A submarine cable state maintenance decision optimization method introducing submarine cable maintenance cost

Abstract

The application discloses a kind of submarine cable state maintenance decision optimization methods of introducing submarine cable maintenance cost, comprising: constructing submarine cable comprehensive health index model: establish submarine cable static health index model, establish submarine cable implementation health index model, obtain the comprehensive health index model of submarine cable by fusing two kinds of health index calculation model, obtain the comprehensive health index of submarine cable;Submarine cable maintenance cost model is constructed: Markov decision model and cost model are established, model is fused, submarine cable maintenance decision optimization model is constructed, submarine cable long-term operation time average unit time cost, combined with formula K Bellman equation of state value function is constructed;The strategy iteration method is used to solve maintenance decision optimization problem, the value function under current strategy is obtained by iteration Bellman equation, strategy is updated according to value function, value function is calculated based on the strategy after updating, the above process is recycled until the optimal objective function and strategy are obtained by strategy convergence.

Description

Technical Field

[0001] This invention relates to the field of submarine cable condition-based maintenance decision-making technology, and more specifically to an optimization method for submarine cable condition-based maintenance decision-making that incorporates submarine cable maintenance costs. Background Technology

[0002] Currently, electrical equipment is characterized by its wide variety, high cost, and significant impact after failure. Maintenance, as an indispensable and crucial component of electrical equipment operation, is a vital means of maintaining the normal operation of the power system, reducing power companies' maintenance costs while improving asset utilization. Submarine cables, situated in the complex marine environment, face difficulties in condition-based maintenance. For a long time, submarine cable maintenance relied on reactive methods, addressing fault conditions only after they occurred. Prolonged power outages during these operations often resulted in substantial economic losses. Thanks to the development of online condition monitoring technology, the real-time operating status of submarine cables can be acquired, providing favorable conditions for their inspection. Under these circumstances, it is essential to rationally utilize condition information, draw on condition-based maintenance models for terrestrial cables, and formulate a reasonable condition-based maintenance strategy for submarine cables.

[0003] However, most domestic and international research on electrical equipment maintenance decisions starts from the results of risk assessment and condition assessment, combined with economic objectives such as maintenance costs and power outage costs, and reliability objectives such as reliability, availability, and risk value, to analyze and determine maintenance recommendations. Currently, research on condition-based maintenance of electrical equipment has developed significantly, and certain models have been established, requiring practical analysis based on the specific characteristics of each piece of equipment. However, the maintenance strategies developed for condition-based maintenance of electrical equipment mentioned above are relatively one-sided, failing to achieve a comprehensive decision encompassing maintenance methods and timing. Furthermore, most condition-based maintenance strategies are based on the current state, without considering changes in the condition of electrical equipment during operation, potentially leading to under-maintenance and neglecting the economic efficiency of maintenance costs.

[0004] Therefore, it is necessary to provide an optimization method for submarine cable condition maintenance decision-making that incorporates submarine cable maintenance costs, so as to solve the problem that the existing submarine cable maintenance decision-making ignores the maintenance economy in the submarine cable maintenance process, which is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a submarine cable condition-based maintenance decision optimization method that incorporates submarine cable maintenance costs; constructs a comprehensive health index calculation model for submarine cables; constructs a submarine cable maintenance cost model with maintenance method and maintenance time as decision variables; constructs a submarine cable maintenance decision optimization model with long-term unit time maintenance cost as the objective function and replacement cost as the constraint; and obtains the condition-based maintenance scheme with the optimal submarine cable maintenance cost by solving the decision optimization model using the strategy iteration method.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An optimization method for submarine cable condition-based maintenance decision-making that incorporates submarine cable maintenance costs includes the following steps:

[0008] S1. Construct a comprehensive health index model for submarine cables: Establish a static health index model for submarine cables, establish an implementation health index model for submarine cables, integrate the two health index calculation models to obtain a comprehensive health index model for submarine cables, and calculate the comprehensive health index of submarine cables.

[0009] S2. Construct a cost model for submarine cable maintenance: Establish a Markov decision model and a cost model, integrate the two models, construct an optimization model for submarine cable maintenance decisions, calculate the average unit time cost of submarine cables under long-term operation, and construct the Bellman equation for the state value function using formula K.

[0010] S3. The maintenance decision optimization problem is solved by using the strategy iteration method. The value function under the current strategy is obtained by iterating the Bellman equation. Then, the strategy is updated according to the value function. The value function is calculated based on the updated strategy. The above process is repeated until the strategy converges and the optimal objective function and strategy are obtained.

[0011] Preferably, step S1 specifically includes:

[0012] S11. Based on the power transmission and transformation guidelines, corresponding evaluation standards are formulated for the state variables of power cables. State information is evaluated and scored, with the final score used as a health index. A correction factor is added to obtain the overall health index HI1 for periodic information of submarine cables.

[0013]

[0014] Among them, K Y The age-based correction factor is 0.95 for operations exceeding 25 years, and 1 otherwise; K F α is the family defect correction factor, set to 0.95 if there is a family defect, and 1 otherwise; i Weights for each component; HI 1i These are the health index values ​​for each component.

[0015] S12. Let the measured data of the submarine cable online monitoring be xi,k, where k = 1, 2, 3 correspond to the air section, J-type pipe section, and buried section, respectively. The health index expression obtained from the standardized processing of the submarine cable online monitoring data is given. The value of ω is related to the properties of each monitoring quantity. ω = -1, ω = 1, and ω = 0 correspond to the "smaller is better" type, the "larger is better" type, and the "intermediate" type, respectively.

[0016]

[0017] Where, x i,k The monitoring value of the i-th online monitoring status quantity of the submarine cable in the k-th segment; The maximum value of the online monitoring status variable i for section k of the submarine cable; Let i be the minimum value of the online monitoring status variable i for section k of the submarine cable; The optimal value of the online monitoring status variable i for section k of the submarine cable;

[0018] The health index of the lowest-scoring segment is taken as the quantification of health status for that monitoring quantity, i.e.:

[0019] h j =min[h i,k ],(j=0,1,2)

[0020] Based on multiple online monitoring status indicators, the expression for the time-varying health index of submarine cables based on online monitoring data is obtained:

[0021]

[0022] Where m is the number of online monitoring items for submarine cables, β j The weight of the monitored quantity j;

[0023] S13. Based on the overall health index HI1 and the time-varying health index HI2 of the submarine cable, the comprehensive health index of the submarine cable is obtained:

[0024] HI = ω1HI1 + ω2HI2

[0025] Among them, ω1 and ω2 represent the degree of influence of the two parts of the submarine cable on the overall operation status of the submarine cable.

[0026] Preferably, step S2 specifically includes:

[0027] S21. Construct the Markov model {S,A,{P},R,γ}:

[0028] S211. The state set S is a finite state set. According to the submarine cable health index, the state of the submarine cable is represented as "normal", "attention", "abnormal" and "serious". The state set can be denoted as S{1,2,3,4}. The higher the state value, the worse the state of the submarine cable.

[0029] S212. Action set A is the available decision space for state s (s∈S), representing the set of maintenance methods and maintenance times for all transition states when the submarine cable is in state s at a certain decision point, and maintenance method W(s) and maintenance time T(s) are adopted, i.e., action a (a∈A). When the submarine cable is in state s, it transitions to state s′ through a certain action a. The strategy π is the basis for generating action a, that is, the strategy π is the mapping π from state to action: s→a;

[0030] S213. The state transition probability P is the set of state transition probabilities of the system, representing the probability that when the submarine cable is in state s at a certain decision point and takes action a, ... This represents the set of probabilities that the submarine cable will be in state s′ at the next decision moment, i.e.:

[0031]

[0032] Among them, S t The current state of the submarine cable decision point; S t+1 This refers to the subsequent state of the submarine cable; A t This is the current action set for the submarine cable.

[0033] S214. The reward function R represents the real-value reward of the system in state s at a certain decision point, using maintenance method W(s) and maintenance time T(s), which is the maintenance cost generated by the maintenance action.

[0034] S215. The discount factor γ calculates the cumulative return, which is the degree to which the decision at the current moment is affected by the decision at the future moment. γ is a number between 0 and 1. The smaller the value, the smaller the degree of influence, and the more the decision-maker focuses on short-term interests. Conversely, the larger the value, the greater the degree of influence and the more the decision-maker focuses on long-term interests.

[0035] S22. Establish a cost model, including direct maintenance costs R. d (s,W(s)), testing cost R j Random fault repair cost R r (s,W(s)), natural deterioration maintenance cost In the formula: P s',k t represents the probability of a natural degradation fault occurring when the submarine cable transitions to state s'; W(s)The maintenance time required when using the W(s) maintenance method for submarine cables is considered. Therefore, a comprehensive maintenance cost R for submarine cables, integrating the maintenance method and maintenance time, is constructed. a (s,W(s),T(s)) is represented as

[0036] R A (s,W(s),T(s))=R d (s,W(s))+R j +R r (s,W(s))+R n (s,W(s),T(s));

[0037] S23. Define a state-value function, which represents the cumulative expected reward obtained by transitioning from state s to state s' using policy π, expressed in the form of expectation:

[0038] V π (s)=E π [R t+1 +γV π (s′)|S t =s]

[0039] Among them, V π (s) is the state-value function under policy π, s' is the next state, and R t+1 The reward for the next state;

[0040] Define an action-value function to represent the relationship between the state-value function of the current state and the state-value function of the next state:

[0041] Q π (s,a)=E π [Rt +1 +γQ π (S t+1 A t+1 )|S t =s,A t =a]

[0042] Among them, Q π (S,a) is the action value function under strategy π; A t A is the set of actions for the current state. t+1 The set of actions for the next state;

[0043] Use π * Let the optimal policy be represented by the state-value function and action-value function under this policy:

[0044]

[0045]

[0046] Among them, V * (s) is the optimal state value function; Q * (S,a) is the optimal action value function.

[0047] A state-value function in iterative form is constructed using the Bellman equation to create a decision-making model for submarine cable maintenance cost.

[0048]

[0049] For the maintenance decision-making problem of submarine cables, the stage from the k-th decision point to the (k+1)-th decision point is defined as the k-th stage, and the total cost of this stage is expressed as... The time of this stage is represented as t. k Therefore, the average unit time cost ρ of the submarine cable under long-term operation can be obtained through the averaging criterion. π for:

[0050]

[0051] Constraining long-term maintenance costs:

[0052] ρ π ×(T(s)+t W(s) ≤R g

[0053] Among them, R g Cost of replacing submarine cables;

[0054] Using maintenance methods and maintenance time as decision variables, and with the objective of minimizing the average total cost per unit time over the long-term operation of submarine cables, and with replacement cost as a constraint, a condition-based maintenance optimization model for submarine cables is constructed:

[0055]

[0056] The Bellman equation for the state-value function, constructed by combining the iterative form of the submarine cable maintenance cost decision-making model, is as follows:

[0057]

[0058] Preferably, step S3 specifically includes:

[0059] S31. Randomly select an initial strategy π0 from the set of maintenance strategies, and make the strategy satisfy:

[0060] π=π0

[0061] S32. If the unit time cost of the submarine cable under the initial strategy is 0, then the state value function of the submarine cable under this initial strategy is:

[0062]

[0063] Solve the system of linear equations consisting of the state-value functions under each state to obtain the long-run unit time cost ρ under the selected strategy. π The state value function Vi(s) corresponding to all states is calculated as follows:

[0064]

[0065] S33. For each state s of the submarine cable, calculate V using the corresponding maintenance strategy A(s). i The value of (s) is used to compare the new strategy π' with the strategy selected in step S32. When it meets the replacement cost and reliability constraints, the new strategy π' corresponding to all states of the submarine cable is obtained.

[0066] S34. Compare the new strategy π' with the original strategy π. If π' = π, then the original strategy π is the optimal strategy. If π' ≠ π, then let the new strategy π' be the original strategy. Start calculating from step S32 until the new strategy and the original strategy are equal. The iteration ends, and the state maintenance scheme with the optimal maintenance cost for submarine cables is obtained.

[0067] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a submarine cable condition maintenance decision optimization method that incorporates submarine cable maintenance costs; constructs a submarine cable comprehensive health index calculation model; constructs a submarine cable maintenance cost model with maintenance method and maintenance time as decision variables; constructs a submarine cable maintenance decision optimization model with long-term unit time maintenance cost as objective function and replacement cost as constraint condition; and obtains the condition maintenance scheme with optimal submarine cable maintenance cost by solving the decision optimization model using the strategy iteration method. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0069] Figure 1 The attached figure is a schematic diagram of the classification of bottom cable operating status information provided in an embodiment of the present invention.

[0070] Figure 2 The attached figure is a schematic diagram of the structure of the comprehensive health index calculation model for submarine cables provided in an embodiment of the present invention.

[0071] Figure 3The attached figure is a schematic diagram of the solution process of the strategy iteration algorithm provided in the embodiment of the present invention.

[0072] Figure 4 The attached figure is a schematic diagram comparing the long-term average maintenance cost with a fixed maintenance time, according to an embodiment of the present invention. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] This invention discloses an optimization method for submarine cable condition-based maintenance decisions that incorporates submarine cable maintenance costs, comprising the following steps:

[0075] S1. Construct a comprehensive health index model for submarine cables: Establish a static health index model for submarine cables, establish an implementation health index model for submarine cables, integrate the two health index calculation models to obtain a comprehensive health index model for submarine cables, and calculate the comprehensive health index of submarine cables.

[0076] S2. Construct a cost model for submarine cable maintenance: Establish a Markov decision model and a cost model, integrate the two models, construct an optimization model for submarine cable maintenance decisions, calculate the average unit time cost of submarine cables under long-term operation, and construct the Bellman equation for the state value function using formula K.

[0077] S3. The maintenance decision optimization problem is solved by using the strategy iteration method. The value function under the current strategy is obtained by iterating the Bellman equation. Then, the strategy is updated according to the value function. The value function is calculated based on the updated strategy. The above process is repeated until the strategy converges and the optimal objective function and strategy are obtained.

[0078] To further optimize the above technical solution, step S1 specifically includes:

[0079] S11. Based on the power transmission and transformation guidelines, corresponding evaluation standards are formulated for the state variables of power cables. State information is evaluated and scored, with the final score used as a health index. A correction factor is added to obtain the overall health index HI1 for periodic information of submarine cables.

[0080]

[0081] Among them, K Y The age-based correction factor is 0.95 for operations exceeding 25 years, and 1 otherwise; K Fα is the family defect correction factor, set to 0.95 if there is a family defect, and 1 otherwise; i Weights for each component; HI 1i These are the health index values ​​for each component.

[0082] S12. Let the measured data of the submarine cable online monitoring be xi,k, where k = 1, 2, 3 correspond to the air section, J-type pipe section, and buried section, respectively. The health index expression obtained from the standardized processing of the submarine cable online monitoring data is given. The value of ω is related to the properties of each monitoring quantity. ω = -1, ω = 1, and ω = 0 correspond to the "smaller is better" type, the "larger is better" type, and the "intermediate" type, respectively.

[0083]

[0084] Where, x i,k The monitoring value of the i-th online monitoring status quantity of the submarine cable in the k-th segment; The maximum value of the online monitoring status variable i for section k of the submarine cable; Let i be the minimum value of the online monitoring status variable i for section k of the submarine cable; The optimal value of the online monitoring status variable i for section k of the submarine cable;

[0085] The health index of the lowest-scoring segment is taken as the quantification of health status for that monitoring quantity, i.e.:

[0086] h j =min[h i,k ],(j=0,1,2)

[0087] Based on multiple online monitoring status indicators, the expression for the time-varying health index of submarine cables based on online monitoring data is obtained:

[0088]

[0089] Where m is the number of online monitoring items for submarine cables, β j The weight of the monitored quantity j;

[0090] S13. Based on the overall health index HI1 and the time-varying health index HI2 of the submarine cable, the comprehensive health index of the submarine cable is obtained:

[0091] HI = ω1HI1 + ω2HI2

[0092] Among them, ω1 and ω2 represent the degree of influence of the two parts of the submarine cable on the overall operation status of the submarine cable.

[0093] To further optimize the above technical solution, step S2 specifically includes:

[0094] S21. Construct the Markov model {S,A,{P},R,γ}:

[0095] S211. The state set S is a finite state set. According to the submarine cable health index, the state of the submarine cable is represented as "normal", "attention", "abnormal" and "serious". The state set can be denoted as S{1,2,3,4}. The higher the state value, the worse the state of the submarine cable.

[0096] S212. Action set A is the available decision space for state s (s∈S), representing the set of maintenance methods and maintenance times for all transition states when the submarine cable is in state s at a certain decision point, and maintenance method W(s) and maintenance time T(s) are adopted, i.e., action a (a∈A). When the submarine cable is in state s, it transitions to state s′ through a certain action a. The strategy π is the basis for generating action a, that is, the strategy π is the mapping π from state to action: s→a;

[0097] S213. The state transition probability P is the set of state transition probabilities of the system, representing the probability that when the submarine cable is in state s at a certain decision point and takes action a, ... This represents the set of probabilities that the submarine cable will be in state s′ at the next decision moment, i.e.:

[0098]

[0099] Among them, S t The current state of the submarine cable decision point; S t+1 This refers to the subsequent state of the submarine cable; A t This is the current action set for the submarine cable.

[0100] S214. The reward function R represents the real-value reward of the system in state s at a certain decision point, using maintenance method W(s) and maintenance time T(s), which is the maintenance cost generated by the maintenance action.

[0101] S215. The discount factor γ calculates the cumulative return, which is the degree to which the decision at the current moment is affected by the decision at the future moment. γ is a number between 0 and 1. The smaller the value, the smaller the degree of influence, and the more the decision-maker focuses on short-term interests. Conversely, the larger the value, the greater the degree of influence and the more the decision-maker focuses on long-term interests.

[0102] S22. Establish a cost model, including direct maintenance costs R. d (s,W(s)), testing cost R j Random fault repair cost R r (s,W(s)), natural deterioration maintenance cost In the formula: P s',kt represents the probability of a natural degradation fault occurring when the submarine cable transitions to state s'; W(s) The maintenance time required when using the W(s) maintenance method for submarine cables is considered. Therefore, a comprehensive maintenance cost R for submarine cables, integrating the maintenance method and maintenance time, is constructed. a (s,W(s),T(s)) is represented as

[0103] R A (s,W(s),T(s))=R d (s,W(s))+R j +R r (s,W(s))+R n (s,W(s),T(s));

[0104] S23. Define a state-value function, which represents the cumulative expected reward obtained by transitioning from state s to state s' using policy π, expressed in the form of expectation:

[0105] V π (s)=E π [R t+1 +γV π (s′)|S t =s]

[0106] Among them, V π (s) is the state-value function under policy π, s' is the next state, and R t+1 The reward for the next state;

[0107] Define an action-value function to represent the relationship between the state-value function of the current state and the state-value function of the next state:

[0108] Q π (s,a)=E π [R t+1 +γQ π (S t+1 A t+1 )|S t =s,A t =a]

[0109] Among them, Q π (S,a) is the action value function under strategy π; A t A is the set of actions for the current state. t+1 The set of actions for the next state;

[0110] Use π * Let the optimal policy be represented by the state-value function and action-value function under this policy:

[0111]

[0112]

[0113] Among them, V * (s) is the optimal state value function; Q * (S,a) is the optimal action value function.

[0114] A state-value function in iterative form is constructed using the Bellman equation to create a decision-making model for submarine cable maintenance cost.

[0115]

[0116] For the maintenance decision-making problem of submarine cables, the stage from the k-th decision point to the (k+1)-th decision point is defined as the k-th stage, and the total cost of this stage is expressed as... The time of this stage is represented as t. k Therefore, the average unit time cost ρ of the submarine cable under long-term operation can be obtained through the averaging criterion. π for:

[0117]

[0118] Constraining long-term maintenance costs:

[0119] ρ π ×(T(s)+t W(s) ≤R g

[0120] Among them, R g Cost of replacing submarine cables;

[0121] Using maintenance methods and maintenance time as decision variables, and with the objective of minimizing the average total cost per unit time over the long-term operation of submarine cables, and with replacement cost as a constraint, a condition-based maintenance optimization model for submarine cables is constructed:

[0122]

[0123] The Bellman equation for the state-value function, constructed by combining the iterative form of the submarine cable maintenance cost decision-making model, is as follows:

[0124]

[0125] To further optimize the above technical solution, step S3 specifically includes:

[0126] S31. Randomly select an initial strategy π0 from the set of maintenance strategies, and make the strategy satisfy:

[0127] π=π0

[0128] S32. If the unit time cost of the submarine cable under the initial strategy is 0, then the state value function of the submarine cable under this initial strategy is:

[0129] V π0 =0

[0130] Solve the system of linear equations consisting of the state-value functions under each state to obtain the long-run unit time cost ρ under the selected strategy. π The state value function Vi(s) corresponding to all states is calculated as follows:

[0131]

[0132] S33. For each state s of the submarine cable, calculate V using the corresponding maintenance strategy A(s). i The value of (s) is used to compare the new strategy π' with the strategy selected in step S32. When it meets the replacement cost and reliability constraints, the new strategy π' corresponding to all states of the submarine cable is obtained.

[0133] S34. Compare the new strategy π' with the original strategy π. If π' = π, then the original strategy π is the optimal strategy. If π' ≠ π, then let the new strategy π' be the original strategy. Start calculating from step S32 until the new strategy and the original strategy are equal. The iteration ends, and the state maintenance scheme with the optimal maintenance cost for submarine cables is obtained.

[0134] 1. Validation of the comprehensive health index calculation model for submarine cables:

[0135] Taking a 35kV cross-linked polyethylene submarine cable of an offshore platform as the research object, this study calculates the comprehensive health index of the submarine cable based on static data obtained from inspections and time-varying state information obtained from online monitoring, to verify the rationality and effectiveness of the health index calculation model. The submarine cable is 6.15km long, with a rated voltage of 35kV and a load current of 101A. The weights of various state variables of the submarine cable are quantitatively analyzed using the analytic hierarchy process (AHP), and the results are shown in the following three tables:

[0136] Table 1. Weighting of each health index on the condition of submarine cables.

[0137]

[0138] Table 2 shows the weighting results of each key parameter for periodic information.

[0139]

[0140] Table 3 shows the weighting results of each key parameter on online monitoring information.

[0141]

[0142] The health management of submarine cables adopts a differentiated inspection strategy, adjusting the inspection cycle as necessary based on changes in sections and time periods. Inspection results of the studied submarine cables since commissioning were collected, revealing the following defect status at a specific monitoring time: the submarine cable operated beyond its rated load for a short period (≤3 hours); infrared thermography of the cable sheath showed a phase-to-phase relative temperature difference greater than 4℃.

[0143] Furthermore, the submarine cable has been in operation for no more than 25 years, confirming no family history defects. Based on the calculation method of the static health index during regular inspections, the operating status of components was analyzed and points were deducted, as shown in Table 4.

[0144] Table 4. Evaluation Deduction Values ​​and Health Index Values ​​for Various Components of Submarine Cables

[0145]

[0146] The characteristic data of the submarine cable during normal operation were continuously collected and analyzed and calculated using the above-mentioned health index model. Taking the characteristic values ​​of each time-varying characteristic parameter in each section collected at the same monitoring time as the above-mentioned periodic health index as an example, the time-varying health index is shown in Table 5.

[0147] Table 5. Values ​​of Time-Varying Characteristic Parameters of Submarine Cables

[0148]

[0149]

[0150] Combining Tables 4 and 5, the overall health index (HI) of the submarine cable at this moment is 86.33. At this time, the submarine cable is in a "Caution" state. Analysis of the submarine cable's operation at this moment reveals that the cable is currently under heavy load, the monitored temperature value significantly exceeds the standard value calculated by IEC-60287, and the inspection revealed a short-term overload situation. The submarine cable itself is in a "Caution" state, resulting in an abnormal overall health status and a decline in its health level. Comparing the actual operating status of the submarine cable, the results are consistent with expectations, proving the effectiveness of the health status evaluation method. Furthermore, it comprehensively covers various status information of the submarine cable, fully considers the actual operating conditions of the submarine cable, and the analysis results are comprehensive.

[0151] 2. Validation of the submarine cable maintenance decision optimization model:

[0152] Taking a 35KV cross-linked polyethylene submarine cable as an example, the optimal strategy for the maintenance of this submarine cable is determined as follows:

[0153] 1) Data preparation

[0154] (1) Classification of health status

[0155] Based on the health index of submarine cables, the operating status of submarine cables is divided into four states: normal, warning, abnormal, and critical. The corresponding state space is S = {1, 2, 3, 4}.

[0156] (2) Maintenance measures and related costs

[0157] The cost of a 35kV submarine cable is generally between 600,000 and 1.5 million yuan per kilometer, while the time spent on different levels of maintenance varies from 8 hours to one week. Based on field survey data, the costs of various maintenance measures for submarine cables are analyzed and set. The direct maintenance cost of submarine cables is related to the maintenance method. For any two maintenance methods, if the degree of maintenance by one method is greater than that by the other, then the corresponding maintenance cost will be greater. Maintenance costs are directly proportional to the current condition of the equipment; the higher the degree of deterioration, the higher the maintenance cost. The setting of maintenance costs also needs to consider the labor costs of personnel and the cost of tools and materials. Table 6 calculates and sets the direct maintenance costs of submarine cables.

[0158] Table 6. Direct Repair Costs of Submarine Cables (RMB 10,000 / time)

[0159]

[0160] Let the cost of a single inspection of a submarine cable be: R j =50,000 yuan / time·km.

[0161] Table 7 Average maintenance time (h) for submarine cables

[0162]

[0163] The risk cost of submarine cables consists of the random failure costs during maintenance of sudden faults and the power outage costs during maintenance of natural deterioration faults. Sudden fault costs do not cause a change in the state, but are related to the current state of the submarine cable. The random fault maintenance costs are set in Table 8 compared with the direct maintenance costs.

[0164] Table 8. Cost of Random Faults in Submarine Cables (RMB 10,000 / fault)

[0165]

[0166] Calculating the repair cost of natural degradation faults requires analyzing and calculating the state transition probability during the natural degradation process of submarine cables. This is achieved through the formula for calculating the repair cost of natural degradation faults. and Table 3 in the accompanying drawingsThe cost of repairing submarine cables due to natural deterioration can be calculated. Taking the cost of repairing submarine cables to a "normal" state by means of maintenance as an example, the cost of repairing submarine cables due to natural deterioration is set at RMB 1,000 / h. The cost of repairing submarine cables due to natural deterioration under normal conditions is shown in Table 9.

[0167] Table 9. Cost of Natural Deterioration of Submarine Cables (RMB 10,000 / time)

[0168]

[0169] (3) Maintenance decision

[0170] In the context of submarine cable maintenance, the health status of submarine cables changes from poor to good. Therefore, considering the positive impact of maintenance on the health status of submarine cables, at the decision-making point, when the submarine cable is in "normal" state 1, no strategy is taken; when the submarine cable is in "attention" state 2, Class C, Class B, or Class A maintenance can be carried out; when the submarine cable is in "abnormal" state 3, Class B, Class A, or replacement can be carried out; when the submarine cable is in "serious" state 4, only Class A maintenance can be carried out. For submarine cables in different states, maintenance can be completed within the prescribed time limits for immediate, prompt, timely, and standard maintenance cycles.

[0171] 2) Calculation and solution process

[0172] The model is solved using a strategy iteration algorithm. First, an initial strategy is determined. To simplify the iteration process and reduce the number of iterations, strategies with higher returns under each state are selected as the initial strategy based on the composition of maintenance costs. Therefore, the initial strategies are set as shown in Table 10. When the submarine cable is in a "normal" state, no maintenance measures are taken. However, for calculation convenience, the maintenance method for normal state is set as "Class D maintenance," and it is carried out according to the baseline cycle. When the submarine cable is in a "severe" state, reflecting an extremely poor operating condition, Class A maintenance is adopted by default, involving partial or complete replacement of the cable.

[0173] Table 10 Initial Strategy Table

[0174]

[0175] Setting the unit time cost to 0 under the initial strategy, we then solve the four-dimensional equations, i.e., the system of linear equations under each state, to calculate the long-term unit time maintenance cost generated by the submarine cable maintenance strategy. Substituting the relevant data on submarine cable maintenance into the optimization model, we perform calculations using the strategy iteration method. The iterative process of the submarine cable maintenance decision-making is shown in Table 11.

[0176] Table 11 Iterative Decision-Making Process for Submarine Cable Maintenance

[0177]

[0178]

[0179] After five iterations of calculation, the optimal condition-based maintenance strategy was obtained. The results of the optimization calculation are shown in Table 12.

[0180] Table 12 Optimal Condition Maintenance Strategy

[0181]

[0182] Table 12 shows that when the submarine cable is in a "Caution" state, the recommended maintenance method is "Category C maintenance" and the recommended maintenance time is "timely implementation"; when the submarine cable is in an "Abnormal" state, the recommended maintenance method is "Category B maintenance" and the recommended maintenance time is "immediate implementation"; and when the submarine cable is in a "Severe" state, the recommended maintenance method is "Category A maintenance" and the recommended maintenance time is "immediate implementation". It can be seen that the decision results are consistent with the expectations. When the submarine cable is in a "Caution" state, it reflects a general defect that does not affect operation. Performing Category C maintenance once a year will not affect the reliability of the submarine cable and will not waste maintenance resources. However, when the submarine cable is in an "Abnormal" or "Severe" state, it reflects a health condition or a major defect. If the entire cable or its components are not immediately repaired, the probability of the submarine cable turning into a fault will increase. Therefore, using a Markov decision process to handle the submarine cable maintenance decision problem can yield a reasonable set of maintenance methods and maintenance times.

[0183] As can be seen from the iterative process of maintenance decision-making shown in Table 11, this method actually adjusts the maintenance time based on the determined maintenance method. Compared with the maintenance strategy in this paper, the maintenance strategy in the guidelines is usually fixed. Figure 1 Comparing the long-term average maintenance costs in this method with those in the guidelines, the long-term average maintenance cost under the optimal maintenance strategy is lower than that under fixed maintenance time. Therefore, the condition-based maintenance strategy presented in this paper is more economical. Furthermore, this method provides a more detailed breakdown of maintenance costs related to submarine cables, while the guidelines offer a broader description of costs and more generalized strategy results. In contrast, the method presented in this paper is more realistic, enabling the precise formulation of condition-based maintenance strategies for submarine cables and yielding richer and more specific results.

[0184] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0185] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of subsea cable condition maintenance decision optimization incorporating subsea cable maintenance costs, characterized by, The method comprises the following steps: S1, constructing a submarine cable comprehensive health index model: establishing a submarine cable static health index model, establishing a submarine cable implementation health index model, and fusing the two health index calculation models to obtain a submarine cable comprehensive health index model, and calculating the submarine cable comprehensive health index; S2, constructing a submarine cable maintenance cost model: establishing a Markov decision model and a cost model, fusing the two models, constructing a submarine cable maintenance decision optimization model, and constructing a state value function Bellman equation of the average unit time cost of the submarine cable under long-term operation time combined with formula K; S3, solving the maintenance decision optimization problem by using a policy iteration method, obtaining the value function under the current policy by iterating the Bellman equation, then updating the policy according to the value function, calculating the value function based on the updated policy, and repeating the above process until the optimal target function and policy are obtained through policy convergence; The step S2 specifically comprises: S21, constructing a Markov model {S, A, {P}, R, γ}: S211, the state set S is a finite state set, the state of the submarine cable is represented as "normal", "attention", "abnormal" and "serious" according to the submarine cable health index, and the state set can be recorded as S{1, 2, 3, 4}, and the higher the state value, the worse the submarine cable state; S212, the action set A is the available decision space of the state s (s∈S), which represents that when the submarine cable is in the state s at a certain decision point, the set of maintenance mode and maintenance time under all transition states is obtained by using the maintenance mode W(s) and the maintenance time T(s) of the action a (a∈A); when the submarine cable is in the state s, it is converted to the state s by a certain action a ′ The strategy π is the basis for generating the action a, that is, the strategy π is the mapping from the state to the action π:s→a. S213, the state transition probability P is a set of state transition probabilities of the system, indicating that when the submarine cable is in a state s at a certain decision point, an action a is taken, a probability set that indicates that at the next decision time, the submarine cable is in a state s ′ , that is: wherein S t is the state of the current decision point of the submarine cable; S t+1 is the successor state of the submarine cable; A t is the set of actions for the current state of the submarine cable; S214, the reward function R represents the real value reward of the system in a certain decision point, that is, the maintenance cost generated by the maintenance action, when the system is in the state s and adopts the maintenance mode W(s) and the maintenance time T(s); S215, the discount factor γ calculates the cumulative return, which is the degree of influence of the future decision on the current decision, and γ is a number between 0 and 1, the smaller the value, the smaller the degree of influence, and the decision maker pays more attention to short-term interests, and vice versa, the greater the degree of influence, and more attention is paid to long-term interests; S22, establish cost model, including direct repair cost R d (s, W(s)), test cost R j , random failure repair cost R r (s, W(s)), natural degradation repair cost In the formula: P s',k is the probability of natural degradation failure when the submarine cable state moves to s'; t W(s) is the repair time required when the submarine cable adopts W(s) repair mode, and the above is summarized to build a comprehensive repair cost R a (s, W(s), T(s)) represents R A (s, W(s), T(s)) = R d (s, W(s)) + R j + R r (s, W(s)) + R n (s, W(s), T(s)); S23, defining a state value function, which represents the cumulative expected return obtained by adopting the strategy π to transfer from the state s to the state s', and is represented in the form of expectation: V π (s) = E π [R t+1 +γV π (s′)|S t = s] where V π (s) is the state value function under policy π, s' is the next state, R t+1 is the reward for the next state; Defining an action value function represents the relationship between the state value function of the current state and the state value function of the next state: Qπ(s, a) = Eπ[Rt +1 + γQπ(St +1 , At +1 )|St= s, At= a] wherein Qπ(s, a) is the action value function under policy π; Atis the current state action set; At +1 is the action set for the next state. Using π* to represent the optimal strategy, the corresponding state value function and action value function under the strategy are represented as: Wherein, V*(s) is the optimal state value function; Q*(s, a) is the optimal action value function The state value function of the iterative form of the submarine cable maintenance decision cost decision model is constructed through the Bellman equation: For the maintenance decision problem of submarine cable, the stage between the kth decision point and the k+1th decision point is defined as the kth stage, and the total cost of the stage is represented as The time of the stage is represented as t k Then the average unit time cost ρ of the submarine cable under the long-term operation time is obtained by the average criterion π is: The long-term maintenance cost is constrained: ρπ×(T(s)+tW(s))≤Rg Wherein, Rg is the replacement cost of the submarine cable; Taking the maintenance mode and the maintenance time as decision variables, taking the minimum average unit time total cost of the submarine cable under long-term operation time as the target, and taking the replacement cost as the constraint condition, a state maintenance optimization model of the submarine cable is constructed: The Bellman equation of the state value function is constructed in combination with the state value function of the iterative form of the submarine cable maintenance decision cost decision model:

2. The method of claim 1, wherein, The step S1 specifically comprises: S11, based on the state quantity of power cable in the power transmission and transformation guide, the corresponding evaluation standard is formulated, the state information is evaluated and scored, and the final score is used as the health index. A correction factor is added to obtain the overall health index HI1 of the submarine cable periodic information Wherein, KY is the age correction factor, 0.95 for more than 25 years, otherwise 1; KF is the family defect correction factor, 0.95 for family defects, otherwise 1; ai is the weight of each component; HI 1i is the health index value of each component. S12, the measured data of the submarine cable online monitoring is recorded as xi,k, k=1, 2, 3, which respectively corresponds to the air section, J type pipe section and buried section. The health index expression obtained by standardizing the submarine cable online monitoring data is ω, the value of which is related to the properties of each monitoring quantity. ω=-1, ω=1, ω=0 respectively correspond to the smaller the better type, the larger the better type, and the intermediate optimal type wherein xi ,k is the monitoring value of the i-th on-line monitoring state quantity of the submarine cable at the k-th section; is the maximum value of the i-th on-line monitoring state quantity of the submarine cable at the k-th section; is the minimum value of the i-th on-line monitoring state quantity of the submarine cable at the k-th section; is the optimal value of the i-th on-line monitoring state quantity of the submarine cable at the k-th section; The health index of the section with the lowest score is the health state quantization result of the monitoring quantity, that is: hj=min[hi,k],(j=0,1,2) Based on multiple online monitoring state indicators, the expression of the time-varying health index of the submarine cable based on online monitoring data is obtained: Wherein, m is the number of online monitoring quantities of the submarine cable, and βj is the weight of the monitoring quantity j. S13, based on the overall health index HI1 of the submarine cable and the time-varying health index HI2 of the submarine cable, the comprehensive health index of the submarine cable is obtained: HI=ω1HI1+ω2HI2 Wherein, ω1, ω2 are the influence degree of the two parts of the submarine cable on the comprehensive operation state of the submarine cable.

3. The method of claim 1, wherein, The step S3 specifically comprises: S31, an initial strategy π0 is randomly selected from the maintenance strategy set, and the strategy satisfies: π＝π0 S32, let the unit time cost of the submarine cable under the initial strategy be 0, then the state value function of the submarine cable under the initial strategy is: Solving the linear equations of state value functions in each state to obtain the long-term unit time cost p under the selected strategy π and the state value function Vi(s) corresponding to all states, which is calculated as S33, for each state s of the submarine cable, the value of Vi(s) is calculated by the maintenance strategy A(s) corresponding to the state, and a new strategy π ‘ In comparison with the selected strategy in step S32, when it satisfies the replacement cost and reliability constraints, a new strategy π ‘ ; S34, compare new strategy π ‘ and the original strategy π, if π ‘ = π, then the original strategy π is the optimal strategy; if π ‘ ≠ π, then let the new strategy π ‘ The original strategy is calculated from step S32 until the new strategy and the original strategy are equal, the iteration ends, and the optimal state maintenance scheme of the submarine cable maintenance cost is obtained.

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