Equipment maintenance method and system based on exponential distribution dynamic aging model, medium and equipment

Abstract

The invention relates to an equipment maintenance method and system based on an exponential distribution dynamic aging model, a medium and equipment. The method comprises the following steps: acquiring source data of the equipment; determining parameters of the exponential distribution dynamic aging model; calculating the instantaneous failure rate and the average aging failure rate of the equipment at different time points based on the parameters of the exponential distribution dynamic aging model and the equipment maintenance record; according to the average aging failure rate, a target maintenance period is determined by adjusting the maintenance period and calculating a corresponding average aging failure rate ratio; making a maintenance plan based on the target maintenance period, the average aging failure rate ratio and the actual working condition information; and performing maintenance operation on the equipment based on the maintenance plan. According to the method, a scientific quantitative basis can be provided for maintenance decision, the problems of excessive maintenance and insufficient maintenance can be avoided, the maintenance cost is reduced, and the economic benefits of enterprises are improved; the reliability and the operation stability of the equipment are improved, and the model is updated in combination with real-time data to adapt to dynamic changes of equipment aging characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of equipment maintenance, and more particularly to an equipment maintenance method, system, medium and equipment based on an exponential distribution dynamic aging model. Background Art

[0002] Currently, fixed-cycle maintenance is commonly used for equipment maintenance. However, fixed-cycle maintenance generally fails to account for individual differences in equipment aging, resulting in maintenance cycles that do not match actual conditions and wasted maintenance costs. For example, equipment maintenance methods based on the Weibull model assume a monotonically increasing failure rate but fail to quantify the inhibitory effect of maintenance on the aging rate, making them unable to adapt to the needs of dynamic maintenance. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide an equipment maintenance method, system, medium and equipment based on an exponential distribution dynamic aging model in response to the problems existing in the prior art.

[0004] The technical solution adopted by the present invention to solve the technical problem is to construct an equipment maintenance method based on an exponential distribution dynamic aging model, including the following steps:

[0005] Get the source data of the device;

[0006] Analyzing and processing the source data to determine parameters of an exponential distribution dynamic aging model;

[0007] Calculate the instantaneous failure rate and average aging failure rate of the equipment at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the equipment;

[0008] According to the average aging failure rate, the maintenance cycle is adjusted and the corresponding average aging failure rate ratio is calculated to determine the target maintenance cycle;

[0009] Formulate a maintenance plan based on the target maintenance cycle and the actual operating condition information of the equipment;

[0010] Perform maintenance operations on the equipment based on the maintenance plan.

[0011] In the equipment maintenance method based on the exponential distribution dynamic aging model of the present invention, analyzing and processing the source data to determine the parameters of the exponential distribution dynamic aging model includes:

[0012] Obtain equipment failure event data, failure rate data, predicted failure rate before maintenance, and measured failure rate after maintenance;

[0013] Performing calculations based on the failure event data to obtain an initial failure rate;

[0014] Calculating based on the failure rate data and the initial failure rate to obtain a failure rate growth rate;

[0015] Calculating based on the initial failure rate, the predicted failure rate before maintenance, and the measured failure rate after maintenance to obtain a maintenance effectiveness parameter;

[0016] The initial failure rate, the failure rate growth rate, and the maintenance effectiveness parameter are parameters of the exponential distribution dynamic aging model.

[0017] In the device maintenance method based on the exponential distribution dynamic aging model of the present invention, calculating the instantaneous failure rate and the average aging failure rate of the device at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the device includes:

[0018] Determine the maintenance cycle division;

[0019] Calculate the time points within the target period;

[0020] Substituting the maintenance cycle division and the time points within the target cycle into the exponential distribution dynamic aging model for calculation to obtain the instantaneous failure rate at different time points;

[0021] The average aging failure rate is obtained by integrating and averaging the instantaneous failure rates at different time points.

[0022] In the equipment maintenance method based on the exponential distribution dynamic aging model of the present invention, adjusting the maintenance cycle and calculating the corresponding average aging failure rate ratio based on the average aging failure rate to determine the target maintenance cycle includes:

[0023] Determine the average aging failure rate of the new cycle and the average aging efficiency of the original cycle according to the average aging failure rate;

[0024] Determining an average aging failure rate ratio based on the average aging failure rate of the new cycle and the average aging efficiency of the original cycle;

[0025] Determine the objective function;

[0026] Determine safety constraints and reliability constraints;

[0027] Get input data;

[0028] Establish a cycle-cost correlation model;

[0029] Determine screening constraints;

[0030] The target maintenance cycle is obtained by performing calculations based on the objective function, the safety constraint, the reliability constraint, the input data, the cycle-cost association model, and the screening constraint.

[0031] In the equipment maintenance method based on the exponential distribution dynamic aging model of the present invention, formulating a maintenance plan based on the target maintenance cycle and actual operating condition information of the equipment includes:

[0032] Determine the basic maintenance time nodes;

[0033] Determine maintenance content and resource allocation;

[0034] A maintenance plan is formulated based on the basic maintenance time nodes, the maintenance content and resource allocation, the target maintenance cycle, the average aging failure rate ratio, and the actual working condition information of the equipment.

[0035] In the equipment maintenance method based on the exponential distribution dynamic aging model of the present invention, determining maintenance content and resource allocation includes:

[0036] Determine the maintenance level based on the current aging status of the equipment;

[0037] determining maintenance content based on the maintenance level;

[0038] Allocate resources based on maintenance complexity, failure probability, and downtime.

[0039] In the equipment maintenance method based on the exponential distribution dynamic aging model of the present invention, the exponential distribution dynamic aging model is:

[0040]

[0041] λ m+1 (t): failure rate at time t between the mth and m+1th maintenance activities, m = 1, 2, 3, ...;

[0042] λ0: initial failure rate (determined by historical data and statistical methods);

[0043] γ: failure rate growth rate (reflecting the inherent aging characteristics of the equipment);

[0044] t: time;

[0045] ω: maintenance effectiveness parameter;

[0046] t m : The time after the mth maintenance is performed, m = 1, 2, 3, ...

[0047] The present invention also provides an equipment maintenance system based on an exponential distribution dynamic aging model, comprising:

[0048] A data acquisition unit, used to acquire source data of the device;

[0049] a parameter calculation unit, configured to analyze and process the source data to determine parameters of an exponential distribution dynamic aging model;

[0050] a failure rate calculation unit, configured to calculate the instantaneous failure rate and the average aging failure rate of the device at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the device;

[0051] a target maintenance cycle determining unit, configured to determine a target maintenance cycle by adjusting the maintenance cycle and calculating a corresponding average aging failure rate ratio according to the average aging failure rate;

[0052] A maintenance plan formulation unit, configured to formulate a maintenance plan based on the target maintenance cycle and actual operating condition information of the equipment;

[0053] A maintenance operation unit is used to perform maintenance operations on the equipment based on the maintenance plan.

[0054] The present invention also provides a storage medium storing a computer program, wherein the computer program is suitable for being loaded by a processor to execute the steps of the equipment maintenance method based on the exponential distribution dynamic aging model as described above.

[0055] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the steps of the equipment maintenance method based on the exponential distribution dynamic aging model as described above by calling the computer program stored in the memory.

[0056] The equipment maintenance method, system, medium, and equipment based on the exponential distribution dynamic aging model of the present invention have the following beneficial effects: including: obtaining source data of the equipment; determining the parameters of the exponential distribution dynamic aging model; calculating the instantaneous failure rate and average aging failure rate of the equipment at different time points based on the parameters of the exponential distribution dynamic aging model and the equipment maintenance records; determining the target maintenance cycle according to the average aging failure rate by adjusting the maintenance cycle and calculating the corresponding average aging failure rate ratio; formulating a maintenance plan based on the target maintenance cycle, the average aging failure rate ratio, and actual working condition information; and performing maintenance operations on the equipment based on the maintenance plan. The present invention can provide a scientific and quantitative basis for maintenance decisions, avoid the problems of over-maintenance and under-maintenance, reduce maintenance costs, and improve the economic benefits of the enterprise; improve the reliability and operational stability of the equipment, and update the model in combination with real-time data to adapt to the dynamic changes in the aging characteristics of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0058] Figure 1 This is a flow chart of an embodiment of a device maintenance method based on an exponential distribution dynamic aging model provided by the present invention;

[0059] Figure 2 is a flow chart of another embodiment of the equipment maintenance method based on the exponential distribution dynamic aging model provided by the present invention;

[0060] Figure 3 This is a logic block diagram of the equipment maintenance system based on the exponential distribution dynamic aging model provided by the present invention. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0062] The present invention provides an equipment maintenance method based on an exponentially distributed dynamic aging model, which can be applied to predictive maintenance in high-reliability scenarios (such as nuclear energy and aerospace equipment). It reduces maintenance costs and improves equipment reliability through dynamic aging modeling and optimization strategies.

[0063] In a preferred embodiment, Figure 1 As shown, the equipment maintenance method based on the exponential distribution dynamic aging model includes the following steps:

[0064] Step S100: Acquire source data of the device.

[0065] Equipment source data includes: equipment failure event data, failure rate data, predicted failure rates before maintenance, and measured failure rates after maintenance. Specifically, this includes historical data and real-time data. Historical data includes maintenance records (time, content, and cost), failure records (time, component, and failure mode), and operating parameters (temperature, vibration, load, etc., collected in real time via sensors). Real-time data includes the current equipment operating status parameters (used to calibrate the model's real-time failure rate).

[0066] Among them, after obtaining the source data, the data needs to be cleaned, such as cleaning abnormal data (such as mutation values ​​caused by sensor failure) and organizing it into a structured table according to time series (an example is shown in Table 1 below).

[0067] Table 1

[0068]

[0069]

[0070] Next, the processed data is imported into the database to create a digital twin file of the equipment, associating basic information such as equipment number, model, and service time.

[0071] Step S200: Analyze and process the source data to determine the parameters of the exponential distribution dynamic aging model.

[0072] In the embodiment of the present invention, the parameters of the exponential distribution dynamic aging model include: initial failure rate, failure rate growth rate and maintenance effectiveness parameter.

[0073] In some embodiments, analyzing and processing source data to determine parameters of an exponentially distributed dynamic aging model includes: obtaining failure event data, failure rate data, predicted failure rate before maintenance, and measured failure rate after maintenance of the equipment; performing calculations based on the failure event data to obtain an initial failure rate; performing calculations based on the failure rate data and the initial failure rate to obtain a failure rate growth rate; and performing calculations based on the initial failure rate, predicted failure rate before maintenance, and measured failure rate after maintenance to obtain a maintenance effectiveness parameter.

[0074] In the embodiment of the present invention, the initial efficiency λ0 can be obtained through the frequency statistics of the initial failure data, which can reflect the reliability of the equipment in the "new state". The failure growth rate γ can be obtained through the logarithmic linear regression of the aging process, which can quantify the growth rate of the failure rate over time. The maintenance effectiveness parameter ω can be obtained by comparing the failure rates before and after maintenance, which can quantify the inhibitory effect of maintenance on aging. The three together constitute the core parameters of the dynamic aging model, support the optimization of maintenance cycles (such as calculating the ratio R) and the formulation of maintenance plans, and realize the closed loop from "data collection → parameter calibration → model application". In high-reliability scenarios, strict verification is required in combination with industry standards (such as nuclear power equipment requires parameter confidence ≥ 99%) to ensure that the model accuracy meets safety requirements.

[0075] (1) Calculation of initial failure rate λ0:

[0076] Initial failure rate λ0: The failure rate of the device in the ideal initial state (no aging, new or just after maintenance), in time -1 (e.g., times / hour). It can be fitted with historical failure data (e.g., maximum likelihood estimation method) to take the average failure rate before the first maintenance. The initial failure rate λ0 is used as a benchmark parameter of the dynamic model to reflect the inherent reliability level of the equipment. The calculation process of the initial failure rate λ0 is as follows:

[0077] First, determine the data range:

[0078] If the equipment is new, the data range is: failure data from the first time the equipment is put into use to the first maintenance; if the equipment is in service, the data range is: "no maintenance interval" data before the first failure after historical maintenance.

[0079] Next, determine the data format:

[0080] Record the occurrence time t of each failure event i , forming a failure time series {t1, t2, ..., t n}, n is the number of failure events.

[0081] Next, calculate the initial failure rate λ0 (using the maximum likelihood estimation method):

[0082] Assuming that the failure rate of the equipment in the initial stage follows an exponential distribution (constant failure rate), the likelihood function is:

[0083]

[0084] Take the logarithm and then differentiate and set the derivative to 0:

[0085]

[0086] Solving equation (2) yields:

[0087]

[0088] Example: If the equipment runs for 1000 hours before its first maintenance and 5 failures occur during this period, then λ0 = 5 / 1000 = 0.005 failures / hour.

[0089] Finally, perform data optimization (small sample correction):

[0090] If the failure data is insufficient (n<5), use Bayesian estimation combined with prior knowledge:

[0091]

[0092] Among them, α and β are industry prior parameters (such as hyperparameters corresponding to the historical average failure rate of similar equipment).

[0093] (2) Calculation of failure growth rate γ:

[0094] Failure growth rate γ: describes the rate at which the failure rate increases exponentially over time due to equipment aging, in units of time -1 , γ>0 indicates accelerated aging. Its mathematical model is: the failure rate changes with time as (Natural aging process before maintenance). The calculation process of the failure growth rate γ is as follows:

[0095] First, determine the data range:

[0096] Failure rate monitoring data of equipment in an unmaintained state, or "aging accumulation period" data before each maintenance;

[0097] Record different time points t j The measured failure rate (Reverse inference through fault frequency or sensor parameters).

[0098] Next, calculate the failure growth rate γ (using linear regression):

[0099] Perform logarithmic transformation on the mathematical model of failure growth rate γ, that is, Taking the natural logarithm, we get:

[0100] lnλ(t)=lnλ0+γt(3);

[0101] Fitting straight line based on formula (3): With time t as the horizontal axis, lnλ 实测 As the vertical axis, perform a linear regression, and the slope is γ and the intercept is lnλ0.

[0102] Regression equation: in λ is measured, a=lnλ0;

[0103] The least squares method is used to solve the problem:

[0104]

[0105] (3) Calculation of maintenance effectiveness parameter ω:

[0106] Maintenance effectiveness parameter ω: quantifies the inhibitory effect of maintenance on aging. ω = 0 means that maintenance has no effect (failure rate continues to increase at the original rate), and ω = 1 means that maintenance completely resets the aging state (failure rate returns to a certain point before maintenance). Its mathematical model is: After maintenance, the starting point of the failure rate is adjusted to That is, the accumulation of aging time is shortened by ω. The calculation process of the maintenance effectiveness parameter ω is as follows:

[0107] Obtain the predicted failure rate before maintenance. The predicted failure rate before maintenance is calculated based on the aging model before maintenance and the maintenance time t m The theoretical failure rate is:

[0108]

[0109] Obtain the failure rate measured after maintenance. Among them, the failure rate measured after maintenance is: the failure rate detected immediately after maintenance is completed The measurement must be performed after the device has been restarted and has been running stably for more than one hour.

[0110] The calculation method is:

[0111]

[0112] The specific derivation process is:

[0113] The post-maintenance failure rate model is At the maintenance time t=t m hour:

[0114]

[0115] Taking the logarithm of both sides of equation (5) and rearranging them, we can obtain equation (4).

[0116] The specific engineering verification (average of multiple maintenance) is as follows:

[0117] A single maintenance may be affected by accidental factors (such as fluctuations in spare parts quality), so it is necessary to average the data from multiple maintenance sessions:

[0118]

[0119] (6) In formula, M is the number of historical maintenance times, and outliers are eliminated (for example, a sudden increase in failure rate after a certain maintenance may be a maintenance error and needs to be excluded).

[0120] The following is a complete example of how to calculate the initial failure rate λ0, the failure growth rate γ, and the maintenance effectiveness parameter ω. Taking a nuclear power pump as an example,

[0121] Equipment overview: Model: KSB-100; Service time: 2000 hours; Historical maintenance times: 3 times (m=1, 2, 3).

[0122] Calculate the initial failure rate λ0:

[0123] Before the first maintenance (0-500 hours), three failures occurred at 100, 300, and 450 hours:

[0124] λ0=3 / (100+300+450)=3 / 850≈0.00353 times / hour.

[0125] Calculate the failure growth rate γ:

[0126] Collect pre-maintenance failure rate data (as shown in Table 2):

[0127] Table 2

[0128]

[0129] The linear regression calculates the slope, which is the failure growth rate γ:

[0130]

[0131] Calculate the maintenance effectiveness parameter ω:

[0132] The second maintenance time t2 = 1000 hours, the predicted failure rate before maintenance:

[0133]

[0134] After each maintenance, press the latest Update ω and iteratively optimize λ0 and γ using the newly added failure data (e.g., recursive least squares method to adapt to non-stationary aging processes).

[0135] Step S300: Based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the equipment, the instantaneous failure rate and the average aging failure rate of the equipment at different time points are calculated.

[0136] In some embodiments, based on the parameters of the exponential distribution dynamic aging model and the maintenance records of the current operating status of the equipment, calculating the instantaneous failure rate and the average aging failure rate of the equipment at different time points includes: determining the maintenance cycle division; calculating the time points within the target cycle; substituting the maintenance cycle division and the time points within the target cycle into the exponential distribution dynamic aging model for calculation to obtain the instantaneous failure rate at different time points; and integrating and averaging the instantaneous failure rates at different time points to obtain the average aging failure rate.

[0137] In the embodiment of the present invention, the exponential distribution dynamic aging model is:

[0138]

[0139] (7) Where: m+1 (t): failure rate at time t between the mth and m+1th maintenance activities, where m = 1, 2, 3, etc.; λ0: initial failure rate (determined by historical data and statistical methods); γ: failure rate growth rate (reflecting the inherent aging characteristics of the equipment); t: time; ω: maintenance effectiveness parameter; t m : The time after the mth maintenance is performed, m = 1, 2, 3, ...

[0140] The exponential distribution dynamic aging model describes the exponential growth of failure rate over time within a maintenance cycle, where γ reflects the inherent aging rate of the equipment and ω quantifies the inhibitory effect of maintenance on aging. For example, if ω = 0.8 after a maintenance, the aging time will only accumulate to 20% of the actual time (i.e., t-0.8t m ), indicating that maintenance effectively delayed aging.

[0141] Specifically, the calculation process of the instantaneous failure rate at different time points is as follows:

[0142] Step 1: Determine the maintenance cycle division.

[0143] Taking the equipment life cycle timeline as an example, the maintenance time sequence is {t0=0,t1,t2,……t m}, where: t0 = 0: the time when the equipment is put into use (before the first maintenance); t m =t m-1 +N m-1 : The mth maintenance time, which is N in the previous cycle m-1 Decide.

[0144] Step 2: Calculate the time point t within the target period.

[0145] Assume that the maintenance period (t∈[t m ,t m+1 ))'s failure rate:

[0146] Let τ = tt m (The time elapsed within the period, 0≤τ <N m+1 ), the formula can be simplified to:

[0147]

[0148] (8) In the formula, The initial failure rate of the cycle is denoted as λ m,start , which represents the failure rate immediately after maintenance.

[0149] Step 3: Substitute the parameters to calculate the instantaneous failure rate.

[0150] Before the first maintenance (m=0, no maintenance):

[0151] ω=0 (no maintenance intervention before the first maintenance by default), the formula is:

[0152] λ1(τ)=λ0·e γτ (τ=t,0≤t <t1);

[0153] After the mth maintenance:

[0154] Obtain t based on maintenance records m and ω, calculate the failure rate at any time τ within the period (e.g. τ = 10 hours, τ = N m+1 / 2, etc.).

[0155] A specific example (instantaneous failure rate within two maintenance cycles) is as follows:

[0156] Scenario setting: The first maintenance of the equipment is completed at t1 = 100 hours, and the maintenance effectiveness ω1 = 0.7; the second maintenance cycle N2 = 150 hours, that is, t2 = t1 + N2 = 250 hours.

[0157] Model parameters: λ0 = 0.001 times / hour, γ = 0.0005 hours -1 .

[0158] Before the first maintenance (m=0, 0≤t<100 hours):

[0159] λ1(t)=0.001·e 0.0005t .

[0160] t = 50 hours: λ1(50) = 0.001·e 0.025 ≈0.001025 times / hour.

[0161] t = 100 hours (immediately before maintenance): λ1(100) = 0.001·e 0.05 ≈0.001051 times / hour.

[0162] After the first maintenance (m = 1, 100 ≤ t < 250 hours, τ = t – 100):

[0163] λ2(τ)=0.001·e 0.0005×100(1―0.7) ·e 0.0005τ =0.001·e 0.015 ·e 0.0005τ ≈0.001015·e 0.0005τ .

[0164] Immediately after maintenance (τ = 0): λ2(0) = 0.001015 times / hour (because ω = 0.7, the failure rate is lower than 0.001051 before maintenance, reflecting the maintenance effect);

[0165] Midpoint of the cycle (τ = 75 hours): λ2(75) = 0.001015·e 0.0375 ≈0.001054 times / hour.

[0166] Calculation of average aging failure rate:

[0167] Instantaneous failure rate λ m+1 (t): reflects the failure risk at a specific moment and is used for real-time risk assessment (such as predicting the failure probability of equipment at the future time t0).

[0168] Average aging failure rate

[0169]

[0170] As can be seen from Equation (9), the average aging failure rate is the integral average of the instantaneous failure rate within a period, which is mainly used for maintenance period optimization (such as calculating the ratio R) and cost models. The specific integral derivation process is as follows:

[0171] Integrate Equation (7) over the period N = t m+1 -t m to find the average:

[0172]

[0173] As can be seen from Equation (9), the average aging failure rate is the weighted average of the instantaneous failure rate within a period, and its core depends on the exponential growth characteristic of the instantaneous failure rate.

[0174] Step S4**00**: According to the average aging failure rate, adjust the maintenance period, calculate the corresponding average aging failure rate ratio, and determine the target maintenance period. [[ID=1**8]]

[0175] In some embodiments, according to the average aging failure rate, adjusting the maintenance period, calculating the corresponding average aging failure rate ratio, and determining the target maintenance period includes: determining the average aging failure rate of the new period and the average aging efficiency of the original period according to the average aging failure rate; determining the average aging failure rate ratio according to the average aging failure rate of the new period and the average aging efficiency of the original period; determining the objective function; determining the safety constraint conditions and reliability constraint conditions; obtaining the input data; establishing a period-cost association model; determining the screening constraint conditions; calculating according to the objective function, safety constraint conditions, reliability constraint conditions, input data, period-cost association model, and screening constraint conditions to obtain the target maintenance period.

[0176] In the embodiments of the present invention, the average aging failure rate ratio is the ratio of the average aging failure rates of the new period and the original (old) period, denoted by R, and specifically:

[0177]

[0178] In Equation (10), λ′ m+1 is the average aging failure rate within the new maintenance period, that is, the maintenance period is adjusted from N to kN (k is a positive multiple parameter (k = 1 means the period remains unchanged, k > 1 means the period is extended, 0 < k < 1 means the period is shortened)). As can be seen from Equation (10), the ratio R is only related to N (the original maintenance period), k (the period adjustment multiple), and γ (the failure rate growth rate). By calculating the ratio R, the impact of the new period on the average aging failure rate of the equipment can be quantitatively evaluated.

[0179] Among them, the impact evaluation logic based on the ratio R is as follows:

[0180] (1)R < 1: The average failure rate in the new cycle decreases; that is, the average aging rate of the equipment in the new cycle is lower than that in the original cycle, which may mean that: If k > 1 (lengthen the cycle): When the maintenance interval is extended, the average failure rate is still lower than that in the original cycle, indicating that the combination of the equipment aging characteristic (γ) and the cycle adjustment multiple (k) does not significantly exacerbate aging, and there may be room for optimization (such as reducing the maintenance frequency to save costs). If 0 < k < 1 (shorten the cycle): The average failure rate further decreases after shortening the cycle, but it is necessary to evaluate whether there is over-maintenance in combination with the maintenance cost (which may increase costs). Applicable scenarios: When the equipment reliability requirement is high and γ is small (slow aging), lengthening the cycle and R < 1 can reduce the maintenance frequency while ensuring reliability.

[0181] (2)R = 1: The average failure rate in the new cycle remains unchanged; that is, after adjusting the cycle, the average failure rate is the same as that in the original cycle, indicating that the aging effect in the new cycle is equivalent to that in the original cycle. It can be used as a reference for the critical state. At this time, it is necessary to make a further decision in combination with the maintenance cost (such as lengthening the cycle may reduce the number of maintenance times and lower the labor cost).

[0182] (3)R > 1: The average failure rate in the new cycle increases; that is, the average aging rate of the equipment in the new cycle is higher than that in the original cycle, and it is necessary to be vigilant that: If k > 1 (lengthen the cycle): Extending the interval leads to accelerated aging, which may increase the failure risk, and it is necessary to evaluate whether the reliability meets the requirements (such as strict R thresholds in nuclear energy and aerospace scenarios). If 0 < k < 1 (shorten the cycle): The failure rate increases after shortening the cycle, indicating that the model parameters may need to be corrected (such as γ or the fitting error of historical data), or there may be irrationality in the maintenance strategy (such as over-maintenance may damage the equipment). It should be noted that the larger R is, the more obvious the aging effect exacerbation is. It is necessary to prioritize reliability to avoid a sharp increase in the failure probability due to excessive pursuit of cost reduction.

[0183] Comprehensively evaluate in combination with the equipment characteristics and constraints:

[0184] (1) Influence of the failure rate growth rate γ:

[0185] High γ (equipment with rapid aging): Lengthening the cycle (k > 1) will cause R to rise rapidly (exponential growth characteristic). For example, when γN is large, e γkN [[ID=十七]]is much greater than k (e γN -1), and k needs to be strictly restricted (to avoid R exceeding the standard). Typical scenarios: Mechanical transmission components, equipment operating under high load.

[0186] Low γ (equipment with slow aging): Lengthening the cycle may make R close to or less than 1 (for example, when γN is small, e γkN ≈​​​​​When R is less than or equal to 1, a moderate extension of the cycle is permitted to reduce costs. Typical scenarios: electronic components and precision instruments that operate stably.

[0187] (2) Balancing maintenance costs and reliability: If R is slightly higher than 1 but the maintenance frequency is significantly reduced (k is large), the trade-off between maintenance cost savings and potential failure losses needs to be calculated (e.g., using a risk decision model). High-safety scenarios (e.g., nuclear power) require R ≤ 1 or a strict upper limit on R (e.g., R ≤ 1.1) to ensure that aging effects do not significantly increase the risk of failure.

[0188] (3) Dynamic adjustment and iterative optimization: After each maintenance, the model parameters (λ0, γ, ω) are updated through real-time data, R is recalculated, and the rationality of the latest cycle is evaluated, forming a "prediction-evaluation-adjustment" closed loop (such as the maintenance plan feedback mechanism mentioned in the technical solution).

[0189] Specific examples of impact assessment are as follows:

[0190] Scenario 1: The original cycle N = 100 hours, γ = 0.001 / hour, and the planned cycle is extended to k = 1.5 (N' = 150 hours). The calculated value is R ≈ 0.95 < 1, indicating that the average failure rate decreases after the cycle is extended, which can reduce maintenance frequency while maintaining reliability.

[0191] Scenario 2: The original cycle, N = 50 hours, γ = 0.01 / hour, is planned to be extended to k = 2 (N' = 100 hours). The calculated value is R ≈ 1.2 > 1, indicating that the extended cycle increases the average failure rate by 20%. It is necessary to assess whether this exceeds the equipment reliability threshold. If the risk is unacceptable, the original cycle should be maintained or shortened.

[0192] Therefore, the key to evaluating the impact of a new cycle using the ratio R is to compare R with 1 to determine whether the average failure rate is decreasing, unchanged, or increasing; to analyze trends by combining γ and k to identify the sensitivity of equipment aging characteristics to cycle adjustments; and to balance reliability and cost, selecting the optimal k within safety constraints to form a dynamically optimized maintenance strategy. The ultimate goal is to achieve "precision maintenance" through quantitative analysis, avoiding the blindness of fixed-cycle maintenance and achieving "precision maintenance." This means neither excessive maintenance that wastes resources nor insufficient maintenance that causes failures.

[0193] In the embodiment of the present invention, the target maintenance cycle is the optimal maintenance cycle determined by combining factors such as the equipment's operational safety, reliability requirements, and maintenance cost budget. The specific process is as follows:

[0194] First, determine the objective function, which is to minimize the total cost of full-cycle maintenance.

[0195] Total cost = regular maintenance cost + potential failure loss cost;

[0196] Among them, regular maintenance costs (fixed costs): labor, spare parts, downtime losses, etc. for each maintenance, recorded as C m (Yuan / time). Potential failure loss cost (related to failure rate): the loss caused by equipment failure during the maintenance cycle, and the average aging failure rate Positive correlation, denoted as where k f is the failure loss coefficient corresponding to unit failure rate (yuan / unit failure rate).

[0197] Second, safety and reliability constraints are determined.

[0198] Safety constraint: average failure rate of the new cycle in The maximum average failure rate threshold allowed for an industry or equipment (determined by safety standards, such as nuclear power equipment requirements Very low).

[0199]

[0200] Shown as:

[0201]

[0202] Next, determine the optimal maintenance cycle.

[0203] Step 1: Input Data:

[0204] Historical maintenance data (maintenance time t m , maintenance cost C m ), failure data (used to fit the initial failure rate λ0 and failure rate growth rate γ); maintenance effectiveness parameter ω (inversely inferred by the decline in failure rate after maintenance, such as ); Cost parameter: C m 、k f , safety threshold Reliability threshold [R].

[0205] Step 2: Establish a cycle-cost correlation model:

[0206] (1) The average aging failure rate is calculated (based on formula (9)):

[0207]

[0208] Due to t m is the historical maintenance time, which can be regarded as a constant when optimizing the current cycle (assuming that t m =0, that is

[0209] (2) Single-cycle total cost function:

[0210]

[0211] in is the maintenance cost per unit time (the longer the cycle, the lower the cost per unit time), is the failure loss cost per unit time (the longer the cycle, the higher the failure rate and the higher the loss cost).

[0212] Step 3: Introduce constraints to screen feasible solutions:

[0213] Security filtering: Exclude The period N.

[0214] Reliability filtering: exclude the period N that makes R(N) < [R], that is:

[0215]

[0216] Step 4: Solve the unconstrained optimization problem (find the extreme cost point):

[0217] Derivative the total cost function TC(N) and set the derivative to 0:

[0218]

[0219] Simplifying, we get:

[0220]

[0221] This equation is a transcendental equation and needs to be solved by numerical methods (such as Newton iteration method) to find the optimal maintenance cycle N. * .

[0222] Step 5: Modify the optimal solution based on the constraints:

[0223] If N obtained in step 4 * Satisfies the safety and reliability constraints, then it is a candidate solution; if N * Constraints not satisfied (e.g. ), then take the constraint boundary value (Right now The minimum period when ) is taken as the corrected solution.

[0224] Step 6: Multiple scheme comparison and dynamic optimization:

[0225] Discretization cycle candidate set: Generate candidate cycles N∈{N1,N2,…,N k}, calculate TC(N) for each cycle, R(N). Pareto optimality analysis: If multiple solutions satisfy the constraints, select the optimal solution for the cost-reliability balance (e.g., the point with the lowest cost and highest reliability). Iterative optimization: After each maintenance, update λ0, γ, and ω based on new data and recalculate the optimal maintenance cycle (forming a closed-loop feedback loop).

[0226] The following are some examples:

[0227] Assume: First maintenance cycle optimization (t m =0), ω = 0.8 (maintenance effectively inhibits aging), λ0 = 0.001 / hour, γ = 0.0005 / hour; maintenance cost C m = 10,000 yuan / time, failure loss coefficient k f =50,000 yuan per hour; safety threshold Reliability threshold [R] = 0.95.

[0228] Calculate the average failure rate and reliability:

[0229]

[0230] Build the total cost function:

[0231]

[0232] Take the derivative to find the extreme value:

[0233]

[0234] Simplified:

[0235]

[0236] Calculate N by numerical calculation * ≈45 hours, verification:

[0237] (Satisfy safety constraints);

[0238] R(45)=exp(-2(e 0.0225 ―1))≈0.952>[R]=0.95(satisfies reliability constraint);

[0239] Determine the optimal solution:

[0240] Finally, N=45 hours was selected as the optimal maintenance cycle, balancing cost and safety and reliability.

[0241] It should be noted that after each maintenance, the actual failure data and maintenance effects are recorded, and the model parameters are updated (for example, ω may change due to maintenance quality); when the equipment operating environment changes (such as load adjustment), the re-optimization process is triggered to ensure that the cycle always adapts to the current aging status of the equipment.

[0242] Step S500: Formulate a maintenance plan based on the target maintenance cycle and the actual working condition information of the equipment.

[0243] In some embodiments, formulating a maintenance plan based on a target maintenance cycle and actual equipment operating condition information includes: determining basic maintenance time nodes; determining maintenance content and resource allocation; and formulating a maintenance plan based on the basic maintenance time nodes, maintenance content and resource allocation, target maintenance cycle, average aging failure rate ratio, and actual equipment operating condition information. Determining maintenance content and resource allocation includes: determining a maintenance level based on the current aging state of the equipment; determining maintenance content based on the maintenance level; and allocating resources based on maintenance complexity, failure probability, and downtime.

[0244] Specifically, first determine the basic maintenance time nodes:

[0245] Initial cycle setting: If it is the first maintenance plan, set the initial cycle N0 based on historical data or industry standards, calculate the initial R0 and evaluate its rationality. If it is not the first maintenance, update the model parameters (λ0,γ,ω) according to the equipment status after the last maintenance and recalculate the optimal cycle N * .

[0246] Time node derivation: The time of the mth maintenance is t m =t m-1 +N * m-1 , where N * m-1 This is the maintenance cycle after optimization of the previous cycle.

[0247] Next, clarify the maintenance content and resource allocation:

[0248] Maintenance content customization: According to the current aging status of the equipment (through dynamic model λ m (t) calculation) to determine the maintenance level (such as preventive maintenance, predictive replacement of key components). For example: if R>1 and the failure rate increases significantly, improve component inspection accuracy or replace components prone to aging; if R<1 and there are significant cost savings, simplify routine inspection procedures.

[0249] Resource planning (allocation): Manpower: assign technicians according to the complexity of maintenance (e.g. nuclear power equipment requires certified engineers); Spare parts: reserve vulnerable parts in advance based on the probability of failure (e.g. through Calculate the probability of spare parts demand); Downtime: coordinate production planning and reduce maintenance time t m Schedule it during low-load periods to reduce downtime losses.

[0250] Second, embed security and reliability constraints:

[0251] Mandatory inspection items: When the reliability R is close to the safety threshold (such as R ≥ 0.95 but < 1), add the calibration task of the real-time condition monitoring sensor to the maintenance plan to ensure the accuracy of dynamic tracking of failure rate. Redundant design adaptation: For high reliability systems (such as dual redundant equipment in aerospace), if the optimal cycle N * This results in an increase in the aging difference between the main and standby components, and it is necessary to add cross-detection steps to balance the aging progress of the components.

[0252] Finally, generate the maintenance plan:

[0253] The maintenance plan shall include at least: equipment information, maintenance time, maintenance objectives, operation steps, resource list, risk plan, record feedback, etc., as shown in Table 3.

[0254] Table 3

[0255]

[0256] Step S600: Perform maintenance operations on the equipment based on the maintenance plan.

[0257] In the embodiment of the present invention, after the equipment is maintained according to the established maintenance plan, dynamic feedback and plan iteration are also performed. The details are as follows:

[0258] Data closed loop after maintenance:

[0259] Parameter update: After maintenance is completed, the initial failure rate λ of the equipment after maintenance is collected through sensors 维修后 , combined with the formula Inversely infer the actual value of ω (such as ), correct the model parameters.

[0260] Cycle re-optimization:

[0261] Before the next maintenance plan is generated, R and N are recalculated using the latest ω and failure data. * , forming a closed loop of "maintenance-data collection-model update-plan adjustment".

[0262] Abnormal scenario response:

[0263] Sudden failure event: If the device fails within the period (the actual failure time t f <N * ), immediately trigger the following actions: When the record is invalid t f and the failure rate λ(t f ), update γ (by Backtracking); shorten the next cycle N * 新 =k·N* (k<1, such as k=0.8), and add the root cause analysis task of failed components to the plan.

[0264] Maintenance effect attenuation: If ω continues to decrease after multiple maintenance attempts (e.g., from 0.8 to 0.6), it indicates that the maintenance measures have weakened their ability to inhibit aging, and the maintenance plan needs to be upgraded (e.g., replacing more durable spare parts or adjusting the maintenance process).

[0265] Among them, the entire process of equipment maintenance is as follows Figure 2 shown.

[0266] refer to Figure 3 The present invention also provides an equipment maintenance system based on an exponential distribution dynamic aging model. Figure 3 As shown, the equipment maintenance system based on the exponential distribution dynamic aging model includes:

[0267] A data acquisition unit 301 is used to acquire source data of a device;

[0268] The parameter calculation unit 302 is used to analyze and process the source data to determine the parameters of the exponential distribution dynamic aging model;

[0269] The failure rate calculation unit 303 is used to calculate the instantaneous failure rate and average aging failure rate of the device at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the device;

[0270] The target maintenance cycle determination unit 304 is configured to determine the target maintenance cycle by adjusting the maintenance cycle and calculating the corresponding average aging failure rate ratio according to the average aging failure rate;

[0271] A maintenance plan formulation unit 305 is used to formulate a maintenance plan based on a target maintenance cycle and actual operating condition information of the equipment;

[0272] The maintenance operation unit 306 is configured to perform maintenance operations on the equipment based on the maintenance plan.

[0273] The present invention can be connected to an existing computer maintenance management system, automatically importing the generated maintenance plan into the computer maintenance management system, linking the work order system, inventory management system (such as triggering spare parts procurement applications), and production scheduling system (coordinating downtime). During equipment operation, IoT sensors monitor failure rate-related parameters (such as vibration and temperature) in real time. If the deviation between the measured value and the model prediction value exceeds a threshold (such as ±15%), an automatic warning is issued and a suggestion is made to advance or postpone the maintenance plan, thus realizing monitoring linkage. At the same time, standardized documents can also be generated and output.

[0274] Specifically, the specific coordination operation process between the units in the equipment maintenance system based on the exponential distribution dynamic aging model can refer to the above-mentioned equipment maintenance method based on the exponential distribution dynamic aging model, which will not be repeated here.

[0275] Compared with traditional methods, the present invention has the advantages of reasonable prediction, cost reduction, improved reliability and dynamic adaptability, specifically: Reasonable prediction: By establishing an equipment failure prediction module based on the exponential distribution aging model, the failure probability of the equipment can be more reasonably predicted, providing a scientific quantitative basis for maintenance decisions, and reducing the blindness and uncertainty of traditional maintenance methods. Cost reduction: Scientific and reasonable maintenance plans are formulated to avoid the problems of over-maintenance and under-maintenance, effectively reduce the maintenance cost of the equipment, and improve the economic benefits of the enterprise. Improved reliability: Reasonably predict the potential failure hazards of the equipment, perform maintenance and repairs in advance, improve the reliability and operational stability of the equipment, and reduce the impact of sudden equipment failures on production. Dynamic adaptability: Combined with real-time data update models, adapt to the dynamic changes in equipment aging characteristics.

[0276] In addition, an electronic device of the present invention includes a memory and a processor; the memory is used to store a computer program; the processor is used to execute the computer program to implement an equipment maintenance method based on an exponential distribution dynamic aging model as described above. Specifically, according to an embodiment of the present invention, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed by an electronic device and, when executed, performs the above-mentioned functions defined in the method of the embodiment of the present invention. The electronic device in the present invention can be a terminal such as a notebook, a desktop, a tablet computer, a smart phone, or a server.

[0277] In addition, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned equipment maintenance methods based on an exponentially distributed dynamic aging model. Specifically, it should be noted that the storage medium of the present invention may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. Computer-readable storage media may be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. In the present invention, a computer-readable signal medium may include a data signal transmitted in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device. Program code embodied on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wires, optical cables, RF (radio frequency), or any suitable combination thereof.

[0278] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device.

[0279] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0280] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the components and steps of each example according to their functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0281] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0282] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the present invention and implement it accordingly. They are not intended to limit the scope of protection of the present invention. All equivalent variations and modifications within the scope of the claims of the present invention are intended to be covered by the claims of the present invention.

Claims

1. A device maintenance method based on an exponential distribution dynamic aging model, characterized in that: The following steps are involved: Get the source data of the device; Analyzing and processing the source data to determine parameters of an exponential distribution dynamic aging model; Calculate the instantaneous failure rate and average aging failure rate of the equipment at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the equipment; According to the average aging failure rate, the maintenance cycle is adjusted and the corresponding average aging failure rate ratio is calculated to determine the target maintenance cycle; Formulate a maintenance plan based on the target maintenance cycle and the actual operating condition information of the equipment; Perform maintenance operations on the equipment based on the maintenance plan.

2. The equipment maintenance method based on the exponential distribution dynamic aging model according to claim 1 is characterized in that: The analyzing and processing the source data to determine the parameters of the exponential distribution dynamic aging model includes: Obtain equipment failure event data, failure rate data, predicted failure rate before maintenance, and measured failure rate after maintenance; Performing calculations based on the failure event data to obtain an initial failure rate; Calculating based on the failure rate data and the initial failure rate to obtain a failure rate growth rate; Calculating based on the initial failure rate, the predicted failure rate before maintenance, and the measured failure rate after maintenance to obtain a maintenance effectiveness parameter; The initial failure rate, the failure rate growth rate, and the maintenance effectiveness parameter are parameters of the exponential distribution dynamic aging model.

3. The equipment maintenance method based on the exponential distribution dynamic aging model according to claim 1 is characterized in that: Calculating the instantaneous failure rate and average aging failure rate of the device at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the device includes: Determine the maintenance cycle division; Calculate the time points within the target period; Substituting the maintenance cycle division and the time points within the target cycle into the exponential distribution dynamic aging model for calculation to obtain the instantaneous failure rate at different time points; The average aging failure rate is obtained by integrating and averaging the instantaneous failure rates at different time points.

4. The equipment maintenance method based on the exponential distribution dynamic aging model according to claim 1 is characterized in that: The step of adjusting the maintenance cycle and calculating the corresponding average aging failure rate ratio based on the average aging failure rate, and determining the target maintenance cycle includes: Determine the average aging failure rate of the new cycle and the average aging efficiency of the original cycle according to the average aging failure rate; Determining an average aging failure rate ratio based on the average aging failure rate of the new cycle and the average aging efficiency of the original cycle; Determine the objective function; Determine safety constraints and reliability constraints; Get input data; Establish a cycle-cost correlation model; Determine screening constraints; The target maintenance cycle is obtained by performing calculations based on the objective function, the safety constraint, the reliability constraint, the input data, the cycle-cost association model, and the screening constraint.

5. The equipment maintenance method based on the exponential distribution dynamic aging model according to claim 1 is characterized in that: Formulating a maintenance plan based on the target maintenance cycle and actual operating condition information of the equipment includes: Determine the basic maintenance time nodes; Determine maintenance content and resource allocation; A maintenance plan is formulated based on the basic maintenance time nodes, the maintenance content and resource allocation, the target maintenance cycle, the average aging failure rate ratio, and the actual working condition information of the equipment.

6. The equipment maintenance method based on the exponential distribution dynamic aging model according to claim 1 is characterized in that: Determining maintenance content and resource allocation includes: Determine the maintenance level based on the current aging status of the equipment; determining maintenance content based on the maintenance level; Allocate resources based on maintenance complexity, failure probability, and downtime.

7. The equipment maintenance method based on the exponential distribution dynamic aging model according to any one of claims 1 to 6, characterized in that: The exponential distribution dynamic aging model is: λ m+1 (t): failure rate at time t between the mth and m+1th maintenance activities, m = 1, 2, 3, ...; λ0: initial failure rate (determined by historical data and statistical methods); γ: failure rate growth rate (reflecting the inherent aging characteristics of the equipment); t: time; ω: maintenance effectiveness parameter; t m : The time after the mth maintenance is performed, m = 1, 2, 3, ...

8. An equipment maintenance system based on an exponential distribution dynamic aging model, characterized in that: include: A data acquisition unit, used to acquire source data of the device; a parameter calculation unit, configured to analyze and process the source data to determine parameters of an exponential distribution dynamic aging model; a failure rate calculation unit, configured to calculate the instantaneous failure rate and the average aging failure rate of the device at different time points based on the parameters of the exponential distribution dynamic aging model and the maintenance record of the current operating status of the device; a target maintenance cycle determining unit, configured to determine a target maintenance cycle by adjusting the maintenance cycle and calculating a corresponding average aging failure rate ratio according to the average aging failure rate; A maintenance plan formulation unit, configured to formulate a maintenance plan based on the target maintenance cycle and actual operating condition information of the equipment; A maintenance operation unit is used to perform maintenance operations on the equipment based on the maintenance plan.

9. A storage medium, characterized in that: The storage medium stores a computer program, which is suitable for being loaded by a processor to execute the steps of the equipment maintenance method based on the exponential distribution dynamic aging model according to any one of claims 1 to 7.

10. An electronic device, characterized in that: The device comprises a memory and a processor, wherein a computer program is stored in the memory, and the processor executes the steps of the equipment maintenance method based on the exponential distribution dynamic aging model according to any one of claims 1 to 7 by calling the computer program stored in the memory.

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