Multi-objective optimization method for reliability redundancy design of electrical system based on synergic balance

Abstract

The application discloses a kind of based on the multi-objective optimization method of electrical system reliability redundancy design of coordination balance, solve the influence of traditional optimization method only considering single subsystem redundancy unit change to system reliability, expense, volume, mass and power consumption, lead to optimization result can only calculate the local optimal result in certain range;The application completes the global optimization with system reliability, expense, volume, mass and power consumption as target by considering the influence of redundancy unit coordination change to each subsystem;The multi-objective optimization method of reliability redundancy design based on subsystem and redundancy unit coordination balance of the application, algorithm is clear, implementation process is simple, and optimal result can be calculated within 10 iterations calculation times generally.Just like genetic algorithm, particle swarm optimization algorithm, ant colony algorithm and other intelligent algorithms, the implementation process of the application is simpler, and the iteration calculation times within 10 times are significantly less than the iteration calculation of general intelligent algorithm 100 times and above, and the calculation cost is lower.

Description

Technical Field

[0001] This invention belongs to the field of reliability design technology, specifically relating to a multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing. Background Technology

[0002] With the development of science and technology, the demand for electrical systems in aerospace, aviation, marine, rail transportation, automotive, and manufacturing industries is increasing. To improve the reliability of electrical systems, reliability optimization design methods are gaining increasing attention. Reliability redundancy design, as an important means of improving the reliability of complex systems, increases the system's reliability by increasing the number of redundancies. However, increasing the number of redundancies inevitably increases system cost, size, weight, and power consumption. Therefore, it is essential to minimize the number of redundancies while meeting reliability, cost, size, weight, and power consumption requirements. Multi-objective optimization in electrical system reliability redundancy design typically includes two optimization objectives: (1) maximizing the reliability of the electrical system by correctly configuring each subsystem unit under constraints such as system cost, size, weight, and power consumption; (2) minimizing system cost, size, weight, or power consumption by correctly configuring each subsystem unit under constraints such as electrical system reliability indicators.

[0003] Pattern search and heuristic optimization methods typically use the impact of subsystem unit changes on the overall reliability, cost, size, weight, and power consumption of the electrical system as the optimization basis to determine whether to add or remove new units from the subsystem. Similar to the "hill climbing" method, these methods easily calculate local optima, but often neglect the impact of inter-subsystem interactions on the overall system reliability. In recent years, reliability redundancy system optimization methods based on intelligent algorithms (genetic algorithms, particle swarm optimization, ant colony optimization, artificial intelligence neural network methods, etc.) have also gradually developed, successfully achieving the optimization goals of reliability redundancy systems. However, the implementation of these optimization methods suffers from complexity and high computational costs. Summary of the Invention

[0004] In view of this, the purpose of this invention is to develop a multi-objective optimization method for reliability redundancy design of electrical systems based on the cooperative balancing of subsystems and redundant units. This method fully considers the impact of changes in redundant units within the system on the performance parameters of complex systems, such as reliability, cost, volume, mass, and power consumption, and can achieve the global optimization objective of reliability redundancy design in engineering applications.

[0005] A multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing includes:

[0006] Step 1: Input the initial balanced sample;

[0007] Step 2: Based on the initial equilibrium sample from Step 1, enumerate the changes in equilibrium state according to three states: adding one unit, removing one unit, or keeping it unchanged for each subsystem, and construct a sample change dataset.

[0008] Step 3: Calculate the new equilibrium state sample set based on the sample change dataset;

[0009] Step 4: Calculate the system reliability, cost, volume, mass, and power consumption for each new sample in the new sample set;

[0010] Step 5: Select the optimal sample based on reliability, cost, size, weight, and power consumption requirements;

[0011] Step 6: Compare the optimal sample selected in Step 5 with the initial sample in Step 1. If they are consistent, it indicates that the initial balanced sample is the optimal reliability redundancy design; otherwise, use the optimal sample as the initial balanced sample and return to Step 2 to continue iterative calculation.

[0012] Preferably, in step one, the electrical system includes n subsystems, and each subsystem is composed of multiple units connected in parallel;

[0013] The initial equilibrium sample can be given by estimation. The initial equilibrium sample should be a feasible solution of the redundant system after the first round of calculation. If the above condition is not met, the initial equilibrium sample should be given again and the calculation should be returned to step two.

[0014] The initial equilibrium sample can also be determined directly through calculation, and the calculation method varies depending on the optimization objective:

[0015] (1) Within the requirements of cost, volume, mass and power consumption, find the equilibrium state sample with the highest reliability. The calculation method of the initial input sample is to assume that the cost, volume or mass of each subsystem is the same, and find the number of units in each subsystem that meets the requirements of cost, volume, mass and / or power consumption.

[0016] (2) Solve for the optimal cost, volume, mass and / or power consumption requirements within the reliability requirements. The initial input sample is calculated by assuming that the reliability of each subsystem is the same and solving for the number of subsystem units that meet the reliability requirements.

[0017] Ideally, the total number of state changes for a reliable system is 3. n kind.

[0018] Preferably, in step five, the method for selecting the optimal sample is as follows:

[0019] (1) Select the sample with the highest reliability within the range of cost, volume, weight and power consumption requirements;

[0020] Or (2) Achieve the lowest cost, size, weight or power consumption sample within the specified reliability range.

[0021] Preferably, within the requirements of cost, volume, mass, and power consumption, the equilibrium state sample with the highest reliability is obtained. Step five specifically includes:

[0022] Step 5-1: Select samples from the new sample set that meet the system cost, volume, mass and / or power consumption requirements, and generate sample set A;

[0023] Step 5-2: Select samples from sample set A that have a non-zero number of samples in the subsystem to generate sample set B;

[0024] Step 5-3: Select the sample with the highest system reliability from sample set B, which is the optimal sample.

[0025] Preferably, within the reliability requirements, the optimal cost, volume, weight, and / or power consumption requirements are determined. Step five specifically includes:

[0026] Step 5-1: In the new sample set, screen for systems whose reliability meets R. s Generate a sample set A from all balanced samples with R0 > 0;

[0027] Step 5-2: Select the samples with the lowest cost, volume, mass and / or power consumption from sample set A to generate sample set B;

[0028] Step 5-3: Select samples with a non-zero number of samples from sample set B to generate sample set C;

[0029] Step 5-4: Select the sample with the highest system reliability from the sample set C, which is the optimal sample.

[0030] Preferably, the electrical system includes, but is not limited to, electrical equipment used in the fields of aviation, aerospace, marine, rail transportation, automobile, or manufacturing.

[0031] Preferably, the unit is an electronic component or electronic device that can quantitatively describe reliability, including resistors, inductors, voting devices, sensors, or functional circuits.

[0032] The present invention has the following beneficial effects:

[0033] This invention presents a multi-objective optimization method for reliability redundancy design based on the coordinated balancing of subsystems and redundant units. It addresses the problem that traditional optimization methods only consider the impact of changes in redundant units of individual subsystems on system reliability, cost, size, weight, and power consumption, resulting in optimization results that can only calculate locally optimal outcomes within a certain range. This invention, by considering the impact of coordinated changes in redundant units on each subsystem, achieves global optimization with the objectives of system reliability, cost, size, weight, and power consumption.

[0034] This invention presents a multi-objective optimization method for reliability redundancy design based on the collaborative balancing of subsystems and redundant units. The algorithm is clear and the implementation process is simple, typically requiring no more than 10 iterations to calculate the optimal result. Compared to intelligent algorithms such as genetic algorithms, particle swarm optimization, and ant colony optimization, this invention is simpler to implement, requiring significantly fewer than 10 iterations compared to the 100 or more iterations typically required by intelligent algorithms, resulting in lower computational costs.

[0035] This invention fully considers the synergistic balancing effect between subsystems and redundant units, overcoming the limitations of existing balancing optimization methods that only consider the impact of changes in redundant units of a single subsystem on system reliability, cost, size, weight, and power consumption. It develops a new multi-objective optimization method based on the synergistic balancing of subsystems and redundant units, enhancing the practical engineering application value of this method. Furthermore, the calculation process of this invention is simple and can be easily implemented using common commercial software (such as Matlab). Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating the implementation of the multi-objective optimization method for reliability redundancy design based on collaborative balancing in this invention.

[0037] Figure 2 This is a schematic diagram of a bridge-type reliability redundancy system for a certain type of electrical equipment in Embodiment 1 of the present invention;

[0038] Figure 3 This is a schematic diagram of a five-level parallel-series reliability redundancy system for a certain type of electrical equipment in Embodiment 2 of the present invention. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0040] A multi-objective optimization method for reliability redundancy design based on cooperative balancing, such as... Figure 1 As shown, the optimization method includes:

[0041] Step 1: Propose an initial balanced sample;

[0042] Step 2: Enumerate the changes in equilibrium state according to the three states of adding, removing, and keeping the subsystem unchanged, and construct a sample change dataset;

[0043] Step 3: Calculate the new equilibrium state sample set based on the sample change data;

[0044] Step 4: Calculate the reliability, cost, volume, mass, and power consumption of each new sample in the new sample set;

[0045] Step 5: Select the optimal sample under constraints of reliability, cost, size, weight, and power consumption;

[0046] Step 6: Determine the optimal sample and output the optimal sample.

[0047] The above method, in the multi-objective optimization process of reliability redundancy design, considers not only the impact of redundant units on subsystems but also the impact of the coordinated balancing of redundant units among subsystems on the reliability of complex electrical systems, ultimately achieving deep optimization of electrical system reliability redundancy design. Furthermore, the calculation process of this invention is simple, requires few iterations, and is easy to implement. The system consists of multiple subsystems connected in series and parallel, and each subsystem can be divided into 1 to x subsystems. i Each unit is indivisible.

[0048] Furthermore, in step one, the initial equilibrium sample can be determined through an estimation method. The initial equilibrium sample must become a feasible solution for the redundant system after the first round of calculations. If this requirement is not met, a new initial equilibrium sample should be provided, and the calculation should be repeated. Alternatively, the initial equilibrium sample can be used to directly determine a feasible solution through calculation. The calculation method varies depending on the optimization objective. The specific calculation method is as follows:

[0049] (1) Within the range of cost, volume, mass, and power consumption requirements, find the equilibrium state sample with the highest reliability. The initial input sample is calculated by assuming that the cost, volume, mass, or power consumption of each subsystem is the same, and then finding the number of units in each subsystem that meets the cost, volume, mass, and power consumption requirements.

[0050] (2) Solve for the optimal cost, volume, mass or power consumption design within the reliability requirements. The initial input sample is calculated by assuming that the reliability of each subsystem is the same and solving for the number of subsystem units that meet the reliability requirements.

[0051] Furthermore, in step two, each subsystem enumerates the state change library of the reliability system according to three states: increase (+1), decrease (-1), and remain unchanged (+0). Based on the number of subsystems, the total number of state changes for the reliability system is 3. n The sample variations are shown in Table 1.

[0052] Table 1 Sample Variation Library

[0053]

[0054]

[0055] Furthermore, the calculation method for the new sample set in step three includes, but is not limited to,

[0056]

[0057] Furthermore, the expression for calculating the reliability of the reliability redundancy system in step four is as follows:

[0058] R s =F R [R(x1),R(x2),…,R(x i ),…,R(x n )]

[0059] In the formula, R s It is the system cost of a reliable redundant system, R(x) i F is the reliability of the i-th subsystem. R Indicates R s It is related to R(x) i Related functions, x1, x i ,x n These represent the number of units in the 1st, i, and nth subsystems, respectively. Based on the differences in the reliability models of the series and parallel connections of the various subsystems within the electrical system, the function F... R There are also differences.

[0060] Furthermore, the calculation expressions for the cost, volume, mass, and power consumption of the reliability redundancy system in step four are as follows:

[0061] C s =F C (C1,…,C i ,…,C n ,x1,…x i ,…,x n )

[0062] V s =F V (V1,…,V i ,…,V n ,x1,…x i ,…,x n )

[0063] W s =F W (W1,…,W i ,…,W n ,x1,…x i ,…,x n )

[0064] P s =F P (P1,…,P i ,…,P n ,x1,…x i ,…,x i )

[0065] In the formula, C sIt is the system cost of a reliable redundant system, C i V is the cost of each unit in the i-th subsystem. s V is the system volume of a reliable redundant system. i W is the volume of each unit in the i-th subsystem. s It refers to the system quality of a reliable and redundant system, W. i P is the mass of each unit in the i-th subsystem. s It is the system power consumption of the reliability redundancy system, P i x is the power consumption of each unit in the i-th subsystem. i F is the number of units in the i-th subsystem. C F V F W F P These are functions of system cost, size, mass, and power consumption, respectively.

[0066] Furthermore, the constraint model for selecting the optimal function in step five includes:

[0067] (1) Given the minimum reliability requirements of the system, solve for the redundancy design that satisfies the minimum cost, size, weight, or power consumption requirements of the electrical system:

[0068]

[0069] (2) Given the system's highest cost, size, weight, or power consumption requirements, solve for the redundancy design with the highest reliability of the electrical system:

[0070]

[0071] Furthermore, in step six, the output equilibrium state sample is the same as the input initial equilibrium state sample, which indicates that the algorithm converges to the optimal equilibrium state result.

[0072] Furthermore, the application fields of the electrical system include, but are not limited to, electrical equipment used in aviation, aerospace, marine, rail transportation, automobile, and manufacturing industries. The scope of application of redundant system units includes, but is not limited to, electronic components or electrical units that can quantitatively describe reliability, such as resistors, inductors, voting devices, and functional circuits.

[0073] The purpose of this embodiment 1 is to optimize the redundancy design of a bridge reliability system using a multi-objective optimization method based on cooperative balancing, in order to illustrate the implementation process of the invention and verify its accuracy. The optimization object of this embodiment is the bridge reliability redundancy design of an electrical system, which includes 5 subsystems, each subsystem consisting of numbers 1 to x. i A redundant system is composed of redundant units, such as Figure 2As shown. The optimization design requires achieving the lowest system cost while ensuring system reliability R0 > 0.99. Based on reliability principles, the expression for calculating the reliability of a bridge system is:

[0074] R s =R(X5)[R(X1)+R(X3)-R(X1)R(X3)][R(X2)+R(X4)-R(X2)R(X4)]+[1-R(X5)][R(X1)R(X2)+R(X3)R(X4)-R(X1)R(X2)R(X3)R(X4)]

[0075] In the formula, R s It is the system reliability, R(x) i ) represents the reliability of the i-th subsystem. The formula for calculating the cost of a bridge reliability system is:

[0076]

[0077] In the formula, C s It refers to system reliability, C i It is the cost of the redundant unit of the i-th subsystem, x i This represents the number of redundant units in the i-th subsystem. See Table 2 for details of the redundant unit parameters for each subsystem.

[0078] Table 2 Reliability and Cost of Redundant Units in Each Subsystem

[0079]

[0080] In this embodiment, the computing platform is MATLAB, and the optimization method implementation process is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0081] Step 1: Input the initial equilibrium sample, that is, determine the number of units in each subsystem;

[0082] Provided that the design requirements are met after one iteration, the initial number of units for each subsystem can be estimated using a predictive method, such as 1,1,1,1,1 or 5,5,5,5,5.

[0083] Furthermore, the initial equilibrium sample can also be determined directly through calculation, as follows:

[0084] Assuming that all subsystems have the same reliability, the number of subsystem units that meet the reliability requirements can be calculated as follows:

[0085] R(x1)=R(x2)=R(x3)=R(x4)=R(x5)>0.931

[0086] According to the formula The initial number of redundant units in each subsystem is calculated to be 3, 2, 2, 2, 2.

[0087] Step 2: Enumerate the state change library of the reliability system according to the three states of increasing (+1), decreasing (-1), and remaining unchanged (+0) for the number of units in each subsystem. The total number of state changes for the bridge reliability system is 243, as detailed in Table 3.

[0088] Table 3 Dataset of Bridge System State Changes

[0089]

[0090] Step 3: Calculate the new sample set. The expression for calculating the new sample set is:

[0091]

[0092] Step 4: Calculate the reliability and cost of each new sample in the new sample set;

[0093] Step 4-1: According to the principle of reliability, the expression for calculating system reliability is as follows:

[0094] R s =R(x5)[R(x1)+R(x3)-R(x1)R(x3)][R(x2)+R(x4)-R(x2)R(x4)]+[1-R(x5)][R(x1)R(x2)+R(x3)R(x4)-R(x1)R(x2)R(x3)R(x4)]

[0095] The reliability calculation expressions for each subsystem are as follows:

[0096]

[0097] In the formula, r i It represents the reliability of a unit in the i-th subsystem.

[0098] Step 4-2: Based on the cost model, the calculation expression for the cost of a bridge reliability system is as follows:

[0099]

[0100] Step 5: Select the optimal sample;

[0101] Step 5-1: Screen the system reliability R in the new sample set. s Generate sample set A from all balanced samples with a value greater than 0.99.

[0102] Step 5-2: Select the sample with the lowest cost from sample set A to generate sample set B;

[0103] Step 5-3: Select samples with a non-zero number of samples from sample set B to generate sample set C;

[0104] Step 5-4: Select the sample with the highest system reliability from the sample set C, which is the optimal sample.

[0105] Step 6: Determine the optimal sample and output the optimal sample.

[0106] Compare the optimal sample output in step 5-4 with the initial balanced sample. If they match, it indicates that the initial balanced sample represents the optimal reliability redundancy design. Otherwise, use the optimal sample as the initial balanced sample and return to step 2 to continue the iterative calculation.

[0107] In this embodiment, when the input is 3, 2, 2, 2, 2, the calculated optimal redundancy design is 1, 2, 3, 1, 2, with 4 iterations. When the input is 5, 5, 5, 5, 5, the calculated optimal redundancy design is 1, 2, 3, 1, 2, with 5 iterations. When the input is 1, 1, 1, 1, 1, the calculated optimal redundancy design is 1, 2, 3, 1, 2, with 3 iterations. The final optimization result in this embodiment is always 1, 2, 3, 1, 2. With a system reliability greater than 0.99, the system cost is reduced to 19. This demonstrates that the present invention is superior to the traditional balanced optimization method. Detailed results are shown in Table 4.

[0108] Table 4 Comparison of Optimization Results

[0109]

[0110] The purpose of this embodiment 2 is to optimize the parallel-series redundancy design of a certain type of electrical equipment using a multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing, so as to illustrate the implementation process of the present invention and verify its accuracy. The optimization object of this embodiment is a five-level parallel-series electrical system, such as... Figure 3 As shown. The optimization model expression for the five-stage parallel-series system is:

[0111]

[0112] In the formula, C0, V0 and W0 are cost, volume and mass constraints, respectively. The model parameters are detailed in Table 5.

[0113] Table 5 Model Parameters

[0114]

[0115] The optimal results of the above examples were obtained using the cooperative balancing optimization method, and compared with the results of the GAG1 method and the GAG1 combined particle swarm optimization method. The comparison results are detailed in Table 6. It can be seen that, under the premise of electrical system cost, volume, and quality requirements, the redundancy system designed using the cooperative balancing optimization method has a reliability of 0.9331, which is significantly higher than the reliability of the redundancy system designed using the GAG1 method and the GAG1 combined particle swarm optimization method (0.9045). The cooperative balancing optimization method of this invention has superior performance.

[0116] Table 6 Comparison of optimization results in Example 2

[0117]

[0118] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing, characterized in that, include: Step 1: Input the initial balanced sample; The electrical system includes Each subsystem consists of multiple units connected in parallel. The initial equilibrium sample is given by prediction. The initial equilibrium sample should become a feasible solution of the redundant system after the first round of calculation. If the above condition is not met, the initial equilibrium sample should be given again and the calculation should be returned to step two. Alternatively, the initial equilibrium sample can be determined directly through calculation, with the calculation method varying depending on the optimization objective: (1) Within the requirements of cost, volume, mass and power consumption, solve the equilibrium state sample with the highest reliability. The calculation method of the initial input sample is to assume that the cost, volume or mass of each subsystem is the same, and solve the number of units in each subsystem that meets the requirements of cost, volume, mass and / or power consumption. (2) Solve for the optimal cost, volume, mass and / or power consumption requirements within the reliability requirements. The initial input sample is calculated by assuming that the reliability of each subsystem is the same and solving for the number of subsystem units that meet the reliability requirements. Step 2: Based on the initial equilibrium sample from Step 1, enumerate the changes in equilibrium state according to three states: adding one unit, removing one unit, or keeping it unchanged for each subsystem, and construct a sample change dataset. Step 3: Calculate the new equilibrium state sample set based on the sample change dataset; Step 4: Calculate the system reliability, cost, volume, mass, and power consumption for each new sample in the new sample set; Step 5: Select the optimal sample based on reliability, cost, size, weight, and power consumption requirements; Step 6: Compare the optimal sample selected in Step 5 with the initial sample in Step 1. If they are consistent, it indicates that the initial balanced sample is the optimal reliability redundancy design; otherwise, use the optimal sample as the initial balanced sample and return to Step 2 to continue iterative calculation.

2. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 1, characterized in that, The total number of state changes of a reliable system is kind.

3. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 1, characterized in that, In step five, the method for selecting the optimal sample is as follows: (1) Select the sample with the highest reliability within the range of cost, volume, weight and power consumption requirements; Or (2) Achieve the lowest cost, size, weight or power consumption sample within the specified reliability range.

4. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 3, characterized in that, Within the constraints of cost, volume, mass, and power consumption, the fifth step involves finding the equilibrium state sample with the highest reliability. Step 5-1: Select samples from the new sample set that meet the system cost, volume, mass and / or power consumption requirements, and generate sample set A; Step 5-2: Select samples from sample set A that have a non-zero number of samples in the subsystem to generate sample set B; Step 5-3: Select the sample with the highest system reliability from sample set B, which is the optimal sample.

5. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 3, characterized in that, Step five involves finding the optimal design for cost, volume, weight, and / or power consumption within the reliability requirements. Step 5-1: Screen the new sample set for systems that meet the reliability requirements. Generate a sample set A from all balanced samples; Step 5-2: Select the samples with the lowest cost, volume, mass and / or power consumption from sample set A to generate sample set B; Step 5-3: Select samples with a non-zero number of samples from sample set B to generate sample set C; Step 5-4: Select the sample with the highest system reliability from the sample set C, which is the optimal sample.

6. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 1, characterized in that, The electrical system includes, but is not limited to, electrical equipment used in the fields of aviation, aerospace, marine, rail transportation, automobile, or manufacturing.

7. The multi-objective optimization method for reliability redundancy design of electrical systems based on cooperative balancing as described in claim 5, characterized in that, The unit is an electronic component or electronic device that can quantitatively describe reliability, including resistors, inductors, voting devices, sensors, or functional circuits.

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