A maintenance optimization method for a two-component series system considering shielding failure

Abstract

The present invention discloses a maintenance optimization method for a two-component series system considering shielding faults, and belongs to the technical field of preventive maintenance decision-making. The present invention comprises (1) establishing a mathematical model of a semi-Markov decision process: establishing a state space of the two-component series system, a maintenance action set, the cost of executing the corresponding maintenance action in each state, the probability of transferring to any state after executing the corresponding maintenance action in each state, and the expected stay time after executing the corresponding maintenance action in each state. (2) solving the optimal preventive replacement cycle and the corresponding optimal maintenance strategy of the two-component series system by numerical iteration algorithm and two-dimensional search algorithm. The present invention considers two maintenance methods when a shielding fault occurs in the system: replacing the failed component after inspection and directly performing corrective replacement on the entire system. When one component reaches the preventive replacement cycle, the other component is opportunistically maintained. The optimization goal is to minimize the long-term average maintenance cost, formulate the corresponding optimal maintenance strategy, and solve the optimal preventive replacement cycle by a two-dimensional search algorithm.

Description

Technical Field

[0001] The patent of this invention relates to the technical field of preventive maintenance decision-making, specifically a maintenance optimization method for a two-component series system considering shielding faults. Background Art

[0002] Preventive maintenance is an effective method to reduce industrial maintenance costs. It has been widely used in various industrial fields, such as manufacturing machinery parts, power machinery parts, critical infrastructure, and transportation networks. Formulating a reasonable preventive maintenance plan can strike a balance between reducing the risk of failure and saving maintenance resources, thereby improving the availability of mechanical parts and reducing maintenance costs. Among time-based maintenance strategies, the preventive replacement strategy based on the service life of mechanical parts is the most common strategy. When the service life reaches the preset threshold, the used parts are replaced by new parts. However, due to the high integration of new technologies, complex systems and equipment structures are becoming increasingly complex and sophisticated, functions are gradually integrated and intelligent, and performance and capacity parameters are constantly improving. Equipment maintenance decisions face unprecedented challenges. When a system fails, due to the complexity of the system, the specific faulty component cannot be directly observed. Professional equipment is required to diagnose the corresponding faulty component. This fault is called a shielding fault. In the preventive replacement cycle, it is necessary to formulate a corresponding maintenance strategy to deal with the maintenance problem of a two-component series system considering shielding faults. Due to modern modular design and manufacturing, when a shielding failure occurs in the system, maintenance personnel can use professional equipment to diagnose the corresponding faulty components and repair and replace the faulty components. At the same time, they can also directly repair and replace the entire system, saving the cost and time of using professional equipment for diagnosis. In the maintenance decision problem of multi-component systems, when there is a correlation between components, repairing one component will bring the opportunity to repair another component to reduce the system maintenance cost. Replacing one component provides an opportunity to replace another component. Replacing two components at the same time can save downtime or installation costs, which is called opportunistic maintenance. How to propose appropriate maintenance optimization methods and formulate maintenance strategies for two-component series systems considering shielding failures is a challenge facing contemporary society. Summary of the invention

[0003] In order to solve the problem of reducing the downtime cost caused by "under-maintenance" and the waste of resources caused by "over-maintenance", the present invention proposes a maintenance optimization method for a two-component series system considering shielding faults based on a semi-Markov decision process.

[0004] The technical solution of the present invention is: a maintenance optimization method for a two-component series system considering shielding failure, the method comprising:

[0005] Step 1: Establish a semi-Markov decision process model for maintenance optimization of a two-component series system considering shielding failures;

[0006] To establish a semi-Markov decision process model for maintenance optimization of a two-component series system considering shielding faults, five elements are required: state space, maintenance action set, cost of performing corresponding maintenance actions in each state, probability of transferring to any state after performing corresponding maintenance actions in each state, and expected stay time after performing corresponding maintenance actions in each state;

[0007] Step 1.1: The state space of the two-component series system;

[0008] Set T 1 , T 2 is the working age threshold of the two components, using (v 1 ,v 2 ) to represent the state of the system at each decision moment. 1 ∈[0,T 1 ],v 2 ∈[0,T 2 ], the corresponding discrete state is defined as iδ≤v 1 <(i+1)δ, jδ≤v 2 <(j+1)δ; space [0,T 1 ]×[0,T 2 ] is discretized into S = {0,δ,2δ,...,T 1 -δ,T 1}×{0,δ,2δ,...,T 2 -δ,T 2}, δ represents the step size, and S represents the system state space;

[0009] Step 1.2: Maintenance action set;

[0010] The maintenance actions that can be taken by the two-component series system at the decision time include: a=0 direct corrective replacement of the system, a=1 replacement of the failed component after inspection, a=2 preventive replacement of component 1, a=3 preventive replacement of component 2, and a=4 preventive replacement of the entire system. 1 ,v 2 ) Action Set for:

[0011]

[0012] The above formula is explained as follows: Once a shielding fault occurs in the system, action a=0 is performed to correct the entire system or a=1 is performed to replace the failed component after inspection; when the service life of component 1 reaches T, preventive replacement is performed. 1When the service life of component 2 reaches the preventive replacement time T, execute action a=2 to preventively replace component 1 or action a=4 to preventively replace the entire system. 2 When action a=3 is executed to preventively replace component 2 or action a=4 is executed to preventively replace the entire system, the service life of component 1 and component 2 reaches T at the same time. 1 ,T 2 , execute a=4 to preventively replace the entire system;

[0013] Step 1.3: The cost of performing the corresponding maintenance action in each state;

[0014] Set the system status to (v 1 ,v 2 ), there are two failure modes, namely, component 1 fails and component 2 is normal, and component 2 fails and component 1 is normal, and the specific failure mode is uncertain;

[0015] set up They are respectively at the current decision moment (v 1 ,v 2 ) after the corresponding maintenance action is performed, the service life of component 1 and component 2, It means that the system is at the decision time (v 1 ,v 2 ) is the system state after the corresponding maintenance action is performed. At the current decision moment (v 1 ,v 2 ), where v 1 <T 1 ,v 2 <T 2 , execute action a=0 to directly perform corrective replacement on the system. The system state after executing the action is When executing action a=1, check and replace the failed component, if at the current decision moment (v 1 ,v 2 ) After inspection, it is found that the system failure mode is that component 1 fails and component 2 is normal, so component 1 is correctively replaced. The system status after the action is executed is Another situation is that after inspection, it is found that the system failure mode is that component 2 fails and component 1 is normal. Component 2 is correctively replaced. At this time, the system status after the action is executed is

[0016] Assume that the system made the last decision at the time (w 1 ,w 2 ), where w 1 <T 1 ,w 2 <T 2 , the system state after executing action (a=0) and the current decision moment (v 1 ,v 2 ) is:

[0017]

[0018] The system is at the decision moment (v 1 ,v 2 ) The probability P that the failure mode is that component 1 fails and component 2 is normal when a shielding failure occurs 1 (v 1 ,v 2 ) is shown in the following formula:

[0019]

[0020] in, Indicates that the initial service life of component 1 is The probability density function of the time until the next failure occurs, Indicates that the initial service life of component 2 is The probability density function of the time until the next failure occurs is expressed as Denote the corresponding cumulative distribution function:

[0021]

[0022]

[0023] Among them, f 1 (t), f 2 (t) represents the probability density function of the Weibull distribution of component 1 and component 2 respectively, F 1 (t) and F 2 (t) represents the cumulative distribution function of the Weibull distribution obeyed by the life of component 1 and component 2 respectively;

[0024] The Weibull distribution is defined as follows:

[0025]

[0026] Where β is the shape parameter, β>0, η is the scale parameter, η>0;

[0027] The probability density function and failure rate function corresponding to the Weibull distribution are as follows:

[0028]

[0029]

[0030] The system is at the decision moment (v 1 ,v 2) When a shielding fault occurs, the probability that the failure mode is component 2 failure and component 1 normal is:

[0031] P 2 (v 1 ,v 2 )=1-P 1 (v 1 ,v 2 )

[0032] Combined with the failure mode probability of the system, when the decision time is (v 1 ,v 2 ), action a is executed, and the corresponding maintenance cost as follows:

[0033]

[0034] in, and denote the cost of performing corrective replacement on component 1, component 2, and the entire system, respectively; and are the costs of preventive replacement of component 1, component 2, and the entire system, respectively; C I represents the cost of performing the diagnosis;

[0035] Step 1.4: The probability of transferring to any state after performing the corresponding maintenance action in each state;

[0036] At the current decision moment (v 1 ,v 2 ), execute action a, and transfer to state (u 1 ,u 2 )The corresponding probability is:

[0037]

[0038] Step 1.5: Expected stay time after performing corresponding maintenance actions in each state;

[0039] It means that the system is at the decision time (v 1 ,v 2 ) Execute an action The corresponding expected stay time is

[0040]

[0041] Step 2: Solve the optimal preventive replacement cycle and the corresponding optimal maintenance strategy of the two-component series system through numerical iteration algorithm and two-dimensional search algorithm;

[0042] Step 2.1: Set the preventive replacement period of the two components of the system to (T 1 ,T 2 ) and maintenance costs C I ;

[0043] Step 2.2: Choose a constant τ that satisfies

[0044] Step 2.3: Initialize the system's initial strategy π and execute action a=0 in any state;

[0045] Step 2.4:

[0046] by is an iterative formula, and a numerical iterative algorithm is used to solve the preventive replacement cycle (T 1 ,T 2 ), and then use δ as the step size to find the optimal preventive replacement cycle through a two-dimensional search algorithm in:

[0047]

[0048] Among them, S represents the system state, π n is the optimal maintenance strategy for the two-component series system at the nth iteration, It means the nth iteration system at the decision time (v 1 ,v 2 ) executes the value function corresponding to the optimal action, (u 1 ,u 2 ) means that at the current decision moment (v 1 ,v 2 ) The next decision moment after executing action a;

[0049] The optimal preventive replacement cycle is solved through numerical iteration algorithm and two-dimensional search algorithm. Optimal preventive replacement cycle The corresponding minimum long-term average maintenance cost and the optimal strategy π * ; Methods such as Figure 1 ;

[0050] The beneficial effects of the present invention are:

[0051] This optimization method proposes a maintenance optimization method for a two-component series system considering shielding faults based on a semi-Markov decision process. When one component of the system reaches the preventive replacement cycle, the other component is opportunistically maintained, which increases the economic applicability of the method. At the same time, this method does not predetermine the structure of the maintenance strategy, which ensures the optimality of the final maintenance strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 To solve the optimal preventive maintenance strategy through numerical iteration algorithm and two-dimensional search algorithm And its corresponding minimum long-term average maintenance cost Flowchart of

[0053] Figure 2 is the long-term average maintenance cost C(T 1 ,T 2 ) and preventive replacement cycle (T 1 ,T 2 ) relationship diagram;

[0054] Figure 3 For optimal preventive replacement cycle The corresponding optimal maintenance strategy diagram. Specific implementation methods

[0055] In this section, we will conduct a numerical study on the solenoid valve to demonstrate our proposed model. The solenoid valve consists of two parts: the solenoid coil and the valve body. There are two failure modes of the solenoid valve, namely, the solenoid coil failure caused by electrophoresis or spikes and the valve body failure caused by debris accumulation. Both failure modes will cause the solenoid valve to fail. Two maintenance actions can be taken to eliminate the fault, namely, replacement of the faulty part after inspection and corrective replacement of the solenoid valve. In addition, when the actual service life of any part of the solenoid valve reaches the preventive replacement period, the part can be replaced preventively and the other part can be replaced opportunistically.

[0056] Assume that the life of the solenoid valve coil and the valve body of the solenoid valve obeys the Weibull distribution, which has been widely used to describe the life of mechanical systems and shows good performance. The shape parameters and scale parameters of the two components are m and 1 =3,η 1 =13,m 2 =2,η 2 = 8. Finally, we set the maintenance costs to C I =15.

[0057] Using the algorithm in step 4, set the initial preventive replacement cycle (T 1,T 2 )=(9,6), initialize the initial maintenance strategy π of the mechanical parts. Through the numerical iteration algorithm and the two-dimensional search algorithm, the long-term average maintenance cost C(T 1 ,T 2 ) and preventive maintenance cycle (T 1 ,T 2 ) Figure 2 As shown. Figure 2 The optimal preventive replacement cycle is The corresponding minimum long-term average maintenance cost

[0058] In addition, within a preventive replacement cycle, the optimal maintenance strategy for a two-component series system is Figure 3 When the service life of the two components is relatively young, the system will perform an action check and then replace them when a shielding fault occurs. When the service life of the two components is relatively old, a corrective replacement will be directly performed on the system when a shielding fault occurs. When the service life of component 1 reaches the preventive replacement T 1 When the service life of component 2 is shorter, only component 1 will be replaced preventively. If the service life of component 2 is longer, component 2 will be replaced preventively when component 1 is replaced. Similarly, when the service life of component 2 reaches the preventive replacement time T 2 When the service life of component 1 is young, only component 2 will be replaced preventively. If the service life of component 1 is old, the opportunity of replacing component 2 will be used to replace component 1 preventively.

Claims

1. A maintenance optimization method for a two-component series system considering shielding failures, characterized in that: A mathematical model of a semi-Markov decision process for a maintenance optimization method of a two-component series system considering shielding failures is established to solve the optimal preventive replacement cycle of the two-component series system and the corresponding optimal maintenance strategy, including the following steps; Step 1: Establish a semi-Markov decision process model for maintenance optimization of a two-component series system considering shielding failures; To establish a semi-Markov decision process model for maintenance optimization of a two-component series system considering shielding faults, five elements are required: state space, maintenance action set, cost of performing corresponding maintenance actions in each state, probability of transferring to any state after performing corresponding maintenance actions in each state, and expected stay time after performing corresponding maintenance actions in each state; Step 1.1: The state space of the two-component series system; Set T1 and T2 as the service life thresholds of the two components, use (v1, v2) to represent the state of the system at each decision moment, for any v1∈[0,T1], v2∈[0,T2], the corresponding discrete state is defined as iδ≤v1<(i+1)δ, jδ≤v2<(j+1)δ; the space [0,T1]×[0,T2] is discretized into S={0,δ,2δ,...,T1-δ,T1}×{0,δ,2δ,...,T2-δ,T2}, δ represents the step size, and S represents the system state space; Step 1.2: Maintenance action set; The maintenance actions that can be taken by the two-component series system at the decision time include: a = 0 to perform corrective replacement on the system, a = 1 to replace the failed component after inspection, a = 2 to perform preventive replacement on component 1, a = 3 to perform preventive replacement on component 2, and a = 4 to perform preventive replacement on the entire system; at the decision time (v1, v2), the action set for: The above formula is explained as follows: once a shielding fault occurs in the system, perform action a=0 to perform corrective replacement on the entire system or a=1 to replace the failed component after inspection; when the service life of component 1 reaches the preventive replacement T1, perform action a=2 to perform preventive replacement on component 1 or action a=4 to perform preventive replacement on the entire system; when the service life of component 2 reaches the preventive replacement T2, perform action a=3 to perform preventive replacement on component 2 or action a=4 to perform preventive replacement on the entire system; when the service life of component 1 and component 2 reaches T1 and T2 at the same time, perform action a=4 to perform preventive replacement on the entire system; Step 1.3: The cost of performing the corresponding maintenance action in each state; When the decision time is (v1, v2), action a is executed, and the corresponding maintenance cost is as follows: in, and denote the cost of performing corrective replacement on component 1, component 2, and the entire system, respectively; and are the costs of preventive replacement of component 1, component 2, and the entire system, respectively; C I represents the cost of performing the diagnosis, P1(v1,v2) represents the probability that the failure mode is component 1 failure and component 2 normal when a shielding fault occurs in the system at the decision time (v1,v2); Step 1.4: The probability of transferring to any state after performing the corresponding maintenance action in each state; At the current decision moment (v1, v2), the corresponding probability of executing action a and transferring to state (u1, u2) is: Step 1.5: Expected stay time after performing corresponding maintenance actions in each state; Indicates that the system performs an action at the decision time (v1, v2) The corresponding expected stay time is Step 2: Solve the optimal preventive replacement cycle and the corresponding optimal maintenance strategy of the two-component series system through numerical iteration algorithm and two-dimensional search algorithm; Step 2.1: Set the preventive replacement period of the two components of the system to (T1, T2), and the maintenance cost C I ; Step 2.2: Choose a constant τ that satisfies Step 2.3: Initialize the system's initial strategy π and execute action a=0 in any state; Step 2.4: by The optimal maintenance strategy within the preventive replacement cycle (T1, T2) is solved by a numerical iterative algorithm, and then the optimal preventive replacement cycle is sought through a two-dimensional search algorithm with a step size of δ. in: Among them, S represents the system state, π n is the optimal maintenance strategy for the two-component series system at the nth iteration, represents the value function corresponding to the optimal action executed by the system at the decision time (v1, v2) in the nth iteration, (u1, u2) represents the next decision time after the maintenance action a is executed at the current decision time (v1, v2); The optimal preventive replacement cycle is solved through numerical iteration algorithm and two-dimensional search algorithm. Optimal preventive replacement cycle The corresponding minimum long-term average maintenance cost and the optimal strategy π * .

2. A maintenance optimization method for a two-component series system considering shielding failures as described in claim 1, characterized in that: In step 1.3, the probabilities of different failure modes when a shielding failure occurs in the system at the decision moment are derived as follows; When a shielding failure occurs in the system, the state is set to (v1, v2). There are two failure modes: component 1 fails and component 2 is normal, and component 2 fails and component 1 is normal. The specific failure mode is uncertain. Let be the ages of Component 1 and Component 2 respectively after performing the corresponding maintenance actions at the current decision-making moment (v1, v2). Then represents the system state after performing the corresponding maintenance actions at the decision-making moment (v1, v2); at the current decision-making moment (v1, v2), where v1 < T1 and v2 < T2, performing action a = 0 directly performs a corrective replacement on the system, and the system state after the action is When performing action a = 1 to check and replace the failed component, if it is found after inspection at the current decision-making moment (v1, v2) that the system failure mode is that Component 1 fails and Component 2 is normal, then a corrective replacement is performed on Component 1, and the system state after the action is Another situation is that it is found after inspection that the system failure mode is that Component 2 fails and Component 1 is normal, and a corrective replacement is performed on Component 2. At this time, the system state after the action is The system state after the setting system executed the action (a = 0) at the previous decision-making moment (w1, w2), where w1 < T1 and w2 < T2 The relationship with the current decision-making moment (v1, v2) is as follows: When a shielding fault occurs in the system at the decision time (v1, v2), the probability P1(v1, v2) that the failure mode is component 1 failure and component 2 normal is as follows: in, Indicates that the initial service life of component 1 is The probability density function of the time until the next failure occurs, Indicates that the initial service life of component 2 is The probability density function of the time until the next failure occurs is expressed as Denote the corresponding cumulative distribution function: Where, f1(t) and f2(t) represent the probability density functions of the Weibull distribution obeyed by the life of component 1 and component 2, respectively; F1(t) and F2(t) represent the cumulative distribution functions of the Weibull distribution obeyed by the life of component 1 and component 2, respectively; When a shielding fault occurs in the system at time (v1, v2), the probability that the failure mode is component 2 failure and component 1 normal is: P2(v1,v2)=1-P1(v1,v2).

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