A fuel cell fault-tolerant control method based on deep reinforcement learning

Abstract

The application discloses a fuel cell fault tolerance control method based on deep reinforcement learning. The method comprises the following steps: judging the fault type of a fuel cell stack for a fuel cell system, wherein the fuel cell system comprises the fuel cell stack, an anode humidifier, a cathode humidifier, a water pump and a radiator; in the case that the fuel cell stack fails, an optimal fault tolerance control strategy meeting a set target function is output by using a control model based on deep reinforcement learning, so as to cooperatively control the anode humidifier, the cathode humidifier, the water pump and the radiator, and perform corresponding recovery operations according to the fault type. The application can realize intelligent fault recovery and adaptive control of the fuel cell system, and ensure the stability and reliability of the fuel cell system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fuel cell fault-tolerant control, and more particularly to a fuel cell fault-tolerant control method based on deep reinforcement learning. BACKGROUND

[0002] Fuel cells are widely used in electric vehicles, portable power sources, and combined heat and power systems due to their high energy conversion efficiency and environmental friendliness. Fuel cells convert the chemical energy in fuel into electrical energy through the oxidation-reduction reaction of hydrogen and oxygen, and the power generation process can achieve zero emissions. In proton exchange membrane fuel cells, water and heat management is a very complex and important task. Water and heat management mainly involves controlling the temperature and humidity inside the fuel cell to ensure normal operation and improve its efficiency. The operation of fuel cells requires appropriate temperature and humidity conditions, and excessively high or low temperatures can affect the performance and lifespan of fuel cells. Water and heat management can be achieved through various methods, including the use of coolants, heat transfer plates, circulating air flows, and humidity control. These methods can help maintain the temperature of the fuel cell within a suitable range and control the humidity to prevent the membrane from drying out or being too wet. Because water and heat management is crucial to the performance and lifespan of fuel cells, careful consideration of water and heat management strategies and appropriate measures to optimize the performance and reliability of fuel cells are needed in the design and operation of fuel cell systems.

[0003] In the prior art, the fault-tolerant control methods of fuel cells are mainly divided into passive fault-tolerant control and active fault-tolerant control. Passive fault-tolerant control is the expected compensation for faults, while active fault-tolerant control can respond to any changes in system faults. Compared with passive fault-tolerant control which only works for a small range of predefined faults, active fault-tolerant control has become a research hotspot in the field of fault-tolerant control because of its introduction of diagnostic and decision-making systems and the ability to handle a variety of different faults. The fault-tolerant control methods currently used mainly include PID-based, nonlinear controller-based and model-based methods. For example, the document (Yan, C., et al. (2020). "Model-Based Fault Tolerant Control for the Thermal Management of PEMFC Systems." IEEE Transactions on Industrial Electronics 67(4): 2875-2884.) consists of a cascade PID and a sliding mode controller. Experimental results show that the temperature of the proton exchange membrane fuel cell can be accurately maintained at the reference value even if the sensor fails. The document (Wu, X. and B. Zhou (2016). "Fault tolerance control for proton exchange membrane fuel cell systems." Journal of Power Sources 324: 804-829.) proposes a scheme that can simultaneously diagnose and control faults in proton exchange membrane fuel cells. The scheme first detects the type of current fault by the fault diagnosis module, then selects the backup controller according to the diagnosis results by the reconstruction mechanism module, and finally performs fault-tolerant control by the nonlinear controller based on the feedback linearization method. Patent application CN114976133A discloses a model-based fault-tolerant control method for water management of proton exchange membrane fuel cells, which first constructs a fuel cell water transport model and designs a water flooding fault factor, then constructs a water management fault-tolerant controller based on the fault factor, and adjusts the cathode air flow to suppress water flooding to improve the stability of the system.

[0004] Although the existing solutions have achieved certain effects in fuel cell fault-tolerant control, there are still some defects. For example, the PID-based and model-based methods are more dependent on the system model, and if the system model is inaccurate or difficult to obtain, the performance of the control may be affected. In addition, the PID control algorithm has limited control ability for nonlinear and complex systems. The nonlinear controller based on feedback linearization usually relies on a complete or accurate approximate system model, and incomplete modeling errors will have a serious impact on the control performance, and feedback linearization is more complex for high-dimensional input-output systems, which is more challenging for the design, tuning and implementation of the control system. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art described above, and to provide a fuel cell fault-tolerant control method based on deep reinforcement learning. The method comprises the following steps:

[0006] For a fuel cell system containing a fuel cell stack, an anode humidifier, a cathode humidifier, a water pump and a radiator, the fault type of the fuel cell stack is determined;

[0007] In the case of a fault in the fuel cell stack, an optimal fault-tolerant control strategy that meets a set target function is output by a control model based on deep reinforcement learning, to cooperatively control the anode humidifier, the cathode humidifier, the water pump and the radiator, and to perform corresponding recovery operations according to the fault type;

[0008] The control model takes the fault-tolerant control strategy as an agent, takes the fuel cell stack as an environment, and the agent interacts with the environment and obtains a reward signal, and then learns the optimal fault-tolerant control strategy based on the reward signal.

[0009] Compared with the prior art, the fuel cell fault-tolerant control method based on deep reinforcement learning has the advantages that the optimal control strategy is learned through interaction with the environment, which is beneficial to better handle complex and dynamic environments, and the agent continuously interacts with the environment to learn the control strategy autonomously, which can handle complex nonlinear systems, thereby having strong adaptability and generalization ability.

[0010] Other features and advantages of the present application will become apparent from the following detailed description of exemplary embodiments thereof, taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0011] The accompanying drawings incorporated in and forming a part of the specification, illustrate embodiments of the present application and, together with the description, serve to explain the principles of the application.

[0012] Figure 1is a flow chart of a deep reinforcement learning based fuel cell fault-tolerant control method according to an embodiment of the present application

[0013] Figure 2 is a fuel cell system structure diagram according to an embodiment of the present application;

[0014] Figure 3 is a process diagram of fuel cell fault diagnosis and fault-tolerant control according to an embodiment of the present application;

[0015] Figure 4 is a fuel cell fault-tolerant control process diagram based on a SoftActor-Critic algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0016] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of the components and steps set forth in the embodiments, numerical expressions, and numerical values set forth in the embodiments are not limiting to the scope of the present application unless otherwise specifically stated.

[0017] The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the scope of the application its application or uses.

[0018] Techniques, methods, and devices known to those of ordinary skill in the relevant art can not be discussed in detail herein. However, the techniques, methods, and devices are sufficiently described herein such that any person skilled in the art can practice the application.

[0019] In all of the examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not limiting. Thus, other examples of the exemplary embodiments can have different values.

[0020] It should be noted that like reference numerals and letters refer to like items throughout the several views, and thus, once an item is defined in one view, it does not need to be discussed further in a subsequent view.

[0021] Referring to Figure 1 As shown, the deep reinforcement learning based fuel cell fault-tolerant control method provided includes the following steps:

[0022] At step S110, fault diagnosis is performed on the fuel cell system, and the fault type is determined.

[0023] Figure 2is a structural diagram of a fuel cell system. The system generally includes a water tank, a humidifier, a radiator, and a fuel cell stack (or simply a fuel cell). In the system, the generated heat is first brought to the water tank by the water pump through the control of the cooling water flow, and then the heat is brought to the radiator, which discharges the heat to the air by controlling the air flow. The humidifier is mainly used to control the relative humidity of the air. The water pump controls the outlet temperature of the fuel cell stack by controlling the circulation flow of the cooling water, and the radiator controls the inlet temperature of the fuel cell stack by controlling the air flow. In this paper, the humidifier located at the cathode of the fuel cell stack is called the cathode humidifier, and the humidifier located at the anode of the fuel cell stack is called the anode humidifier.

[0024] In combination Figure 3 As shown in the figure, before the fault-tolerant control of the fuel cell, first, fault diagnosis is performed, and the fault type of the fuel cell stack is determined. For example, the output voltage of the fuel cell is compared with the ideal output voltage to determine whether a fault has occurred. If the output voltage is not within the normal range, it is determined that there is a fault. Next, under a given power demand, the pressure drop of the inlet and outlet of the cathode is compared with the normal pressure drop. If the pressure drop exceeds the normal range, it is determined to be a water flooding fault. If the pressure drop is within the normal range, it is determined to be a membrane dry fault. Through this fault diagnosis method based on voltage and pressure drop, it can quickly and accurately determine whether the fuel cell has a water flooding or a membrane dry fault, thereby providing an accurate fault diagnosis basis for subsequent fault-tolerant control, so that the fault-tolerant control strategy can perform corresponding recovery operations according to the fault type, and ensure the stable operation of the fuel cell system.

[0025] Step S120, constructing a fault-tolerant control model of deep reinforcement learning.

[0026] In the case of detecting a fault of the fuel cell, a fault-tolerant control model based on deep reinforcement learning is used to perform fault recovery operations. The fault-tolerant control model is an intelligent decision system, mainly including four basic elements: agent, environment, action, and reward function. In this paper, the control strategy is regarded as the agent, and the fuel cell in the fault state is regarded as the environment. The core idea is that the fault-tolerant control strategy interacts with the environment and obtains a reward signal. The reinforcement learning algorithm learns the optimal fault-tolerant control strategy according to the reward signal feedback from the environment, which can take corresponding measures according to different fault conditions to realize the performance recovery of the proton exchange membrane fuel cell.

[0027] Step S130, using the fault-tolerant control model to output the optimal fault-tolerant control strategy that meets the set target function, and performing corresponding recovery operations according to the fault type.

[0028] In one embodiment, the reinforcement learning algorithm used is SoftActor-Critic (SAC). In combinationFigure 4 As shown, the fault-tolerant control strategy based on the algorithm can process high-dimensional state space input, control the anode humidifier, cathode humidifier, water pump and radiator, and is applicable to continuous action space. In addition, it also has good exploration ability, accurate strategy evaluation ability, etc.

[0029] Unlike traditional deep reinforcement learning algorithms, SAC considers maximum entropy while pursuing maximum cumulative reward. Entropy is an indicator of the uncertainty of a random policy, and the randomness of the policy increases with the increase of entropy in reinforcement learning, which makes the SAC algorithm have stronger exploration ability. Therefore, the action entropy value is introduced into the objective function, which is represented as:

[0030]

[0031] Wherein, π * is the optimal policy function, s t is the state at time t, a t is the action at time t, τ π is the trajectory distribution under the policy π, r is the reward, γ is the discount factor, is the entropy under the current policy, α is the entropy regularization coefficient, s0=s represents the initial state of the system, s represents the initial state, T represents the total time, represents the expectation.

[0032] For a fixed policy, the soft Q value function can be calculated iteratively by applying the modified Bellman backup operator, which is represented as:

[0033]

[0034] Wherein:

[0035]

[0036] In addition, the soft Q function can be fitted by a neural network Q θ with parameters θ, and θ can be trained by minimizing the soft Bellman residual:

[0037]

[0038] Wherein, D is an experience replay buffer for storing past experiences. is the value function of state s t+1 , s t+1 is the next state. The soft Q value function can be implicitly parameterized, and can be updated by stochastic gradient:

[0039]

[0040] Wherein, is the parameter of the target soft Q-function, φ is the parameter of the policy function, and can be obtained by minimizing the KL divergence:

[0041]

[0042] where Π is the set of policies, D KL is the divergence, Z π (s t ) is used to normalize the distribution. Meanwhile, the action adopts the re-parameterization technique, which is denoted as:

[0043]

[0044] where f function outputs the mean and variance, ε t is the input noise vector, which can be sampled from a fixed distribution, μ represents the mean, and σ represents the variance. The update of φ can be derived from equation (6), which is denoted as:

[0045]

[0046] where, denotes the noise distribution, denotes the neural network.

[0047] Taking the gradient of the above formula, we get the following form:

[0048]

[0049]

[0050] where λ π denotes the soft update coefficient, denotes the gradient operator.

[0051] The fuel cell fault-tolerant control method based on SAC algorithm will be described in detail below.

[0052] Specifically, to realize the collaborative control of components such as anode humidifier, cathode humidifier, water pump, and radiator, the observation state space is set as:

[0053] S = [T out , RH anode , RH cathode , ΔV, ΔP, Q] (11)

[0054] where T out denotes the outlet temperature of the fuel cell stack, RH anode denotes the relative humidity of the anode, RH cathodeRHcat, ΔV, ΔP, Q) = (RHcat, ΔV, ΔP, Q) + (ΔRHcat, ΔV, ΔP, ΔQ) (1) where RHcat represents the relative humidity of the cathode, relative humidity refers to the percentage of water vapor pressure in the air to the saturated water vapor pressure at the same temperature, ΔV represents the difference between the output voltage of the fuel cell and the ideal output voltage, ΔP represents the difference between the inlet and outlet pressure drop of the cathode and the normal pressure drop under the current power requirement, and Q represents the fault type, where the normal state, membrane dry fault and water flooding fault are represented as [0, 0], [1, 0] and [0, 1] respectively. The action space taken is represented as:

[0055] A = [W anode , W cathode , f water , f air ] (12)

[0056] where W anode represents the amount of water injected by the anode humidifier, W cathode represents the amount of water injected by the cathode humidifier, f water represents the cooling water flow rate, and f air represents the air flow rate of the radiator. The reward function is set as:

[0057]

[0058] where T target and RH target in the first and second terms represent the target temperature and humidity, i.e. to control the temperature and humidity of the fuel cell to remain within the target range, the third term is a limit on the difference in fuel cell output voltage, the fourth term represents the modulo of the vector Q, which is 1 if the fuel cell is still in fault, otherwise 0; and the fifth term represents the difference between the reduced pressure drop difference of the fuel cell inlet and outlet and the normal pressure drop difference. In addition, α, β, γ, represent the preposition coefficients respectively.

[0059] Under the given conditions of the relative humidity of the anode and cathode, and the outlet temperature of the fuel cell stack, the SAC-based control process is as follows: if the fuel cell has a membrane dry or water flooding fault, the agent can give the actions of the anode humidifier, cathode humidifier, water pump and radiator according to the state of the relative humidity of the anode and cathode, the outlet temperature of the fuel cell stack, etc. by the policy network. Among them, the anode humidifier and the cathode humidifier are mainly used to control the relative humidity of the anode and cathode air. The water pump controls the outlet temperature of the fuel cell stack by controlling the circulation flow rate of the cooling water, and the radiator controls the inlet temperature of the fuel cell stack by controlling the air flow rate. The agent will produce a new state after the action is issued, thus completing a complete control cycle.

[0060] In summary, according to the fault diagnosis judgment result, the anode humidifier, the cathode humidifier, the water pump and the radiator and other components are controlled by the fault-tolerant control model based on the deep reinforcement learning algorithm to maintain the temperature and humidity of the fuel cell at the target value in the running process under the fuel cell fault state. Through the fault-tolerant control model based on deep reinforcement learning, intelligent fault recovery and adaptive control of the fuel cell system can be realized to ensure the stability and reliability of the fuel cell system.

[0061] In summary, compared with the prior art, the present application has the following advantages:

[0062] 1) Compared with the PID algorithm and the nonlinear control algorithm based on feedback linearization, the fault-tolerant control strategy based on deep reinforcement learning proposed by the present application has better adaptability and generalization ability, can handle complex nonlinear systems and has the ability of self-adaptation and autonomous learning without relying on artificial rules. Through computer simulation verification, the present application can be popularized to the internal management of fuel cells to improve the reliability of fuel cells.

[0063] 2) The temperature and water content in the fuel cell have an important influence on the performance and even the life of the fuel cell. The higher the internal temperature of the fuel cell, the more the evaporation of liquid water, which leads to membrane dehydration and voltage drop of the fuel cell. The lower the internal temperature of the fuel cell, the more likely it is to cause waterlogging in the cathode flow channel, which seriously affects the performance of the fuel cell. To solve these problems, the present application provides an effective fault-tolerant control scheme, which enables the fuel cell system to automatically adjust the running state when membrane drying, waterlogging and other faults occur, reduces the influence of faults on the performance of the system, and improves the reliability and stability of the system.

[0064] The present application can be a system, a method and / or a computer program product. The computer program product can include a computer readable storage medium having computer readable program instructions loaded thereon for causing a processor to implement various aspects of the present application.

[0065] Computer readable storage media can be tangible storage media which can retain and store instructions for use by an instruction execution device. Computer readable storage media can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer readable storage media include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0066] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0067] Computer readable program instructions for carrying out operations of the present application can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate array (FPGA), or programmable logic array (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present application.

[0068] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0069] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0070] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0071] The flow diagrams and the block diagrams in the drawings are presented to illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flow diagrams and the block diagrams can represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logic functions. In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flow diagrams, and combinations thereof, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and

[0072] Embodiments of the application have been described above. The description is illustrative of the embodiments of the application and is not meant to be limiting. Numerous modifications and variations are possible in light of the above teachings without departing from the scope and spirit of the described embodiments of the application. No limitation is intended to the details of construction or design except as described in the claims.

Claims

1. A fault-tolerant control method for fuel cells based on deep reinforcement learning, comprising the following steps: For a fuel cell system, the fault type of the fuel cell stack is determined. The fuel cell system includes a fuel cell stack, an anode humidifier, a cathode humidifier, a water pump, and a radiator. The fault types include flooding faults and membrane dryness faults. In the event of a fuel cell stack failure, the optimal fault-tolerant control strategy that satisfies the set objective function is output by a control model based on deep reinforcement learning. This strategy is used to coordinate the control of the anode humidifier, cathode humidifier, water pump, and radiator, and to perform corresponding recovery operations according to the type of failure. The control model uses the fault-tolerant control strategy as an agent and the fuel cell stack as the environment. The agent interacts with the environment and obtains reward signals, and then learns the optimal fault-tolerant control strategy based on the reward signals. The reward signal is obtained according to the following reward function: in, Indicates the reward signal value. Indicates the target temperature of the fuel cell stack. Indicates the target humidity of the fuel cell stack. This indicates the relative humidity of the anode in a fuel cell stack. This indicates the relative humidity of the cathode in the fuel cell stack. This represents the difference between the output voltage of the fuel cell stack and the ideal output voltage. This represents the difference between the inlet and outlet pressure drops of the fuel cell stack cathode and the normal pressure drop under current power demand. Indicates the fault type. Represents a vector The modulus is taken as 1 if the fuel cell stack is in a fault state, and 0 otherwise. , , , , This indicates the pre-coefficient.

2. The method according to claim 1, characterized in that, The fault types for determining the fuel cell stack include: The output voltage of the fuel cell stack is compared with the ideal output voltage. If the output voltage is not within the set normal range, a fault is determined. If a fault is detected, the pressure drop at the inlet and outlet of the fuel cell stack cathode is compared with the set normal pressure drop range under a given power demand. If the pressure drop exceeds the normal pressure drop range, it is determined to be a flooding fault. If the pressure drop is within the normal pressure drop range, it is determined to be a membrane dry fault.

3. The method according to claim 1, characterized in that, The observation state space of the control model is represented as follows: in, This indicates the outlet temperature of the fuel cell stack. This indicates the relative humidity of the anode in a fuel cell stack. The relative humidity of the cathode in a fuel cell stack. This represents the difference between the output voltage of the fuel cell stack and the ideal output voltage. This represents the difference between the inlet and outlet pressure drops of the fuel cell stack cathode and the normal pressure drop under current power demand. Indicates the fault type.

4. The method according to claim 1, characterized in that, The action space representation adopted by the control model is as follows: in, This indicates the amount of extra water injected into the anode humidifier. This indicates the amount of extra water injected into the cathode humidifier. Indicates the cooling water flow rate. This indicates the airflow rate of the radiator.

5. The method according to claim 1, characterized in that, The deep reinforcement learning uses the SoftActor-Critic algorithm.

6. The method according to claim 5, characterized in that, The objective function is set as follows: in, It is the optimal fault-tolerant control strategy function. yes The state at any given moment, yes Momentary actions It is a strategy Trajectory distribution below, It's a reward. It is a discount factor. It is the entropy under the current strategy. It is the entropy regularization coefficient, and T is the total number of time steps. Indicates the initial state of the system. The state is represented by T, and the total number of time points is represented by T. It expresses expectation.

7. The method according to claim 1, characterized in that, The fuel cell system is installed in electric vehicles, portable power sources, or combined heat and power systems.

8. A computer-readable storage medium having a computer program stored thereon, wherein, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 7.

9. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

Images