CN113326584B - Electrical equipment optimization design method taking robustness and reliability into consideration - Google Patents
Electrical equipment optimization design method taking robustness and reliability into consideration Download PDFInfo
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- CN113326584B CN113326584B CN202110627549.3A CN202110627549A CN113326584B CN 113326584 B CN113326584 B CN 113326584B CN 202110627549 A CN202110627549 A CN 202110627549A CN 113326584 B CN113326584 B CN 113326584B
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- G06F30/00—Computer-aided design [CAD]
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- G06F30/17—Mechanical parametric or variational design
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/25—Design optimisation, verification or simulation using particle-based methods
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- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
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- G06—COMPUTING; CALCULATING OR COUNTING
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Abstract
The invention relates to the technical field of optimal design of electrical equipment under the influence of uncertain factors, in particular to an optimal design method of electrical equipment, which has robustness and reliability. The method fully considers uncertain factors in the optimal design of the electrical equipment. Wherein, the robustness is ensured by establishing a new objective function based on the original objective function: the first sub-function is the ratio of the objective function to the objective function value obtained from the deterministic optimization problem; the second sub-function is the ratio of the standard deviation function of the objective function to the standard deviation value of the objective function corresponding to the optimal solution under deterministic optimization. The system reliability index is reflected by the constraint condition of the optimization problem being satisfied under a certain probability. And combining the robustness index and the reliability index, and selecting a proper reliability analysis method and an optimization algorithm to solve. The optimal solution searched by the method can improve both reliability and robustness, and fully improves the disturbance rejection capability of the electrical product.
Description
Technical Field
The invention relates to the technical field of optimal design of electrical equipment under the influence of uncertain factors, in particular to research on an optimal design method (RBRDO) of electrical equipment, which has the advantages of both robustness and Reliability and has uncertain material parameters and geometric dimensions of the electrical equipment.
Background
With the development of technology, the design standard of engineering products is higher and higher. Such as better product performance, lower cost, higher reliability and robustness. To balance these conflicting performance metrics, the designer may perform a related optimization design, and the optimization design process may take into account uncertainty factors.
Uncertainty can be generally categorized into stochastic uncertainty and cognitive uncertainty. The former is an inherently random nature and the latter refers to uncertainty due to lack of data or related knowledge. These uncertainties are not negligible, otherwise the product performance will not meet the expected criteria. The deterministic optimization design usually ignores the influence of uncertain factors, and the calculated result has certain limitation, so that the research on the optimization design method under the influence of uncertain factors has important significance.
In the design and manufacturing process of the product, the actual values and the nominal values of some physical quantities such as material parameters, geometric dimensions and the like often deviate, the existence of uncertain factors in engineering brings great challenges to the reliability of electrical equipment, and the current uncertain mathematical description method mainly comprises three types of probability statistical models, fuzzy models and convex set models.
The design under the uncertainty condition is widely applied to various fields of electrical engineering, mechanical engineering and the like, and the reliability optimization design and the robustness optimization design are two main design methods for dealing with uncertainty. Reliability design refers to a design that allows constraints to seek a solution that is optimal for certain performance under certain probability. The development of the reliability theory is subjected to a long process, a plurality of domestic and foreign scholars make great contribution to the development of the reliability theory, and the reliability optimization design method is continuously innovated and has an increasingly wide application range. The present reliability analysis method can be mainly divided into an approximate analysis method, a numerical simulation method and an auxiliary function method. While the robustness optimization design aims at finding the optimal solution of performance insensitive to the influence of uncertain factors, it is the stability of performance that is, the less sensitive the performance is to the influence of disturbance, the stronger the robustness is. The optimization design method considering robustness can be divided into two types, one is a random probability design method and the other is a non-probability robust optimization design method. The existing researches are based on one type of uncertainty design method, namely, reliability optimization design or robustness design, and few documents comprehensively consider two types of design methods, so that reliability robustness design can be carried out by combining the two types of design methods, random uncertainty can be processed, and meanwhile, the influence of parameter variation on performance stability is considered. In view of this, how to build a feasible and effective robust optimization design method and a reliability optimization design method becomes an important research direction in the optimization field.
Disclosure of Invention
Object of the Invention
In order to take probability uncertainty factors affecting the safe and stable operation of electrical equipment into consideration in a design stage, the influence of the uncertainty factors on the electrical equipment is measured by introducing reliability analysis and robustness analysis simultaneously, a robust optimization design model based on the reliability analysis is researched and established, a design scheme is manufactured by the model, the obtained design result has higher reference value, accords with the actual situation, and has stronger applicability in engineering.
Technical proposal
An electrical equipment optimization design method taking robustness and reliability into consideration is characterized by comprising the following steps:
step one, solving a deterministic optimization design problem; vector x= [ x ] for n design variables described in equation (1) 1 ,x 2 ,...,x n ] T In a determined design space [ x L ,x U ]In, search satisfies constraint g i (x) An optimal solution x for minimizing the objective function f (x) at 0 * ：
minimize f(x)
subject to g i (x)≤0 i＝1,...,m (1)
x L ≤x≤x U
Wherein x is an n-dimensional design variable vector; f (x) is an objective function of the optimal design model, g (x) is less than or equal to 0 and is a constraint condition, m is the number of constraint functions, and x L To design the lower limit of the variable vector x, x U The upper limit of the variable vector x is designed;
the influence of uncertainty factors is then processed to calculate the standard deviation of the objective function: assuming that each variable in x contains an uncertainty factor, let the standard deviation of the kth design variable be sigma x,k ，σ 2 x,k For its variance; the optimal solution x of the formula (1) * Taking into formula (2), obtaining standard deviation of the objective function f (x), and recording as
Step two, respectively calculating the average ratio of the objective functions under the reliability optimizationStandard deviation ratio of optimal solution and objective function +.>Is the optimal solution of (a); wherein mu f ＝f(μ x ) Nominal value mu is taken for the design variable x The corresponding objective function value, sigma f The standard deviation of the objective function corresponding to the design variable vector x; />Representing an objective function value corresponding to an optimal solution obtained under deterministic optimization; r is R t,i Representing the target reliability corresponding to the ith constraint function:
wherein P () represents the reliability calculated from the probability distribution of the design variable uncertainty factor, the mean function ratioThe optimal solution from reliability optimization equation (4) is denoted as x 1 * Standard deviation function ratioThe optimal solution from reliability optimization equation (5) is denoted as x 2 * ；
Step three, calculating weight factors, and calculating two indexes f of the structure according to the optimal solution obtained in the step two 1 (x)＝μ f /μ * f And f 2 (x)＝σ f /σ * f Respectively corresponding weight factor omega 1 ，ω 2 ；
Step four, according to the weight factor omega obtained in step three 1 ，ω 2 And constructing a new optimal design model, and selecting a proper reliability analysis method and an optimization algorithm to solve the new optimal design model.
In the third step, the calculation method of the weight factor is shown in formula (6):
wherein f 1 (x 1 * ) The optimal solution x of equation (4) 1 * A corresponding objective function value; f (f) 2 (x 2 * ) The optimal solution x of equation (5) 2 * A corresponding objective function value; f (f) 2 (x 1 * ) Representing the optimal solution x of equation (4) 1 * Substituting the objective function value obtained in the model of the formula (5); f (f) 1 (x 2 * ) Representing the optimal solution x of equation (5) 2 * Substituting the target obtained in the model of the formula (4)The function value is marked.
In the fourth step, a specific optimization model with both robustness and reliability is shown in formula (7):
wherein f RBRDO The method is characterized in that a novel objective function is established for an optimization model under uncertain factors on the premise of ensuring robustness on the basis of an original objective function;
the reliability analysis method is a weight index Monte Carlo simulation method; selecting a particle swarm optimization algorithm by a global optimization method; and (3) solving the optimization model of the formula (7) by adopting a reliability analysis method and a global optimization method.
The advantages and effects:
1. the uncertainty factors in the optimal design of the electrical equipment are fully considered, a new optimal design method which takes robustness and reliability into consideration is established, and theory and technology with reference value are provided for a designer to manufacture related design schemes of the electrical equipment.
2. The reliability robust design is performed, so that random uncertainty can be processed, and meanwhile, the influence of parameter variation on performance stability is considered.
3. The optimal solution searched by the method can improve both reliability and robustness, and fully improves the disturbance rejection capability of the electrical product.
Drawings
FIG. 1 is a solving block diagram of an optimization design model considering robustness and reliability;
FIG. 2 is a block diagram of an optimal design model solution taking robustness and reliability into account in engineering.
Detailed Description
For the purpose of making the object of the present invention, the technical solution, the advantages of which are more clearly apparent, the present invention will be further described in detail with reference to the accompanying drawings and the specific application in engineering.
An electrician equipment optimization design method which combines robustness and reliability. The specific implementation steps are as follows:
step one: the design variables, the upper limit and the lower limit of the electrical equipment optimization design, the objective function and the constraint function of the electrical equipment optimization design are determined, and the expression of the constraint function in engineering problems is unknown in general, so that an auxiliary model needs to be constructed to be approximated, the method for constructing the auxiliary model is selected by the inventor to be an adaptive sampling Kriging method, other methods can be selected by other technicians, and the method is not limited to the method. First, a deterministic optimization design model is introduced, and the deterministic optimization design model is specifically shown in the following formula:
min f(x)
s.t.g i (x)≤0 i＝1，…，m
x L ≤x≤x U
wherein x is an n-dimensional design variable vector; f (x) is an objective function of the optimal design model; g (x) is less than or equal to 0 and is a constraint condition, and m is the number of constraint functions; x is x L To design the lower limit of the variable x, x U Is the upper limit of the design variable x.
Step two: reliability design refers to the constraint condition being met under a certain probability, and a solution with optimal performance is sought on the basis of the constraint condition. While the robustness optimization design aims at finding the optimal solution of performance insensitive to the influence of uncertain factors, it is the stability of performance that is, the less sensitive the performance is to the influence of disturbance, the stronger the robustness is. The invention provides an uncertain factor optimization model which establishes a novel objective function f on the basis of an original objective function on the premise of ensuring robustness RBRDO Meanwhile, the constraint condition is enabled to meet certain probability, so that the reliability of the solution is ensured. By combining the two methods, the aim of combining robustness and reliability to be applied to the optimal design under the influence of uncertain factors is fulfilled. The optimization model which is established on the basis of the first step and gives consideration to reliability and robustness is as follows:
s.t.P(g i (x)≤0)≥R t，i i＝1，...，m
x L ≤x≤x U
where μ f ＝f(μ x )
wherein, the liquid crystal display device comprises a liquid crystal display device,and->The objective function value and standard deviation corresponding to the optimal solution x obtained by the deterministic optimization problem (1) are represented; mu (mu) x Represents the nominal value, mu, of the design variable x f Nominal value mu for design variable x x Corresponding objective function value, σ, when ignoring uncertainty f The variance of the objective function corresponding to any design scheme x. Omega 1 ，ω 2 As a weight factor, R t，i And representing the target reliability corresponding to the ith constraint function. Sigma (sigma) 2 x，k Represents the kth design variable x k (k=1,., n, n is the dimension of the design variable) the corresponding variance under the influence of an uncertainty factor.
Step three: solving an optimal solution under deterministic optimization, and calculating a corresponding objective function valueAnd standard deviation function value->And obtaining an objective function value and an optimal solution corresponding to the optimization model.
Step four: determining the mean function ratioReliability optimization optimal solution x of (2) 1 * Namely, the following was obtainedOptimizing an optimal solution of the model.
s.t.P(g i (x)≤0)≥R t，i i＝1，...，m
x L ≤x≤x U
Step five: find standard deviation function ratioReliability optimization optimal solution x of (2) 2 * Namely, the following optimal solution of the optimization model is obtained.
s.t.P(g i (x)≤0)≥R t，i i＝1，...，m
x L ≤x≤x U
Step six: the optimal solution x obtained in the fourth step and the fifth step is calculated 1 * ，x 2 * The formula of the calculation weight is carried in, and the two-term function ratio f can be calculated 1 ，f 2 Respectively corresponding weight factor omega 1 ，ω 2 。
Weight coefficient omega 1 ，ω 2 The calculation method of (2) is shown as follows:
ω 2 ＝1-ω 1
wherein f 1 (x 1 * ) Optimal solution x representing optimization problem 1 * A corresponding objective function value; f (f) 2 (x 2 * ) Optimal solution x representing optimization problem 2 * A corresponding objective function value; f (f) 2 (x 1 * ) Representing the optimal solutionx 1 * Substituting the target function value obtained by the model; f (f) 1 (x 2 * ) Representing the optimal solution x 2 * Substituting the obtained objective function value. If the objective function of the optimization problem contains p subfunctions, the weight calculation can be performed by using the following popularization formula.
Wherein f 1 (x),...,f p (x) Respectively represent 1 st to p th subfunctions, x 1 * ,...,x p * Respectively represent the subfunctions f 1 (x),...,f p (x) The optimal solution obtained under the reliability optimization can be used for calculating each sub-function f according to a formula through the solution sum functions 1 (x),...,f p (x) The weight omega corresponding to the previous 1 ,...,ω p 。
Step seven: according to the weight factor omega obtained in the step six 1 ，ω 2 And constructing a new optimal design model for solving. The reliability analysis method can be selected according to the self requirements of a designer, and the reliability analysis method is selected by a weight exponential type Monte Carlo simulation method and a particle swarm optimization algorithm to solve an optimization model. The specific optimization model is as follows:
s.t.P(g i (x)≤0)≥R t,i i＝1,...,m
x L ≤x≤x U
in summary, a specific implementation flow of the electrical equipment optimization design method taking both robustness and reliability into consideration is shown in fig. 1.
For the problem of optimizing design of electrical equipment, the relationship between performance and design variables is often implicit. It is necessary to build an auxiliary model for the objective function and performance constraints in order to implement the method described in the present invention. The robustness and reliability optimization design method based on the auxiliary model is shown in a flow chart in fig. 2.
The technical characteristics form the embodiment of the invention, have stronger adaptability and implementation effect, and can increase or decrease unnecessary technical characteristics according to actual needs so as to meet the requirements of different situations.
Claims (2)
1. An electrical equipment optimization design method taking robustness and reliability into consideration is characterized by comprising the following steps:
step one, solving a deterministic optimization design problem; vector x= [ x ] for n design variables described in equation (1) 1 ,x 2 ,...,x n ] T In a determined design space [ x L ,x U ]In, search satisfies constraint g i (x) An optimal solution x for minimizing the objective function f (x) at 0 * ：
Wherein x is an n-dimensional design variable vector; f (x) is an objective function of the optimal design model, g (x) is less than or equal to 0 and is a constraint condition, m is the number of constraint functions, and x L To design the lower limit of the variable vector x, x U The upper limit of the variable vector x is designed;
the influence of uncertainty factors is then processed to calculate the standard deviation of the objective function: assuming that each variable in x contains an uncertainty factor, let the standard deviation of the kth design variable be sigma x,k ，σ 2 x,k For its variance; the optimal solution x of the formula (1) * Taking into formula (2), obtaining standard deviation of the objective function f (x), denoted as sigma * f ：
Step two, respectivelySolving the mean ratio of the objective function under the reliability optimizationStandard deviation ratio of optimal solution and objective function +.>Is the optimal solution of (a); wherein mu f ＝f(μ x ) Nominal value mu is taken for the design variable x The corresponding objective function value, sigma f The standard deviation of the objective function corresponding to the design variable vector x; />Representing an objective function value corresponding to an optimal solution obtained under deterministic optimization; r is R t,i Representing the target reliability corresponding to the ith constraint function:
wherein P () represents the reliability calculated from the probability distribution of the design variable uncertainty factor, the mean function ratioThe optimal solution from reliability optimization equation (4) is denoted as x 1 * Standard deviation function ratioObtained by a reliability optimization formula (5)The optimal solution is marked as x 2 * ；
Step three, calculating weight factors, and calculating two indexes of the structure according to the optimal solution obtained in the step twoAnd->Respectively corresponding weight factor omega 1 ，ω 2 ；
Step four, according to the weight factor omega obtained in step three 1 ，ω 2 A new optimal design model is built, a reliability analysis method and an optimization algorithm are selected to solve the model, and the method specifically comprises the following steps:
the specific optimization model taking the robustness and the reliability into consideration is shown in a formula (7):
wherein f RBRDO The method is characterized in that a novel objective function is established for an optimization model under uncertain factors on the premise of ensuring robustness on the basis of an original objective function;
the reliability analysis method is a weight index Monte Carlo simulation method; selecting a particle swarm optimization algorithm by a global optimization method; and (3) solving the optimization model of the formula (7) by adopting a reliability analysis method and a global optimization method.
2. The method for optimizing design of electrical equipment with both robustness and reliability according to claim 1, wherein in the third step, the calculation method of the weight factor is as shown in formula (6):
wherein f 1 (x 1 * ) The optimal solution x of equation (4) 1 * A corresponding objective function value; f (f) 2 (x 2 * ) The optimal solution x of equation (5) 2 * A corresponding objective function value; f (f) 2 (x 1 * ) Representing the optimal solution x of equation (4) 1 * Substituting the objective function value obtained in the model of the formula (5); f (f) 1 (x 2 * ) Representing the optimal solution x of equation (5) 2 * Substituting the objective function value obtained in the model of the formula (4).
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| CN112016727A (en) * | 2019-05-30 | 2020-12-01 | 天津大学 | Cooling system robust optimization design method considering cooling load uncertainty |
| CN112307654A (en) * | 2020-10-10 | 2021-02-02 | 南昌航空大学 | PMA (physical random access memory) reliability optimization method based on mixed reliability model and neural network response surface |
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| US7653522B2 (en) * | 2005-12-07 | 2010-01-26 | Utah State University | Robustness optimization system |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006293483A (en) * | 2005-04-06 | 2006-10-26 | Japan Aerospace Exploration Agency | Problem processing method which solves robust optimization problem, and its apparatus |
| CN106909718A (en) * | 2017-01-23 | 2017-06-30 | 沈阳航空航天大学 | A kind of Optimum design of engineering structures method under Uncertain environments |
| CN107591844A (en) * | 2017-09-22 | 2018-01-16 | 东南大学 | Consider the probabilistic active distribution network robust reconstructing method of node injecting power |
| CN112016727A (en) * | 2019-05-30 | 2020-12-01 | 天津大学 | Cooling system robust optimization design method considering cooling load uncertainty |
| CN112307654A (en) * | 2020-10-10 | 2021-02-02 | 南昌航空大学 | PMA (physical random access memory) reliability optimization method based on mixed reliability model and neural network response surface |
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