A reliability evaluation method, device and medium for parameter-dependent Gamma degradation model based on Bayes

Abstract

The present invention provides a reliability assessment method, device and medium of a parameter-correlated Gamma degradation model based on Bayes, which can improve the reliability of the assessment. The method comprises the following steps: obtaining sample degradation data through equal interval measurement; describing the parameter correlation of the degradation data distribution, and deriving a posterior distribution model of the degradation quantity distribution parameters by using a Bayesian model; sampling the posterior distribution according to the idea of ​​the mixed Gibbs algorithm in the MH algorithm to obtain a sampling result; obtaining a posterior parameter estimation result according to the sampling result; and evaluating the product reliability by using the posterior parameter estimation result to obtain the product reliability. The present invention considers the correlation of parameters on the basis that the product degradation trajectory obeys the Gamma process. Since there is no way to know the form and degree of parameter correlation, it is considered to use Jeffreys information-free prior distribution to describe the correlation of parameters, and then through the Bayesian method, combined with the measured degradation data, a model for evaluating product reliability can be obtained.

Description

Technical Field

[0001] The invention belongs to the field of reliability assessment, and in particular relates to reliability assessment of a Gamma degradation process product taking into account parameter correlation. Background Art

[0002] Due to the complex product structure of construction machinery, the traditional independent distribution cannot fully summarize the real product degradation process. Considering only the independent case, the reliability evaluation of the system structure such as multi-component series and parallel cannot be properly handled, which will seriously underestimate or overestimate the product reliability. Therefore, a reliability evaluation model that considers correlation (including data correlation, parameter correlation, mode correlation, etc.) is urgently needed.

[0003] In the present invention, the abbreviations and key terms are defined as follows:

[0004] MLE - Maximum Likelihood Estimation

[0005] MCMC——Markov Chain Monte Carlo Method

[0006] MH algorithm——Metropolis-Hastlings algorithm

[0007] Bayes——Bayesian model

[0008] Definitions of Key Terms:

[0009] Parameter correlation - there is correlation between the parameters in the distribution

[0010] Full conditional distribution - distribution with the regularization constant removed

[0011] The main existing technical solutions for product reliability assessment methods considering correlation are as follows:

[0012] 1. Product reliability evaluation method based on equivalent normalized variable transformation method:

[0013] This type of method converts related variables into independent equivalent normal distributions through polynomial transformations, such as Rosenblatt transformation and Nataf transformation, and then conducts product reliability assessment through statistical inference of the equivalent normal distribution.

[0014] 2. Product reliability evaluation method based on linear programming boundary method:

[0015] This type of method represents system events as a series of "mutually independent and completely exhaustive" events, and uses their corresponding probabilities as design variables. The reliability of the system is represented by the product of the probability vector corresponding to the state vector of the "mutually independent and completely exhaustive events", and finally the reliability boundary problem is solved.

[0016] 3. Product reliability evaluation based on Copula method:

[0017] This method uses the Copula function to describe the correlation existing in the product system as a connection function, combined with the sample joint density function to form a likelihood function, and obtains parameter estimates through the MLE or MCMC method to ultimately obtain a product reliability assessment.

[0018] However, the prior art has the following disadvantages

[0019] 1. Product reliability evaluation method based on equivalent normalized variable transformation method:

[0020] The calculation is performed by converting the related variables into independent equivalent normal distributions. The three commonly used transformation methods are Orthogonal transformation, Rosenblatt transformation, and Nataf transformation. However, Nataf and Orthogonal will be affected by the coefficient of variation of the variables, and Rosenblatt transformation will be affected by the order of variable transformation. In short, the transformation method itself uses an indirect method to evaluate the reliability of related variables, which will lose information during the transformation process and is greatly affected by external factors.

[0021] 2. Product reliability evaluation method based on linear programming boundary method

[0022] This type of method focuses on using linear programming to analyze the reliability of complex systems. On the one hand, it can only describe the first-order overall linear relationship. On the other hand, since it needs to solve the linear programming problem, it may not be able to be solved if the dimension of the applicable problem is too high, and there are situations where the joint probability density function cannot be determined.

[0023] 3. Product reliability evaluation based on Copula method

[0024] This type of method selects a suitable connection function from a given function to describe the correlation between variables. The function form is complex, and since there are many unknown parameters, a large sample size is required for the final parameter estimation, and a small sample may lead to overfitting. Summary of the invention

[0025] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a Bayes-based parameter-dependent Gamma degradation model reliability assessment method, device and medium, which can improve the reliability of the assessment.

[0026] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0027] In a first aspect, the present invention provides a parameter-dependent Gamma degradation model reliability assessment method based on Bayes, comprising the following steps:

[0028] Obtain sample degradation data through equally spaced measurements;

[0029] Describe the parameter correlation of the degradation data distribution, and use the Bayesian model to derive the posterior distribution model of the degradation distribution parameters;

[0030] According to the idea of ​​the hybrid Gibbs algorithm in the MH algorithm, sampling of the posterior distribution is performed to obtain the sampling results;

[0031] Obtain the posterior estimation results of parameters based on the sampling results;

[0032] The product reliability is evaluated based on the parameter posterior estimation results to obtain the product reliability.

[0033] Furthermore, the sample degradation data is the performance degradation amount X(t i ),i=1,2,...,n

[0034] The method of describing the parameter correlation of the degraded data distribution includes describing the parameter correlation of the degraded data distribution with Jeffreys uninformative prior distribution;

[0035] The method of describing the parameter correlation of the degradation data distribution and deriving the posterior distribution model of the degradation amount distribution parameters by using the Bayesian model includes:

[0036] The degradation amount X(t i ) obeys the Gamma process, selects the parameter prior distribution as Jeffreys uninformative prior distribution, establishes the Bayes model, and obtains the parameter posterior distribution density function under the data. The joint posterior density function of the distribution parameters is

[0037]

[0038] In the formula, ΔX ti =X ti -X ti-1 , ΔX={ΔX ti ,i=1,2,...,n-1}, parameters α,λ are the distribution parameters of ΔX, ψ′(αΔt) is the derivative of the digamma function ψ(αΔt)

[0039] The full conditional distribution of each parameter is

[0040]

[0041]

[0042] In the formula, “∝” represents full conditional distribution, “~” represents the obeyed distribution, and Gamma represents Gamma distribution.

[0043] Further, the method of describing the parameter correlation of the degradation data distribution includes:

[0044] When the sample data is sufficient, the Copula function is used to describe the parameter correlation of the degenerate data distribution.

[0045] Furthermore, the method may use the Wiener degradation process to replace the Gamma degradation process.

[0046] Furthermore, according to the idea of ​​the hybrid Gibbs algorithm in the MH algorithm, the posterior distribution is sampled, and the method for obtaining the sampling result includes:

[0047] Choose appropriate initial values ​​of (α,λ) [α (0) ,λ (0) ];

[0048] In the MH algorithm, the proposed distribution is selected in the manner of the Gibbs algorithm, and samples are drawn starting from the initial value [α (t) ,λ (t) ]:

[0049] Considering Metropolis selection, the symmetric distribution-normal distribution is selected as the recommended distribution, that is, the new state α′ in the Markov chain (t-1) From N(α (t-1) ,σ 2 ), where σ 2 is a given constant. At this time, the acceptance function g(·) is

[0050]

[0051] At this time, the transfer core of the chain is stably distributed with π(α|ΔX,λ).

[0052] Generate a random value u from a uniform distribution on [0,1]. Considering that there may be too many values ​​in the posterior distribution, the discriminant is in logarithmic form, then

[0053]

[0054] According to the idea of ​​Gibbs algorithm, the conditional distribution π[λ|ΔX,α (t) ] as the proposed distribution to extract samples λ (t) ;

[0055] The iterative value of (α, λ) is updated through the above extraction steps, and the extraction is repeated to obtain the sampling result.

[0056] Furthermore, the method of obtaining a posterior estimation result of the parameter according to the sampling result includes:

[0057] Select the mean of the later sample extraction values ​​as the estimate of (α,λ)

[0058] Furthermore, a method for obtaining a posterior parameter estimation result based on the sampling result and evaluating the product reliability based on the posterior parameter estimation result includes:

[0059] Set the failure threshold to D. According to the parameter estimation results, set the time from the first degradation of the product to failure to T. Calculate the product reliability R(t) as:

[0060]

[0061] Where D is the failure threshold, is the distribution parameter estimate of ΔX, T is the time from the first degradation to failure of the product, P(T>t) represents the probability that the product life is greater than time t, F T (t) represents the probability of product failure at time t, t represents time, x represents life span,

[0062] In a second aspect, the present invention provides a parameter-dependent Gamma degradation model reliability assessment device based on Bayes, comprising:

[0063] Acquisition module: used to obtain sample degradation data through equal interval measurements;

[0064] Model description module: used to describe the parameter correlation of the degradation data distribution and derive the posterior distribution model of the degradation distribution parameters using the Bayesian model;

[0065] Sampling module: used to sample the posterior distribution according to the idea of ​​the mixed Gibbs algorithm in the MH algorithm to obtain the sampling results;

[0066] Evaluation module: used to obtain the posterior estimation results of parameters based on the sampling results;

[0067] Output module: used to evaluate product reliability based on the parameter posterior estimation results to obtain product reliability.

[0068] In a third aspect, the present application provides a reliability assessment device for a parameter-dependent Gamma degradation model based on Bayes, comprising a processor and a storage medium;

[0069] The storage medium is used to store instructions;

[0070] The processor is used to operate according to the instructions to execute the steps of the method described in the first aspect.

[0071] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. The present invention does not generate new parameters to be estimated and does not increase the solution dimension during parameter estimation.

[0074] 2. The specific form and degree of correlation between parameters in the present invention are unknown, and the uninformative prior distribution can give the joint prior distribution of related parameters through the sample information amount.

[0075] 3. The present invention is not limited to the overall first-order linear relationship, but is applicable to complex correlation relationships.

[0076] 4. The present invention directly performs statistical inference through the measured degradation amount, making full use of sample information. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is a flow chart of the method of the present invention;

[0078] Figure 2 Display graphs for MCMC sampling results;

[0079] Figure 3 is the reliability function graph. DETAILED DESCRIPTION

[0080] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0081] Embodiment 1:

[0082] The purpose of the present invention is to use Jeffreys uninformative prior distribution to describe the correlation between parameters in the Gamma degradation process, and then establish a Bayesian model through the joint density function of the degradation data to obtain the posterior estimation of the parameters of the degradation distribution, so as to perform reliability assessment on the degradation process with parameter correlation.

[0083] This embodiment provides a parameter-dependent Gamma degradation model reliability assessment method based on Bayes, and the specific steps are as follows: Figure 1 As shown:

[0084] Step 1: Measure the performance degradation X(t i ),i=1,2,...,n;

[0085] Step 2: Let the degradation amount X(ti ) obeys the Gamma process, selects the parameter prior distribution as Jeffreys uninformative prior distribution, establishes the Bayes model, and obtains the parameter posterior distribution density function under the data. The joint posterior density function of the distribution parameters is

[0086]

[0087] In the formula, ΔX ti =X ti -X ti-1 , ΔX={ΔX ti ,i=1,2,...,n-1}, parameters α,λ are the distribution parameters of ΔX, ψ′(αΔt) is the derivative of the digamma function ψ(αΔt)

[0088] The full conditional distribution of each parameter is

[0089]

[0090]

[0091] In the formula, “∝” represents full conditional distribution, “~” represents the distribution that complies with the condition, and Gamma represents the Gamma distribution.

[0092] Step 3: Choose appropriate initial values ​​of (α,λ) [α (0) ,λ (0) ];

[0093] Step 4: Mix the MH algorithm with the Gibbs algorithm to select the proposed distribution and start sampling with the initial value in step 3 [α (t) ,λ (t) ]:

[0094] Considering Metropolis selection, the symmetric distribution-normal distribution is selected as the recommended distribution, that is, the new state α′ in the Markov chain (t-1) From N(α (t-1) ,σ 2 ), where σ 2 is a given constant. At this time, the acceptance function g(·) is

[0095]

[0096] At this time, the transfer core of the chain is stably distributed with π(α|ΔX,λ).

[0097] Generate a random value u from a uniform distribution on [0,1]. Considering that there may be too many values ​​in the posterior distribution, the discriminant is in logarithmic form, then

[0098]

[0099] Step 5: According to the idea of ​​Gibbs algorithm, conditional distribution π[λ|ΔX,α (t) ] as the proposed distribution to extract samples λ (t) ;

[0100] Step 6: Update the iterative value of (α, λ) through the above extraction steps and repeat the extraction;

[0101] Step 7: When the number of sampling repetitions t is large enough, the sample values ​​are stable near a certain value. Therefore, the mean of the later sample values ​​is selected as the estimate of (α, λ)

[0102] Step 8: Set the failure threshold to D. According to the parameter estimation results in the previous step, set the time from the first degradation to failure of the product to T. Calculate the product reliability expression as

[0103]

[0104] Where D is the failure threshold, is the distribution parameter estimate of ΔX, T is the time from the first degradation to failure of the product, P(T>t) represents the probability that the product life is greater than time t, F T (t) represents the probability of product failure at time t, t represents time, x represents life span,

[0105] Use Jeffreys uninformative prior distribution to describe the correlation of parameters;

[0106] Through the Bayesian method, combined with the measured degradation data, the posterior estimation of the parameters of the product degradation process distribution is obtained, and finally the model for product reliability evaluation is obtained.

[0107] It should also be noted in this embodiment that when the sample data is sufficient, the Copula function can be used instead of the function describing the parameter correlation.

[0108] The Gamma degenerate process can be replaced by the Wiener degenerate process.

[0109] The parameter estimation method of the model, that is, steps 3-7 can also be replaced by the EM algorithm.

[0110] To provide an implementation simulation case for the above technical solution, assume that the degradation data of a certain online running product is as shown in the table.

[0111] Table 1 Historical degradation information of online running products

[0112]

[0113]

[0114] Substitute the above degenerate data into the Bayes posterior distribution model in step 2, and use the MCMC sampling method to calculate the parameter estimates starting from step 3. After 100,000 samplings, the MCMC sampling is as follows Figure 2 shown.

[0115] Select the mean of the last 50,000 times as the estimation result, and we can get

[0116]

[0117] Set the failure threshold D to 40

[0118]

[0119] The reliability function graph is as follows Figure 3 shown.

[0120] Compared with the prior art, the present invention has the following advantages:

[0121] No new parameters to be estimated are generated, and the solution dimension for parameter estimation will not be increased.

[0122] The specific form and degree of correlation between parameters are unknown. The uninformative prior distribution can give the joint prior distribution of related parameters through the sample information.

[0123] It is not limited to the overall first-order linear relationship and is applicable to complex correlation relationships.

[0124] Statistical inference is directly performed through the measured degradation amount, making full use of sample information.

[0125] It should be noted that during the specific implementation process:

[0126] When the sample data is sufficient, Copula functions can be used instead of functions that describe parameter correlations.

[0127] The Gamma degenerate process can be replaced by the Wiener degenerate process.

[0128] The parameter estimation method of the model can be replaced by the EM algorithm.

[0129] The method of this embodiment is a new method for describing the correlation of degradation process parameters, using Jeffreys uninformative prior distribution to describe the correlation of parameters. The MH algorithm for solving the parameters to be estimated in the Bayes posterior distribution selects the suggested distribution in the MH algorithm in the manner of the Gibbs algorithm to perform parameter estimation of the Bayes posterior distribution model.

[0130] Embodiment 2:

[0131] This embodiment provides a parameter-dependent Gamma degradation model reliability assessment device based on Bayes, including:

[0132] Acquisition module: used to obtain sample degradation data through equal interval measurements;

[0133] Model description module: used to describe the parameter correlation of the degradation data distribution and derive the posterior distribution model of the degradation distribution parameters using the Bayesian model;

[0134] Sampling module: used to sample the posterior distribution according to the idea of ​​the mixed Gibbs algorithm in the MH algorithm to obtain the sampling results;

[0135] Evaluation module: used to obtain the posterior estimation results of parameters based on the sampling results;

[0136] Output module: used to evaluate product reliability based on the parameter posterior estimation results to obtain product reliability.

[0137] The device of this embodiment can be used to implement the method described in the first embodiment.

[0138] Embodiment three:

[0139] This embodiment provides a parameter-dependent Gamma degradation model reliability assessment device based on Bayes, including a processor and a storage medium;

[0140] The storage medium is used to store instructions;

[0141] The processor is used to operate according to the instructions to execute the steps of the method described in embodiment 1.

[0142] Embodiment 4:

[0143] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method described in the first embodiment are implemented.

[0144] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0145] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0146] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0147] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0148] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A reliability assessment method for parameter-dependent Gamma degradation model based on Bayes, characterized in that: The following steps are involved: Obtain sample degradation data through equally spaced measurements; Describe the parameter correlation of the degradation data distribution, and use the Bayesian model to derive the posterior distribution model of the degradation distribution parameters; According to the idea of ​​the hybrid Gibbs algorithm in the MH algorithm, sampling of the posterior distribution is performed to obtain the sampling results; Obtain the posterior estimation results of parameters based on the sampling results; The product reliability is evaluated based on the parameter posterior estimation results to obtain the product reliability; The sample degradation data is the performance degradation amount X(t i ),i=1,2,...,n The method of describing the parameter correlation of the degraded data distribution includes describing the parameter correlation of the degraded data distribution with Jeffreys uninformative prior distribution; The method of describing the parameter correlation of the degradation data distribution and deriving the posterior distribution model of the degradation amount distribution parameters by using the Bayesian model includes: The degradation amount X(t i ) obeys the Gamma process, selects the parameter prior distribution as Jeffreys uninformative prior distribution, establishes the Bayes model, and obtains the parameter posterior distribution density function under the data. The joint posterior density function of the distribution parameters is In the formula, Parameters α, λ are the distribution parameters of ΔX, ψ′(αΔt) is the derivative of the Digamma function ψ(αΔt) The full conditional distribution of each parameter is In the formula, "∝" represents full conditional distribution, "~" represents the obeyed distribution, and Gamma represents Gamma distribution.

2. The parameter-dependent Gamma degradation model reliability assessment method based on Bayes according to claim 1, characterized in that: Methods for describing the parametric dependence of the distribution of degraded data include: When the sample data is sufficient, the Copula function is used to describe the parameter correlation of the degenerate data distribution.

3. The parameter-dependent Gamma degradation model reliability assessment method based on Bayes according to claim 1, characterized in that: This method can use the Wiener degradation process to replace the Gamma degradation process.

4. The parameter-dependent Gamma degradation model reliability assessment method based on Bayes according to claim 1, characterized in that: According to the idea of ​​the hybrid Gibbs algorithm in the MH algorithm, the posterior distribution is sampled and the methods for obtaining the sampling results include: Choose appropriate initial values ​​of (α,λ) [α (0) ,λ (0) ]; In the MH algorithm, the proposed distribution is selected in the manner of the Gibbs algorithm, and samples are drawn starting from the initial value [α (t) ,λ (t) ]: Considering Metropolis selection, the symmetric distribution-normal distribution is selected as the recommended distribution, that is, the new state α′ in the Markov chain (t-1) From N(α (t-1) ,σ 2 ), where σ 2 is a given constant; the accepted function g(·) is At this time, the transfer core of the chain is stably distributed with π(α|ΔX,λ); Generate a random value u from a uniform distribution on [0,1]. Considering that there may be too many values ​​in the posterior distribution, the discriminant is in logarithmic form, then According to the idea of ​​Gibbs algorithm, the conditional distribution π[λΔX,α (t) ] as the proposed distribution to extract samples λ (t) ; The iterative value of (α, λ) is updated through the above extraction steps, and the extraction is repeated to obtain the sampling result.

5. The parameter-dependent Gamma degradation model reliability assessment method based on Bayes according to claim 1, characterized in that: Methods for obtaining parameter posterior estimation results based on sampling results include: Select the mean of the later sample extraction values ​​as the estimate of (α,λ) 6. The parameter-dependent Gamma degradation model reliability assessment method based on Bayes according to claim 1, characterized in that: The method of obtaining the parameter posterior estimation result based on the sampling result and using the parameter posterior estimation result to evaluate the product reliability includes: Set the failure threshold to D. According to the parameter estimation results, set the time from the first degradation of the product to failure to T. Calculate the product reliability R(t) as: Where D is the failure threshold, is the distribution parameter estimate of ΔX, T is the time from the first degradation to failure of the product, P(T>t) represents the probability that the product life is greater than time t, F T (t) represents the probability of product failure at time t, t represents time, x represents life span, 7. A reliability assessment device for parameter-dependent Gamma degradation model based on Bayes, characterized in that: include: Acquisition module: used to obtain sample degradation data through equal interval measurements; Model description module: used to describe the parameter correlation of the degradation data distribution and derive the posterior distribution model of the degradation distribution parameters using the Bayesian model; Sampling module: used to sample the posterior distribution according to the idea of ​​the mixed Gibbs algorithm in the MH algorithm to obtain the sampling results; Evaluation module: used to obtain the posterior estimation results of parameters based on the sampling results; Output module: used to evaluate product reliability based on the parameter posterior estimation results to obtain product reliability; The sample degradation data is the performance degradation amount X(t i ),i=1,2,...,n The method of describing the parameter correlation of the degraded data distribution includes describing the parameter correlation of the degraded data distribution with Jeffreys uninformative prior distribution; The method of describing the parameter correlation of the degradation data distribution and deriving the posterior distribution model of the degradation amount distribution parameters by using the Bayesian model includes: The degradation amount X(t i ) obeys the Gamma process, selects the parameter prior distribution as Jeffreys uninformative prior distribution, establishes the Bayes model, and obtains the parameter posterior distribution density function under the data. The joint posterior density function of the distribution parameters is In the formula, Parameters α, λ are the distribution parameters of ΔX, ψ′(αΔt) is the derivative of the Digamma function ψ(αΔt) The full conditional distribution of each parameter is In the formula, "∝" represents full conditional distribution, "~" represents the obeyed distribution, and Gamma represents Gamma distribution.

8. A reliability assessment device for parameter-dependent Gamma degradation model based on Bayes, characterized in that: including processor and storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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