Optimization method of two-stage condition-based maintenance policy for two-stage deteriorating equipment
By employing a two-stage condition-based maintenance strategy and a particle swarm optimization algorithm, the detection interval and preventive maintenance threshold of the equipment are optimized, thus solving the maintenance cost problem in the two-stage degradation process of the equipment and achieving cost savings and improved reliability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- JILIN UNIVERSITY
- Filing Date
- 2023-03-29
- Publication Date
- 2026-04-28
AI Technical Summary
Existing technologies are insufficient to effectively address the maintenance costs of equipment during the two-stage degradation process, and traditional scheduled maintenance strategies may lead to resource waste and unnecessary downtime.
A two-stage condition-based maintenance strategy is adopted, which combines a two-stage degradation process model and a particle swarm optimization algorithm to optimize the detection interval and preventive maintenance threshold, thereby reducing long-term operating costs.
By optimizing inspection intervals and preventative maintenance thresholds, the long-term operating costs of the equipment can be significantly reduced, while improving its availability and reliability.
Smart Images
Figure CN116305996B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of equipment condition-based maintenance technology, specifically relating to an optimization method for a two-stage condition-based maintenance strategy for equipment experiencing two-stage degradation. Background Technology
[0002] During equipment operation, failures can lead to high costs and potentially dangerous consequences. Preventative maintenance, performed before failures occur, can reduce the likelihood of unexpected breakdowns and avoid losses. Typically, equipment undergoes a series of degradation states before ultimately failing. Monitoring equipment degradation and performing timely repairs can reduce maintenance costs, downtime, and eliminate safety hazards. This approach, distinct from time-based scheduled maintenance, is called condition-based maintenance. Condition-based maintenance incorporates equipment status data into maintenance decisions, making them more flexible and accurate. Several research examples demonstrate that condition-based maintenance strategies are more economical than time-based maintenance.
[0003] During equipment operation, characteristic quantities representing equipment performance can be used to reflect the equipment's degradation status. Over time, degradation gradually increases, eventually leading to equipment failure. By analyzing the degradation mechanism and extracting and analyzing degradation data, mathematical models can be established to obtain the temporal distribution of degradation failure. Typically, degradation process models employ stochastic processes such as the Wiener process or the Gamma process, and the failure time distribution can be derived based on a given failure threshold. For the Wiener process, the failure time distribution follows an inverse Gaussian (IG) distribution.
[0004] Some equipment exhibits a two-stage degradation process. Once degradation reaches a certain level, the degradation mechanism changes, altering the degradation rate. Using a two-stage Wiener process model to describe this two-stage degradation process yields the equipment lifespan distribution. Based on this distribution, developing appropriate two-stage condition-based maintenance strategies can reduce costs.
[0005] Typical condition-based maintenance strategies set a preventative maintenance threshold. Once the detected degradation level reaches the threshold, maintenance measures are taken. The basic idea behind condition-based maintenance is to regularly monitor the equipment and adjust the preventative maintenance threshold and monitoring intervals to achieve the lowest possible maintenance costs. In summary, condition-based maintenance is a more flexible model and has proven its superior cost-saving advantages. In the case of two-stage equipment degradation, the appropriate use of a two-stage condition-based maintenance strategy can save costs and achieve better results. Summary of the Invention
[0006] In response to the two-stage degradation phenomenon that occurs during equipment operation, this invention provides a two-stage condition-based maintenance strategy adapted to it, in order to save costs.
[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:
[0008] A method for optimizing a two-stage condition-based maintenance strategy for components experiencing two-stage degradation includes the following steps:
[0009] Step 1: Use a two-stage degradation process model to describe the two-stage degradation process of the equipment;
[0010] Step 2: Determine the implementation method for the equipment condition-based maintenance strategy;
[0011] Step 3: Establish a condition-based maintenance strategy optimization model based on the average cost rate under long-term equipment operation.
[0012] Furthermore, the two-stage degradation process model described in step one is specifically as follows:
[0013] Let X = {X(t): t ≥ 0} represent the degradation process, X P This represents a fixed turning point threshold; once the degradation reaches X... P If the degradation exceeds the failure threshold D, the device will fail.
[0014] Assuming X(0) = 0, the two-stage degradation process, taking the Wiener process as an example, is represented as follows:
[0015]
[0016] Where t P It is the first time that X(t) reaches X P The time, μ1, μ2 are the drift coefficients of the two stages, σ1, σ2 are the diffusion coefficients of the two stages, and B(t)~N(0,t) is the standard Brownian motion;
[0017] In each stage, the first arrival time for a fixed increment Δx follows an inverse Gaussian distribution, i.e.:
[0018]
[0019] Calculating the time when the degradation first reaches the degradation threshold D requires the use of double integrals; therefore, the reliability calculation formula for the device is:
[0020]
[0021] Furthermore, the equipment condition-based maintenance strategy implementation method described in step two specifically includes:
[0022] The equipment is subjected to a two-stage inspection, with inspection intervals of I1 and I2. Inspection is performed at intervals of I1, and when the detected equipment degradation X(t) > X... P, the detection is carried out at an interval of I2. When the detected degradation amount is greater than the preventive maintenance threshold and less than the failure threshold τ ≤ X(t) < D, preventive replacement of the equipment is performed. When the detected degradation amount is greater than the failure threshold X(t) ≥ D, corrective replacement of the equipment is required; after replacement, the equipment returns to a brand-new state and the degradation amount is reset to zero.
[0023] Furthermore, the calculation method of the average cost rate of the equipment under long-term operation in step three is as follows:
[0024] The costs involved in calculating the average cost rate of the equipment under long-term operation include the detection cost, preventive replacement cost and corrective replacement cost. Let the single detection cost, preventive replacement cost and corrective replacement cost be C I , C P , C C ; The decision variables to be determined in the strategy optimization process are the two-stage detection intervals I1, I2 and the preventive maintenance threshold τ;
[0025] According to the renewal process, the average cost rate of the equipment under long-term operation is calculated using the expected cost within one cycle. The formula for the average cost rate of the equipment under long-term operation is as follows
[0026]
[0027] where C(t) is all the costs generated at time t, C T is the cost within the cycle, T P 0>is the cycle length; P1, P2 are the probabilities that the renewal cycle ends with preventive replacement or corrective replacement; N is the number of detections within the cycle;
[0028] The calculation formulas for each item involved in formula (4) are as follows:
[0029]
[0030]
[0031]
[0032]
[0033] where represents rounding up a to the nearest integer;
[0034] Furthermore, for the calculation method of the average cost rate of the equipment under long-term operation in step three, an adaptation value simplification calculation method is proposed, and the simplified calculation formula is as follows:
[0035]
[0036] The calculation formulas for each item involved in formula (9) are as follows:
[0037]
[0038]
[0039]
[0040]
[0041] Where M is a sufficiently large positive integer chosen according to the required computational precision; u1=δ,u i+1 -u i =Δu, δ, Δu is a sufficiently small number chosen based on the calculation precision; This means rounding up 'a'.
[0042] Furthermore, based on the condition-based maintenance strategy optimization model mentioned in step three, the availability calculation formula for this maintenance strategy is as follows:
[0043]
[0044] in
[0045]
[0046] A two-stage condition-based maintenance strategy optimization method further includes step four: using particle swarm optimization algorithm to solve for the condition-based maintenance strategy implementation scheme; and obtaining the final condition-based maintenance strategy based on the optimal values of I1, I2, τ obtained from the solution.
[0047] Furthermore, the process of the particle swarm optimization algorithm includes: (1) setting the particle swarm optimization algorithm parameters; (2) initializing the position and velocity variables of the particle swarm; (3) particle migration; (4) calculating the fitness value; and (5) determining the stopping condition and outputting the optimal solution or continuing the loop calculation.
[0048] Compared with the prior art, the beneficial effects of the present invention are:
[0049] This invention proposes a two-stage inspection maintenance strategy to adapt to situations where equipment exhibits two-stage degradation, resulting in cost savings compared to a single inspection cycle. The model solved using a particle swarm optimization algorithm demonstrates good stability. Attached Figure Description
[0050] Figure 1 This is a flowchart of the two-stage condition-based maintenance strategy optimization method for two-stage degraded equipment as described in this invention;
[0051] Figure 2 This is a schematic diagram of the two-stage degradation process described in this invention, using the Wiener process as an example;
[0052] Figure 3 This is a schematic diagram of the two-stage condition-based maintenance strategy for two-stage degradation equipment according to the present invention;
[0053] Figure 4 This is a flowchart of the particle swarm optimization algorithm described in this invention;
[0054] Figure 5 This is a graph showing the convergence curve of the fitness values obtained using the particle swarm optimization algorithm. Detailed Implementation
[0055] The present invention will now be described in detail with reference to the accompanying drawings.
[0056] The two-stage condition-based maintenance strategy for two-stage degradation includes the following steps:
[0057] Step 1: Use a two-stage degradation process model to describe the two-stage degradation process of the equipment;
[0058] Step 2: Determine the implementation method for the equipment condition-based maintenance strategy;
[0059] Step 3: Establish a condition-based maintenance strategy optimization model based on the average cost rate under long-term equipment operation;
[0060] Step 4: Use the particle swarm optimization algorithm to solve the problem and obtain the implementation plan for the condition-based maintenance strategy.
[0061] The specific method for step one is as follows:
[0062] Let X = {X(t): t ≥ 0} represent the degradation process, X P This represents a fixed turning point threshold; once the degradation reaches X... P If the degradation exceeds the failure threshold D, the device fails.
[0063] Assuming X(0) = 0, the two-stage degradation process, taking the Wiener process as an example, is represented as follows:
[0064]
[0065] Where t P It is the first time that X(t) reaches X P The time is given, μ1 and μ2 are the drift coefficients of the two stages, σ1 and σ2 are the diffusion coefficients of the two stages, and B(t)~N(0,t) is the standard Brownian motion.
[0066] In each stage, the first arrival time for a fixed increment Δx follows an inverse Gaussian distribution, i.e.:
[0067]
[0068] To calculate the time when the degradation amount first reaches the degradation threshold D, i.e., the equipment failure time, a double integral is required. Then the reliability calculation formula for the equipment is:
[0069]
[0070] The specific method of Step 2 is as follows:
[0071] The equipment is subjected to two-stage detection, and the detection intervals for the two stages are I1 and I2 respectively. Detection is carried out at an interval of I1. When it is detected that the equipment degradation amount X(t) > X P , then detection is carried out at an interval of I2. When it is detected that the degradation amount is greater than the preventive maintenance threshold and less than the failure threshold τ ≤ X(t) < D, preventive replacement of the equipment is carried out. When it is detected that the degradation amount is greater than the failure threshold X(t) ≥ D, corrective replacement of the equipment is required. After replacement, it returns to a brand-new state and the degradation amount is reset to zero.
[0072] The specific method of Step 3 is as follows:
[0073] The costs involved in the above process include detection cost, preventive replacement cost, and corrective replacement cost. Let the single detection cost, preventive replacement cost, and corrective replacement cost be C I , C P , C C . The decision variables to be determined in the strategy optimization process are the two-stage detection intervals I1, I2, and the preventive maintenance threshold τ.
[0074] Based on the renewal process, an opportunistic maintenance strategy optimization model is constructed, and the above decision variables are solved with the long-term operating cost rate as the optimization goal.
[0075] The specific method of Step 4 is as follows:
[0076] The particle swarm optimization method is used to solve the opportunistic maintenance strategy optimization model to obtain the corresponding decision variables that minimize the long-term operating cost rate, i.e., the two-stage detection intervals I1, I2, and the preventive maintenance threshold τ, thereby determining the final maintenance strategy. The process of the particle swarm optimization algorithm includes: (1) setting the parameters of the particle swarm optimization algorithm; (2) initializing the position variables and velocity variables of the particle swarm; (3) particle migration; (4) calculating the fitness value; (5) judging the stop condition and outputting the optimal solution or continuing the loop calculation.
[0077] In step four, an appropriate optimization algorithm is required to solve the problem (the solution method is given by taking particle swarm optimization algorithm as an example in this invention). Based on the optimal values of I1, I2, and τ obtained by the solution, the final condition-based maintenance strategy is obtained. The specific implementation method is described in step two.
[0078] See Figure 1 The two-stage condition-based maintenance strategy optimization method of the present invention includes the following steps: using a two-stage degradation process model to describe the two-stage degradation process of the equipment; determining the implementation method of the condition-based maintenance strategy; establishing a strategy optimization model based on the average cost rate under long-term operation of the equipment; and using the particle swarm optimization algorithm to solve the problem and obtain the implementation scheme of the condition-based maintenance strategy.
[0079] I. Two-stage degradation process model
[0080] Let X = {X(t): t ≥ 0} represent the degradation process, X P This represents a fixed turning point threshold; once the degradation reaches X... P If the degradation exceeds the failure threshold D, the device fails. The degradation process is as follows: Figure 2 As shown.
[0081] Assuming X(0) = 0, the two-stage degradation process, taking the Wiener process as an example, is represented as follows:
[0082]
[0083] Where t P It is the first time that X(t) reaches X P The time is given, μ1 and μ2 are the drift coefficients of the two stages, σ1 and σ2 are the diffusion coefficients of the two stages, and B(t)~N(0,t) is the standard Brownian motion.
[0084] In each stage, the first arrival time for a fixed increment Δx follows an inverse Gaussian distribution, i.e.:
[0085]
[0086] Calculating the time when the degradation first reaches the degradation threshold D requires the use of double integrals; therefore, the reliability calculation formula for the device is:
[0087]
[0088] II. Two-stage condition-based maintenance strategy
[0089] The equipment is tested in two stages, with intervals I1 and I2. Testing is performed at interval I1. When the equipment degradation X(t) > X is detected... P, the detection is carried out at an interval of I2. When the detected degradation amount is greater than the preventive maintenance threshold and less than the failure threshold τ ≤ X(t) < D, preventive replacement of the equipment is carried out. When the detected degradation amount is greater than the failure threshold X(t) ≥ D, corrective replacement of the equipment is required. After replacement, the equipment returns to a brand-new state and the degradation amount returns to zero. The implementation method of the two-stage condition-based maintenance strategy is as Figure 3 shown.
[0090] III. Condition-based Maintenance Strategy Optimization Model
[0091] The costs involved in the above process include detection cost, preventive replacement cost and corrective replacement cost. Let the single detection cost, preventive replacement cost and corrective replacement cost be C I , C P , C C respectively. The decision variables to be determined in the strategy optimization process are the detection intervals I1, I2 of the two stages and the preventive maintenance threshold τ.
[0092] According to the renewal process, the long-term operating cost rate can be calculated by the expected cost within one cycle. The long-term operating cost rate formula is as follows
[0093]
[0094] where C(t) is all the costs generated at time t, C T is the cost within the cycle, T L is the cycle length. P1 and P2 are the probabilities that the renewal cycle ends with preventive replacement or corrective replacement. N is the number of detections within the cycle.
[0095] The calculation formulas for each item involved in formula (4) are as follows:
[0096]
[0097] The first term in formula (5) represents the probability of preventive replacement at time N1I1, and the second term represents the probability of preventive replacement at time N1I1 + n2I2 (n2 = 1, 2,...); N1 represents the number of detections with a detection interval of I1, represents rounding up a to the nearest integer. is equivalent to {X(N1I1+(n2 - 1)I2) < τ, τ ≤ X(N1I1 + n2I2) < D}; u + y represents the corresponding time when the degradation amount reaches the preventive maintenance threshold τ, and u + y + z represents the corresponding time when the degradation amount reaches the failure threshold D.
[0098]
[0099] In formula (6), the first term represents the probability of performing a corrective replacement at time N1I1, and the second term represents the probability of performing a corrective replacement at time N1I1+n2I2 (n2=1,2,…). Equivalent to {X(N1I1+(n2-1)I2)<τ,X(N1I1+n2I2)≥D}; v=y+z.
[0100]
[0101]
[0102] As a preferred embodiment, the present invention proposes a simplified method for calculating fitness values.
[0103] The simplified calculation formula is as follows:
[0104]
[0105] The calculation formulas for each item involved in formula (9) are as follows:
[0106]
[0107]
[0108]
[0109]
[0110] Where M is a sufficiently large positive integer chosen according to the required computational precision. u1=δ,u i+1 -u i =Δu, δ, Δu is a sufficiently small number chosen based on the calculation precision; Indicates t P The value is u i The number of tests in the first phase of the test. This means rounding up 'a'. Indicates t P The value is u i The corresponding integration interval at time.
[0111] This invention does not use availability as the optimization objective, but equipment availability under different maintenance strategies can serve as an indicator of the effectiveness of those strategies. According to the maintenance strategy model mentioned in this invention, the availability calculation formula is as follows:
[0112]
[0113] in
[0114]
[0115] IV. Model Solving Method and Condition-Based Maintenance Strategy Implementation Plan Taking Particle Swarm Optimization Algorithm as an Example
[0116] The solution process of the particle swarm optimization algorithm is as follows: Figure 4 As shown. The textual description is as follows:
[0117] (1) Set the parameters of the particle swarm optimization algorithm: lower limit of variables L and upper limit of variables U; population size z; learning factors c1, c2; convergence decision algebra H; iteration accuracy ξ.
[0118] (2) Randomly obtain the position x and velocity v of the initial search point, and calculate the fitness value of the initial search point to initialize the optimal position of the individual and the optimal position of the group.
[0119] (3) Particle migration. Update the particle position according to formula (17).
[0120]
[0121] in, Let i be the position of the i-th particle in the t-th iteration;
[0122] Let be the velocity of the i-th particle in the t-th iteration;
[0123] w represents the inertia weight;
[0124] c1 and c2 are learning factors;
[0125] r1 and r2 are random numbers in the interval [0, 1].
[0126] The optimal position is reached by the i-th particle in the t-th iteration;
[0127] The optimal position for all particles in the t-th iteration;
[0128] (4) Calculate the fitness value of the updated particles and update the individual best position and the global best position.
[0129] (5) Determine if the stopping condition has been met. If the current iteration count reaches the preset maximum number, or the fitness value of consecutive H iterations is less than the predetermined convergence accuracy ξ, then stop the iteration and output the optimal solution; otherwise, go to step (2).
[0130] The final condition-based maintenance strategy is obtained based on the optimal values of I1, I2, and τ obtained from the solution. The specific implementation method is described in step two.
[0131] Example
[0132] Adopt the two-phase degradation data of the hydraulic coupler mentioned by Yan Weian et al. in the literature (Real-time reliability evaluation of two-phase Wiener degradation process, published in Communications in Statistics - Theory and Methods in 2016) to illustrate the specific implementation method of this patent.
[0133] First, use the two-phase degradation model to describe the degradation process, with parameters μ1 = 0.2112, σ1 2 = 0.2084, μ2 = 0.009, σ2 2 = 0.0009, D = 29.5mm, X P = 15.3mm. Determine the maintenance strategy. The maintenance cost parameters are set as C I = 10, C P = 400, C c = 1000. After establishing the maintenance model, use the particle swarm optimization algorithm to solve it. Observe the results after running the particle swarm optimization algorithm multiple times. In this example, it is run 5 times. The results of each run are shown in Table 1. The fitness value convergence curves in each run are shown in Figure 5 . Select the run result with the smallest optimal value among multiple runs to guide the maintenance strategy. If the optimal value results of multiple runs are the same, choose any one of the run results. In this example, the first run result can be selected. That is, in the first stage of detection, the detection interval I1 is set to 1342.5. When the detected device degradation amount X(t)>X P , then detect at an interval of I2. The second-stage detection interval I2 is set to 118.1. When the detected degradation amount is greater than the preventive maintenance threshold and less than the failure threshold τ ≤ X(t) < D, perform preventive replacement on the device. When the detected degradation amount is greater than the failure threshold X(t) ≥ D, corrective replacement of the device is required. The average cost per unit time using this maintenance strategy is 0.2825, and the average availability is 0.9998.
[0134] In this example, compared with the maintenance strategy that only adopts a single fixed detection cycle, the method proposed in this patent can save 10% of the cost and improve the availability by 0.02%.
[0135] Table 1 Algorithm operation result table
[0136]
[0137] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be included within the scope of protection of the present invention. Furthermore, all content not described in detail in this specification is prior art known to those skilled in the art.
Claims
1. A method for optimizing a two-stage condition-based maintenance strategy for components experiencing two-stage degradation, characterized in that, Includes the following steps: Step 1: Use a two-stage degradation process model to describe the two-stage degradation process of the equipment; Step 2: Determine the implementation method for the equipment condition-based maintenance strategy; Step 3: Establish a condition-based maintenance strategy optimization model based on the average cost rate under long-term equipment operation; The two-stage degradation process model described in step one is as follows: make Indicates the degradation process. This represents a fixed turning point threshold; once the degradation reaches a certain level... If the degradation exceeds the failure threshold, the degradation will proceed to the second stage; if the degradation exceeds the failure threshold, the degradation will proceed to the second stage. If so, the equipment will fail; Assumption The two-stage degradation process, taking the Wiener process as an example, is represented as follows: in yes First time reaching Time, These are the drift coefficients for the two stages, respectively. These are the diffusion coefficients for the two stages, respectively. It is standard Brownian motion; In each stage, for a fixed increment The first arrival time follows an inverse Gaussian distribution, that is: The calculation shows that the degradation amount first reaches the degradation threshold. Since the time requires the use of double integrals, the reliability calculation formula for the equipment is:
2. The two-stage condition-based maintenance strategy optimization method according to claim 1, characterized in that: The equipment condition-based maintenance strategy implementation method described in step two specifically includes: The equipment undergoes a two-stage inspection, with the inspection intervals for the two stages being as follows: ;by Detection is performed at intervals, and when equipment degradation is detected... Then Testing is performed at intervals, and when the detected degradation is greater than the preventive maintenance threshold but less than the failure threshold... When necessary, preventative replacement of the equipment is performed, and when the detected degradation exceeds the failure threshold, the equipment is replaced. If this happens, the equipment needs to be correctively replaced; after replacement, it will be restored to a brand-new state, and the degradation will be reduced to zero.
3. The two-stage condition-based maintenance strategy optimization method according to claim 1, characterized in that: The method for calculating the average cost rate of the equipment under long-term operation as described in step three is as follows: The average cost rate (ACR) of the calculated equipment over long-term operation includes inspection costs, preventative replacement costs, and corrective replacement costs. Let the cost per inspection, preventative replacement cost, and corrective replacement cost be... The decision variable that needs to be determined during the strategy optimization process is the two-stage detection interval. With preventive maintenance threshold ; Based on the update process, the average cost rate under long-term equipment operation is calculated using the expected cost over one period. The formula for the average cost rate under long-term equipment operation is as follows: in for All costs already incurred at that moment, Costs within the period, The period length; , The probability that the update cycle ends with preventative or corrective replacement; The number of tests within the period; The calculation formulas for each item involved in formula (4) are as follows: in , Indicates to Round up; ; .
4. The two-stage condition-based maintenance strategy optimization method according to claim 3, characterized in that: The method for calculating the average cost rate of equipment under long-term operation described in step three is supplemented by a simplified calculation method based on the fitness value. The simplified calculation formula is as follows: The calculation formulas for each item involved in formula (9) are as follows: Where M is a sufficiently large positive integer chosen according to the required computational precision; , A sufficiently small number chosen based on the required calculation precision; , Indicates to Round up. , .
5. The two-stage condition-based maintenance strategy optimization method according to claim 1, characterized in that: Based on the condition-based maintenance strategy optimization model mentioned in step three, the availability calculation formula for this maintenance strategy is as follows: in 6. The two-stage condition-based maintenance strategy optimization method according to claim 2, characterized in that: It also includes step four, using the particle swarm optimization algorithm to solve for the condition-based maintenance strategy implementation plan; based on the solution... The optimal value leads to the final condition-based maintenance strategy.
7. The two-stage condition-based maintenance strategy optimization method according to claim 6, characterized in that: The process of particle swarm optimization algorithm includes: (1) setting particle swarm optimization algorithm parameters; (2) initializing the position and velocity variables of the particle swarm; (3) particle migration; (4) calculating fitness value; (5) determining the stopping condition, outputting the optimal solution or continuing the loop calculation.