Method for managing an explosion in a real environment

Abstract

According to one aspect, the invention relates to a method (100) for managing a first explosion in a real environment, the real environment comprising at least one obstacle and the method (100) comprising the steps of: - determining (30) an area of effect of the zero-order wave of the first explosion; - determining (40) at least one second waveform characterising at least one first-order diffracted wave and / or at least one first-order reflected wave, generated by the first explosion; - calculating (60), for at least one point of the model, a pressure signal resulting from a set of waves generated by the first explosion, the set of waves comprising at least the zero-order wave and the at least one first-order diffracted wave and / or the at least one first-order reflected wave, the calculation of the pressure signal comprising calculating a contribution of each wave of the set of waves; and - displaying (80), for the at least one point of the model, a result of the calculation of the pressure signal.

Description

DESCRIPTION TITLE: Method for managing an explosion in a real environment TECHNICAL FIELD OF THE INVENTION

[0001] The technical field of the invention is that of managing an explosion in a real environment.

[0002] The present invention relates to a method for managing an explosion in a real environment and in particular to a method for managing an explosion in a real environment comprising a calculation of a pressure signal resulting from a set of waves generated by the explosion. TECHNOLOGICAL BACKGROUND OF THE INVENTION

[0003] An explosion can be defined by the rapid increase in a volume of gas and by an extreme release of energy. In other words, the explosion generates a sudden release of energy that causes the propagation of at least one blast or shock wave and therefore an overpressure in the surrounding environment. An explosion can be caused by multiple sources: an attack, a military strike, an industrial accident or the malfunction of an object such as a pressurized capacity or an electric vehicle battery. For the purposes of this application, only explosions in a fluid, gas or liquid medium are considered.

[0004] An explosion can cause human and material damage in a real environment. The real environment may correspond in the present application to an urban area, for example a district of a city, or inside a building, for example a car park, or inside a vehicle, such as an aircraft or a train or a bus. The real environment includes at least one obstacle which may correspond to a building when the real environment is an urban area. The obstacle may also correspond to a post or a wall or to an object such as a seat when the real environment is the interior of a building or a vehicle. An obstacle is, in the present application, any object or thing causing an obstruction to the propagation of at least one wave linked to the explosion. In other words, the term "obstacle" means in the present application anything that stops, reflects or slows down the waves emitted by the explosion(s).

[0005] In this application, explosion management may correspond to the prevention of such human and material damage by carrying out a simulation of a possible explosion that may occur in the future. Explosion management may also correspond to the actions implemented to limit or prevent such human and material damage by carrying out a simulation of a possible explosion that may occur in the future.For example, the management of an explosion may include: the sending, by one or more operational personnel such as firefighters, bomb disposal experts, intervention forces, of an alert signal or an evacuation order, and / or the evacuation, by the operational personnel, of an area of the real environment or of a building, and / or the development of an area of the real environment such as, for example, the reinforcement of the structure of a building, the replacement of standard windows with reinforced windows, the addition of an anti-explosion device, and / or, the sizing of emergency resources and / or the definition of a response strategy in the face of an explosion scenario, etc.

[0006] In order to improve explosion management, there are numerical methods for simulating an explosion based, for example, on a finite element, finite difference or finite volume model representing the real environment in which the explosion has occurred or is likely to occur. These methods use the resolution of physical equations, discretized in time and space, to evaluate overpressures for each cell of the finite element, difference or finite volume model at a given time. These methods present several problems preventing effective explosion management.

[0007] First of all, these methods require excessive computing resources and / or computing times and / or technical skills for implementation and / or to be able to be used directly in the field by an operational person. Thus, these methods are not suitable for use in emergency situations. In addition, the discretization of the signal, particularly spatially using the model mesh, acts as a low-pass filter. Thus, these prior art methods lack precision, particularly for assessing damage related to the explosion, particularly at a great distance from the explosive source. Indeed, the very high frequency components generated by the explosion are not taken into account with these methods because of the model mesh. To limit this low-pass filter problem, it is possible to reduce the size of the model meshes. However, this solution is not compatible with the use of such methods for managing an explosion since the computation time and / or the computational resources required to implement these methods increase polynomially with the reduction of the model mesh size.

[0008] Thus, there is a need to provide a method of managing an explosion which limits, at least partially, the problems associated with the use of prior art methods. SUMMARY OF THE INVENTION

[0009] The invention offers a solution to the problems mentioned above, based in particular on a model representing the real environment comprising a continuous medium representing a gas or a liquid. In addition, the invention adopts an innovative approach. For example, the method is based on a unified methodology for determining the spatial extents of the different unit waves generated by the explosion(s). The method according to the invention thus spatially analyzes the propagation of at least one wave generated by the explosion. Indeed, the method according to the invention is based on a vision of the propagation of the air shock wave, not temporal as in a numerical calculation, but rather spatial, or rather a succession of waves generated by different physical phenomena from the initial wave emitted from the site of the explosion. In addition, each unit wave is associated with geometric elements.

[0010] One aspect of the invention relates to a computer-implemented method for managing a first explosion in a real environment, the real environment comprising at least one obstacle and the method comprising the steps of: obtaining a model representing the real environment, the model comprising: a continuous medium representing a gas or a liquid, and at least one geometric shape representing the at least one obstacle, obtaining a position of the first explosion within said model and a first waveform characterizing a zero-order wave generated by the first explosion, determining a zone of effect of the zero-order wave of the first explosion, the zone of effect of the zero-order wave corresponding to the visible points of the model from the position of the first explosion, determining at least a second waveform characterizing at least one first-order diffracted wave and / or at least one first-order reflected wave and a zone of effect for each first-order diffracted wave and / or each first-order reflected wave, generated by the first explosion, calculating, for at least one point of the model, a pressure signal resulting from a set of waves generated by the first explosion, the set of waves comprising at least the zero-order wave and the at least one first-order diffracted wave and / or the at least one reflected wave of order one,calculating the pressure signal including calculating a time contribution of each wave of the set of waves, and displaying, for the at least one point of the model, a result of the calculation of the pressure signal.,

[0011] Thanks to the invention, the management of an explosion is reliable, efficient and precise. Indeed, the method according to the invention is based on a model comprising a continuous medium, thus the low-pass filter problem is solved. In addition, the method according to the invention does not require significant computing resources and / or computing time and / or specific technical skills. Thus, an operational person, potentially from the real environment, can use a standard laptop computer to obtain the display of a result of the calculation of the pressure signal resulting from an explosion. The result is provided in only a few minutes, for example between 1 and 10 minutes. This rapid execution time of the method according to the invention therefore allows an operational person to make decisions based on precise information in a sufficiently short time to act urgently.In addition, the speed of the execution time of the method according to the invention also makes it possible to carry out a large number of explosion scenarios in a short time and while consuming fewer resources, particularly energy.

[0012] In addition to the characteristics which have just been mentioned in the preceding paragraph, the method according to one aspect of the invention may have one or more additional characteristics among the following, considered individually or according to all technically possible combinations: the method further comprises a final step of arranging the real environment, and / or sending an alert indicating a danger, the method further comprises a step of determining, for the at least one point of the model, at least one additional waveform characterizing at least one additional wave of order N with N > 2, the step of determining the at least one additional waveform being implemented after the determination of at least one second waveform and before the calculation of a pressure signal, a terrain of the real environment is flat and has a first altitude,and the at least one obstacle is described in the model by a polygonal footprint and a second altitude greater than the first altitude, and the first explosion takes place at ground level and an explosive, responsible for the first explosion, has a hemispherical shape, at least one second explosion is managed in the real environment, the second explosion being less than 1 second apart in time from the first explosion, and the calculation, for the at least one point of the model, of the pressure signal further comprises taking into account the set of waves generated by the at least one second explosion. the real environment represents an urban environment, the continuous medium represents the ambient air and the at least one obstacle represents a building, and a step of assessing material damage caused to said at least one building, the step of assessing the damage being implemented after the calculation of the pressure signal.,

[0013] A second aspect of the invention relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the latter to implement the method according to the invention.

[0014] A third aspect of the invention relates to a computer-readable recording medium comprising instructions which, when executed by a computer, cause the latter to implement the method according to the invention.

[0015] A fourth aspect of the invention relates to a system configured to perform the method according to the invention.

[0016] The invention and its various applications will be better understood by reading the following description and examining the accompanying figures. BRIEF DESCRIPTION OF THE FIGURES

[0017] The figures are presented for information purposes only and in no way limit the invention. Figure 1 shows a block diagram illustrating the steps of an example of the method 100 according to the invention. Figure 2 shows an example of propagation of a zero-order wave in a medium in the presence of obstacles, and in particular the corresponding spatial extent. Figure 3 shows an example of a so-called “modified Friedlander” analytical waveform that can be used in the method according to the invention to describe each unit wave. Figure 4 shows an example of variation of each of the parameters of the so-called “modified Friedlander” waveform as a function of a reduced distance Z for a unit wave propagating in the “free field” spatial extent. Figure 5 shows an example of a recursive tree of unit waves that can be used in the method according to the invention. Figure 6 shows an example of propagation of a zeroth order wave and first order reflected and diffracted waves and the corresponding spatial extents. Figure 7 shows a first example of displaying the result of the calculation of the pressure signal compatible with the method according to the invention. Figure 8 shows a second example of displaying the result of the calculation of the pressure signal compatible with the method according to the invention. Figure 9 shows a third example of displaying the result of the calculation of the pressure signal compatible with the method according to the invention. DETAILED DESCRIPTION

[0018] Unless otherwise specified, the same element appearing in different figures has a single reference.

[0019] Figure 1 is a block diagram illustrating the steps of an example of the method 100 according to the invention. The mandatory steps of the example of the method 100 are indicated by a solid rectangle and the optional steps are indicated by a dotted rectangle.

[0020] The method 100 according to the invention is computer-implemented. By "computer-implemented" it is understood that the steps, or substantially all of the steps, of the method 100 are executed by at least one computer or processor or any other similar system. Thus, steps are performed by the computer, possibly fully automatically, or semi-automatically. In examples, the triggering of at least some of the steps of these methods may be performed by user-computer interaction. The level of user-computer interaction required may depend on the intended level of automation and balanced against the need to implement the user's wishes. In examples, this level may be user-defined and / or predefined.

[0021] A typical example of a computer implementation of the method 100 is to execute the method 100 with a system adapted for this purpose. The system may include a processor coupled to a memory and a graphical user interface (GUI), the memory having recorded thereon a computer program comprising instructions for implementing the method. The memory may also store a database. The memory is any hardware adapted for such storage, possibly comprising several distinct physical parts.

[0022] Alternatively, the computer implementation of the method 100 comprises executing at least some steps of the method 100 on a remotely located server, the server executing the method in response to a request sent by a client system, for example a laptop or a mobile phone. smart, for "smartphone" in English. The request can for example be transmitted via a web-type application, in response to a user interaction, and when the server has finished performing the calculations, the server can transmit the results to the client system which can then display them. The transmission of information between the server and the client system can be carried out using a wireless mobile network, for example 3 ème or 4 ème generation.

[0023] The method 100 is a method for managing a first explosion in a real environment. Optionally, the method 100 may allow for managing several explosions. In one example, at least one second explosion may take place in the real environment and be taken into account by the method 100. For example, the second explosion may be less than a few microseconds apart in time from the first explosion, which leads to the effects of the two explosions being combined. The terms "management of one or more explosions" may mean in the present application the mitigation of the consequences of one or more explosions. For example, the method may be used to determine a dangerous zone, for example a building that is at risk of collapsing, which must be evacuated as quickly as possible.The term "management of one or more explosions" may also mean in this application the prevention of the consequences of one or more explosions that may occur. For example, the method may be used to determine an area to be modified in anticipation of one or more potential explosions, for example a building whose architecture must be reinforced or whose windows must be modified. The method may therefore be used for the design and manufacture of a room and / or a building and / or even a district in which one or more explosions could occur, for example due to the location of a factory. The actual environment includes at least one obstacle.

[0024] In one example, the terrain of the real environment is flat. The terrain of the real environment has a constant first elevation, for example, zero. Each obstacle in the real environment is described in the model by a polygonal footprint and a second elevation greater than the first elevation. The second elevation can also be constant. In this example, the first explosion occurs at the terrain level. In other words, the simulation of the first explosion is performed for an explosion that can occur or has occurred at the terrain level. In addition, the explosive that is responsible for the first explosion has a shape hemispherical. This example simplifies the calculations of the method 100 and therefore reduces the computing resources as well as the computing time required for its execution.

[0025] In one example, consistent with the previous example, the real-world environment represents an urban setting, such as a city district or an industrial and / or commercial area. In this example, an obstacle may represent a building such as a house, a building, or a commercial and / or industrial building.

[0026] In another example, consistent with the previous examples, the real environment represents a building and at least one obstacle is a wall and / or furniture and / or a vehicle. For example, the real environment may represent an underground parking lot and obstacles may be the walls of the parking lot but also parked cars.

[0027] A first step 10 of the method 100 comprises obtaining a model representing the real environment. The model is said to be “continuous,” that is, it does not require spatial discretization. Thus, the model is not discretized, for example using a mesh. Numerical methods of the finite element or finite volume or finite difference type as well as particle methods, for example smoothed particle hydrodynamics, are therefore not compatible with the method 100.

[0028] A continuous medium can therefore be defined as a medium: in which the distance between any two points is a continuous function, for example between any two calculation points and in particular between two points visible from each other, in which the properties (such as maximum overpressure, impulse, arrival time, positive phase duration) of shock waves, for example unit shock waves, are continuous functions of space, and for which calculations can be carried out at any point, excluding obstacles, with arbitrary coordinates.

[0029] It is also possible to note that by using a finite element or finite volume or finite difference type method, or even a particle method, it is possible to carry out calculations at all points, however these points are always attached to a mesh of the model or to a discretized element of the model.

[0030] The continuous medium may represent, for example, a gas, such as air, or a liquid, such as water. The obstacles are represented, for example, by 2D polygons or 3D polyhedra. The term “obtaining” may mean, in the present application, “receiving” and / or “generating”. For example, the model may be received by the computer implementing the method 100 or by querying a reference database, for example, the BD TOPO® database provided by the National Institute of Geographic and Forest Information or the OpenStreet Maps database. In another example, building data may be extracted from digital twins of buildings, commonly referred to as a BIM approach, for Building and Information Modeling.In another example, the model can be generated from data such as 3D scans, for 3 dimensions, or LiDAR images, for "Light Detection and Ranging" in English, of the real environment or by 3D reconstruction from photographs.

[0031] A second step 20 of the method 100 comprises obtaining a position of the first explosion within said model. Thus, this position makes it possible to locate the first explosion in the model representing the real environment. In addition, the second step 20 comprises obtaining a first analytical waveform linked to the first explosion. This first waveform characterizes a zero-order wave generated by the first explosion. A zero-order wave is a wave propagating in a free field, i.e. not having been in contact with an obstacle. Figure 2 illustrates the propagation of such a zero-order wave on a model comprising three obstacles. In Figure 2, the first explosion takes place at position 201, the obstacles 203, 204 and 205 are positioned close to position 201. The zero-order wave generated by the first explosion propagates over the entire area 202.The analytical waveform is used to represent the overpressure signal generated by the first explosion. In a free field, the overpressure signal generated by an air shock wave is characterized by a sharp rise followed by an exponential decrease, possibly disturbed by secondary peaks. In the case of experimental signals, the signal may be noisy. It is possible to. represent the overpressure signal by an analytical waveform. An analytical waveform is a function of time that depends on a small number of parameters used to reproduce the main characteristics of a real signal, whose revolution as a function of reduced distance makes it possible to reconstruct the time pressure signal. The so-called "modified Friedlander" wave can be used in the method 100 as the first waveform. The so-called "modified Friedlander" wave can be defined by the following equation: otherwise

[0033] With :

[0034] ToA, the time, in seconds, of arrival of the wave,

[0035] toP max , the maximum overpressure, in pascals, otherwise called the peak,

[0036] a, the coefficient of exponential decay,

[0037] At + , the duration, in seconds, during which the overpressure is positive.

[0038] Figure 3 illustrates an example of an analytical waveform 301 called “modified Friedlander” that can be used in the method 100. In Figure 3, the vertical axis represents the pressure, expressed in pascals; the horizontal axis the time expressed in seconds, and: the arrival time of the wave ToA is noted 302, the maximum overpressure P max is noted 303, the coefficient a of the exponential decay is noted 304, and the duration At + during which the overpressure is positive is noted 305.

[0039] It can be noted that the consequences of an explosion depend on the value of the maximum overpressure P max of the wave generated by the explosion but also of the positive pulse l+, time integral of the positive phase of the overpressure signal. For the modified Friedlander waveform, the positive pulse 1+ is expressed analytically by:

[0041] Several waveforms for representing the overpressure signal generated by the explosion are compatible with the method 100. For example, as an alternative and / or complementary to the use of a “modified Friedlander” waveform, it is possible to use a simple Friedlander waveform or the derivative of a Powell-Friedlander waveform, or even a Landau wavelet. In addition, it is possible to use different waveforms depending on the different types of explosions.

[0042] Determining waveform parameters, for example, the parameters of the so-called "modified Friedlander" wave, can be done by digital or experimental signal processing. For example, experiments can use pressure sensors that record the pressure time signal. Similarly, digital simulations can be performed with virtual pressure sensors. Processing signals from real or virtual sensors allows determining the chosen waveform parameters by minimizing the deviations between the signal and the waveform. Alternatively, the waveform parameters can be predetermined.

[0043] In order, for example, to be able to compare signals from different explosions, having varying mass and distance, the concept of "reduced distance" Z can be used. In an example, compatible with the previous examples, the first waveform depends on the concept of "reduced distance" Z. It is for example possible to use a reduced distance Z called "Hopkinson-Cranz". The reduced distance Z called "Hopkinson-Cranz" has the formula:

[0045] With : R, the distance, in meters, between the point of interest, for example the location of a sensor, and the center of the explosion, and m, the mass, in kilograms, of the explosive.

[0046] Thus, for the same explosive and the same reduced distance R, the maximum overpressure at P max is identical. For example, the maximum overpressure at P maxgenerated by an explosion having a distance R equal to 1 meter and a mass m of 1 kg is equal to the maximum overpressure P max generated by an explosion having a distance R equal to 10 meters and a mass m of 1000 kg. In fact, in both cases, the reduced distance Z is equal to 1 m.kg -3 . Other reduced variables of interest such as the positive impulse l+, the arrival time of the wave ToA and the duration At +during which the overpressure is positive are calculated for example by dividing them by the cubic root of the mass of the explosive denoted ^m in a "Hopkinson-Cranz" approach for a 3D space. For a 2D space, the mass m is expressed in units of length L m / L, with m, the mass and L, the length and the reduced distance is expressed by the real distance divided by the square root of the mass denoted m. For a 1-dimensional space, the mass m is expressed in units of surface A m / A with m, the mass and A, the surface, and the reduced distance is expressed by the real distance divided by m / A.

[0047] Thus, it is possible to determine the variation of the waveform parameters as a function of the reduced distance Z and therefore to determine the evolution of the reference signal in free field as a function of the reduced distance Z. Figure 4 shows an example of variation of each of the parameters of the so-called “modified Friedlander” waveform as a function of the reduced distance Z, expressed in meters: the maximum overpressure AP max , expressed in pascals, is illustrated on graph 401, the positive pulse l+, expressed in XX, is illustrated on graph 402, the arrival time of the wave ToA, expressed in seconds, is illustrated on graph 403, the duration At + , expressed in seconds, during which the overpressure is positive is illustrated in graph 404, and the coefficient a of the exponential decay is illustrated in graph 405.

[0048] A third step 30 of the method 100 comprises determining a zone of effect of the zero-order wave of the first explosion. This zone of effect of the zero-order wave corresponds to the visible points of the model from the position of the first explosion. The term “visible” here means that it is possible from any point of the zone of effect of the zero-order wave to see the position of the first explosion, that is to say that it is possible to trace a segment between said point and the position of the first explosion without this segment crossing an obstacle. This area of effect of the zero-order wave can for example be determined using the ray casting technique, called in English "raycasting" or "raytracing". Figure 2 illustrates an example of an area of effect of the zero-order wave. Thus, the calculation of the visibility polygon in 2D, or the visibility polyhedron in 3D, is defined as the set of points of the plane, or of space in 3D, visible from a given point, possibly limited by a maximum distance.

[0049] In an example, compatible with the previous examples, it is therefore possible to describe the signal corresponding to any point of this zero-order effect zone by “free field” functions, in particular the function expressing the maximum overpressure P max as a function of the reduced distance Z, noted APmax(Z).

[0050] A fourth step 40 of the method 100 comprises the determination of at least one second waveform and an area of effect for each first-order diffracted wave and / or each first-order reflected wave. This second waveform characterizes at least one diffracted and / or reflected wave generated by the first explosion. This analytical wave is said to be of order 1. A area of effect is determined for each first-order analytical wave. The determination of the area of effect of each first-order analytical wave can be carried out in a manner similar to the determination of the area of effect of the zero-order wave, i.e. based on one or more polygons and / or polyhedra of visibility from the position of the origin of the wave. Thus, the method 100 comprises the determination of at least one second waveform from:

[0051] a diffracted wave of order 1, and / or

[0052] a reflected wave of order 1.

[0053] The first-order reflected wave may comprise regular reflections and / or so-called "Mach" reflections. For example, determining at least one second waveform may comprise determining a first-order diffracted wave and a first-order reflected wave.

[0054] A reflected wave of order 1 is generated by the reflection of the zeroth order wave. A diffracted wave of order 1 is generated by the diffraction of the zeroth order wave. More generally, an Nth order reflected wave is generated by the reflection of an Nth - 1st order wave and an Nth order diffracted wave is generated by the diffraction of the wave of a wave of order N - 1 . Thus, each wave of order N can be considered as a new initial wave generating in turn diffracted and reflected waves of order N + 1 . Figure 5 illustrates an example of this recursive approach, with element 501 representing the wave of order zero, elements 502 representing the reflected waves of order N and elements 503 representing the diffracted waves of order N. As illustrated in Figure 5 the recursive approach, working by successive calculations of wave generations can be represented mathematically by a tree.

[0055] In one example, compatible with the previous examples, the calculation of each wave generation can be performed partially. Thus, early stopping conditions can be used to reduce calculation times. For example, it is possible to terminate the calculation of a branch of the recursive tree: when the polygon representing the parent wave has a surface area below a certain threshold; in fact, the “child” waves would only cover a very small part of the study area, when the characteristics of the wave at any point in the parent area (overpressure, impulse, etc.) are below one or more predetermined values; these predetermined values being, for example, set according to any damage that may be generated by the wave, including after a final reflection.

[0056] The reflected wave of order 1 is generated by the surfaces, i.e. surfaces of the polyhedron representing at least part of a 3D obstacle and segments of the polygon representing at least part of a 2D obstacle, visible from one of the explosions. This reflected wave can for example be modeled as being emitted from a virtual source, symmetrical to the position of the first explosion with respect to the segment. The position of the virtual source can be determined by a mirror image method. This reflected wave propagates in an angular sector whose support is the segment in question. In addition, the corresponding signal can be described at any point in this area using for example the “free field” function APmax(Z) calculated from the virtual source. Finally, it should be noted that each segment generating a reflected wave can generate, depending on the case, 0, 1 or 2 diffracted waves on either side of the area of effect of the reflection.Finally, it should be noted that. These remarks are also applicable to reflected waves of order N, except of course that the segments are determined taking into account waves of order N-1.

[0057] In order to determine the characteristics of the reflected waves of order N in the method 100, a traditional approach called mirror images can be used. However, this traditional approach of mirror images is only strictly valid for sonic waves. Thus, it is possible to modify the “mass / distance” parameter pair of the “mirror image” approach in order to accurately determine the regular reflection zone.It is possible, for example, to consider that the reflected wave would come from a virtual origin of mass different from the mass of the load from which the N-1 wave comes and / or that this virtual origin is located at a different distance from the 2D reflecting segment, respectively from the 3D reflecting surface, than that of the load from which the N-1 wave comes. In addition, it is also possible to further consider the Mach waves, and in particular their reference points, in order to determine the characteristics of the reflected waves of order N in the method 100. Finally, it should be noted that when an N-1 order wave generates, from the same segment of the model, both a regular wave and a Mach wave, a Boolean operation on the polygons representative of the latter can be used to avoid double counting of the reflected wave.

[0058] Concerning diffracted waves of order 1, each obstacle angle, i.e. each vertex of the polygon representing the obstacle in 2D, respectively edge or vertex of the polyhedron representing the obstacle in 3D, respecting certain criteria, such as the geometric position relative to the apex of the wave 0, can create a diffracted wave. In 2D, this wave propagates from the obstacle angle, also called apex, and in an angular sector limited by a surface of the obstacle, also called polygon segment, and by a segment of the zone of effect of the wave of order zero. The corresponding signal is for example described at any point of this zone by the Bazhenova functions Me at the apex and by the decreases of the free field function AP + (Z) at a distance from the apex. Bazhenova functions at the apex can be described by:

[0059] Me =f(Mo,O)

[0060] With 0, the angular distance between the line coming from the apex and passing through the point of interest and the segment of the “free field” zone.

[0061] In one example, consistent with the preceding examples, the method 100 may also take into account the intensification effects during propagation between obstacles, for example in streets, as a consequence of the interaction of the different shock waves reflected on the walls of urban canyons. This effect is commonly called "channeling". The effects of urban canyons result in the gradual transition from a "3D" wave, in a free field, to a "2D" wave, with the corollary of a lower pressure reduction than in a free field and therefore potentially larger danger zones. The same effects occur during propagation between two planar obstacles, for example a floor and a ceiling, one application being propagation in an underground parking floor. Similar effects also occur in tunnels, or corridors, in a building, where a gradual transition from a "3D" wave to a "1D" wave is observed.These propagation change effects have been theorized, or rather empirically modeled, through volumetric approaches independently by Borgers et al., in BW Borgers, JM Ndambi, J. Vantomme. A volume approach to predict air blast parameters. 20. thMABS, Norway, Oslo, August 31 -September 5, 2008, and M. Silvestrini, B. Genova, F.J. Leon Trujillo. Energy concentration factor. A simple concept of blast propagation in partially confined geometries. Journal of Loss Prevention in the Process Industries, vol. 22, 449-454, 2009. DOI: 10.1016 / j.jlp.2009.02.018. The principle underlying these approaches is that the overpressure at a given distance from the charge depends only on the total volume traveled by the shock wave from the explosion point. We can then reduce simple 1D geometries, in the case of tunnels for example, or 2D geometries, for streets or underground parking lots for example, to an equivalent spherical or hemispherical geometry that will allow us to calculate the overpressure as a function of the distance from the charge by the classical AP+(Z) laws.

[0062] In one example, consistent with the preceding examples, the method 100 may also take into account the effects of bypassing the urban canopy. For example, the method 100 may take into account the bypassing of waves generated by the explosion(s) occurring above obstacles or certain obstacles whose altitude is below a predetermined threshold. To model a wave having bypassed the obstacles from above, it is possible to consider that this wave will follow a shortest path from the position of the explosion to the point of interest. This path is easily determined by a convex hull algorithm, after processing the different building heights. It is possible to notice that a free-field propagation wave can be taken into account as well as one or more diffraction waves. Thus, it is possible to remain in a 2D configuration and the functions describing diffraction can be used. It should be noted that the hypothesis is not systematically true, because there may be a building in a direct line that is too tall. In this case, the shortest path may pass next to this building and the bypass through the urban canopy may no longer be 2D, and therefore may no longer appear as a straight line segment on the plan view. In this case, a 3D approach may be more appropriate.

[0063] In an example compatible with the previous examples, each unit wave of order N can therefore be described by: the reference of its “parent” wave of order N-1, in order to, for example, calculate the Mach number or the reduced distance Z to the apex, a zone of influence, using for example the polygon, the apex, the angular range and the support segment, and the analytical functions making it possible to obtain, for example, the positive overpressure AP + of the wave generated by the explosion or the positive impulse l + at any point in the area of influence.

[0064] Thus, in this example, the description of each unit wave of order N makes it possible to calculate, in an optimized manner, at any point of the model the pressure signal generated by the explosion. By "unit wave", is meant the zero-order wave, the diffraction waves and the reflection waves of order N, including the regular reflection and the Mach reflection, which are all individually representable by an analytical waveform in their respective spatial extents. Figure 6 shows an example of propagation of a zero-order wave and reflected and diffraction waves of order 1 on a model. In Figure 6, the first explosion takes place at position 201, the obstacles 203, 204 and 205 are positioned close to position 201, thus the zero-order wave generated by the first explosion propagates over the entire zone of effect or propagation 202.The area of effect or propagation of the first order diffracted wave is noted 206 and the area of effect or propagation of. the reflected wave of order one is noted 207. In addition, the zones 202, 206 and 207 can of course overlap. Finally, the surfaces 208 of the different obstacles generating reflected waves of order one are indicated with a widened line and the angles 209 of the different obstacles generating diffracted waves of order one are indicated with a circle.

[0065] A fifth optional step 50 of the method 100 comprises the determination, for at least one point of the model, of at least one additional waveform characterizing at least one additional wave of order N with N > 2. In other words, the method 100 with this optional step 50 can take into account waves of order N > 2. Figure 5 shows for example a method 100 taking into account waves of order N = 3. In one example, N can be equal to any positive integer, knowing that it has been found empirically that for propagation in an urban environment the values N=2 or N=3 represented a good compromise between precision and calculation time.

[0066] A sixth step 60 of the method 100 comprises calculating, for the at least one point of the model, a pressure signal resulting from a set of waves generated by the first explosion. The set of waves generated by the first explosion comprises at least the zeroth order wave and a first order diffracted wave and / or first order reflected wave. The calculation of the pressure signal comprises calculating a temporal contribution of each wave of the set of waves for a period whose duration depends on the duration of the temporal contribution of each wave of the set of waves or whose duration can be predetermined, for example between 0 and 1 second. The period can start at the time of the first explosion. When several explosions are taken into account in the method 100, the period can start at the time of the first explosion from a temporal point of view among the several explosions taken into account in the method 100.The period may end at the end of the time contribution of the different waves of the calculated wave set, this end time being calculated for example as the maximum of the sum between the arrival time of the wave ToA and the positive phase duration At+ of each unit wave. During this step 60, a point of interest or a series of points of interest are selected, for example by a user or automatically. For example, a series of points of interest may be selected automatically to restore an image at the end of the calculation. Thus, for each point of interest. selected, the set of effect zones to which this point of interest belongs is determined and the calculation of the contribution of each analytical wave is carried out, for example by going back in the recursion tree to the direct wave of order zero. The sum of the unit time signals, described for example by the modified Friedlander function, can be linear, the overpressure at a given time being the sum of the overpressures of the unit waves at the same time, or be based on the LAMB approach described in Hikida, C.E. Needham. Low Altitude Multiple Burst (LAMB) Model, Volume l-Shock Description. DNA, 58632, 1981 or any other technique of nonlinear addition of the contributions of the unit waves.Finally, when at least one second explosion takes place in the real environment and is taken into account in the method 100, the calculation 60, for at least one point of the model, of the pressure signal further comprises taking into account the set of waves generated by the at least one second explosion. In other words, the simulation of the two explosions is carried out so as to take into account the waves generated by the two explosions.

[0067] A seventh optional step 70 of the method 100 comprises an assessment of material or human damage caused by the explosion(s). When the real environment represents an urban environment, the assessment of material damage may concern, for example, a building. More generally, step 70 may concern any material damage caused by the explosion(s) in the real environment.

[0068] An eighth step 80 of the method 100 comprises displaying, for the at least one point of the model, a result of the calculation of the pressure signal. An example of such a display is illustrated in FIG. 7. FIG. 7 shows a diagram whose vertical axis corresponds to the pressure in the air expressed in Pascals and the horizontal axis is the time in seconds. The curve 701 shows the pressure signal calculated for a point of the model. In addition, the curve 701 may also include a graphical characteristic making it possible to distinguish the contribution of the different ones as a function of time. For example, a first color, such as on the part 702 of the curve 701, may be used to indicate that the 0th order wave contributes to the pressure signal. In one example, compatible with the previous examples, the display of the result is carried out directly on a view of the model representing the real environment. For example, for the point(s) of the model for which the calculation has been performed, it is possible to indicate, by a color or other graphic distinction, the value of one or more characteristics of the calculated pressure signal. For example, the color may be dependent on the maximum overpressure value, expressed in Pascals, of the pressure signal calculated for the point(s) of the model. An example of such a display is shown in Figure 8. In another example, compatible with the previous example, a color or other graphic distinction may be dependent on material damage such as the proportion of broken windows on buildings. Figure 9 illustrates three examples of similar displays for calculations performed taking into account respectively the waves of order 1 for the diagram noted A, of order 2 for the diagram noted B and of order 3 for the diagram noted C.

[0069] A ninth optional step 90 of the method 100 comprises the study of means of mitigating the effects of the explosive charge, for example by virtual positioning of an additional obstacle, such as a wall, or of a technical means of reducing the effects of the explosion, such as the use of aqueous foam, sandbags, in order to quickly determine the effect of such a means on the extent of the danger zones.

[0070] A tenth optional step 95 of the method 100 comprises the arrangement of the real environment. This optional step 95 may also comprise the sending of an alert indicating a danger, and / or the evacuation of an area of the real environment. This optional step 95 may therefore comprise any modification of the real environment, or of the use of the real environment by people, making it possible to prevent the risks linked to one or more future explosions or to reduce the risks linked to one or more past explosions. This optional step 95 may be implemented automatically or semi-automatically or by means of a user. For example, a user, after consulting the display 80 of the result of the calculation of the pressure signal or carrying out a study in step 90, may implement the optional step 95.

Claims

CLAIMS

1. A computer-implemented method (100) of managing a first explosion in a real environment, the real environment comprising at least one obstacle and the method (100) comprising the steps of: - obtaining (10) a model representing the real environment, the model comprising: o a continuous medium representing a gas or a liquid, and o at least one geometric shape representing the at least one obstacle, - obtaining (20) a position of the first explosion within said model and a first waveform characterizing a zero-order wave generated by the first explosion, - determination (30) of a zone of effect of the zero-order wave of the first explosion, the zone of effect of the zero-order wave corresponding to the visible points of the model from the position of the first explosion, - determination (40) of at least one second waveform characterizing at least one diffracted wave of order one and / or at least one reflected wave of order one and of an area of effect for each diffracted wave of order one and / or each reflected wave of order one, generated by the first explosion, - calculation (60), for at least one point of the model, of a pressure signal resulting from a set of waves generated by the first explosion, the set of waves comprising at least the zeroth order wave and the at least one first order diffracted wave and / or the at least one first order reflected wave, the calculation of the pressure signal comprising the calculation of a temporal contribution of each wave of the set of waves whose zone of effect comprises the point of the current model, and - display (80), for the at least one point of the model, of a result of the calculation of the pressure signal.

2. The method (100) of claim 1 further comprising a final step (95) of: arrangement of the real environment, and / or sending an alert indicating danger. [Claim s] Method (100) according to any one of the preceding claims further comprising a step (50) of determining, for the at least one point of the model, at least one additional waveform characterizing at least one additional wave of order N with N > 2, the step (50) of determining the at least one additional waveform being implemented after the determination (40) of at least one second waveform and before the calculation (60) of a pressure signal.

4. A method (100) according to any preceding claim wherein: - A terrain of the real environment is flat and has a first altitude, - at least one obstacle is described in the model by a polygonal footprint and a second altitude greater than the first altitude, and - the first explosion takes place at ground level and an explosive, responsible for the first explosion, has a hemispherical shape. [Claim s] A method (100) according to any preceding claim wherein: - At least one second explosion is managed in the real environment, the second explosion being less than 1 second apart in time from the first explosion, and - the calculation (60), for the at least one point of the model, of the pressure signal further comprises taking into account the set of waves generated by the at least one second explosion.

6. A method (100) according to any preceding claim wherein the real environment represents an urban environment, the continuous medium represents ambient air and the at least one obstacle represents a building.

7. Method (100) according to the preceding claim further comprising a step (70) of evaluating material damage caused to said at least one building, the step (70) of damage assessment being implemented after the calculation (60) of the pressure signal.

8. A computer program product comprising instructions which, when the program is executed by a computer, cause the latter to implement the method according to any one of claims 1 to 7.

9. A computer-readable recording medium comprising instructions which, when executed by a computer, cause the computer to carry out the method of any one of claims 1 to 7.

10. A system configured to perform the method of any one of claims 1 to 7.

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