A representative volume element modeling method based on deep reinforcement learning

Abstract

This invention discloses a representative volumetric unit modeling method based on deep reinforcement learning, belonging to the field of deep learning. The method includes: defining volume parameters and fiber parameters of the representative volumetric unit to be modeled for a random short-fiber composite material; inputting an initial state image of the fiber distribution into a pre-trained deep reinforcement learning model; the deep reinforcement learning model, based on a predefined Markov quadruple, calculates the action value mapping function value for each fiber filled at different positions and angles, selecting the position and angle corresponding to the maximum action value mapping function to fill the current fiber; until the desired number of fibers is reached, a representative volumetric unit model of the random short-fiber composite material is obtained. This scheme, by introducing deep reinforcement learning to construct an intelligent model, can significantly improve the accuracy and efficiency of fiber filling.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and in particular to a representative volumetric unit modeling method based on deep reinforcement learning. Background Technology

[0002] Fiber-reinforced composites, due to their high strength, high stiffness, and flexible design, have been widely used in engineering structures in aerospace, transportation, and other fields. Among them, random short fiber composites (RSFCs) are increasingly used in complex components and mass production scenarios due to their convenient molding process and low cost. To reasonably characterize the microscopic non-uniformity and random fiber distribution characteristics of random short fiber composites in macroscopic analysis and design, it is usually necessary to construct representative volume elements (RVEs) of the random short fiber composites and conduct microscopic numerical simulations and multi-scale analyses based on them.

[0003] Traditional random adsorption methods for establishing RVE models require continuous calculation of the distances between newly added fibers and all existing fibers to determine the effectiveness of fiber filling. This calculation process is time-consuming. Furthermore, as fibers are continuously added, the likelihood of subsequent fibers intersecting with existing fibers increases. The simple random filling method is blind and inefficient, which is highly detrimental to subsequent mechanical analysis of the material.

[0004] Therefore, there is an urgent need to provide a representative volumetric unit modeling method based on deep reinforcement learning. Summary of the Invention

[0005] To address the problems of blind and inefficient traditional random adsorption methods, this invention provides a representative volumetric unit modeling method based on deep reinforcement learning.

[0006] On the one hand, a representative volumetric unit modeling method based on deep reinforcement learning is provided, the method comprising: Define the volume parameters and fiber parameters of the representative volume unit to be modeled in the random short fiber composite material, and input the initial state image of the fiber distribution into the pre-trained deep reinforcement learning model; the fiber parameters include at least the number of fibers; The deep reinforcement learning model is based on a predefined Markov quadruple and calculates the action value mapping function value for each fiber to be filled at different positions and angles, so as to select the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model, and the convolutional neural network is used to determine whether there is fiber crossing in the input fiber distribution image in order to calculate the reward value; Until the specified number of fibers is reached, a representative volumetric element model of the random short fiber composite material is obtained.

[0007] On the other hand, a representative volumetric unit modeling apparatus based on deep reinforcement learning is provided for implementing the steps described in any method embodiment of the specification, the apparatus comprising: An initialization unit is used to define the volume parameters and fiber parameters of the representative volume unit to be modeled in the random short fiber composite material. The initial state image of the fiber distribution is input into the pre-trained deep reinforcement learning model. The fiber parameters include at least the number of fibers. The filling unit, the deep reinforcement learning model, is based on a predefined Markov quadruple and calculates the action value mapping function value for each fiber to be filled at different positions and angles, so as to select the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model, the convolutional neural network is used to determine whether there is fiber crossing in the input fiber distribution image, so as to calculate the reward value; The output unit is used to obtain a representative volumetric element model of the random short fiber composite material until the number of fibers is reached.

[0008] On the other hand, a computer device is provided, the computer device including a memory and a processor, the memory for storing a computer program, and the processor for executing the computer program stored in the memory to implement the steps of the method described above.

[0009] On the other hand, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when the computer program is executed by a processor, it implements the steps of the method described above.

[0010] On the other hand, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the method described above.

[0011] The technical solution provided by this invention can bring at least the following beneficial effects: By using the selection of the direction and position of the filling fibers as the decision actions of the deep reinforcement learning model, and the fiber distribution image as the state of the deep reinforcement learning model, and by using a convolutional neural network to provide action reward values ​​to the deep reinforcement learning model, the action value mapping function of the deep reinforcement learning model is trained. This enables the deep reinforcement learning model to make fiber action decisions quickly and accurately, and intelligently fill fibers to obtain a representative volumetric unit model of random short fiber composite materials. Compared with the traditional random adsorption method, this scheme, by introducing deep reinforcement learning to build an intelligent model, can greatly improve the accuracy and efficiency of fiber filling. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart of a representative volumetric unit modeling method based on deep reinforcement learning, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of the training process of a deep reinforcement learning model provided in an embodiment of the present invention; Figure 3 This is a structural diagram of a representative volumetric unit modeling device based on deep reinforcement learning, provided in an embodiment of the present invention. Figure 4 This is a hardware architecture diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0015] The specific implementation of the above concept is described below.

[0016] Please refer to Figure 1 This invention provides a representative volumetric unit modeling method based on deep reinforcement learning, the method comprising: Step 100: Define the volume parameters and fiber parameters of the representative volume unit to be modeled for the random short fiber composite material, and input the initial state image of the fiber distribution into the pre-trained deep reinforcement learning model; the fiber parameters include at least the number of fibers; Step 102: The deep reinforcement learning model, based on a predefined Markov quadruple, calculates the action value mapping function value for each fiber filled at different positions and angles, and selects the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model, and the convolutional neural network is used to determine whether there are fiber crossings in the input fiber distribution image in order to calculate the reward value; Step 104: Until the fiber number is reached, a representative volumetric element model of the random short fiber composite material is obtained.

[0017] In this embodiment of the invention, the direction and position selection of the filling fibers are used as the decision actions of the deep reinforcement learning model, and the fiber distribution image is used as the state of the deep reinforcement learning model. A convolutional neural network is used to provide action reward values ​​to the deep reinforcement learning model, thereby training the action value mapping function. This enables the deep reinforcement learning model to make fiber action decisions quickly and accurately, intelligently filling fibers to obtain a representative volumetric unit model of the random short fiber composite material. Compared to the traditional random adsorption method, this scheme, by introducing deep reinforcement learning to construct an intelligent model, can greatly improve the accuracy and efficiency of fiber filling.

[0018] The following description Figure 1 The execution method for each step is shown.

[0019] For step 100: In this embodiment, the volume parameters of the representative volume unit include the side length, and the fiber parameters include the fiber aspect ratio, fiber width, and fiber number.

[0020] Regarding step 102: It's important to note that traditional reinforcement learning methods (Q-learning, Sarsa) store Q-values ​​using a Q-matrix. Their state spaces are discrete and exhaustively enumerable. For problems with large state or action spaces, a sufficiently large Q-matrix cannot be constructed to fully represent the state and action spaces. To enable reinforcement learning algorithms to handle inexhaustible action and state spaces, non-linear neural networks are used to model the Q-matrix. Deep reinforcement learning (DQN) models utilize a convolutional neural network as a non-linear mapping function Q(s) that maps action values ​​to states, thus modeling the Q-matrix and achieving a fully end-to-end learning process.

[0021] It is understandable that once a deep reinforcement learning model is trained, without the need for a convolutional neural network, the action value mapping function value can be calculated for each fiber placed at different positions and angles. The position and angle corresponding to the maximum action value mapping function can then be selected to fill the current fiber until the required number of fibers are filled, thus obtaining a representative volumetric unit model of the random short fiber composite material.

[0022] Next, we will explain how to train deep reinforcement learning models.

[0023] You can refer to this. Figure 2 In some implementations, the deep reinforcement learning model is trained as shown in steps S1-S7 below: S1 initializes the parameters of the deep reinforcement learning network and the convolutional neural network; S2 generates an initial state sample with 1 fiber. For each initial state sample, the following is executed: S3, using a predefined action space, fill the current initial state sample with the next fiber at different positions and angles to generate several state samples with a fiber count of 2; S4, input all state samples into the convolutional neural network and the deep reinforcement learning network respectively; S5, the convolutional neural network extracts features from the state samples and determines whether there are fiber crossings in the input state samples. The reward values ​​of each state sample are then input into the deep reinforcement learning network. S6. The deep reinforcement learning network calculates the action value mapping function value based on each state sample, calculates the corresponding action value true value using the reward value of each state sample input by the convolutional neural network, and calculates the loss function using the action value true value and the action value mapping function value to adjust the network parameters of the deep reinforcement learning network. S7, based on probability coefficients, selects from several state samples with 2 fibers to put into the experience pool until all initial state samples are filled and trained; S8: For each state sample with 2 fibers in the experience pool, the next fiber at different positions and angles is filled into the state sample using a predefined action space to generate several state samples with 3 fibers. Then, the process jumps to input all state samples into the convolutional neural network and the deep reinforcement learning network respectively until the required number of fibers is reached, thus completing this round of training for the deep reinforcement learning network.

[0024] In this embodiment, the Markov quadruple is (S, A, P, R), where S is the set of all possible states s, i.e., the fiber distribution state diagram after each fiber is added. A is the spatial set of all actions a that the agent can take: a∈A, where action a is the position and angle selected during fiber addition. P is the state transition probability, i.e., the probability of the agent reaching another state after taking action a in one state, a random factor for action selection, adjusted according to the network training process; where for The next state reached after taking an action; R is the reward function, which is the immediate reward obtained by the model after taking an action, denoted as r(s,a). It needs to be tested during training. It can be assumed that when the newly added fiber meets the requirements, r>0, otherwise r<0.

[0025] In this embodiment of the invention, the action space is represented by the following formula: In the formula, For the action space, This represents the filling position of the fiber center point in the state sample. Let the angle of the fiber in the state sample be denoted as . This represents the side length of a three-dimensional representative volume element model.

[0026] In this embodiment, Discretize the fiber into N actions, each representing a specific fiber position and orientation parameter. Let the number of fiber positions be locationNum, and the orientation be discretized from 0 to 2π as orientationNum. Then N is calculated as follows: N = locationNum × orientationNum.

[0027] In some implementations, when the state sample represents a three-dimensional representative volumetric unit model, the pixel grayscale values ​​in the state sample characterize the depth direction information of the three-dimensional representative volumetric unit model, and the correspondence between the pixel grayscale values ​​and the depth direction information in the state sample is as follows: In the formula, Midpoint of the state sample pixel grayscale values, This represents the Z-coordinate value along the depth direction of the point corresponding to the representative three-dimensional volume element model. Let be the depth-direction side length of the representative three-dimensional volume element model. Here is the Z-coordinate value of the first endpoint of the fiber in the three-dimensional representative volume element model. Midpoint of the state sample The distance to the first end of the fiber. Euler angles; In this embodiment, step S5, determining whether there are fiber crossings in the input state sample, includes: Based on the grayscale value of each pixel in each fiber in the state sample, calculate the position of each pixel in the three-dimensional representative volume unit model; Calculate whether the distance between the centerlines of any two fibers is greater than the fiber width; If so, confirm that the two fibers do not cross each other; If not, it is determined that the two fibers intersect.

[0028] In this embodiment, the basic condition for fiber distribution during the filling process is that they cannot cross each other. Therefore, when the new fiber filled by action a does not cross with other fibers, a positive reward is given; when the new fiber filled by action a crosses with other fibers, a negative reward is given.

[0029] Therefore, the reward value for each state sample is calculated using the following formula: In the formula, For filling action Formed state samples The corresponding reward value, This indicates that the fibers are effective, meaning there is no cross-linking between them; This indicates that the fiber is invalid, meaning that the fiber crosses. This indicates that the fiber filling has reached the required number of fibers, and the modeling ends; v>>t>0, u<0.

[0030] In this embodiment, Figure 2 The flowchart of the deep reinforcement learning in this embodiment is given. The input to the convolutional neural network (CNN) is a state sample after adding new fibers using different actions. Features are extracted from the state samples, and it is determined whether fiber crossings exist in the input state samples. The reward value for each state sample is then calculated. Input into a deep reinforcement learning network.

[0031] A deep reinforcement learning network is essentially a non-linear mapping function Q(s) that maps action values ​​to states. The input is no longer discrete actions, but rather state samples with new fibers added based on different actions. Through convolution, pooling, non-linear, and fully connected layers, image features are extracted layer by layer and regressed into action value mapping function values ​​[Q(s,a1), Q(s,a2), Q(s,a3), ..., Q(s,aN)]. During training, the reward values ​​of each state sample input to the convolutional neural network are used to calculate the corresponding ground truth action value, ensuring that the ground truth action value equals the action value mapping function value. This process iteratively trains the network parameters of the deep reinforcement learning network. The formula is: Wherein, is the true value of the action value, is the reward value of the state sample input by the convolutional neural network, is the interest weight, is the maximum action value mapping function value among all actions, is the action value mapping function value calculated by the deep reinforcement learning network.

[0032] It can be understood that after training the deep reinforcement learning model, the action corresponding to the maximum Q is selected as the action to be executed by the agent.

[0033] [[ID=​​​​​​​​​​​​​​​​​​​​In some implementations, when the number of samples in the experience pool reaches a set value, state samples are extracted from the experience pool for memory replay training of the deep reinforcement learning network.

[0037] In this embodiment, after obtaining an experience pool of a certain size, a small batch of data is randomly selected from the experience pool as training samples.

[0038] The loss function is calculated using the following formula: In the formula, For the true value of the corresponding action, This is the action-value mapping function value calculated by the deep reinforcement learning network. Therefore, the memory playback process is a step-by-step approximation process, making the predicted value gradually approach the true value, thus making the estimate more accurate.

[0039] Regarding step 104: It is understandable that a trained deep reinforcement learning model is used to calculate the action value mapping function value when each fiber is filled at different positions and angles. The position and angle corresponding to the maximum action value mapping function are selected to fill the current fiber. By gradually filling the fiber to reach the required number of fibers, a representative volumetric unit model of random short fiber composite material without fiber intersections is obtained.

[0040] Please refer to Figure 3 This invention provides a representative volumetric unit modeling device based on deep reinforcement learning, used to implement the steps of any method embodiment in the specification. The device includes: Initialization unit 301 is used to define the volume parameters and fiber parameters of the representative volume unit to be modeled in the random short fiber composite material. The initial state image of the fiber distribution is input into the pre-trained deep reinforcement learning model; the fiber parameters include at least the number of fibers. Filling unit 302: The deep reinforcement learning model is based on a predefined Markov quadruple and calculates the action value mapping function value when each fiber is filled at different positions and angles, so as to select the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model. The convolutional neural network is used to determine whether there is fiber crossing in the input fiber distribution image in order to calculate the reward value; Output unit 303 is used to obtain a representative volumetric element model of the random short fiber composite material until the fiber number is reached.

[0041] It should be noted that the representative volumetric unit modeling device based on deep reinforcement learning provided in the above embodiments is only an example of the division of the above functional units. In practical applications, the above functions can be assigned to different functional units as needed, that is, the internal structure of the device can be divided into different functional units to complete all or part of the functions described above. In addition, the above device embodiments and method embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0042] Embodiments of this application also provide a computer device, please refer to... Figure 4 The computer device includes a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, at least one program, code set or instruction set being loaded and executed by the processor to implement the representative volumetric unit modeling method based on deep reinforcement learning provided in the above-described method embodiments.

[0043] Embodiments of this application also provide a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, at least one program, code set, or instruction set is loaded and executed by a processor to implement the representative volumetric unit modeling method based on deep reinforcement learning provided in the above-described method embodiments.

[0044] Embodiments of this application also provide a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium and executes the computer program, causing the computer device to perform any of the representative volumetric unit modeling methods based on deep reinforcement learning in the above embodiments.

[0045] For ease of description, the above systems or devices are described separately as various modules or units based on their functions. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware components.

[0046] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of the embodiments of this application.

[0047] Finally, it should be noted that in this document, relational terms such as first, second, third, and fourth are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0048] The above are merely preferred embodiments of this application. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A representative volumetric unit modeling method based on deep reinforcement learning, characterized in that, The method includes: Define the volume parameters and fiber parameters of the representative volume unit to be modeled in the random short fiber composite material, and input the initial state image of the fiber distribution into the pre-trained deep reinforcement learning model; the fiber parameters include at least the number of fibers; The deep reinforcement learning model is based on a predefined Markov quadruple and calculates the action value mapping function value for each fiber to be filled at different positions and angles, so as to select the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model, and the convolutional neural network is used to determine whether there is fiber crossing in the input fiber distribution image in order to calculate the reward value; Until the specified number of fibers is reached, a representative volumetric element model of the random short fiber composite material is obtained.

2. The method as described in claim 1, characterized in that, The deep reinforcement learning model is trained in the following way: Parameters are initialized for the deep reinforcement learning network and the convolutional neural network; Generate an initial state sample with 1 fiber. For each initial state sample, perform the following: Using a predefined action space, fill the current initial state sample with the next fiber at different positions and angles to generate several state samples with a fiber count of 2; All state samples are respectively input into the convolutional neural network and the deep reinforcement learning network; The convolutional neural network extracts features from the state samples and determines whether there are fiber crossings in the input state samples. The reward values ​​of each state sample are then input into the deep reinforcement learning network. The deep reinforcement learning network calculates the action value mapping function value based on each state sample, calculates the corresponding action value true value using the reward value of each state sample input by the convolutional neural network, calculates the loss function using the action value true value and the action value mapping function value, and adjusts the network parameters of the deep reinforcement learning network. Based on probability coefficients, select from several state samples with 2 fibers and add them to the experience pool until all initial state samples are filled and trained. For each state sample with 2 fibers in the experience pool, the next fiber at different positions and angles is filled into the state sample using a predefined action space, generating several state samples with 3 fibers. Then, the process jumps to input all state samples into the convolutional neural network and the deep reinforcement learning network respectively, until the number of fibers is reached, thus completing this round of training of the deep reinforcement learning network.

3. The method as described in claim 2, characterized in that, When a state sample represents a three-dimensional representative volume element model, the pixel grayscale values ​​in the state sample characterize the depth direction information of the three-dimensional representative volume element model. The correspondence between the pixel grayscale values ​​in the state sample and the depth direction information is as follows: In the formula, The midpoint of the state sample pixel grayscale values, This represents the Z-coordinate value along the depth direction of the point corresponding to the representative three-dimensional volume element model. Let be the depth-direction side length of the representative three-dimensional volume element model. Here is the Z-coordinate value of the first endpoint of the fiber in the three-dimensional representative volume element model. The midpoint of the state sample The distance to the first end of the fiber. Euler angles; The determination of whether fiber crossings exist in the input state sample includes: Based on the grayscale value of each pixel in each fiber in the state sample, calculate the position of each pixel in the three-dimensional representative volume unit model. Calculate whether the distance between the centerlines of any two fibers is greater than the fiber width; If so, confirm that the two fibers do not cross each other; If not, it is determined that the two fibers intersect.

4. The method according to claim 2, characterized in that, The action space is represented by the following formula: In the formula, For the action space, This represents the filling position of the fiber center point in the state sample. Let the angle of the fiber in the state sample be denoted as . The side length of the representative three-dimensional volume element model; The reward value for each state sample is calculated using the following formula: In the formula, For filling action Formed state samples The corresponding reward value, This indicates that the fibers are effective, meaning there is no cross-linking between them; This indicates that the fiber is invalid, meaning that the fiber crosses. This indicates that the fiber filling has reached the required number of fibers, and the modeling process is complete. v>>t>0, u<0.

5. The method according to claim 2, characterized in that, The selection of states from a pool of two fiber samples based on probability coefficients includes: Obtain the current probability coefficient and the random number generated before filling the first fiber with the current initial state sample; wherein, the probability coefficient gradually decays with the number of training iterations; Determine whether the random number is less than the current probability coefficient; If so, then all state samples with a fiber count of 2 generated based on the current initial state sample will be placed into the experience pool; If not, the state sample with the largest action value mapping function value among several state samples with a fiber count of 2 generated based on the current initial state sample will be placed into the experience pool.

6. The method according to claim 2, characterized in that, When the number of samples in the experience pool reaches a set value, state samples are extracted from the experience pool for memory replay training of the deep reinforcement learning network.

7. A representative volumetric unit modeling apparatus based on deep reinforcement learning, used to implement the steps of the method according to any one of claims 1-6, characterized in that, The device includes: An initialization unit is used to define the volume parameters and fiber parameters of the representative volume unit to be modeled in the random short fiber composite material. The initial state image of the fiber distribution is input into the pre-trained deep reinforcement learning model. The fiber parameters include at least the number of fibers. The filling unit, the deep reinforcement learning model, is based on a predefined Markov quadruple and calculates the action value mapping function value for each fiber to be filled at different positions and angles, so as to select the position and angle corresponding to the maximum action value mapping function to fill the current fiber; wherein, the deep reinforcement learning network is trained based on a pre-trained convolutional neural network to obtain the deep reinforcement learning model, the convolutional neural network is used to determine whether there is fiber crossing in the input fiber distribution image, so as to calculate the reward value; The output unit is used to obtain a representative volumetric element model of the random short fiber composite material until the number of fibers is reached.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the steps of the method according to any one of claims 1-6.

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