CN114282320A - Method for optimizing engineering parameters by using Bayesian optimization algorithm - Google Patents
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Abstract
The application discloses a method for optimizing engineering parameters by utilizing a Bayesian optimization algorithm, which is used for optimizing performance parameters having functional relations with the engineering parameters under engineering constraint conditions. The method defines a new acquisition function, the acquisitionThe function introduces an adaptive target value ytarget(k)Optimal solution item y replacing traditional expected lifting criterion in the prior artminWhile introducing an adaptive weight coefficient term wkAnd evolving the traditional expected lifting criterion into an adaptive jump weighting expected lifting criterion. The method can reduce the occurrence of over development and over exploration to a certain extent, accelerate optimization efficiency, reduce the waste of computing resources and obtain better optimization effect.
Description
Technical Field
The application relates to the field of engineering design, in particular to a method for optimizing engineering parameters by using a Bayesian optimization algorithm, and particularly relates to a method for optimizing shape parameters of a turbine disk.
Background
In the field of engineering design, situations often face where engineering parameters need to be designed to bring performance close to the limit with engineering constraints. At this time, if the performance and the engineering parameters have a known functional relationship, and the function is a complex function or the extremum is calculated at a very expensive cost, the engineering parameters can be determined by a bayesian optimization algorithm to solve the problem. For example, in the design process of a turbine disk, the maximum allowable equivalent stress is an engineering constraint, and engineering designers need to face the condition that the turbine disk is made to be the lightest as possible under the condition of meeting the stress requirement by designing the geometric parameters of the turbine disk. In this case, there is a clear functional relationship between the mass of the turbine disk and the geometric parameters, while the maximum equivalent stress is related to the geometric parameters and the given operating conditions. Thus, a Bayesian optimization algorithm can be used to determine the geometry of the turbine disk.
The bayesian optimization algorithm has two core components: (1) a complex objective function with high cost is originally evaluated by using a probability agent model; (2) and (3) constructing an active selection strategy, namely an acquisition function by utilizing posterior probability information of the agent model, and selecting the next most potential evaluation point by maximizing the acquisition function.
The probability agent model technology is relatively mature, and more linear models, beta-Bernoulli models and other parametric models, Gaussian process models, random forests, deep neural networks and other non-parametric models are applied. The Gaussian process model has high flexibility and expandability, and can proxy any linear and nonlinear functions theoretically, so that the application range is widest.
In addition, currently, more types of collection functions are used, including a lifting-based strategy (including Probability of Improvement (PI), Expected Improvement (EI)); confidence boundary policies (including Upper Confidence Bound policy (UCB), Lower Confidence Bound policy (LCB)); information-based strategies (including Thompson Sampling (TS), Entropy Search strategy (ES)); combining strategies, and the like. In many types of acquisition functions, the strategy based on promotion has the widest application range. The strategy selects a position with a promoted current optimal objective function value (smaller than the current optimal objective function value) as a new evaluation point, and can consider local development and global exploration during point selection. Local development is to add points near the current optimal value, so that the local approximation precision near the optimal solution of the current agent model can be improved, the convergence is better, but the defect that the local optimal solution is easy to fall into exists; the global exploration is to add points at a sparse position or a region with high uncertainty of a design space sample point, has good global searchability, can improve the overall approximation precision of the proxy model, but is lack of local search, so that the accuracy of an optimal solution cannot be ensured, and the convergence is poor.
The promotion-based strategy includes: probability lifting criterion PI and expected lifting criterion EI. The probability boosting criterion can select the evaluation point with the highest boosting probability, but it considers all boosting as equal, only reflecting the probability of boosting and not the magnitude of the boosting amount. The expected lifting criterion integrates the lifting probability and can reflect different lifting amounts, so that the expected lifting criterion has more advantages than the probability lifting criterion in the application range.
In the prior art, a method for optimizing engineering parameters based on a bayesian optimization algorithm of a traditional expected lifting criterion to optimize performance parameters having a functional relationship with the engineering parameters generally includes the following steps:
s1: acquiring an initial engineering parameter sample set, generally acquiring the initial engineering parameter sample set by an optimal Latin hypercube test design method, and of course, acquiring the initial engineering parameter sample set by other methods;
s2: acquiring a performance parameter corresponding to each engineering parameter sample in the initial engineering parameter sample set by using a functional relation between the engineering parameters and the performance parameters;
s3: the sampling process implemented iteratively specifically includes:
s3.1: constructing a Gaussian process model based on all engineering parameters and corresponding performance parameters in the engineering parameter sample set to obtain a posterior mean value and a posterior variance;
s3.2: constructing an acquisition function, wherein the expression of the acquisition function in the prior art is as follows:
wherein, yminObtaining the optimal performance parameter value in the performance parameters based on all sampled engineering parameters before the iteration; phi (x) is a distribution function of a standard normal distribution; phi (x) is a density function of a standard normal distribution;
is the posterior mean value; sk(x) Is the posterior mean square error, which is the value after the posterior variance is squared;
s3.3: maximizing the collection function to determine the engineering parameters of the sampling;
s3.4: obtaining corresponding performance parameters based on the engineering parameters determined to be sampled;
s3.5: updating the engineering parameter sample set;
s3.6: terminating the iteration after the iteration termination condition is reached, and continuing the iteration after the iteration termination condition is not reached; wherein, the iteration termination condition may be that the iteration number reaches a preset value; or under the condition that the optimal performance parameter is known, the performance parameter corresponding to at least one sampling engineering parameter is close to the optimal performance parameter and is within a preset value range.
In the above scheme, the expression of the collection function is composed of two parts, the former part represents the current optimal solution yminAnd the predicted value
The difference between, and the probability of being boosted is a penalty, where
The smaller, the larger this term represents local development; the latter part represents a global exploration, the larger this term is when the larger the error s (x), i.e. the greater the uncertainty of the prediction. When a new evaluation point is selected, the traditional expected lifting criterion is subjected to "over development" or "over exploration", so that not only is the bayesian optimization easily trapped in local optimization (i.e., converged to a local optimal solution), but also the waste of computing resources is generated, and the optimization efficiency is reduced. Therefore, aiming at the defect that the local development point adding or the global exploration point adding cannot be adjusted according to actual needs, the invention of the point adding strategy capable of automatically balancing the local development and the global exploration on the basis of the traditional expected lifting criterion is urgently needed, so that the optimization performance of the Bayesian optimization method is improved. Therefore, the selection of the engineering parameters and the improvement of the performance parameters are faster and more efficient.
Disclosure of Invention
The present application aims to overcome the above-mentioned defects or problems in the background art, and provides a method for optimizing engineering parameters by using a bayesian optimization algorithm, which is used for optimizing performance parameters having a functional relationship with the engineering parameters under the engineering constraint condition, and can accelerate the optimization efficiency and obtain a better optimization result.
In order to achieve the purpose, the following technical scheme is adopted:
a method for optimizing engineering parameters by using a Bayesian optimization algorithm is used for optimizing performance parameters having functional relations with the engineering parameters under engineering constraint conditions, the Bayesian optimization algorithm is based on an expected lifting criterion and at least comprises an iteratively implemented sampling process, and the sampling process comprises a step of constructing a Gaussian process model based on all the engineering parameters and corresponding performance parameters in an engineering parameter sample set to obtain posterior mean and posterior variance, a step of constructing an acquisition function, a step of maximizing the acquisition function to determine the sampled engineering parameters, a step of obtaining corresponding performance parameters based on the engineering parameters determined to be sampled and a step of updating the engineering parameter sample set; in each sampling process, the acquisition function is configured to:
wherein:
ytarget(k)＝ymin(k)-DIk；
yk-1＝yreal(k-1)+p；
in the above formula:
k is an iteration serial number of the sampling process, and the value range of k is a natural number which is more than or equal to 1; w is akThe self-adaptive weight coefficient is the self-adaptive weight coefficient in the k iteration;
the posterior mean value is obtained by a Gaussian process model in the kth iteration; sk(x) The posterior mean square error of the kth iteration is a value obtained by a Gaussian process model after the posterior mean square error is solved; phi (x) is a distribution function of a standard normal distribution; phi (x) is a density function of a standard normal distribution; y istarget(k)The performance parameter self-adaptive target value is the performance parameter self-adaptive target value in the k iteration; y ismin(k)Obtaining the optimal performance parameter value in the performance parameters based on all sampled engineering parameters before the kth iteration; y isk-1The nominal performance parameter value corresponding to the engineering parameter determined to be sampled in the k-1 iteration; y isreal(k-1)Obtaining corresponding performance parameters based on the engineering parameters which are determined to be sampled during the (k-1) th iteration; DIkThe expected optimal performance parameter promotion amount for the kth iteration is obtained; p is an engineering constraint penalty value, when the engineering parameters determined to be sampled during the (k-1) th iteration do not meet the engineering constraint conditions, p is a preset penalty value, when the engineering parameters determined to be sampled during the (k-1) th iteration meet the engineering constraint conditions, p is 0, and all the engineering parameters determined to be sampled without the engineering constraint conditions meet the engineering constraint conditions; a. b, c are preset values, and a<b，c>0。
Further, the bayesian optimization algorithm based on the expected lifting criterion further comprises, before the iteratively implemented sampling engineering: the method comprises the steps of obtaining an initial engineering parameter sample set and obtaining performance parameters corresponding to each engineering parameter sample in the initial engineering parameter sample set.
Further, an initial engineering parameter sample set is obtained through an optimal Latin hypercube test design method.
Further, the sampling process of the iterative implementation terminates the iteration after reaching an iteration termination condition; after the iteration is terminated, the engineering parameter samples are concentrated, and the engineering parameters which meet the engineering constraint conditions and are optimal in performance parameters are the optimal engineering parameters.
Further, the iteration termination condition includes that the iteration number reaches a preset value.
Further, under the condition that the optimal performance parameter is known, the iteration termination condition includes that at least one sampling engineering parameter meets the engineering constraint condition and the corresponding performance parameter is close to the optimal performance parameter and is within a preset value range.
Further, the engineering parameters are undetermined parameters in the shape parameters of the turbine disc; the performance parameter is the mass of the turbine disc and the optimization objective is to minimize the mass of the turbine disc; the engineering constraint is that the maximum equivalent stress of the turbine disk, which is determined by the shape of the turbine disk, must be less than the maximum allowable equivalent stress based on the given operating conditions of the turbine disk.
Further, when the turbine disc is rotationally symmetric about its axis of rotation, the engineering parameters include hub width, hub thickness, spoke plate outer radius, spoke plate outer width, spoke plate inner radius and spoke plate inner side thickness.
Compared with the prior art, the scheme has the following beneficial effects:
the optimization method is based on the expected lifting criterion, and the main technical contribution is to define a new acquisition function, and the new acquisition function introduces a self-adaptive target value ytarget(k)Optimal solution item y replacing traditional expected lifting criterion in the prior artminWhile introducing an adaptive weight coefficient term wkThe conventional expected lifting criterion (EI) is evolved into an adaptive jump weighted expected lifting criterion (asweii). In brief, the ratio of the performance parameter lift to the expected lift in the last iteration (representing the target value y set before the previous iteration starts) is obtained according to the actual performance parameter value of the point added in the previous iteration cycletarget(k-1)The completion condition) and the value of the target value (or the expected lifting amount) and the weight coefficient which are required to be set by the iteration loop are determined by taking the value of the ratio as a judgment standard, then the weight ratio of the front item and the rear item of the collection function expression is controlled according to the set target value and the weight coefficient, and further the iteration is controlled adaptively to carry out local development adding point or global exploration adding point, and the relationship between the local development and the global exploration is balanced automatically. Therefore, the situations of over development and over exploration can be reduced to a certain extent, the optimization efficiency is accelerated, the waste of computing resources is reduced, and a better optimization effect is obtained. The method can be used in the field of structural optimization or pneumatic optimization of aerospace, and can achieve the purpose of reducing weight of a turbine disc by optimizing the structural parameters of the turbine disc of the aero-engine, so that the thrust-weight ratio, the stability, the reliability and the service life of the aero-engine are improved.
Another technical contribution of the optimization method is that a function of meeting the engineering constraint condition is realized in the optimization method, namely, an engineering constraint penalty value p is introduced, so that the performance parameter corresponding to the engineering parameter which is iteratively acquired last time can be punished when the engineering constraint condition is not met, and global exploration can be carried out as soon as possible under the condition.
Drawings
In order to more clearly illustrate the technical solution of the embodiments, the drawings needed to be used are briefly described as follows:
FIG. 1 is a schematic view of a typical turbine disk shape;
FIG. 2 is a graph comparing the optimal mass for optimizing the weight of a turbine disk using the optimization method of the example and using the optimization method of the comparative example;
FIG. 3 is a graph of maximum equivalent stress versus weight for a turbine disk optimized using the optimization method of the example and using the optimization method of the comparative example;
fig. 4 is a graph comparing the number of iteration steps to achieve the optimum mass by optimizing the weight of the turbine disk using the optimization method of the example and the optimization method of the comparative example.
Detailed Description
In the claims and specification, unless otherwise specified the terms "first", "second" or "third", etc., are used to distinguish between different items and are not used to describe a particular order.
In the claims and specification, unless otherwise specified, the terms "central," "lateral," "longitudinal," "horizontal," "vertical," "top," "bottom," "inner," "outer," "upper," "lower," "front," "rear," "left," "right," "clockwise," "counterclockwise," and the like are used in the orientation and positional relationship indicated in the drawings and are used for ease of description only and do not imply that the referenced device or element must have a particular orientation or be constructed and operated in a particular orientation.
In the claims and the specification, unless otherwise defined, the terms "fixedly" or "fixedly connected" are to be understood in a broad sense as meaning any connection which is not in a relative rotational or translational relationship, i.e. including non-detachably fixed connection, integrally connected and fixedly connected by other means or elements.
In the claims and specification, unless otherwise defined, the terms "comprising", "having" and variations thereof mean "including but not limited to".
The technical solution in the embodiments will be clearly and completely described below with reference to the accompanying drawings.
The embodiment relates to application of a method for optimizing engineering parameters by utilizing a Bayesian optimization algorithm in weight reduction optimization of a turbine disk. The method for optimizing the engineering parameters by using the Bayesian optimization algorithm in the embodiment is mainly used for optimizing the performance parameters having the functional relation with the engineering parameters under the engineering constraint condition.
Turbine disks are the core components of aircraft engines and tend to be subjected to significant thermal and inertial centrifugal loads. The design quality of the turbine disk directly influences the performances of the aero-engine such as thrust-weight ratio, stability, reliability and service life. Therefore, weight-reduction optimization design of the aeroengine turbine disc is always the focus of the researchers.
According to the method, the shape of the turbine disk is subjected to weight reduction optimization by using a Bayes optimization algorithm optimization engineering parameter method based on an adaptive jump weighting expected lifting criterion (ASWEI) introducing a new acquisition function, and meanwhile, the shape of the turbine disk is subjected to weight reduction optimization by using a Bayes optimization algorithm optimization engineering parameter method based on a traditional expected lifting criterion (EI) in a comparative example. The performance advantage of optimizing the engineering parameters by the Bayes optimization algorithm based on the adaptive jump weighting expected lifting criterion (ASWEI) is verified by comparing the weight reduction effect and other effects between the embodiment and the comparative example.
For the design of the turbine disk, firstly, a turbine disk geometric model can be established through UG10.0 software, then the geometric model is imported into Hypermesh2019 software to automatically generate a computational grid, PLANE183 with rotationally symmetric element types is selected, finally, the APDL language of finite element analysis software ANSYS is used for automatically carrying out numerical simulation, and a design scheme with the minimum turbine disk quality is selected as an optimization result through two optimization algorithms.
The actual geometry of the turbine disc and the loads it is subjected to are complex, difficult to analyse accurately and do not require very detailed and accurate calculations in the engine design stage. Therefore, in order to meet the requirement of rapid scheme optimization in the scheme design stage, the structure of the actual turbine disk is reasonably simplified, and a two-dimensional axisymmetric model of the turbine disk as shown in fig. 1 is established.
As shown in fig. 1, the shape parameters of a typical turbine disk include: rim radius R1237mm, rim width W1Rim thickness H40 mm17.5mm, hub radius R283mm, hub width W290.0mm, hub thickness H227.5mm, outer radius of the web R3206mm, width W outside the web314.5mm, inner radius R of the spoke plate4165mm, web inner thickness W4＝17mm。
The rim radius R1, rim width W1, rim thickness H1 and hub radius R2 are typically determined due to the fit of the turbine disk and other components, and therefore remain unchanged during weight reduction optimization design for the turbine disk. The rest shape parameters are undetermined parameters and can be used as optimized engineering parameters. The mass of the turbine disk can be used as a performance parameter to be optimized, and the optimization aim is to minimize the mass of the turbine disk. It is known that the mass of a turbine disk has a functional relationship with all shape parameters of the turbine disk for a given material. In the optimization process of the turbine disk, stress needs to be considered, that is, the maximum equivalent stress of the turbine disk corresponding to the shape parameter of the turbine disk under a given working condition needs to be smaller than the maximum allowable equivalent stress, and in this embodiment, the maximum allowable equivalent stress is 930 Mpa. In this embodiment, the material of the turbine disk is selected from GH 4169.
In this embodiment, the mathematical model for optimizing the structure of the turbine disk may be established as follows:
minM(x)
find x＝(H2,R3,R4,W2,W3,W4)
where M (x) is the mass of the turbine disk, σeqmaxTo maximum equivalent stress, [ sigma ]eq]The maximum allowable equivalent stress.
The method for optimizing the engineering parameters by using the Bayesian optimization algorithm based on the adaptive jump weighted expected lifting criterion (ASWEI) to perform weight reduction optimization on the shape of the turbine disk and the method for optimizing the engineering parameters by using the Bayesian optimization algorithm based on the traditional expected lifting criterion (EI) to perform weight reduction optimization on the shape of the turbine disk are consistent in the whole steps, and the main difference is that the acquisition functions are different. The steps of the method for optimizing the engineering parameters by the Bayesian optimization algorithm based on the adaptive jump weighting expected lifting criterion (ASWEI) are introduced, and finally, the acquisition function in the method for optimizing the engineering parameters by the Bayesian optimization algorithm based on the traditional expected lifting criterion (EI) is introduced as a comparative example.
The method for optimizing the engineering parameters by using the Bayes optimization algorithm based on the adaptive jump weighted expected lifting criterion (ASWEI) comprises the following steps of:
s1: acquiring an initial engineering parameter sample set, generally acquiring the initial engineering parameter sample set by an optimized Latin hypercube test design method, and of course, acquiring the initial engineering parameter sample set by other methods; in this embodiment, the engineering parameter is an undetermined shape parameter, i.e., the hub thickness H2Outer radius of the spoke plate R3Inner radius of the spoke plate R4Width W of hub2Width W of outer side of web3Inner thickness W of the web4。
S2: acquiring a performance parameter corresponding to each engineering parameter sample in the initial engineering parameter sample set by using a functional relation between the engineering parameters and the performance parameters; in this embodiment, the performance parameter is turbine disk mass m (x);
s3: the sampling process implemented iteratively specifically includes:
s3.1: constructing a Gaussian process model based on all engineering parameters and corresponding performance parameters in the engineering parameter sample set to obtain a posterior mean value and a posterior variance;
s3.2: constructing an acquisition function, wherein the expression of the acquisition function is as follows:
wherein:
ytarget(k)＝ymin(k)-DIk；
yk-1＝yreal(k-1)+p；
in the above formula:
k is an iteration serial number of the sampling process, and the value range of k is a natural number which is more than or equal to 1;
wkthe self-adaptive weight coefficient is the self-adaptive weight coefficient in the k iteration;
sk(x) The posterior mean square error of the kth iteration is a value obtained by a Gaussian process model after the posterior mean square error is solved;
phi (x) is a distribution function of a standard normal distribution;
phi (x) is a density function of a standard normal distribution;
ytarget(k)the performance parameter self-adaptive target value is the performance parameter self-adaptive target value in the k iteration;
ymin(k)obtaining the optimal performance parameter value in the performance parameters based on all sampled engineering parameters before the kth iteration;
yk-1the nominal performance parameter value corresponding to the engineering parameter determined to be sampled in the k-1 iteration;
yreal(k-1)obtaining corresponding performance parameters based on the engineering parameters which are determined to be sampled during the (k-1) th iteration;
DIkthe expected optimal performance parameter promotion amount for the kth iteration is obtained;
p is an engineering constraint penalty value, when the engineering parameter determined to be sampled during the (k-1) th iteration does not satisfy the engineering constraint condition, p is a preset penalty value, in the embodiment, a large value of 100 is used, when the engineering parameter determined to be sampled during the (k-1) th iteration satisfies the engineering constraint condition, p is 0, and no engineering constraint condition is considered that all the engineering parameters determined to be sampled satisfy the engineering constraint condition; in the embodiment, the engineering constraint condition is the maximum equivalent stress sigma of the turbine disc corresponding to the shape parameter of the turbine disc under the given working conditioneqmaxLess than the maximum allowable equivalent stress [ sigma ]eq]；
a. b, c are preset values, and a < b, c > 0. In this example, a is 0.05, b is 2, and c is 10%;
s3.3: maximizing the collection function to determine the engineering parameters of the sampling;
s3.4: obtaining corresponding performance parameters based on the engineering parameters determined to be sampled;
s3.5: updating the engineering parameter sample set;
s3.6: terminating the iteration after the iteration termination condition is reached, and continuing the iteration after the iteration termination condition is not reached; wherein, the iteration termination condition may be that the iteration number reaches a preset value; or under the condition that the optimal performance parameter is known, the performance parameter corresponding to at least one sampling engineering parameter is close to the optimal performance parameter and is within a preset value range. In this embodiment, the iteration termination condition is that the number of iterations reaches 300.
In the comparative example, in step S3.2, the expression of the acquisition function is:
wherein, yminObtaining the optimal performance parameter value in the performance parameters based on all sampled engineering parameters before the iteration; phi (x) is a distribution function of a standard normal distribution; phi (x) is a density function of a standard normal distribution;
is the posterior mean value; sk(x) Is the posterior mean square error, which is the value after the posterior variance is squared.
To reduce the effect of randomness of the optimal latin hypercube approach, 5 sets of tests were performed on each of the examples and comparative examples. And (4) carrying out statistical comparison on the mass of the 5 groups of turbine disks obtained by optimization, the maximum equivalent stress and the iteration step number of the obtained optimal mass in a half-violin graph mode. The turbine disk quality optimization result is shown in fig. 2, the maximum equivalent stress optimization result is shown in fig. 3, and the number of iteration steps for obtaining the optimal quality is shown in fig. 4. Wherein EI-BO represents the data of comparative example, and ASWI-BO represents the data of example.
The semi-violin diagram is a combination of a violin diagram and a bee group diagram. The left side of the semi-violin graph is a bee group graph which shows the specific positions of data points, and the right side is a violin graph which shows the ranges of the mean value, median and standard deviation of 5 groups of test result data.
From fig. 2, it can be seen that the mass of the turbine disk obtained by the optimization of the embodiment is obviously smaller than that of the comparative example in terms of median or mean value. As can be seen from FIG. 3, the optimization of the embodiment significantly improves the maximum equivalent stress of the turbine disk under the allowable equivalent stress. As can be seen from fig. 4, the number of iterations for obtaining the optimum quality of the turbine disk in the example is slightly smaller than that in the comparative example.
Table 1 describes the results of engineering parameters, performance parameters before optimization, optimization by comparative examples and optimization by examples.
Table 1: optimal engineering parameters and optimal performance parameters before optimization, optimization by comparative examples, and optimization by examples
As can be seen from fig. 2 and table 1, the mass of the turbine disk obtained by the optimization of the example is obviously smaller than that of the comparative example in terms of median or mean value, the optimal mass of the turbine disk of the example is reduced by 20.73% compared with that before the optimization, and the optimal mass of the turbine disk of the comparative example is reduced by 19.05% compared with that before the optimization. As can be seen from FIG. 3 and Table 1, the optimization of the embodiment significantly improves the maximum equivalent stress of the turbine disk under the allowable equivalent stress, and better utilizes the maximum equivalent stress lifting space. As can be seen from fig. 4 and table 1, the number of iterations for obtaining the optimum quality of the turbine disk in the example is slightly smaller than that in the comparative example.
As can be seen from the comparison between the examples and the comparative examples, the main technical contribution of the optimization method of the present application is to define a new acquisition function, and the new acquisition function introduces the adaptive target value ytarget(k)Optimal solution item y replacing traditional expected lifting criterion in the prior artminWhile introducing an adaptive weight coefficient term wkThe conventional expected lifting criterion (EI) is evolved into an adaptive jump weighted expected lifting criterion (asweii). In brief, the ratio of the performance parameter lift to the expected lift in the last iteration (representing the target value y set before the previous iteration starts) is obtained according to the actual performance parameter value of the point added in the previous iteration cycletarget(k-1)The completion condition) and the value of the target value (or the expected lifting amount) and the weight coefficient which are required to be set by the iteration loop are determined by taking the value of the ratio as a judgment standard, then the weight ratio of the front item and the rear item of the collection function expression is controlled according to the set target value and the weight coefficient, and further the iteration is controlled adaptively to carry out local development adding point or global exploration adding point, and the relationship between the local development and the global exploration is balanced automatically. Thereby reducing excessive development to a certain extentAnd the occurrence of over-exploration, the optimization efficiency is accelerated, and the waste of computing resources is reduced. The method can be used in the field of structural optimization or pneumatic optimization of aerospace, and can achieve the purpose of reducing weight of a turbine disc by optimizing the structural parameters of the turbine disc of the aero-engine, so that the thrust-weight ratio, the stability, the reliability and the service life of the aero-engine are improved. Another technical contribution of the optimization method adopted in the embodiment is that a function of meeting the engineering constraint condition is realized in the optimization method, that is, an engineering constraint penalty value p is introduced, so that the performance parameter corresponding to the engineering parameter which is iteratively acquired last time can be punished when the engineering constraint condition is not met, and global exploration can be performed as soon as possible under the condition.
The description of the above specification and examples is intended to be illustrative of the scope of the present application and is not intended to be limiting.
Claims (8)
1. A method for optimizing engineering parameters by using a Bayesian optimization algorithm is used for optimizing performance parameters having functional relations with the engineering parameters under engineering constraint conditions, the Bayesian optimization algorithm is based on an expected lifting criterion and at least comprises an iteratively implemented sampling process, and the sampling process comprises a step of constructing a Gaussian process model based on all the engineering parameters and corresponding performance parameters in an engineering parameter sample set to obtain posterior mean and posterior variance, a step of constructing an acquisition function, a step of maximizing the acquisition function to determine the sampled engineering parameters, a step of obtaining corresponding performance parameters based on the engineering parameters determined to be sampled and a step of updating the engineering parameter sample set; characterized in that, in each sampling process, the acquisition function is structured as:
wherein:
ytarget(k)＝ymin(k)-DIk；
yk-1＝yreal(k-1)+p；
in the above formula:
k is an iteration serial number of the sampling process, and the value range of k is a natural number which is more than or equal to 1;
wkthe self-adaptive weight coefficient is the self-adaptive weight coefficient in the k iteration;
sk(x) The posterior mean square error of the kth iteration is a value obtained by a Gaussian process model after the posterior mean square error is solved;
phi (x) is a distribution function of a standard normal distribution;
phi (x) is a density function of a standard normal distribution;
ytarget(k)the performance parameter self-adaptive target value is the performance parameter self-adaptive target value in the k iteration;
ymin(k)obtaining the optimal performance parameter value in the performance parameters based on all sampled engineering parameters before the kth iteration;
yk-1the nominal performance parameter value corresponding to the engineering parameter determined to be sampled in the k-1 iteration;
yreal(k-1)obtaining corresponding performance parameters based on the engineering parameters which are determined to be sampled during the (k-1) th iteration;
DIkfor the k-th iterationExpecting an optimal performance parameter boost;
p is an engineering constraint penalty value, when the engineering parameters determined to be sampled during the (k-1) th iteration do not meet the engineering constraint conditions, p is a preset penalty value, when the engineering parameters determined to be sampled during the (k-1) th iteration meet the engineering constraint conditions, p is 0, and all the engineering parameters determined to be sampled without the engineering constraint conditions meet the engineering constraint conditions;
a. b, c are preset values, and a < b, c > 0.
2. The method as claimed in claim 1, wherein the bayesian optimization algorithm based on the expected lifting criterion further comprises, before the iteratively applied sampling process: the method comprises the steps of obtaining an initial engineering parameter sample set and obtaining performance parameters corresponding to each engineering parameter sample in the initial engineering parameter sample set.
3. The method of claim 2, wherein the initial engineering parameter sample set is obtained by an optimal Latin hypercube test design method.
4. A method for optimizing engineering parameters using bayesian optimization algorithms as recited in claim 3, wherein said iteratively applied sampling process terminates an iteration after an iteration termination condition is reached; after the iteration is terminated, the engineering parameter samples are concentrated, and the engineering parameters which meet the engineering constraint conditions and are optimal in performance parameters are the optimal engineering parameters.
5. The method of claim 4, wherein the iteration termination condition comprises a number of iterations reaching a predetermined value.
6. The method as claimed in claim 4, wherein the iteration termination condition includes that at least one sampled engineering parameter has been satisfied with the engineering parameter constraint condition and the corresponding performance parameter has been close to the optimal performance parameter within a preset range, when the optimal performance parameter is known.
7. A method for optimizing engineering parameters by using a Bayesian optimization algorithm as recited in any one of claims 1 to 6, wherein the engineering parameters are undetermined parameters in turbine disk shape parameters; the performance parameter is the mass of the turbine disc and the optimization direction is to minimize the mass of the turbine disc; the engineering constraint is that the maximum equivalent stress of the turbine disk, which is determined by the shape of the turbine disk, must be less than the maximum allowable equivalent stress based on the given operating conditions of the turbine disk.
8. A method for optimizing engineering parameters using a bayesian optimization algorithm as recited in claim 7, wherein said engineering parameters include hub width, hub thickness, web outer radius, web outer width, web inner radius, and web inner thickness when said turbine is rotationally symmetric about its axis of rotation.
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