Method, System, Device and Storage Medium for Obtaining Inertia Matrix of Vehicle Center of Mass

Abstract

The present invention provides a method, system, device and storage medium for obtaining the centroid inertia matrix of an automobile, belonging to the field of measurement technology. The method includes the following steps: obtaining the inertia parameters of the automobile and the state parameters of the automobile vibration table; constructing a centroid calculation model through the inertia parameters, calculating the centroid position of the whole of the automobile and the tooling and the centroid position of the tooling through the centroid calculation model, and calculating the centroid position of the automobile according to the centroid position of the whole of the automobile and the tooling and the centroid position of the tooling; constructing a centroid inertia calculation model through the inertia parameters of the automobile and the state parameters of the automobile vibration table, and calculating the centroid inertia matrix of the whole of the automobile and the tooling and the centroid inertia matrix of the tooling through the centroid inertia calculation model; calculating the centroid inertia matrix of the automobile according to the centroid position of the whole of the automobile and the tooling, the centroid position of the tooling, the centroid position of the automobile, the centroid inertia matrix of the whole of the automobile and the tooling, and the centroid inertia matrix of the tooling.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement, and particularly relates to a method, system, device and storage medium for obtaining the centroid inertia matrix of an automobile. Background Art

[0002] The centroid inertia matrix of an automobile describes the rotational inertia characteristics of the automobile around its centroid. In automotive engineering, understanding the rotational inertia of an automobile is crucial for designing stability, suspension systems, and vehicle dynamics performance.

[0003] Existing methods for obtaining the centroid inertia matrix include the compound pendulum method, single-wire torsion pendulum method, free-fall method, three-wire pendulum method, mass line method, etc. The compound pendulum method is not applicable to large objects; the free-fall method and single-wire pendulum method are applicable to components with axisymmetric distribution such as gyro rotors; the three-wire pendulum method is difficult to measure the swing period and is not suitable for measuring the moment of inertia of large-mass components; the mass line method has a complex theoretical basis, difficult to guarantee the test accuracy, and poor test repeatability.

[0004] In summary, the existing technology lacks a method for simply and accurately obtaining the centroid inertia matrix of large objects such as automobiles. Summary of the Invention

[0005] In order to overcome the deficiencies of the above-mentioned existing technology, the present invention provides a method for obtaining the centroid inertia matrix of an automobile. The automobile is fixedly arranged on the top of an automobile vibration table through a tooling. The method includes the following steps:

[0006] Obtain the inertia parameters of the automobile and the state parameters of the automobile vibration table;

[0007] Construct a centroid calculation model through the inertia parameters, calculate the centroid position of the whole of the automobile and the tooling and the centroid position of the tooling through the centroid calculation model, and calculate the centroid position of the automobile according to the centroid position of the whole of the automobile and the tooling and the centroid position of the tooling;

[0008] Construct a centroid inertia calculation model through the inertia parameters of the automobile and the state parameters of the automobile vibration table, and calculate the centroid inertia matrix of the whole of the automobile and the tooling and the centroid inertia matrix of the tooling through the centroid inertia calculation model;

[0009] Calculate the centroid inertia matrix of the automobile according to the centroid position of the whole of the automobile and the tooling, the centroid position of the tooling, the centroid position of the automobile, the centroid inertia matrix of the whole of the automobile and the tooling, and the centroid inertia matrix of the tooling.

[0010] Preferably, the centroid calculation model of the automobile is:

[0011] r A ×f A +r B ×f B +rC ×f C +r D ×f D +M A +M B +M C +M D +ρ 0 ×R T m p g = 0

[0012] where f A , f B , f C , f D are the readings of the force sensors, r A , r B , r C , r D are the vectors from the origin of the coordinate system of the connection system to the installation points of the force sensors, ρ 0 is the position vector of the center of mass in the connection system, R is the direction cosine matrix, m p is the measurement model of the vehicle mass.

[0013] Preferably, the calculation formula for the position of the center of mass of the vehicle is:

[0014]

[0015] where m a is the total mass of the vehicle and the tooling, m f is the mass of the tooling, ρ ca is the position vector of the center of mass of the vehicle and the tooling as a whole, ρ cf is the position vector of the center of mass of the tooling.

[0016] Preferably, the calculation model for the moment of inertia of the center of mass is:

[0017]

[0018] where is the representation of the vector from the center of mass to the installation point of the force sensor in the connection system, I pp is the moment of inertia matrix of the center of mass in the connection system, ω is the vector representation of the overall angular velocity in the inertial system, ω p = R T ω is the representation of the angular velocity in the connection system, M A , M B , M C , M D are the torques measured by the force sensors in the connection system, is the derivative with respect to ω.

[0019] Preferably, the inertial matrix of the center of mass of the vehicle is determined by the following formula:

[0020]

[0021] Wherein, m a is the total mass of the vehicle and the tooling, ρ ca is the position vector of the center of mass of the vehicle and the tooling, I ppa is the inertia matrix of the center of mass of the vehicle and the tooling, m f is the mass of the tooling, ρ cf is the position vector of the center of mass of the tooling, I ppf is the inertia matrix of the center of mass of the tooling; m L is the mass of the vehicle under test, ρ cL is the position vector of the center of mass of the vehicle, I 3×3 is the identity matrix.

[0022] Preferably, the inertial parameters are obtained by a plurality of force sensors disposed on the top of the vehicle shaker.

[0023] Preferably, the state parameters of the vehicle shaker include the attitude, angular velocity and angular acceleration when the vehicle shaker rotates about the median line.

[0024] The present invention also provides a system for obtaining the inertia matrix of the vehicle center of mass, including:

[0025] A parameter acquisition module, configured to fix the vehicle on the top of the vehicle shaker through the tooling, and acquire the inertial parameters of the vehicle and the state parameters of the vehicle shaker;

[0026] A vehicle center of mass position acquisition module, configured to construct a center of mass calculation model through the inertial parameters, calculate the center of mass positions of the vehicle and the tooling as a whole and the center of mass position of the tooling through the center of mass calculation model, and calculate the center of mass position of the vehicle according to the center of mass positions of the vehicle and the tooling as a whole and the center of mass position of the tooling;

[0027] A center of mass inertia calculation model acquisition module, configured to construct a center of mass inertia calculation model through the inertial parameters of the vehicle and the state parameters of the vehicle shaker, and calculate the center of mass inertia matrix of the vehicle and the tooling as a whole and the center of mass inertia matrix of the tooling through the center of mass inertia calculation model;

[0028] A vehicle center of mass inertia acquisition module, configured to calculate the center of mass inertia matrix of the vehicle according to the center of mass positions of the vehicle and the tooling as a whole, the center of mass position of the tooling, the center of mass position of the vehicle, the center of mass inertia matrix of the vehicle and the tooling as a whole, and the center of mass inertia matrix of the tooling.

[0029] The present invention also provides a computer device, including a memory and a processor; the memory stores a computer program, and the processor is configured to run the computer program in the memory to execute the method for obtaining the inertia matrix of the vehicle center of mass.

[0030] The present invention also provides a computer-readable storage medium storing a computer program, which is adapted to be loaded by a processor to execute the method for obtaining the centroid inertia matrix of an automobile.

[0031] The method, system, device and storage medium for obtaining the centroid inertia matrix of an automobile provided by the present invention have the following beneficial effects:

[0032] The present invention avoids the disadvantages of the existing measurement methods, such as low test accuracy, complex measurement steps, and limited measurement objects. At the same time, the present invention can utilize the existing automobile test devices without adding additional measurement equipment.

[0033] By constructing a centroid calculation model and a centroid inertia calculation model, the present invention can obtain the centroid position of the whole automobile and tooling, the centroid position of the tooling, the centroid position of the automobile, the centroid inertia matrix of the whole automobile and tooling, and the centroid inertia matrix of the tooling; the centroid inertia matrix of the automobile can be calculated through the centroid position of the whole automobile and tooling, the centroid position of the tooling, the centroid position of the automobile, the centroid inertia matrix of the whole automobile and tooling, and the centroid inertia matrix of the tooling; the high-precision centroid inertia of the automobile can be obtained simply and quickly by the method of the present invention, and there are no excessive restrictions on the structure and volume of the object. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention and its design, the drawings required for this embodiment will be briefly introduced below. The drawings in the following description are only partial embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0035] Figure 1 It is a flowchart of the method for obtaining the centroid inertia matrix of an automobile according to an embodiment of the present invention;

[0036] Figure 2 It is a loading position diagram of a force sensor;

[0037] Figure 3 It is a data acquisition system diagram;

[0038] Figure 4 It is a drawing of a specific embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] In order to enable those skilled in the art to better understand the technical solutions of the present invention and implement them, the present invention will be described in detail below with reference to the drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be used to limit the protection scope of the present invention.

[0040] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. are based on the orientation or positional relationships shown in the drawings. These are only for the convenience of describing the technical solutions of the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention.

[0041] In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. In the description of the present invention, it should be noted that unless otherwise clearly specified or limited, the terms "connected" and "coupled" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. In the description of the present invention, unless otherwise stated, the meaning of "a plurality" is two or more, which will not be elaborated here.

[0042] Embodiment

[0043] The present invention provides a method for obtaining the centroid inertia matrix of an automobile, specifically as Figure 1 shown, including the following steps:

[0044] Step 1: Fix the automobile on the top of the automobile vibration table through a tooling, and obtain the inertia parameters of the automobile and the state parameters of the automobile vibration table.

[0045] Figure 2 Shows the installation positions A, B, C, and D of the force sensors of a certain type of automobile vibration table. The installation positions of the force sensors can be determined in advance. The position coordinate values and real-time inertia parameters of the automobile are obtained through multiple force sensors arranged on the top of the automobile vibration table. The vibration platform is driven by actuators in three directions of X, Y, and Z to provide the required spatial pose. The state parameters of the automobile vibration table include the attitude, angular velocity, and angular acceleration when the automobile vibration table rotates around the median line. The measured automobile is fixed on the platform through tooling.

[0046] The data acquisition process of the present invention is obtained through a data acquisition module, which consists of three modules: a vibration table motion module ①, a force sensor acquisition module ②, and an inertial parameter measurement module ③. Among them, module ① transmits the real-time three states (attitude, angular velocity, and angular acceleration) of the vibration table motion to module ③, and module ② transmits the pre-measured position coordinate values and real-time force acquisition values to the inertial parameter measurement module ③ through communication by the vibration table motion module ①.

[0047] Step 2: Construct a centroid calculation model through inertial parameters, calculate the centroid positions of the whole vehicle and the tooling through the centroid calculation model, and calculate the centroid position of the vehicle according to the centroid positions of the whole vehicle and the tooling.

[0048] Specifically, the centroid calculation model is:

[0049] r A ×f A +r B ×f B +r C ×f C +r D ×f D +M A +M B +M C +M D +ρ 0 ×R T m p g = 0

[0050] In the formula, f A , f B , f C , f D are the readings of the force sensors, r A , r B , r C , r D are the vectors from the origin of the connected system coordinates to the force sensor installation points, ρ 0 is the position vector of the centroid in the connected system, R is the direction cosine matrix, and m p is the measurement model of the vehicle mass.

[0051] Among them, m p = -(f Az + f Bz + f Cz + f Dz ) / 9.81

[0052] In the formula, f Az , f Bz , f Cz , f Dz are the readings of the z-axis sensitive axis of the force sensor.

[0053] The present invention calculates the centroid position of the whole vehicle and tooling and the centroid position of the tooling through the above centroid calculation model, and then calculates the centroid position of the vehicle based on the centroid position of the whole vehicle and tooling and the centroid position of the tooling. The calculation formula for the centroid position of the vehicle is as follows:

[0054]

[0055] In the formula, m a is the total mass of the vehicle and tooling, m f is the mass of the tooling, ρ ca is the centroid position vector of the whole vehicle and tooling, ρ cf is the centroid position vector of the tooling.

[0056] Step 3: Construct a centroid inertia calculation model through the inertia parameters of the vehicle and the state parameters of the vehicle shaker, and calculate the centroid inertia matrix of the whole vehicle and tooling and the centroid inertia matrix of the tooling through the centroid inertia calculation model.

[0057] The specific centroid inertia calculation model is as follows:

[0058]

[0059] In the formula, is the representation of the vector from the centroid to the force sensor installation point in the body coordinate system, I pp is the centroid inertia matrix in the body coordinate system, ω is the vector representation of the overall angular velocity in the inertial coordinate system, ω p =R T ω is the representation of the angular velocity in the body coordinate system, M A , M B , M C , M D are the torques measured by the force sensors in the body coordinate system, is the derivative with respect to ω.

[0060] Through this model, the present invention can calculate the centroid inertia matrix of the whole vehicle and tooling and the centroid inertia matrix of the tooling respectively.

[0061] Step 4: Calculate the centroid inertia matrix of the vehicle based on the centroid position of the whole vehicle and tooling, the centroid position of the tooling, the centroid position of the vehicle, the centroid inertia matrix of the whole vehicle and tooling, and the centroid inertia matrix of the tooling.

[0062] Through Step 2 and Step 3 of the present invention, the centroid position of the whole vehicle and tooling, the centroid position of the tooling, the centroid position of the vehicle, the centroid inertia matrix of the whole vehicle and tooling, and the centroid inertia matrix of the tooling can be obtained. By substituting the centroid position of the whole vehicle and tooling, the centroid position of the tooling, the centroid position of the vehicle, the centroid inertia matrix of the whole vehicle and tooling, and the centroid inertia matrix of the tooling into the following formula for the centroid inertia matrix of the vehicle, the centroid inertia matrix of the vehicle can be obtained:

[0063] I ppL = I ppa - (I ppf + m f ((ρ ca - ρ cf )) T (ρ ca - ρ cf )I 3×3 - (ρ ca - ρ cf )(ρ ca - ρ cf )) T ))

[0064] - (m a - m f )((ρ ca - ρ cL )) T (ρ ca - ρ cL )I 3×3 - (ρ ca - ρ cL )(ρ ca - ρ cL )) T )

[0065] In the formula, m a is the mass of the whole vehicle and tooling, ρ ca is the centroid position vector of the whole vehicle and tooling, I ppa is the centroid inertia matrix of the whole vehicle and tooling, m f is the mass of the tooling, ρ cf is the centroid position vector of the tooling, I ppf is the centroid inertia matrix of the tooling; m L is the mass of the vehicle to be measured, ρ cL is the centroid position vector of the vehicle, and I 3×3 is the identity matrix.

[0066] The present invention also provides a system for obtaining the centroid inertia matrix of a vehicle, including:

[0067] A parameter acquisition module, which is used to fix the vehicle on the top of the vehicle vibration table through a tooling, and acquire the inertial parameters of the vehicle and the state parameters of the vehicle vibration table;

[0068] A vehicle centroid position acquisition module, which is used to construct a centroid calculation model through inertial parameters, calculate the centroid position of the whole vehicle and tooling and the centroid position of the tooling through the centroid calculation model, and calculate the centroid position of the vehicle according to the centroid position of the whole vehicle and tooling and the centroid position of the tooling;

[0069] A centroid inertia calculation model acquisition module, which is used to construct a centroid inertia calculation model through the inertial parameters of the vehicle and the state parameters of the vehicle vibration table, and calculate the centroid inertia matrix of the whole vehicle and tooling and the centroid inertia matrix of the tooling through the centroid inertia calculation model;

[0070] A vehicle centroid inertia acquisition module, which is used to calculate the centroid inertia matrix of the vehicle according to the centroid position of the whole vehicle and tooling, the centroid position of the tooling, the centroid position of the vehicle, the centroid inertia matrix of the whole vehicle and tooling, and the centroid inertia matrix of the tooling.

[0071] The present invention also provides a computer device, including a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the method for acquiring the centroid inertia matrix of the vehicle.

[0072] The present invention also provides a computer-readable storage medium, which stores a computer program, and the computer program is suitable for being loaded by a processor to execute the method for acquiring the centroid inertia matrix of the vehicle.

[0073] Embodiment 2

[0074] Table 1 and Table 2 respectively list the centroid and centroid inertia data (which can be used as an accurate value) of the standard parts in three directions (X direction, Y direction, Z direction) and the centroid and centroid inertia data of the research object obtained by using the method of the present invention. The measurement error is the difference between the measurement result and the standard part data, and is used to measure the accuracy of the data obtained by the method of the present invention. It can be seen from Table 1 and Table 2 that the data obtained by using the method of the present invention has very high accuracy.

[0075] Table 1 Centroid measurement results

[0076]

[0077] Table 2 Products of inertia of the inertia matrix

[0078]

[0079] The above-described embodiments are only preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any simple variations or equivalent substitutions of technical solutions that can be obviously obtained by those skilled in the art within the technical scope disclosed by the present invention all fall within the protection scope of the present invention.

Claims

1. A method for obtaining the inertia matrix of the center of mass of a vehicle, characterized in that: The car is fixed on the top of the car vibration table by a tooling, and the method comprises the following steps: Obtain the inertia parameters of the vehicle and the state parameters of the vehicle vibration table; Constructing a center of mass calculation model through the inertia parameters, calculating the center of mass position of the vehicle and the tooling as a whole and the center of mass position of the tooling through the center of mass calculation model, and calculating the center of mass position of the vehicle according to the center of mass position of the vehicle and the tooling as a whole and the center of mass position of the tooling; A mass center inertia calculation model is constructed by using the inertia parameters of the vehicle and the state parameters of the vehicle vibration platform, and a mass center inertia matrix of the vehicle and the tooling as a whole and a mass center inertia matrix of the tooling are calculated by using the mass center inertia calculation model; Calculate the center of mass inertia matrix of the vehicle according to the center of mass position of the vehicle and tooling as a whole, the center of mass position of the tooling, the center of mass position of the vehicle, the center of mass inertia matrix of the vehicle and tooling as a whole, and the center of mass inertia matrix of the tooling; The centroid calculation model is: r A ×f A +r B ×f B +r C ×f C +r D ×f D +M A +M B +M C +M D +ρ0×R T m p g=0, f A 、f B 、f C 、f D is the force sensor reading, r A 、r B 、r C 、r D is the vector from the origin of the connection system coordinate system to the force sensor installation point, ρ0 is the position vector of the center of mass under the connection system, R is the direction cosine matrix, m p is the measurement model of automobile mass, M A 、M B 、M C 、M D is the torque measured by the force sensor in the connection system, g is the acceleration due to gravity; The center of mass inertia calculation model is: In the formula, is the vector from the center of mass to the force sensor installation point in the connection system, I pp is the mass center inertia matrix of the connected system, ω is the vector representation of the overall angular velocity in the inertial system, ω p =R T ω is the angular velocity in the connected system, M A 、M B 、M C 、M D is the torque measured by the force sensor in the connection system, To find the derivative with respect to ω; The center of mass inertia matrix of the vehicle is determined by the following formula: I ppL =I ppa -(I ppf +m f ((r ca -r cf ) T (r ca -r cf )I 3×3 -(r ca -r cf )(r ca -r cf ) T )) -(m a -m f )((r ca -r cL ) T (r ca -r cL )I 3×3 -(r ca -r cL )(r ca -r cL ) T ) In the formula, m a is the mass of the vehicle and tooling as a whole, ρ ca is the mass center position vector of the vehicle and tooling as a whole, I ppa is the mass center inertia matrix of the vehicle and tooling as a whole, m f is the tooling mass, ρ cf is the center of mass position vector of the tooling, I ppf is the center of mass inertia matrix of the tooling; m L is the mass of the car being tested, ρ cL is the center of mass position vector of the car, I 3×3 is the identity matrix.

2. The method for obtaining the vehicle center of mass inertia matrix according to claim 1, characterized in that: The calculation formula of the center of mass position of the car is: In the formula, m a is the overall mass of the car and tooling, m f is the tooling mass, ρ ca is the center of mass position vector of the vehicle and tooling as a whole, ρ cf is the center of mass position vector of the tooling.

3. The method for obtaining the vehicle center of mass inertia matrix according to claim 1, characterized in that: The inertial parameters are obtained through a plurality of force sensors arranged on the top of the automobile vibration table.

4. The method for obtaining the vehicle center of mass inertia matrix according to claim 1, characterized in that: The state parameters of the vehicle vibration platform include the posture, angular velocity and angular acceleration of the vehicle vibration platform when it rotates around the midline.

5. A system for acquiring the inertia matrix of the center of mass of a vehicle, characterized in that: include: A parameter acquisition module is used to fix the car on the top of the car vibration table through a tooling to obtain the inertia parameters of the car and the state parameters of the car vibration table; A vehicle mass center position acquisition module, used to construct a mass center calculation model through the inertia parameters, calculate the mass center position of the vehicle and the tooling as a whole and the mass center position of the tooling through the mass center calculation model, and calculate the mass center position of the vehicle according to the mass center position of the vehicle and the tooling as a whole and the mass center position of the tooling; A mass center inertia calculation model acquisition module is used to construct a mass center inertia calculation model through the inertia parameters of the vehicle and the state parameters of the vehicle vibration platform, and calculate the mass center inertia matrix of the vehicle and the tooling as a whole and the mass center inertia matrix of the tooling through the mass center inertia calculation model; The vehicle mass center inertia acquisition module is used to calculate the vehicle's mass center inertia matrix based on the mass center position of the vehicle and tooling as a whole, the mass center position of the tooling, the mass center position of the vehicle, the mass center inertia matrix of the vehicle and tooling as a whole, and the mass center inertia matrix of the tooling; Wherein, the centroid calculation model is: r A ×f A +r B ×f B +r C ×f C +r D ×f D +M A +M B +M C +M D +ρ0×R T m p g=0 In the formula, f A 、f B 、f C 、f D is the force sensor reading, r A 、r B 、r C 、r D is the vector from the origin of the connection system coordinate system to the force sensor installation point, ρ0 is the position vector of the center of mass under the connection system, R is the direction cosine matrix, m p is the measurement model of automobile mass, M A 、M B 、M C 、M D is the torque measured by the force sensor in the connection system, g is the acceleration due to gravity; The center of mass inertia calculation model is: In the formula, is the vector from the center of mass to the force sensor installation point in the connection system, I pp is the mass center inertia matrix of the connected system, ω is the vector representation of the overall angular velocity in the inertial system, ω p =R T ω is the angular velocity in the connected system, M A 、M B 、M C 、M D is the torque measured by the force sensor in the connection system, To find the derivative with respect to ω; The center of mass inertia matrix of the vehicle is determined by the following formula: I ppL =I ppa -(I ppf +m f ((r ca -r cf ) T (r ca -r cf )I 3×3 -(r ca -r cf )(r ca -r cf ) T ))-(m a -m f )((r ca -r cL ) T (r ca -r cL )I 3×3 -(r ca -r cL )(r ca -r cL ) T ) In the formula, m a is the mass of the vehicle and tooling as a whole, ρ ca is the mass center position vector of the vehicle and tooling as a whole, I ppa is the mass center inertia matrix of the vehicle and tooling as a whole, m f is the tooling mass, ρ cf is the center of mass position vector of the tooling, I ppf is the center of mass inertia matrix of the tooling; m L is the mass of the car being tested, ρ cL is the center of mass position vector of the car, I 3×3 is the identity matrix.

6. A computer device, characterized in that: The method comprises a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the method according to any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor to execute the method according to any one of claims 1 to 4.

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