CN111309582A - Optimization method for reliability evaluation of complex redundant system - Google Patents
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Abstract
The invention discloses an optimization method for reliability evaluation of a complex redundant system, which comprises the following steps: step 1: connecting subsystems in series and assemblies in parallel, and arranging a cold and hot backup assembly to complete a series-parallel redundant backup system model; step 2: calculating fault probability distribution and fault time failure distribution; and step 3: calculating the system reliability and the system task cost; and 4, step 4: performing first optimization calculation based on an ant colony genetic algorithm to obtain an optimal solution of an initialization sequence and initial pheromones; and 5: and performing second optimization calculation according to the optimal solution of the initialization sequence and the initial pheromone to complete the optimization of reliability evaluation. The invention solves the problems of poor reliability and high cost of the backup components of the traditional complex system, optimizes the influence of the distribution and the sequencing of the redundant backup components in the subsystem on the reliability of the system by adopting an ant colony genetic algorithm combining ant colony and heredity, improves the reliability of the system and reduces the cost overhead of system tasks.
Description
Technical Field
The invention relates to the technical field of complex system reliability, in particular to an optimization method for reliability evaluation of a complex redundant system.
Background
With the rapid development of computer technology, users have increasingly high requirements for the reliability of complex systems. In the age of rapid development of information technology, the complex system has penetrated into the daily life of people and even the field of national defense, so that the improvement of the reliability of the complex system is an important link in the product design and production process. The reliability of the complex system is high or low, and analysis and calculation are needed, and the two are related to each other.
The reliability of equipment or tasks can be detected, the fault mechanism of most systems can be guaranteed, effective modification suggestions can be obtained for later tests, the stability of the system reliability is further met, the product operation life is prolonged, and the system operation cost is reduced. It can be seen that the reliability of the system is not only stability, but also cost, etc.
Due to the profound development of the reliability research theory, the scientific technology supplies excellent assistant analysis methods for the reliability research theory. Therefore, in the reliability engineering technology of the real world, how to explore a high reliability technology which is convenient to analyze and satisfies the use becomes the core of exploration.
The reliability of the system is satisfied by redundant backup techniques, i.e., one or more modules or components in the system, with other system components or modules acting as backup components. When a component in the system which is already in working state fails, the failed component is disconnected, replaced by a standby component and executed. Most of the existing optimization works are dedicated to hot or cold standby redundant systems or their combination, however, for a complex redundant system, the standby components of the system have to have a series-parallel problem in the system, which needs to be explored.
Disclosure of Invention
The invention aims to provide an optimization method for reliability evaluation of a complex redundant system. The method aims to solve the problems of poor reliability and high cost of backup components of the traditional complex system, and optimizes the influence of the distribution and the sequencing of redundant backup components in a subsystem of the complex system on the system reliability by adopting an ant colony genetic algorithm combining ant colony and heredity, improves the system reliability of the complex system and reduces the cost and expense of system tasks.
In order to achieve the above object, the present invention provides an optimization method for reliability evaluation of a complex redundant system, comprising the following steps:
step 1: connecting all subsystems in a complex redundant system in series, connecting all components in each subsystem in parallel, and setting backup components in a cold form and a hot form to complete the design of a serial-parallel redundant backup system model;
step 2: respectively calculating fault probability distribution and fault time failure distribution of the fault component based on discrete mathematical probability distribution and Weibull distribution;
and step 3: respectively calculating the system reliability and the system task cost expense of the complex redundant system based on the failure probability distribution and the failure time distribution;
and 4, step 4: performing first optimization calculation based on an ant colony genetic algorithm according to the system reliability and the system task cost overhead to obtain an initialization sequence optimal solution and initial pheromones of each component of each subsystem in the complex redundant system;
and 5: and performing second optimization calculation based on the ant colony genetic algorithm according to the initialized sequence optimal solution and the initial pheromone to obtain the sequence distribution optimal solution of each component in each system in the complex redundant system, and finishing the optimization of reliability evaluation.
Most preferably, the failure probability distribution of the kth component in the task time t of the complex redundant system is Fk(t) the failure time failure distribution of the kth component in the ith time unit is pj(i) (ii) a And a failure probability distribution Fk(t) satisfies:
wherein, ηkIs a proportional variable of Weibull distribution, βkShape of Weibull distributionA variable; time to failure distribution pj(i) Satisfies the following conditions:
wherein, Δ i is the task time t of the whole complex redundant system and is divided into m identical time units.
Most preferably, the calculation of the system reliability comprises the steps of:
step 3.1: starting a kth standby component in the serial-parallel redundant backup system model when a fault component occurs;
step 3.2: according to the fault probability distribution pj(i) And time to failure distribution Fk(t) calculating the conditional failure probability P of the kth backup componentj；
Step 3.3: according to conditional fault probability PjCalculating the component reliability P of the kth spare componentr(ii) a Component reliability PrSatisfies the following conditions:
wherein e isjkKeeping the operation state of the kth standby component in the jth subsystem in m time units; x is the failure or fault of the component at a certain time interval m, and x is an integer and satisfies that x is more than or equal to 0 and less than m-1; qk-1(x) A probability density function of time intervals for k components in the subsystem to fail the last component in the predetermined order, and satisfies:
wherein y is the state that the component is activated to run in y time intervals; x-y is the time interval from the activation of the component to the failure fault; sjkA kth standby component which is sequentially activated in the jth subsystem;
step 3.4: according to component reliability PrCalculating the subsystem reliability r of the jth subsystemj(ii) a Subsystem reliability rjSatisfies the following conditions:
step 3.5: according to subsystem reliability rjCalculating the system reliability R of the complex redundant system; the system reliability R satisfies:
wherein J is the number of subsystems in the complex redundant system.
Most preferably, the conditional failure probability PjThree conditions are satisfied:
case 1: when the kth standby component is a hot standby component and the working time is less than the threshold value i0Time, conditional failure probability Pj1Satisfies the following conditions:
Pj1＝Pj(is,i0)＝Fk(Δ(dj×is+i0))；
case 2: when the kth standby component is a hot standby component and the working time is more than a threshold value i0Time, conditional failure probability Pj2Satisfies the following conditions:
Pj2＝Pj(is,i0)＝Fj(Δ(dj×is+i0+1))-Fj(Δ(dj×is+i0))；
case 3: conditional failure probability P when the kth backup component is a cold backup componentj3Satisfies the following conditions:
Pj3＝Pj(is,0)＝Fj(Δdj×is)
wherein isFor the time that the kth standby component is in standby; djIs a deceleration factor; 1 denotes that the kth backup component is a hot backup component; 0 is the kth standby component which is the cold standby component.
Most preferably, the first optimization calculation comprises the steps of:
step 4.1: determining a target function G and a fitness function omega according to the system reliability R and the system task cost overhead C;
step 4.2: randomly selecting any group of feasible real number codes from J subsystems of a complex redundancy system and 1-N + J-1 numbers of N components;
step 4.3: based on the ant colony genetic algorithm, u excellent ants are selected from Z ants, and the first genetic algorithm calculation is carried out to obtain the optimal solution of the initialization sequence and the initial pheromone of each component of each subsystem in the complex redundancy system.
Most preferably, the first genetic algorithm further comprises the steps of:
step 4.3.1: selecting individual modules from the group of spare modules by adopting a roulette method according to different fitness function G values of different modules;
step 4.3.2: obtaining a component sequence set with high fitness through the genetically selected component individuals, randomly selecting two component sequences as parents, and performing cross operation to generate two new component individuals;
step 4.3.3: randomly selecting two gene exchange positions from two new assembly individuals, and carrying out mutation operation;
step 4.3.4: and repeating the steps 4.3.1-4.3.3 for recursive iteration to obtain the optimal solution of the initialization sequence and the initial pheromone of each component of each subsystem in the complex redundant system.
Most preferably, the objective function G satisfies:
G＝min C(s.t R≥R*)
wherein R is the minimum required reliability level of the complex redundant system; the fitness function Ω satisfies:
Ω＝M-C-σmin{0,R*-R}
wherein M is a constant with a maximum value; and sigma is a penalty coefficient.
Most preferably, the second optimization calculation comprises the steps of:
step 5.1: calculating according to the optimal solution of the initialization sequence to obtain the initial distribution of the attraction strength and construct a set diagram of a complex redundant system;
step 5.2: based on ant colony genetic algorithm, selecting the rest Z-u ants in the Z ants to be put on the collective graph according to the initial pheromone taugPerforming a second genetic calculation to obtain an updated pheromone tau;
step 5.3: judging whether all ants Z complete the whole path or not; if not, repeating step 5.2; if the completion is finished, outputting the updated pheromone tau;
step 5.4: and performing updating calculation according to the updating pheromone tau to obtain the optimal solution of the sequence distribution of each component in each system in the complex redundant system.
Most preferably, the second genetic calculation further comprises the steps of:
step 5.2.1: calculating the moving probability P of Z-u ants moving from the ith node to the jth node of the set graphm(i,j)；
Step 5.2.2: according to the probability of movement Pm(i, j), transferring each ant to the j +1 th node to form an integral cycle;
step 5.2.3: under the whole circulation, the pheromone local updating is executed, and the pheromone updating value tau is calculatedc；
Step 5.2.4: from the initial pheromone τgAnd pheromone update value τcCalculating to obtain an update pheromone tau, and satisfying:
τ＝τg+τc。
most preferably, the collective graph includes node V1Node V2And edge set E1(ii) a Node V1Is a subsystem in a complex redundant system and satisfies the following conditions:
V1＝{1,2,3…,J}；
node V2Is a component of each subsystem in a complex redundant system, and satisfies:
V2＝{1,2,3…Njmax}
wherein N isjmaxIs the maximum value of the number of components in the jth system; edge set E1To connect said node V1And stationThe node V2The edge of (2).
By applying the invention, the problems of poor reliability and high cost of the backup component of the traditional complex system are solved, the ant colony genetic algorithm combining ant colony and heredity is adopted, the influence of the distribution and sequencing of the redundant backup component in the subsystem on the system reliability is optimized, the system reliability is improved, and the system task cost overhead is reduced.
Compared with the prior art, the invention has the following beneficial effects:
1. the redundancy backup component model based on the series-parallel connection structure is formed by combining two different connection modes, and the reliability of the system is improved.
2. The redundant backup assembly in each subsystem of the invention comprises a cold backup mode and a hot backup mode, and the running cost of the system is reduced on the premise of keeping the reliability of the system.
3. The method adopts the ant colony genetic algorithm to combine two different algorithms, and obtains a plurality of groups of queue sets of optimal solutions through the genetic algorithm; and then, an ant colony algorithm is used for solving the optimal solution under the set, the two algorithms are relevant to each other and are indispensable, and different permutation and combination can be quickly screened out to obtain the optimal solution.
Drawings
FIG. 1 is a flow chart of an optimization method for reliability evaluation of a complex redundancy system according to the present invention;
FIG. 2 is a schematic structural diagram of a serial-parallel redundancy backup system according to the present invention;
FIG. 3 is a flowchart of a double optimization method of the ant colony genetic algorithm provided by the present invention;
FIG. 4 is a graph of the variation trend of the system reliability R and the system task cost C over the time interval m, which is explored by the simulation experiment provided by the present invention;
FIG. 5 is a genetic iteration profile of the system task cost overhead C of the standby component provided by the present invention;
FIG. 6 is a relationship between system reliability R, system task cost overhead C and genetic iteration number provided by the present invention;
fig. 7 is a graph showing a relationship between system reliability R and system task cost C obtained by ant colony genetic algorithm optimization provided by the present invention.
Detailed Description
The invention will be further described by the following specific examples in conjunction with the drawings, which are provided for illustration only and are not intended to limit the scope of the invention.
The invention provides an optimization method for reliability evaluation of a complex redundancy system, which comprises the following steps as shown in figure 1:
step 1: all subsystems in the complex redundant system are connected in series, all components in each subsystem are connected in parallel, and backup components in a cold mode and a hot mode are arranged to complete the design of a serial-parallel redundant backup system model.
In this embodiment, as shown in fig. 2, there are J subsystems in the complex redundant system, and at least one component in each subsystem is in an operating state to keep the system operating normally.
The hot backup component plays an important role in the redundant backup of the complex system, when a certain running component in the complex system fails, the hot backup component in the parallel mode is activated to take over a task according to a preset sequence, and the running is quickly recovered without initialization; however, the hot backup component is always in operation, which increases the cost and energy consumption of the system.
The cold backup component is not initialized after the system is operated, and when the system fails, the cold backup component needs a corresponding time interval to be initialized, so that the system is in a high-delay state; but the cold backup component reduces the cost overhead of the system.
Therefore, the cold backup component and the hot backup component are mixed, and a mixed redundant backup system model is designed to optimize the complex system.
Step 2: and respectively calculating the fault probability distribution and the fault time failure distribution of the fault assembly based on the discrete mathematical probability distribution and the Weibull (Weibull) distribution. In this embodiment, based on an exponential distribution function and a Weibull distribution.
WhereinThe failure probability distribution of the kth component in the task time t of the complex redundant system is Fk(t) and a failure probability distribution Fk(t) satisfies:
wherein, ηkIs a proportional variable of Weibull distribution, βkIs the shape variable of the Weibull distribution.
The failure time failure distribution of the kth component in the ith time unit is pj(i) (ii) a Time to failure distribution pj(i) Satisfies the following conditions:
pj(i)＝exp{-[Δi/ηk]βk}-exp{-[Δ(i+1)/ηk]βk}
wherein, Δ i is the task time t of the whole complex redundant system and is divided into m identical time units.
And step 3: failure probability distribution p based on failed componentsj(i) And time to failure distribution FkAnd (t) respectively calculating the system reliability R and the system task cost C of the complex redundant system.
The method for calculating the system reliability of the complex redundant system comprises the following steps:
step 3.1: and starting the kth standby component in the serial-parallel redundant backup system model when the fault component occurs.
Step 3.2: according to the fault probability distribution pj(i) And time to failure distribution Fk(t) calculating the conditional failure probability P of the kth backup componentj。
Wherein the conditional fault probability PjThe following three conditions are satisfied:
case 1: when the kth standby component is a hot standby component and the working time is less than the threshold value i0Time, conditional failure probability Pj1Satisfies the following conditions:
Pj1＝Pj(is,i0)＝Fk(Δ(dj×is+i0))；
case 2: when in useThe kth standby component is a hot standby component and the working time is more than a threshold value i0Time, conditional failure probability Pj2Satisfies the following conditions:
Pj2＝Pj(is,i0)＝Fj(Δ(dj×is+i0+1))-Fj(Δ(dj×is+i0))；
case 3: conditional failure probability P when the kth backup component is a cold backup componentj3Satisfies the following conditions:
Pj3＝Pj(is,0)＝Fj(Δdj×is)
wherein isFor the time that the kth standby component is in standby; djIs a deceleration factor; 1 is a kth standby component which is a hot standby component; 0 is the kth standby component which is the cold standby component.
Step 3.3: according to conditional fault probability PjCalculating the component reliability P of the kth spare componentr(ii) a Component reliability PrSatisfies the following conditions:
wherein e isjkKeeping the operation state of the kth standby component in the jth subsystem in m time units; x is the failure or fault of the component at a certain time interval m, and x is an integer and satisfies x is more than or equal to 0 and less than m-1; qk-1(x) A probability density function of time intervals for k components in the subsystem to fail the last component in the predetermined order, and satisfies:
wherein y is the state that the component is activated to run in y time intervals; x-y is the time interval from the activation of the component to the failure fault; sjkFor the kth standby component that is sequentially active in the jth subsystem.
Step 3.4: according to component reliability PrCalculating the subsystem reliability r of the jth subsystemj(ii) a Subsystem reliability rjSatisfies the following conditions:
step 3.5: according to subsystem reliability rjCalculating the system reliability R of the complex redundant system; the system reliability R satisfies:
wherein J is the number of subsystems in the complex redundant system.
At the same time, the probability distribution p of the failure in combination with the failed componentj(i) Time to failure distribution Fk(t) calculating the cost overhead C of the system task of the complex redundant system according to the starting cost of different cold and hot standby components; the system task cost overhead C is calculated similarly to the system reliability R.
And 4, step 4: as shown in fig. 3, according to the system reliability R and the system task cost overhead C, the first optimization calculation is performed based on the ant colony genetic algorithm to obtain the optimal solution of the initialization sequence and the initial pheromone τ of each component of each subsystem in the complex redundant systemg。
Wherein, the first optimizing calculation comprises the following steps:
step 4.1: and determining a target function G and a fitness function omega of the complex redundant system according to the system reliability R and the system task cost overhead C.
The objective function G of the complex redundant system minimizes the system task cost overhead C of the complex redundant system under the condition that the system reliability R of the complex redundant system is ensured, namely the objective function G meets the following requirements:
G＝min C(s.t R≥R*)
wherein R is the minimum required reliability level of the complex redundant system; the fitness function Ω satisfies:
Ω＝M-C-σmin{0,R*-R}
wherein M is a constant with a maximum value; sigma is a penalty coefficient;
when the penalty coefficient sigma is 0, the objective function G is the minimum task cost for solving the complex redundancy system;
when penalty factor σ → + ∞ and R*The objective function G is the maximum reliability for solving the complex redundant system, which is 1.
The task cost is that the cost of the cold and hot components in the complex system is different, the hot backup keeps the running state all the time, and because the hot backup keeps the running state all the time, the system has more resource occupation and high cost, and the system can be kept to run continuously without intervals when waiting for the running component to be in fault or failure; the cold backup needs initialization, needs time, and the complex system can run with time delay, so the cold backup does not occupy resources, the cost is low, and the hot backup occupies resources, and the cost is high.
The minimum task cost means that the reliability factor is ignored, and the task cost is minimum according to the cold-hot backup parameters (such as the size of the cold-hot backup overhead) and the system running time.
Step 4.2: and randomly selecting any group of feasible real number codes from the J subsystems of the complex redundant system and the numbers of 1-N + J-1 of the N components.
Where a number greater than N is distributed in the sequence to represent the sequence separator of each subsystem. In this embodiment, 3 random real code sequences of the 7 spare components of the subsystem are shown in table 1 below:
TABLE 1 random real number coding sequence of spare blocks
Step 4.3: based on ant colony genetic algorithm, selecting u excellent ants from Z ants, and performing first genetic algorithm calculation to obtain the optimal solution of initialization sequence and initial pheromone tau of each component of each subsystem in the complex redundancy systemg。
Wherein the first genetic algorithm further comprises the following steps:
step 4.3.1: selecting individual modules from the group of spare modules by adopting a roulette method according to different fitness function G values of different modules; in the group of spare components, the probability of being selected is higher as the value of the fitness function G of the component individual is larger.
Step 4.3.2: and obtaining a component sequence set with high fitness through the genetically selected component individuals, randomly selecting two component sequences as parents, and performing cross operation to generate two new component individuals.
In this example, the two possible parents (2519 & 38467) and (4281 & 39675) are interleaved to obtain two new assembly individuals, namely (251948367) and (428159367), wherein & represents the break of the chromosome.
Step 4.3.3: randomly selecting two gene exchange positions from two new assembly individuals, and carrying out mutation operation;
step 4.3.4: obtaining the optimal solution of the initialization sequence and the initial pheromone tau of each component of each subsystem in the complex redundant system by repeating the recursive iteration of the steps 4.3.1-4.3.3g。
And 5: optimal solution and initial pheromone tau according to initialization sequencegAnd performing second optimization calculation based on the ant colony genetic algorithm to obtain the optimal solution of the sequence distribution of each component in each system in the complex redundant system, and completing the optimization of reliability evaluation.
Wherein, the second optimizing calculation comprises the following steps:
step 5.1: calculating according to the optimal solution of the initialization sequence to obtain the initial distribution of the attraction strength and construct a set diagram of a complex redundant system;
the aggregate graph includes node V1Node V2And edge set E1(ii) a Node V1Is a subsystem in a complex redundant system and satisfies the following conditions:
V1＝{1,2,3…,J}；
node V2For each child in a complex redundant systemThe components of the system, and satisfy:
V2＝{1,2,3…Njmax}
wherein N isjmaxIs the maximum value of the number of components in the jth system; edge set E1To connect node V1And node V2The edge of (2).
Step 5.2: based on ant colony genetic algorithm, selecting the rest Z-u ants in the Z ants to be put on the collective graph according to the initial pheromone taugAnd performing second genetic calculation to obtain the updated pheromone tau.
Wherein the second genetic calculation further comprises the steps of:
step 5.2.1: calculating the moving probability P of Z-u ants moving from the ith node to the jth node of the set graphm(i,j)；
Step 5.2.2: according to the probability of movement Pm(i, j), transferring each ant to the j +1 th node to form an integral cycle;
step 5.2.3: under the whole circulation, the pheromone local updating is executed, and the pheromone updating value tau is calculatedc；
Step 5.2.4: from the initial pheromone τgAnd pheromone update value τcCalculating to obtain an update pheromone tau, and satisfying:
τ＝τg+τc。
step 5.3: judging whether all ants Z complete the whole path or not; if not, repeating step 5.2; if it is completed, the update pheromone τ is output.
Step 5.4: and performing updating calculation according to the updating pheromone tau to obtain the optimal solution of the sequence distribution of each component in each system in the complex redundant system.
Meanwhile, the influence of different task time intervals of m time units on the system reliability R and the system task cost overhead C of the complex redundant system under the same condition is researched. As shown in fig. 4, it is found that when the time interval m is extremely short, a moderate increase in the time interval m has a great influence on the research.
If the time interval m is extremely short, the number m of the time intervals is increased greatly, so that the reliability is accumulated and multiplied for multiple times, and the cost (the probability is less than 1) is reduced; the objective of the ant colony genetic algorithm is to obtain the lowest possible cost, so that in simulation experiments, the reliability is inevitably reduced under the condition that the time interval m is extremely short, and the calculated cost is naturally reduced. Fig. 4 is thus derived, so that it is known that a modest increase in the size of the time interval m, which is as high as possible, can be maintained with a correspondingly low cost.
As shown in fig. 5, as the genetic iterations change, the optimal solution will appear as the task cost tends to stabilize. Due to the small optimization in a complex series-parallel redundancy system, the optimization of the system is huge. As shown in fig. 6, as the number of genetic iterations increases, the system reliability R and the system task cost C of the complex redundant system are optimized, and at the same time, different reliability levels and corresponding sets of initialization sequences can be obtained, so as to draw a graph of the system reliability R and the system task cost C of the complex redundant system, as shown in fig. 7, the system reliability R and the system task cost C of the complex redundant system are substantially proportional.
The working principle of the invention is as follows:
connecting all subsystems in a complex redundant system in series, connecting all components in each subsystem in parallel, and setting backup components in a cold form and a hot form to complete the design of a serial-parallel redundant backup system model; respectively calculating fault probability distribution and fault time failure distribution of the fault component based on discrete mathematical probability distribution and Weibull distribution; respectively calculating the system reliability and the system task cost expense of the complex redundant system based on the failure probability distribution and the failure time distribution; performing first optimization calculation based on an ant colony genetic algorithm according to the system reliability and the system task cost overhead to obtain an initialization sequence optimal solution and initial pheromones of each component of each subsystem in the complex redundant system; and performing second optimization calculation based on the ant colony genetic algorithm according to the initialized sequence optimal solution and the initial pheromone to obtain the sequence distribution optimal solution of each component in each system in the complex redundant system, and finishing the optimization of reliability evaluation.
In summary, the optimization method for reliability evaluation of the complex redundant system solves the problems of poor reliability and high cost of the backup components of the traditional complex system, optimizes the influence of the distribution and the sequencing of the redundant backup components in the subsystem on the reliability of the system by adopting the ant colony genetic algorithm combining ant colony and heredity, improves the reliability of the system, and reduces the cost of system tasks.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (10)
1. An optimization method for reliability evaluation of a complex redundant system is characterized by comprising the following steps:
step 1: connecting all subsystems in a complex redundant system in series, connecting all components in each subsystem in parallel, and setting backup components in a cold form and a hot form to complete the design of a serial-parallel redundant backup system model;
step 2: respectively calculating fault probability distribution and fault time failure distribution of the fault component based on discrete mathematical probability distribution and Weibull distribution;
and step 3: respectively calculating the system reliability and the system task cost expense of the complex redundant system based on the fault probability distribution and the fault time failure distribution;
and 4, step 4: performing first optimization calculation based on an ant colony genetic algorithm according to the system reliability and the system task cost overhead to obtain an optimal solution and initial pheromone of an initialization sequence of each component of each subsystem in the complex redundant system;
and 5: and performing second optimization calculation based on an ant colony genetic algorithm according to the initialization sequence optimal solution and the initial pheromone to obtain a sequence distribution optimal solution of each component in each system in the complex redundant system, and finishing the optimization of reliability evaluation.
2. The method of claim 1, wherein the k-th component has a probability distribution of failure F within a task time t of the complex redundant systemk(t), the failure time failure distribution of the k component in the ith time unit is pj(i) (ii) a And the failure probability distribution Fk(t) satisfies:
wherein, ηkIs the proportional variable of the Weibull distribution, βkA shape variable that is the Weibull distribution; said time to failure distribution pj(i) Satisfies the following conditions:
wherein, Δ i is the task time t of the whole complex redundant system and is divided into m identical time units.
3. The method for optimizing a complex redundant system reliability evaluation according to claim 2 wherein said calculating of system reliability comprises the steps of:
step 3.1: starting a kth standby component in the serial-parallel redundant backup system model when the fault component occurs;
step 3.2: according to the fault probability distribution pj(i) And said time to failure distribution Fk(t) calculating a conditional failure probability P of the kth backup componentj；
Step 3.3: according to the conditional fault probability PjCalculating the component reliability P of the kth spare componentr(ii) a Said component reliability PrSatisfies the following conditions:
wherein e isjkKeeping the active state for the kth standby component in the jth subsystem in m time units; x is the failure or fault of the component in a certain time interval, wherein the integer x is greater than or equal to 0 and less than m-1; qk(x) A probability density function of time intervals for k components in the subsystem to fail the last component in the predetermined order, and satisfies:
wherein y is the activated operation state of the component in y time intervals, and x-y is the time interval from the activation of the component to the failure fault; sjkA kth standby component which is sequentially activated in the jth subsystem;
step 3.4: according to the component reliability PrCalculating the subsystem reliability r of the jth subsystemj(ii) a The subsystem reliability rjSatisfies the following conditions:
step 3.5: according to the subsystem reliability rjCalculating the system reliability R of the complex redundant system; the system reliability R satisfies:
wherein J is the number of subsystems in the complex redundant system.
4. The method of optimizing a complex redundancy system reliability evaluation according to claim 3, wherein the conditional failure probability PjThree conditions are satisfied:
case 1: when the kth standby component is a hot standby component and worksTime is less than threshold i0Time, said conditional failure probability Pj1Satisfies the following conditions:
Pj1＝Pj(is,i0)＝Fk(Δ(dj×is+i0))；
case 2: when the kth standby component is a hot standby component and the working time is more than a threshold value i0Time, said conditional failure probability Pj2Satisfies the following conditions:
Pj2＝Pj(is,i0)＝Fj(Δ(dj×is+i0+1))-Fj(Δ(dj×is+i0))；
case 3: when the kth backup component is a cold backup component, the conditional failure probability Pj3Satisfies the following conditions:
Pj3＝Pj(is,0)＝Fj(Δdj×is)
wherein isFor the time that the kth standby component is in a standby state; djIs a deceleration factor; 1 indicates that the kth backup component is a hot backup component; 0 is that the kth standby component is a cold standby component.
5. The method of optimizing a reliability evaluation of a complex redundant system of claim 1 wherein said first optimization calculation comprises the steps of:
step 4.1: determining a target function G and a fitness function omega according to the system reliability R and the system task cost overhead C;
step 4.2: randomly selecting any group of feasible real number codes from J subsystems of a complex redundancy system and 1-N + J-1 numbers of N components;
step 4.3: based on the ant colony genetic algorithm, u excellent ants are selected from Z ants, and the first genetic algorithm calculation is carried out to obtain the optimal solution of the initialization sequence and the initial pheromone of each component of each subsystem in the complex redundancy system.
6. The method for optimizing a reliability evaluation of a complex redundant system according to claim 5 wherein said first genetic algorithm further comprises the steps of:
step 4.3.1: selecting individual modules from the group of spare modules by a roulette method according to different fitness function G values of different modules;
step 4.3.2: obtaining a component sequence set with high fitness through the genetically selected component individuals, randomly selecting two component sequences as parents, and performing cross operation to generate two new component individuals;
step 4.3.3: randomly selecting two gene exchange positions from the two new assembly individuals, and carrying out mutation operation;
step 4.3.4: and repeating the steps 4.3.1-4.3.3 for recursive iteration to obtain the optimal solution of the initialization sequence and the initial pheromone of each component of each subsystem in the complex redundant system.
7. The method of optimizing a reliability evaluation of a complex redundant system according to claim 5 wherein said objective function G satisfies:
G＝min C(s.t R≥R*)
wherein R is the minimum required reliability level of the complex redundant system; the fitness function Ω satisfies:
Ω＝M-C-σmin{0,R*-R}
wherein M is a constant with a maximum value; and sigma is a penalty coefficient.
8. The method of optimizing a reliability evaluation of a complex redundant system of claim 1 wherein said second optimization calculation comprises the steps of:
step 5.1: calculating according to the optimal solution of the initialization sequence to obtain initial distribution of attraction strength and construct a set diagram of a complex redundant system;
step 5.2: selecting the rest Z-u ants from the Z ants to be placed on the collective graph based on an ant colony genetic algorithm according to the initial pheromone taugPerforming a second genetic calculation to obtain an updated pheromone tau;
step 5.3: judging whether all ants Z complete the whole path or not; if not, repeating step 5.2; if the completion is finished, outputting the updated pheromone tau;
step 5.4: and performing updating calculation according to the updating pheromone tau to obtain the optimal solution of the sequence distribution of each component in each system in the complex redundant system.
9. The method for optimizing a reliability assessment of a complex redundant system according to claim 8 wherein said second genetic calculation further comprises the steps of:
step 5.2.1: calculating the moving probability P of the Z-u ants moving from the ith node to the jth node of the set graphm(i,j)；
Step 5.2.2: according to the movement probability Pm(i, j), transferring each ant to the j +1 th node to form an integral cycle;
step 5.2.3: under the whole circulation, the pheromone local updating is executed, and the pheromone updating value tau is calculatedc；
Step 5.2.4: according to the initial pheromone taugAnd pheromone update value τcAnd calculating the update pheromone tau, and satisfying the following conditions:
τ＝τg+τc。
10. the method of optimizing reliability evaluations for a complex redundant system of claim 8 wherein said aggregate graph comprises node V1Node V2And edge set E1(ii) a The node V1Is a subsystem in a complex redundant system and satisfies the following conditions:
V1＝{1,2,3…,J}；
the node V2Is a component of each subsystem in a complex redundant system, and satisfies:
V2＝{1,2,3…Njmax}
wherein N isjmaxIs the jth systemMaximum number of components in the system; the edge set E1To connect said node V1And said node V2The edge of (2).
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