Maintenance period optimization method for fire detector of nuclear power plant

Abstract

The invention relates to the technical field of maintenance cycle optimization of fire detectors, in particular to a maintenance cycle optimization method of a nuclear power plant fire detector. The method comprises the following steps: constructing a survival function of a detector, and defining emergency replacement cost based on the survival function and a conditional probability theory; converting the future maintenance cost to a current value based on the discount factor to define a preventive maintenance cost that takes into account the time value; constructing a comprehensive cost function model based on the emergency replacement cost, the preventive maintenance cost and predefined safety risk cost, false alarm cost and management cost; and based on the comprehensive cost function model, determining an optimal maintenance interval through a grid search method. According to the method, the optimal maintenance interval is searched by using the comprehensive cost function model and the grid search optimization method, and the optimal maintenance interval is determined by minimizing the annual average total cost through the grid search method, so that the optimal maintenance interval and the corresponding lowest annual average cost are calculated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of maintenance cycle optimization of fire detectors, and particularly relates to a maintenance cycle optimization method for fire detectors in a nuclear power plant. BACKGROUND

[0002] Safety is a basic requirement for the production and operation of a nuclear power plant. Fire not only causes casualties and property losses, but also causes environmental pollution and even nuclear leakage. Fire has become a disaster that seriously threatens the safety of a nuclear power plant. Therefore, accurately, reliably and timely detecting fire is an important condition for fully exerting the function of fire extinguishing measures, reducing the loss caused by fire, and protecting the safety of life and property. A fire detector, like a "sensory organ", continuously detects the initial signals of a fire in a protected area, and is used to monitor whether a fire occurs in the environment. Once a fire occurs, the characteristic physical quantities of the fire, such as smoke concentration, temperature, gas and radiation intensity, are converted into electrical signals, and the signals are sent to a fire control host and an alarm is given. A fire detector is also called a probe or a sensitive head, which is usually composed of four parts: a sensitive element, a circuit, a fixing component and a shell. It is the core component of a fire automatic alarm system and an indispensable part of a modern fire and automatic fire extinguishing system. Its working condition will directly affect the normal operation of the entire fire protection system.

[0003] Fire is one of the accidents with the highest safety risks in a nuclear power plant. According to the statistics of the M&M insurance consulting company in the United States, the loss caused by fire in a nuclear power plant accounts for 90% of the total loss. A nuclear power plant is equipped with multiple safety protection systems with various functions, and the safety protection systems are equipped with redundant devices. If a general safety accident occurs, the probability of causing a major nuclear safety accident is extremely low. In comparison, once a fire occurs, especially a large-area fire involving cables and power supply systems, the power plant is likely to lose all control over the unit state, and the safety protection system may also lose its function. In addition, due to the existence of a large amount of combustible materials (a large amount of oil, gas, cables, etc.) in a nuclear power plant, the risk of fire is high, and the loss caused by fire in a nuclear power plant accounts for a major part of the total property loss.

[0004] The related research results show that the environmental factors have a serious influence on the performance of the fire detector. In the production operation process, the fire detector is affected by the environmental factors, and inevitably appears the aging phenomenon under the action of different environmental stresses, causes the occurrence of false alarm, no alarm and other faults. The environmental factors of the nuclear power plant mainly include high temperature, low temperature, humidity, dryness, air pressure, dust, salt fog and the like. Among these factors, the influence of humidity and temperature is the most obvious. The humidity can accelerate the corrosion of the metal, changes the electrical characteristics of each medium, and causes the performance degradation of the equipment. And under the action of long-term heat radiation, the characteristics of the material are often changed due to the slow physical and chemical processes, and then affect the reliability of the electronic device. In addition, the heat radiation can dry the seal in the component, and let the moisture enter the electronic device, causing the performance degradation. SUMMARY

[0005] The purpose of the present application is to provide a maintenance cycle optimization method of the fire detector of the nuclear power plant, so as to solve the problems in the background art.

[0006] The present application provides a maintenance cycle optimization method of the fire detector of the nuclear power plant, which comprises:

[0007] Constructing a survival function of the detector, defining an emergency replacement cost based on the survival function and the conditional probability theory;

[0008] Converting the future maintenance cost into the current value based on the discount factor to define the preventive maintenance cost considering the time value;

[0009] Based on the emergency replacement cost, the preventive maintenance cost and the predefined safety risk cost, false alarm cost and management cost, constructing a comprehensive cost function model;

[0010] Based on the comprehensive cost function model, determining the optimal maintenance interval by the grid search method.

[0011] As a preferred embodiment, the mathematical expression of the comprehensive cost function model C total (τ) is:

[0012] C total (τ) = C fixed + C prev (τ) + C emerg (τ) + C safety (τ) + C false (τ) + C admin (τ)

[0013] Wherein, τ represents the maintenance interval, C safety (τ) represents the safety risk cost, C false (τ) represents the false alarm cost, and C admin (τ) represents the management cost.

[0014] As a preferred embodiment, the mathematical expression of the survival function is:

[0015]

[0016] where S(t) is the survival function, representing the probability that a detector is still alive at time t, d i At time t i The number of failed devices, n i At time t i The number of detectors at risk, T represents the failure time random variable of the detector.

[0017] As a preferred embodiment, the mathematical expression of the emergency replacement cost C emerg (τ) is:

[0018] C emerg (τ) = P emerg (τ) · C replace · U

[0019]

[0020] where P emerg (τ) is calculated by the conditional failure probability, C replace is the cost of a single detector, and U is a random variable subject to normal distribution.

[0021] As a preferred embodiment, the mathematical expression of the preventive maintenance cost is:

[0022]

[0023] where C maint represents the total cost of a single preventive maintenance activity, usually including labor cost, material cost, equipment downtime cost and management cost, r is the discount rate, t is the time point of each maintenance, represents the number of maintenances within the analysis period, and T is the analysis time range.

[0024] 6. The method of claim 3, wherein the mathematical expression of the safety risk cost C safety (τ) is:

[0025] C safety (τ) = τ · β safety · exp(ρ(τ)) · U

[0026] where ρ(τ) = 1 - S(τ) is the risk factor, β safetyAs a safety risk factor, the survival probability S(τ) is transformed into an exponentially increasing cost;

[0027] False alarm cost C false The mathematical expression for (τ) is:

[0028] C false (τ)=n·C alarm ·λ(τ)·U

[0029]

[0030] Among them, C alarm It is the cost of a single false alarm. The exponent α can capture the non-linear impact of equipment aging on the false alarm rate. α>1 indicates an increasing failure rate.

[0031] Management cost C admin The mathematical expression for (τ) is:

[0032] C admin_prev (τ)=n·C admin_base ·γ

[0033] C admin_emerg (τ)=P emerg ·C admin_base ·δ

[0034] C admin (τ)=C admin_prev (τ)+C admin_emerg (τ)

[0035] Among them, C admin_base γ represents the basic management cost per maintenance cycle, δ represents the complexity factor, and δ represents the additional management cost coefficient for emergency situations.

[0036] As a preferred embodiment, the step of determining the optimal maintenance interval using the grid search method includes:

[0037] Generate candidate intervals, uniformly generating 200 candidate τs over [30, 3×365] days:

[0038] τ∈{τ1,τ2,...,τ 200}

[0039] Calculate the average annual cost for each τ:

[0040] C annual (τ i for i = 1, 2, ..., 200

[0041] Choose the τ that minimizes cost:

[0042]

[0043] As a preferred embodiment, the optimal maintenance interval is determined by a grid search method under the constraint condition of the total annual cost cannot exceed the annual budget B annual and the minimum maintenance interval τ is found under the premise that the total annual cost cannot exceed the annual budget B

[0044] Compared with the prior art, the present application has the following beneficial effects: the present application uses a comprehensive cost function model and a grid search optimization method to find the optimal maintenance interval, and the optimal maintenance interval is determined by minimizing the annual total cost by a grid search method (GridSearch), and the optimal maintenance interval and the corresponding minimum annual cost can be calculated by the above method, so as to optimize the maintenance period of the fire detector of the nuclear power plant. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a graph of the relationship between the survival function and the cumulative risk function in the embodiment of the present application;

[0046] Figure 2 is a graph of the change of the discount factor with time in the embodiment of the present application;

[0047] Figure 3 is a simulation flowchart for processing the uncertainty of the model parameters by the Monte Carlo method in the embodiment of the present application;

[0048] Figure 4 is a survival curve of the air sampling detector in the embodiment of the present application;

[0049] Figure 5 is a survival curve of the air sampling detector and a recommended maintenance time point in the embodiment of the present application;

[0050] Figure 6 is a multi-dimensional optimization analysis graph of the maintenance interval in the embodiment of the present application;

[0051] Figure 7 is a key parameter sensitivity analysis result of the maintenance cost model in the embodiment of the present application;

[0052] Figure 8 is a comprehensive comparison and analysis graph of the traditional maintenance strategy and the optimized strategy in the embodiment of the present application. DETAILED DESCRIPTION

[0053] The present application will be further described below in conjunction with the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0054] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the drawings and embodiments.

[0055] The embodiment provides a maintenance cycle optimization method for a fire detector of a nuclear power plant. The maintenance interval is optimized based on a cost function model. The embodiment is based on survival analysis theory and reliability engineering principles, and a device maintenance decision model is constructed by comprehensively considering time value, uncertainty and multiple cost factors. Survival analysis algorithm is used to analyze each detector, and the failure probability of each detector is calculated. On the basis of the failure probability, the optimal maintenance interval is calculated by using the constraint condition of the average annual cost and reliability. In the optimal maintenance interval, the average annual cost is the lowest, and the reliability is 85.5%.

[0056] According to a non-parametric estimation method, the survival function of the device is defined as:

[0057]

[0058] Where S(t) is the survival function, indicating the probability of the detector still surviving at time t, d i At time t i The number of devices that have failed, n i At time t i The number of detectors at risk, T represents the failure time random variable of the detector. Based on the risk theory of Nelson and Aalen, the cumulative risk function and the survival function have the following relationship:

[0059] H(t) = -log(S(t)) (2)

[0060] The cumulative risk function represents the cumulative risk up to time t. The instantaneous risk rate h(t) represents the conditional failure rate of the detector at time t, which is defined as:

[0061]

[0062] This formula reflects the change of the failure risk of the detector over time, calculates the conditional failure probability in a certain time period, and is used to estimate the emergency replacement cost in the optimization model. Formulas (1)-(3) establish a mathematical bridge from observed data to risk assessment, and provide a probability theory basis for subsequent cost analysis. As Figure 1 The survival probability and the cumulative risk function change over time as shown in the curve.

[0063] The unconditional failure probability directly calculates the global probability of the device failing in the interval [t, t+Δt], without considering the current state of the device and ignoring the survival time of the device. This may overestimate the risk and cause the emergency cost to skyrocket when the failure rate increases. The embodiment uses the conditional failure probability to calculate the probability of the device failing in the interval [t, t+Δt] under the condition that the device has survived to time t.

[0064]

[0065] More realistic scenario, with the age of the device, the conditional failure probability will change dynamically, help to identify the time point of sudden increase in failure risk, so as to dynamically adjust the maintenance frequency. In the cost model, the probability directly determines the expected value of the emergency maintenance cost.

[0066] In addition, to avoid choosing a short-term cheap but long-term expensive strategy due to the neglect of the time value of money, this embodiment introduces a discount factor to handle the inter-period cost comparison:

[0067]

[0068] Where r is the discount rate, reflecting the time value of money and opportunity cost. The future cost is discounted to the current value, and the time value of money is considered, which improves the accuracy of long-term cost estimation. The discount factor changes over time as shown in Figure 2 , reflecting the change of the present value of future cash flow over time.

[0069] Further, the total cost objective function in this embodiment is a comprehensive cost function based on the life cycle cost theory (Fabrycky and Blanchard):

[0070] C total (τ)=C fixed +C prev (τ)+C emerg (τ)+C safety (τ)+C false (τ)+C admin (τ) (6)

[0071] Where τ is the maintenance interval, and each cost component is defined as follows:

[0072] To avoid overestimating long-term costs, future maintenance costs are converted to current values by a discount factor, and preventive maintenance costs considering time value are defined:

[0073]

[0074] The formula is based on the update theory (Ross), which regards maintenance activities as a periodic update process. Where C maint represents the total cost of a single preventive maintenance activity, usually including labor cost, material cost, equipment downtime cost and management cost, t is the time point of each maintenance, represents the number of maintenance within the analysis period, T is the analysis time range.

[0075] Based on the conditional probability theory, the emergency replacement cost is defined as:

[0076] C emerg (τ)=P emerg(τ) · C replace · U (8)

[0077] Where the emergency replacement probability is calculated by piecewise method:

[0078]

[0079] Where P emerg (τ) is calculated by conditional failure probability, which accurately calculates the failure risk in each maintenance period, avoiding the approximation error in traditional methods, C replace is the cost of a single detector, and U is a random variable following normal distribution. By directly associating the conditional failure probability with the cost, the financial impact of unpredictable events can be quantified. The disturbance factor is introduced to reflect the fluctuations of parameters in reality.

[0080] Based on the risk amplification effect theory in reliability engineering, the safety risk cost is modeled by exponential function:

[0081] C safety (τ) = τ · β safety · exp(ρ(τ)) · U (10)

[0082] Where ρ(τ) = 1 - S(τ) is the risk factor, and β safety is the safety risk factor. The exponential form reflects the nonlinear characteristics of safety risk, consistent with Heinrich's accident pyramid theory and modern risk theory Aven. The survival probability S(τ) is converted into an exponentially growing cost, reflecting the high risk cost brought by low reliability. And the quantification of safety cost meets the industry safety standards (such as NFPA72).

[0083] Based on the device aging theory, the false alarm cost is defined as the false alarm rate changing with time and following Weibull distribution:

[0084] C false (τ) = n · C alarm · λ(τ) · U (11)

[0085]

[0086] Where C alarm is the cost of a single false alarm. The index α captures the nonlinear impact of device aging on false alarm rate, more accurately reflecting the degradation of device performance over time and improving the accuracy of long-term maintenance cost estimation. The Weibull aging model is widely used in electronic device reliability analysis (Dodson), and the parameter α > 1 represents the increasing failure rate, consistent with the aging characteristics of electronic products.

[0087] To avoid underestimating the high costs of emergency management activities, and to quantify emergency costs to drive reliability improvements, clearly demonstrating the trade-off between "more prevention" and "less emergency response," management costs are typically divided into the management costs of preventative maintenance and the management costs of emergency repairs.

[0088] C admin_prev (τ)=n·C admin_base ·γ (13)

[0089] C admin_emerg (τ)=P emerg ·C admin_base ·δ (14)

[0090] C admin (τ)=C admin_prev (τ)+C admin_emerg (τ) (15)

[0091] Where C admin_base γ represents the basic management cost of a single maintenance operation, γ is the complexity factor reflecting the management difficulty of maintenance activities, and δ is the additional management cost coefficient for emergency situations.

[0092] For uncertainty modeling, this embodiment uses the Monte Carlo method to handle the uncertainty of model parameters. A random perturbation is applied to each key parameter (see Equation 16). The distribution characteristics of the average annual cost are calculated through 1000 independent samples, ultimately giving a 90% confidence interval (see Equation 17).

[0093]

[0094] Where, θ k σ is the baseline value of the k-th parameter, ∈ is a random disturbance term following a normal distribution. k The degree of uncertainty (standard deviation) of the parameters. By simulating the uncertainty of parameters in actual engineering, the problem of underestimating risk in deterministic models is effectively solved. This method is based on Bayesian statistical theory (Gelman et al.) and uncertainty quantification theory (Smith). The Monte Carlo simulation process is as follows: Figure 3 As shown, a cost model is constructed by randomly sampling model parameters using the Bayesian method. The model is simulated and iterated 1000 times to generate a probability distribution. The standard deviation and confidence interval are calculated based on the simulation results, and the simulation results support decision-making.

[0095] As for the optimization problem construction and optimization method, the embodiment uses a grid search method instead of a traditional optimization algorithm to find the optimal maintenance interval. The optimal maintenance interval is determined by minimizing the annual total cost through grid search. First, a set of candidate intervals (such as 30 days to 3 years, divided into 200 points) is generated and the annual cost corresponding to each interval is calculated, and then the interval with the lowest cost is selected as the optimal solution. This method avoids the problem that gradient descent and other optimization algorithms may fall into local optimum.

[0096] The optimization problem includes unconstrained optimization and constrained optimization. Constrained optimization is to find the minimum maintenance interval under the condition of a given annual budget. The basic optimization problem of unconstrained optimization can be expressed as:

[0097]

[0098] where τ * is the optimal maintenance interval, i.e. the maintenance interval that minimizes the total cost expectation.

[0099] The basic optimization problem of constrained optimization can be expressed as:

[0100]

[0101] where is the constraint condition, the annual total cost cannot exceed the annual budget B annual to find the minimum maintenance interval τ.

[0102] The grid search method is used to find the optimal maintenance interval. First, generate candidate intervals, uniformly generate 200 candidate τ in [30, 3x365] days:

[0103] τ∈{τ1,τ2,...,τ 200} (20)

[0104] Calculate the annual cost of each τ:

[0105] C annual (τ i )for i=1,2,...,200 (21)

[0106] Select the τ with the lowest cost:

[0107]

[0108] Further, through sensitivity analysis, the influence degree of emergency replacement cost, safety risk cost, preventive maintenance cost, discount rate and aging index on the optimal interval and total cost can be quantified, defined as:

[0109]

[0110] Where S θ The sensitivity index for parameter θ measures τ * The sensitivity to changes in θ, where θ is the cost coefficient. If S θ ≥1 indicates that τ * It is highly sensitive to θ and requires precise estimation of θ; if S θ ≈1, Explanation of τ * The model is insensitive to θ and is robust to this parameter.

[0111] Robustness testing assesses the probabilistic impact of random parameter fluctuations on results, calculates the failure probability of the optimal solution in a real environment, and verifies whether theoretical assumptions lead to overly optimistic predictions. It is defined as follows:

[0112]

[0113] Where CV is the coefficient of variation, which measures C total The relative volatility, This represents the average annual cost. A smaller CV indicates a higher cost per unit area (C). total The lower the volatility, the stronger the model stability.

[0114] To illustrate with a specific embodiment, this embodiment uses a survival analysis algorithm to calculate the failure probability of the air sampling detector and marks recommended maintenance at 10%, 25%, and 80% of its average lifespan. The figure below shows a visualization of the survival curve and the times for recommended maintenance marked on the curve. Figure 4 and Figure 5 As shown.

[0115] Table 1 details the critical fault replacement probability time points and the recommended actions.

[0116] Table 1 Recommendations for Equipment Maintenance Plan

[0117]

[0118] This will significantly increase the risk of equipment failure. While all other factors showed numerical differences, none reached statistical significance.

[0119] The optimal maintenance interval is found using a cost model and grid search optimization method, with the optimal interval determined by minimizing the average annual total cost through grid search. This method calculates the optimal maintenance interval and its corresponding minimum average annual cost. The relationship between average annual cost and maintenance interval, the proportion of each cost component at the optimal maintenance interval, the reliability-cost trade-off, and the probability distribution of cost estimates are also visualized. Figure 6 As shown.

[0120] Subplot (a) shows a U-shaped cost curve, with the lowest annual cost of 378.86 yuan at 613 days, verifying the trade-off between preventative maintenance and risk costs: preventative costs dominate when the interval is less than 613 days, while risk costs increase exponentially when the interval is greater than 613 days. The light blue area represents the 90% confidence interval, reflecting the model's sensitivity to aging rates. Subplot (b) shows that fixed costs account for the largest proportion (35.2%) in the optimal strategy, while emergency replacement accounts for only 11.2%. Subplot (c) indicates that the optimal solution is located at the Pareto front with a reliability of 85.5%, and increasing reliability will lead to a sharp increase in marginal cost of 23% / 0.01 unit. Subplot (d) shows an average annual cost of 379.65 yuan, with a deviation of less than 0.2% from the theoretical value, and the right-skewed distribution suggests a need for a 6% budget buffer. Table 2 further illustrates the cost uncertainty under the optimal interval.

[0121] Table 2 Uncertainty Analysis

[0122]

[0123] The constrained budget approach aims to find the optimal maintenance interval that meets the budget given the average annual cost. This is illustrated in Table 3.

[0124] Table 3 Budget Constraint Analysis

[0125]

[0126] Sensitivity analysis was used to examine the relationship between emergency replacement costs, safety risk costs, preventative maintenance costs, discount rates, and aging indices, and the optimal maintenance interval and minimum annual cost. This analysis assessed the impact of systematically changing individual parameter values ​​on the optimal maintenance interval (left subplot) and the minimum annual cost (right subplot). Figure 7 The results show that emergency replacement costs have a small impact on the optimal maintenance interval, but linearly increase the total cost, requiring close control. The safety risk cost coefficient is strongly negatively correlated with the maintenance interval and significantly increases the total cost, making it a key factor in strategy formulation. Increased preventative maintenance costs extend the maintenance interval, with a moderate increase in total cost, reflecting a cost-frequency tradeoff. The discount rate has a limited impact on the maintenance interval but significantly reduces the total cost, consistent with the present value theory. The equipment aging index has a small impact on the interval but moderately increases the total cost. Sensitivity analysis results indicate that the safety risk cost coefficient is the most sensitive parameter affecting maintenance strategy, followed by emergency replacement costs and preventative maintenance costs. These findings provide important guidance for parameter optimization and risk management in practical applications, suggesting that the accuracy of safety risk assessment should be a key focus when formulating maintenance strategies, and that an effective emergency response mechanism should be established to control related costs.

[0127] The annual average cost under the optimal maintenance interval is compared with the annual average cost under the traditional maintenance. The traditional maintenance standards include manufacturer recommendations (ISO 14224), regulatory requirements (NFPA 72), industry standards (IEEE 493), insurance requirements (FM Global), empirical rules - monthly inspection, empirical rules - bi-monthly inspection, minimum legal requirements, and critical equipment standards. The cost comparison between the traditional strategy and the optimized strategy, the cost savings relative to the traditional strategy, and the relationship between each maintenance strategy and the cost can be visualized. As shown in FIG. 1. Figure 8

[0128] Figure 8 The performance of the optimized maintenance strategy is compared with the traditional method. Subplot (a) shows that the annual average cost of the optimized strategy is about 400 yuan, which is significantly lower than that of the traditional strategy, among which the insurance requirement strategy has the highest cost. Subplot (b) shows that the optimized strategy can save 35%-85% of the cost, with the largest saving for the insurance requirement strategy. Subplot (c) shows that the red star of the optimized strategy achieves the best balance between high reliability and low cost. Subplot (d) indicates that 88% of the traditional strategies are only "considered", and 12% are "not recommended", highlighting the advantages of the data-driven method.

[0129] The comprehensive analysis shows that the maintenance strategy optimization method based on the cost model can achieve 35%-85% cost savings while ensuring the reliability of the equipment, providing a scientific basis and quantitative support for equipment maintenance decision-making. Table 4 shows the differences between the traditional maintenance strategy and the optimized strategy in more detail.

[0130] Table 4 Comparison and analysis of traditional strategy and optimized strategy

[0131]

[0132] The above only describes the preferred embodiments of the present application. It should be noted that for those skilled in the art, without departing from the technical principles of the present application, several improvements and modifications can be made, and these improvements and modifications should also be considered as the protection scope of the present application.​

Claims

1. A method for optimizing the maintenance cycle of fire alarm detectors in nuclear power plants, characterized in that, include: Construct a survival function for the detector, and define an emergency replacement cost based on the survival function and conditional probability theory; Preventive maintenance costs that take into account the time value are defined by converting future maintenance costs into present value based on a discount factor. Based on the aforementioned emergency replacement cost, preventive maintenance cost, and predefined safety risk cost, false alarm cost, and management cost, a comprehensive cost function model is constructed. Based on the comprehensive cost function model, the optimal maintenance interval is determined by the grid search method.

2. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 1, characterized in that, Comprehensive cost function model C total The mathematical expression for (τ) is: C total (τ)=C fixed +C prev (t)+C emerg (t)+C safety (t)+C false (t)+C admin (t) Where τ represents the maintenance interval, C safety (τ) represents the cost of security risks, C false (τ) represents the cost of false alarms, C admin (τ) represents management costs.

3. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 2, characterized in that, The mathematical expression for the survival function is: Where S(t) is the survival function, representing the probability that the detector is still alive at time t, and d i At time t i The number of devices that failed, n i At time t i The number of detectors at risk, where T represents the random variable of detector failure time.

4. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 3, characterized in that, Emergency replacement cost C emerg The mathematical expression for (τ) is: C emerg (τ)=P emerg (t)·C replace ·U Among them, P emerg (τ) is obtained through the conditional failure probability calculation, C replace is the cost of a single detector, and U is a random variable that follows a normal distribution.

5. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 2, characterized in that, The mathematical expression for the cost of preventative maintenance is: Among them, C maint This represents the total cost of a single preventative maintenance activity, typically including labor costs, material costs, equipment downtime costs, and administrative costs. r is the discount rate, and t is the time point in time when each maintenance occurs. This indicates the number of maintenance operations during the analysis period, where T is the analysis time range.

6. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 4, characterized in that, Safety risk cost C safety The mathematical expression for (τ) is: C safety (t)=t·b safety ·exp(ρ(τ))·U Where ρ(τ)=1-S(τ) is the risk factor, β safety As a safety risk factor, the survival probability S(τ) is transformed into an exponentially increasing cost; False alarm cost C false The mathematical expression for (τ) is: C false (τ)=n·C alarm ·λ(τ)·U Among them, C alarm It is the cost of a single false alarm. The exponent α can capture the non-linear impact of equipment aging on the false alarm rate. α>1 indicates an increasing failure rate. Management cost C admin The mathematical expression for (τ) is: C admin_prev (τ)=n·C admin_base ·c C admin_emerg (τ)=P emerg ·C admin_base ·d C admin (τ)=C admin_prev (t)+C admin_emerg (t) Among them, C admin_base γ represents the basic management cost per maintenance cycle, δ represents the complexity factor, and δ represents the additional management cost coefficient for emergency situations.

7. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 1, characterized in that, The steps for determining the optimal maintenance interval using the grid search method include: Generate candidate intervals, uniformly generating 200 candidate τs over [30, 3×365] days: τ∈{τ1,τ2,...,τ 200 } Calculate the average annual cost for each τ: C annual (τ i )for i=1,2,...,200 Choose the τ that minimizes cost:

8. The method for optimizing the maintenance cycle of a nuclear power plant fire alarm detector according to claim 7, characterized in that, The optimal maintenance interval is determined using a grid search method. Under the constraint that the total annual cost cannot exceed the annual budget B. annual Find the minimum maintenance interval τ under the premise of...

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