CN114519299A - Multi-objective optimization method for double-wall structure of integrated support plate flame stabilizer - Google Patents
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Abstract
The invention discloses a multi-objective optimization method for a double-wall structure of an integrated support plate flame stabilizer, and belongs to the field of aero-engine intensified cooling design and thermal protection. The method takes the maximum comprehensive cooling efficiency and the minimum relative pressure loss of the double-wall cooling structure of the flame stabilizer of the integrated stressing support plate of the aircraft engine as optimization targets, and takes the aperture d of the impact holeiThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of air film hole rows, the number n of hole rows, and the ratio H/d of the impact distance to the diameter of the impact holeiAnd as a parameter to be optimized, establishing a radial basis function neural network mathematical model and coupling a genetic optimization algorithm to perform global optimization. Such optimizationThe method has the advantages of strong learning ability, high approximation precision, wide coverage range, strong robustness and the like, and can provide technical support for the structural design of the integrated afterburning support plate of the afterburner of the high-performance aircraft engine.
Description
Technical Field
The invention relates to a multi-objective optimization method for a double-wall cooling structure of an integrated stressing support plate flame stabilizer of an aircraft engine, and belongs to the field of thermal protection of aircraft parts.
Background
The integrated stress application support plate of the aircraft engine is the key content of the research in the field of the current engines, and the mixer, the fuel spray rod, the flame stabilizer and the like are combined and designed, so that the total weight of the engine is reduced, the energy loss is reduced, the thrust-weight ratio is increased, and the overall efficiency of the engine is improved. Due to the turbulent flow effect of the blunt body, a high-temperature area is formed behind the integrated stressing support plate, in order to enable the integrated stressing support plate to stably work in a high-temperature environment, a double-wall cooling structure is arranged at the tail edge of the integrated stressing support plate, a proper amount of cold air is introduced from a culvert to cool the integrated stressing support plate, and meanwhile, flame is prevented from moving to the front end of the integrated stressing support plate to influence the working performance of the integrated stressing support plate.
Double-wall cooling is an advanced composite structure and is widely applied in the field of aviation. This cooling structure comprises impingement plate, impact chamber and air film plate, and air conditioning assaults the target surface through assaulting the pore pair, reinforces the heat transfer, flows to flow to around again by the air film hole afterwards, forms the air film with outside air current effect, protection hot junction part.
A Radial Basis Function (RBF) neural network is an artificial neural network using a radial basis function as an activation function, belongs to a feedforward type neural network, can approach any continuous function with any precision, is particularly suitable for solving the classification problem, and is widely applied to multiple fields. The genetic algorithm is a global optimization probability algorithm, and can effectively perform global search in a probability sense by searching for an optimal solution by simulating a selected genetic rule in the nature.
Disclosure of Invention
The purpose of the invention is as follows: the method for optimizing the double-wall structure of the flame stabilizer of the integrated support plate of the aircraft engine can efficiently and accurately design the double-wall cooling structure according to actual engineering requirements, and guarantee that a hot end part continuously and stably works at high temperature.
The technical scheme is as follows: a multi-objective optimization method for a double-wall structure of an integrated support plate flame stabilizer of an aircraft engine comprises the following steps:
step 1, determining parameters of a structure to be optimized and a parameter range of the structure to be optimized of a double-wall cooling structure of an integrated stressing support plate flame stabilizer;
and 5, carrying out global optimization on the double-wall structure of the integrated stressing support plate flame stabilizer by using a genetic algorithm.
Further, the structural parameters to be optimized in step 1 include the aperture d of the impact holeiThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the columns of the air film holes, the number n of the rows of the air film holes, and the ratio H/d of the impact distance to the aperture of the impact holeiImpact hole diameter di0.8 to 1.5mm, df/di0.4 to 1.0, m is 37 to 73, n is 4 to 7, H/di1 to 2.5.
Further, in step 2, the design step of the sample includes:
step 2.1, the aperture d of the impact hole with the structural parameter to be optimizediThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the gas film hole columns, the number n of the hole rows, and the ratio H/d of the impact space to the aperture of the impact holesiCombining, and selecting 32 groups of representative samples from the comprehensive combination as training samples of the radial neural network according to orthogonality by utilizing orthogonal test design;
step 2.2, the aperture of the impact hole with the structural parameter to be optimizeddiThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the air film hole rows, the number n of the hole rows, and the ratio H/d of the impact space to the aperture of the impact holeiCombining, and randomly extracting 8 groups of samples as test samples;
step 2.3, aiming at different unit scales of different sample parameters, normalization processing is carried out on the structural parameters to be optimized of the selected sample, and the unit scales of the different parameters are arranged in the range of (0, 1):
wherein y is the normalized result, xiIs a sample parameter variable, xmax，xminThe maximum and minimum values of the sample parameter variables, respectively.
Further, in step 3, the objective functions of the integrated cooling efficiency and the relative pressure loss are respectively defined as:
F(di,df/di,m,n,H/di)＝1/η
F(di,df/di,m,n,H/di)＝ΔP
where η is the overall cooling efficiency and Δ P is the relative pressure loss.
Further, in step 4, the radial basis function neural network receives training samples by the input layer, and the hidden layer maps the input samples to a new space through the radial basis functions:
wherein x represents a training sample, ciRepresenting the central vector, δ, of the radial basis functioniRepresents the kernel width of the radial basis function;
the output layer realizes linear weighted summation in a new space, and outputs the result:
in the formula, wiThe connection weights of the hidden layer and the output layer,
is a radial basis function, y is an output result, and M is the number of hidden layer nodes;
determining diffusion coefficients of the radial basis function neural network by adopting a trial and error method, verifying the correctness of the radial basis function neural network, calculating the radial basis function neural network corresponding to different diffusion coefficients based on training samples, selecting a diffusion coefficient value with the minimum root mean square error through iterative computation, and expressing the root mean square error of a computational fluid dynamics computation result and a prediction result of the radial basis function neural network as follows:
wherein N is the total number of data, yt(k) And
respectively calculated data and predicted data.
Further, in the step 5, the detailed steps of utilizing the genetic algorithm to carry out global optimization on the double-wall structure of the integrated stressing support plate flame stabilizer are as follows:
step 5.1, initialization operation: chromosome coding, determining population quantity, and setting crossover, mutation probability and maximum iteration step number;
step 5.2, initializing the population: randomly generating a first generation population;
step 5.3, calculating a fitness value based on a radial basis function neural network mathematical model, and evaluating a population, wherein the individual fitness comprises the maximum comprehensive cooling efficiency and the minimum relative pressure loss of the double-wall cooling structure of the integrated stressing support plate flame stabilizer;
step 5.4, judging whether the algorithm convergence criterion is met, if so, terminating, outputting the optimal solution, otherwise, continuing to operate;
and 5.5, selecting the population according to the principle of high-out and low-out, crossing and varying the population according to the crossing probability and the variation probability to form a new generation of population, returning to the step 5.3, and obtaining the optimal individual, namely the optimal integrated stressing support plate flame stabilizer double-wall cooling structure after evolution iteration of a plurality of generations.
The invention has the beneficial effects that:
the double-wall cooling structure of the flame stabilizer of the integrated stressing support plate is globally searched by adopting a radial basis function neural network coupling genetic algorithm, the complex structural design problem is digitalized and simplified, and the optimal design can be obtained by using a small amount of training samples and test samples; the radial basis function neural network can determine a corresponding network topology structure according to specific problems, has high approximation precision and strong learning capability, and can process data at high speed in parallel; the invention adopts a genetic optimization algorithm, has good convergence, less calculation time and high robustness.
Drawings
FIG. 1 is a flow chart of a multi-objective optimization method for a double-walled structure of an integrated support plate flame holder;
FIG. 2 is a geometric model of an integrated afterburner support plate, wherein FIG. 2(a) is a three-dimensional view of the afterburner, FIG. 2(b) is a three-dimensional view of the integrated afterburner support plate, and FIG. 2(c) is a schematic view of a part A of the integrated afterburner support plate;
FIG. 3 is a hole layout of a double-walled cooling structure at the trailing edge, wherein FIG. 3(a) is a schematic view of the hole layout of a support plate, and FIG. 3(b) is a partially enlarged view;
FIG. 4 is a RBF neural network architecture;
FIG. 5 is a Pareto leading edge solution set for multi-objective optimization.
Detailed Description
The technical scheme of the invention is explained in detail in the following by combining the drawings and specific examples.
Referring to FIG. 1, the invention provides a multi-objective optimization method for a double-wall structure of an integrated support plate flame stabilizer. The method aims at the optimization target of an afterburner integrated afterburner plate 1 as shown in fig. 2 (b). Wherein the integrated afterburner plate 1 is disposed within an afterburner chamber 2 as shown in fig. 2 (a).
Comprises the following steps.
Step 1, selecting the aperture d of an impact holeiThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of air film hole rows, the number n of hole rows, and the ratio H/d of the impact distance to the diameter of the impact holeiAs a structural parameter to be optimized, the diameter d of the impingement holei0.8 to 1.5mm, df/di0.4 to 1.0, m is 37 to 73, n is 4 to 7, H/di1 to 2.5. The double-wall structure of the integrated support plate flame stabilizer consists of an impact plate, a gas film plate and an impact cavity between the two plates, wherein the impact distance refers to the impact distance between impact flow in an impact hole and an impact target surface (the inner wall surface of the gas film plate). Wherein the impact holes are arranged on the impact plate 3 and the air film holes are arranged on the air film plate 4, such as the holes 5 arranged on the integrated stressing support plate 1 shown in fig. 2 (c). The arrangement of the air film holes and the impact holes can be referred to fig. 3(a) and fig. 3 (b).
TABLE 1
Aiming at different unit scales of different sample parameters, normalization processing is carried out on the structural parameters to be optimized of the selected sample, and the unit scales of the different parameters are arranged in the range of (0, 1):
wherein y is the normalized result, xiIs a sample parameter variable, xmax，xminThe maximum and minimum values of the sample parameter variables, respectively.
F(di,df/di,m,n,H/di)＝1/η
F(di,df/di,m,n,H/di)＝ΔP
where η is the overall cooling efficiency and Δ P is the relative pressure loss.
The comprehensive cooling efficiency of the double-wall cooling structure of the integrated stress application support plate flame stabilizer is as follows:
in the formula, TgIs the inlet temperature, T, of the main stream high-temperature gas flowcFor secondary cooling of the inlet temperature, T, of the gas streamw,eThe temperature of the side wall surface of the high-temperature airflow is of a double-wall structure.
The relative pressure loss of the double-wall cooling structure of the integrated stress application support plate flame stabilizer is as follows:
in the formula (I), the compound is shown in the specification,
the average total pressure at the inlet of the double-wall impingement holes,
the average total pressure at the outlet of the double-walled gas film hole.
And 4, self-programming on an MATLAB platform, establishing a mathematical model of the RBF neural network based on the training sample, verifying the correctness of the model by using the test sample, and outputting the diffusion coefficient of the RBF neural network, as shown in FIG. 4.
Wherein, the RBF neural network receives training samples by an input layer, and the hidden layer maps the input samples to a new space through a radial basis function:
wherein x represents a training sample, ciRepresenting the central vector, δ, of the radial basis functioniRepresents the kernel width of the radial basis function;
the output layer realizes linear weighted summation in a new space, and outputs the result:
in the formula, wiThe connection weights of the hidden layer and the output layer,
is a radial basis function, y is an output result, and M is the number of hidden layer nodes;
determining diffusion coefficients of the RBF neural network by adopting a trial and error method, verifying the correctness of the RBF neural network, calculating radial basis function neural networks corresponding to different diffusion coefficients based on training samples, selecting a diffusion coefficient value with the minimum Root Mean Square Error (RMSE) through iterative calculation, and expressing the root mean square error of CFD calculation results and RBF neural network prediction results as follows:
wherein N is the total number of data, yt(k) And
respectively calculated data and predicted data.
And 5, calling a genetic algorithm and a direct search tool kit (GADS) of an MATLAB self-contained system, compiling a fitness function by adopting a RBF neural network mathematical model, and setting a population size, a selection function, a variation function, a cross function and a maximum iteration step length in the tool kit.
The detailed steps of utilizing a genetic algorithm to carry out global optimization on the double-wall structure of the integrated stressing support plate flame stabilizer are as follows:
step 5.1, initialization operation: chromosome coding, determining population quantity, and setting crossover, mutation probability and maximum iteration step number;
step 5.2, initializing the population: randomly generating a first generation population;
step 5.3, calculating a fitness value based on the RBF neural network mathematical model, and evaluating population, wherein the individual fitness comprises the maximum comprehensive cooling efficiency and the minimum relative pressure loss of the double-wall cooling structure of the integrated stressing support plate flame stabilizer;
step 5.4, judging whether the algorithm convergence criterion is met, if so, terminating, outputting an optimal solution, otherwise, continuing to operate;
and 5.5, selecting the population according to the principle of high-out and low-out, crossing and varying the population according to the crossing probability and the variation probability to form a new generation of population, returning to the step 5.3, and obtaining the optimal individual, namely the optimal integrated stressing support plate flame stabilizer double-wall cooling structure after evolution iteration of a plurality of generations.
FIG. 5 is a Pareto leading edge solution set for multi-objective optimization. The Pareto front edge solution sets are all non-inferior solutions, point A is the position with the maximum comprehensive cooling efficiency, point C is the position with the minimum relative pressure loss, point B is a median point, and the weights of the two objective functions are (0.5 ).
The above-mentioned embodiments are merely preferred embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A multi-objective optimization method for a double-wall structure of an integrated support plate flame stabilizer is characterized by comprising the following steps: the method comprises the following steps:
step 1, determining parameters of a structure to be optimized and a parameter range of the structure to be optimized of a double-wall cooling structure of an integrated stressing support plate flame stabilizer;
step 2, designing a training sample and a testing sample of the radial basis function neural network;
step 3, taking the maximum comprehensive cooling efficiency and the minimum relative pressure loss of the double-layer wall cooling structure of the integrated stress application support plate flame stabilizer as optimization targets, constructing a fitness function and calculating a target function of a selected sample by calculating fluid dynamics;
step 4, establishing a mathematical model of the radial basis function neural network based on the training sample, verifying the correctness of the model by using the test sample, and outputting the diffusion coefficient of the radial basis function neural network;
and 5, carrying out global optimization on the double-wall structure of the integrated stressing support plate flame stabilizer by using a genetic algorithm.
2. The multi-objective optimization method of claim 1, wherein: in step 1, the structural parameters to be optimized comprise the aperture d of the impact holeiThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the columns of the air film holes, the number n of the rows of the air film holes, and the ratio H/d of the impact distance to the aperture of the impact holeiDiameter d of impact holei0.8 to 1.5mm, df/di0.4 to 1.0, m is 37 to 73, n is 4 to 7, H/di1 to 2.5.
3. The multi-objective optimization method of claim 2, wherein: in step 2, the design step of the sample comprises:
step 2.1, the aperture d of the impact hole of the structural parameter to be optimizediThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the air film hole rows, the number n of the hole rows, and the ratio H/d of the impact space to the aperture of the impact holeiCombining, and selecting 32 groups of representative samples from the comprehensive combination as training samples of the radial neural network according to orthogonality by utilizing orthogonal test design;
step 2.2, the aperture d of the impact hole with the structural parameter to be optimizediThe ratio d of the pore diameter of the air film pore to the pore diameter of the impact poref/diThe number m of the gas film hole columns, the number n of the hole rows, and the ratio H/d of the impact space to the aperture of the impact holesiCombining, and randomly extracting 8 groups of samples as test samples;
step 2.3, aiming at different unit scales of different sample parameters, normalization processing is carried out on the structural parameters to be optimized of the selected sample, and the unit scales of the different parameters are arranged in the range of (0, 1):
wherein y is the result after normalization, xiIs a sample parameter variable, xmax，xminThe maximum and minimum values of the sample parameter variables, respectively.
4. The multi-objective optimization method of claim 3, wherein: in step 3, the objective functions of the integrated cooling efficiency and the relative pressure loss are respectively defined as:
F(di，df/di，m，n，H/di)＝1/η
F(di，df/di，m，n，H/di)＝ΔP
where η is the overall cooling efficiency and Δ P is the relative pressure loss.
5. The multi-objective optimization method of claim 4, wherein: in step 4, the radial basis function neural network receives training samples by the input layer, and the hidden layer maps the input samples to a new space through the radial basis function:
wherein x represents a training sample, ciRepresenting the central vector, δ, of the radial basis functioniRepresents the kernel width of the radial basis function;
the output layer realizes linear weighted summation in a new space, and outputs the result:
in the formula, wiThe connection weights of the hidden layer and the output layer,
is a radial basis function, y is an output result, and M is the number of hidden layer nodes;
determining diffusion coefficients of the radial basis function neural network by adopting a trial-and-error method, verifying the correctness of the radial basis function neural network, calculating the radial basis function neural network corresponding to different diffusion coefficients based on training samples, selecting the diffusion coefficient value with the minimum root mean square error through iterative calculation, and expressing the root mean square error of a computational fluid dynamics calculation result and a prediction result of the radial basis function neural network as follows:
wherein N is the total number of data, yt(k) And
respectively calculated data and predicted data.
6. The multi-objective optimization method of claim 5, wherein: in the step 5, the detailed steps of utilizing a genetic algorithm to carry out global optimization on the double-wall structure of the integrated stressing support plate flame stabilizer are as follows:
step 5.1, initialization operation: chromosome coding, determining population quantity, and setting crossover, mutation probability and maximum iteration step number;
step 5.2, initializing the population: randomly generating a first generation population;
step 5.3, calculating a fitness value based on a radial basis function neural network mathematical model, and evaluating a population, wherein the individual fitness comprises the maximum comprehensive cooling efficiency and the minimum relative pressure loss of the double-wall cooling structure of the integrated stressing support plate flame stabilizer;
step 5.4, judging whether the algorithm convergence criterion is met, if so, terminating, outputting the optimal solution, otherwise, continuing to operate;
and 5.5, selecting the population according to a principle of superior and inferior selection, crossing and mutating the population according to the crossing probability and the mutation probability to form a new generation of population, returning to the step 5.3, and obtaining the optimal individual, namely the optimal integrated stressing support plate flame stabilizer double-wall cooling structure after a plurality of generations of evolution iteration.
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