CN116401750A - Multi-objective optimization method for reliability redundancy design of electrical system based on collaborative balance - Google Patents
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Abstract
The invention discloses a multi-objective optimization method for electric system reliability redundancy design based on cooperative balance, which solves the problem that the traditional optimization method only considers the influence of single subsystem redundancy unit change on system reliability, cost, volume, quality and power consumption, so that an optimization result can only calculate a local optimal result within a certain range; the invention completes the global optimization aiming at the reliability, cost, volume, quality and power consumption of the system by considering the influence of the cooperative change of the redundant units on each subsystem; the multi-objective optimization method based on the reliability redundancy design of the cooperative balance of the subsystem and the redundancy unit has clear algorithm and simple implementation process, and can calculate the optimal result usually by iterative computation within 10 times. Compared with intelligent algorithms such as genetic algorithm, particle swarm optimization algorithm, ant colony algorithm and the like, the method has the advantages that the implementation process is simpler, the iterative computation times within 10 times are obviously less than 100 times or more of the iterative computation of a general intelligent algorithm, and the computation cost is lower.
Description
Technical Field
The invention belongs to the technical field of reliability design, and particularly relates to a multi-objective optimization method for reliability redundancy design of an electrical system based on collaborative balance.
Background
With the development of science and technology, the requirements of the fields of aerospace, aviation, navigation, rail traffic, automobile, manufacturing industry and the like on an electrical system are increasing. In order to improve the working reliability of an electrical system, the reliability optimization design method of the electrical system is gaining more and more importance. Reliability redundancy design is an important means for improving the reliability of complex systems by increasing the redundancy of the system. However, increasing the number of redundancy units necessarily increases the cost, volume, mass, power consumption, etc. of the system, and therefore, it is necessary to minimize the number of redundancy while meeting the requirements of reliability, cost, volume, mass, power consumption. Multi-objective optimization of electrical system reliability redundancy designs generally includes two optimization objectives: the method comprises the steps of taking system cost, volume, mass, power consumption and the like as constraints, and correctly configuring each subsystem unit to enable the reliability of an electrical system to be maximum; and secondly, the reliability index of the electrical system is used as constraint, and each subsystem unit is correctly configured, so that the system cost, the volume, the mass or the power consumption and the like are minimized.
The optimization method based on pattern search and heuristic method generally takes the influence of subsystem unit change on the whole reliability, cost, volume, mass, power consumption and other factors of the electrical system as an optimization basis, so as to determine whether the subsystem is added or reduced with new units. The method is similar to a mountain climbing method, and the calculation of the local optimal solution is easy to realize, but the influence of the synergistic effect among subsystems on the overall reliability of the system is usually ignored. In recent years, the reliability redundancy system optimization method based on intelligent algorithms (genetic algorithm, particle swarm algorithm, ant colony algorithm, artificial intelligent neural network method and the like) is gradually developed, and the optimization target of the reliability redundancy system is successfully realized. However, the implementation process of the optimization method has the problems of complex implementation process, high calculation cost and the like.
Disclosure of Invention
In view of the above, the invention aims to develop a multi-objective optimization method for the reliability redundancy design of an electrical system based on the cooperative balance of a subsystem and a redundancy unit.
The electric system reliability redundancy design multi-objective optimization method based on cooperative balance comprises the following steps:
step one, inputting an initial balance sample;
step two, based on the initial balance sample in the step one, enumerating the balance state variable quantity according to three states of adding a unit, reducing a unit or keeping unchanged of each subsystem, and constructing a sample change data set;
step three, calculating a new balance state sample set according to the sample change data set;
calculating the system reliability, cost, volume, quality and power consumption of each new sample in the new sample set;
step five, screening an optimal sample based on reliability, cost, volume, quality and power consumption requirements;
step six, comparing the optimal sample screened in the step five with the initial sample in the step one, wherein the optimal sample and the initial sample are consistent to show that the initial balance sample is the optimal reliability redundancy design; otherwise, taking the optimal sample as an initial balance sample, and returning to the second step to continue iterative computation.
Preferably, in the first step, the electrical system includes n subsystems, and each subsystem is formed by connecting a plurality of units in parallel;
the initial sample balance sample can be given through estimation, the initial balance sample is required to become a feasible solution of the redundant system after the first round of calculation is completed, the initial balance sample is required to be given again when the conditions are not met, and the step is returned to perform the re-calculation;
the initial balance sample can also be directly determined through calculation, and the calculation method has a difference according to the optimization target:
(1) Solving a balance state sample with highest reliability in the required range of cost, volume, mass and power consumption, wherein the calculation mode of an initial input sample is to solve the number of units in each subsystem meeting the requirements of cost, volume, mass and/or power consumption on the assumption that the cost, volume or mass of each subsystem is the same;
(2) And solving the design of optimal cost, volume, quality and/or power consumption requirements in the reliability requirement range, wherein the calculation mode of the initial input sample is to solve the number of subsystem units meeting the reliability requirement on the assumption that the reliability of each subsystem is the same.
Preferably, the total number of state changes of the reliability system is 3 n A kind of module is assembled in the module and the module is assembled in the module.
Preferably, in the fifth step, the method for screening the optimal sample includes:
(1) Screening out samples with highest reliability in the requirements of cost, volume, quality and power consumption;
or (2) to achieve the lowest cost, volume, mass, or power consumption sample within a specified reliability range.
Preferably, the method solves the balance state sample with highest reliability in the requirements of cost, volume, mass and power consumption, and the fifth step specifically comprises the following steps:
step 5-1, screening samples meeting the requirements of system cost, volume, quality and/or power consumption in a new sample set to generate a sample set A;
step 5-2, screening samples with non-zero subsystem sample numbers from the sample set A to generate a sample set B;
and 5-3, screening out a sample with highest system reliability from the sample set B, namely the optimal sample.
Preferably, the design of optimal cost, volume, quality and/or power consumption requirements is solved within the range of reliability requirements, and the fifth step specifically comprises:
step 5-1, screening out that the reliability of the system in the new sample set meets R s >R 0 Generating a sample set a;
step 5-2, screening out samples with the lowest cost, volume, mass and/or power consumption from the sample set A to generate a sample set B;
step 5-3, screening samples with non-zero sample number from the sample set B to generate a sample set C;
and 5-4, screening out a sample with highest system reliability from the sample set C, namely the optimal sample.
Preferably, the electrical system includes, but is not limited to, electrical equipment used in the aerospace, marine, rail traffic, automotive or manufacturing industries.
Preferably, the unit is an electronic component or an electric stand-alone unit which comprises a resistor, an inductor, a voter, a sensor or a functional circuit and the like and can quantitatively describe the reliability.
The invention has the following beneficial effects:
the multi-objective optimization method based on the reliability redundancy design of the cooperative balance of the subsystem and the redundant unit solves the problem that the traditional optimization method only considers the influence of the change of the redundant unit of the single subsystem on the reliability, cost, volume, quality and power consumption of the system, so that the optimization result can only calculate the local optimal result within a certain range. The invention completes the global optimization aiming at the reliability, the cost, the volume, the quality and the power consumption of the system by considering the influence of the cooperative change of the redundant units on each subsystem.
The multi-objective optimization method based on the reliability redundancy design of the cooperative balance of the subsystem and the redundancy unit has clear algorithm and simple implementation process, and can calculate the optimal result usually by iterative computation within 10 times. Compared with intelligent algorithms such as genetic algorithm, particle swarm optimization algorithm, ant colony algorithm and the like, the method has the advantages that the implementation process is simpler, the iterative computation times within 10 times are obviously less than 100 times or more of the iterative computation of a general intelligent algorithm, and the computation cost is lower.
The invention fully considers the cooperative balance effect of the subsystem and the redundant unit, solves the limitation that the conventional balance optimization method only considers the influence of the change of the redundant unit of the single subsystem on the reliability, cost, volume, quality and power consumption of the system, develops a novel multi-objective optimization method based on the cooperative balance of the subsystem and the redundant unit, and improves the practical engineering application value of the method. In addition, the calculation process is simple, and the calculation process can be conveniently realized by means of common commercial software (e.g. Matlab).
Drawings
FIG. 1 is a flow chart of an implementation of a collaborative balance-based reliability redundancy design multi-objective optimization method of the present invention;
FIG. 2 is a schematic diagram of a bridge type reliability redundancy system for a type of electrical equipment according to embodiment 1 of the present invention;
fig. 3 is a schematic diagram of a five-stage parallel-serial reliability redundancy system for a certain type of electrical equipment in embodiment 2 of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
A reliability redundancy design multi-objective optimization method based on collaborative balance is shown in fig. 1, and the optimization method comprises the following steps:
step one, an initial balance sample is proposed;
step two, enumerating balance state variable quantity according to three states of adding and reducing one unit and keeping unchanged of the subsystem, and constructing a sample change data set;
step three, calculating a new balance state sample set according to sample change data;
calculating the reliability, cost, volume, quality and power consumption of each new sample in the new sample set;
step five, screening an optimal sample under the constraints of reliability, cost, volume, quality and power consumption;
and step six, judging the optimal sample, and outputting the optimal sample.
In the method, in the multi-objective optimization process of the reliability redundancy design, the influence of the redundancy units on the subsystems is considered, the influence of the cooperative balance of the redundancy units among the subsystems on the reliability of the complex electrical system is also considered, and finally, the deep optimization of the reliability redundancy design of the electrical system is realized. In addition, the method has the advantages of simple calculation process, less iteration times and convenient implementation. The system is formed by connecting a plurality of subsystems in series and in parallel, and the subsystems can be split into 1 to x i Units, units not detachable。
Further, the step one of determining an initial balance sample by a pre-estimation method, wherein the initial balance sample is required to become a feasible solution of the redundant system after the first round of calculation, and the initial balance sample is required to be given again when the requirement is not met, and the re-calculation is returned; the initial balance sample can also directly determine a feasible solution through calculation, and the calculation method has a difference according to an optimization target, and the specific calculation method is as follows:
the method comprises the steps of solving a balance state sample with highest reliability in the range of requirements on cost, volume, mass and power consumption, and solving the number of units in each subsystem meeting the requirements on cost, volume, mass and power consumption by assuming that the cost, volume, mass or power consumption of each subsystem is the same.
And solving the optimal cost, volume, quality or power consumption design in the reliability requirement range, wherein the calculation mode of the initial input sample is to solve the number of subsystem units meeting the reliability requirement on the assumption that the reliability of each subsystem is the same.
Further, each subsystem enumerates the state change library of the reliability system in terms of three states, increasing (+1), decreasing (-1), and remaining unchanged (+0) in step two. The total number of state changes of the reliability system is 3 according to the number of subsystems n Sample changes are shown in table 1.
Table 1 sample change library
Further, the calculation method of the new sample set in the third step includes, but is not limited to,
further, in the fourth step, the calculation expression of the reliability redundancy system is:
R s ＝F R [R(x 1 ),R(x 2 ),…,R(x i ),…,R(x n )]
wherein R is s Is the system cost of a reliability redundancy system, R (x i ) Is the reliability of the ith subsystem, F R Indicating R s Is with R (x) i ) Related function, x 1 ,x i ,x n The number of units in the 1, i, n sub-systems, respectively. According to the reliability model difference of the systems formed by the series and parallel connection of all subsystems of the electrical system, a function F R There are also differences.
Further, in the fourth step, the calculation expressions of the cost, the volume, the quality and the power consumption of the reliability redundant system are respectively:
C s ＝F C (C 1 ,…,C i ,…,C n ,x 1 ,…x i ,…,x n )
V s ＝F V (V 1 ,…,V i ,…,V n ,x 1 ,…x i ,…,x n )
W s ＝F W (W 1 ,…,W i ,…,W n ,x 1 ,…x i ,…,x n )
P s ＝F P (P 1 ,…,P i ,…,P n ,x 1 ,…x i ,…,x i )
wherein C is s System cost for a reliable redundant system, C i Is the cost per unit in the ith subsystem, V s System volume, V, which is a reliability redundancy system i Is the volume, W, of each unit in the ith subsystem s System quality, W, of a reliability redundancy system i Is the mass, P, of each element in the ith subsystem s System power consumption, P, of a reliable redundancy system i Is the power consumption, x, of each unit in the ith subsystem i Is the number of units in the i-th subsystem. F (F) C ，F V ，F W ，F P Respectively as a function of system cost, volume, mass, power consumption.
Further, the constraint model for screening the optimal function in the fifth step includes:
the method comprises the steps of solving redundancy design meeting minimum cost, volume, quality or power consumption requirements of an electrical system according to minimum reliability requirements of a known system:
secondly, the highest cost, volume, quality or power consumption requirements of the known system are met, and the redundancy design with highest reliability of the electrical system is solved:
further, in the step six, the output balance state sample is the same as the input initial balance state sample, that is, the algorithm converges to the optimal balance state result is indicated.
Further, the application field of the electrical system includes but is not limited to electrical equipment applied to the fields of aviation, aerospace, navigation, rail transit, automobiles, manufacturing industry and the like, and the application range of the redundant system unit includes but is not limited to resistors, inductors, voters, functional circuits and other electronic components or electric units capable of quantitatively describing reliability.
The objective of this embodiment 1 is to complete the redundancy design optimization of the bridge type reliability system by adopting the reliability redundancy design multi-objective optimization method based on the collaborative balance, so as to illustrate the implementation process of the invention and verify the accuracy. The optimization object of the embodiment is an electrical system bridge type reliability redundancy design, and comprises 5 subsystems, wherein each subsystem is formed by 1 to x i The redundant units constitute a redundant system as shown in fig. 2. The optimization design requires that the reliability of the system meets R 0 >A minimum system cost design is achieved at 0.99. According to the reliability principle, the calculation expression of the reliability of the bridge system is as follows:
R s ＝R(X 5 )[R(X 1 )+R(X 3 )-R(X 1 )R(X 3 )][R(X 2 )+R(X 4 )-R(X 2 )R(X 4 )]+[1-R(X 5 )][R(X 1 )R(X 2 )+R(X 3 )R(X 4 )-R(X 1 )R(X 2 )R(X 3 )R(X 4 )]
wherein R is s Is the system reliability, R (x i ) Is the i-th subsystem reliability. The computational expression of the bridge reliability system cost is:
wherein C is s Is the system reliability, C i Is the cost of the ith subsystem redundancy unit, x i Is the number of redundant units in the i-th subsystem. The redundant unit parameters of each subsystem are detailed in table 2.
TABLE 2 reliability and cost of redundant units for subsystems
The computing platform of the embodiment is MATLAB, the implementation flow of the optimization method is shown in figure 1, and the specific implementation steps are as follows:
on the premise of ensuring that the design requirement is met after one iteration, the number of initial units of each subsystem, such as 1,1 or 5,5,5,5,5, can be proposed by adopting a pre-estimation method.
Further, the initial balance sample can also be directly determined through calculation, and the calculation method is as follows:
assuming that the reliability of each subsystem is the same, solving the number of each subsystem unit meeting the reliability requirement can obtain:
R(x 1 )＝R(x 2 )＝R(x 3 )＝R(x 4 )＝R(x 5 )>0.931
according to the formula
The initial number of redundant units for each subsystem is 3,2,2,2,2.
Table 3 bridge system state change data set
Step 3, calculating a new sample set, wherein the calculation expression of the new sample set is as follows
Step 4, calculating the reliability and cost of each new sample in the new sample set;
step 4-1, according to the reliability principle, the calculation expression of the system reliability is as follows
R s ＝R(x 5 )[R(x 1 )+R(x 3 )-R(x 1 )R(x 3 )][R(x 2 )+R(x 4 )-R(x 2 )R(x 4 )]+[1-R(x 5 )][R(x 1 )R(x 2 )+R(x 3 )R(x 4 )-R(x 1 )R(x 2 )R(x 3 )R(x 4 )]
The calculation expression of the reliability of each subsystem is as follows:
wherein r is i Is the reliability of the unit in the ith subsystem.
Step 4-2, according to the cost model, the calculation expression of the bridge type reliability system cost is as follows:
step 5, screening an optimal sample;
step 5-1, screening out the system reliability R in the new sample set s >All balanced samples of 0.99, generating a sample set a;
step 5-2, screening out a sample with the lowest cost from the sample set A to generate a sample set B;
step 5-3, screening samples with non-zero sample number from the sample set B to generate a sample set C;
and 5-4, screening out a sample with highest system reliability from the sample set C, namely the optimal sample.
And 6, judging the optimal sample, and outputting the optimal sample.
Comparing the optimal sample output in the step 5-4 with the initial balance sample, wherein the two samples are consistent to indicate that the initial balance sample is the optimal reliability redundancy design. Otherwise, the optimal sample is taken as an initial balance sample, the step 2 is returned, and iterative calculation is continued.
When the input of the embodiment is 3,2,2,2,2, the calculated optimal redundancy is 1,2,3,1,2, and the iteration number is 4; when the input of the embodiment is 5,5,5,5,5, the calculated optimal redundancy is 1,2,3,1,2, and the iteration number is 5; when the input of this embodiment is 1, the calculated optimal redundancy is 1,2,3,1,2, and the number of iterations is 3. The final optimization results of this example were 1,2,3,1,2, and the system cost was reduced to 19 under the condition that the system reliability was greater than 0.99, so that the present invention is superior to the conventional balance optimization method, and the detailed results are compared with table 4.
Table 4 comparison of optimized results
The objective of this embodiment 2 is to complete parallel-serial redundancy design optimization of a certain type of electrical equipment by adopting a multi-objective optimization method for reliability redundancy design of an electrical system based on collaborative balance, so as to illustrate the implementation process of the invention and verify accuracy. The optimization objective of the embodiment is a five-stage parallel-series electrical system, as shown in fig. 3. The five-stage parallel-serial system optimization model expression is:
c in the formula 0 ，V 0 And W is 0 Cost, volume and mass constraints, respectively, model parameters are detailed in table 5.
TABLE 5 model parameters
The optimal results of the above examples are solved by a synergistic balance optimization method, and compared with the calculated results of the GAG1 method and the GAG1 combined particle swarm method, and the comparison results are shown in Table 6. Therefore, on the premise of the requirements of the cost, the volume and the quality of the electrical system, the redundancy system designed by adopting the collaborative balance optimization method is 0.9331, which is far higher than the reliability of the redundancy system designed by combining the GAG1 method and the GAG1 method with the particle swarm method by 0.9045. The collaborative balance optimization method has better performance.
Table 6 example 2 comparison of optimized results
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. The multi-objective optimization method for the reliability redundancy design of the electric system based on cooperative balance is characterized by comprising the following steps of:
step one, inputting an initial balance sample;
step two, based on the initial balance sample in the step one, enumerating the balance state variable quantity according to three states of adding a unit, reducing a unit or keeping unchanged of each subsystem, and constructing a sample change data set;
step three, calculating a new balance state sample set according to the sample change data set;
calculating the system reliability, cost, volume, quality and power consumption of each new sample in the new sample set;
step five, screening an optimal sample based on reliability, cost, volume, quality and power consumption requirements;
step six, comparing the optimal sample screened in the step five with the initial sample in the step one, wherein the optimal sample and the initial sample are consistent to show that the initial balance sample is the optimal reliability redundancy design; otherwise, taking the optimal sample as an initial balance sample, and returning to the second step to continue iterative computation.
2. The method for optimizing the design of multiple objectives for reliability redundancy of an electrical system based on collaborative balancing according to claim 1, wherein in the first step, the electrical system comprises n subsystems, each subsystem is composed of a plurality of units connected in parallel;
the initial sample balance sample can be given through estimation, the initial balance sample is required to become a feasible solution of the redundant system after the first round of calculation is completed, the initial balance sample is required to be given again when the conditions are not met, and the step is returned to perform the re-calculation;
the initial balance sample can also be directly determined through calculation, and the calculation method has a difference according to the optimization target:
(1) Solving a balance state sample with highest reliability in the required range of cost, volume, mass and power consumption, wherein the calculation mode of an initial input sample is to solve the number of units in each subsystem meeting the requirements of cost, volume, mass and/or power consumption on the assumption that the cost, volume or mass of each subsystem is the same;
(2) And solving the design of optimal cost, volume, quality and/or power consumption requirements in the reliability requirement range, wherein the calculation mode of the initial input sample is to solve the number of subsystem units meeting the reliability requirement on the assumption that the reliability of each subsystem is the same.
3. The method for optimizing the reliability redundancy design of an electrical system based on collaborative balancing according to claim 2, wherein the total number of state changes of the reliability system is 3 n A kind of module is assembled in the module and the module is assembled in the module.
4. The method for optimizing the design of the multiple objectives for the reliability redundancy of the electrical system based on the collaborative balance according to claim 1, wherein in the fifth step, the method for screening the optimal samples is as follows:
(1) Screening out samples with highest reliability in the requirements of cost, volume, quality and power consumption;
or (2) to achieve the lowest cost, volume, mass, or power consumption sample within a specified reliability range.
5. The method for optimizing the reliability redundancy design of an electrical system based on collaborative balance according to claim 4, wherein the step five specifically comprises the steps of:
step 5-1, screening samples meeting the requirements of system cost, volume, quality and/or power consumption in a new sample set to generate a sample set A;
step 5-2, screening samples with non-zero subsystem sample numbers from the sample set A to generate a sample set B;
and 5-3, screening out a sample with highest system reliability from the sample set B, namely the optimal sample.
6. The method for optimizing the reliability redundancy design of an electrical system based on collaborative balancing according to claim 4, wherein the step five specifically comprises the steps of:
step 5-1, screening out that the reliability of the system in the new sample set meets R s >R 0 Generating a sample set a;
step 5-2, screening out samples with the lowest cost, volume, mass and/or power consumption from the sample set A to generate a sample set B;
step 5-3, screening samples with non-zero sample number from the sample set B to generate a sample set C;
and 5-4, screening out a sample with highest system reliability from the sample set C, namely the optimal sample.
7. The method for optimizing the design of multiple objectives for reliability redundancy of an electrical system based on collaborative balancing according to claim 1, wherein the electrical system includes but is not limited to electrical equipment used in the field of aviation, aerospace, marine, rail transit, automotive or manufacturing.
8. The method for optimizing the reliability redundancy design of the electric system based on the collaborative balance according to claim 6, wherein the unit is an electronic component or an electric stand-alone machine which comprises a resistor, an inductor, a voter, a sensor or a functional circuit and the like and can quantitatively describe the reliability.
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