Preventive maintenance decision model of electric vehicle charging pile based on mutation operator and life cycle optimization

This paper proposes a preventive maintenance decision model for electric vehicle charging stations based on mutation operators and lifecycle optimization to address the impact of potential faults on maintenance effectiveness. By introducing the particle swarm optimization algorithm with mutation operator, a comprehensive analysis of opportunity service age factor and safety failure probability factor was conducted to establish an indicator system for the operation status of charging piles, and a potential fault identification model was constructed. By optimizing the life cycle, the balance problem between optimal maintenance life and optimal opportunity maintenance life has been solved, thus completing preventive maintenance decisions. The experimental results show that the accuracy of this method in preventive maintenance decision‐making for electric vehicle charging piles can reach 98%, with an average preventive maintenance decision‐making time of 1.6 s for load piles. At the same time, the risk probability value and load loss value are effectively controlled. This study has good application prospects in improving the preventive maintenance effect of electric vehicle charging piles.


| INTRODUCTION
In recent years, electric vehicles have been gradually developed and widely used in many countries due to their advantages of cleanliness, environmental protection, and efficiency.Relevant supporting charging facilities are also becoming more and more important.It is necessary to build convenient charging infrastructure to improve the user charging experience. 1,2As the infrastructure for national development, the safety, reliability, and compatibility of electric vehicle charging facilities have been highly valued by the regulatory authorities, automobile enterprises, transportation departments, and other relevant units.At present, the planning, construction and operation, and maintenance of electric vehicle charging facilities still face many problems, for example, the operation and maintenance level of charging stations is relatively backward, the state assessment technology of charging piles is lagging behind, the failure rate of charging piles is high, there are many unqualified items in routine inspection, and some charging piles have safety hazards, and so on. 3These problems are difficult to meet the current management requirements for charging facilities, which will cause adverse social impact and even lead to accidents.
Cui et al. 4 takes into account the mileage, distribution of electric vehicles and passenger distribution factors that affect the location of charging stations.This method establishes an uncertain polynomial model to minimize the total service distance of the vehicle by simulating the optimized charging station location based on Anylogic.Reference 5 developed a distributed energy management system based on multiagent system for efficient charging of electric vehicles.The energy management system proposed by this method reduces the peak charging load and load change of electric vehicles by about 17% and 29% respectively, without moving and delaying the charging of electric vehicles.Adaikkappan and Sathiyamoorthy 6 proposes that a new charging method is designed after considering the constraints of charging time, charging efficiency, charging state, health state, charging voltage threshold, and so on.These methods or models can judge the fault of the charging pile or optimize the charging quality to a certain extent, but the operating state parameters of the charging pile are not much involved, and only include the fault detection of key components.The scope of fault detection investigated is not clear enough, and the accuracy of judgment is not high. 7Similarly, with the increase in the number of charging piles and the increasing complexity of charging facilities and systems, the above methods are also difficult to detect faults in batches.Therefore, more effective methods are needed to make preventive maintenance decisions for electric vehicle charging piles.Scholars have also studied the application of different types of particle swarm optimization algorithms for charging station detection.Particle swarm optimization is a heuristic optimization algorithm inspired by the behavior of social groups such as bird or fish schools.It continuously updates the velocity and position of particles by simulating the process of searching for the optimal solution in the solution space, to achieve the global optimization goal.The particle swarm optimization algorithm can be used to optimize parameter settings in preventive maintenance decisions, such as maintenance cycles, maintenance thresholds, and so on.By continuously adjusting parameters, particles can search for the optimal maintenance strategy in the solution space to improve maintenance effectiveness and cost-effectiveness.The particle swarm optimization algorithm can be used to construct a potential fault identification model for charging piles.By analyzing operational status indicators and historical fault data, the particle swarm optimization algorithm can find the optimal feature combination, establish an efficient and accurate fault identification model, and help identify potential faults in a timely manner and take corresponding maintenance measures. 8,9der the above research background, this paper proposes a preventive maintenance decision model of electric vehicle charging pile based on mutation operator and life cycle optimization.By establishing a preventive maintenance decision model for electric vehicle charging piles, potential faults can be identified in a timely manner and appropriate maintenance measures can be taken, thereby improving the reliability and service quality of the charging piles.This is of great significance for meeting the growing demand for electric vehicles, improving user experience, and promoting sustainable transportation development.

| CONFIRMATION OF ELECTRIC VEHICLE CHARGING PILE MAINTENANCE INDEX BASED ON PSO ALGORITHM
The traditional particle swarm optimization algorithm 9 is always set parameters in terms of particle search inertia, search range, search direction, and search speed.It is simple and easy to operate in an algorithm.However, in complex and changeable practical projects, a single constant parameter cannot perfectly solve the problem, often resulting in inconsistent tracking results with expectations.In this paper, the particle swarm optimization algorithm with mutation operator can change the inertia coefficient of particles, the range of particle search, the speed of particle search, etc. during the iteration process, thus improving the convergence speed and accuracy.

| Introduction of mutation operator
In the complex application of electric vehicle charging pile maintenance, to avoid the algorithm falling into a local optimal solution, this paper integrates the mutation operator into the traditional particle swarm optimization algorithm, and the mutation operation is as follows: where, x k id is particle; λ is the mutation operator 9 ; r is a random number of 0-1; L is the search range of the n particle in the iterative evolution process.
The mutation operator can make the search range of particles larger in the iterative evolution process, but it is not to make every particle perform mutation operation in each iteration.To improve the optimization ability of particles and better adapt to the complex nonlinear process of particle swarm search, this paper adopts the following mutation rate: where, p max and p min are the maximum variation rate and the minimum variation rate respectively; k is the number of iterations; N is the maximum iteration.With the increase of k, the variation rate decreases exponentially.

| Construction of electric vehicle charging pile operation status indicator system
Based on the obtained variation rate, the opportunity service age factor and safety failure probability factor are analyzed to build the operation status indicator system of electric vehicle charging pile.

| Analysis of impact factors
From the perspective of failure generation and development, the factors affecting the failure probability of electric vehicle charging piles can be divided into two categories: one is the cumulative factor of service life, including the aging (material fatigue aging and wear) brought by the increase of service life.Generally speaking, the aging process is long, and will not directly lead to the failure of electric vehicle charging piles; The other is the state inducing factors, such as insulation damage, partial discharge, 10 winding short circuit, and other defects.The severity can be characterized by the state evaluation results of the electric vehicle charging pile.During the service life of the electric vehicle charging pile, the cumulative factor of service life will gradually develop toward the state inducement factor (deterioration causes defects).However, before the defects are formed, the failure rate will also gradually increase with the process of cumulative damage.Once the defects are formed, the failure probability of the electric vehicle charging pile will show a step increase. 11,12Based on the above analysis, the opportunity service age factor and safety failure probability factor that affect the preventive maintenance decision of electric vehicle charging piles are analyzed respectively, laying the foundation for building the operation status indicator system of electric vehicle charging piles and clarifying the operation status of charging piles and corresponding maintenance strategies.
(1) Analysis of opportunity age factor Based on Weibull distribution and exponential function, combined with the aging factors, influencing factors, and safety faults of electric vehicle charging piles, a comprehensive analysis can be conducted on the life distribution and failure probability of charging piles.The aging process of electric vehicle charging piles is influenced by various factors, including material strength, fatigue life, environmental conditions, and so on.In the model, these aging factors should be comprehensively considered to more accurately describe the distribution and trend of the life of charging piles.In addition to aging factors, other factors that may affect the life and safety of charging piles need to be considered, such as usage frequency, maintenance quality, charging pile design, and so on.By comprehensively considering these factors, a more comprehensive model is established to more accurately evaluate the lifespan and safety failure probability of charging piles. 13In this paper, the Weibull benchmark failure rate function is used to express the relationship between the failure efficiency of electric vehicle charging piles and the cumulative change of service age: where, γ represents the distribution of life of electric vehicle charging piles, η represents the distribution of life of electric vehicle charging piles, and t represents the opportunity age factor.When γ < 1, the failure rate shows a downward trend; When γ = 1, the loss efficiency is constant; when γ > 1, the failure rate shows an upward trend.(2) Safety failure probability factor analysis Exponential function is used to describe the failure probability of electric vehicle charging piles.This method considers that when the state of electric vehicle charging piles deteriorates, the failure rate increases exponentially: where, K represents the proportional parameter, C represents the curvature parameter, and p z ( ) repre- sents the failure probability of the electric vehicle charging pile.

| Construction of electric vehicle charging pile operation status indicator system
In an N -dimensional search space, the original particle swarm optimization (PSO) can be expressed as a number of random particles, 14 which can be described as a particle swarm.The i-particle can be described as a N -dimensional vector: , , , ) , ⋯ i m = 1, 2, , , which represents the coordinate of the i-particle in the N -dimensional search space as x i , that is, the coordinates of all particles can be described as a potential solution in the search space.15,16 The fitness value of particles i is evaluated by the optimization function.The fitness value can be obtained by integrating x i into the objective function, and the advantages and disadvantages of x i can be evaluated by the size of the value.Each particle also has a certain speed.The size and direction of its flight can be evaluated by the speed value.The flight efficiency of the i-th particle can be expressed as , and each velocity vector appears randomly in a certain range in the first time.
Set the optimal coordinate obtained by the i particle search as , , ) , and the fitness value of this coordinate is expressed as P besti , that is, the optimal coordinate obtained by the particle swarm search so far is , , , ) , and the fitness value of this coordinate is g best .PSO uses the following formula to process particles: where, the acceleration factors c 1 and c 2 and the inertia weight w represent nonnegative constants, and v max represents the maximum flight speed of particles.To prevent the particle swarm optimization algorithm from falling into the local optimum, 17 the mutation operator is introduced to update the inertia weight w, that is, the w value is gradually reduced as the number of iterations increases.

(
) where, σ represents a positive coefficient to adjust the change efficiency of w, k max represents the threshold of the number of iterations, and w 0 represents the upper limit of w k ( ).According to the above analysis, combined with the analysis results of mutation operator, opportunity service age factor and safety failure probability factor, the operating status indicator system of electric vehicle charging pile is constructed.
Combined with the fault degree, maintenance experience, and expert analysis of the charging pile, the state classification strategy is given.Each indicator of the charging pile is standardized according to the threshold level of the operating state.According to the advantages and disadvantages of the operating parameters, it can be divided into four risk levels: health, normal, minor failure, and serious failure.The corresponding state set is S S S S S = { , , , } 1 2 3 4 , where S S S S , , , 1 2 3 4 corresponds to health, normal, minor fault and serious fault respectively.
Health S 1 means that all operating parameters of the charging pile are within a reasonable range, very close to the set value, stable operation without inspection, and the inspection cycle may be delayed for a long time; Normal S 2 indicates that the individual parameters of the charging pile operation state exceed the set value, but there is no trend of deterioration, and the inspection time can be delayed or the maintenance can be planned; Minor fault S 3 means that the operating parameters of the charging pile have reached the set value, and there are many faults and the trend of deterioration.It is in the state of waiting for maintenance, which requires further observation or arrangement for a maintenance; Serious fault S 4 means that the operating parameters of the charging pile have reached the set value, and some functions have failed or have serious faults, which can not work normally.Stop the machine immediately for inspection.The operation status and corresponding maintenance strategy of the charging pile are shown in Table 1 (Figure 1).

| POTENTIAL FAULT IDENTIFICATION OF ELECTRIC VEHICLE CHARGING PILE
The charging model of the DC charging pile is shown in Figure 2 below: On the left is the off board charger (i.e., DC charging station), and on the right is the electric vehicle, which are connected through vehicle plugs and sockets.We can clearly see that the charging model is mainly composed of three parts: "off board charger," "vehicle interface," and "electric vehicle." The failure of the charging pile may be caused by many factors, the most common of which is the external environment and operation and maintenance frequency.Therefore, this paper constructs a potential fault identification model of electric vehicle charging pile from the above two aspects.Preventive maintenance factors include the timeliness of the maintenance department, the hardware quality of the charging station, the timeliness of maintenance, and the duration of power outages in the charging area.To quantify how these factors affect the current operating status of charging stations or the likelihood of faults occurring, a potential fault identification model is constructed between the occurrence of electric vehicle charging station faults and the frequency of operation and maintenance, as follows: where, S o is the current operation status of the electric vehicle charging pile, S S S S S = { , , , } are the j preventive maintenance factors that affect the i charging pile, including the timeliness rate of the maintenance department D it , the hardware quality of the charging pile Z it , the timeliness rate of the maintenance W it , the duration of the power outage in the charging area C it , and ε i are the failure impact factors.Select the impact index of operation and maintenance frequency on the occurrence of faults as an indicator to evaluate the impact of operation and maintenance frequency on the occurrence of charging station faults.Through this index, the maintenance department can understand whether the current operating maintenance frequency is sufficient and whether adjustments are needed.Then the index is: where, Y index i can not only identify the failure caused by the operation and maintenance frequency, but also be used for the daily management and supervision of the charging pile by the maintenance department.
The impact of the external environment is mainly reflected in the impact of the weather on the failure of the charging pile.Its model is as follows: where, is the environmental factor j of the i-th charging pile, including wind direction χ 1 , wind force χ 2 , rain and snow χ 3 , temperature χ 4 , and so on.Based on the environmental factors in Equation (10), the environmental impact index is calculated to help identify potential failure risks of charging stations in the current working environment.It can be expressed as: In the formula, T index i can identify the potential fault of the charging pile under the current operating environment.
A potential fault identification model for electric vehicle charging stations was established by combining the Environmental Impact Index and the Preventive Maintenance Impact Index.Through this model, the impact of external environment and operation and maintenance frequency on the occurrence of charging station faults can be comprehensively considered, thereby more accurately identifying potential faults.This model is: The potential fault identification of electric vehicle charging pile can be realized through Equation (12).
PSO algorithm and fault identification flow is shown in Figure 3.

| PREVENTIVE MAINTENANCE DECISION MODEL UNDER LIFE CYCLE OPTIMIZATION
This paper considers the maintenance costs of the electric vehicle charging pile during its life cycle, including preventive maintenance costs, minor repair costs of unexpected failures, preventive replacement costs, and the cost of shutdown loss of the electric vehicle charging pile due to maintenance.Taking the minimum dynamic maintenance cost rate of the electric vehicle charging pile as the goal, and taking the effectiveness of the electric vehicle charging pile and the reliability of the electric vehicle charging pile as the constraint conditions, the nonperiodic preventive maintenance decision-making model is established, and the model solving steps and methods are given to obtain the optimal maintenance times.

| Establishment of preventive maintenance model
With the minimum dynamic maintenance cost as the optimization objective, the preventive maintenance decision-making model is established with the effectiveness of the electric vehicle charging pile and the reliability of the electric vehicle charging pile as the constraints: CAI ET AL.
| 2621 where, C m represents the total overhaul cost of the charging pile in its life cycle; T i represents the life cycle of the i charging pile 18 ; A represents the validity of the charging pile; C r represents the preventive replacement cost of the charging pile.

| Solve the service life of preventive maintenance
The service life of electric vehicle charging piles will be reduced after preventive maintenance, and the service age retrogression is related to the preventive maintenance times and preventive maintenance effect of electric vehicle charging piles.The effective service life before and after the first preventive maintenance is: The effective service life before and after the second preventive maintenance is: By analogy, the effective service life before and after the J preventive maintenance of the electric vehicle charging pile can be obtained as follows:

| Solve the service life of opportunity maintenance
Set τ 1 , τ 2 , τ 3 , and τ 4 as the troubleshooting time, preventive maintenance time, fixed detection period, and opportunity maintenance time of the electric vehicle charging pile; f a , f b , f c , and f d are the frequency of fault maintenance, preventive maintenance, incomplete maintenance and opportunity maintenance of electric vehicle charging piles.The simulation process is described below.
Step 1: Initialize the simulation and define the relevant data information of the electric vehicle charging pile included in the model, including: the opportunity service age factor of different electric vehicle charging piles, the safety failure probability factor, and the failure impact factor ε i , the fixed detection period τ 3 of the electric vehicle charging pile, and so on.
Step 2: Regenerate the random troubleshooting time τ 1 , preventive maintenance time τ 2 , and fixed detection period τ 3 of each electric vehicle charging pile.The reliability function is randomly sampled to obtain the random fault maintenance time; The preventive maintenance time is calculated according to the reliability function of the electric vehicle charging pile and the preset preventive maintenance threshold, and the fixed detection period is set according to the maintenance plan.
Step 3: Obtain the maintenance time of the electric vehicle charging pile and the corresponding maintenance electric vehicle charging pile.The maintenance time of electric vehicle charging pile is the minimum of random fault maintenance time, preventive maintenance time, and fixed detection period.
Step 4: Maintenance decision.In case of random failure of any electric vehicle charging pile in the electric vehicle charging pile, it is necessary to carry out postmaintenance and update the failure maintenance frequency f a ; When the reliability of any electric vehicle charging pile in the electric vehicle charging pile reaches the preventive maintenance threshold, take preventive maintenance and update the preventive maintenance frequency f b ; When a certain electric vehicle charging pile in the electric vehicle charging pile reaches the fixed detection period, the maintenance personnel shall obtain the operation information of the electric vehicle charging pile.If the real-time reliability of the electric vehicle charging pile is lower than the preset preventive maintenance threshold, the state of the electric vehicle charging pile is considered to be seriously degraded, and preventive replacement maintenance shall be taken, otherwise, incomplete maintenance shall be taken to improve the operation state of the electric vehicle charging pile; Finally, generate and update random troubleshooting time, preventive maintenance time and fixed detection period for each EV charging pile in the EV charging pile.
Step 5: Update the maintenance frequency and simulation running time of each electric vehicle charging pile in the electric vehicle charging pile.
Step 6: If the simulation time of the electric vehicle charging pile does not reach the operation cycle, return to step 2; Otherwise, output the maintenance frequency of each electric vehicle charging pile in the electric vehicle charging pile.

| Experimental objects and data processing
The experimental subjects are from DC charging piles of electric vehicles in a certain area.In this paper, the data of 626 cases of confirmed serious faults collected from the actual charging station and 174 cases of data observed after early warning and alarm on the online operation platform form a sample database of 800 cases.The data of 800 charging piles in the sample database are randomly divided and processed.640 charging piles are selected to form the training set, and the remaining 160 charging piles constitute the test set.Table 2 is the failure efficiency data of electric vehicle charging piles longitudinally calculated according to the service age information.Table 3 is the failure data based on the horizontal statistics of the status information, and the health status of the electric vehicle charging pile is shown in Table 1.
The preventive maintenance reliability threshold and fixed detection period of each electric vehicle charging pile are always provided in advance according to the maintenance plan and operation environment.The operation cycle of the electric vehicle charging pile is set to 30 years, and the maintenance frequency of various maintenance methods of each electric vehicle charging pile in each simulation process is recorded; The total number of simulations preset by the analysis and calculation is 1000.Each simulation of the electric vehicle charging pile generates a new random number.Clean and process the raw data to remove errors, omissions, or outliers to ensure data quality.During the simulation process, 1000 simulations were conducted and the maintenance frequency of each electric vehicle charging station during each simulation process was recorded, ensuring the accuracy and stability of the simulation results.Thus, the accuracy of the model data was ensured, and a model that can truly reflect the preventive maintenance situation of electric vehicle charging piles was established on this basis.

| Experimental results and discussion
(1) Evaluation accuracy analysis of different models To verify the effectiveness of this model, the preventive maintenance decision of the electric vehicle charging pile is evaluated through simulation experiments.Comparing the evaluation accuracy of the model in this paper, the model in Cui et al. 4 and the model in Adaikkappan and Sathiyamoorthy, 6 the experimental results are shown in Figure 4: It can be seen from the analysis of Figure 4 that there are certain differences in the evaluation accuracy of the three models for the preventive maintenance decision of the charging pile.When the maintenance frequency is 4, the accuracy of the model evaluation in this paper is about 96%, the accuracy of the model in Cui et al. 4 is about 87%, and the accuracy of the model in Adaikkappan and Sathiyamoorthy 6 is about 84%; When the maintenance frequency is 10, the accuracy of the model evaluation in this paper is about 98%, the accuracy of the model in Cui et al. 4 is about 91%, and the accuracy of the model in Adaikkappan and Sathiyamoorthy 6 is about 85%.Through the comparison of the evaluation accuracy data of the three models, it can be seen that the model in this paper has a better effect in the decision-making evaluation of the preventive maintenance of the charging pile, up to 98%, and has certain reliability.
(2) Analysis of decision-making efficiency of preventive maintenance of charging piles with different models To verify the application effect of this model in the preventive maintenance decision-making of charging piles, the decision-making efficiency of this model, the Cui et al. 4 model and the Adaikkappan and Sathiyamoorthy 6 model were compared in the experiment, and the decision-making time of each model was recorded.The experimental results are shown in Figure 5: It can be seen from the analysis of Figure 5 that with the change of maintenance frequency, the decision-making time of the three models will change accordingly.When the maintenance frequency is 3, the decision-making time of the model in this paper is about 1.5 s, that of the model in Cui et al. 4  It can be seen from Table 4 that the risk probability value in the model in this paper is slightly lower than that in the comparison model, but the difference between the risk values in the three models is relatively small, because the model in this paper considers the impact of the opportunity service age factor and the safety failure probability factor on its life cycle during the preventive maintenance operation of the electric vehicle charging pile.Figure 6 shows the comparison results of risk consequences of preventive maintenance decisions made by three models: The risk consequence of preventive maintenance decision of electric vehicle charging pile is actually the load loss value.During the implementation of the preventive maintenance operation of electric vehicle charging piles, by comparing the load loss of three models, it can be found that the load loss value of the preventive maintenance decision of electric vehicle charging piles made by the model in this paper is significantly smaller than that of the comparison model after considering the impact of the opportunity service age factor and the safety failure probability factor on its life cycle, all below 0.7 p.u.It can be seen that the model in this paper is more applicable to the actual situation of electric vehicle charging during the preventive maintenance of electric vehicle charging piles.

| CONCLUSION
Considering the actual situation of the operation of the electric vehicle charging pile, that is, with the increase of the operation time of the electric vehicle charging pile, the failure rate is higher and higher, and the maintenance frequency is higher and higher.At the same time, considering the dynamic characteristics of the preventive maintenance cost, that is, with the increase of the

Single order
Model in this paper/×10 −4 Cui et al. 4  maintenance times of the electric vehicle charging pile, the maintenance cost is also increasing.This paper studies and analyzes the preventive maintenance decision model of the electric vehicle charging pile based on the mutation operator and life cycle optimization, The decision-making model of preventive maintenance is established.However, the operation parameter data resources of the charging pile are limited, and cannot be further supplemented and improved according to the actual station operation scenario to obtain a more comprehensive and stable state evaluation or prediction.

F I U R E 4
Comparison of accuracy of preventive maintenance decision evaluation of charging piles in different models.F I G U R E 5 Comparison of time for preventive maintenance decision of charging piles in different models.T A B L E 4 Risk value comparison of charging pile operation.
Operation status of charging pile and corresponding maintenance strategy.
T A B L E 1 I G U R E 2Charging model of the DC charging pile.

Table 4 :
4s about 4.3 s, and that of the model in Adaikkappan and Sathiyamoorthy 6 is about 5.1 s; When the maintenance frequency is 7, the decisionmaking time of the model in this paper is about 1.6 s, that of the model in Cui et al.4is about 6.0 s, and that of the model in Adaikkappan and Sathiyamoorthy 6 is about 6.8 s.It can be seen from the comparison that the decision-making time of the model in this paper T A B L E 2 Statistical table of electric vehicle charging pile failure efficiency.Risk value comparison of charging pile operation Using Cui et al. 4 model and Adaikkappan and Sathiyamoorthy 6 model as experimental comparison methods, the risk results of charging pile operation after preventive maintenance operation using three models are shown in model/×10−4