CN109636072B - Elevator door system preventive maintenance decision multi-objective optimization method based on non-inferior sorting genetic algorithm - Google Patents
Elevator door system preventive maintenance decision multi-objective optimization method based on non-inferior sorting genetic algorithm Download PDFInfo
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Abstract
The invention discloses a multi-objective optimization method for preventive maintenance decision of an elevator door system based on a non-inferior sorting genetic algorithm, which comprises the following steps: 1) Carrying out historical fault record collection and statistics on key components of the elevator door system, and obtaining two-parameter Weibull distribution shape parameters and scale parameters of service life of the key components of the elevator door system by using a method of best linear unbiased estimation; 2) Calculating the fault rate function of key components of the elevator door system and taking the maximum value to obtain the fault rate function of the door system; 3) Constructing an average maintenance rate objective function in a service life period of the door system and an average reliability objective function in a single preventive maintenance period, and constructing a preventive maintenance decision optimization model of the door system; 4) And carrying out multi-objective optimization solution on the door system preventive maintenance decision optimization model by adopting a non-inferior sorting genetic algorithm to obtain optimal preventive maintenance times and preventive maintenance period length.
Description
Technical Field
The invention relates to the technical field of equipment preventive maintenance strategy research, in particular to a multi-objective optimization method for preventive maintenance decision of an elevator door system based on a non-inferior sorting genetic algorithm.
Background
Along with the annual increase of the elevator preservation amount in China, the requirements on the safety and reliability of elevator operation are higher and higher, and the corresponding maintenance requirements are higher and higher. The elevator door system is used as an important component of an elevator and has the characteristics of frequent contact with passengers, complex working environment and high failure occurrence. And once the door system fails, the elevator is stopped due to light weight, and the elevator falling event is caused due to heavy weight, so that serious harm is brought to the life and property safety of passengers. How to improve the operation reliability of the elevator door system and reduce the failure rate through a scientific maintenance strategy while maintaining the cost as low as possible, and has great significance for ensuring the high-quality operation of the elevator.
Aiming at the elevator door system, the traditional post-maintenance strategy can not ensure the running reliability of equipment, and has high maintenance cost and low maintenance efficiency. While the current regular preventive maintenance strategies generally adopted can reduce the failure rate of equipment to a certain extent, the maintenance period length has a certain blindness, so that the problem of excessive maintenance or insufficient maintenance is caused. In the research of the existing electromechanical equipment preventive maintenance strategy, firstly, the fault rate of the equipment needs to be well fitted, which is a precondition for the optimization and development of the follow-up maintenance strategy. While elevator door systems are composed of several sub-components, performance degradation of critical sub-components will lead to reduced system performance, so how to fit the failure rate of the door system well is a critical issue in studying preventive maintenance decisions for the door system. In the aspect of maintenance target optimization, most of the existing researches are to treat multi-target optimization problems such as maintenance rate, reliability and the like into single-target optimization problems so as to simplify the treatment, so that the optimization is difficult to achieve in the aspect of compatibility among targets. Therefore, the multi-objective optimization of maintenance rate and reliability is researched, the global optimal solution is obtained, and the method has great significance for preventive maintenance decision of the elevator door system.
Disclosure of Invention
The invention aims to: the invention aims to provide a multi-objective optimization method for preventive maintenance decision of an elevator door system based on a non-inferior sorting genetic algorithm, which can realize scientific formulation of preventive maintenance strategy of the elevator door system, reduce maintenance cost and improve operational reliability of the door system, thereby improving maintenance efficiency, and solving the problems that most of existing researches treat multi-objective optimization problems such as maintenance rate, reliability and the like as single-objective optimization problems to simplify the treatment and that the optimization is difficult to achieve in terms of compatibility among objectives.
The technical scheme is as follows: the invention discloses a multi-objective optimization method for preventive maintenance decision of an elevator door system based on a non-inferior sorting genetic algorithm, which comprises the following steps:
1) Carrying out historical fault record collection and statistics on key components of the elevator door system, and obtaining two-parameter Weibull distribution shape parameters and scale parameters of service life of the key components of the elevator door system by using a method of best linear unbiased estimation;
2) Calculating the fault rate function of key components of the elevator door system and taking the maximum value to obtain the fault rate function of the door system;
3) Constructing an average maintenance rate objective function in a service life period of the door system and an average reliability objective function in a single preventive maintenance period, and constructing a preventive maintenance decision optimization model of the door system;
4) And carrying out multi-objective optimization solution on the door system preventive maintenance decision optimization model by adopting a non-inferior sorting genetic algorithm to obtain optimal preventive maintenance times and preventive maintenance period length.
Further, the step 2) specifically includes the following steps:
21 Assuming that the gate system has K critical components, each critical component lifetime obeys a two-parameter weibull distribution, the failure rate of the kth critical component can be expressed as:
wherein m is k And eta k The shape parameter and the size parameter of the service life Weibull distribution of the kth key sub-component are respectively represented, K is more than or equal to 1 and less than or equal to K, and t represents the working time;
22 Assuming that the door system is being serviced for one time every time the door system is operated for a period of time, so that the performance of each key component is restored; preventive replacement is performed at the end of the life cycle of the door system, so that each key component is recovered as new; each key component does not simultaneously fail in a single preventive maintenance period, if the key component fails, minor repair is carried out, and the minor repair does not change the failure rate of the component;
23 The failure rate of the kth critical component during the ith preventative maintenance cycle may be expressed as:
wherein i represents a preventive maintenance cycle number, T represents an operation time of the door system in two adjacent preventive maintenance cycles, T represents a preventive maintenance cycle length, and N represents a total preventive maintenance number of times, wherein the nth time is preventive replacement; lambda (lambda) k,i (t) represents the failure rate of the kth critical component at time t during the ith preventive maintenance period; θ k Representing a kth critical component failure rate decay factor; delta k,j Represent the service life back factor, delta, of the kth critical component at the jth preventative maintenance k,j ＝a k j ，a k To prevent maintenance investment adjustment factor, 0 < a k ＜1；
24 The failure rate of the door system can be expressed as:
λ i (t)＝max{λ k,i (t)|1≤k≤K,1≤i≤N}
wherein lambda is i And (t) representing the failure rate of the door system at the time t in the ith preventive maintenance period, wherein K is the total number of key components of the door system.
Further, the step 3) specifically includes the following steps:
31 An average service rate objective function over the service life of the door system may be expressed as:
wherein C (N, T) represents an average maintenance rate over the life cycle, C f Representing the average cost of a repair made each time a door system fails, C p Represents average cost of preventive maintenance, C r Indicating the average cost of preventing replacement, t p Mean time for preventive maintenance, t r Mean time spent on preventive replacement, N represents total preventive maintenance frequency, f i Representing the number of failures of the door system that occur during the ith preventative maintenance cycle:
wherein lambda is i (t) represents the failure rate of the door system at time t in the ith preventive maintenance period;
32 Calculating the average reliability of each key component of the door system in the ith preventive maintenance period and taking the minimum value to obtain the average reliability of the door system in the ith preventive maintenance period:
r i ＝min{r k,i |1≤k≤K,1≤i≤N}
wherein r is k,i Representing the average reliability of the kth critical sub-component during the ith preventative maintenance cycle, r i Indicating the average reliability of the door system during the ith preventive maintenance period, r k (t) represents the reliability function of the kth critical component:
wherein m is k And eta k The shape parameter and the size parameter of the life Weibull distribution of the kth key sub-component are respectively represented;
33 The average reliability objective function for a door system over a single preventative maintenance cycle is expressed as:
r(N,T)＝min{r i |1≤i≤N}
wherein r (N, T) represents the minimum value of the average reliability of the door system in each preventive maintenance period;
34 A preventive maintenance decision optimization model of the door system is expressed as:
further, in the step 4), a non-inferior sorting genetic algorithm is adopted to perform optimization solution on a door system preventive maintenance decision optimization model, wherein decision variables are preventive maintenance times N and preventive maintenance period length T, and an average maintenance rate C and an average reliability minimum r of the door system are used as two optimization targets. And finally carrying out iterative optimization on the obtained Pareto optimal solution set by a non-inferior sorting genetic algorithm, adopting a certain constraint, screening out an optimal solution meeting the condition, and obtaining the optimal preventive maintenance times N and preventive maintenance period length T of the gate system.
The invention has the beneficial effects that:
1. the fault rate and reliability functions of the elevator door system can be well fitted, so that the optimization and formulation of a subsequent maintenance strategy are facilitated.
2. The method comprises the steps of constructing an average maintenance rate objective function in the service life period of a door system and an average reliability objective function in a single preventive maintenance period, constructing a preventive maintenance decision optimization model of the door system, performing multi-objective optimization by adopting a non-inferior sorting genetic algorithm, realizing global optimization, and making a maintenance strategy capable of meeting the requirements of low maintenance cost and high reliability.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flowchart of an algorithm for multi-objective optimization using a non-inferior ranking genetic algorithm.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The invention is further described below with reference to the accompanying drawings and examples:
as shown in fig. 1, the invention relates to a multi-objective optimization method for preventive maintenance decision of an elevator door system based on a non-inferior sorting genetic algorithm, which comprises the following steps:
1) Firstly, determining key components of an elevator door system, collecting and counting historical fault records of the key components of the elevator door system, and obtaining two-parameter Weibull distribution shape parameters and scale parameters of service life of the key components of the elevator door system by using a best linear unbiased estimation method, wherein the key components determined in the embodiment are shown in the following table 1:
TABLE 1 key components of elevator door system
2) Calculating a fault rate function of key components of the elevator door system and taking the maximum value to obtain the fault rate function of the door system, and specifically comprising the following steps:
21 Assuming that the gate system has K critical components, each critical component lifetime obeys a two-parameter weibull distribution, the failure rate of the kth critical component can be expressed as:
wherein m is k And eta k The shape parameter and the size parameter of the service life Weibull distribution of the kth key sub-component are respectively represented, K is more than or equal to 1 and less than or equal to K, and t represents the working time;
22 Assuming that the door system is being serviced for one time every time the door system is operated for a period of time, so that the performance of each key component is restored; preventive replacement is performed at the end of the life cycle of the door system, so that each key component is recovered as new; each key component does not simultaneously fail in a single preventive maintenance period, if the key component fails, minor repair is carried out, and the minor repair does not change the failure rate of the component;
23 The failure rate of the kth critical component during the ith preventative maintenance cycle may be expressed as:
wherein i represents a preventive maintenance cycle number, T represents an operation time of the door system in two adjacent preventive maintenance cycles, T represents a preventive maintenance cycle length, and N represents a total preventive maintenance number of times, wherein the nth time is preventive replacement; lambda (lambda) k,i (t) represents the failure rate of the kth critical component at time t during the ith preventive maintenance period; θ k Representing a kth critical component failure rate decay factor; delta k,j Represent the service life back factor, delta, of the kth critical component at the jth preventative maintenance k,j ＝a k j ，a k To prevent maintenance investment adjustment factor, 0 < a k < 1; the relevant parameters of the failure rate of each key component determined in this embodiment are shown in the following table 2:
TABLE 2 Critical component failure Rate related parameters
24 The failure rate of the door system can be expressed as:
λ i (t)＝max{λ k,i (t)|1≤k≤K,1≤i≤N}
wherein lambda is i (t) represents the failure rate of the door system at time t in the ith preventive maintenance period, K is the total number of key components of the door system, and k=4 in this embodiment.
3) And constructing an average maintenance rate objective function in the service life period of the door system and an average reliability objective function in a single preventive maintenance period, and constructing a preventive maintenance decision optimization model of the door system. The method specifically comprises the following steps:
31 An average service rate objective function over the service life of the door system may be expressed as:
wherein C (N, T) represents an average maintenance rate over the life cycle, C f Representing the average cost of a repair made each time a door system fails, C p Represents average cost of preventive maintenance, C r Indicating the average cost of preventing replacement, t p Mean time for preventive maintenance, t r Mean time spent on preventive replacement, N represents total preventive maintenance frequency, f i Representing the number of failures of the door system that occur during the ith preventative maintenance cycle:
wherein lambda is i (t) represents the failure rate of the door system at time t in the ith preventive maintenance period; the parameters related to the average maintenance rate of the and gate system in this embodiment are shown in table 3 below:
table 3 and average maintenance rate related parameters for door system
32 Calculating the average reliability of each key component of the door system in the ith preventive maintenance period and taking the minimum value to obtain the average reliability of the door system in the ith preventive maintenance period:
r i ＝min{r k,i |1≤k≤K,1≤i≤N}
wherein r is k,i Representing the average reliability of the kth critical sub-component during the ith preventative maintenance cycle, r i Indicating the average reliability of the door system during the ith preventive maintenance period, r k (t) represents the reliability function of the kth critical component:
wherein m is k And eta k The shape parameter and the size parameter of the life Weibull distribution of the kth key sub-component are respectively represented;
33 The average reliability objective function for a door system over a single preventative maintenance cycle is expressed as:
r(N,T)＝min{r i |1≤i≤N}
wherein r (N, T) represents the minimum value of the average reliability of the door system in each preventive maintenance period;
34 A preventive maintenance decision optimization model of the door system is expressed as:
4) And carrying out multi-objective optimization solving on the gate system preventive maintenance decision optimization model by adopting a non-inferior sorting genetic algorithm, wherein decision variables are preventive maintenance times N and preventive maintenance period length T, and an average maintenance rate C and an average reliability minimum value r of the gate system are taken as two optimization targets. And finally carrying out iterative optimization on the obtained Pareto optimal solution set by a non-inferior sorting genetic algorithm, adopting a certain constraint, screening out an optimal solution meeting the condition, and obtaining the optimal preventive maintenance times N and preventive maintenance period length T of the gate system. The constraint adopted in the embodiment is that the individual with the minimum average maintenance rate in the solution set is taken under the condition that the minimum value r of the average reliability of the door system is not less than 0.85. The algorithm flow of the non-inferior ordering genetic algorithm multi-objective optimization is shown in fig. 2.
Claims (2)
1. The elevator door system preventive maintenance decision multi-objective optimization method based on the non-inferior sorting genetic algorithm is characterized by comprising the following steps of:
1) Carrying out historical fault record collection and statistics on key components of the elevator door system, and obtaining two-parameter Weibull distribution shape parameters and scale parameters of service life of the key components of the elevator door system by using a method of best linear unbiased estimation;
2) Calculating the fault rate function of key components of the elevator door system and taking the maximum value to obtain the fault rate function of the door system;
3) Constructing an average maintenance rate objective function in a service life period of the door system and an average reliability objective function in a single preventive maintenance period, and constructing a preventive maintenance decision optimization model of the door system;
4) Carrying out multi-objective optimization solution on a door system preventive maintenance decision optimization model by adopting a non-inferior sorting genetic algorithm to obtain optimal preventive maintenance times and preventive maintenance period length;
the step 2) specifically comprises the following steps:
21 Assuming that the gate system has K critical components, each critical component lifetime obeys a two-parameter weibull distribution, the failure rate of the kth critical component can be expressed as:
wherein m is k And eta k The shape parameter and the size parameter of the service life Weibull distribution of the kth key sub-component are respectively represented, K is more than or equal to 1 and less than or equal to K, and t represents the working time;
22 Assuming that the door system is being serviced for one time every time the door system is operated for a period of time, so that the performance of each key component is restored; preventive replacement is performed at the end of the life cycle of the door system, so that each key component is recovered as new; each key component does not simultaneously fail in a single preventive maintenance period, if the key component fails, minor repair is carried out, and the minor repair does not change the failure rate of the component;
23 The failure rate of the kth critical component during the ith preventative maintenance cycle may be expressed as:
wherein i represents a preventive maintenance cycle number, T represents an operation time of the door system in two adjacent preventive maintenance cycles, T represents a preventive maintenance cycle length, and N represents a total preventive maintenance number of times, wherein the nth time is preventive replacement; lambda (lambda) k,i (t) representsThe failure rate of the kth critical component at time t in the ith preventive maintenance period; θ k Representing a kth critical component failure rate decay factor; delta k,j Represent the service life back factor, delta, of the kth critical component at the jth preventative maintenance k,j ＝a k j ，a k To prevent maintenance investment adjustment factor, 0 < a k ＜1；
24 The failure rate of the door system can be expressed as:
λ i (t)＝max{λ k,i (t)|1≤k≤K,1≤i≤N}
wherein lambda is i And (t) representing the failure rate of the door system at the time t in the ith preventive maintenance period, wherein K is the total number of key components of the door system.
2. The elevator door system preventive maintenance decision multi-objective optimization method based on a non-inferior ranking genetic algorithm according to claim 1, wherein: the step 3) specifically comprises the following steps:
31 An average service rate objective function over the service life of the door system may be expressed as:
wherein C (N, T) represents an average maintenance rate over the life cycle, C f Representing the average cost of a repair made each time a door system fails, C p Represents average cost of preventive maintenance, C r Indicating the average cost of preventing replacement, t p Mean time for preventive maintenance, t r Mean time spent on preventive replacement, N represents total preventive maintenance frequency, f i Representing the number of failures of the door system that occur during the ith preventative maintenance cycle:
wherein lambda is i (t) shows the door system at the first positioni failure rates at time t in preventive maintenance cycles;
32 Calculating the average reliability of each key component of the door system in the ith preventive maintenance period and taking the minimum value to obtain the average reliability of the door system in the ith preventive maintenance period:
r i ＝min{r k,i |1≤k≤K,1≤i≤N}
wherein r is k,i Representing the average reliability of the kth critical sub-component during the ith preventative maintenance cycle, r i Indicating the average reliability of the door system during the ith preventive maintenance period, r k (t) represents the reliability function of the kth critical component:
wherein m is k And eta k The shape parameter and the size parameter of the life Weibull distribution of the kth key sub-component are respectively represented;
33 The average reliability objective function for a door system over a single preventative maintenance cycle is expressed as:
r(N,T)＝min{r i |1≤i≤N}
wherein r (N, T) represents the minimum value of the average reliability of the door system in each preventive maintenance period;
34 A preventive maintenance decision optimization model of the door system is expressed as:
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