CN115859762A - Hybrid teaching and learning optimization method for fingertip sealing structure parameters - Google Patents
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Abstract
The invention relates to a mixed teaching and learning optimization method for fingertip sealing structure parameters, and belongs to the technical field of flexible sealing performance optimization. The method comprises the steps of using a uniform test design method and ANSYS software to simulate and obtain a plurality of groups of structural parameters and corresponding hysteresis factors epsilon and average contact pressure P as a training data set of the BP neural network; secondly, respectively constructing a mapping relation among the hysteresis rate epsilon, the average contact pressure P and the fingertip sealing structure parameters by training a BP neural network; finally, according to the mapping relation, combining a Pareto matching method, and optimizing the structural parameters of the fingertip seal by adopting a mixed teaching and learning optimization method with the aim of minimizing the hysteresis rate epsilon and the average contact pressure P; the method has higher stability and optimization performance, and can reasonably search the solution space of the fingertip sealing structure parameter optimization problem; the acquired Pareto optimal solution set can meet the requirement of multi-preference decision-making in actual engineering; the method has the characteristics of easy understanding, easy transplanting, few parameters, simple framework, strong parallel search capability, convenient popularization and the like.
Description
Technical Field
The invention relates to a mixed teaching and learning optimization method for fingertip sealing structure parameters, and belongs to the technical field of flexible sealing performance optimization.
Background
With the rapid development of the aviation technology, the traditional sealing structure is difficult to meet the working condition requirement of the modern aviation engine, the advanced sealing technology plays an important role in improving the overall performance of the engine, and the excellent cost performance characteristic of the advanced sealing technology is also recognized by researchers. The finger tip sealing is the energy generated after the grate tooth sealing and the brush sealingAdvanced flexible seals that can accommodate rotor axial and radial runout without compromising seal integrity performance. Researches find that the key for improving the working performance and the service life of the fingertip seal is to solve the problems of delay and abrasion. The retardation and abrasion are mainly influenced by the parameters of the fingertip sealing structure, the main structural parameter of the fingertip sealing structure is the base radius r b The number n of the fingertip beams and the height x of the fingertip boot g Downstream protection height g d . The two performances of the fingertip seal, namely the hysteresis and the abrasion, are mutually contradictory on the structure of the fingertip seal, and the mutually contradictory performance indexes form a typical multi-objective optimization problem. At present, a multi-objective optimization method of fingertip sealing performance only provides a decision scheme for a decision maker, but only provides a decision scheme which is difficult to reflect the essence and the characteristics of a multi-objective optimization problem, and the preference of the decision maker in reality is diversified due to the actual requirements of engineering. Therefore, a fingertip dense structure parameter multi-objective performance optimization research capable of obtaining various decision schemes needs to be developed.
Disclosure of Invention
The invention aims to provide a mixed teaching and learning optimization method for fingertip sealing structure parameters, which is used for providing various decision schemes with different preferences for a decision maker while improving the fingertip sealing performance so as to meet the requirements of engineering actual diversity.
The technical scheme adopted by the invention is as follows: a mixed teaching and learning optimization method for fingertip seal structure parameters comprises the steps of firstly, using a uniform test design method and ANSYS software simulation to obtain a plurality of groups of structure parameters and corresponding hysteresis rate epsilon and average contact pressure P thereof as a training data set of a BP neural network; secondly, respectively constructing a mapping relation among the hysteresis rate epsilon, the average contact pressure P and the fingertip sealing structure parameters by training a BP neural network; finally, according to the mapping relation, combining a Pareto matching method, and optimizing the structural parameters of the fingertip seal by adopting a mixed teaching and learning optimization method with the aim of minimizing the hysteresis rate epsilon and the average contact pressure P; the method comprises the following specific steps:
step1, obtaining multiple groups of fingertip sealing structure parameters by using uniform test design method
Wherein x is i Represents the i-th group of structural parameters, i.e. the decision variable, <' >>
Representing the radius of the base circle, n, in the i-th set of structural parameters i Represents the number of fingertip beams in the ith group of structural parameters and is used for judging whether the fingertip beams are located in the ith group of structural parameters>
Represents the fingertip shoe height in the i-th set of structural parameters, is greater than or equal to>
Representing the downstream protection height in the ith group of structural parameters;
step2, carrying out finite element simulation analysis on the fingertip sealing structure corresponding to each group of structural parameters in Step1 by using ANSYS software to obtain a corresponding hysteresis rate epsilon and an average contact pressure P, thereby obtaining a training data set for the BP neural network;
step3, training a BP neural network by adopting the training data set in Step2, and respectively constructing an implicit mapping relation between the hysteresis rate epsilon, the average contact pressure P and the parameters of the pointed sealing structure in Step 1;
and Step4, establishing a fingertip sealing structure parameter optimization model with the aim of simultaneously minimizing the hysteresis rate epsilon and the average contact pressure P according to the Step 3:
minF(x)＝[ε(x),P(x)] (1)
ε(x)＝net 1 (x) (2)
P(x)＝net 2 (x) (3)
wherein F (x) represents the optimization objective, ∈ (x) represents the hysteresis rate, P (x) represents the mean contact pressure, x represents the decision variable, net 1 Representing a mapping relationship, net, established between hysteresis rate and structural parameters 2 Representing the mapping relation established between the average contact pressure and the structural parameters;
the decision variables are:
x＝[r b ,n,x g ,g d ] (4)
wherein r is b Denotes the radius of the base circle, n denotes the number of finger-tip beams, x g Indicates the height of the fingertip boot, g d Indicating a downstream protection height;
the constraint conditions are as follows:
10mm≤r b ≤14mm (5)
24≤n≤54 (6)
0.3mm≤x g ≤0.7mm (7)
0.2mm≤g d ≤0.4mm (8)
the optimization result is as follows:
x * ＝arg{F(x)}→min (9)
wherein x is * Represents the optimal decision variable when minimizing both the hysteresis rate epsilon and the average contact pressure P;
step5, according to the mapping relation of Step3, combining a Pareto matching method, and carrying out optimization solution on the optimization model of Step4 by adopting a mixed teaching and learning optimization method, wherein the mixed teaching and learning optimization method is mainly divided into two stages of teaching and inter-learning, a teacher in the mixed teaching and learning optimization method is an individual corresponding to a solution randomly generated from a current Pareto solution set, and students are individuals which are generated in each generation of the algorithm and the solution of which is not contained in the Pareto solution set;
the concrete solving steps are as follows:
1): initializing algorithm parameters and randomly generating an initial population, wherein the population size is set to be 50, the maximum iteration number of the algorithm is set to be 200, and the initial population is
2): calculating an optimization index for each individual in the initial population according to the formulas (2) and (3), such as the individual
Then there is ε (x) 1 )＝net 1 (x 1 )，P(x 1 )＝net 2 (x 1 )；
3): obtaining or updating a Pareto solution set of the existing population according to a Pareto matching method, wherein the Pareto matching method is mainly used for evaluating the solution of the multi-objective optimization problem;
4): in the teaching stage, a solution is randomly selected from Pareto solutions, and the corresponding individual is taken as a teacher "
"students" in a population>
Sequentially obtaining new student individuals in a mode of learning to teacher
Then, in>
De-subscriber of>
And/or>
De-subscriber of>
Evaluation is carried out using the Pareto rule of disposition, if ^ is greater than>
Can be Pareto dominant { (R) }>
In combination with:>
replacement->
Or else>
Remaining unchanged, the algorithm continues to run, and>
the generation mode is shown as formula (11):
wherein, delta i Represents the difference value between the ith student and teacher, rand i Represents the ith random number of 0 to 1,
representing the average value of the Pareto solution set corresponding to the individual, wherein T represents a random number with the value of 1 or 2;
5): the "learning each other" stage, for every "student" after the "teaching" stage "
Executing: (1) optionally another "student>
If>
Is released and is>
Can be Pareto dominant->
Solution of (2)
Then a new "student" individual is generated in accordance with equation (12)>
Otherwise a new "student" individual is generated in accordance with equation (13)>
(2) If/or>
De-subscriber of>
Can be Pareto dominant { (R) }>
De-subscriber of>
Then use>
Replacement>
Otherwise->
Remains unchanged and is taken out>
And & ->
The same, the algorithm continues to run;
wherein, rand i The definitions of (A) are the same as those of formula (11);
6): and judging whether the algorithm meets a termination condition, if so, updating the Pareto solution set of the population, and outputting a final optimization result, otherwise, skipping to execute the step 3).
And setting the range of each parameter in the constraint condition in practical application according to the boundary condition of each structural parameter sealed by the fingertips in the BP neural network training data set.
The beneficial effects of the invention are as follows:
1. the mixed teaching and learning optimization method has higher stability and optimization performance, and can reasonably search the solution space of the fingertip seal structure parameter optimization problem, thereby obtaining a better solution set scheme;
2. the Pareto optimal solution set obtained by the mixed teaching and learning optimization method comprises various decision schemes, and can meet the requirement of multiple preference decisions in actual engineering;
3. the mixed teaching and learning optimization method has the characteristics of easy understanding, easy transplantation, few parameters, simple framework, strong parallel search capability, convenient popularization and the like, and engineering application personnel can flexibly use the method without strong professional background;
4. the mixed teaching and learning optimization method provides a universal effective method for fingertip sealing structure parameter optimization.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a flow chart of the hybrid teaching and learning optimization method of the present invention.
Detailed Description
Example 1: as shown in fig. 1-2, a hybrid teaching and learning optimization method for fingertip seal structure parameters includes that firstly, a uniform test design method and ANSYS software simulation are used to obtain a plurality of groups of structure parameters and corresponding hysteresis factors epsilon and average contact pressure P as training data sets of a BP neural network; secondly, respectively constructing a mapping relation among the hysteresis rate epsilon, the average contact pressure P and the fingertip sealing structure parameters by training a BP neural network; finally, according to the mapping relation, combining a Pareto matching method, and optimizing the structural parameters of the fingertip seal by adopting a mixed teaching and learning optimization method with the aim of minimizing the hysteresis rate epsilon and the average contact pressure P; the method comprises the following specific steps:
step1, obtaining multiple groups of fingertip sealing structure parameters by using uniform test design method
Wherein x is i Representing the ith group of structural parameters, namely decision variables; />
Representing the base circle radius in the ith set of structural parameters; n is i Representing the number of fingertip beams in the ith group of structural parameters; />
Representing the fingertip shoe height in the ith set of structural parameters; />
Representing the downstream protection height in the ith group of structural parameters;
step2, carrying out finite element simulation analysis on the fingertip sealing structure corresponding to each group of structural parameters in Step1 by using ANSYS software to obtain a corresponding hysteresis rate epsilon and an average contact pressure P, thereby obtaining a training data set for the BP neural network;
step3, training a BP neural network by adopting the training data set in Step2, and respectively constructing an implicit mapping relation between the hysteresis rate epsilon, the average contact pressure P and the parameters of the finger tip sealing structure in Step 1;
and Step4, establishing a fingertip sealing structure parameter optimization model with the aim of simultaneously minimizing the hysteresis rate epsilon and the average contact pressure P according to the Step 3:
minF(x)＝[ε(x),P(x)] (1)
ε(x)＝net 1 (x) (2)
P(x)＝net 2 (x) (3)
wherein F (x) represents the optimization objective, ∈ (x) represents the hysteresis rate, P (x) represents the average contact pressure, and x is shown in the tableIndicating a variable, net 1 Representing a mapping relationship, net, established between hysteresis rate and structural parameters 2 Representing the mapping relation established between the average contact pressure and the structural parameters;
the decision variables are:
x＝[r b ,n,x g ,g d ] (4)
wherein r is b Denotes the radius of the base circle, n denotes the number of finger-tip beams, x g Indicates the height of the fingertip boot, g d Indicating a downstream protection height;
the constraint conditions are as follows:
10mm≤r b ≤12mm (5)
24≤n≤48 (6)
0.3mm≤x g ≤0.7mm (7)
0.2mm≤g d ≤0.4mm (8)
the optimization result is as follows:
x * ＝arg{F(x)}→min (9)
wherein x is * Represents the optimal decision variable at which both the hysteresis rate ε and the average contact pressure P are minimized;
step5, according to the mapping relation of Step3 and in combination with a Pareto matching method, carrying out optimization solution on the optimization model of Step4 by adopting a mixed teaching and learning optimization method, wherein the concrete solution steps are as follows:
1): initializing algorithm parameters and randomly generating an initial population, wherein the population size is set to be 50, the maximum iteration times of the algorithm is set to be 200, and the initial population is
2): calculating optimization index of each individual in the initial population according to formulas (2) and (3), such as individual
Then there is ε (x) 1 )＝net 1 (x 1 )，P(x 1 )＝net 2 (x 1 )；
3): obtaining or updating a Pareto solution set of the existing population according to a Pareto matching method, wherein the Pareto matching method is mainly used for evaluating the solution of the multi-objective optimization problem;
4): in the teaching stage, one solution is randomly selected from the Pareto solutions in a centralized way, and the corresponding individual is taken as a teacher "
"students" in a population>
Sequentially acquiring new student individuals in a mode of learning to teacher
Then, is taken up or taken off>
Is released and is>
And/or>
Is released and is>
Evaluation is carried out using Pareto rule if &>
Can be determined by Pareto dominate->
The solution of (4) is then used>
Replacement->
Or else>
Remains unchanged, the algorithm continues to run, and>
the generation mode is shown as formula (11):
wherein, delta i Represents the difference value between the ith student and teacher, rand i Represents the ith random number of 0 to 1,
representing the average value of the Pareto solution set corresponding to the individual, wherein T represents a random number with the value of 1 or 2;
5): the "learning each other" stage, for every "student" after the "teaching" stage "
Executing: (1) optionally a further student>
If/or>
Is released and is>
Can be Pareto dominant { (R) }>
Solution of (2)
Then a new "student" individual is generated in accordance with equation (12)>
Otherwise, a new student individual is generated according to the formula (13)>
(2) If>
Is released and is>
Can be Pareto dominant->
Is released and is>
Then use>
Replacement->
Or else>
Remains unchanged and is taken out>
Replacement of (2) rule AND>
The same, the algorithm continues to run;
wherein, rand i The definitions of (A) are the same as those of formula (11);
6): and judging whether the algorithm meets a termination condition, if so, updating the Pareto solution set of the population, and outputting a final optimization result, otherwise, skipping to execute the step 3).
Example 2: as shown in fig. 1-2, a hybrid teaching and learning optimization method for fingertip seal structure parameters includes that firstly, a uniform test design method and ANSYS software simulation are used to obtain a plurality of groups of structure parameters and corresponding hysteresis factors epsilon and average contact pressure P as training data sets of a BP neural network; secondly, respectively constructing a mapping relation among the hysteresis rate epsilon, the average contact pressure P and the fingertip sealing structure parameters by training a BP neural network; finally, according to the mapping relation, combining a Pareto matching method, and optimizing the structural parameters of the fingertip seal by adopting a mixed teaching and learning optimization method with the aim of minimizing the hysteresis rate epsilon and the average contact pressure P; the method comprises the following specific steps:
step1, obtaining multiple groups of fingertip sealing structure parameters by using uniform test design method
Wherein x is i Representing an i-th group of structural parameters, i.e. decision variables>
Representing the base radius, n, in the i-th set of structural parameters i Represents the number of fingertip beams in the ith group of structural parameters and is used for judging whether the fingertip beams are located in the ith group of structural parameters>
Represents the fingertip shoe height in the i-th group of structural parameters, in combination with a key or key combination>
Representing the downstream protection height in the ith set of structural parameters;
step2, carrying out finite element simulation analysis on the fingertip sealing structures corresponding to each group of structural parameters in Step1 by using ANSYS software, and obtaining corresponding hysteresis rate epsilon and average contact pressure P so as to obtain a training data set for the BP neural network;
step3, training a BP neural network by adopting the training data set in Step2, and respectively constructing an implicit mapping relation between the hysteresis rate epsilon, the average contact pressure P and the parameters of the pointed sealing structure in Step 1;
and Step4, establishing a fingertip sealing structure parameter optimization model with the aim of simultaneously minimizing the hysteresis rate epsilon and the average contact pressure P according to the Step 3:
minF(x)＝[ε(x),P(x)] (1)
ε(x)＝net 1 (x) (2)
P(x)＝net 2 (x) (3)
wherein F (x) represents the optimization objective, ∈ (x) represents the hysteresis rate, P (x) represents the mean contact pressure, x represents the decision variable, net 1 Representing a mapping relationship, net, established between hysteresis rate and structural parameters 2 Representing the mapping relation established between the average contact pressure and the structural parameters;
the decision variables are:
x＝[r b ,n,x g ,g d ] (4)
wherein r is b Represents the radius of the base circle, n represents the number of the fingertip beams, x g Indicates the height of the fingertip boot, g d Indicating a downstream protection height;
the constraint conditions are as follows:
10mm≤r b ≤14mm (5)
30≤n≤54 (6)
0.3mm≤x g ≤0.7mm (7)
0.2mm≤g d ≤0.4mm (8)
the optimization result is as follows:
x * ＝arg{F(x)}→min (9)
wherein x is * Represents the optimal decision variable at which both the hysteresis rate ε and the average contact pressure P are minimized;
step5, carrying out optimization solution on the optimization model of Step4 by adopting a mixed teaching and learning optimization method according to the mapping relation of Step3 and combining a Pareto matching method, wherein the concrete solution steps are as follows:
1): initializing algorithm parameters and randomly generating an initial population, wherein the population size is set to be 50, the maximum iteration times of the algorithm is set to be 200, and the initial population is
2): calculating an optimization index for each individual in the initial population according to the formulas (2) and (3), such as the individual
Then there is ε (x) 1 )＝net 1 (x 1 )，P(x 1 )＝net 2 (x 1 )；
3): obtaining or updating a Pareto solution set of the existing population according to a Pareto matching method, wherein the Pareto matching method is mainly used for evaluating a solution of a multi-objective optimization problem;
4): in the teaching stage, one solution is randomly selected from the Pareto solutions in a centralized way, and the corresponding individual is taken as a teacher "
"students" in a population>
Sequentially acquiring new student individuals in a mode of learning to teacher
Then, in>
De-subscriber of>
And &>
De-subscriber of>
Evaluation is carried out using Pareto rule if &>
Can be determined by Pareto dominate->
In combination with:>
replacement>
Otherwise->
Remains unchanged, the algorithm continues to run, and>
the generation mode is shown as formula (11):
wherein, delta i Represents the difference value between the ith student and teacher, rand i Represents the ith random number of 0 to 1,
representing the average value of the Pareto solution set corresponding to the individual, wherein T represents a random number with the value of 1 or 2;
5): the "learning each other" stage, for every "student" after the "teaching" stage "
Executing: (1) optionally a further student>
If/or>
Is released and is>
Can be Pareto dominant->
Solution of (2)
Then a new "student" individual is generated in accordance with equation (12)>
Otherwise, a new student individual is generated according to the formula (13)>
(2) If>
De-subscriber of>
Can be Pareto dominant { (R) }>
Is released and is>
Then use>
Replacement->
Otherwise->
Remains unchanged and is taken out>
And & ->
The same, the algorithm continues to run;
wherein, rand i The definitions of (b) are the same as those of formula (11);
6): and judging whether the algorithm meets a termination condition, if so, updating the Pareto solution set of the population, and outputting a final optimization result, otherwise, skipping to execute the step 3).
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (2)
1. A mixed teaching and learning optimization method for fingertip sealing structure parameters is characterized by comprising the following steps: firstly, simulating and obtaining a plurality of groups of structural parameters and corresponding hysteresis rates epsilon and average contact pressures P thereof as a training data set of the BP neural network by using a uniform test design method and ANSYS software; secondly, respectively constructing a mapping relation among a hysteresis rate epsilon, an average contact pressure P and fingertip sealing structure parameters by training a BP neural network; finally, according to the mapping relation, combining a Pareto matching method, and optimizing the structural parameters of the fingertip seal by adopting a mixed teaching and learning optimization method with the aim of minimizing the hysteresis rate epsilon and the average contact pressure P; the method comprises the following specific steps:
step1, obtaining multiple groups of fingertip sealing structure parameters by using uniform test design method
Wherein x is i Represents the structural parameters of the ith group, i.e. the decision variables,
representing the base radius, n, in the i-th set of structural parameters i Represents the number of fingertip beams in the ith group of structural parameters, and>
represents the fingertip shoe height in the i-th set of structural parameters, is greater than or equal to>
Representing the downstream protection height in the ith set of structural parameters;
step2, carrying out finite element simulation analysis on the fingertip sealing structure corresponding to each group of structural parameters in Step1 by using ANSYS software to obtain a corresponding hysteresis rate epsilon and an average contact pressure P, thereby obtaining a training data set for the BP neural network;
step3, training a BP neural network by adopting the training data set in Step2, and respectively constructing an implicit mapping relation between the hysteresis rate epsilon, the average contact pressure P and the parameters of the pointed sealing structure in Step 1;
and Step4, establishing a fingertip sealing structure parameter optimization model aiming at simultaneously minimizing the hysteresis rate epsilon and the average contact pressure P according to the Step 3:
minF(x)＝[ε(x),P(x)] (1)
ε(x)＝net 1 (x) (2)
P(x)＝net 2 (x) (3)
wherein F (x) represents the optimization objective, ε (x) represents the hysteresis rate, P (x) represents the mean contact pressure, x represents the decision variable, net 1 Representing a mapping relationship, net, established between hysteresis rate and structural parameters 2 Shows the mapping of the mean contact pressure to the build-up of structural parametersA correlation relationship;
the decision variables are:
x＝[r b ,n,x g ,g d ] (4)
wherein r is b Denotes the radius of the base circle, n denotes the number of finger-tip beams, x g Indicates the height of the fingertip boot, g d Indicating a downstream protection height;
the constraint conditions are as follows:
10mm≤r b ≤14mm (5)
24≤n≤54 (6)
0.3mm≤x g ≤0.7mm (7)
0.2mm≤g d ≤0.4mm (8)
the optimization result is as follows:
x * ＝arg{F(x)}→min (9)
wherein x is * Represents the optimal decision variable at which both the hysteresis rate ε and the average contact pressure P are minimized;
step5, according to the mapping relation of Step3 and in combination with a Pareto matching method, carrying out optimization solution on the optimization model of Step4 by adopting a mixed teaching and learning optimization method, wherein the concrete solution steps are as follows:
1): initializing algorithm parameters and randomly generating an initial population, wherein the population size is set to be 50, the maximum iteration times of the algorithm is set to be 200, and the initial population is
2): calculating an optimization index for each individual in the initial population according to the formulas (2) and (3), such as the individual
Then there is epsilon (x) 1 )＝net 1 (x 1 )，P(x 1 )＝net 2 (x 1 )；
3): obtaining or updating a Pareto solution set of the existing population according to a Pareto matching method, wherein the Pareto matching method is mainly used for evaluating a solution of a multi-objective optimization problem;
4): in the teaching stage, one solution is randomly selected from the Pareto solutions in a centralized way, and the corresponding individual is taken as a teacher "
"students" in a population>
Sequentially acquiring new student individuals in a mode of learning to teacher
Then, is taken up or taken off>
Is released and is>
And &>
De-subscriber of>
Evaluation is carried out using Pareto rule if &>
Can be determined by Pareto dominate->
In combination with:>
replacement->
Otherwise->
Remains unchanged, the algorithm continues to run, and>
the generation mode is shown as formula (11):
wherein, delta i Means the difference between the ith student and teacher, rand i Represents the ith random number of 0 to 1,
representing the average value of the Pareto solution set corresponding to the individual, wherein T represents a random number with the value of 1 or 2;
5): the "learning each other" stage, for every "student" after the "teaching" stage "
Executing: (1) optionally another "student>
If>
De-subscriber of>
Can be Pareto dominant->
Solution of (2)
Then a new "student" individual is generated in accordance with equation (12)>
Otherwise, a new student individual is generated according to the formula (13)>
(2) If>
Is released and is>
Can be Pareto dominant { (R) }>
De-subscriber of>
Then use>
Replacement>
Otherwise
Remains unchanged and is taken out>
And & ->
The same, the algorithm continues to run;
wherein, rand i The definitions of (A) are the same as those of formula (11);
6): and judging whether the algorithm meets a termination condition, if so, updating the Pareto solution set of the population, and outputting a final optimization result, otherwise, skipping to execute the step 3).
2. The hybrid teaching and learning optimization method of fingertip seal structure parameters of claim 1, characterized in that: and setting the range of each parameter in the constraint condition in practical application according to the boundary condition of each structural parameter sealed by the fingertips in the BP neural network training data set.
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