madrid PowerTech) provides a so-called physics-informed detection method for high-impedance faults in microgrids (therefore, this is a different type of discharge than arc generation). More specifically, this detection is based on a method derived from machine learning and physical knowledge of the phenomenon to be detected. However, the physical information in this document does not come from a complete knowledge model of discharge behavior. The physical information related to the discharge is actually derived by measuring the difference between the voltage-current phase diagrams of the fault-free network and the faulty network.

[0020] Therefore, existing technological methods generally cannot provide the reliability and robustness required for use in aviation. Thus, there is a need for an arc detection method that can significantly improve the detection capability of existing methods, especially for series arcs. Summary of the Invention

[0021] This invention provides a detection method that designs a semi-physical arc detection model based on experimental data and physical knowledge through learning, thus offering a solution to the problems previously discussed.

[0022] Therefore, a first aspect of the present invention relates to a computer-implemented process for detecting the presence of an electric arc on a power line using a machine learning method, which learns to perform the following:

[0023] - Multiple measurements related to the formation of the electric arc, each of which includes the arc voltage V. arc Current I and source voltage V source Time-related measurements;

[0024] - Knowledge model, which will include arc voltage V arc The current I is related to a constant that depends on the knowledge model.

[0025] According to one aspect of the invention, the process is implemented using a learning model derived from a learning phase, during which a learning model adjustment step is implemented using multiple measurements and a knowledge model, the learning model including current I and source voltage V. source As input, and providing the arc voltage V arc The constants of the knowledge model are used as outputs. Learning is performed using a cost function L, which is given by the following relationship: L = L1 + L2, where L1 is the first cost sub-function used to measure the arc voltage predicted by the learning model. With the measured arc voltage V arc The first difference between them:

[0026]

[0027] Furthermore, L2 is the second cost subfunction, used to measure the second difference between the predicted value and the measured value of the knowledge model.

[0028] According to one aspect of the invention, the method includes a detection phase, the detection phase comprising:

[0029] - Continuously measure the current I and source voltage V of the power line. source Steps to be taken in the measurement window Internal acquisition of current I and source voltage V source The relevant input data, where M is the number of measurement points in the measurement window, and I(t) m ) is at time t m The current at that time, and V source (t m ) is at time tm Source voltage at that time;

[0030] - As measured during the measurement step, along with the current I and source voltage V measured on the power line. source The function for the last M input data uses a decision function to continuously determine the presence of an electric arc, which is a function of the second sub-function.

[0031] This invention enables the prediction of partial behavior of faulty arcs using the physical properties of electric arcs (based on an arc knowledge model), thereby facilitating model learning. Compared to learning models based on existing techniques, this allows for more efficient decision-making and reduces the amount of raw data required for learning (e.g., by limiting the load signal quantity derived from the aircraft architecture). This result is achieved, in particular, by combining experimental information with physical laws. Furthermore, the variation in arc length does not require prior knowledge, as it is implicit in the variables of the knowledge model.

[0032] In addition to the features discussed in the preceding paragraph, the process according to the first aspect of the invention may also have one or more of the following additional features, which may be considered individually or in combination of all technically feasible features.

[0033] In one embodiment, the decision function is defined by the following expression:

[0034]

[0035] Among them, X m ={I(t) m V source (t m )), ε is the detection threshold, and L2(X m The value is determined using a learning model and at point X. m The value of the second cost subfunction L2 calculated at the location.

[0036] In one embodiment, the knowledge model is a Mayr model, and the second cost subfunction L2 takes the following form:

[0037]

[0038] Where τ is the arc constant and P0 is the cooling power.

[0039] In one embodiment, the knowledge model is a Cassie model, and the second cost subfunction L2 takes the following form:

[0040]

[0041] Where τ is the arc constant, and V0 is a constant corresponding to the minimum arc voltage (i.e., the minimum voltage value on the wire where the arc occurs).

[0042] In one embodiment, the knowledge model is a Shavemaker model, and the second cost subfunction L2 takes the following form:

[0043]

[0044] Where τ is the arc constant, P0 is the cooling power, and V0 is a constant corresponding to the minimum arc voltage (i.e., the minimum voltage value on the wire where the arc occurs).

[0045] In one embodiment, the power line is equipped with a cutting device for cutting off the current in the line, the method comprising the steps of: when an arc is detected during a detection step, sending a command to the cutting device to cut off the current in the line under consideration.

[0046] In one embodiment, the learning model is constructed using a formal neural network.

[0047] In one embodiment, the learning model is constructed using a support vector machine.

[0048] Therefore, a data labeling method is needed that allows for the acquisition of data characterizing fault arc formation phenomena, particularly data characterizing series arcs of DC voltage type. A detection method is also needed to utilize the data labeled using this method during the learning phase.

[0049] In one embodiment, the method addresses the previously discussed problems by ensuring that data from electrical measurements of the fault arc are correctly labeled and by allowing the following:

[0050] - Associate this binary label (electric arc or non-electric arc) with a supervised machine learning classification method;

[0051] - Ensure that electric arcs are detected in a robust and reliable manner;

[0052] -Automatic arc detection.

[0053] Another objective of this method is to optimize the time spent labeling data during the model training phase for arc detection and to reduce the resources required for labeling.

[0054] Therefore, in one embodiment, the method includes:

[0055] - The design phase involves machine learning of the decision function using multiple measurements. This design phase includes:

[0056] ■ For each of the multiple measurements, the step of marking the arc current measurement with its associated arc voltage measurement;

[0057] ■ Steps for extracting descriptors from the labeled measurements;

[0058] ■ Learning steps are used to determine a decision function based on at least a portion of the descriptors extracted in the extraction step;

[0059] -The detection phase includes:

[0060] ■ Steps for measuring the current flowing in a circuit;

[0061] ■ The step of extracting descriptors from the current measurement values ​​obtained in the previous current measurement step;

[0062] ■ The steps for detecting the presence of an electric arc are based on a descriptor extracted from the current measurement value and a decision function determined during the design phase.

[0063] Furthermore, in the process according to this embodiment, for each of the plurality of measurements and for each time interval t of the considered measurements, the marking step includes:

[0064] -When the measured arc voltage U arc First time exceeding the predetermined threshold U s At that time, the interval under consideration is recorded as the starting point t of the electric arc. d Steps;

[0065] -When the measured arc voltage U arc First drop back to the predetermined threshold U s In the following case, the interval preceding the considered interval is recorded as the end point t of the arc. e The steps.

[0066] Through this process, the labeling logic combines the physical characteristics of the electric arc, automated procedures, and, in some cases, human expertise. Therefore, the vast majority (if not all) of electric arc signals or nominal signals can be correctly labeled, and this labeling is performed efficiently by automated procedures, correcting for algorithmic inaccuracies caused by variability in arc characteristics (when human expertise is required), labeling windows as precisely as possible (down to the individual sample level), and creating a labeled database suitable for designing machine learning classifiers for electric arc detection.

[0067] An embodiment of this process can itself form a detection process implemented by a computer and using machine learning methods. The learning is performed using multiple measurements related to the formation of the arc, each of which includes time-related measurements of the arc voltage and arc current. The method includes the steps of the embodiment described above.

[0068] In one embodiment, for each measurement, a tag is associated with a measurement window used for learning, the window being defined by intervals P. g ×min((t e -t d ), T max ); P d ×min((t e -t d ), T max Given, where T max It is the predefined maximum window duration, P g It is point t d The left spacing, which has a normalized value for the duration of the window under study, and P d It is point t d The right spacing, which has the relation P d =1-P g The given normalized value is the duration of the study window.

[0069] In one embodiment, the method includes the steps of: acquiring signals required for learning prior to the learning phase in order to obtain multiple measurements, each measurement including time-related measurements of arc voltage and arc current.

[0070] In one embodiment, the design phase includes the following steps: prior to the marking step, manually pre-identifying all arcs that meet predetermined criteria in each of the multiple measurements using expertise, thereby defining the position of each arc in each of the multiple measurements.

[0071] In one embodiment, the design phase includes the following steps: after the labeling step, manually verify the output of the labeling step using expertise to verify that the labeled measurements include all regions intended for learning.

[0072] In one embodiment, the descriptor used during the decision function determination step includes the spectral entropy and / or autocorrelation of the arc current.

[0073] In one embodiment, the design phase includes a descriptor classification and selection step between the step of extracting descriptors from the labeled measurements and the step of determining the decision function, in order to retain the most relevant subset of descriptors. For example, the Gram-Schmidt method can be used to perform classification, and an incremental method can be used to perform selection. Of course, other methods can also be used for classification or selection.

[0074] In one embodiment, the decision function determination step includes multiple iterations of the following two sub-steps:

[0075] - The sub-step of designing a classifier through learning; and

[0076] - A sub-step to verify the classifier based on the labeled data;

[0077] Repeat these sub-steps until the optimal classifier is obtained, and then determine the decision function based on the optimal classifier.

[0078] A second aspect of the invention relates to an apparatus for detecting the presence of an electric arc in a power line, the apparatus comprising: a measuring device configured to measure the current flowing in the power line; and a means configured to implement the method according to the first aspect of the invention.

[0079] A third aspect of the invention relates to a computer program comprising instructions that, when executed by a computer, cause a device according to a second aspect of the invention to perform a method according to a first aspect of the invention.

[0080] The fourth aspect of the invention relates to a computer-readable medium having a computer program, according to the third aspect of the invention, recorded thereon.

[0081] A fifth aspect of the invention relates to an aircraft including the arc detection device as defined above.

[0082] A better understanding of the invention and its various applications will be gained by reading the following description and referring to the accompanying drawings. Attached Figure Description

[0083] The accompanying drawings are provided to illustrate the invention and are not intended to limit the scope of the invention in any way.

[0084] [ Figure 1 The diagram illustrates a first flowchart of a process according to an exemplary embodiment of the present invention.

[0085] [ Figure 2 The diagram shows a second flowchart of a process according to an example of the present invention.

[0086] [ Figure 3This shows a schematic representation of the time-dependent arc voltage and arc current measurements.

[0087] [ Figure 4 This shows a schematic representation of the arc voltage and arc current measurements over time after pre-identification.

[0088] [ Figure 5 The diagram shows a flowchart of a marking step according to an example of the present invention.

[0089] [ Figure 6 The illustration shows a schematic representation of the marking principle according to the present invention based on time-dependent arc voltage and arc current measurements.

[0090] [ Figure 7 This shows a schematic representation of arc voltage as a function of arc length.

[0091] [ Figure 8 The diagram illustrates a schematic representation of a device according to an exemplary embodiment of the present invention. Detailed Implementation

[0092] The accompanying drawings are provided to illustrate the invention and are not intended to limit the scope of the invention in any way.

[0093] The process used to detect the presence of electric arcs on power lines.

[0094] like[ Figure 1 As illustrated in the figure, the first aspect of the invention relates to a computer-implemented process 100 for detecting the presence of an electric arc on a power line using a machine learning method. More specifically, in the process according to the invention, the learning is performed using a plurality of measurements related to the formation of the electric arc, each of the plurality of measurements including an arc voltage V. arc Current I and source voltage V source Time-related measurements.

[0095] The process according to the invention is particularly novel in that, in addition to the learning model, its design is also based on the use of a knowledge model, which is used to process the arc voltage V. arc The current I is related to a constant that depends on the choice of the knowledge model. More specifically, the principles of this invention are based on the implementation of a learning phase PA that uses two techniques: machine learning modeling and knowledge modeling. This allows full utilization of the capabilities of machine learning modeling and the expertise provided by methods derived from the physical characteristics of the fault arc mechanism.

[0096] It should be noted that the learning model uses mathematical regression tools derived from machine learning methods. For example, this tool can take the form of a formal neural network. However, this type of approach is sometimes called "black box" modeling, where only measurements are used, and it has some limitations, especially because the database used in the learning process is not exhaustive and does not contain all the types of arcs to be detected.

[0097] It should also be noted that knowledge modeling allows for at least a partial description of the physical behavior of the electric arc being attempted to be detected. However, this modeling also has some limitations. Specifically, the generalizability of this approach may be questionable: for example, its effectiveness and performance may be reduced due to the high variability of parameters of the electric arc and its environment.

[0098] The method of the present invention provides a process 100 that corrects the limitations of each method by combining these methods. More specifically, in the process according to the invention, a knowledge model derived from the physical properties of the arc allows for the definition of a framework for the fault behavior to be detected. Thus, in cases where data for adjusting the model through learning is scarce, this knowledge model allows for decision-making that does not deviate from the known operation of the mechanism under study (in this case, the fault arc).

[0099] On the other hand, any inaccuracies in the knowledge model can be adjusted using data containing information about all variations of the quantity of interest. More precisely, the learning model is trained by identifying arc characteristics in the experimental data. Simultaneously, this learning phase must be guided by expertise derived from one or more physical laws based on the knowledge of the physical properties of the arc.

[0100] In summary, in this invention, arc detection is designed and adjusted using tools derived from machine learning and knowledge derived from the physical properties of the system.

[0101] Learning stage

[0102] The process according to the invention first includes a learning phase. The purpose of this phase is to adjust the black-box model using a knowledge model and thus obtain a decision function that, based on measurements taken on the power line, gives a Boolean value (or any other equivalent representation) characterizing the presence of a fault arc on the power line.

[0103] For this learning to take place, multiple measurements are required, each of which includes current I, source voltage V, etc. source and arc voltage V arc Time-dependent measurements. "Time-dependent" refers to current measurements I and source voltage measurements V measured at the same time t, with the same horizontal axis t.source and arc voltage measurement value V arc .

[0104] If these measurements are unavailable, it may be necessary to collect them, for example, during laboratory measurements. To this end, in one embodiment, the learning phase PA includes the step of acquiring multiple measurements, each including current I, source voltage V, etc. source and arc voltage V arc The time-related measurements. As already mentioned, this step is typically performed in a laboratory setting, where tests are conducted to generate a database that includes multiple raw measurements.

[0105] At the end of this step, multiple measurements are obtained, each of which is described using the following notation:

[0106]

[0107] Among them, t m It is discrete time, I(t) m ) is as t m The current, V, is a function of the current. arc (t m ) is as t m The arc voltage, V, is a function of the arc voltage. source (t m ) is as t m The source voltage is a function of M, where M is the total number of points available in the considered measurements.

[0108] The learning phase PA also includes: using multiple measurements, step E1: adjusting the learning model, which will use the current I and source voltage V source As input, and the arc voltage V arc The constants associated with the selected knowledge model (e.g., the arc constant τ and cooling power P0 when the knowledge model is a Mayr model) are output. During this step E1, learning is performed using a cost function L to be minimized, given by the following relationship L = L1 + L2. It should be noted that the cost function is a parameterizable function used to define the error. The closer the result of the cost function is to 0, the smaller the error.

[0109] In the above relationship, the term L1 is defined as the comparison between the output value calculated by the learning model and the measured value, and this error applies only to the arc voltage V. arc And is calculated. Therefore, L1 represents the arc voltage predicted by the learned model. With the measured arc voltage V arc The difference between them is given by the following equation:

[0110]

[0111] The term L2 represents the difference between the predicted value from the knowledge model and the measured value. Therefore, its expression depends on the knowledge model used. In any case, the knowledge model used must be able to provide the arc voltage V. arc As output.

[0112] In one embodiment, which will be described as an example in the remainder of the specification, the knowledge model used is the Mayr model. In this embodiment, the learned and adapted model is constructed using a formal neural network.

[0113] In an alternative embodiment, the knowledge model is a Cassie model. In this embodiment, the learned and adjusted model can be constructed using a support vector machine.

[0114] In an alternative embodiment, the knowledge model is a Shavamaker model. In this embodiment, the learned and adjusted model can be constructed using a support vector machine.

[0115] For ease of explanation, the Mayr model will be used in the following text. It should be noted that the Mayr model is derived from the energy balance between the amount lost due to cooling and the amount supplied by the circuit. Specifically, the Mayr model provides the following dynamic equation:

[0116]

[0117] in Let be the conductance of the arc column (ignoring the influence of the arc root). This equation can be written as:

[0118]

[0119] Where τ is the arc time constant, τ=τ(T,P,l); and P0 is the cooling power, P0=P0(T,P,l), where T is the room temperature, P is the ambient pressure, and l is the arc length.

[0120] The cost function L2 can be written as follows:

[0121]

[0122] Therefore, the learning steps primarily aim to refine the mathematical model, which will determine the function:

[0123] f:(I(t m V source (t m ))→(V arc (t m ), τ, P0)

[0124] More specifically, learning algorithms use measured values ​​to determine the output variable (V). arc (t m ), τ, P0). However, among the multiple measurements, only the arc voltage V arc (t m The knowledge model already selected will be used to determine the pair (τ, P0) (in the case of the Mayr model), which must satisfy the equation.

[0125] Therefore, at the end of step E1, the previously introduced function f is determined (and does not change during the detection phase described below).

[0126] PD detection phase

[0127] Once the learning phase is complete, the resulting model (which minimizes L in the optimal way) can be used to calculate the input from the arc signal (I(t)). m V source (t m Correctly predict the output (V) arc (t m ), τ, P0).

[0128] During the detection phase (PD), the model will receive M inputs. These inputs represent the signal window obtained from the sensor (typically the line current I and the source-side voltage V). source However, other quantities can also be expected to be functions of the knowledge model, such as temperature and pressure. Next, the learning model processes the M outputs through the previously introduced function f. Predictions are made, and these outputs depend on the chosen knowledge model. The outputs calculated by the model are used to evaluate the error function L2, and thus determine whether the corresponding signal is an arc (if the prediction is correct, i.e., the error function value is low) or a non-arc (if the prediction is incorrect, i.e., the error function value is not low).

[0129] The principle stated in the previous paragraph can be simply expressed using the previously introduced error function L2, as follows:

[0130]

[0131] The threshold ε will be adjusted based on the availability of so-called nominal data. The sensitivity of this threshold may vary depending on the application domain. It can be defined empirically (possibly through calibration) as a function of the expected performance of the detection model. Performance can be evaluated, for example, as the ratio of false negatives to false positives.

[0132] Therefore, the detection phase PD of the process according to the present invention includes step E2, which continuously measures the current I and the source voltage V on the power line. source Based on these continuous measurements, a window containing M measurements can then be created, denoted as... (As previously introduced). Of course, this is a sliding window that changes as measurements are acquired during measurement step E2.

[0133] It is through this sliding window that continuous detection of fault arcs becomes possible.

[0134] The detection phase PD also includes step E3, which involves measuring the current I and source voltage V on the power line during the measurement step. source The function that takes the last M input data points uses a decision function to continuously determine the presence of an electric arc. As an example, this decision function is defined by the following expression:

[0135]

[0136] Where X m ={I(t) m V source (t m )}.

[0137] In one embodiment, the power line is equipped with a current interruption device for interrupting the current in the line where the detection is performed. The process 100 according to the invention includes: when an arc is detected during step E3 of determining the presence of an arc, sending a command to the interruption device to interrupt the current in the line under consideration. This allows damage associated with arc formation on the power line under consideration to be prevented or at least limited.

[0138] Design of decision functions

[0139] In one embodiment, the process 100 according to the invention occurs in at least two phases, referred to herein as PC and PD:

[0140] - The design phase PC is used to determine the decision function, which takes multiple descriptors derived from the current measurements as input and outputs a Boolean value (or any equivalent representation) characterizing whether an arc exists in the considered measurements;

[0141] -Detection Phase PD: During this phase, the current on the power line is measured in order to extract the descriptor identified during the Design Phase PC from the measurement, and the decision function determined during the Design Phase PC is used to detect the presence of an arc.

[0142] Optionally, when multiple measurements required during the design phase are unavailable, the method may further include an acquisition phase aimed at obtaining the multiple measurements.

[0143] Measurement value acquisition

[0144] As already mentioned, if measurements are unavailable, it may be necessary to collect them. Therefore, in one embodiment, process 100 includes an acquisition phase prior to the design phase (PC) that includes steps for acquiring multiple measurements, each including time-related measurements of arc voltage and arc current. Such measurements are as follows: [...] Figure 3 The diagram illustrates the arc current measurement at the top and the corresponding arc voltage measurement at the bottom, both of which are time-dependent (i.e., arc current and arc voltage measurements with the same horizontal axis t measured at the same time t). For example, the power line is an aircraft network power line.

[0145] This stage is typically conducted in a laboratory setting, where tests are performed to generate a database containing multiple raw measurements. These raw measurements are accompanied by information related to them, particularly:

[0146] - The sampling frequency during the measurement, for example, 1MHz;

[0147] - A description of the measured signal, including:

[0148] ■Measured value of arc current (or line current);

[0149] ■Measured value of arc voltage;

[0150] - Database size: Number of tests (and therefore the number of nominal and arc regions - preferably large enough, such as hundreds or thousands of windows).

[0151] Furthermore, in each measurement, the arc voltage and current measurements are time-dependent.

[0152] To learn the information that leads to a high true positive rate (reliability aspect) and a low false positive rate (robustness aspect), two types of signals are needed: arc characteristics and nominal regions. The nominal region refers to all characteristics where an arc does not exist. Therefore, this corresponds to the nominal state of an electrical load connected to the network and powered by a supervised cable, but also to abnormal states (surges, load reconfigurations, etc.). Therefore, the database must include these signals as broadly as possible (aircraft loads, tests in harsh representative environments).

[0153] Once measurements have been acquired, preprocessing them to facilitate analysis can be advantageous. Therefore, in one embodiment, the acquisition phase of the process according to the invention includes a step of preprocessing the acquired measurements. This preprocessing step, in particular, enables the acquisition to be standardized and eliminates biases and faults in the measurement chain.

[0154] Decision function design phase

[0155] In one implementation, process 100 includes a stage PC for designing a decision function using multiple measurements (possibly preprocessed as described above). This stage aims to determine the decision function as described above, which is a function that takes multiple descriptors extracted from the arc current measurements as input and outputs a Boolean value (or any equivalent representation) characterizing the presence of an arc.

[0156] Pre-identification steps

[0157] Preferably, the design phase PC first includes a preliminary identification step using expert knowledge, which involves a coarse identification of all arcs meeting predetermined criteria (accuracy not within a single sample). In this first step, the expert coarsely identifies all arcs in all tests across all measurements. This identification accuracy is not within a single sample. It simply defines the location of each arc within the acquired data. Figure 4 The image shows these data after pre-identification, with two electric arcs (arc 1 and arc 2) identified by dashed circles.

[0158] In one embodiment, this pre-identification is performed based on metric standards such as minimum arc duration, minimum arc voltage, etc. In another embodiment, measurements from multiple measurements are stored in one or more files, and the time location and number of arcs for each measurement file are stored in a summary file.

[0159] Although this step is optional, it can improve the performance of the decision function obtained at the end of the design phase PC.

[0160] Marking steps

[0161] The learning phase includes a marking step E11. The novelty of marking step E11 in this invention lies in its application of logic based on the physical characteristics of the electric arc: for each measurement, it uses an arc voltage measurement (available only in the laboratory) as a reference to automatically mark the arc current (or line current—available in the laboratory and later during the detection phase PD) measurement. During this step E11, an algorithm (described below) scans all measurements among the multiple measurements to accurately identify the arc start and end information in each arc voltage measurement, and thus selects the relevant portion (in other words, the marked portion corresponding to the measurement window) in each corresponding arc current measurement. The relevant portion thus selected from each arc current measurement among the multiple measurements is then used for learning. The marked window is thus marked and saved. Therefore, it is possible to base learning on a pre-selected criterion (e.g., threshold voltage U). s -See the detailed description of the tagging steps below to tag the data.

[0162] Verification steps

[0163] Preferably, the design phase PC includes a step of manually verifying the markings using expert knowledge at the end of the marking step. During this step, one or more experts verify the set of windows thus saved. During this step, windows that have not yet been marked but correspond to the occurrence of the arc can therefore be manually marked. Similarly, incorrectly marked windows (because the phenomenon has atypical characteristics) can also be remarked. As a general rule, marked windows are saved, while other measurements are anonymized and removed from the save. In other words, this step allows verification that the marked measurements include all areas intended for learning, i.e., windows including measurements before arc formation, measurements corresponding to arc formation, and windows including measurements after arc formation.

[0164] While optional, this step is very useful because some arcs may not be correctly identified during the marking step E11. Therefore, this optional step can help improve the decision function obtained at the end of the design phase PC.

[0165] Manual identification steps

[0166] Preferably, the design phase PC includes a step for manually identifying remaining arcs (i.e., missing arcs) at the end of the marking step. During this step, a check is performed to examine the differences in the number and location of arcs identified during the pre-identification step (when the same step is performed) and during the marking verification step (when the same step is performed). All arcs identified during the pre-identification step and all arcs not marked at the end of the marking verification step are then manually marked, with the goal of marking all arcs present in the measurements across multiple measurements.

[0167] Although this step is optional, it helps to improve the decision function obtained at the end of the design phase PC.

[0168] Descriptor extraction steps

[0169] The design phase PC also includes step E12, where, for each of the multiple measurements, a descriptor is extracted from each window of the arc current measurement that was marked during the marking step E11. In fact, to tune the learning model, descriptors need to be extracted from the data window associated with each measurement characterizing the phenomenon to be detected, which has already been identified during the marking step E11. These descriptors are informational characteristics about the measurement window being analyzed, and therefore also informational characteristics about the phenomenon to be detected (in this case, the formation of the arc).

[0170] Extraction step E12 can be performed in at least two different ways:

[0171] - Use unsupervised learning methods, such as autoencoders; in this case, the descriptors have no physical interpretation.

[0172] -Use prior physical knowledge that may be contained in the measurements, for example:

[0173] ■ Frequency components, such as those following Fourier transform or wavelet transform;

[0174] ■ Statistical moments, such as mean, standard deviation, kurtosis, and skewness;

[0175] ■Time analysis.

[0176] Preferably, in process 100 according to the invention, prior physical knowledge is used to extract descriptors, and the descriptors include the spectral entropy and / or autocorrelation of the arc current measurements within the selected window.

[0177] In one embodiment, the process includes a step of normalizing the measurements among a plurality of measurements after the descriptor extraction step.

[0178] Descriptor classification and selection steps

[0179] In one embodiment, the design-phase PC also includes steps for classifying and selecting descriptors. In reality, not all extracted descriptors necessarily possess properties that lead to correct isolation of the two existing window categories (arcs and nominals). Therefore, analyzing the importance and relevance levels of descriptors to window labels can be useful and can improve the performance of the decision function. In fact, poor descriptors can potentially corrupt predictions, thereby (sometimes drastically) degrading the final performance of the decision function. Descriptor selection can generally lead to better learning performance, such as higher efficiency, lower computational cost, and more effective automatic arc detection models. Therefore, this embodiment is particularly advantageous when a large number of descriptors are available.

[0180] Therefore, the purpose of the descriptor selection step is to maximize relevance and minimize information redundancy. In one exemplary embodiment, this step is performed using a supervised filtering method.

[0181] In one exemplary embodiment, the Gram-Schmidt method can be used for classification, and an incremental method can be used for selection. Of course, other methods can also be used for classification or selection.

[0182] Although this step is optional, it helps to improve the decision function obtained at the end of the design phase PC.

[0183] Decision function determination steps

[0184] The design phase PC also includes a step E13 to determine the decision function, hereinafter denoted as f(X) (where X represents a descriptor extracted from the arc current measurement and provided as input to the decision function).

[0185] In one embodiment, this step E13 includes multiple iterations of the following two sub-steps:

[0186] - The sub-step of designing a classifier through learning; and

[0187] - A sub-step to verify the classifier based on the labeled data.

[0188] Furthermore, these sub-steps are repeated until the most effective classifier is obtained, i.e., a classifier that minimizes the classification error based on unlearned data to below a threshold (in order to ensure the generalization ability of the classifier). The decision function f(X) is then determined by this classifier.

[0189] Therefore, determining the classifier allows for the acquisition of an efficient classifier through learning (corresponding to multiple iterations of the aforementioned sub-steps), thereby enabling effective decision-making.

[0190] To implement step E13, several supervised classification methods can be used. The choice of method is particularly likely to be influenced by the desired detection time: some methods may have higher computational complexity but better performance. Preferably, the classification method used in this step is the support vector machine method. Since this method is well known to those skilled in the art, it will not be described in detail here.

[0191] In an alternative embodiment, the classification method is selected from one of the following methods:

[0192] - Formal neural networks (simple, convolutional, recurrent);

[0193] -Hidden Markov Model;

[0194] -K-nearest neighbor method;

[0195] - Decision tree;

[0196] - Ensemble learning (pairing two methods from the methods listed above).

[0197] All the steps E11-E13 described above are performed before the detection phase (PD), and by the end of the design phase (PC), the decision function (and thus the detection strategy) has been established. Therefore, the descriptors selected during the design phase (PC) will be used during the detection phase (PD). During the detection phase (PD), these same descriptors will thus be extracted from the measured signal (e.g., via signal processing) and used as input to the decision function, which assigns the signal to either the "arc" category or the "nominal regime" category (i.e., no arc).

[0198] Detailed description of the marking steps

[0199] In the following text, the following symbols will be used to illustrate the marking step E11:

[0200] -t is the time period to be considered;

[0201] -t end This is the total duration of the current test;

[0202] -T max It is the maximum window duration;

[0203] -T min It is the minimum window duration;

[0204] -P g It is the left-hand step; its value has been normalized according to the duration of the window under study and is between [0, 1].

[0205] -P d It's a right-side step; P d=1-P g Therefore, it is also a value normalized for the duration of the window under study, and it lies between [0, 1].

[0206] -t d It is the time when the electric arc begins;

[0207] -t e It is the arc extinction time;

[0208] -t evaluation It is higher than U before the arc begins s The percentage of points evaluated in the evaluation time;

[0209] -U arc It is the arc voltage;

[0210] -I arc It is arc current;

[0211] -U s It is the minimum voltage threshold at which the existence of an electric arc is considered true; this voltage threshold (or threshold voltage) is a function of knowledge of the physical properties of the electric arc.

[0212] As previously detailed, the marking step E11 according to the invention occurs after the signal acquisition step, and even after the signal preprocessing step. In the case of the electrical characteristics of a fault arc, the only information that guarantees the existence of the arc is the measured value of the voltage across its terminals (arc voltage), because this value is zero in the absence of discharge, and only greater than a certain value when an arc is present. It should be noted that the arc voltage information is not measured during the detection phase (PD) (because it is unavailable). This information is only accessible and usable during the design phase (PC). Therefore, the marking strategy according to the invention is defined based on this information. In other words, the arc voltage measurement is only used to mark the current measurement (for learning and verification of data acquired in the laboratory), and this use is limited to the design phase (PC).

[0213] Furthermore, during the labeling step E11, the characteristics of the phenomenon to be detected must be explicitly defined. These characteristics indicate the specificity of the fault being sought to be detected.

[0214] In one exemplary embodiment, the characteristics of the arc to be detected are as follows:

[0215] - Arc duration ≥ 1 millisecond;

[0216] - The arc voltage increases from 0 to a minimum of 10V.

[0217] In one exemplary embodiment, the characteristics of the window marked as an electric arc are as follows:

[0218] - Window duration is between 1 and 10 ms;

[0219] - There is a negative time offset, the duration of which is proportional to the length of the window;

[0220] - There are no arc termination characteristics (related to the arc voltage dropping to 0V).

[0221] These values ​​are provided as examples only and do not imply any limitation on the invention.

[0222] In the prior art, marking is a delicate and time-consuming operation. However, in the process 100 according to the invention, this step E11 is automated, ensuring the same result as manual implementation while optimizing the time spent.

[0223] Therefore, the marking step E11, for each measurement and each time interval t of the considered measurements, includes the following sub-steps:

[0224] -When the measured arc voltage U arc First time exceeding the predetermined threshold U s When (i.e., when the following relation first appears: U) arc (t)>U s And U arc (t-1) s Where t is the interval under consideration), the interval under consideration is recorded as the starting point of the arc (in other words, t). d =t) steps;

[0225] -When the measured arc voltage U arc The price first falls back to the predetermined threshold U s The following occurs (i.e., when the following relationship first appears: U) arc (t) s And U arc (t-1)>U s Where t is the interval under consideration), the interval before the interval under consideration (i.e., t-1) is recorded as the end point of the arc (in other words, t). e =t-1) steps.

[0226] These two sub-steps are illustrated in the form of a flowchart in [ Figure 5 In this flowchart, the measured arc voltage is compared to a threshold arc voltage. If the measured arc voltage is higher than the threshold arc voltage, the previous arc voltage value is verified. If none of the previous values ​​were higher than the threshold, meaning the arc voltage has exceeded the threshold for the first time, a signal is sent to indicate the start of the arc. Otherwise, no action is taken. Similarly, if the measured arc voltage is lower than the threshold, while the threshold is higher than the same threshold, the signal indicates the arc voltage has fallen back below the threshold, and a signal is sent to indicate the end of the arc. ​​

[0227] In one embodiment, for each measurement, a tag is associated with a measurement window used for learning, the window being defined by intervals [P]. g ×min((t e -t d ), T max ); P d ×min((t e -t d ), T max The measurement window is given as follows: Descriptors will be extracted from the data within this interval. This measurement window is like […]. Figure 6 The figure shown illustrates the arc current as a function of time at the top and the arc voltage as a function of time at the bottom. This is a simplified representation of the electrical curves that appear in the case of a series arc of DC voltage on an electrical system supplying a resistive load. Figure 6 In the example shown, the appearance of an electric arc is represented by a voltage rise of several or tens of volts on the voltage curve. On the current curve, this is represented by a current drop occurring at the same moment. In addition to these drops, the marking step also attempts to preserve a small portion of the signal to the left of the drop (the nominal region) and a larger portion of the signal to the right of the drop (the established arc) in order to store the important frequency components of the phenomenon. As already mentioned, at time t... d At that time, the start of the electric arc is first identified by the measured arc voltage U. arc Exceeding a predetermined threshold U selected based on the physical properties of the electric arc s The moment of time. In one embodiment, U s The value is given by the sum of the voltage drops at the anode and cathode; for example, the sum of the two voltage drops in air is 20V.

[0228] Once the start of the arc has been identified, its end is determined in the same way (t). e However, the end point indicates the moment when the voltage returns to below a predetermined threshold value. Therefore, the duration of the analyzed arc (d = t) can be identified. e -t d If the duration is greater than the maximum window size expected in the detection (T) max If the arc duration is less than the predetermined window duration but greater than the minimum acceptable arc duration (T), then this predefined maximum value is taken as a reference. Otherwise, if the arc duration is less than the predetermined window duration but greater than the minimum acceptable arc duration (T), then... min If the arc duration is selected as the reference window, then the arc duration is used as a percentage of that reference duration (P). d +P g =1), t d The areas on the left and right sides are added together. Then, all the arcs are marked in this way.

[0229] In one embodiment, the threshold voltage is determined based on a process of measuring the voltage on the arc as a function of the arc length, in […]. Figure 7 This is illustrated in the diagram. Three zones can be identified in the figure. In the zones located at the beginning and end of the arc, the arc voltage varies non-linearly. These zones are the anode and cathode zones, where the arc voltage drop represents a significant, unavoidable value that is systematically greater than 0V. Generally, under aerospace environmental conditions, V c +V a The value is between 10 and 25V. The third interval is the central interval, in which the arc voltage increases linearly as a function of the arc travel distance, and is not particularly of concern in the implementation of this invention. In other words, the occurrence of an arc will systematically be accompanied by the generation of an arc voltage, the value of which will be defined by the minimum threshold explained by the voltage drop across the electrodes.

[0230] Testing phase

[0231] To detect the presence of an electric arc on a power line, the method includes a detection phase (PD) following the design phase (PC). In this phase, a decision function obtained during the PC phase is used to determine whether an arc is present in the current measurement. Unlike the PC phase, where the arc voltage is a usable measurement, in real-world situations (outside the laboratory), during the PD phase, only the arc current measurement may be available. Therefore, detection will preferably be based solely on this measurement.

[0232] More specifically, the detection phase PD first includes step E14, which measures the current flowing in the power line. This step E14 is performed continuously in real time to enable rapid detection of the presence of an electric arc.

[0233] The detection phase (PD) also includes step E15, which extracts descriptors from the current measurements. As already mentioned, the descriptors extracted during step E15 are the same as those selected during the design phase (PC) and are used as input data for the decision function. These descriptors are also extracted continuously as current measurements are acquired.

[0234] The detection phase (PD) also includes step E16, which detects the presence of an electric arc while measuring the current flowing on the power line LI. This step uses a descriptor extracted from the current measurement and a decision function determined during the design phase (PC).

[0235] In one embodiment, a current-cutting device can be used to cut off the current in the power line LI on which the detection is performed, and the process 100 according to the invention includes the step of sending an instruction to the cutting device MMC to cut off the current on the line LI under consideration when an arc is detected during the detection step E16. This makes it possible to prevent or at least limit the damage associated with the formation of an arc on the power line LI under consideration.

[0236] The quality of detection depends on the quality of learning, which in turn depends on the quality of data and labeling. One contribution of the process according to the invention is the automation of labeling by using multiple measurements (typically performed in a laboratory), each measurement including time-related measurements of arc voltage and arc current.

[0237] Device for detecting the presence of electric arc

[0238] like[ Figure 8 The second aspect of the invention illustrated in [figure] relates to a device DI comprising means configured to implement process 100 according to the invention. More specifically, the device includes a computing device MC (e.g., a processor or ASIC card) associated with a memory MM (e.g., RAM and / or a hard disk), the memory MM being configured to store data and instructions required to implement process 100 according to the invention. The device DI according to the invention also includes a measuring device CPT configured to measure in real time the current flowing through the power line LI when connected to the power line LI, and to transmit the measured value to the computing device MC of the device DI according to the invention. In one exemplary embodiment, the device is an RCCB (Remote Controller Circuit Breaker) or an SSPC (Solid State Power Controller).

[0239] In one embodiment, the current transmitted through the power line LI can be interrupted by a remotely controllable current interruption device MCC, and the device DI according to the invention is configured such that when the presence of an electric arc is detected on the power line LI, it sends a command to the current interruption device MCC to interrupt the current in the power line.

Claims

1. A computer-implemented process (100) for detecting the presence of electric arcs on power lines (LI) using machine learning methods, learning to perform the following: - Multiple measurements related to the formation of the electric arc, each of which includes the arc voltage V. arc Current I and source voltage V source Time-related measurements; - Knowledge model, which will include arc voltage V arc The current I is related to a constant that depends on the knowledge model; Process (100) is implemented using a learning model derived from the learning phase (PA), during which steps (E1) are implemented to adjust the learning model using multiple measurements and a knowledge model. The learning model incorporates current I and source voltage V. source As input, and providing the arc voltage V arc The constants of the knowledge model are used as outputs, and learning is performed using a cost function L, which is given by the following relationship: L = L1 + L2, where L1 is the first cost sub-function used to measure the arc voltage predicted by the learning model. With the measured arc voltage V arc The first difference between them: Furthermore, L2 is the second cost subfunction, used to measure the second difference between the predicted value and the measured value of the knowledge model; The method includes a detection phase (PD), which includes: - Step (E2): Continuously measure the current I and source voltage V on the power line (LI). source So that in the measurement window Internal acquisition of current I and source voltage V source The relevant input data, where M is the number of measurement points in the measurement window, and I(t) m ) is at time t m The current at that time, and V source (t m ) is at time t m Source voltage at that time; - Step (E3): As measured during the measurement step, the current I and source voltage V measured on the power line (LI) are... source The function for the last M input data uses a decision function to continuously determine the presence of an electric arc, which is a function of the second sub-function.

2. The process according to the preceding claim, wherein the decision function is defined by the following expression: in, X m ={I(t) m V source (t m )), ε is the detection threshold, and L2(X m ) is used at point X m The value of the second cost subfunction L2 determined by the learning model calculated at the location.

3. The process according to the preceding claims, wherein the knowledge model is a Mayr model, and the second cost sub-function L2 takes the following form: Where τ is the arc constant and P0 is the cooling power.

4. The process according to claim 1, wherein the knowledge model is a Cassie model, and the second cost sub-function L2 takes the following form: Where τ is the arc constant, and V0 is the minimum arc voltage.

5. The process according to claim 1, wherein, The knowledge model is the Shavemaker model, and the second cost subfunction L2 takes the following form: Where τ is the arc constant, P0 is the cooling power, and V0 is the minimum arc voltage.

6. The process (100) according to any one of the preceding claims, wherein the power line (LI) is equipped with a cutting device (MCC) for cutting off the current in the line, the process (100) comprising the step of sending an instruction to the cutting device (MCC) to cut off the current on the line (LI) under consideration when an arc is detected during the detection step (E3).

7. The process (100) according to claim 1, wherein the process further comprises: - The design phase (PC) uses multiple measurements and machine learning to design the decision function. The design phase (PC) includes: ■ Step (E11): For each of the multiple measurements, the arc current measurement is marked with its associated arc voltage measurement. ■ Step (E12): Extract descriptors from the labeled measurements derived in the labeling step; ■ Step (E13): Determine the decision function using machine learning based on at least a portion of the descriptors extracted during extraction step (E12); The stage (PD) for detecting the presence of an electric arc includes: ■Step (E14): Measure the current flowing in the line (LI); ■ Step (E15): Extract the descriptor from the current measurement value obtained in the previous current measurement step (E14); ■ Step (E16): Detect the presence of an electric arc in the current measurement from a portion of the descriptor extracted during the previous step and using the decision function determined during the design phase (PC). For each of the multiple measurements and for each time interval t of the considered measurements, the labeling step (E11) includes: -When the measured arc voltage U arc First time exceeding the predetermined threshold U s At that time, the interval under consideration is recorded as the starting point t of the electric arc. d Steps; -When the measured arc voltage U arc First drop back to the predetermined threshold U s In the following case, the interval preceding the considered interval is recorded as the end point t of the arc. e The steps.

8. The process of claim 7, wherein for each measurement, a label is associated with a measurement window for learning, the window being defined by intervals [P]. g ×min((t e -t d ), T max ); P d ×min((t e -t d ), T max The given information is T. max It is the predefined maximum window duration, P g It is t d The left spacing, which has a normalized value for the duration of the window under study; while P d It is t d The right spacing, which has the relation P d =1-P g The given normalized value is the duration of the window for the study.

9. The process according to any one of claims 7 or 8, comprising: Prior to the design phase, the necessary signal acquisition steps are learned in order to obtain multiple measurements, each including time-dependent measurements of arc voltage and arc current.

10. The process according to any one of claims 7 to 9, wherein the design phase includes the step of: prior to the marking step, manually pre-identifying all arcs that meet predetermined criteria in each of the plurality of measurements using expertise, thereby defining the position of each arc in each of the plurality of measurements.

11. The process according to any one of claims 7 to 10, wherein the design phase includes the step of: at the end of the marking step (E11), manually verifying the output of the marking step using expertise to verify that the marked measurements include all regions intended for learning.

12. The process according to any one of claims 7 to 11, wherein the descriptor used during the step (E13) of determining the decision function includes the spectral entropy and / or autocorrelation of the arc current.

13. An apparatus (DI) for detecting the presence of an electric arc in a current line (LI), the apparatus comprising: A measuring device (CPT) configured to measure the current flowing in a current circuit; And an apparatus configured to carry out the process (100) according to any one of claims 1 to 5.

14. A computer program comprising instructions that, when executed by a computer, cause the device according to claim 13 to perform the process according to any one of claims 1 to 12.

15. A computer-readable medium having a computer program recorded thereon according to claim 14.

16. An aircraft comprising the detection device according to claim 13.

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