Configuration optimization method based on low-demand and non-low-demand ship spare parts

Abstract

The invention discloses a configuration optimization method based on low-demand and non-low-demand ship spare parts, and belongs to the technical field of water surface JT equipment guarantee, and the method comprises the steps: solving a low-demand ship spare part configuration optimization model through employing improved gray Markov prediction; a TOPSIS-fused multi-target particle swarm optimization algorithm is adopted to solve the non-low-demand ship spare part configuration optimization model; and performing analogue simulation on an optimal spare part configuration list obtained by solving the multi-target particle swarm optimization model by adopting Monte Carlo, performing a simulation experiment by utilizing the configuration model, and verifying the multi-target particle swarm optimization model. According to the method, the low-demand spare part configuration optimization model and the non-low-demand spare part configuration optimization model are fused, and a better ship spare part configuration optimization method is realized by virtue of respective advantages, so that continuous, safe and reliable operation of a ship is ensured. And the configuration optimization efficiency and accuracy are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of surface JT equipment support, and more specifically, to a configuration optimization method based on low-demand and non-low-demand ship spare parts. Background Art

[0002] With the rapid development of global trade and the sustained growth of the marine economy, ships, as important logistics tools, play an increasingly important role in my country's economic development. Their operating efficiency and safety are receiving more and more attention. When ships are on long-distance missions, they need to complete multiple subtasks, including departure, navigation, return and other mission stages. In most cases, shipping companies will reserve a certain amount of spare parts to ensure the safety of ship operation. Therefore, ship spare parts are crucial to maintaining the normal operation of ships and play a core role in ship operation. However, at present, only a single task is usually considered in the management of ship spare parts, and there is a lack of scientificity in spare parts management. Excessive spare parts inventory may lead to waste of warehouse space and increase storage costs; on the contrary, insufficient inventory may delay the maintenance of ship equipment, disrupt the maintenance progress, and interfere with the execution of ship missions. Therefore, the configuration optimization of ship spare parts has great engineering significance and academic value for preventing accidents and maintaining the normal operation of equipment.

[0003] Currently, the commonly used methods include low-demand ship spare parts configuration optimization and non-low-demand ship spare parts configuration optimization. The former is based on ship spare parts whose demand does not exceed a preset small number of units for configuration optimization, while the latter is based on ship spare parts whose demand exceeds a preset number for configuration optimization.

[0004] However, a single low-demand spare parts configuration optimization or non-low-demand spare parts configuration optimization model is difficult to fully and accurately predict the demand for ship spare parts. Therefore, it is necessary to integrate the two and use their respective advantages to achieve a better ship spare parts configuration optimization method to ensure that the ship can continue to operate safely and reliably. Improving the efficiency and accuracy of configuration optimization has certain engineering application value. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention proposes a configuration optimization method based on low-demand and non-low-demand ship spare parts, which integrates the low-demand spare parts configuration optimization model or the non-low-demand spare parts configuration optimization model, and uses their respective advantages to achieve a better ship spare parts configuration optimization method to ensure that the ship can operate continuously, safely and reliably. Improve the efficiency and accuracy of configuration optimization. Solve the problem that the single low-demand spare parts configuration optimization model or the non-low-demand spare parts configuration optimization model in the prior art is difficult to comprehensively and accurately predict the demand for ship spare parts.

[0006] To achieve the above object, the present invention provides a configuration optimization method based on low-demand and non-low-demand ship spare parts, comprising:

[0007] The improved grey Markov prediction is used to solve the optimization model of spare parts configuration for ships with low demand.

[0008] The multi-objective particle swarm optimization algorithm integrated with TOPSIS is used to solve the optimization model of spare parts configuration for ships with non-low demand.

[0009] The optimal spare parts configuration list obtained by solving the multi-objective particle swarm configuration optimization model is simulated using Monte Carlo, and the configuration model is used for simulation experiments to verify the multi-objective particle swarm algorithm optimization model.

[0010] In some optional implementation schemes, the method of using improved grey Markov prediction to solve the low-demand ship spare parts configuration optimization model includes:

[0011] The GM(1,1) model is used to obtain the predicted values, and the predicted results are compared with the actual observed data to calculate the relative error index;

[0012] According to the size of the relative error, different intervals are set as different state transfer intervals;

[0013] A state transfer matrix is ​​constructed based on the state transfer interval, and the transition probability between states is calculated. The most likely state in the transition probability matrix is ​​used to estimate the future development trend.

[0014] In some optional implementation schemes, the GM (1,1) model is used to obtain the predicted value, and the predicted result is compared with the actual observed data to calculate the relative error index, including:

[0015] Depend on Set the time series of spare parts consumption data, where n is the length of the time series of the selected initial spare parts consumption data, x( 0 )(k) is the time series sub-item of spare parts consumption data;

[0016] Depend on The original data is accumulated to generate a new sequence;

[0017] x (1) Perform mean processing to generate a sequence

[0018] Depend on Establish the grey differential equation, a is the development coefficient, which represents the changing trend of the cumulative sequence and the original sequence, and b is the grey action value;

[0019] By using the least squares method, we can get [a,b] T =(B TB) -1 B T Y, where

[0020]

[0021] Solve the differential equation to get the demand forecast model for low-demand spare parts

[0022] Depend on Restore the demand forecast value sequence of ship spare parts, where k = 1, 2, 3, ..., n;

[0023] Depend on The residual of the predicted value of the grey prediction GM(1,1) model is obtained by Get the relative error of the predicted value of the grey prediction GM(1,1) model.

[0024] In some optional implementation schemes, constructing a state transition matrix based on the state transition region, calculating the transition probability between each state, and estimating the future development trend using the most likely state in the transition probability matrix include:

[0025] By S1<X min +f,X max -2f<S2<X max -f,X max -f<S3<X max The state transition interval is divided into three states, among which X max and X min Respectively represent the maximum and minimum values ​​of the relative error value, f = (X max -X min ) / 3, S1, S2 and S3 represent state 1, state 2 and state 3 respectively;

[0026] Depend on Calculate the state transition probability p ij , where k represents the number of steps of state change, p ij Meaning state S i After k steps, we reach S j The probability of n i Indicates that S in the sample i The total number of occurrences, Indicates S i After k steps, we reach S j The number of

[0027] Depend on Construct state transfer matrix;

[0028] Depend on Correct the grey prediction value. express Prediction value of grey GM model, b k is the upper limit value, l k is the lower limit, y (0) (k+1) is the final value of the grey Markov model;

[0029] Depend on An improved Markov prediction model is established, where S() is the state probability.

[0030] In some optional implementation schemes, the multi-objective particle swarm optimization algorithm integrated with TOPSIS is used to solve the non-low demand ship spare parts configuration optimization model, including:

[0031] The optimization problem of spare parts configuration for ships with non-low demand is described;

[0032] Based on the described non-low demand ship spare parts configuration optimization problem, a non-low demand ship spare parts configuration optimization mathematical model is constructed;

[0033] A multi-objective particle swarm optimization method integrating TOPSIS is used to solve the mathematical model of spare parts configuration optimization for ships with non-low demand.

[0034] In some optional implementation schemes, the non-low demand ship spare parts configuration optimization problem is described, including:

[0035] The spare parts of the ship are all field replaceable units (LRUs), and the failure rate of LRUs is λ i , and obeys exponential distribution, i is the spare part number on board, i=1,2,···,I, I is the number of spare parts;

[0036] The guarantee probability of the i-th spare part is P i , the utilization rate is R i , the guarantee probability of spare parts for the entire ship system is P s , the utilization rate is R s ;

[0037] The unit configuration cost of the i-th spare part is C i ;

[0038] Maintenance activities on board are all breakdown maintenance, and preventive maintenance is not considered;

[0039] The onboard inventory of the i-th spare part is S i ;

[0040] The total constraint of the configuration scheme is C s .

[0041] In some optional embodiments, the non-low demand ship spare parts configuration optimization mathematical model is constructed based on the described non-low demand ship spare parts configuration optimization problem, including:

[0042] Depend on Get the spare parts utilization rate, when S i <S' i When the spare parts supply is insufficient, the available spare parts can reach the steady state. i -S' i The steady-state value of is the expected shortage of the i-th spare part EBO i , Depend on The utilization rate of a single spare part when the supply is insufficient is obtained by Get system utilization;

[0043] When S i >S' i When the spare parts are in sufficient supply, The spare parts utilization rate is obtained by Get the system utilization of spare parts;

[0044] By R s =1-P s +P s R s 2 The model for the system utilization of spare parts is obtained by Get the guarantee probability P of the i-th spare part i ;

[0045] Depend on The probability statistics of spare parts system support for ship equipment are obtained by The probability of spare parts system protection is obtained, where l increases from 0 to S i , so that P i ≥ the specified guarantee probability, the corresponding S i The value is the required spare parts demand, N i is the number of spare parts used in the machine, t i is the supply cycle of the i-th spare part, S i ' is the actual consumption of the i-th ship spare part, n i The number of times the i-th ship spare part is repaired or replaced due to failure during the warranty period;

[0046] Depend on Determine the cost constraints by Establish an optimal configuration model for onboard spare parts.

[0047] In some optional implementation schemes, the multi-objective particle swarm fusion TOPSIS is used to solve the non-low demand ship spare parts configuration optimization mathematical model, including:

[0048] Multi-objective particle swarm optimization is used to generate a set of Pareto optimal solutions. The optimal compromise solution is screened out from the Pareto optimal solution set through TOPSIS, and the best compromise non-low-demand ship spare parts configuration optimization scheme is obtained.

[0049] In some optional implementation schemes, the optimal spare parts configuration list obtained by solving the multi-objective particle swarm configuration optimization model is simulated using Monte Carlo, and a simulation experiment is performed using the configuration model to verify the multi-objective particle swarm algorithm optimization model, including:

[0050] Set the simulation startup parameters, task time T, number of simulations N, and input the best compromise non-low demand ship spare parts configuration optimization plan;

[0051] Generate exponentially distributed random numbers X based on the life distribution of each component and spare part i,t , if ΣX i,t <T, indicating that the component fails at this moment and needs to be replaced for repair;

[0052] If ∑X i,t ≥T, record the demand for each spare part at this time X={x i ,i=1,2,…,I}, and calculate the spare parts guarantee probability P at this time according to the actual spare parts configuration plan n (1≤n≤N);

[0053] Determine whether the number of simulations has been reached and calculate the average value of the spare parts guarantee probability of N simulations The spare parts configuration optimization scheme obtained by simulation is compared and analyzed with the spare parts guarantee probability under the particle swarm optimization strategy to verify its feasibility and rationality.

[0054] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0055] 1) The present invention divides spare parts into different types and establishes different configuration models. For low-demand ship spare parts, the improved grey Markov prediction solution is adopted. For non-low-demand ship spare parts, the multi-objective particle swarm optimization algorithm integrated with TOPSIS is adopted to solve. This realizes the rationalization and optimization of spare parts configuration, reduces inventory costs, and improves the operation efficiency and safety of ships.

[0056] 2) The present invention adopts a real-time adjustment configuration scheme, which can be flexibly adjusted according to the actual operation of the ship and the actual demand for spare parts. For low-demand ship spare parts, the improved grey Markov prediction solution is adopted, and for non-low-demand ship spare parts, the multi-objective particle swarm optimization algorithm integrated with TOPSIS is adopted to solve, thereby improving the flexibility and adaptability of spare parts configuration.

[0057] 3) The present invention can comprehensively and accurately evaluate the feasibility and accuracy of spare parts configuration schemes through the Monte Carlo-based simulation verification method, providing a scientific decision-making basis for ship spare parts configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of a method flow provided by an embodiment of the present invention;

[0059] Figure 2 This is a flow chart of a multi-objective particle swarm solution integrating TOPSIS provided by an embodiment of the present invention;

[0060] Figure 3 This is a simulation result diagram of a compromise optimal solution provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0062] like Figure 1 As shown, a configuration optimization method based on low-demand and non-low-demand ship spare parts is provided. This example takes ship spare parts as the object and includes the following steps in sequence:

[0063] Step A: Construction of optimization model for spare parts configuration of ships with low demand

[0064] Low-demand spare parts refer to spare parts whose demand does not exceed a preset small number of units in a year (or each quarter). Traditional demand forecasting models have limitations in predicting the random volatility of demand for such spare parts. Therefore, it is assumed that spare parts demand is based only on the current situation and does not depend on past consumption records, which conforms to the Markov principle.

[0065] The configuration optimization model of ship spare parts for low demand and non-low demand is constructed, in which the gray Markov model is constructed to solve the optimization of low demand ship spare parts configuration. First, in the initial stage, the GM (1,1) model is used to obtain the predicted value, and then these estimated results are compared with the actual observation data to calculate the relative error. Then, according to the different ranges of relative error, multiple state transition regions are divided. Secondly, the state transition probability is calculated, and then the state transition matrix is ​​constructed and the gray prediction value is corrected. Finally, an improved gray Markov prediction model is established.

[0066] Step B: Construction of optimization model for spare parts configuration of non-low-demand ships

[0067] For the construction of the optimization model of non-low-demand ship configuration, a model with spare parts utilization and guarantee probability as optimization objectives is constructed, considering the non-low-demand spare parts configuration of ships, and performing refined optimization design under the premise of limiting spare parts costs. The multi-objective particle swarm optimization technology integrated with TOPSIS is used to solve the model and obtain the optimization solution for the spare parts configuration of non-low-demand ships.

[0068] Step C: Monte Carlo simulation is used to simulate the optimal spare parts configuration list obtained by solving the multi-objective particle swarm algorithm configuration optimization model, and simulation experiments are performed using the configuration model to verify the feasibility and accuracy of the multi-objective particle swarm algorithm optimization model.

[0069] The step A comprises the following steps in sequence:

[0070] Step A1: The GM(1,1) prediction model of grey system theory has good prediction effect for uncertain systems such as "small sample" and "poor information". The ship spare parts demand prediction process of the GM(1,1) model is analyzed as follows.

[0071] (1) Set the time series of spare parts consumption data to:

[0072] x (0) ={x (0) (1),x (0) (2),···,x (0) (n)}

[0073] x (0) (k)≥0,k=1,2,···,n

[0074] Where n is the length of the time series of the selected initial spare parts consumption data, x( 0 )(k) is the time series sub-item of spare parts consumption data.

[0075] (2) The new sequence generated by adding the original data is:

[0076]

[0077] (3) For x (1) The sequence generated by mean processing is:

[0078]

[0079] (4) The grey differential equation is established as follows: a is the development coefficient, which represents the changing trend of the cumulative sequence and the original sequence and is used to reflect the fluctuation of the sample; b is the grey action value.

[0080]

[0081] The least squares method can be used to solve:

[0082] [a,b] T =(B T B) -1 B T Y

[0083] in,

[0084] (5) Solving the differential equation gives the spare parts demand forecasting model:

[0085]

[0086] (6) The reduced form of the demand forecast value series of ship spare parts is:

[0087]

[0088] Among them, k = 1, 2, 3, ..., n.

[0089] (7) Calculate the residual and relative error of the predicted value

[0090] The residual of the predicted value of the grey prediction GM(1,1) model is:

[0091]

[0092] The relative error of the predicted value of the grey prediction GM(1,1) model is:

[0093]

[0094] Step A2: Solving the improved grey Markov prediction model

[0095] The main idea of ​​the Grey Markov solution is to obtain the predicted values ​​through the GM(1,1) model, and then compare these predicted values ​​with the actual observed values ​​to calculate the relative error. Then, according to the size of the relative error, different intervals are set as different state transition intervals. Based on these intervals, the state transition matrix is ​​constructed, and the transition probability between each state is calculated. Finally, the most likely state in the transition probability matrix is ​​used to estimate the future development trend.

[0096] (1) Classification of states:

[0097] Divide f into three equal parts according to the range of relative error value. max -X min ) / 3, which divides the interval into three states:

[0098] Let S1<X min +f,X max -2f<S2<X max -f,Xmax -f<S3<X max In the formula, X max and X min Represent the maximum and minimum values ​​of the relative value respectively. S1, S2 and S3 represent state 1, state 2 and state 3 respectively.

[0099] (2) State transition probability p ij Calculation:

[0100]

[0101] In this formula, k represents the number of steps of state change, p ij Meaning state S i After k steps, we reach S j The probability of n i Indicates that S in the sample i The total number of occurrences, Indicates S i After k steps, we reach S j Since the data for the last year is not clear, it is not included in the final calculation.

[0102] (3) State transfer matrix construction:

[0103] p ij For the transition probability, the probability transition state matrix is ​​established as follows:

[0104]

[0105] (4) Grey prediction value correction:

[0106]

[0107] express Prediction value of grey GM model, b k is the upper limit value, l k is the lower limit, y( 0 )(k+1) is the final value of the grey Markov model.

[0108] (5) Establish an improved Markov prediction model.

[0109] The state transition probability matrix calculated by the actual state occurrence frequency may show a certain degree of instability. In order to reduce the error caused by a single state transition, this paper adopts a continuous three-step averaging method combined with prediction to improve the stability and prediction accuracy of the state transition probability matrix.

[0110] Define the state probability vector. The vector S of the probability that all states may appear at a certain stage = (S1, S2, ..., Sn ), the following conditions are met:

[0111]

[0112] Among them, S i is the state probability, which indicates the possibility that the system is in a state at a certain stage.

[0113] As long as the state and state transition probability matrix of stage tk are known, the state vector of any stage after stage tk can be predicted in theory. The calculation formula is as follows:

[0114] S(t)=S(tk)×P(k)

[0115] Where P(k) is the k-step state transition probability matrix. If the initial state probability vector S(0) and the transition probability matrix P(1) are known, the state probability vector of the system at any stage can be calculated.

[0116] The calculation formula of the three-step averaging method is as follows:

[0117]

[0118] Taking the quarterly demand data of some low-demand spare parts for ships as an example, Table 1 shows the consumption of these low-demand spare parts during 13 quarters. On this basis, the present invention selects the spare parts quantity of the first 8 quarters as sample data to predict the spare parts quantity of the last five quarters, and conducts an empirical study on the constructed grey Markov prediction method.

[0119] 1) The consumption statistics of heat exchanger spare parts in the first eight quarters are used as the time series of initial spare parts consumption. Through simulation, the grey model prediction value of spare parts consumption in the first eight quarters can be obtained, and the corresponding residual and relative error are calculated as shown in Table 2.

[0120] Table 1 Historical consumption statistics of some important spare parts of ships

[0121]

[0122] Table 2 Prediction results of grey prediction model for heat exchanger spare parts

[0123]

[0124] 2) Analysis of prediction results. As can be seen from Table 2, the average residual of the prediction results of the constructed grey prediction model is 0.7244, and the average relative error is 0.1330. By dividing the states, the respective spatial states are (E2, E2, E1, E3, E2, E3, E2, E2).

[0125] According to the established improved grey Markov forecasting model, the spare parts demand value in the next five quarters is predicted, and the residual, relative error, average residual and average relative error in the next five quarters are calculated as shown in Table 3.

[0126] Table 3 Prediction results of heat exchanger grey Markov prediction model

[0127]

[0128]

[0129] 3) The turbocharger demand is predicted by improving the grey Markov prediction model, as shown in Table 4.

[0130] Table 4 Prediction results of supercharger grey Markov prediction model

[0131]

[0132] (4) Analysis of spare parts demand forecast results. According to the data in Tables 3 and 4, the average residuals of the demand forecasts for heat exchangers and superchargers in the next five months are 0.6 and 0.5, respectively, while the relative errors are 0.1167 and 0.1067, respectively. Compared with the gray prediction, the accuracy is higher. Therefore, the prediction accuracy meets the preset standard.

[0133] In summary, the grey Markov forecasting model performs well in forecasting the demand for ship spare parts with scarce data, insufficient information and high uncertainty, and can effectively implement and provide relatively accurate forecast results. This model has significant practical significance in forecasting the demand for ship spare parts.

[0134] The step B comprises the following steps in sequence:

[0135] Step B1: Description of the optimization problem of spare parts configuration for non-low-demand ships

[0136] In the optimization process, spare parts guarantee probability and spare parts utilization rate are taken as optimization objectives together, and cost is taken as a constraint, aiming to improve the spare parts supply guarantee efficiency of ships and achieve efficient utilization of resources.

[0137] To simplify and illustrate the problem, the following assumptions are made:

[0138] (1) All ship spare parts are liner replaceable units (LRUs), and the failure rate of LRUs is λ i , and obeys exponential distribution, i is the spare part number on board (i=1,2,···,I), and I is the number of spare parts.

[0139] (2) The guarantee probability of the i-th spare part is P i , the utilization rate is Ri , the guarantee probability of spare parts for the entire ship system is P s , the utilization rate is R s .

[0140] (3) The unit configuration cost of the i-th spare part is C i .

[0141] (4) All maintenance activities on board are breakdown maintenance, and preventive maintenance is not considered.

[0142] (5) The onboard inventory of the i-th spare part is S i .

[0143] (6) The total constraint condition of the configuration scheme is C s .

[0144] Step B2: Construction of mathematical model for optimizing spare parts configuration for ships with non-low demand

[0145] (1) Spare parts utilization rate

[0146] Spare parts utilization is

[0147]

[0148] Transform the above formula into

[0149]

[0150] There may be a sufficient supply or insufficient supply of spare parts, i.e.

[0151]

[0152] When S i <S' i When the spare parts supply is insufficient, the available spare parts can reach the steady state. i -S' i The steady-state value of is the expected shortage of the i-th spare part EBO i . Its expression is:

[0153]

[0154] Therefore, the utilization rate of a single spare part when the supply is insufficient is:

[0155]

[0156] At this time, the system utilization for:

[0157]

[0158] When S i >S'i When , it indicates that the spare parts supply is sufficient. The spare parts utilization rate at this time is:

[0159]

[0160] Similarly, the system utilization rate of spare parts

[0161] The system utilization rate R of spare parts is obtained from the conditional probability s The model is:

[0162]

[0163] (2) Spare parts guarantee probability

[0164] Since the spare parts life follows an exponential distribution, the guarantee probability P of the i-th spare part is i The calculation formula is:

[0165]

[0166] In the formula, when l increases from 0 to S i , so that P i ≥ the specified guarantee probability, the corresponding S i The value is the required spare parts demand. i is the number of spare parts used in the machine, t i is the supply cycle of the i-th spare part.

[0167] According to the definition of guarantee probability, the guarantee probability statistics of spare parts system of ship equipment are obtained as follows:

[0168]

[0169] In the formula, S i ' is the actual consumption of the i-th ship spare part, n i The number of times the i-th ship spare part is repaired or replaced due to failure during the warranty period.

[0170] From the above formula, the probability of spare parts system protection is:

[0171]

[0172] (3) Constraints

[0173] The ship spare parts cost will be used as a constraint to determine the reasonable combination of spare parts types. Under strict cost restrictions, through precise calculation and evaluation, the optimal combination of spare parts types will be determined to optimize the system spare parts guarantee probability and utilization rate. The total ship spare parts guarantee cost should not exceed the given guarantee cost index, and the calculation formula is:

[0174]

[0175] (4) Optimizing mathematical models

[0176] Taking the cost limitation into consideration and taking it as the constraint condition of the model, the spare parts system guarantee probability and utilization rate are taken as the optimization target to establish the optimal configuration model of onboard spare parts:

[0177]

[0178] Step B3: Multi-objective particle swarm solution integrating TOPSIS

[0179] (1) Multi-objective particle swarm solution process. First, the population initialization module randomly initializes the position and speed of the particles. The fitness value calculation module evaluates the fitness value of each particle according to the predetermined fitness value calculation formula. The particle optimal update module updates the individual optimal particle based on the position information of the new particle. The non-inferior solution set update module will filter out the non-inferior solution set in the current population based on the dominance relationship between the new particles. The particle speed and position update module updates the particle speed and position according to the individual optimal particle position and the global particle position;

[0180] (2) TOPSIS method for multi-attribute decision making. In the multi-objective particle swarm optimization problem, the algorithm ultimately generates a set of Pareto optimal solutions. In order to screen out the optimal compromise solution from this solution set, the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is introduced. By calculating the relative distance between each feasible solution and the positive ideal solution and the negative ideal solution, the relative closeness of each solution is evaluated. A higher relative closeness means that the solution is closer to the positive ideal solution and thus has better target performance. Figure 2 As shown, the specific steps of TOPSIS method are as follows.

[0181] 1) Since the life loss target and the economic cost target in the present invention have different dimensions, the z-score method is used to dimensionalize the data: Where: x ij is the jth target value of the i-th feasible solution, μ is the mean of the j-th target, δ is the standard deviation of the j-th target, r ij For x ij The value after dimensionalization;

[0182] 2) Based on the actual conditions and needs of the ship, decision makers first determine the weights of each goal.

[0183] 3) Determine the positive ideal solution S + (all objectives are optimal) and negative ideal solution S- (Each objective achieves the worst solution).

[0184] 4) Calculate the distance from each feasible solution to the positive ideal solution and the distance to the negative ideal solution Then the relative closeness of each feasible solution is calculated and these solutions are sorted. The sorting results show that the higher the relative closeness of the solution, the closer it is to the positive ideal solution. Therefore, the solution closest to the positive ideal solution is regarded as the optimal compromise solution.

[0185]

[0186] Where: is the optimal solution for the jth objective, is the worst solution for the jth objective, c i is the relative closeness of the i-th feasible solution.

[0187] The best compromise optimization scheme for spare parts configuration of non-low-demand ships is obtained.

[0188] Taking the ship spare parts parameter information as an example, based on the relevant data in Table 5, the parameters are set as follows: the population size is set to 50, the number of iterations is set to 200, and the initial inertia weight ω max =0.8,ω min =0.1, speed update parameters c1 and c2 are set to 1.5, and the failure rate coefficient k is set differently for different mission stages: k1=1 in the navigation stage, k2=1.1 in the mission execution stage, and k3=1.25 in the return stage.

[0189] Table 5 System component spare parts parameter information

[0190]

[0191]

[0192] The multi-objective particle swarm configuration optimization scheme is shown in Table 6. It can be concluded that the configuration optimization scheme when the target guarantee probability is the largest is the 8th row of Table 6, and the maximum guarantee probability is 0.9344; the configuration optimization scheme when the target utilization rate is the largest is the 2nd row of Table 6, and the maximum utilization rate is 0.6473. The simulation results of the compromise optimal solution are shown in Figure 3 , which is the second row of Table 6, the configuration optimization scheme is (5,1,3,2,2,3,1,3,4,3,1,3,1,4,3,2,3,1,1,4), the guarantee probability is 0.8789, and the utilization rate is 0.6473.

[0193] Table 6 Multi-objective particle swarm configuration optimization scheme

[0194]

[0195]

[0196] The step C comprises the following steps in sequence:

[0197] The simulation of ship spare parts support configuration adopts discrete event simulation technology and Monte Carlo simulation technology to predict the spare parts demand of ships during sea operations based on the constructed particle swarm model. The core steps are as follows:

[0198] (1) Set the simulation startup parameters, task time T, number of simulations N, and input the particle swarm spare parts optimization plan.

[0199] (2) Generate an exponentially distributed random number X based on the life distribution of each component and spare part i,t , if ∑X i,t <T means that the component fails at this moment and needs to be replaced. i,t ≥T, record the demand for each spare part at this time X={x i ,i=1,2,…,I}, and calculate the spare parts guarantee probability P at this time according to the actual spare parts configuration plan n (1≤n≤N).

[0200] (3) Determine whether the number of simulations has been reached and calculate the average value of the spare parts guarantee probability for N simulations The spare parts configuration optimization scheme obtained by simulation is compared and analyzed with the spare parts guarantee probability under the particle swarm optimization strategy to verify its feasibility and rationality.

[0201] The simulation times N=10000 are set, and the multi-objective particle swarm configuration optimization scheme in Table 6 is compared with the simulated spare parts configuration scheme. The results are shown in Table 7.

[0202] Table 7 Comparison of simulation guarantee probabilities

[0203]

[0204] According to the analysis of simulation results, it can be seen that the difference between the guarantee probability obtained by Monte Carlo simulation and the guarantee probability of the multi-objective particle swarm is relatively small, and the feasibility of the multi-objective particle swarm algorithm has been verified.

[0205] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0206] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A configuration optimization method based on low-demand and non-low-demand ship spare parts, characterized in that: include: The improved grey Markov prediction is used to solve the optimization model of spare parts configuration for ships with low demand. The multi-objective particle swarm optimization algorithm integrated with TOPSIS is used to solve the optimization model of spare parts configuration for ships with non-low demand. The optimal spare parts configuration list obtained by solving the multi-objective particle swarm configuration optimization model is simulated using Monte Carlo, and the configuration model is used for simulation experiments to verify the multi-objective particle swarm algorithm optimization model.

2. The method according to claim 1, characterized in that The improved grey Markov prediction method is used to solve the low-demand ship spare parts configuration optimization model, including: The GM(1,1) model is used to obtain the predicted values, and the predicted results are compared with the actual observed data to calculate the relative error index; According to the size of the relative error, different intervals are set as different state transfer intervals; A state transfer matrix is ​​constructed based on the state transfer interval, and the transition probability between states is calculated. The most likely state in the transition probability matrix is ​​used to estimate the future development trend.

3. The method according to claim 2, characterized in that The GM (1,1) model is used to obtain the predicted value, and the predicted result is compared with the actual observed data to calculate the relative error index, including: Depend on Set the time series of spare parts consumption data, where n is the length of the time series of the selected initial spare parts consumption data, x( 0 )(k) is the time series sub-item of spare parts consumption data; Depend on The original data is accumulated to generate a new sequence; x (1) Perform mean processing to generate a sequence Depend on Establish the grey differential equation, a is the development coefficient, which represents the changing trend of the cumulative sequence and the original sequence, and b is the grey action value; By using the least squares method, we can get [a,b] T =(B T B) -1 B T Y, where Solve the differential equation to get the demand forecast model for low-demand spare parts Depend on Restore the demand forecast value sequence of ship spare parts, where k = 1, 2, 3, ..., n; Depend on The residual of the predicted value of the grey prediction GM(1,1) model is obtained by Get the relative error of the predicted value of the grey prediction GM(1,1) model.

4. The method according to claim 3, characterized in that The state transition matrix is ​​constructed based on the state transition region, and the transition probability between each state is calculated, and the most likely state in the transition probability matrix is ​​used to estimate the future development trend, including: By S1<X min +f,X max -2f<S2<X max -f,X max -f<S3<X max The state transition interval is divided into three states, among which X max and X min Respectively represent the maximum and minimum values ​​of the relative error value, f = (X max -X min ) / 3, S1, S2 and S3 represent state 1, state 2 and state 3 respectively; Depend on Calculate the state transition probability p ij , where k represents the number of steps of state change, p ij Meaning state S i After k steps, we reach S j The probability of n i Indicates that S in the sample i The total number of occurrences, Indicates S i After k steps, we reach S j The number of Depend on Construct state transfer matrix; Depend on Correct the grey prediction value. express Prediction value of grey GM model, b k is the upper limit value, l k is the lower limit, y( 0 )(k+1) is the final value of the grey Markov model; Depend on An improved Markov prediction model is established, where S() is the state probability.

5. The method according to any one of claims 1 to 4, characterized in that: The multi-objective particle swarm optimization algorithm integrated with TOPSIS is used to solve the non-low demand ship spare parts configuration optimization model, including: The optimization problem of spare parts configuration for ships with non-low demand is described; Based on the described non-low demand ship spare parts configuration optimization problem, a non-low demand ship spare parts configuration optimization mathematical model is constructed; A multi-objective particle swarm optimization method integrating TOPSIS is used to solve the mathematical model of spare parts configuration optimization for ships with non-low demand.

6. The method according to claim 5, characterized in that The above-mentioned description of the optimization problem of spare parts configuration for non-low-demand ships includes: The spare parts of the ship are all field replaceable units (LRUs), and the failure rate of LRUs is λ i , and obeys exponential distribution, i is the spare part number on board, i=1,2,···,I, I is the number of spare parts; The guarantee probability of the i-th spare part is P i , the utilization rate is R i , the guarantee probability of spare parts for the entire ship system is P s , the utilization rate is R s ; The unit configuration cost of the i-th spare part is C i ; Maintenance activities on board are all breakdown maintenance, and preventive maintenance is not considered; The onboard inventory of the i-th spare part is S i ; The total constraint of the configuration scheme is C s .

7. The method according to claim 6, characterized in that The non-low demand ship spare parts configuration optimization mathematical model is constructed based on the described non-low demand ship spare parts configuration optimization problem, including: Depend on Get the spare parts utilization rate, when S i <S' i When the spare parts supply is insufficient, the available spare parts can reach the steady state. i -S' i The steady-state value of is the expected shortage of the i-th spare part Depend on The utilization rate of a single spare part when the supply is insufficient is obtained by Get system utilization; When S i >S' i When the spare parts are in sufficient supply, The spare parts utilization rate is obtained by Get the system utilization of spare parts; Depend on The model for the system utilization of spare parts is obtained by Get the guarantee probability P of the i-th spare part i ; Depend on The probability statistics of spare parts system support for ship equipment are obtained by The probability of spare parts system protection is obtained, where l increases from 0 to S i , so that P i ≥ the specified guarantee probability, the corresponding S i The value is the required spare parts demand, N i is the number of spare parts used in the machine, t i is the supply cycle of the i-th spare part, S i ' is the actual consumption of the i-th ship spare part, n i The number of times the i-th ship spare part is repaired or replaced due to failure during the warranty period; Depend on Determine the cost constraints by Establish an optimal configuration model for onboard spare parts.

8. The method according to claim 7, characterized in that The multi-objective particle swarm fusion TOPSIS is used to solve the non-low demand ship spare parts configuration optimization mathematical model, including: Multi-objective particle swarm optimization is used to generate a set of Pareto optimal solutions. The optimal compromise solution is screened out from the Pareto optimal solution set through TOPSIS, and the best compromise non-low-demand ship spare parts configuration optimization scheme is obtained.

9. The method according to claim 8, characterized in that The optimal spare parts configuration list obtained by solving the multi-objective particle swarm configuration optimization model is simulated by Monte Carlo, and the configuration model is used to perform simulation experiments to verify the multi-objective particle swarm algorithm optimization model, including: Set the simulation startup parameters, task time T, number of simulations N, and input the best compromise non-low demand ship spare parts configuration optimization plan; Generate exponentially distributed random numbers X based on the life distribution of each component and spare part i,t , if ∑X i,t <T, indicating that the component fails at this moment and needs to be replaced for repair; If ∑X i,t ≥T, record the demand for each spare part at this time X={x i ,i=1,2,…,I}, and calculate the spare parts guarantee probability P at this time according to the actual spare parts configuration plan n (1≤n≤N); Determine whether the number of simulations has been reached and calculate the average value of the probability of spare parts guarantee for N simulations The spare parts configuration optimization scheme obtained by simulation is compared and analyzed with the spare parts guarantee probability under the particle swarm optimization strategy to verify its feasibility and rationality.

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