A method, system and computer program product for generating an initial arrangement of low-noise tire pitch

Abstract

The present invention relates to the field of tire design technology, and in particular to a method, system and computer program product for generating an initial arrangement of low-noise tire pitches. The method generates a uniform and low-noise initial population by strictly controlling the difference in adjacent pitch lengths and the number of continuous arrangements of the same pitch in the pitch arrangement, thereby improving the optimization efficiency and accuracy of the genetic algorithm. The method automatically generates 200 pitch arrangements that meet the noise control requirements through programming in just 3 seconds, which greatly shortens the optimization time compared to the 5 minutes of manual screening after traditional random generation. The optimized initial arrangement not only reduces the noise level of the tire, but also effectively extends the service life of the tire and improves the comfort and performance of the tire. It is applicable to various types of tire designs, including all-steel, semi-steel radial tires and engineering tires. The method has the advantages of high efficiency, accuracy and automation, and provides a more reliable and economical optimization tool for tire manufacturers.

Description

Technical Field

[0001] The present invention relates to the technical field of tire design, and in particular to a method, system and computer program product for generating an initial arrangement of low-noise tire pitches. Background Art

[0002] Tire noise is an important factor affecting driving comfort and vehicle environmental performance. Studies have shown that the tire pattern design, especially the arrangement of the pattern pitch, has a significant impact on the tire noise level. The pattern pitch refers to the periodic interval of the pattern on the tire surface, which is directly related to the way the tire contacts the road surface and the flow pattern between the air and the tire, thus affecting the noise generated by the tire.

[0003] Existing tire noise optimization methods mainly reduce noise by optimizing the tire tread pitch. Traditional pitch optimization methods are mostly based on simulation and empirical methods, but these methods are often limited to linear design thinking and have difficulty dealing with complex multi-dimensional noise influencing factors. At the same time, traditional optimization methods, such as initial population generation based on simulated annealing or random algorithms, often have the problem of lack of diversity and balance in the generated initial pitch arrangement, resulting in inefficient optimization process and even difficulty in finding the optimal solution that meets design requirements.

[0004] Especially when using genetic algorithms to optimize pitch arrangement, the initial population of the genetic algorithm has a crucial impact on the optimization results. At present, most existing technologies use random generation when generating the initial population, which will cause the generated pitch arrangement to often have the same pitch continuously arranged for a long period of time or the length difference between adjacent pitches is too large. This unbalanced pitch arrangement will not only affect the noise performance of the tire, but also may cause uneven wear of the tire, further affecting the service life and comfort of the tire.

[0005] In order to improve the service life and comfort of tires while meeting the low noise requirements, how to optimize the initial population generation method in the genetic algorithm to ensure that the generated initial pitch arrangement meets certain arrangement rules and constraints has become an urgent problem to be solved in the field of tire design. At present, the Chinese invention patents applied by the applicant (such as patent 2021116135564, patent 2022100923567 and patent 2022105620611) have proposed several simulation analysis methods for tire performance, but most of the related technical means have failed to control the number of continuous arrangements of the same pitch length and the distribution of the difference in adjacent pitch lengths when generating the initial pitch. Therefore, a new method is needed to solve this problem and further improve the comfort, noise control and service life of the tire. Summary of the invention

[0006] In order to solve the above-mentioned technical problems, the purpose of the present invention is to provide a method for generating an initial arrangement of low-noise tire pitches using a genetic algorithm. The method controls the number of consecutive pitch lengths of the same pitch and the length difference between adjacent pitches during the initial arrangement of the genetic algorithm, thereby improving the comfort and service life of the tire, and through an algorithm, realizes the rapid and automatic generation of pitch arrangements that meet restricted conditions, thereby improving the efficiency and accuracy of the generation.

[0007] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0008] A method for generating an initial arrangement of low-noise tire pitches for a genetic algorithm, the method comprising the following steps:

[0009] 1) Define the tire pitch type and the number of each pitch, and define the population target number M;

[0010] 2) Define pitch-constrained arrangement rules, the rules including:

[0011] i. The difference between the first and last pitch types in the sequence is ≤ m;

[0012] ii. The numerical difference between any two adjacent pitch types in the sequence is ≤ m;

[0013] iii. The number of consecutive identical pitch types in the sequence is ≤ n;

[0014] m is the difference between adjacent pitch values, and n is the number of consecutive identical pitch types;

[0015] 3) randomly generating a pitch sequence, wherein the sequence is composed of the pitch types defined in step 1);

[0016] 4) checking and adjusting the randomly generated pitch sequence to satisfy the pitch-constrained arrangement rule in step 2);

[0017] 5) Repeat steps 3) and 4) until a population of a predetermined size is generated.

[0018] Preferably, the pitch-restricted arrangement rule defined in step 2) is: the numerical difference between any two adjacent pitch types in the sequence is ≤ m, where the value of m is 2.

[0019] Preferably, the pitch-restricted arrangement rule defined in step 2) is: the number of consecutive identical pitch types in the sequence ≤ n, where n is calculated from the total number of pitches N, and n is equal to N divided by 10 and rounded to the nearest integer.

[0020] Preferably, the adjustment method in step 4) includes:

[0021] a) Check the head-to-tail connection. If the difference between the first and last pitch type values ​​in the sequence is greater than m, the sequence is randomly reshuffled until the condition is met. b) Check the length of adjacent pitches. For each pair of adjacent pitch values ​​pitch[i] and pitch[i+1], calculate their difference. If the difference is greater than m, perform a swap operation.

[0022] c) Check for continuous identical pitches: identify a sequence of continuous identical pitch values. If the length is greater than n, swap one of the pitch values ​​until the condition is met.

[0023] Preferably, the exchange operation comprises: searching for a pitch value pitch[j] that can be exchanged with pitch[i+1] in the pitch arrangement list, so that the difference between pitch[i] and pitch[j] after the exchange is ≤m.

[0024] Preferably, the step of checking for continuous identical pitches comprises: traversing the pitch arrangement list, identifying all continuous identical pitch value sequences, and performing a swap operation on each sequence to ensure that the sequence length is ≤ n.

[0025] Furthermore, the present invention also discloses a low-noise tire pitch initial arrangement generation system for a genetic algorithm, wherein the system implements the method described, including:

[0026] 1) A definition module for defining tire pitch types and the number of each pitch;

[0027] 2) A rule definition module for defining pitch-constrained arrangement rules;

[0028] 3) A generation module for randomly generating a pitch sequence;

[0029] 4) an adjustment module for checking and adjusting the randomly generated pitch sequence to satisfy the pitch-constrained arrangement rule;

[0030] 5) A control module for repeating the generation and adjustment steps until a population of a predetermined size is generated.

[0031] Preferably, the adjustment module further includes: a head-to-tail connection check module, an adjacent pitch length check module and a continuous same pitch check module; the head-to-tail connection check module is used to check whether the numerical difference between the head and tail pitch types in the pitch sequence meets the conditions, and if not, the sequence is reshuffled; the adjacent pitch length check module is used to traverse the pitch arrangement list, calculate their difference for each pair of adjacent pitch values, and perform a swap operation when the difference is greater than a predetermined threshold to meet the difference requirement.

[0032] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instruction stored thereon, and the method is implemented when the computer program or instruction is executed by a processor.

[0033] Furthermore, the present invention also provides a computer program product, comprising a computer program or instructions, which implement the method when executed by a processor.

[0034] The present invention adopts the above technical solution, and the method controls the number of consecutive identical pitch lengths and the length difference of adjacent pitches during the initial arrangement of the genetic algorithm, thereby improving the comfort and service life of the tire, and realizes the rapid and automatic generation of pitch arrangements that meet the restricted conditions through the algorithm, thereby improving the efficiency and accuracy of the generation. It has the following significant beneficial effects:

[0035] 1. Effectively reduce tire noise: By controlling the length difference between adjacent pitches and the number of consecutive identical pitches in the pitch arrangement, the present invention can generate a more uniform and balanced pitch arrangement, thereby effectively reducing the noise level of the tire. It avoids problems such as excessive difference in the length of adjacent pitches and the same pitch arrangement for a long period of time, which will lead to increased tire noise. The optimized initial arrangement of the present invention can significantly improve the comfort of the tire and meet the low noise design requirements.

[0036] 2. Improve the optimization efficiency of genetic algorithms: The traditional random initial population generation method often requires a lot of screening and adjustment to meet the design requirements, which is time-consuming and laborious. The present invention sets a specific pitch arrangement rule, and automatically screens out the pitch arrangement that meets the noise control and uniformity requirements when generating the initial population, thereby improving the optimization efficiency of the genetic algorithm. It only takes 3 seconds to generate 200 pitch sequences that meet the arrangement rules using the method of the present invention, while the traditional random arrangement and manual screening method takes at least 5 minutes, which significantly shortens the optimization time.

[0037] 3. Improve tire service life and comfort: By controlling the difference in adjacent pitch lengths and the number of consecutive arrangements of the same pitch, the present invention can avoid unbalanced shear force on the tire and reduce the occurrence of irregular wear. This not only helps to extend the service life of the tire, but also further improves the comfort performance of the tire in actual use.

[0038] 4. Automation and rapid generation: The method of the present invention uses a programmed algorithm to quickly and automatically generate a pitch sequence that conforms to a specific arrangement rule, avoiding the cumbersome manual intervention in traditional methods. While meeting technical requirements, the method provides an efficient and repeatable solution, adapting to the high requirements of modern tire design for optimization efficiency and precision.

[0039] 5. Wide applicability: The method for generating the initial arrangement of low-noise tire pitches of the present invention is applicable to various types of tire designs, such as all-steel radial tires, semi-steel radial tires, bias tires, and engineering tires. Whether it is a car, a truck, or a special-purpose engineering machinery, the method can generate a suitable low-noise pitch arrangement to meet the optimization requirements of different types of tires.

[0040] 6. Enhance the stability and accuracy of the genetic algorithm: The present invention reduces the instability of the genetic algorithm caused by the imbalance of the initial population during the optimization process by controlling the initial arrangement quality of the population, improves the convergence and accuracy of the algorithm, and ensures that the optimization results are more accurate and effective.

[0041] In summary, the present invention not only improves the noise control performance of the tire, but also enhances the optimization efficiency of the genetic algorithm, extends the service life of the tire, and has wide applicability and significant industrial application value through an innovative low-noise tire pitch initial arrangement generation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0043] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] like Figure 1 The method for generating the initial arrangement of low-noise tire pitches for a genetic algorithm is shown. The method controls the number of consecutive pitch lengths of the same pitch and the length difference of adjacent pitches during the initial arrangement of the genetic algorithm, improves the comfort and service life of the tire, and realizes the rapid automatic generation of pitch arrangements that meet the restricted conditions through the algorithm, thereby improving the efficiency and accuracy of the generation. Specifically, the method includes the following steps:

[0045] Step 1: Define the tire pitch type and the number of each pitch, and define the population target number M;

[0046] Step 2: Define the pitch-restricted arrangement rules:

[0047] i. The difference between the first and last pitch types in the sequence is ≤ m, preferably m=2;

[0048] ii. The numerical difference between any two adjacent pitch types in the sequence is ≤ m, preferably m=2;

[0049] iii. The number of consecutive identical pitch types in the sequence is ≤ n. Preferably, the maximum number n of consecutive identical pitch types is calculated based on the total number of pitches N, where n is equal to N divided by 10 and rounded to the nearest integer;

[0050] Step 3: Randomly generate a pitch sequence: the sequence consists of the pitch types defined in step 1;

[0051] Step 4: for the sequence randomly generated in step 3, check and adjust the pitch arrangement to meet the pitch-constrained arrangement rule defined in step 2;

[0052] (5) Repeat steps 3 and 4 until a population of a predetermined size is generated.

[0053] Furthermore, the method for adjusting the sequence in step 4 includes:

[0054] (1) End-to-end check: If the difference in the first and last pitch type values ​​in the sequence is greater than m, the sequence is randomly shuffled until the condition is met;

[0055] (2) Adjacent pitch length inspection:

[0056] i. Traverse the pitch permutation list, and for each pair of adjacent pitch values ​​pitch[i] and pitch[(i +1) ] in the list, calculate their difference;

[0057] ii. If the difference calculated in step i is greater than m, perform the following operations:

[0058] a. Find a pitch value pitch[j] in the pitch permutation list that can be exchanged with pitch[(i + 1)], so that the difference between pitch[i] and pitch[j] after the exchange is ≤m;

[0059] b. Perform the swap operation pitch[i + 1], pitch[j] = pitch[j], pitch[i + 1];

[0060] c. Check whether the difference between all adjacent pitch values ​​in the swapped pitch list meets the requirements. If not, continue to look for the next swap point that meets the conditions;

[0061] d. Repeat steps a to c until the difference between all adjacent pitch values ​​in the pitch list is ≤ m;

[0062] (3) Continuous same pitch inspection:

[0063] i. Traverse the pitch permutation list and identify all consecutive identical pitch value sequences;

[0064] ii. For each identified sequence, if the sequence length is > n, perform the following operations:

[0065] a. Determine the pitch value in the sequence;

[0066] b. Find all other pitch values ​​whose difference with the pitch value is ≤ m and not equal to the pitch value;

[0067] c. Find the pitch value that meets the conditions in the pitch arrangement;

[0068] d. Swap any pitch value in the same continuous pitch value sequence with the pitch value that meets the conditions;

[0069] e. Check whether the pitch arrangement after the exchange satisfies the requirement that the difference between all adjacent pitch values ​​is ≤ m. If not, continue to look for the next pitch value that meets the condition for exchange until the requirement is met or all possible exchanges have been tried;

[0070] f. If the pitch arrangement after the exchange meets the requirements, the exchange result is retained and the next sequence is checked;

[0071] iii. Repeat step ii until the length of all consecutive identical pitch value sequences is ≤ n.

[0072] A preferred embodiment of the method of the present invention is given below, and the implementation steps are as follows:

[0073] 1. Parameter setting:

[0074] Set the pitch arrangement population size, pitch type, pitch number, restriction conditions, etc., as shown in Table 1.

[0075] Table 1: Parameter settings

[0076]

[0077] 2. Initialize the pitch arrangement population:

[0078] For each individual, generate a list containing all the pitches.

[0079] Use the random function to shuffle the list of pitches to create an initial random arrangement.

[0080] 3. End-to-end inspection:

[0081] Check the difference between the first and last pitch values ​​in the pitch list. If the difference is greater than 2, re-randomize the pitch list until the condition is met.

[0082] 4. Check the length of adjacent pitches:

[0083] Traverse the pitch list, for each pair of adjacent pitch values, if their difference is greater than 2, use the method described in step 4 to find a suitable pitch value to exchange so that the difference does not exceed 2.

[0084] 5. Processing of continuous same pitch:

[0085] Traverse the pitch list and identify all consecutive identical pitch value sequences. For sequences longer than 4, use the method described in step 4 to find different pitch values ​​that can be adjacent to the pitch values ​​in the sequence and swap them. After swapping, check whether the entire sequence meets the requirement for the difference in adjacent pitch lengths. If not, swap again until the requirement is met or all possible swaps have been tried.

[0086] 6. Generate the initial population:

[0087] Through the above steps, 200 pitch arrangements that meet the requirements are generated as the initial population of the genetic algorithm. Table 2 shows 10 pitch arrangement individuals that meet the conditions.

[0088] Table 2: Individual pitch arrangements that meet the conditions

[0089] serial number Pitch arrangement 1 4, 2, 4, 5, 4, 2, 2, 1, 2, 3, 5, 5, 3, 2, 1, 3, 5, 4, 4,5, 4, 4, 3, 1, 1, 1, 3, 5, 5, 3, 1, 1, 2, 3, 2, 1,2, 4, 5,4, 2, 2, 4, 4, 4, 5, 3, 2, 1, 3, 3, 1, 3, 4, 4, 5, 3, 4,3, 3, 3, 2, 3, 4 2 3, 2, 3, 3, 5, 5, 3, 1, 1, 3, 4, 4, 4, 4, 3, 1, 2, 1, 2,4, 5, 5, 3, 2, 2, 4, 2, 1, 3, 4, 5, 5, 3, 5, 4, 2,4, 5, 4,2, 1, 1, 2, 4, 3, 3, 3, 2, 3, 4, 5, 4, 2, 3, 1, 3, 5, 4,4, 3, 1, 1, 2, 4 3 3, 3, 2, 4, 5, 3, 1, 1, 1, 2, 4, 4, 3, 5, 3, 1, 1, 3, 4,5, 5, 4, 2, 2, 4, 5, 5, 4, 2, 2, 3, 5, 5, 4, 2, 1,2, 3, 1,3, 4, 4, 3, 1, 3, 4, 4, 3, 3, 1, 2, 4, 4, 3, 2, 4, 5, 4,2, 3, 1, 3, 5, 2 4 4, 2, 3, 5, 4, 2, 4, 2, 2, 4, 3, 3, 5, 5, 5, 4, 2, 1, 1,3, 2, 1, 3, 4, 4, 2, 1, 1, 1, 1, 3, 5, 5, 4, 5, 3,2, 2, 4,3, 1, 3, 3, 2, 4, 3, 2, 3, 5, 4, 3, 4, 3, 4, 4, 4, 3, 1,2, 1, 3, 5, 4, 5 5 3, 5, 3, 2, 4, 4, 5, 4, 2, 3, 3, 1, 3, 2, 3, 5, 4, 3, 2,4, 5, 3, 2, 1, 3, 5, 5, 4, 2, 1, 1, 1, 2, 4, 4, 4,3, 4, 3,3, 1, 2, 4, 3, 1, 1, 2, 4, 4, 4, 2, 2, 4, 5, 5, 3, 2, 3,3, 4, 5, 5, 1, 1 6 3, 4, 4, 4, 3, 1, 2, 4, 4, 5, 5, 3, 2, 2, 2, 2, 4, 3, 5,4, 3, 1, 2, 2, 2, 3, 5, 4, 2, 1, 1, 3, 1, 1, 3, 4,4, 5, 4,5, 3, 5, 5, 3, 2, 3, 3, 4, 4, 3, 1, 1, 3, 3, 5, 4, 4, 3,1, 1, 2, 2, 4, 5 7 3, 4, 2, 1, 3, 4, 5, 3, 3, 3, 1, 2, 4, 5, 3, 1, 2, 4, 3,4, 2, 4, 2, 3, 1, 1, 2, 4, 5, 5, 3, 1, 3, 4, 4, 4,4, 5, 3,2, 1, 1, 2, 4, 5, 3, 2, 3, 5, 3, 1, 1, 3, 4, 5, 5, 3, 2,2, 4, 5, 4, 2, 4 8 2, 4, 2, 4, 5, 5, 4, 2, 1, 1, 1, 2, 4, 5, 3, 1, 3, 5, 4,4, 4, 5, 4, 5, 4, 3, 1, 1, 2, 4, 5, 3, 3, 3, 4, 4,2, 1, 3,4, 5, 3, 2, 3, 3, 3, 1, 2, 2, 3, 5, 3, 2, 2, 1, 1, 2, 4,5, 4, 3, 3, 3, 4 9 4, 4, 4, 4, 3, 1, 1, 1, 2, 3, 3, 3, 2, 1, 2, 1, 3, 4, 2,2, 2, 4, 5, 4, 3, 5, 3, 1, 3, 4, 2, 1, 2, 3, 5, 3,2, 4, 3,5, 5, 5, 4, 4, 2, 2, 3, 3, 3, 4, 5, 3, 1, 2, 1, 1, 3, 5,4, 5, 4, 4, 4, 5 10 4, 2, 4, 2, 1, 1, 2, 4, 3, 1, 3, 5, 4, 3, 5, 5, 5, 3, 1,1, 3, 4, 4, 2, 3, 4, 2, 3, 2, 2, 1, 3, 4, 4, 4, 3,1, 2, 1,3, 5, 4, 5, 5, 5, 4, 2, 1, 2, 3, 5, 3, 1, 3, 2, 4, 4, 5,3,3, 3, 4, 2, 4

[0090] It only takes 3 seconds to generate 200 pitch sequences that meet the first arrangement rule using the method of the present invention. If random arrangement is used and then the sequences that do not meet the restricted conditions are manually screened out, it will take at least 5 minutes.

[0091] Table 3 shows the time taken to obtain N pitch arrangements that meet the restricted conditions by using the method of the present invention and manual screening after random arrangement:

[0092] Table 3

[0093]

[0094] The above is a description of the embodiments of the present invention. Through the above description of the disclosed embodiments, professionals and technicians in the field can implement or use the present invention. Various modifications to these embodiments will be apparent to professionals and technicians in the field. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown in this article, but will conform to the widest range consistent with the principles and novelties disclosed herein.

Claims

1. A method for generating an initial arrangement of low-noise tire pitches using a genetic algorithm, characterized in that: The method comprises the following steps: 1) Define the tire pitch type and the number of each pitch, and define the population target number M; 2) Define pitch-constrained arrangement rules, the rules including: i. The difference between the first and last pitch types in the sequence is ≤ m; ii. The numerical difference between any two adjacent pitch types in the sequence is ≤ m; iii. The number of consecutive identical pitch types in the sequence is ≤ n; m is the difference between adjacent pitch values, and n is the number of consecutive identical pitch types; 3) randomly generating a pitch sequence, wherein the sequence is composed of the pitch types defined in step 1); 4) checking and adjusting the randomly generated pitch sequence to satisfy the pitch-constrained arrangement rule in step 2); 5) Repeat steps 3) and 4) until a population of a predetermined size is generated; The adjustment methods in step 4) include: a) Check the head-to-tail connection. If the difference between the head and tail pitch type values ​​in the sequence is greater than m, the sequence is randomly shuffled again until the condition is met; b) Check the length of adjacent pitches. Traverse the pitch permutation list and calculate the difference between each pair of adjacent pitch values ​​pitch[i] and pitch[i+1]. If the difference is greater than m, perform the swap operation. c) Check for continuous identical pitches: identify a sequence of continuous identical pitch values. If the length is greater than n, swap one of the pitch values ​​until the condition is met.

2. The method according to claim 1, characterized in that The pitch-constrained arrangement rule defined in step 2) is: the numerical difference between any two adjacent pitch types in the sequence is ≤ m, where the value of m is 2.

3. The method according to claim 1, characterized in that The pitch-restricted arrangement rule defined in step 2) is: the number of consecutive identical pitch types in the sequence is ≤ n, where n is calculated from the total number of pitches N, and n is equal to N divided by 10 and rounded to the nearest integer.

4. The method according to claim 1, characterized in that The exchange operation includes: searching for a pitch value pitch[j] that can be exchanged with pitch[i+1] in the pitch arrangement list, so that the difference between pitch[i] and pitch[j] after the exchange is ≤m.

5. The method according to claim 1, characterized in that The step of checking for continuous identical pitches includes: traversing the pitch arrangement list, identifying all continuous identical pitch value sequences, and performing an exchange operation on each sequence to ensure that the sequence length is ≤ n.

6. A low-noise tire pitch initial arrangement generation system for genetic algorithm, characterized in that: The system implements the method according to any one of claims 1 to 5, including: 1) A definition module for defining tire pitch types and the number of each pitch; 2) A rule definition module for defining pitch-constrained arrangement rules; 3) A generation module for randomly generating a pitch sequence; 4) an adjustment module for checking and adjusting the randomly generated pitch sequence to satisfy the pitch-constrained arrangement rule; 5) A control module for repeating the generation and adjustment steps until a population of a predetermined size is generated.

7. The system according to claim 6, characterized in that The adjustment module further includes: a head-to-tail connection check module, an adjacent pitch length check module and a continuous same pitch check module; the head-to-tail connection check module is used to check whether the numerical difference between the head and tail pitch types in the pitch sequence meets the conditions, and if not, the sequence is reshuffled; the adjacent pitch length check module is used to traverse the pitch arrangement list, calculate their difference for each pair of adjacent pitch values, and perform a swap operation when the difference is greater than a predetermined threshold to meet the difference requirement.

8. A computer-readable storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

9. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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