CN112711800B - Method for optimally designing strength and rigidity parameters of metal wing - Google Patents
Method for optimally designing strength and rigidity parameters of metal wing Download PDFInfo
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Abstract
The invention belongs to the field of strength calculation, and particularly relates to a method for optimally designing strength and rigidity parameters of a metal wing. The method comprises the following steps: analyzing the parameter sensitivity of the metal wing model, and screening out typical working conditions influencing strong strength constraint and strong rigidity constraint; randomly generating populations of optimized variables according to the typical working conditions, and determining information transfer modes among the populations and among individuals corresponding to different populations; defining a fitness function and carrying out genetic algorithm optimization on the analysis object according to the fitness function to obtain an optimal population; after the optimal population is obtained through optimization, performing small-amplitude optimization parameter adjustment on the optimal population according to all working conditions until strength and rigidity constraints are met to obtain a parameter-adjusted population; and (4) carrying out thickness averaging treatment on the population after parameter adjustment to obtain the average thickness of the unit individuals. The method solves the problem of comprehensive optimization of strength and rigidity under the optimization scene of multiple working conditions, multiple constraints and multiple variables.
Description
Technical Field
The invention belongs to the field of strength calculation, and particularly relates to a method for optimally designing strength and rigidity parameters of a metal wing.
Background
The current universal optimization software has good universality and higher calculation efficiency, but has the problems of poor pertinence, such as difficulty in embedding engineering criteria and stability constraint control, and generally needs customized development. Especially under the optimization scenes of multiple working conditions, multiple constraints and multiple variables, a reasonable result of convergence is difficult to obtain.
Disclosure of Invention
The invention aims to: the method for optimizing the strength and rigidity parameters of the metal wing is provided, and the problem of comprehensive optimization of the strength and rigidity in the optimization scene of multiple working conditions, multiple constraints and multiple variables is solved.
The technical scheme is as follows:
in a first aspect, a method for optimally designing strength and rigidity parameters of a metal wing is provided, which comprises the following steps:
the method comprises the following steps: analyzing the parameter sensitivity of the metal wing model, and screening out typical working conditions influencing strong strength constraint and strong rigidity constraint;
step two: randomly generating populations of optimized variables according to the typical working conditions, and determining information transfer modes between the populations and between individuals corresponding to different populations, wherein the variable corresponding to each grid divided by finite elements is an individual, and the variables corresponding to all grids of an analysis object are used as the populations;
step three: defining a fitness function and carrying out genetic algorithm optimization on the analysis object according to the fitness function to obtain an optimal population;
step four: after the optimal population is obtained through optimization, performing small-amplitude optimization parameter adjustment on the optimal population according to all working conditions until strength and rigidity constraints are met to obtain a parameter-adjusted population;
step five: and (4) carrying out thickness averaging treatment on the population after parameter adjustment to obtain the average thickness of the unit individuals.
Further, the first step specifically includes:
obtaining the sensitivity of each constraint of the metal wing model;
dividing the constraint into a strong constraint and a weak constraint according to the sensitivity;
and (4) screening out typical working conditions influencing strong strength constraint and strong rigidity constraint by carrying out preliminary finite element calculation analysis on the metal wing model.
Further, the second step specifically includes:
dividing an analysis object into a plurality of grids according to a finite element method;
and taking the variable corresponding to each grid divided by the finite element as an individual, taking the variables corresponding to all grids of an analysis object as a population, carrying out individual local strength constraint optimization on the individuals among different populations, and carrying out overall rigidity constraint optimization on the whole different populations.
Further, the third step specifically comprises:
defining a fitness function of individual local strength constraint optimization, namely a jth individual fitness f of an ith population ij ，
Wherein x is ij Denotes the safety margin, s, of the jth unit individual of the ith population i Is the overall fitness value of the ith population, and K1 and K2 are weighting coefficients
Defining a fitness function of global stiffness constraint optimization, namely global fitness s of ith population i ，
Wherein S is a deformation constraint extreme value, S max And S min For the upper and lower limits of the deformation constraint, K3 and K4 are weighting coefficients,
and optimizing the local strength and the overall rigidity of the analysis object according to the two fitness functions.
Further, the fourth step specifically includes:
defining a set of margins for different individuals { (x) 1 ,y 1 ),...,(x n ,y n )}，x i ,y i Respectively the lower limit and the upper limit of the structure margin,
determining a margin parameter auto-update function
Wherein, at the ith pair margin (x) i ,y i ) Loss function J of (c) with respect to parameter x i ,y i Has a gradient of
Learning rate of α, J = Δ D k /ΔW k ，ΔD k The variation of model deformation, Δ W, for the kth iteration k The weight variation of the model of the kth iteration step;
and adjusting the individual variables by using the updated parameters until the strength and rigidity constraints are met.
Further, the fifth step specifically includes:
the thickness of each cell is mapped to the node according to the area ratio of each cell and the regularized coefficient, so that the average thickness at the node shared by each cell can be obtained
Wherein t is the individual thickness, k j M is the number of units sharing the node, n is the number of nodes, i is the ith node, j is the process variable value from 1 to n,
and feeding back the thickness of the node to each unit, and carrying out homogenization treatment on all nodes of the unit to obtain the average thickness of the unit.
Further, the deformation constraints S include wing tip deformation, wing twist angle.
Further, performing local intensity optimization on the analysis object specifically includes:
according to the fitness value, carrying out roulette selection on corresponding individuals of different populations to obtain a better individual;
and carrying out single-point crossing and basic bit variation after carrying out binary coding on the variable of each population individual.
Further, the overall rigidity optimization of the analysis object specifically comprises:
selecting an optimal retention strategy for different populations according to the fitness value to obtain a better population;
and carrying out multipoint random intersection and multipoint random variation on the variable sets of the individuals in each population.
Has the advantages that:
compared with general optimization software, the comprehensive optimization technology for the rigidity and the strength of the wing has the following characteristics:
a) The self-definition degree is high, and the stress-strain criterion, the stability criterion and the like of general metal are integrated inside the composite material;
b) The method has a geometric topological identification function, can automatically identify the geometric topological characteristics of a finite element model, realizes the association of the stringer and the skin unit, and identifies the topological characteristics of the natural grid in a grid encryption state, so that the parameters are updated, and the intensity calculation is more reasonable and accurate;
c) The global convergence is good, and the problem that the acceptable optimization result can not be obtained under the conditions of multiple working conditions, multiple variables and multiple constraints of the general optimization software can be solved
Drawings
FIG. 1 is a schematic diagram of information delivery;
FIG. 2 is a schematic diagram of a two-stage genetic algorithm;
FIG. 3 is a basic flow for an optimization algorithm program implementation;
fig. 4 is a schematic view of a thickness-uniformizing treatment method.
Detailed Description
And (4) realizing the optimization design of the strength and rigidity parameters of the metal wing based on a hierarchical optimization strategy.
Firstly, carrying out parameter sensitivity analysis on a metal wing model.
Preliminarily acquiring the sensitivity of each constraint of the metal wing model, and dividing the constraint into strong constraint and weak constraint according to the sensitivity; the metal wing model is subjected to preliminary finite element calculation analysis, typical working conditions influencing strong strength constraint and strong rigidity constraint are screened out, the key points can be highlighted, and the optimization of the iteration speed is accelerated;
and a second step of randomly generating a population of optimized variables aiming at the typical working conditions, wherein the most severe working conditions of each individual are considered in the population optimizing process, the optimized variables comprise thickness and area, and information transmission modes among the populations and between individuals corresponding to different populations are determined.
And (4) from two levels of unit individuals and population integration, respectively emphasizing the treatment of the constraints of two levels of local strength and overall rigidity. Dividing an analysis object into a plurality of grids according to a finite element method, wherein variables corresponding to each grid divided by the finite element method are individuals, and taking the variables corresponding to all the grids of the analysis object as a population.
Information transmission is carried out among individuals among different populations, and optimization of unit local strength constraint is mainly focused; and the information transmission among different population groups focuses on the optimization of the integral rigidity constraint. The two-stage coupling information transmission mode can give consideration to both local strength constraint and integral rigidity constraint, and the information transmission principle is shown in figure 1;
thirdly, defining two-stage fitness function, and in the first-stage genetic algorithm optimization (namely information transfer between individuals), the fitness f of the jth individual of the ith population ij The values are shown in formula (1).
x ij Denotes the safety margin, s, of the jth unit individual of the ith population i The overall fitness value of the ith population is obtained, so that the overall fitness of the population can be considered by the individual fitness, and as shown in a formula, K1 and K2 are weighting coefficients.
In the second-stage genetic algorithm (i.e. information transfer between different population groups), the overall fitness s of the ith population i The values are shown in formula (2).
S is an extreme value of a deformation constraint (e.g., wing tip deformation, wing twist angle, etc.), S max And S min For the upper and lower limits of the deformation constraint, K3 and K4 are weighting coefficients.
Fourthly, two-level genetic algorithm optimization is adopted, and fitness evaluation, selection, coding and decoding, crossing and variation are respectively carried out on the local unit individuals and the global integral variable set in two levels; and establishing a memory base according to the fitness evaluation, and keeping the elite population until the optimization converges, as shown in figure 2. The basic implementation flow of the optimization program is shown in fig. 3.
And fifthly, after the optimal population is obtained through optimization, all working conditions are introduced, and small-amplitude optimization parameter adjustment (individual variable) is carried out until strength and rigidity constraints are met, so that the rapid optimization of all working conditions is realized. Specifically, the set of margins for different individuals is { (x) 1 ,y 1 ),...,(x n ,y n )}，x i ,y i Respectively the lower limit and the upper limit of the structural marginIn general, x i 0, the stiffness loss function is J, J = Δ D k /ΔW k ，ΔD k The variation of model deformation, Δ W, for the kth iteration k The weight variation of the model of the kth iteration step. At the ith pair of margins (x) i ,y i ) Loss function J of (c) with respect to parameter x i ,y i Gradient of
J＝ΔD k /ΔW k Learning rate of alpha, delta D k The variation of model deformation, Δ W, for the kth iteration k For the weight variation of the model in the kth iteration step, the parameters are automatically updated by using a gradient descent method as follows:
and adjusting the individual variables by using the updated parameters until the strength and rigidity constraints are met.
And sixthly, after the small-amplitude optimization parameter adjustment, performing thickness averaging treatment to obtain a final optimization result close to the engineering manufacturing requirement, as shown in fig. 4. First, the thickness of each cell is mapped onto a node according to the area ratio of each cell and a regularized coefficient, so that the average thickness at the node shared by each cell can be obtained, as shown in the following formula, where t is the individual thickness and k is j And m is the number of units sharing the node, n is the number of nodes, i is the ith node, and j is a process variable value from 1 to n.
Then, the node thickness is fed back to each unit, and the homogenization treatment is carried out on all the nodes of the unit, namely the thickness of the unit is equal to the average value of all the nodes, as shown in the following formula, t is the individual thickness, k is the process variable, n is the number of the nodes, and i is the ith node.
Compared with general optimization software, the full-mechanical stiffness and strength comprehensive optimization technology has the following characteristics:
a) The self-definition degree is high, and the general stress-strain criterion, the stability criterion and the like of metal are integrated inside the self-definition degree;
b) The method has a geometric topological identification function, can automatically identify the geometric topological characteristics of a finite element model, realizes the association of the stringer and the skin unit, and identifies the topological characteristics of the natural grid in a grid-encrypted state, so that the parameters are updated, and the intensity calculation is more reasonable and accurate;
c) The global convergence is good, and the problem that the general optimization software cannot obtain an acceptable optimization result under the conditions of multiple working conditions, multiple variables and multiple constraints can be solved.
Claims (6)
1. A method for optimally designing strength and rigidity parameters of a metal wing is characterized by comprising the following steps:
the method comprises the following steps: analyzing the parameter sensitivity of the metal wing model, and screening out typical working conditions influencing strong strength constraint and strong rigidity constraint, wherein the typical working conditions comprise: obtaining the sensitivity of each constraint of the metal wing model; dividing the constraint into a strong constraint and a weak constraint according to the sensitivity; carrying out preliminary finite element calculation analysis on the metal wing model to screen out typical working conditions influencing strong strength constraint and strong rigidity constraint;
step two: for the typical working conditions, randomly generating populations of optimized variables, and determining information transfer modes between the populations and between corresponding individuals of different populations, specifically comprising: dividing an analysis object into a plurality of grids according to a finite element method; the method comprises the following steps of taking a variable corresponding to each grid of a finite element division as an individual, taking variables corresponding to all grids of an analysis object as a population, carrying out individual local strength constraint optimization on the individuals among different populations, and carrying out overall rigidity constraint optimization among the different populations, wherein the variable corresponding to each grid of the finite element division is an individual, and the variables corresponding to all grids of the analysis object are taken as the population;
step three: defining a fitness function and optimizing an analysis object by a genetic algorithm according to the fitness function to obtain an optimal population, wherein the method specifically comprises the following steps: defining fitness function of individual local intensity constraint optimization, namely jth individual fitness f of ith population ij ，
Wherein x is ij Denotes the safety margin, s, of the jth unit individual of the ith population i The overall fitness value of the ith population is K1 and K2 are weighting coefficients; defining a fitness function of integral rigidity constraint optimization, namely the integral fitness s of the ith population i ，
Wherein S is a deformation constraint extreme value, S max And S min Optimizing the local strength and the overall stiffness of the analysis object according to the two fitness functions by taking K3 and K4 as weighting coefficients for the upper and lower limits of deformation constraint; step four: after the optimal population is obtained through optimization, performing small-amplitude optimization parameter adjustment on the optimal population according to all working conditions until strength and rigidity constraints are met to obtain a parameter-adjusted population; step five: and (4) carrying out thickness averaging treatment on the population after parameter adjustment to obtain the average thickness of the unit individuals.
2. The method according to claim 1, wherein step four specifically comprises:
defining a set of margins for different individuals { (x) 1 ,y 1 ),...,(x n ,y n )}，x i ,y i Respectively the lower limit and the upper limit of the structural margin,
determining a margin parameter auto-update function
Wherein, at the ith pair margin (x) i ,y i ) Upper loss function jgateAt parameter x i ,y i Has a gradient of
Learning rate of α, J = Δ D k /ΔW k ，ΔD k The variation of model deformation, Δ W, for the kth iteration k The weight variation of the model of the kth iteration step;
and adjusting the individual variables by using the updated parameters until the strength and rigidity constraints are met.
3. The method according to claim 1, wherein step five specifically comprises:
the thickness of each cell is mapped to the node according to the area ratio of each cell and the regularized coefficient, so that the average thickness at the node shared by each cell can be obtained
Wherein t is the individual thickness, k j M is the number of units sharing the node, n is the number of nodes, i is the ith node, j is the process variable value from 1 to n,
and feeding back the thickness of the nodes to each unit, and carrying out homogenization treatment on all the nodes of the units to obtain the average thickness of the unit.
4. The method of claim 1, wherein the deformation constraints S include wing tip deformation, wing twist angle.
5. The method according to claim 1, wherein the local intensity optimization of the analysis object specifically comprises:
according to the fitness value, carrying out roulette selection on corresponding individuals of different populations to obtain a better individual;
and carrying out single-point crossing and basic bit variation after carrying out binary coding on the variable of each population individual.
6. The method according to claim 1, wherein the global stiffness optimization of the analysis object comprises:
selecting an optimal reservation strategy for different populations according to the fitness value to obtain a better population;
and carrying out multipoint random intersection and multipoint random variation on the variable sets of the individuals in each population.
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