Steel rail grinding opportunity decision model and method
By using a rail grinding timing decision model and deep neural network, the grinding index is calculated based on the rail service status parameters. This allows for precise segmentation and the generation of grinding plans, solving the problems of resource waste and lag associated with fixed-cycle grinding and achieving scientific and rational rail maintenance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- METALS & CHEM RES INST CHINA ACAD OF RAILWAY SCI
- Filing Date
- 2025-12-31
- Publication Date
- 2026-05-01
AI Technical Summary
The existing rail grinding program is mainly based on a fixed cycle, which leads to over-maintenance or delays, waste of resources, and affects the service life of rails and railway safety.
A rail grinding timing decision model is adopted. By obtaining service status parameters, the rail grinding index is calculated. Based on the index, the sections are divided and the grinding timing is determined. A specific grinding plan is generated by combining a deep neural network model.
It enables dynamic maintenance based on rail condition, optimizes resource allocation, improves the timeliness and pertinence of maintenance, and ensures the service condition of rails and the safety of track operation.
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Figure CN121960141A_ABST
Abstract
Description
A decision-making model and method for rail grinding timing Technical Field
[0001] This invention relates to the field of railway track maintenance technology, and in particular to a decision-making model and method for rail grinding timing. Background Technology
[0002] Rail grinding, as an important railway line maintenance technology, can effectively repair or reduce fatigue damage such as rail corrugation, surface cracks, and spalling, extend the service life of rails, improve wheel-rail contact, and enhance the safety and stability of vehicle operation. It has been widely used worldwide.
[0003] Rail grinding can be divided into pre-grinding, preventative grinding, and repair grinding. Pre-grinding is used on newly laid rails to remove the decarburized layer from the rail surface, eliminate surface defects generated during production, welding, transportation, and construction, optimize the rail head profile, and improve the smoothness of welded joints. Preventative grinding is periodic grinding of rails to repair the rail head profile and prevent the occurrence of defects such as rolling contact fatigue and corrugation. Repair grinding is used on rails that have already developed defects to correct the rail head profile and eliminate defects such as rolling contact fatigue cracks, corrugation, and abrasion.
[0004] Current rail maintenance primarily combines preventative and repair-oriented grinding. For example, the "Guiding Opinions on Rail Grinding for Conventional Railways" (Yun Gong Xian Lu Han
[2014] No. 227) stipulates that preventative rail grinding should be determined based on observation data of the rail profile and surface condition, combined with rolling contact fatigue damage. For straight sections and curves with a radius greater than 1200m, grinding is generally performed once every 100Mt of total throughput. For curves with a radius less than or equal to 1200m, grinding is performed every 30-50Mt. The "Management Measures for Rail Grinding for High-Speed Railways" (Tie Zong Yun
[2014] No. 357) states that the preventative rail grinding cycle is determined based on the total throughput and operating condition, and in principle, preventative rail grinding should be performed every 30-50Mt of total throughput, generally not exceeding two years.
[0005] However, preventative grinding (i.e., periodic grinding) plans are determined by total mass or service life and are generally fixed. However, fixed-cycle grinding can lead to over-maintenance, wasting grinding resources and increasing track maintenance costs. Furthermore, fixed-cycle grinding also has a lag effect; early rail damage may occur, but grinding may be delayed because the predetermined cycle has not been reached, accelerating rail failure, shortening service life, and even threatening railway operational safety.
[0006] In view of this, based on years of experience in production design in this and related fields, the inventor has designed a rail grinding timing decision model and method through repeated experiments in order to solve the problems existing in the prior art. Summary of the Invention
[0007] The purpose of this invention is to provide a decision-making model and method for rail grinding timing, which can organize rail grinding construction in a more scientific and reasonable manner based on the site conditions.
[0008] This invention also proposes a rail grinding timing decision model, wherein the rail grinding timing decision model includes:
[0009] The data import module obtains the service status parameters of the line to be evaluated;
[0010] The data processing module calculates the corresponding rail grinding index based on the service status parameters;
[0011] The timing judgment module receives the rail grinding index, divides the line to be ground into multiple sections based on the rail grinding index, and determines whether each section needs to be ground.
[0012] The decision output module outputs the sections that need to be polished.
[0013] To achieve the above objectives, this invention proposes a method for determining the timing of rail grinding, wherein the method includes: obtaining service status parameters of the line to be evaluated; calculating the corresponding rail grinding index GI based on the service status parameters; dividing the line to be evaluated into multiple sections according to the rail grinding index; and determining the grinding timing based on the rail grinding index corresponding to each section.
[0014] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described calculation method.
[0015] The present invention also proposes a computer device, including a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described calculation method.
[0016] Compared with the prior art, the present invention has the following features and advantages:
[0017] The rail grinding timing decision-making model and method proposed in this invention quantifies the service condition of rails based on the rail grinding index, accurately determining the timing of rail grinding according to the service condition, thus transforming rail grinding from the current "periodic maintenance" to "condition-based maintenance." Simultaneously, an intelligent decision-making model for rail grinding based on deep neural networks is established, capable of providing specific grinding schemes and process modes. This allows for the scientific and rational organization of rail grinding construction guided by on-site conditions, ensuring the service condition of rails while fully leveraging the guiding role of the rail grinding index in rail maintenance. Attached Figure Description
[0018] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely illustrative to aid in understanding the invention and do not specifically limit the shapes and proportions of the components. Those skilled in the art, guided by the teachings of this invention, can select various possible shapes and proportions to implement the invention according to specific circumstances.
[0019] Figure 1 is a flowchart of the decision-making method for the timing of rail grinding according to the present invention;
[0020] Figure 2 is a flowchart of the rail grinding timing determination process of the present invention;
[0021] Figure 3 is a flowchart of the timing judgment module construction and verification process of the present invention;
[0022] Figure 4 is a structural diagram of the intelligent decision-making model for rail grinding according to the present invention. Detailed Implementation
[0023] The details of the present invention can be more clearly understood by referring to the accompanying drawings and the description of specific embodiments. However, the specific embodiments of the present invention described herein are for illustrative purposes only and should not be construed as limiting the invention in any way. Under the teachings of this invention, those skilled in the art can conceive of any possible modifications based on the invention, and these should all be considered to fall within the scope of the invention.
[0024] As shown in Figure 1, this invention proposes a decision-making method for the timing of rail grinding. The decision-making method includes: obtaining the service status parameters of the line to be evaluated; calculating the corresponding rail grinding index GI based on the service status parameters; dividing the line to be evaluated into multiple sections according to the rail grinding index; and determining the grinding timing based on the rail grinding index corresponding to each section.
[0025] The rail grinding timing decision method proposed in this invention uses the rail grinding index (GI) to quantitatively evaluate the service status of rails. Based on the rail grinding index, the line to be evaluated is divided into multiple sections. Grinding is carried out based on the actual status of each section of the line to be evaluated, thereby achieving accurate judgment of the timing of rail grinding. This transforms rail grinding from a fixed cycle mode to a state-based dynamic maintenance, effectively ensuring the service status of rails and the safety of line operation while optimizing the allocation of grinding resources and improving the timeliness and pertinence of maintenance.
[0026] In an optional embodiment of the present invention, the service status parameters include rail profile data, rail surface damage data, and rail surface smoothness data. These data serve as foundational data for subsequent calculations of the corresponding rail grinding index, providing data support for the subsequent division of the track sections to be evaluated and the determination of grinding timing. By acquiring rail profile data, rail surface damage data, and rail surface smoothness data as service status parameters, key information reflecting the rail's service status can be comprehensively covered. This provides complete and accurate foundational data for subsequent calculations of the rail grinding index based on these parameters, ensuring that the subsequent quantitative evaluation of the rail's service status is more consistent with the actual condition of the rail. This, in turn, lays a reliable data foundation for accurately dividing the track sections to be evaluated and accurately determining the grinding timing.
[0027] In an optional embodiment of the present invention, the rail grinding index includes a primary index GI and a secondary index, the secondary index including the profile quality index PQI, the rail surface damage index SDI, and the rail surface smoothness index RCI.
[0028] The rail grinding index adopts a hierarchical evaluation system, which includes a comprehensive primary index, the Rail Grinding Index (GI), and three specialized secondary indices. These three secondary indices are: the Profile Quality Index (PQI), which evaluates the degree to which the rail head geometry conforms to the target profile; the Rail Damage Index (SDI), which evaluates the severity of defects such as rail surface cracks; and the Rail Smoothness Index (RCI), which evaluates the longitudinal smoothness of the rail. When calculating the rail grinding index, a predetermined calculation method is used to process the input data on rail profile, rail surface damage, and rail smoothness, thereby obtaining the quantitative results of the primary index and the three secondary indices, which together constitute a complete quantitative description of the rail's condition. By establishing a multi-level evaluation system consisting of the primary index GI and the secondary indices SDI, PQI, and RCI, a three-dimensional and refined quantitative assessment of the rail's service condition can be conducted from both macroscopic overall condition and microscopic specific issues perspectives. This facilitates understanding overall grinding requirements and accurately pinpointing the specific reasons for poor condition.
[0029] In one optional example of this implementation, the rule for dividing the line to be evaluated into multiple segments is as follows: within the same segment, the primary index GI is not greater than the standard value, and any secondary index does not exceed its corresponding threshold; when the primary index GI is greater than the standard value or any secondary index exceeds its corresponding threshold, the mutation point of the secondary index is used as the segment division basis; when multiple secondary indices exceed the limit at the same time, the division basis is determined according to the priority order of the rail surface damage index SDI, the profile quality index PQI, and the rail surface smoothness index RCI.
[0030] Specifically, the division of track sections is based on the primary indicator GI as the core criterion, supplemented by threshold constraints from secondary indicators: Rail Damage Index (SDI), Profile Quality Index (PQI), and Rail Smoothness Index (RCI). Within the same section, GI must be less than or equal to the standard value, and SDI, PQI, and RCI must be less than or equal to their respective thresholds. When GI exceeds the standard value or any secondary indicator exceeds the limit, the abrupt change point of the exceeding indicator is used as the section division point. When GI meets the standard but a secondary indicator involving safety risks (such as SDI) exceeds the limit, that indicator is used as the division basis. For example, if the SDI is 3.5 (exceeding the threshold of 3.0), the section must be cut at the SDI abrupt change point. Furthermore, if multiple secondary indicators exceed the limit simultaneously, the division is based on the priority order of SDI > PQI > RCI. For example, the threshold for the Rail Surface Damage Index (SDI) is 3.1, and the threshold for the Profile Quality Index (PQI) is 4.1. If a section has both an SDI exceeding 3.0 and a PQI exceeding 4.0, the boundary should be demarcated based on the SDI.
[0031] This segmentation rule, by comprehensively considering the threshold conditions of primary and secondary indicators and establishing a clear priority processing logic, can accurately identify the boundaries of areas in the line where the service status changes abruptly or where there is specific damage, thereby scientifically dividing long lines into multiple segments with uniform internal conditions.
[0032] In one optional example, the score for the primary indicator is 3.6, the Profile Quality Index (PQI) score is 5.0, the Rail Surface Damage Index (SDI) score is 3.0, and the Rail Surface Ride Index (RCI) score is 2.0.
[0033] As shown in Table 1, the specific quantitative standards set for section division and grinding timing judgment are as follows: within the same section, the standard value of the primary indicator GI is ≤3.2, and any secondary indicator (PQI / SDI / RCI) does not exceed its threshold (the threshold for profile quality index PQI is 4.0, the threshold for rail surface damage index SDI is 3.0, and the threshold for rail surface smoothness index RCI is 2.0). By clearly defining the standard value of the primary indicator GI and the specific thresholds for profile quality index PQI, rail surface damage index SDI, and rail surface smoothness index RCI, a unified, clear, and operable quantitative benchmark is provided for the evaluation of rail condition and section division.
[0034] Table 1:
[0035]
[0036] In one optional example of this implementation, determining the timing of grinding includes: for each segment after division, determining the timing of grinding in priority order: if the primary index GI of the segment is greater than the standard value, grinding is triggered immediately; if the primary index GI of the segment does not exceed the standard value, the rail surface damage index SDI, profile quality index PQI and rail surface smoothness index RCI are checked in sequence, and grinding is triggered if any secondary index exceeds its threshold.
[0037] Specifically, during this process, if any secondary indicator exceeds its own threshold, grinding of that section is triggered. This decision-making method establishes a clear priority order, prioritizing the comprehensive primary indicator GI to quickly identify sections in poor overall condition, and then systematically screening specific indicators, ensuring a clear and efficient decision-making logic and enabling timely response to various rail damage situations.
[0038] In one optional example, the standard value for the primary metric GI is 3.2.
[0039] As shown in Figure 2, the timing of grinding must be determined according to priority: if the score of the primary indicator GI is ≥3.2, grinding is triggered immediately; if the primary indicator GI does not exceed the standard value, the rail surface damage index SDI, profile quality index PQI, and rail surface smoothness index RCI are checked sequentially, and grinding is triggered if any indicator exceeds the threshold. When the data processing module or intelligent decision-making module calculates and judges any segment, if the value of the primary indicator GI for that segment is greater than the standard value of 3.2, a decision instruction to grind that segment is triggered. By specifying that the standard value of the primary indicator GI is 3.2, a specific and unified quantitative standard is provided for the determination of the primary indicator in the timing of grinding, avoiding deviations in the timing of grinding caused by unclear standard values for the primary indicator GI.
[0040] In an optional embodiment of the present invention, the decision-making method further includes calculating the grinding index of each section based on the rail service condition parameters. As shown in Figure 3, calculating the grinding index of each section using the rail grinding index includes the following steps:
[0041] S1: Establish the basic database
[0042] Historical grinding data for typical railway lines is collected, including rail profile data, rail surface damage data, rail surface smoothness data, and corresponding grinding parameters (grinding speed, number of grinding passes, grinding head distribution angle, and motor power). This data is then imported into the database via manual entry or automatic import. The database supports common data formats such as BAN / TXT / CSV / XML / JSON / JPEG / PNG / BMP. Whether the data is a file directly generated by the equipment containing rail profile data, rail surface damage data, and rail surface smoothness data, or a dataset containing these three types of data after processing by third-party software, it can be imported quickly and accurately.
[0043] S2: Data Processing
[0044] (1) Clean the data collected from the database: use the Z-score method to remove outliers, use a low-pass filter to remove noisy data, and then perform Min-Max normalization.
[0045] (2) Divide the dataset into 70% training set, 15% validation set, and 15% test set.
[0046] (3) Based on the calculation formula of rail grinding index, the processed rail condition parameter data are calculated to obtain the corresponding rail grinding index, including the primary index GI and the secondary indexes: profile quality index PQI, rail surface damage index SDI, and rail surface smoothness index RCI.
[0047] (4) Based on the different service status parameters of the rails, the line is divided into multiple sections, and corresponding grinding parameters are added for each section to facilitate subsequent model training.
[0048] In one optional example, the specific segmentation is shown in Table 2.
[0049] Table 2:
[0050]
[0051] S3: Model Building
[0052] (1) Constructing a multi-layer neural network model: Construct a structure model based on a deep neural network (DNN) (as shown in Figure 4). The input layer has 4 nodes x1~x4, corresponding to the first-level index GI, profile quality index PQI, rail surface damage index SDI, and rail surface smoothness index RCI, respectively. The output layer has 4 nodes y1~y4, outputting the grinding speed v, the number of grinding passes n, the grinding head distribution angle θ, and the motor power P. The hidden layer determines the optimal number of layers and neurons through hyperparameter search (such as grid search).
[0053] (2) Function implementation of each layer:
[0054] 1) Input layer: As the data entry point for the neural network, it is responsible for receiving the rail grinding index data and passing it to the hidden layer.
[0055] 2) Hidden Layers: Located between the input and output layers, these layers are responsible for feature extraction and data abstraction. Neurons within these layers perform a weighted summation of the input signals from the previous layer, adding a bias term, and then outputting the result through a non-linear activation function (such as LeakyReLU: f(x) = max(0.01x, x)). This introduces non-linearity to fit complex relationships. Dropout layers (with a dropout rate of 0.3) are inserted between hidden layers to apply L2 regularization (λ=1e-4) to prevent overfitting and limit model complexity. Weights and biases are generated through random initialization.
[0056] 3) Output Layer: Receives information from the hidden layer, performs inverse normalization, and outputs specific parameters of the grinding scheme (grinding speed v, number of grinding passes n, grinding head distribution angle θ, motor power P). The number of grinding passes refers to the number of cycles in the grinding operation. Each grinding pass corresponds to a specific set of grinding head distribution angles and motor power parameters. Let the number of grinding passes be n. The model will output n sets of corresponding grinding head distribution angles and motor power parameters {(θ1, P1), (θ2, P2), … , (θn, Pn)}. Each grinding head distribution angle set θi (i=1, 2, … , n) may contain multiple specific angle values {θi1, θi2, … , θim}, and each angle value θij (j = 1,2, … ,m) has a precisely matched motor power value Pij, ensuring accurate and efficient grinding operations at different grinding stages and grinding head positions.
[0057] Add constraints to each parameter:
[0058] The grinding speed v∈[5,25] km / h is mapped by a piecewise linear function (such as ReLU6);
[0059] The number of polishing passes n∈{1,2,3,4,5,6} is quantized using an integer function;
[0060] The grinding head distribution angle θ∈[-10°,50°], and the motor power P∈[40%,90%].
[0061] S4: Iterative Training
[0062] The neural network was trained using training data from the database to establish a complex nonlinear relationship between the polishing index and the polishing scheme parameters, thus obtaining a preliminary model.
[0063] The rail grinding index from the training set is passed from the input layer to the hidden layer via forward propagation. The weighted summation of each neuron, after being weighted and biased, is transformed by a nonlinear activation function, ultimately generating a prediction at the output layer. The error between the prediction and the actual value is calculated using a defined loss function, and the weights and biases are updated using backpropagation and optimization algorithms. This process is repeated iteratively for training. As training progresses, the model's weights and biases are continuously adjusted, the loss value gradually decreases, and the accuracy of the mapping model between the rail grinding index and grinding parameters gradually improves, resulting in a preliminary model.
[0064] S5: Model Evaluation
[0065] During training, the model is periodically evaluated using a validation set. Based on performance metrics on the validation set (e.g., root mean square error ≤ 0.15, coefficient of determination ≥ 0.93), the model's hyperparameters (e.g., number of layers, number of neurons, learning rate) are adjusted. Training stops when the model's performance on the validation set no longer improves, yielding the final model. Finally, a test set is used for final evaluation to refine the model.
[0066] In this model, the grinding parameters are directly mapped through the same set of rail grinding indices, eliminating the need for manual consultation of the model library. This achieves seamless integration between index determination and construction parameters, improving the efficiency and consistency of grinding scheme generation.
[0067] In an optional embodiment of the present invention, the decision-making method further includes preprocessing the service status parameters: removing abnormal values and noise data from the service status parameters respectively, and normalizing the service parameters.
[0068] Specifically, data processing employs the Z-score method to remove outliers and a low-pass filter to remove noise. Min-Max normalization is then performed to transform the data into a uniform numerical range, providing high-quality, standardized data input for subsequent index calculations. By preprocessing the original service state parameters using the model, outliers and noise interference are effectively eliminated, and the data scale is standardized, significantly improving the accuracy and reliability of subsequent rail grinding index calculations.
[0069] As shown in Figure 4, in this invention, the above-mentioned decision-making method is implemented through a rail grinding timing decision-making model, wherein the rail grinding timing decision-making model includes:
[0070] The data import module obtains the service status parameters of the line to be evaluated;
[0071] The data processing module calculates the corresponding rail grinding index based on service status parameters;
[0072] The timing judgment module receives the rail grinding index, divides the line to be ground into multiple sections based on the rail grinding index, and determines whether each section needs to be ground.
[0073] The decision output module outputs the sections that need to be refined.
[0074] The data import module, data processing module, timing judgment module, and decision output module are sequentially connected. Through the collaborative work of these modules, a complete process is achieved, from obtaining service status parameters of the track to be evaluated to outputting the sections requiring grinding. The data import module ensures the convenience and compatibility of obtaining service status parameters; the data processing module provides a quantified rail grinding index for subsequent decision-making; the timing judgment module enables precise segment division of the track to be ground and accurate judgment of grinding requirements for each segment; and the decision output module provides clear segment guidance for on-site grinding construction. The overall model can determine the grinding timing based on the on-site service status of the rails, fully leveraging the guiding role of the rail grinding index in maintenance and repair, ensuring the service status of the rails while providing support for the scientific and rational organization of rail grinding construction. This invention also proposes a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the above-described calculation method.
[0075] The present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program that can run on the processor, wherein the processor executes the computer program to implement the steps of the above-described calculation method.
[0076] The detailed explanations of the above embodiments are intended only to explain the present invention so as to facilitate a better understanding of the present invention. However, these descriptions should not be construed as limiting the present invention for any reason. In particular, the various features described in different embodiments can be arbitrarily combined with each other to form other embodiments. Unless there is an explicit description to the contrary, these features should be understood to be applicable to any embodiment, and not limited to the described embodiments.
Claims
1. A decision-making model for the timing of rail grinding, characterized in that, The rail grinding timing decision model includes: a data import module to obtain the service status parameters of the line to be evaluated; a data processing module to calculate the corresponding rail grinding index based on the service status parameters; a timing judgment module to receive the rail grinding index, divide the line to be ground into multiple sections based on the rail grinding index, and determine whether each section needs to be ground; and a decision output module to output the sections that need to be ground.
2. A method for determining the timing of rail grinding, characterized in that, The decision-making method includes: obtaining service status parameters of the line to be evaluated; calculating the corresponding rail grinding index (GI) based on the service status parameters; dividing the line to be evaluated into multiple sections according to the rail grinding index; and determining the timing of grinding based on the rail grinding index corresponding to each section.
3. The rail grinding timing decision method as described in claim 2, characterized in that, The service status parameters include rail profile data, rail surface damage data, and rail surface smoothness data.
4. The method for determining the timing of rail grinding as described in claim 2, characterized in that, The rail polishing index includes a primary index GI and a secondary index. The secondary index includes the profile quality index PQI, the rail surface damage index SDI, and the rail surface smoothness index RCI.
5. The method for determining the timing of rail grinding as described in claim 4, characterized in that, The division rules for the line to be evaluated into multiple segments are as follows: within the same segment, the primary index GI is not greater than the standard value, and any of the secondary indices does not exceed its corresponding threshold; when the primary index GI is greater than the standard value or any of the secondary indices exceeds its corresponding threshold, the abrupt change point of the secondary index is used as the segment division basis; when multiple secondary indices exceed the limit at the same time, the division basis is determined according to the priority order of the rail surface damage index SDI, the profile quality index PQI, and the rail surface smoothness index RCI.
6. The method for determining the timing of rail grinding as described in claim 5, characterized in that, The standard value for the primary indicator is 3.2, the threshold value for the profile quality index (PQI) is 4.0, the threshold value for the rail surface damage index (SDI) is 3.0, and the threshold value for the rail surface smoothness index (RCI) is 2.
0.
7. The method for determining the timing of rail grinding as described in claim 4, characterized in that, Determining the timing of polishing includes: for each of the divided sections, determining the timing of polishing in order of priority: if the primary index GI of the section is greater than or equal to the standard value, polishing is triggered immediately; if the primary index GI of the section does not exceed the standard value, the rail surface damage index SDI, the profile quality index PQI, and the rail surface smoothness index RCI are checked in sequence, and polishing is triggered if any of the secondary indices exceeds its threshold.
8. The method for determining the timing of rail grinding as described in claim 7, characterized in that, The standard value for the primary indicator GI is 3.
2.
9. The method for determining the timing of rail grinding as described in claim 2, characterized in that, The decision-making method also includes calculating the grinding index of each section based on the rail service status parameters.
10. The method for determining the timing of rail grinding as described in claim 2, characterized in that, The decision-making method further includes preprocessing the service status parameters: removing abnormal values and noise data from the service status parameters, and normalizing the service parameters.
11. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the calculation method according to any one of claims 2 to 10.
12. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that, When the processor executes the computer program, it implements the steps of the calculation method according to any one of claims 2 to 10.