Urban rail transit intelligent operation and maintenance decision-making method considering cost optimization

Abstract

The invention discloses an urban rail transit intelligent operation and maintenance decision-making method considering cost optimization, and the method is characterized in that the method comprises the following steps: S1, constructing an urban rail transit equipment opportunity maintenance intelligent decision-making model based on a dynamic time window; s2, constructing an urban rail transit opportunity maintenance and human resource dynamic configuration joint decision model; and S3, constructing an urban rail transit two-stage imperfect opportunity maintenance and spare part inventory joint decision model. According to the method, the maintenance cost of the urban rail transit is predicted, reference is provided for an urban rail transit operation company to reasonably dispatch related maintenance resources and formulate related maintenance budget, the maintenance cost is effectively reduced, and then the whole-life-cycle operation cost of the urban rail transit is reduced; and the construction of green, low-carbon, energy-saving, environment-friendly, efficient and intelligent urban rail transit is facilitated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of urban rail transit intelligent operation and maintenance technology, and particularly relates to a method for urban rail transit intelligent operation and maintenance decision considering cost optimization. BACKGROUND

[0002] As the artery of urban traffic, the operation and maintenance cost of urban rail transit accounts for 10-20% of the total operation cost, of which the maintenance cost (including equipment downtime cost, human resource allocation cost, spare parts resource cost, etc.) is the main expenditure. The traditional maintenance strategy has the following technical bottlenecks: (1) rigid maintenance opportunity: the traditional opportunistic maintenance strategy adopts fixed time window or single trigger threshold, resulting in over-maintenance or under-maintenance, causing waste of reliability utilization value or functional failure risk. For example, the net profit of Zhengzhou Metro in 2023 decreased by 31% year-on-year, showing that the existing maintenance strategy has failed to effectively alleviate the cost pressure; (2) resource isolated optimization: existing researches mostly focus on a single cost factor (such as downtime, spare parts inventory or human resource allocation), while in reality, the three are strongly coupled variables. For example, spare parts inventory research mostly assumes that maintenance resources are unlimited, ignoring the impact of human resource shortage on downtime cost; (3) insufficient decision staticity: although existing dynamic maintenance models introduce the concept of predictive maintenance, they do not establish a closed-loop decision system linked with real-time resource scheduling. In summary, although the existing maintenance models meet the market demand to some extent, there is still a lot of room for improvement in terms of cost, efficiency and time. SUMMARY

[0003] In view of the problems existing in the prior art, the present application provides a method for urban rail transit intelligent operation and maintenance decision considering cost optimization. The present application introduces reliability utilization value and delay penalty cost, establishes an optimization model for opportunity maintenance downtime, and based on the joint optimization decision technology of opportunity maintenance, maintenance human resource allocation and spare parts inventory allocation based on dynamic time window, effectively reduces the maintenance cost and reduces the life cycle operation cost of urban rail transit, providing a feasible reference for the construction and improvement of intelligent urban rail transit system.

[0004] To achieve the above-mentioned purpose, the specific scheme of the present application is as follows:

[0005] A method for urban rail transit intelligent operation and maintenance decision considering cost optimization, characterized in that it comprises the following steps:

[0006] S1: constructing an urban rail transit equipment opportunity maintenance intelligent decision model based on dynamic time window;

[0007] S2: constructing an urban rail transit opportunity maintenance and human resource dynamic allocation joint decision model;

[0008] S3: Constructing a two-stage imperfect opportunity maintenance and spare parts inventory joint decision model for urban rail transit.

[0009] Preferably, the step S1 comprises the following method:

[0010] S101: Establishing a failure evolution model based on the reliability utilization value of urban rail transit equipment to obtain the maintenance period of each component;

[0011] S102: Establishing a delay penalty cost calculation model based on equipment reliability to obtain a dynamically adjusted maintenance opportunity;

[0012] S103: Establishing a dynamic time window intelligent decision model based on the reliability utilization value of equipment and the delay maintenance penalty cost to obtain an optimal maintenance opportunity;

[0013] S104: Establishing a maintenance cost calculation model for urban rail transit equipment based on dynamic time windows to obtain the optimal solution of the system layer maintenance model;

[0014] The step S2 comprises the following method:

[0015] Establishing a human resource intelligent allocation model based on maintenance cost to select the number of maintenance personnel in the planning period;

[0016] The step S3 comprises the following method:

[0017] S301: Establishing a two-stage imperfect opportunity maintenance decision model based on equipment reliability to perform maintenance work;

[0018] S302: Establishing a spare parts inventory intelligent ordering decision model based on operation and maintenance cost to optimize the maximum inventory, safety inventory, and ordering period.

[0019] Preferably, the step S101 comprises the following method:

[0020] The degradation law of the components of urban rail transit equipment conforms to the two-parameter Weibull distribution, so the inherent failure rate of the components is:

[0021]

[0022] In the formula, t is the current running time of the component, β i，j is a shape parameter, and η i，j is a size parameter representing the equipment type and maintenance history;

[0023] The reliability equation of the equipment component is:

[0024]

[0025] The equipment system will produce degradation factors difficult to repair with the increase of service life, so a hybrid failure rate evolution model is used to represent the failure rate evolution law thereof:

[0026] λ i，j+1 i，j λ i，j i，j T i，j

[0027] wherein a i，j is a service life reduction factor, b i，j is a failure rate increase factor, T i，j is the jth maintenance period of the component i, wherein T i，j =t i，j -t i，j-1 , and λ i，j is a failure rate function;

[0028] The maintenance period of each component can be obtained by combining formula (1), formula (2) and formula (3).

[0029] Preferably, the method of step S102 comprises dividing the equipment wear state into three stages: acceptable state, tolerable state and intolerable state based on the reliability of the equipment, and then introducing a linear penalty membership function idea to depict the change of the delay maintenance penalty cost, and the method specifically comprises the following methods:

[0030] The optimal preventive maintenance threshold R Z of the single component in the maintenance planning period is obtained by the minimum total maintenance cost, the reliability tolerance limit R m of the delay maintenance, i.e., the minimum reliability of maintenance, is set, the reliability R y of the component after delay maintenance is set, and different strategies are adopted for dynamic calculation of the penalty cost according to different equipment states;

[0031] When R m <R y <R z , the penalty cost C c of the delay maintenance is calculated according to the linear membership penalty, and is:

[0032]

[0033] wherein c c is a basic penalty cost;

[0034] When R y <R m , the state of the component is intolerable, a delay acceleration penalty factor μ is superimposed, and a nonlinear risk growth is further embodied, and the penalty cost C c of the delay maintenance is: ​​​

[0035]

[0036] The early repair of the component can ensure its reliability, but can cause waste of reliability utilization value, and the waste cost is:

[0037]

[0038] In the formula, c l is the reliability utilization value, R t is the reliability when the component is repaired in advance;

[0039] The adjustment of the repair time will change the minor repair cost of the component, and the change value is:

[0040]

[0041] In the formula, Δt is the change amount of the repair period when the repair time is adjusted;

[0042] Combining the formula (4) to the formula (7), the overall early repair cost C L and the penalty cost C C of the delayed repair of the component can be obtained:

[0043] C L =C l -ΔC d #(8)

[0044] C C =C c +ΔC d #(9)

[0045] Assuming that the number of the components in the kth opportunity repair window is n, the variable cost can be represented as:

[0046]

[0047] When the component is repaired in advance, φ takes the value of 1, and when the component is delayed, φ takes the value of 0, and φ is taken The corresponding time is the downtime after the dynamic adjustment of the kth opportunity repair.

[0048] Preferably, the step S103 comprises dynamically adjusting the downtime, and the specific method is to take the time distance from the first component to the last component in the opportunity repair window as the optimization step length, and to obtain the optimal repair time by comprehensively optimizing the reliability utilization value waste cost of the early repair, the risk penalty cost of the delayed repair and the minor repair cost.

[0049] Preferably, the step S104 comprises:

[0050] Maintenance cost C o including preventive maintenance cost C p and minor repair cost C r ;

[0051]

[0052] where m i is the number of preventive maintenance of component i in the maintenance planning period, is the unit preventive maintenance cost of component i;

[0053]

[0054] where, is the unit minor repair cost of component i, t i，j is the adjusted opportunity maintenance time of component i at the jth maintenance;

[0055] The maintenance cost C o of each component can be expressed as:

[0056] C o = C p + C r #(13)

[0057] In addition to considering the maintenance cost C o of component i, the urban rail transit also includes downtime cost C a and total variable cost C t in a maintenance planning period, and their distributions can be expressed as:

[0058]

[0059]

[0060] where C a is the unit downtime cost, is the maximum value of maintenance component repair in the opportunity maintenance window, K is the number of opportunity maintenance in the planning period, is the unit maintenance adjustment cost of component;

[0061] Considering the structure of each maintenance cost, the urban rail transit equipment maintenance cost calculation model based on dynamic time window is established, and the objective function is:

[0062] min C z = C o + C a + C t #(16)

[0063] Solving min C z , select C zThe smallest window is the optimal opportunity maintenance window, and the optimal solution of the system-level maintenance model can be obtained.

[0064] Preferably, in the step S2, the method for selecting the number of maintenance personnel in the planning period based on the optimal matching method of maintenance personnel and maintenance tasks is that, assuming that the number of components in the set of components to be repaired at each shutdown is n, the set of maintenance times of the components can be represented as:

[0065] If n = 1, the system shutdown duration

[0066] If n = 2, the system shutdown duration

[0067] If n = 3, the system shutdown duration

[0068] If n > 3, the maintenance task allocation step is as follows:

[0069] ①Sort the maintenance times of the components in the set of components to be repaired from large to small, and allocate the first component to the first maintenance personnel, the second component to the second maintenance personnel, the third component to the third maintenance personnel, and then allocate the first component to the first maintenance personnel, and so on, until all components are allocated to the maintenance personnel;

[0070] ②Statistically record the maintenance times of the maintenance personnel Compare the maintenance times, and record the maintenance personnel with the longest maintenance time as and the maintenance personnel with the shortest maintenance time as Let The maintenance task amounts are recorded as f1 and f2 respectively, and the maintenance time sets are recorded as and satisfy

[0071] ③Subtract the maintenance times of the components in and in turn, and the result has f1 x f2 kinds, if then recalculate until the values in and are greater than 0;

[0072] ④Determine whether there is , if there is, exchange the corresponding maintenance tasks of and and return to ②, otherwise execute ⑤;

[0073] ⑤Let the system shutdown duration be:

[0074] ​

[0075] The maintenance personnel configuration cost can be expressed as:

[0076]

[0077] The downtime of r = 1, 2, 3 is calculated respectively The value is brought into the above formula to obtain the configuration cost of different number of maintenance personnel, and the output is min c k The corresponding number of maintenance personnel r is the optimal value of the number of maintenance personnel of this opportunity maintenance, and assuming that K times of opportunity maintenance are performed within the maintenance planning period, the total number of maintenance personnel can be expressed as P = rK;

[0078] The personnel hiring cost C y is:

[0079]

[0080] In the formula, c y is the hiring cost of a single maintenance personnel, and r is the optimal value of the number of maintenance personnel of this opportunity maintenance.

[0081] Preferably, in the step S301, the two-level imperfect opportunity maintenance decision is that when the component is subjected to preventive maintenance, the reliability after primary maintenance is only less than the reliability after the last maintenance, regardless of what level of maintenance is performed last time, and when the component is subjected to advanced maintenance, the reliability after maintenance is only lower than the reliability after the last advanced maintenance, regardless of the reliability after the primary maintenance before.

[0082] The reliability evolution method of the equipment component in the two-level imperfect opportunity maintenance decision is:

[0083] Let be the reliability of the component before primary maintenance, be the reliability of the component after primary maintenance, be the reliability of the component before advanced maintenance, be the reliability of the component after the last advanced maintenance, and when the component is subjected to advanced maintenance at the i-th time, the reliability of the component is only less than the reliability after the last advanced maintenance and greater than the reliability after the last primary maintenance

[0084] The maintenance mode selection factor ω of each component can be expressed as: i

[0085]

[0086] According to the concept of the two-level imperfect maintenance strategy, the age decrement factor a i，j ​and failure rate increasing factor b i，j The expression is:

[0087]

[0088] In the formula, is the age reduction factor after primary maintenance of component i at the jth repair, is the age reduction factor after advanced maintenance of component i at the jth repair, is the failure rate increasing factor after primary maintenance of component i at the jth repair, is the failure rate increasing factor after advanced maintenance of component i at the jth repair;

[0089] The hybrid failure rate evolution model and the reliability equation are shown in formula (23) and formula (24):

[0090] λ i，j+1 (t)=b i，j λ i，j (t+a i，j T i，j )#(23)

[0091]

[0092] The relationship between the component failure rate and reliability is:

[0093]

[0094] In order to make the model expression clearer, the reliability recovery values of the component before and after maintenance are converted into failure rate improvement values by formula (23), formula (24) and formula (25). Since the cost-effectiveness ratio is a reliable method to improve efficiency in the whole process of input and output accurate management, the cost-effectiveness ratio analysis method is used as the evaluation criterion of the economy of maintenance methods, and then the maintenance method is selected through the comparison of the cost-effectiveness ratio. The cost-effectiveness ratio means the ratio of input cost to output benefit, as shown in formula (27) and formula (28). The numerator is the maintenance cost of primary maintenance and advanced maintenance input, and the denominator is the failure rate recovery value of the component after performing different levels of maintenance. The expected input of the component is less after maintenance, and the failure rate improvement is greater. Therefore, the lower the cost-effectiveness ratio of the maintenance method, the more economical the maintenance is;

[0095] The failure rate function of the component before and after maintenance is:

[0096]

[0097] The failure rate recovery value of the component before and after maintenance is Let represent the cost-effectiveness ratio of the component after performing primary maintenance and advanced maintenance, respectively. The specific value can be represented as:

[0098]

[0099]

[0100] In the formula, is the primary maintenance cost of the component, is the primary maintenance downtime cost, is the primary maintenance spare part consumption cost, is the advanced maintenance cost of the component, is the advanced maintenance downtime cost, is the advanced maintenance spare part consumption cost;

[0101] According to the established cost-effectiveness ratio model, the maintenance mode selection factor can be further expressed as:

[0102]

[0103] Preferably, in the step S302, the spare part inventory intelligent ordering decision model is that S is the maximum inventory, s is the safety inventory, kc is the remaining inventory of the spare parts of the urban rail transit multi-component system after each maintenance, it is assumed that the multi-component system is maintained for 3 times within the maintenance planning period, the spare part inventory is checked after each maintenance, the remaining amount of spare parts kc1 and kc3 after the first and third maintenance is less than the safety inventory s, and the spare parts ordering needs to be performed, and the ordering amount is S-kc1 and S-kc3 respectively, and the spare parts arrive after passing through the delivery period; after the second maintenance, the remaining amount of spare parts kc2 is greater than the safety inventory s, and therefore the spare parts ordering is not performed.

[0104] The technical scheme of the present application has the following beneficial effects:

[0105] The present application is based on component reliability, optimizes the maintenance period, intelligently merges the maintenance time of each component based on economy, and further allocates the maintenance tasks to limited maintenance personnel, intelligently and dynamically selects the number of maintenance personnel according to the maintenance task amount, realizes the joint optimization of human resources and maintenance strategy, and simultaneously considers the limitation of spare part resources, formulates the actual joint optimization intelligent decision through a reasonable spare part inventory strategy.

[0106] The present application solves social science problems by using natural science means such as statistical analysis and simulation modeling, realizes the means combining quantitative analysis and qualitative analysis to explore the complex and uncertain maintenance behavior and maintenance cost in the urban rail transit maintenance process, can predict the urban rail transit maintenance cost, provides a reference for the urban rail transit operation company to reasonably dispatch relevant maintenance resources and formulate relevant maintenance budget, effectively reduces the maintenance cost, and further reduces the whole life cycle operation cost of the urban rail transit, is conducive to the construction of green low-carbon, energy-saving and environment-friendly, efficient and intelligent urban rail transit.

[0107] The application can be popularized and applied in the urban rail transit industry, mainly applied to the field of urban rail transit equipment inspection, maintenance and repair, and the expected technical and economic indicators are as follows:

[0108] (1) The developed urban rail transit intelligent operation and maintenance decision system based on maintenance cost can effectively reduce the operation and maintenance cost of urban rail transit by 30% or more;

[0109] (2) Effectively reduce the failure rate of urban rail transit equipment;

[0110] (3) The cost of urban rail transit human resources is saved by 30%-40%;

[0111] (4) The cost of urban rail transit equipment spare parts procurement is saved by 30%-40%; BRIEF DESCRIPTION OF DRAWINGS

[0112] Figure 1 It is a whole method structure schematic diagram of the application;

[0113] Figure 2 It is a component state division schematic diagram in step S102 of the application;

[0114] Figure 3 It is a traditional opportunity maintenance schematic diagram in step S103 of the application;

[0115] Figure 4 It is a dynamic time window-based opportunity maintenance schematic diagram in step S103 of the application;

[0116] Figure 5 It is a reliability evolution law schematic diagram of two-stage imperfect maintenance mode in step S301 of the application;

[0117] Figure 6 It is a spare part intelligent ordering strategy schematic diagram in step S302 of the application. DETAILED DESCRIPTION

[0118] The application is further described below in combination with the drawings and specific embodiments.

[0119] Referring to Figure 1 The application provides a cost optimization considering urban rail transit intelligent operation and maintenance decision method, characterized in that it comprises the following steps:

[0120] S1: Construct an urban rail transit equipment opportunity maintenance intelligent decision model based on a dynamic time window, mainly comprising the following methods:

[0121] S101: Establish a failure evolution model based on the reliability utilization value of urban rail transit equipment to obtain the maintenance period of each component;

[0122] S102: Establish a delay penalty cost calculation model based on equipment reliability to obtain a dynamically adjusted maintenance opportunity;

[0123] S103: Establish a dynamic time window intelligent decision-making model based on equipment reliability utilization value and delay maintenance penalty cost to obtain the optimal maintenance opportunity;

[0124] S104: Establish a city rail transit equipment maintenance cost calculation model based on dynamic time window to obtain the optimal solution of the system layer maintenance model.

[0125] S2: Construct a city rail transit opportunity maintenance and dynamic human resource allocation joint decision-making model, the main method is to establish a human resource intelligent allocation model based on maintenance cost to select the number of maintenance personnel in the planning period.

[0126] S3: Construct a city rail transit two-level imperfect opportunity maintenance and spare parts inventory joint decision-making model, mainly including the following methods:

[0127] S301: Establish a two-level imperfect opportunity maintenance decision-making model based on equipment reliability to perform maintenance work;

[0128] S302: Establish a spare parts inventory intelligent ordering decision-making model based on operation and maintenance cost to optimize the maximum inventory, safety stock, and ordering period.

[0129] Wherein:

[0130] (1) The specific method of step S101 is:

[0131] The degradation law of city rail transit equipment components follows the two-parameter Weibull distribution, so the inherent failure rate of the component is:

[0132]

[0133] Where, t is the current running time of the component, β i，j is the shape parameter, η i，j is the size parameter, representing the equipment type and maintenance history;

[0134] Reliability is the core index to ensure the safety of city rail transit operation, which stipulates that preventive maintenance must be carried out when the reliability of the component reaches the preventive maintenance value to ensure operation safety. The equipment component reliability equation is:

[0135]

[0136] As the age of the equipment system increases, it will produce difficult-to-repair degradation factors, so a mixed failure rate evolution model is used to represent its failure rate evolution law:

[0137] λi，j+1 (t) = b i，j λ i，j (t+a i，j T i，j )#(3)

[0138] Where a i，j is the service age reduction factor, b i，j is the failure rate increasing factor, T i，j is the jth maintenance cycle of component i, where T i，j =t i，j -t i，j-1 ,λ i，j is the failure rate function;

[0139] Combining equations (1), (2) and (3), the maintenance period of each component can be obtained.

[0140] (2) When the timing of maintenance is dynamically adjusted, the maintenance cost will change accordingly. Repairing parts in advance will prevent them from fully realizing their utilization value, while delaying maintenance will carry certain safety risks. Therefore, small delays should be tolerable, while large delays should be intolerable.

[0141] Therefore, the method of step S102 is: based on the reliability of the equipment, the equipment wear state is divided into three stages: acceptable state, tolerable state, and intolerable state, and then the linear penalty membership function concept is introduced to characterize the change of the delayed maintenance penalty cost. Specifically, the method includes the following:

[0142] Reference Figure 2 , set the optimal preventive maintenance threshold R Z , which can be obtained by solving the minimum total maintenance cost of a single component during the maintenance planning period, and setting the reliability tolerance limit R for delayed maintenance m , i.e. the minimum reliability of maintenance, sets the reliability Ry of the component after delayed maintenance, and adopts different strategies to dynamically calculate the penalty cost for different equipment states;

[0143] When R m <R y <R z When the penalty is calculated according to the linear membership, the penalty cost of delayed maintenance is C c for:

[0144]

[0145] Where c c is the basic penalty cost;

[0146] When R y <R mWhen the component state is not tolerable, the delay repair penalty factor μ is superimposed, thus embodying the nonlinear risk growth, at which time the penalty cost C c is;

[0147]

[0148] The early repair of the component can guarantee its reliability, but will cause the waste of reliability utilization value, and the waste cost is:

[0149]

[0150] In the formula, c l is the reliability utilization value, R t is the reliability of the component when it is repaired early;

[0151] The adjustment of the repair opportunity will change the small repair cost of the component, and the change value is:

[0152]

[0153] In the formula, Δt is the change amount of the repair cycle when the repair opportunity is adjusted;

[0154] Combining the formulas (4) to (7), the overall early repair cost C L of the component and the penalty cost C C of the delay repair can be obtained:

[0155] C L =C l -ΔC d #(8)

[0156] C C =C c +ΔC d #(9)

[0157] Suppose that the number of components in the kth opportunity repair window is n, then the variable cost can be expressed as:

[0158]

[0159] When the component is repaired early, φ takes the value of 1, and when the component is repaired late, φ takes the value of 0, and φ is taken The corresponding opportunity is the shutdown opportunity of the kth opportunity repair after the dynamic adjustment.

[0160] (Three) Refer to Figures 3-4 Compared with the traditional opportunity repair strategy, the opportunity repair strategy based on the dynamic time window dynamically adjusts the system shutdown opportunity W. In the traditional opportunity repair strategy, all components in the opportunity repair window are repaired early.

[0161] Therefore, the step S103 comprises dynamically adjusting the shutdown opportunity, and a specific method is as follows: taking a time distance from a first component to a last component in the opportunity maintenance window as an optimization step, and obtaining an optimal maintenance opportunity by comprehensively optimizing a reliability value of early maintenance, a waste cost of value, a risk penalty cost of delayed maintenance, and a minor repair cost.

[0162] (IV) The step S104 comprises:

[0163] A maintenance cost C in a maintenance planning period [0, M] o A preventive maintenance cost C p And a minor repair cost C r ;

[0164]

[0165] In the formula, m i is a preventive maintenance frequency of the component i in the maintenance planning period, is a unit preventive maintenance cost of the component i;

[0166]

[0167] In the formula, is a unit minor repair cost of the component i, t i，j is an adjusted opportunity maintenance time of the component i for the jth time;

[0168] A maintenance cost C of each component o Can be expressed as:

[0169] C o = C p + C r #(13)

[0170] In addition to considering the maintenance cost C of the component i o The urban rail transit also includes a shutdown cost C a And a total variation cost C t In a maintenance planning period, and a distribution thereof can be expressed as:

[0171]

[0172] In the formula, C a is a unit shutdown cost, is a maximum value of a maintenance component in the opportunity maintenance window, K is a number of opportunity maintenances in the planning period, is a unit maintenance adjustment cost;

[0173] Based on the opportunity maintenance concept and considering the maintenance cost structure, an urban rail transit equipment maintenance cost calculation model based on a dynamic time window is established, and an objective function is as follows:

[0174] min C z = C o + C a + C t #(16)

[0175] Solving min C z , select C z The minimum window is the optimal opportunity maintenance window, and the optimal solution of the system-level maintenance model can be obtained.

[0176] (Five) In the maintenance process of urban rail transit system, maintenance personnel is an important factor affecting the implementation of maintenance work. When the number of maintenance personnel is small, the scheduling cost is low, but the system downtime is prolonged, causing additional downtime loss; when the number of maintenance personnel is large, the system downtime can be reduced, saving downtime cost, but the scheduling cost will increase with the increase of the number of maintenance personnel. Therefore, optimizing the configuration of maintenance personnel has certain economic value.

[0177] In this embodiment, 3 or fewer maintenance personnel are taken as the research object. In step S2, the method for selecting the number of maintenance personnel within the planning period based on the maintenance personnel and maintenance task optimization matching method is:

[0178] Suppose the number of components in the set to be repaired at each downtime is n, then the set of maintenance times of each component can be represented as:

[0179] If n = 1, the system downtime is

[0180] If n = 2, the system downtime is

[0181] If n = 3, the system downtime is

[0182] If n > 3, the maintenance task allocation steps are as follows:

[0183] ①Sort the maintenance times of each component in the set to be repaired from large to small, and assign the first component to the first maintenance personnel, the second component to the second maintenance personnel, the third component to the third maintenance personnel, and then assign the first component to the first maintenance personnel, and so on, until all components are assigned to maintenance personnel;

[0184] ②Statistically record the maintenance time of each maintenance personnel Compare the maintenance time, record the longest maintenance time of the maintenance personnel as and the shortest maintenance time as Let The repair task quantities are respectively denoted as f1, f2, and the repair time sets are respectively denoted as and satisfy

[0185] ③The repair time of each component in and is subtracted in turn, and the result has f1 x f2 kinds, if then the value is recalculated until the values in and are all greater than 0;

[0186] ④It is judged whether there is , if there is, the corresponding repair tasks of and are exchanged and then returned to ②, otherwise, ⑤ is executed;

[0187] ⑤The system downtime is:

[0188]

[0189] The repair personnel configuration cost can be expressed as:

[0190]

[0191] The downtime of r = 1, 2, 3 is calculated respectively The value is brought into the above formula to obtain the configuration cost of different number of repair personnel, and the output is min c k The corresponding repair personnel number r is the optimal value of the number of repair personnel this time, and assuming that K times of opportunity maintenance are performed within the maintenance planning period, the total number of personnel participating in maintenance can be expressed as P = rK;

[0192] The personnel hiring cost C y is:

[0193]

[0194] In the formula, c y is the hiring cost of a single repair personnel, and r is the optimal value of the number of repair personnel this time.

[0195] (Six) In order to ensure the normal operation of the urban rail transit system, two-level imperfect opportunity maintenance methods are used to perform maintenance work, and the two-level imperfect opportunity maintenance decision is that when the component is subjected to preventive maintenance, the reliability after primary maintenance is only less than the reliability after the last maintenance, regardless of the level of the last maintenance, and the reliability after high-level maintenance is only lower than the reliability after the last high-level maintenance, regardless of the reliability after the primary maintenance. ​

[0196] Referring to Figure 5 , in step S301, the reliability evolution method of the equipment components in the two-level imperfect opportunity maintenance decision is:

[0197] Let be the reliability of the component before the primary maintenance, be the reliability of the component after the primary maintenance, be the reliability of the component before the advanced maintenance, be the reliability of the component after the last advanced maintenance, when the component performs the advanced maintenance for the i-th time, the reliability of the component is only less than the reliability after the last advanced maintenance but greater than the reliability after the last primary maintenance

[0198] The maintenance mode selection factor ω of each component i can be expressed as:

[0199]

[0200] According to the concept of the two-level imperfect maintenance strategy, the expression of the service-life decrement factor a i，j and the failure rate increment factor b i，j is:

[0201]

[0202] In the formula, is the service-life decrement factor after the primary maintenance of the component i for the j-th time, is the service-life decrement factor after the advanced maintenance of the component i for the j-th time, is the failure rate increment factor after the primary maintenance of the component i for the j-th time, is the failure rate increment factor after the advanced maintenance of the component i for the j-th time;

[0203] The mixed failure rate evolution model and the reliability equation are shown in formula (23) and formula (24):

[0204] λ i，j+1 (t)=b i，j λ i，j (t+a i，j T i，j )#(23)

[0205]

[0206] The relationship between the failure rate and the reliability of the component is:

[0207]

[0208] To make the model more clear, the recovery values of the reliability of the component before and after maintenance are converted into the improvement values of the failure rate by formula (23), formula (24) and formula (25). Since the cost-effectiveness ratio is a reliable method to improve efficiency in the whole process of input and output accurate management, the cost-effectiveness ratio analysis method is adopted as the evaluation criterion of the economy of the maintenance mode in the embodiment, and then the maintenance mode is selected through the comparison of the cost-effectiveness ratios. The cost-effectiveness ratio means the ratio of the input cost to the output benefit, as shown in formula (27) and formula (28). The numerator is the maintenance cost of the primary maintenance and the advanced maintenance, and the denominator is the recovery value of the failure rate of the component after performing the maintenance work of different levels. The component with less expected input cost can achieve greater improvement of the failure rate. Therefore, the lower the cost-effectiveness ratio of the maintenance mode is, the better the economy of the maintenance mode is.

[0209] The failure rate function of the component before and after maintenance is:

[0210]

[0211] The recovery value of the failure rate of the component before and after maintenance is Let respectively represent the cost-effectiveness ratios of the component after performing the primary maintenance and the advanced maintenance. The specific values can be represented as:

[0212]

[0213]

[0214] In the formula, is the primary maintenance cost of the component, is the primary maintenance shutdown cost, is the primary maintenance spare part consumption cost, is the advanced maintenance cost of the component, is the advanced maintenance shutdown cost, is the advanced maintenance spare part consumption cost.

[0215] According to the established cost-effectiveness ratio model, the maintenance mode selection factor can be further represented as:

[0216]

[0217] (Seven) The maintenance level of the urban rail transit in China is gradually transferred from the operational maintenance to the advanced maintenance, and therefore the demand for spare parts is increasing. A reasonable spare part ordering strategy and inventory management mode can improve the operation and maintenance efficiency of the urban rail transit. However, the urban rail transit is a large and complex system, and a large number of spare parts with large volume are required. Due to the limited factory building, it is difficult to store a large number of spare parts. Therefore, an efficient spare part inventory strategy needs to be developed to optimize the maximum inventory, safety inventory, ordering period and the like to reduce the cost.

[0218] In step S302, the spare parts inventory intelligent ordering decision model is as follows: let S be the maximum inventory, s be the safety stock, and kc be the remaining inventory of spare parts for the urban rail transit multi-component system after each maintenance. It is assumed that during the maintenance planning period, the multi-component system is maintained three times in total, and the spare parts inventory is checked after each maintenance.

[0219] Reference Figure 6 After the first and third maintenance, the remaining spare parts quantity kc1 and kc3 are less than the safety stock s, and spare parts need to be ordered. The order quantities are S-kc1 and S-kc3 respectively. The spare parts arrive after the delivery period. After the second maintenance, the remaining spare parts quantity kc2 is greater than the safety stock s, so no spare parts ordering is performed.

[0220] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made by using the contents of the present description and drawings under the inventive concept of the present invention, or direct / indirect application in other related technical fields are included in the protection scope of the present invention.

Claims

1. A cost-optimized urban rail transit intelligent operation and maintenance decision-making method, characterized in that: The steps include: S1: Construct an intelligent decision-making model for opportunistic maintenance of urban rail transit equipment based on dynamic time windows; S2: Construct a joint decision-making model for opportunistic maintenance and dynamic allocation of human resources for urban rail transit; S3: Construct a joint decision-making model for two-level non-perfect opportunistic maintenance and spare parts inventory in urban rail transit.

2. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 1 is characterized in that: The step S1 includes the following method: S101: Establish a fault evolution model based on the reliability utilization value of urban rail transit equipment to obtain the maintenance cycle of each component; S102: Establishing a delay penalty cost calculation model based on equipment reliability to obtain dynamically adjusted maintenance timing; S103: Establish a dynamic time window intelligent decision-making model based on the utilization value of equipment reliability and the penalty cost of delayed maintenance to obtain the optimal maintenance timing; S104: Establishing a maintenance cost calculation model for urban rail transit equipment based on a dynamic time window to obtain an optimal solution for the system-level maintenance model; The step S2 includes the following method: Establish a human resource intelligent deployment model based on maintenance costs to select the number of maintenance personnel during the planning period; The step S3 includes the following method: S301: Establish a two-level imperfect opportunistic maintenance decision model based on equipment reliability to perform maintenance work; S302: Establish an intelligent spare parts inventory ordering decision model based on operation and maintenance costs to optimize maximum inventory, safety stock, and ordering cycle.

3. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: The step S101 includes the following method: The degradation law of urban rail transit equipment components follows a two-parameter Weibull distribution, so the inherent failure rate of the components is: Where t is the current running time of the component, β i，j is the shape parameter, η i，j is a size parameter, representing the equipment type and maintenance history; The reliability equation of equipment components is: As the equipment system ages, it will produce degradation factors that are difficult to repair. Therefore, a hybrid failure rate evolution model is used to characterize the evolution law of its failure rate: λ i，j+1 (t)=b i，j λ i，j (t+a i，j T i，j )#(3) Where a i，j is the service age reduction factor, b i，j is the failure rate increasing factor, T i，j is the jth maintenance cycle of component i, where T i，j =t i，j -t i,j-1 ,λ i，j is the failure rate function; Combining equations (1), (2) and (3), the maintenance period of each component can be obtained.

4. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: The method of step S102 includes dividing the equipment wear state into three stages based on the reliability of the equipment: acceptable state, tolerable state, and intolerable state, and then introducing the concept of linear penalty membership function to characterize the change of delayed maintenance penalty cost, specifically including the following method: The optimal preventive maintenance threshold R is obtained by the minimum total maintenance cost of a single component during the maintenance planning period. Z , set the reliability tolerance limit R for delayed maintenance m , that is, the minimum reliability of maintenance, set the reliability R of the component after delayed maintenance y ,For different equipment states, different strategies are used to dynamically calculate penalty costs; When R m <R y <R z When the penalty is calculated according to the linear membership, the penalty cost of delayed maintenance is C c for: Where c c is the basic penalty cost; When R y <R m When the component status is no longer tolerable, the delay acceleration penalty factor μ is added, which reflects the nonlinear risk growth. At this time, the penalty cost C for delayed maintenance is c for; Premature maintenance of components can ensure their reliability, but it will result in a waste of the reliability value. The waste cost is: Where c l is the reliability utilization value, R t Reliability when pre-empting component repairs; Adjusting the maintenance timing will change the minor repair cost of the component. The change value is: Where Δt is the change in maintenance cycle when adjusting the maintenance timing; Combining equations (4) to (7), we can get the overall advance maintenance cost C of the component: L and the penalty cost C for delayed maintenance C : C L =C l -ΔC d #(8) C C =C c +ΔC d #(9) Assuming that the number of parts within the kth opportunity repair window is n, the variable cost is It can be expressed as: When the component is repaired in advance, φ takes the value of 1; when the component is repaired later, φ takes the value of 0. The corresponding timing is the downtime timing after dynamic adjustment of the kth opportunity maintenance.

5. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: The step S103 includes dynamically adjusting the downtime timing. Specifically, the time distance from the first component to the last component in the opportunity maintenance window is used as the optimization step length, and the optimal maintenance timing is obtained by comprehensively optimizing the reliability utilization value waste cost of early maintenance, the risk penalty cost of delayed maintenance, and the minor repair cost.

6. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: The step S104 includes: The maintenance cost C in the maintenance planning period [0, M] o Including preventive maintenance costs C p and minor repair cost C r ; Where m i is the number of preventive maintenance of component i during the maintenance planning period, is the unit preventive maintenance cost of component i; Where, is the unit minor repair cost of component i, t i，j The opportunity maintenance time after the adjustment of the j-th maintenance of component i; Maintenance cost of each component C o It can be expressed as: C o =C p +C r #(13) In addition to considering the maintenance cost C of component i o In addition, urban rail transit also includes downtime costs C during a maintenance planning period. a and total variable cost C t , its distribution can be expressed as: Where C a is the unit downtime cost, is the maximum repair time of the maintenance component within the opportunity maintenance window, K is the number of opportunity maintenance times within the planning period, Adjust the cost for a single repair of a component; Considering various maintenance cost structures, a maintenance cost calculation model for urban rail transit equipment based on dynamic time windows is established, and the objective function is: my C z =C o +C a +C t #(16) Solve for min C z , select C z The smallest window is the optimal opportunity maintenance window, which can obtain the optimal solution of the system-level maintenance model.

7. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: In step S2, based on the method of optimizing the matching of maintenance personnel and maintenance tasks, the method for selecting the number of maintenance personnel in the planning period is as follows: assuming that the number of components in the set to be repaired during each downtime is n, the set of maintenance times for each component can be expressed as: If n=1, the system downtime If n=2, the system downtime If n=3, the system downtime If n>3, the maintenance task allocation steps are as follows: ① Sort the repair time of each component in the repair set from largest to smallest. After sorting, assign the first component to the first maintenance personnel, the second component to the second maintenance personnel, the third component to the third maintenance personnel, the first component to the first maintenance personnel, and so on, until all components are assigned to maintenance personnel; ② Count the maintenance time of maintenance personnel separately Compare the maintenance time and record the one with the longest maintenance time as The one with the shortest maintenance time is recorded as make The maintenance task amounts are recorded as f1 and f2 respectively, and the maintenance time sets are recorded as and satisfy ③ By and Subtract the maintenance time of each component in turn, and the result is f1×f2. If Then recalculate until and Inside The values ​​of are all greater than 0; ④ Determine whether If the situation exists, and After the corresponding maintenance tasks are exchanged, return to ②, otherwise execute ⑤; ⑤ Set the system downtime to: The maintenance staffing cost can be expressed as: Calculate the downtime when r=1, 2, and 3 respectively Substituting its value into the above formula, we can obtain the configuration cost of different numbers of maintenance personnel, and the output is the same as min c k The corresponding number of maintenance personnel r is the optimal value of the number of maintenance personnel for this opportunity. Assuming that a total of K opportunistic maintenance operations are performed during the maintenance planning period, the total number of maintenance personnel can be expressed as P = rK; Personnel employment cost C y for: Where c y is the cost of hiring a single maintenance worker, and r is the optimal number of maintenance workers for this opportunity.

8. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: In step S301, the two-level non-perfect opportunity maintenance decision is that when a component undergoes preventive maintenance, if primary maintenance is used, the reliability after maintenance is only less than the reliability after the previous maintenance, regardless of the level of maintenance performed last time; and if advanced maintenance is used, the reliability after maintenance is only less than the reliability of the previous advanced maintenance, regardless of the reliability after the previous primary maintenance. The reliability evolution method of equipment components in the two-level imperfect opportunistic maintenance decision is: set up The reliability of the component before primary maintenance, The reliability of the component after primary maintenance, Reliability of components before advanced maintenance, is the reliability of the component after the last advanced maintenance. When the component performs advanced maintenance in the i-th maintenance, its reliability Only less reliable than after the last advanced repair And greater than the reliability after the previous primary maintenance Maintenance method selection factor for each component ω i It can be expressed as: According to the concept of two-level imperfect maintenance strategy, the service life reduction factor a i，j and failure rate increasing factor b i，j The expression is: Where, is the service life reduction factor after primary maintenance for component i during its jth maintenance, is the service life reduction factor of component i after the advanced maintenance is adopted during the jth maintenance, is the failure rate increasing factor after primary maintenance for component i during its jth maintenance, is the failure rate increasing factor after the advanced maintenance is adopted for component i during the jth maintenance; The hybrid failure rate evolution model and reliability equation are shown in Equations (23) and (24): λ i，j+1 (t)=b i，j λ i，j (t+a i，j T i，j )#(23) The relationship between component failure rate and reliability is: In order to make the model expression clearer, the reliability recovery value of the component before and after maintenance is converted into the improvement value of the failure rate through equations (23), (24) and (25). Since the cost-effectiveness ratio is a reliable method to improve the efficiency in the precise management of the whole process of input and output, the cost-effectiveness ratio analysis method is used as the evaluation criterion of the economic efficiency of the maintenance method, and then the maintenance method is selected by comparing the cost-effectiveness ratio. The cost-effectiveness ratio means the ratio of input cost to output benefit, as shown in equations (27) and (28). The numerator is the maintenance cost of primary maintenance and advanced maintenance, and the denominator is the failure rate recovery value of the component after performing different levels of maintenance work. The maintenance component is expected to achieve a greater improvement in failure rate with less cost. Therefore, the lower the cost-effectiveness ratio of the maintenance method, the better the maintenance economy. The failure rate function of the component before and after repair is: The failure rate recovery value before and after component repair is make Respectively represent the cost-effectiveness of the parts after primary maintenance and advanced maintenance. The specific values ​​can be expressed as: Where, is the primary maintenance cost of the component, is the primary maintenance downtime cost, The cost of spare parts for primary maintenance, is the cost of advanced repairs for components, Downtime costs for advanced maintenance, Consume costs for advanced maintenance spare parts; According to the established cost-effectiveness model, the maintenance mode selection factor can be further expressed as:

9. The urban rail transit intelligent operation and maintenance decision-making method considering cost optimization according to claim 2 is characterized in that: In step S302, the intelligent ordering decision model for spare parts inventory is as follows: let S be the maximum inventory, s be the safety stock, and kc be the remaining inventory of spare parts for the urban rail transit multi-component system after each maintenance. Assume that during the maintenance planning period, the multi-component system is repaired three times in total. After each maintenance, the spare parts inventory is checked. After the first and third maintenances, if the remaining spare parts quantities kc1 and kc3 are less than the safety stock s, spare parts need to be ordered, and the order quantities are S-kc1 and S-kc3, respectively. The spare parts arrive after the delivery period. After the second maintenance, the remaining spare parts quantity kc2 is greater than the safety stock s, so no spare parts are ordered.

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