CN116522511B - Thermal protection multi-objective robust optimization method based on interval uncertainty - Google Patents
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Abstract
The invention discloses a thermal protection multi-objective steady optimization method based on interval uncertainty, which utilizes effective target values and steady definition to convert multi-objective optimization problems to determine a thermal protection multi-objective optimization mathematical model; in the initial optimization stage, carrying out deterministic optimization by utilizing subset simulation optimization, taking the sample with the best performance as an initial seed sample and putting the initial seed sample into a sample library; in the robust optimization stage, firstly setting a threshold value of the number of neighborhood samples required by the samples to enter a simulation level, and then comparing the initial seed samples with a sample library to generate neighborhood samples for any seed samples which cannot reach the threshold value; calculating effective target values of all seed samples, randomly selecting one seed sample as a threshold sample, and generating candidate samples by using a multi-target subset simulation optimization method; comparing the candidate sample with a threshold sample, and judging whether to accept the sample; the above process is cycled until the maximum simulation level is reached or the budget is exceeded, obtaining the optimal solution set.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a thermal protection multi-objective steady optimization method based on interval uncertainty.
Background
The aircraft can be subjected to severe pneumatic heating in a flight service environment, and the high temperature of pneumatic heating and the thermal stress in the structure seriously influence the safety of the aircraft structure. Aiming at the influence of high temperature and thermal stress of the structure, the thermal protection system of the aircraft needs to be optimally designed in the structural design of the aircraft. At the same time, the aircraft structure is inevitably affected by uncertainty factors, such as geometrical parameters of materials, mechanical performance parameters, external loads and temperatures, etc. during design, manufacture and service. It is therefore highly desirable to optimize uncertainty in consideration of the effects of uncertainty conditions in the design of aircraft thermal protection structures.
Conventional engineering problem analysis and optimization designs are generally based on determined system parameters and optimization models. However, the problem of multi-objective optimization under uncertain conditions is a critical and unavoidable problem in the engineering design field. According to existing studies, uncertainties in optimization problems can be categorized into three categories, disturbances imposed on design variables, noise affecting objective evaluations, and environmental parameter fluctuations affected by environmental and operating condition variations. These uncertainties may reduce the performance of the engineering design compared to deterministic optimization, even producing unacceptable variations in objective functions and constraints. When the objective function has uncertainty, each solution in the optimization process should verify its robustness. This process makes the optimization process expensive and inefficient. The present invention is therefore primarily directed to developing a new interval-based robust optimization method to solve the multi-objective optimization problem of uncertainty in variables and parameters.
Disclosure of Invention
In order to overcome the technical defects of the prior method and solve the problem of multi-objective optimization under the uncertainty of thermal protection of an airplane, the invention provides a multi-objective robust optimization method for thermal protection based on interval uncertainty.
The technical scheme of the invention is as follows:
a thermal protection multi-objective robust optimization method based on interval uncertainty comprises the following steps:
and step 1, taking uncertainty factors into a multi-objective subset simulation algorithm by using effective target values and class I robustness definitions, and determining a heat protection multi-objective optimization mathematical model.
Step 2, the optimization flow is divided into an initial optimization stage and a steady optimization stage, and the temperature evaluation budget E required in the whole multi-objective steady optimization process is determined before the optimization starts and divided into the calculation budget E of the initial optimization stage N And a computational budget E for a robust optimization phase R ：
1) An initial optimization stage:
(1) deterministic optimization using subset simulation optimization, searching for regions of higher performance (equivalent to the pareto front stack of optimal points) in the input space, obtaining the best performing sample in the initial optimization stage as the initial seed sample x in the robust optimization stage nom The subscript nom indicates that the sample is the best sample to the initial (nominal) optimization stage, and the deterministic optimization is continued until the computational budget E of the initial optimization stage is exceeded N 。
(2) All samples and target values obtained in the initial optimization stage are stored in a sample library B for use in the robust optimization process of the next stage.
2) Robust optimization stage:
(1) setting a threshold value N for the number of neighbor samples required for the sample to enter the first simulation level T Then comparing the initial seed sample provided by the initial optimization stage with a sample library B, and checking the neighborhood samples N owned by the initial seed sample ε And generating N for any seed samples that fail to reach the threshold T - N ε The neighbor samples are added into a sample library B to calculate an effective target value;
(2) calculate all speciesThe effective target value of the subsamples, randomly selecting one of the subsamples as the threshold sample x of the current simulation level (the simulation level corresponds to the current iteration number) T Candidate sample x is generated by using a Markov Monte Carlo method to generate candidate sample cards cand ；
(3) Candidate sample x cand Comparing with the sample library B to determine whether the candidate sample has enough neighbor samples, if so, x is determined cand The target value is changed into the effective target value and is matched with the threshold value sample x T And (3) comparing the effective target values of the samples, accepting the candidate samples if the effective target values are superior to the effective target values of the threshold samples, otherwise rejecting the samples, and selecting the seed samples as candidate sample points for the next simulation level simulation.
Once candidate sample points for the current simulation level are generated, all samples are checked to see if they possess at least N T And (3) neighborhood samples. Those samples meeting this requirement are put into a set S T While those samples with insufficient neighborhood samples are put into another set S I . For set S I Non-dominant ordering, selecting n s The best performing samples (with the maximum or minimum effective target value being optimal) generate N T - N ε And (3) neighborhood samples. To ensure that the samples each have at least N T A number of neighborhood samples and adds them to set S T Among them. To newly supplement S T The samples in the sequence are sorted, and the optimal n is selected s The samples are used as seeds for the next simulation level.
Step 3, looping step 2, wherein the neighborhood sample threshold gradually increases with the increase of the iteration timesAnd (c) wherein L is the current simulation level and m is the maximum number of neighborhood samples to gradually increase the impact of robustness on the optimization process. The value of m may be adjusted according to the user's goal. When the maximum simulation level is reached or the budget is exceededThis isWhen samples in the current simulation level are selected as a solution to the problem, denoted +.>。
Preferably, the effective target value is expressed as:
,
wherein the method comprises the steps ofIs sample->Surrounding neighborhood samples, < >>Is->Is not limited to a volume of a single crystal.
Preferably, the multi-objective optimization mathematical model is: under the condition of meeting the maximum allowable temperature of the material, taking the minimum unit mass and the minimum temperature of the inner surface of the aviation aircraft as design targets; all constraint functions of the multi-objective optimization mathematical model are set to meet certain robust probability, and the heat protection multi-objective optimization mathematical model is converted based on the effective target value.
Advantageous effects
1. The invention provides a novel multi-objective robust optimization technology for solving a robust solution of a multi-objective optimization problem with random uncertainty. The method disclosed by the invention successfully introduces the subset simulation method into the field of robust optimization, utilizes the capability of sampling from a high-dimensional area by multi-objective subset simulation optimization, and evaluates the robustness of a plurality of solutions.
2. The present invention employs several strategies to maximize efficiency and reduce the computational costs involved. (1) An initial deterministic optimization phase: carrying out deterministic optimization solving by utilizing a multi-objective subset simulation algorithm, searching a global Pareto optimal front, storing all samples in a sample library in the optimization solving process, and saving more computing resources for evaluating areas with higher performance for robust optimization; (2) in the robust optimization stage, the solution is compared with samples in a sample library, the comprehensive performance of the region where the robust solution neighborhood samples are located is determined, and significant computational savings are provided by reducing the number of unnecessary evaluations of the robust solution neighborhood samples. Also, adjusting the number of samples and the neighborhood size in the iterative process ensures that the maximum computational overhead is reserved for samples with the most promising robust performance. (3) Before the robust optimization starts, the total calculation cost is predefined, which guarantees the feasibility of the method in practical applications.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below.
FIG. 1 is a side view of a space shuttle orbit according to one embodiment of the invention;
FIG. 2 is a top, bottom view of a space shuttle orbit machine according to one embodiment of the invention;
FIG. 3 is a graph showing a distribution of heat flux density under uncertain conditions according to an embodiment of the present invention;
FIG. 4 is a graph showing the temperature profile of the interior and exterior surfaces of a space vehicle prior to optimization in accordance with one embodiment of the present invention;
FIG. 5 is a graph of the temperature profile of the interior and exterior surfaces of an optimized space shuttle in accordance with one embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Comprehensively considering the thermal protection problem of the aerospace plane shown in fig. 1 and 2, mathematical modeling work is required before the aerospace plane is optimized. For this purpose, firstly, the surface area of the space plane is subjected to meshing, and the purpose of meshing is to observe the temperature distribution condition of the plane when the surface of the plane is subjected to heat flow, and to determine the position of the most severely heated area. The assumed structural boundary condition is the heat flux density qcond shown in fig. 3, where the heat flux density is in W/m 2. Before the optimization work starts, the surface temperature and the inner wall temperature of the space shuttle are analyzed to obtain the highest temperature born by the head of the space shuttle. Therefore, when considering the heat insulation condition of the aircraft surface, the area with the highest temperature is preferentially considered, and the temperature distribution diagram of the inner surface and the outer surface of the area is changed with time as shown in fig. 4.
Step 1: the heat-proof tile made of the reinforced carbon-carbon composite material is considered to be optimized by three layers of materials, namely LI-900 heat-proof ceramic and Nomex heat-proof felt. The relevant material properties are shown in table 1;
TABLE 1 Material Properties
。
The design objective is to meet the maximum allowable temperature of the material with minimum unit mass (minimum weight) and minimum aircraft interior surface temperature. Wherein the RCC material limiting temperature is 1900K, the Nomex heat insulation felt limiting temperature is 917K, and the obtained deterministic optimization mathematical model is:
，
wherein the method comprises the steps of，/>For design variables, the thickness of three different heat insulation materials is respectively +.>The density of the three heat insulation materials respectively, +.>And->Respectively the maximum allowable temperature of the material. And because of the heat insulation material manufacturing and spraying process, the thickness (i.e. design variable) of each material is interval variable, and the transformation interval of each design variable is [ -0.0001,0.0001]m. Setting all constraint functions to meet the robustness probability as 99%, and converting the robustness optimization model into:
wherein the method comprises the steps ofAnd->Representing the effective target value of the objective function, +.>The fluctuation values of the three design variables are respectively.
Step 2: before solving the problems by adopting the uncertainty multi-objective optimization algorithm, the total temperature evaluation budget E is set to 10000 times of temperature evaluation, wherein E is as follows N =4000 times for initial optimization stage, the remainder E R 6000 times for robust optimization phase.
In the initial optimization stage, the subset simulation optimization method is utilized to conduct deterministic optimization of heat protection performance, the population number is set to be 100, the maximum circulation times are 100, and the optimal solution set obtained by solving and outputting is used as an initial seed sample. All samples in these optimal sets and optimization processes are stored in sample library B for the robust optimization stage.
Step 2.2 robust optimization solution judgment robust optimal solution, setting population number as 100 and maximum circulation number as 200And twice. In the robust optimization stage, a threshold value N of the number of neighborhood samples required by the samples entering the simulation level is firstly set T The initial seed samples provided in the initial optimization stage are then compared to sample library B to generate N for any seed samples that fail to meet the threshold T - N ε And each neighborhood sample, and adding the newly generated samples into a sample library B for calculating an effective target value.
Calculating effective target values of all seed samples, and randomly selecting one seed sample as a threshold sample x of the current simulation level T Candidate sample x is generated by using Markov Monte Carlo method cand . Candidate sample x cand And a threshold sample x T Comparing, judging whether to accept the sample: judging whether the candidate sample has enough neighborhood samples, if so, adding x to the sample cand The target value is changed into the effective target value and is matched with the threshold value sample x T And (3) comparing the effective target values of the samples, accepting the candidate samples if the effective target values are superior to the effective target values of the threshold samples, otherwise rejecting the samples, and selecting the seed samples as candidate sample points for the next simulation level simulation.
Once candidate sample points for the current simulation level are generated, all samples are checked to see if they possess at least N T And (3) neighborhood samples. Those samples meeting this requirement are put into a set S T While those samples with insufficient neighborhood samples are put into another set S I . For set S I Non-dominant ordering, selecting n s The best performing samples (with the maximum or minimum effective target value being optimal) generate N T – N s And (3) neighborhood samples. To ensure that the samples each have at least N T A number of neighborhood samples and adds them to set S T Among them. To newly supplement S T The samples in the sequence are sorted, and the optimal n is selected s The samples are used as seeds for the next simulation level.
Step 3, cycling the optimization process of step 2 until reaching the maximum simulation level or exceeding the calculation budget to obtain an optimal solution set, and specifically, gradually increasing the neighborhood sample threshold value along with the increase of the iteration timesAnd (c) wherein L is the current simulation level and m is the maximum number of neighborhood samples to gradually increase the impact of robustness on the optimization process. The value of m may be adjusted according to the user's goal.
Loop optimization until the maximum simulation level is reached or the temperature budget E is exceeded R The samples in the current simulation level are now selected as a solution to the thermal protection optimization problem, denoted as x RS 。
Finally, the optimal solution set is obtained, and 10 typical solutions are randomly selected as shown in table 2:
TABLE 2 optimal solution sets of 10
。
If the thickness of the heat insulation layer material of the spaceflight aircraft is [0.005024,0.085209,0.005], the average value of the internal and external temperatures of the heat insulation material under the thickness condition is calculated, the image is shown in fig. 5, and compared with fig. 4 before optimization, the surface temperature of the aircraft after robust optimization is obviously reduced.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The thermal protection multi-target robust optimization method based on interval uncertainty is characterized by being applied to an aviation aircraft and comprising the following steps of:
step 1, determining a heat protection multi-objective optimization mathematical model by taking uncertainty factors into a multi-objective subset simulation algorithm by using effective target values and class I robustness definitions: namely, under the condition of meeting the maximum allowable temperature of the material, taking the minimum unit mass and the minimum temperature of the inner surface of the aeroplane as design targets;
setting all constraint functions of the multi-objective optimization mathematical model to meet a certain steady probability, and converting the heat protection multi-objective optimization mathematical model based on an effective target value;
the effective target value is expressed as:
in which x is ε Is a neighborhood sample around sample x, |x ε I is x ε Is an ultra-volume of (2);
step 2, optimizing based on the thermal protection multi-objective optimization mathematical model, wherein the optimization flow comprises an initial optimization stage and a steady optimization stage, and the calculation budget E of the steady optimization stage is determined before optimization starts R ；
Step 2.1, in an initial optimization stage, carrying out deterministic optimization by using a subset simulation optimization method, and taking a sample with the best performance as an initial seed sample;
step 2.2, a robust optimization stage, namely firstly setting a threshold value of the number of neighborhood samples required by the samples entering the simulation level, and then comparing the initial seed samples provided by the initial optimization stage with all samples obtained by the optimization of the initial optimization stage to generate neighborhood samples for any seed samples which cannot reach the threshold value; calculating effective target values of all seed samples, randomly selecting one seed sample as a threshold sample of a current simulation level, and generating candidate samples by using a multi-target subset simulation optimization method;
comparing the candidate sample with a threshold sample, and judging whether to accept the sample; the above processes are circulated until the maximum simulation level is reached or the calculation budget is exceeded, and an optimal solution set is obtained;
step 3, cycling the optimization process of step 2 until the maximum simulation level is reached or the budget E is exceeded R At this time, the sample in the current simulation level is selected as heatA solution to the protection optimization problem, denoted as x RS 。
2. The interval uncertainty-based thermal protection multi-objective robust optimization method according to claim 1, wherein the initial optimization stage is specifically:
step 2.1.1, performing deterministic optimization of thermal protection performance by using subset simulation optimization to obtain a sample with the best performance in an initial optimization stage as an initial seed sample x in a robust optimization stage nom ；
And 2.1.2, storing all samples and target values obtained in the initial optimization stage in a sample library B for robust optimization in the next stage.
3. The interval uncertainty-based thermal protection multi-objective robust optimization method according to claim 1 or 2, wherein the method for determining whether to accept the candidate samples in the robust optimization stage is: comparing the candidate sample with a sample library storing all samples and target values thereof, judging whether the candidate sample has enough neighborhood samples, if so, changing the target value of the candidate sample into an effective target value, comparing the effective target value with the effective target value of the threshold sample, if so, accepting the candidate sample, otherwise, rejecting the sample, and selecting a seed sample as a candidate sample point for the next simulation level simulation.
4. The interval uncertainty-based thermal protection multi-objective robust optimization method according to claim 3, wherein after candidate sample points of the current simulation level are generated, all candidate samples are checked to see if each candidate sample has at least N T A number of neighborhood samples; put the candidate sample meeting the requirement into the set S T Placing the sample which does not meet the requirement into another set S I The method comprises the steps of carrying out a first treatment on the surface of the For set S I Non-dominant ordering, selecting n s Best performing sample generation N T -N ε A number of neighborhood samples and adds them to set S T In (a) and (b); for the supplemented set S T The samples are ordered and the best n is selected s The samples are used as seeds for the next simulation level.
5. The interval uncertainty-based thermal protection multi-objective robust optimization method according to claim 1, wherein during the loop step 2, as the number of iterations increases, the neighborhood sample threshold gradually increases to N T =min (Ld, m), where L is the current simulation level and m is the maximum number of neighborhood samples.
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