Method for optimizing engineering parameters by adopting constrained Bayesian optimization algorithm with variable expectation penalty

Abstract

The invention discloses a method for optimizing engineering parameters by adopting a constrained Bayesian optimization algorithm with variable expectation penalty, which comprises the following steps of: in each iteration, constructing a Gaussian process model based on all engineering parameters in an engineering parameter sample set and corresponding constraint performance parameters to obtain a posteriori mean value and a posteriori variance; the acquired data are regarded as a predicted value and a predicted error, a penalty consideration value is obtained according to the predicted value and the predicted error, and then the penalty consideration value is compared with a penalty judgment threshold value, so that whether the acquisition function is penalized or not in the iteration is judged; the constraint performance parameter corresponding to the engineering parameter to be sampled in the iteration is prevented from violating the performance parameter constraint condition, and the optimization method is prevented from further exploring the infeasible region, so that the optimization capability of the optimization method is improved.

Description

Technical Field

[0001] The invention relates to the field of engineering design, and in particular to a method for optimizing engineering parameters by using a constrained Bayesian optimization algorithm with variable expectation penalty. Background Art

[0002] In engineering design, after setting the engineering parameters, the performance parameters with a functional relationship with the engineering parameters can be obtained. The same engineering parameters can obtain different performance parameters according to different functional relationships. Engineering optimization generally refers to selecting a performance parameter as the target performance parameter (the functional relationship between the engineering parameter and the target performance parameter is the objective function). After setting the engineering constraints, find the engineering parameters that meet the engineering constraints and have the best target performance parameters. This engineering parameter is the optimal engineering parameter corresponding to the target performance parameter.

[0003] Engineering constraints generally include engineering parameter constraints and performance parameter constraints, wherein performance parameter constraints refer to constraints on performance parameters of certain non-target performance parameters, which are referred to as constrained performance parameters in this article.

[0004] Due to the low cost of solving the Bayesian optimization algorithm, it has been widely used to obtain the optimal engineering parameters. The acquisition function is the core component of Bayesian optimization. It is constructed according to the posterior probability distribution and selects the next most "potential" evaluation point by maximizing the acquisition function. Generally speaking, the selection of new sample points basically follows the two basic strategies of "global exploration" and "local development". The goal of global exploration is to explore locations with large prediction errors to ensure the global accuracy of the proxy model in the entire design space. The other is local development, which aims to ensure that the currently known most "attractive" area has sufficiently high local accuracy by developing the area near the current optimal point.

[0005] However, since the constraint performance parameters and the target performance parameters are both dependent variables of engineering parameters, the traditional Bayesian optimization algorithm may cause the problem of infeasible regions in the design space when dealing with optimization problems under some engineering constraints, including engineering parameter constraints and performance parameter constraints. This problem refers to the situation where the constraint performance parameters corresponding to the engineering parameters do not meet the performance parameter constraints.

[0006] To this end, the acquisition function in the Bayesian optimization algorithm is adjusted in the prior art, and the penalty value p is introduced so that the constraint performance parameters corresponding to the engineering parameters collected in the last iteration can be penalized when they do not meet the performance parameter constraint conditions, which avoids the problem of infeasible domains in the design space to a certain extent. (See: Yan C, Du H, Kang E, et al. AVEI-BO: an efficient Bayesian optimization using adaptively varied expected improvement [J]. Structural and Multidisciplinary Optimization, 2022, 65 (6): 164.)

[0007] However, there is still some room for improvement in the prior art. Summary of the invention

[0008] The purpose of the present invention is to overcome the above-mentioned defects or problems existing in the background technology and provide a method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty, which is helpful to avoid the problem of infeasible domain appearing in the design space.

[0009] To achieve the above object, the present invention adopts the following technical solution:

[0010] The first technical solution relates to a method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with a variable expectation penalty, which is used to optimize target performance parameters having a functional relationship with engineering parameters under engineering constraints, and at least includes an iterative sampling process, wherein the sampling process includes the steps of constructing a Gaussian process model based on all engineering parameters in an engineering parameter sample set and corresponding target performance parameters to obtain a posterior mean and a posterior variance, constructing an acquisition function, maximizing the acquisition function to determine the sampled engineering parameters, obtaining the corresponding target performance parameters based on the determined sampled engineering parameters, and updating the engineering parameter sample set; wherein the engineering constraints include engineering parameter constraints that constrain engineering parameters and performance parameter constraints that constrain constrained performance parameters, and each sampling process also includes the steps of constructing a Gaussian process model based on all engineering parameters in the engineering parameter sample set and corresponding constrained performance parameters to obtain a posterior mean and a posterior variance, and obtaining the corresponding constrained performance parameters based on the determined sampled engineering parameters, and the acquisition function is constructed as follows:

[0011]

[0012] in:

[0013] y target(k) =ymin(k) -DI k

[0014]

[0015]

[0016] In the above formula:

[0017] k is the iteration number, and its value range is a natural number greater than or equal to 1;

[0018] w k is the adaptive weight coefficient at the kth iteration;

[0019] y target(k) is the adaptive target value of the performance parameter at the kth iteration;

[0020] is the posterior mean obtained by the Gaussian process model corresponding to the target performance parameter at the kth iteration;

[0021] s k (x) is the posterior mean square error at the kth iteration, which is the square root of the posterior variance obtained by the Gaussian process model corresponding to the target performance parameter;

[0022] Φ() is the distribution function of the standard normal distribution;

[0023] φ() is the density function of the standard normal distribution;

[0024] y min(k) is the optimal performance parameter value among the performance parameters obtained based on all sampled engineering parameters before the kth iteration;

[0025] y real(k-1) Obtaining corresponding performance parameters based on the determined sampling engineering parameters at the k-1th iteration;

[0026] C is the penalty value;

[0027] K is the number of constraint performance parameters;

[0028] P wevki is the penalty consideration value corresponding to the i-th constraint performance parameter in the k-th iteration;

[0029] t wevi is the penalty judgment threshold corresponding to the i-th constraint performance parameter, which can be set manually;

[0030] μ wevki (x) is the predicted value corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior mean obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration;

[0031] σ wevki (x) is the prediction error corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior variance obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration;

[0032] a, b, c are artificially set values, and a<b,c> 0.

[0033] The second technical solution is based on the first technical solution, wherein the penalty judgment threshold t corresponding to each constraint performance parameter wevi same.

[0034] The third technical solution is based on the second technical solution, wherein the penalty judgment threshold t corresponding to each constraint performance parameter wevi The value is 0.01.

[0035] The fourth technical solution is based on the first technical solution, and is characterized in that the value of a is 0.05, the value of b is 2, and the value of c is 10%.

[0036] The fifth technical solution is based on the first technical solution, wherein before the iterative sampling process, it also includes: a step of obtaining an initial engineering parameter sample set.

[0037] The sixth technical solution is based on the fifth technical solution, wherein the iterative sampling process terminates the iteration after reaching the iteration termination condition; after the iteration is terminated, among the engineering parameter samples, the engineering parameters that meet the engineering constraints and have the best target performance parameters are the optimal engineering parameters.

[0038] The seventh technical solution is based on the sixth technical solution, wherein the iteration termination condition includes the number of iterations reaching a preset value.

[0039] From the above description of the present invention, it can be seen that compared with the prior art, the present invention has the following beneficial effects:

[0040] The optimization method of the present application is based on AVEI-BO. In each iteration, a Gaussian process model is constructed based on all engineering parameters in the engineering parameter sample set and the corresponding constraint performance parameters to obtain the posterior mean and posterior variance, and then they are regarded as the predicted value and prediction error respectively, and a penalty consideration value is obtained accordingly. The penalty consideration value is then compared with the penalty judgment threshold to determine whether the acquisition function is penalized in this iteration, which is conducive to preventing the optimization method from further exploring infeasible areas. The infeasible area refers to the area where the constraint performance parameters corresponding to the engineering parameters do not meet the performance parameter constraints, thereby improving the optimization ability of the optimization method of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 This is one of the schematic cross-sectional views of the root of a turbine rotor blade in this embodiment.

[0043] Figure 2 This is the second schematic cross-sectional view of the root of the turbine rotor blade in this embodiment.

[0044] Figure 3 It is a schematic diagram of the mid-section of the turbine rotor blade in this embodiment.

[0045] Figure 4 Schematic diagram of the cross-section of the tip of the turbine rotor blade in this embodiment.

[0046] Figure 5 Schematic diagram of the optimized turbine rotor blades in this embodiment. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are preferred embodiments of the present invention and should not be regarded as excluding other embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] In the claims, description and the above-mentioned drawings of the present invention, unless otherwise clearly defined, the use of terms such as "first", "second" or "third" etc. are for distinguishing different objects rather than for describing a specific order.

[0049] In the claims, specification and the above-mentioned drawings of the present invention, unless otherwise explicitly defined, directional words, such as the terms "center", "lateral", "longitudinal", "horizontal", "vertical", "top", "bottom", "inside", "outside", "up", "down", "front", "back", "left", "right", "clockwise", "counterclockwise", etc., indicating directions or positional relationships are based on the directions and positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction or be constructed and operated in a specific direction, and therefore cannot be understood as limiting the specific protection scope of the present invention.

[0050] In the claims, specification and the above drawings of the present invention, unless otherwise clearly defined, if the term "fixed connection" or "fixed connection" is used, it should be understood in a broad sense, that is, any connection method without a displacement relationship and relative rotation relationship between the two, that is to say, including non-detachable fixed connection, detachable fixed connection, integrated connection and fixed connection through other devices or elements.

[0051] In the claims, description and drawings of the present invention, if the terms "include", "have" and their variations are used, they are intended to mean "including but not limited to".

[0052] This embodiment provides a method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty, which is used to optimize target performance parameters that have a functional relationship with engineering parameters under engineering constraints. In this embodiment, the optimization method is applied to the design optimization of turbine rotor blade shape.

[0053] During the operation of an aircraft engine, the staggered operation of the turbine rotors will cause periodic changes in the aerodynamic force on the surface of the downstream turbine rotor blades, which will affect the vibration response of the turbine rotor blades under aerodynamic force to a certain extent. Since the magnitude of the vibration response of the turbine rotor blades is related to whether the engine can operate reliably, it is necessary to optimize it to reduce the vibration response. Generally speaking, the aerodynamic force on the surface of the turbine rotor blades can be directly reduced to indirectly reduce the vibration response, but this indirect optimization idea may not be able to find the blade shape corresponding to the minimum vibration response. Therefore, it is necessary to directly optimize the vibration response of the turbine rotor blade surface.

[0054] In order to minimize the vibration response of the turbine rotor blades under aerodynamic forces and thus improve the reliability of the engine, the maximum surface displacement S of the turbine rotor blades under aerodynamic forces is selected as the target performance parameter. The maximum surface displacement S refers to the displacement corresponding to the node on the surface of the turbine rotor blade where the largest displacement occurs, and the unit is millimeter. After the initial parametric modeling of the turbine rotor blades, there are 33 parameters controlling the blade shape. 10 design variables are selected as engineering parameters, and the remaining design variables remain unchanged. During the optimization process, these 10 engineering parameters are directly adjusted to obtain the corresponding turbine rotor blade shape. In order to avoid performance degradation after the shape of the turbine rotor blades is changed, it is necessary to minimize the total pressure ratio π and flow rate. The change range of the compressor total pressure ratio π and flow rate As a constraint performance parameter. The total pressure ratio π refers to the total pressure ratio of the turbine inlet and outlet, which is the inlet total pressure divided by the outlet total pressure. It refers to the mass of fluid passing through the turbine inlet section per unit time, measured in kg / s.

[0055] The specific optimization mathematical model can be expressed as follows:

[0056] Min:S

[0057] Find

[0058] x=(S1 CAMBER_BETA1 , S1 PS_REAR_SHAPE , S1 SS_REAR_SHAPE , S2 PS_REAR_SHAPE , S2 SS_REAR_SHAPE , S2 TPS_2 , S2 TSS_2 , S2 TSS_3 , S3 TSS_2 , S3 TSS_3 )

[0059]

[0060] Among them, π * To optimize the compressor total pressure ratio of the original turbine rotor blades, The flow rate of the original turbine rotor blades before optimization;

[0061] S1 CAMBER_BETA1 , S1 PS_REAR_SHAPE , S1 SS_REAR_SHAPE , S2 PS_REAR_SHAPE , S2 SS_REAR_SHAPE , S2 TPS_2 , S2 TSS_2 , S2 TSS_3 , S3 TSS_2 , S3 TSS_3 are engineering parameters, total pressure ratio π and flow rate is the constraint performance parameter, and the maximum surface displacement S is the target performance parameter. Figure 1-4 As shown ( Figure 1-4 represents a schematic diagram of the blade profile and its parameters, which does not correspond to the blade profile before or after optimization in this embodiment), S1 CAMBER_BETA1 S1 is the geometric inlet angle of the arc line in the blade root section, in degrees. PS_REAR_SHAPE is the pressure edge offset of the blade root section, S1 SS_REAR_SHAPE is the suction edge offset of the blade root section, S2 PS_REAR_SHAPE is the pressure edge offset of the blade midsection, S2 SS_REAR_SHAPE is the suction edge offset of the blade midsection, S2 TPS_2 S2 is the offset of control point 2 of the leaf midsection fitting curve. TSS_2 S2 is the offset of control point 2 of the leaf midsection fitting curve. TSS_3 Offset of control point 3 of the leaf midsection fitting curve, S3 TSS_2 Offset of control point 2 for the blade tip section fitting curve, S3 TSS_3 Offset control point 3 of the blade tip section fitting curve.

[0062] The specific process of optimization is as follows:

[0063] Step 1: Obtain an initial engineering parameter sample set, which can be obtained by optimizing the Latin hypercube experimental design method or the like. In this embodiment, the "lhsdesign" program provided by MATLAB R2020a is used, and the "maximin" criterion is selected to generate 40 initial sample points.

[0064] Step 2: Using the corresponding functional relationship between engineering parameters and target performance parameters and constraint performance parameters, obtain the target performance parameters and constraint performance parameters corresponding to each engineering parameter sample in the initial engineering parameter sample set.

[0065] Step 3: Iterate the sampling process. Hereinafter, k is the iteration number, and its value range is a natural number greater than or equal to 1. Specifically, it includes:

[0066] Step 3.1: Construct a Gaussian process model based on all engineering parameters and corresponding target performance parameters in the engineering parameter sample set and obtain the posterior mean and posterior variance;

[0067] Step 3.2: After constructing a Gaussian process model based on all engineering parameters and corresponding constraint performance parameters in the engineering parameter sample set, obtain the posterior mean and posterior variance of the Gaussian process model corresponding to each constraint performance parameter;

[0068] Step 3.3: Construct the acquisition function. The expression of the acquisition function is:

[0069]

[0070] in:

[0071] y target(k) =y min(k) -DI k

[0072]

[0073] In the above formula:

[0074] w k is the adaptive weight coefficient at the kth iteration;

[0075] y target(k) is the adaptive target value of the performance parameter at the kth iteration;

[0076] is the posterior mean obtained by the Gaussian process model corresponding to the target performance parameter at the kth iteration;

[0077] s k(x) is the posterior mean square error at the kth iteration, which is the square root of the posterior variance obtained by the Gaussian process model corresponding to the target performance parameter;

[0078] Φ() is the distribution function of the standard normal distribution;

[0079] φ() is the density function of the standard normal distribution;

[0080] y min(k) is the optimal performance parameter value among the performance parameters obtained based on all sampled engineering parameters before the kth iteration;

[0081] y real(k-1) Obtaining corresponding performance parameters based on the determined sampling engineering parameters at the k-1th iteration;

[0082] C is the penalty value;

[0083] K is the number of constraint performance parameters; in this embodiment, the value of K is 2.

[0084] t wevi is the penalty judgment threshold corresponding to the i-th constraint performance parameter, which can be set manually; in this embodiment, the penalty judgment threshold t corresponding to each constraint performance parameter wevi Same, t wevi =0.01,i=1,2,3…K.

[0085] P wevki is the penalty consideration value corresponding to the i-th constraint performance parameter in the k-th iteration. If P wevki Greater than or equal to the corresponding t wevi , then it is judged that the constraint performance parameter corresponding to the sample point to be sampled in this iteration does not violate the performance parameter constraint condition, otherwise it is judged that it violates the performance parameter constraint condition;

[0086] μ wevki (x) is the predicted value corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior mean obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration;

[0087] σ wevki (x) is the prediction error corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior variance obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration;

[0088] a, b, c are artificially set values, and a<b,c> 0, in this embodiment, the value of a is 0.05, the value of b is 2, and the value of c is 10%.

[0089] Step 3.4: Maximize the acquisition function to determine the engineering parameters of sampling;

[0090] Step 3.5: Obtain the corresponding target performance parameters and constraint performance parameters based on the engineering parameters to be sampled;

[0091] Step 3.6: Update the engineering parameter sample set;

[0092] Step 3.7: The iteration is terminated after the iteration termination condition is reached. If the iteration termination condition is not reached, the iteration is continued. The iteration termination condition is that the number of iterations reaches a preset value. In this embodiment, the iteration termination condition is that the number of iterations reaches 200.

[0093] After the iteration is terminated, the engineering parameters in the engineering parameter sample set that meet the engineering constraints and have the best target performance parameters are the optimal engineering parameters.

[0094] The optimization results are shown in the following table:

[0095]

[0096]

[0097] In the above table, Comparative Example 1 is the result of optimization using AVEI-BO in the background technology under the same conditions. Compared with Comparative Example 1, it can be found that the optimization method of this embodiment obtains a smaller surface maximum displacement S within the same number of iterative convergence steps, and the optimization effect is improved by 5.67%.

[0098] In each iteration of the optimization method of this embodiment, after constructing a Gaussian process model based on all engineering parameters and corresponding constraint performance parameters in the engineering parameter sample set to obtain the posterior mean and posterior variance, they are respectively regarded as the predicted value and prediction error and a penalty consideration value is obtained accordingly. The penalty consideration value is then compared with the penalty judgment threshold to determine whether to penalize the acquisition function in this iteration, which is conducive to preventing the optimization method from further exploring infeasible areas. The infeasible area refers to the area where the constraint performance parameters corresponding to the engineering parameters do not meet the performance parameter constraints, thereby improving the optimization capability of the optimization method of this application.

[0099] The description of the above specification and embodiments is used to explain the protection scope of the present invention, but does not constitute a limitation on the protection scope of the present invention. Through the enlightenment of the present invention or the above embodiments, ordinary technicians in this field can obtain modifications, equivalent substitutions or other improvements to the embodiments of the present invention or part of the technical features thereof through logical analysis, reasoning or limited experiments, which should be included in the protection scope of the present invention.

Claims

1. A method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with a variable expectation penalty, which is used to optimize target performance parameters having a functional relationship with engineering parameters under engineering constraints, and which at least includes an iterative sampling process, wherein the sampling process includes the steps of constructing a Gaussian process model based on all engineering parameters and corresponding target performance parameters in an engineering parameter sample set to obtain a posterior mean and a posterior variance, constructing an acquisition function, maximizing the acquisition function to determine the sampled engineering parameters, obtaining corresponding target performance parameters based on the determined sampled engineering parameters, and updating the engineering parameter sample set; characterized in that, The engineering constraint conditions include engineering parameter constraint conditions constraining engineering parameters and performance parameter constraint conditions constraining constrained performance parameters. In each sampling process, the steps of constructing a Gaussian process model based on all engineering parameters and corresponding constrained performance parameters in the engineering parameter sample set to obtain a posterior mean and a posterior variance and a step of obtaining corresponding constrained performance parameters based on the engineering parameters to be sampled are also included. The acquisition function is constructed as follows: in: yes target(k) =y min(k) -IN k In the above formula: k is the iteration number, and its value range is a natural number greater than or equal to 1; w k is the adaptive weight coefficient at the kth iteration; y target(k) is the adaptive target value of the performance parameter at the kth iteration; is the posterior mean obtained by the Gaussian process model corresponding to the target performance parameter at the kth iteration; s k (x) is the posterior mean square error at the kth iteration, which is the square root of the posterior variance obtained by the Gaussian process model corresponding to the target performance parameter; Φ() is the distribution function of the standard normal distribution; φ() is the density function of the standard normal distribution; y min(k) is the optimal performance parameter value among the performance parameters obtained based on all sampled engineering parameters before the kth iteration; y real(k-1) Obtaining corresponding performance parameters based on the determined sampling engineering parameters at the k-1th iteration; C is the penalty value; K is the number of constraint performance parameters; P wevki is the penalty consideration value corresponding to the i-th constraint performance parameter in the k-th iteration; t wevi is the penalty judgment threshold corresponding to the i-th constraint performance parameter, which can be set manually; μ wevki (x) is the predicted value corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior mean obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration; σ wevki (x) is the prediction error corresponding to the i-th constraint performance parameter in the k-th iteration, which is the posterior variance obtained by the Gaussian process model corresponding to the i-th constraint performance parameter and all engineering parameters in the k-th iteration; a, b, c are artificially set values, and a<b,c> 0.

2. The method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 1, characterized in that: The penalty judgment threshold t corresponding to each constraint performance parameter wevi same.

3. The method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 2, characterized in that: The penalty judgment threshold t corresponding to each constraint performance parameter wevi The value is 0.

01.

4. The method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 1, characterized in that: The value of a is 0.05, the value of b is 2, and the value of c is 10%.

5. The method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 1, characterized in that: Before the iterative sampling process, the step of obtaining an initial engineering parameter sample set is also included.

6. The method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 5, characterized in that: The sampling process of the iterative implementation terminates the iteration after reaching the iteration termination condition; after the iteration is terminated, in the engineering parameter sample set, the engineering parameter that meets the engineering constraint condition and has the best target performance parameter is the optimal engineering parameter.

7. A method for optimizing engineering parameters using a constrained Bayesian optimization algorithm with variable expectation penalty as claimed in claim 6, It is characterized in that The iteration termination condition includes the number of iterations reaching a preset value.

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