CN114169100B - Efficient design optimization method and system for super-large variable impeller machinery and application - Google Patents
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Abstract
An ultra-large variable impeller machine efficient design optimization method, a system and application thereof are provided, and an ultra-large variable impeller machine parameterization method is provided; setting a CFD calculation model according to the design working condition of the optimal design; uniformly and initially adding points in a global range and calculating an evaluation value; establishing a high-dimensional PCE fitting model in the global; decomposing the high-dimensional problem into a plurality of low-dimensional sub-problems; performing independent agent model optimization on all the sub-problems, and adding the global PCE model into the HK model as a low-precision data source in the optimization process to realize knowledge migration; combining all sub-problem optimization results to obtain a group of global samples and evaluating the global samples; updating the global model and repeating the steps until the optimization stopping condition is met; the design method can increase the number of variables of the design on the premise of acceptable sample number so as to enlarge the degree of freedom of the design, and has strong parallel expansion capability, short design time and high calculation efficiency.
Description
Technical Field
The invention belongs to the field of impeller machinery optimization, and particularly relates to an ultra-large variable impeller machinery efficient design optimization method, a system and application.
Background
In recent years, in the field of impeller machines, automated optimization design methods are increasingly widely used. The automatic optimization design method needs to manually determine a design space which can be parameterized, and each sample in the space corresponds to a specific geometric design scheme. By taking the result of computer simulation calculation as an optimizing target, the impeller mechanical component with excellent performance can be automatically designed by means of a specific optimizing algorithm. The use of the automated design method can effectively reduce the requirement for experience of designers, and rapidly complete the design with high quality.
Optimization algorithms are often critical in determining the efficiency of automated optimization design methods. The agent model optimization method (SBO) represented by the efficient global optimization algorithm (EGO) has achieved remarkable results in the engineering field. The agent model optimization algorithm can well balance the relation between global search and local optimization, and has high optimization efficiency.
However, as engineering problems are studied deeply, the target problem is necessarily developed towards the direction of higher dimension of the design space, larger single-sample computing resource and more complex relation among design variables. The higher design space dimension enables the engineering design to have a larger degree of freedom, so that richer design possibilities can be explored; the larger computing resource requirement is the result of higher-precision computing simulation; and complex relationships between variables and results increase the necessity of automated design. For such a high-dimensional large-resource black box problem (or simply referred to as the HEB problem), the conventional agent model optimization algorithm with the application range below 15 dimensions is not in the spotlight. Inapplicability of the conventional proxy model optimization method is represented by: (1) An accurate high-dimensional proxy model cannot be built using limited samples. From the point of view of information acquisition, to build a proxy model of the same accuracy, the number of samples required increases exponentially as the problem dimension increases. However, in practical engineering optimization, the number of samples is limited by computational effort and time. (2) The premise of searching and adding new samples is the accuracy of the proxy model, and the subsequent adding points cannot be guided under the condition that the accuracy of the high-dimensional proxy model is low. (3) The time complexity of the proxy model building and optimization search increases dramatically with increasing number of samples and dimensions. (4) The gaussian kernel used by the Kriging model is based on the euler distance, but there are situations where the euler distance fails in high-dimensional space.
Disclosure of Invention
The invention aims to provide an efficient design optimization method, system and application of an oversized variable impeller machine, so as to solve the problems.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
an ultra-large variable impeller machine efficient design optimization method comprises the following steps:
and (3) establishing a design space: taking the impeller mechanical part as a design object to obtain adjustment parameters of the three-dimensional blade;
obtaining a plurality of sample coordinates with more uniform distribution in an established design space by using an LHS method, and performing performance evaluation on the sample coordinates to obtain the stage efficiency values of the plurality of design samples;
establishing a PCE fitting model by using the obtained sample coordinates and sample valuesAfter modeling, carrying out level efficiency evaluation on the coordinates of the model prediction optimal value, and adding the coordinates and the evaluation result into a data list;
selecting the value with the highest level efficiency in all samples as a core point, decomposing the high-dimensional global problem into r low-dimensional problems, and recording the determined decomposition parameters { x } * ,I}；
Operations are completed in parallel and synchronously for r low-dimensional problems: complete independent optimization search is completed in the sub-problem space by using a multi-fidelity agent model HK model and a maximum expected lifting point-adding criterion, and the optimization result is x best,j ；
Updating global PCE model using all evaluated samplesCalculation model->Is added to the data after the coordinate is evaluatedCentralizing;
the r sub-problem optimization results are arranged and combined, and N is screened out according to a global model combine Evaluating each sample; repeating the above until the algorithm meets the stop condition.
Furthermore, a design space is established, a plurality of sections are cut for the three-dimensional blade object to be used as the characteristic sections of the modeling, and a plurality of design parameters are selected to adjust the bending and twisting states of the three-dimensional blade during stacking.
Further, the high-dimensional global problem decomposition is specifically:
finding the sample with the smallest evaluation value in all the evaluated samples, and marking the sample as x * ；
Randomly determining subspace variable allocation method I, i= { I 1 ,I 2 ,I 3 ,...,I r Dividing the variables into
The coordinates in the subspace and the coordinates in the high-dimensional global space have the following one-to-one correspondence: let the partial sitting mark be x local Global sitting is marked x global Has x local ∈S j ，x global ∈S；
x global ＝[x 1 g ,x 2 g ,x 3 g ,...,x D g ]
Further, there are subspaces without regard to adjusting the boundaries of the subspacesThe variables corresponding to each subspace have the following relationship without considering subspace overlapping and pruning the variables:
further, operations are completed in parallel and synchronously for r low-dimensional problems:
in subspaceWherein Latin hypercube algorithm is used for initial dotting, and the number of the initial dotting is N l j,ini General N l j,ini ＝2||I j ||；
Establishing a multi-fidelity proxy model in a subspace, wherein a high-fidelity source is a sample adding point in the subspace, and a low-fidelity source is a part of the global model located in the subspace; the model is built as follows:
for already built modelsThe EI value of the system in the subspace range is calculated, the coordinate position with the largest EI value in the subspace range is obtained through searching, and point addition evaluation is carried out at the position;
repeating the above until the number of iterations reaches the maximum iteration number iter max ，iter max ＝8||I j ||；
And selecting a sample with the optimal sample value from the evaluated samples in all subspaces as an optimization result.
Further, the r sub-problem optimization results are arranged and combined:
obtain a composition comprising 2 r -potential combined sample set X of r-2 samples p combine And useGlobal modelObtaining predictive value of all potential combination samples +.>And the sum of Euclidean distances dist (X) of each potential combined sample and the existing sample p combine )；
Obtaining X by ascending order based on the predicted value sort predict The distance sum is used as the basis to obtain X by ascending order sort dist ；
Sequentially selecting N from two sequences combine Samples, typically N combine ＝||I j ||/2
The selected samples are evaluated.
Further, an ultra-large variable impeller machine efficient design optimization system comprises:
the design space building module is used for taking a standard die of the movable blade of the compressor as a design object to obtain adjustment parameters of the three-dimensional blade;
the stage efficiency value obtaining module is used for obtaining a plurality of sample coordinates with more uniform distribution in the established design space by using an LHS method, and performing performance evaluation on the sample coordinates to obtain stage efficiency values of the plurality of design samples;
a fitting model building module for building a PCE fitting model by using the obtained sample coordinates and sample valuesAfter modeling, carrying out level efficiency evaluation on the coordinates of the model prediction optimal value, and adding the coordinates and the evaluation result into a data list;
the decomposition module is used for selecting the value with the highest level efficiency in all samples as a core point, decomposing the high-dimensional global problem into r low-dimensional problems, and recording the determined decomposition parameters { x } * ,I}；
An optimized search module for synchronously and parallelly completing operations for r low-dimensional problems: using moreThe fidelity agent model HK model and the maximum expected lifting point-adding criterion complete one complete independent optimization search in the sub-problem space, and the optimized result is x best,j ；
A model updating module for updating the global PCE model by using all the evaluated samplesCalculation modelThe minimum predicted value coordinates of (2) are added into the data set after the coordinates are evaluated;
the evaluation module is used for arranging and combining the r sub-problem optimization results and screening N according to the global model combine Evaluating each sample; repeating the above until the algorithm meets the stop condition.
Furthermore, the application of the ultra-large variable impeller machine efficient design optimization system is used for efficient design of the impeller machine.
Compared with the prior art, the invention has the following technical effects:
the invention completes high-dimensional global optimization by means of a decomposition method and transfer learning: and establishing a global model by using a Polynomial Chaos Expansion (PCE) method and all samples, and decomposing the high-dimensional problem into a plurality of low-dimensional sub-problems, wherein migration information transmitted by the global model is utilized to perform acceleration optimization in each sub-problem, so that effective decomposition and degradation of the high-dimensional problem and efficient utilization of all evaluation sample information in the sub-problems are realized. The method has the advantages that the decomposition method is used for decomposing a high-dimensional optimal design problem into a plurality of low-dimensional sub-problems, and then the hierarchical kriging agent model (HK) based on transfer learning is used for optimizing the sub-problems, so that the dimension of the problem to be processed is reduced, the effective utilization rate of sample information is maintained, and the optimization efficiency is improved.
Drawings
Fig. 1 is a schematic diagram of an embodiment of the present invention.
Fig. 2 is a schematic diagram of a specific flow of subspace migration learning optimization according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, the embodiment provides an ultra-large variable impeller machine efficient design optimization method and is applied to the modeling optimization design of a compressor blade, and specifically includes the following steps:
1. creation of design space
The most widely used NASA ROTOR37 compressor blade standard mold was chosen as the design target for this embodiment and the blade was designed and tested by Reid and Moore from the NASA Glenn center. And 5 sections of the three-dimensional blade object are cut as modeling characteristic sections, and 5 control points are selected on the suction surface of each section to adjust the modeling of the suction surface curve. And 3 design parameters are selected to adjust the bending and sweeping state of the three-dimensional blade during stacking. As indicated above, the design space includes 28 design variables in total, which is significantly beyond the range of the number of design variables for a generic proxy model optimization design approach.
2. Building a performance assessment model
The stage efficiency of the compressor is selected as a target parameter of the optimization design, namely, a cascade geometric model with higher stage efficiency is designed. Commercial Computational Fluid Dynamics (CFD) software was used to evaluate the stage efficiency of the geometric design model, and other parameter settings during the calculation were consistent with the standard design conditions of the ROTOR37 blade.
3. Determining user-defined variables in an algorithm
In this embodiment, the global initial sample number is selected to be 50, and the distribution method is Latin hypercube design method (LHS); selecting the highest order of the chaos polynomial as 6; selecting the number of sub-optimal initial samples to be 2 times of the dimension of the corresponding subspace; selecting the maximum iteration number of sub-optimization to be 6 times of the dimension of the corresponding subspace; the maximum number of samples for the entire algorithm is determined to be 1000.
4. Specific process of optimizing design
Referring to fig. 1, the specific process is as follows:
and 4a, obtaining 50 sample coordinates with more uniform distribution in the established design space by using an LHS method, and performing performance evaluation on the 50 sample coordinates to obtain the level efficiency values of the 50 design samples.
And 4b, establishing a 28-dimensional PCE fitting model by using the sample coordinates and the sample values obtained in the step 4a, carrying out stage efficiency evaluation on the coordinates of the model prediction optimal value after modeling, and adding the coordinates and the evaluation result into a data list. (since the goal in the default optimization process is the minimum, the sample value is set to the stage efficiency multiplied by-1)
And 4c, selecting the value with the maximum stage efficiency in all samples as a core point, and randomly decomposing the 28-dimensional problem into 10 low-dimensional sub-problems (8 3-dimensional problems and 2-dimensional problems).
4d, synchronously and parallelly completing the operation on 10 low-dimensional problems, collecting 6 samples for 3-dimensional problems as initial samples, and then carrying out 18 times of iterative dotting; 4 samples are collected for the 2-dimensional problem as initial samples, and 12 iterations and points are added. The specific process of optimization within the subspace is with reference to fig. 2.
4e, adding the sample generated in subspace optimization and the evaluation value thereof into a data set, and reestablishing a global PCE model by using the data set;
and 4f, selecting 14 global samples for evaluation based on the 10 sub-optimization results and the updated global model by using a combined dotting method.
4g. Repeating steps 4 c-4 f until the total number of samples reaches the set number 1000.
5. Results of the optimization design
1000 samples are used in the optimization process, the final stage efficiency is 87.08%, and is improved by 1.62% compared with the stage efficiency 85.46% of the reference design, and the improvement is more remarkable.
The total number of samples used in each decomposition process and the optimization results are shown in table 1 below.
Table 1: optimizing result details
The principle of the invention is as follows:
the method has the greatest characteristic that an innovative optimization algorithm suitable for high dimensionality is used. The method is characterized in that the knowledge of the global model is migrated to the local model, and the process is realized through a layered Kriging model. The layered kriging model is an algorithm that combines two different precision data into one proxy model, commonly referred to as a high precision source and a low precision source, respectively. In the application of the invention, the high-precision source is a sample in the corresponding sub-problem, and the low-precision source is a global polynomial chaotic fitting model updated in the last round. The former can continuously add samples as sub-optimization proceeds, while the latter remains unchanged throughout the sub-optimization process.
The predictive value formula of the layered kriging model is as followsWherein f L (x) Is an independently determined global fitting model, y H -f L (X H ) And making a difference between the actual evaluation value of the model in the subspace and the global fitting model prediction value. When the model f has been determined L (x) When the trend of the model is consistent with the trend of the optimization object in the actual subspace, a proxy model with higher accuracy can be established and optimization is guided by only a small number of samples in the subspace, so that the optimization process is greatly accelerated.
The invention sets up the impeller machinery parameterization method of the ultra-large variable; setting a CFD calculation model according to the design working condition of the optimal design; uniformly and initially adding points in a global range and calculating an evaluation value; establishing a high-dimensional PCE fitting model in the global; decomposing the high-dimensional problem into a plurality of low-dimensional sub-problems; performing independent agent model optimization on all the sub-problems, and adding the global PCE model into the HK model as a low-precision data source in the optimization process to realize knowledge migration; combining all sub-problem optimization results to obtain a group of global samples and evaluating the global samples; updating the global model and repeating the steps until the optimization stopping condition is met; the design method can increase the number of variables of the design on the premise of acceptable sample number so as to enlarge the degree of freedom of the design, and has strong parallel expansion capability, short design time and high calculation efficiency.
Claims (5)
1. The efficient design optimization method for the oversized variable impeller machine is characterized by comprising the following steps of:
and (3) establishing a design space: taking a standard die of the movable blade of the compressor as a design object to obtain adjustment parameters of the three-dimensional blade;
obtaining a plurality of sample coordinates with more uniform distribution in an established design space by using an LHS method, and performing performance evaluation on the sample coordinates to obtain the stage efficiency values of the plurality of design samples;
establishing a PCE fitting model by using the obtained sample coordinates and sample valuesAfter modeling, carrying out level efficiency evaluation on the coordinates of the model prediction optimal value, and adding the coordinates and the evaluation result into a data list;
selecting the value with the highest level efficiency in all samples as a core point, decomposing the high-dimensional global problem into r low-dimensional problems, and recording the determined decomposition parameters { x } * ,I}；
Operations are completed in parallel and synchronously for r low-dimensional problems: complete independent optimization search is completed in the sub-problem space by using a multi-fidelity agent model HK model and a maximum expected lifting point-adding criterion, and the optimization result is x best,j ；
Updating global PCE model using all evaluated samplesCalculation model->The minimum predicted value coordinates of (2) are added into the data set after the coordinates are evaluated;
the r sub-problem optimization results are arranged and combined according to a global modelScreening N combine Evaluating each sample; repeating the above until the algorithm meets the stop condition;
the high-dimensional global problem decomposition is specifically as follows:
finding the sample with the smallest evaluation value in all the evaluated samples, and marking the sample as x * ；
Randomly determining subspace variable allocation method I, i= { I 1 ,I 2 ,I 3 ,...,I r Dividing the variables into
The coordinates in the subspace and the coordinates in the high-dimensional global space have the following one-to-one correspondence: let the partial sitting mark be x local Global sitting is marked x global Has x local ∈S j ，x global ∈S；
x global ＝[x 1 g ,x 2 g ,x 3 g ,...,x D g ]
Without taking into account the adjustment of the boundaries of the subspaces, there are subspacesThe variables corresponding to each subspace have the following relationship without considering subspace overlapping and pruning the variables:
operations are completed in parallel and synchronously for r low-dimensional problems:
in subspaceWherein Latin hypercube algorithm is used for initial dotting, and the number of the initial dotting is N l j,ini General N l j,ini ＝2||I j ||；
Establishing a multi-fidelity proxy model in a subspace, wherein a high-fidelity source is a sample adding point in the subspace, and a low-fidelity source is a part of the global model located in the subspace; the model is built as follows:
for already built modelsThe EI value of the system in the subspace range is calculated, the coordinate position with the largest EI value in the subspace range is obtained through searching, and point addition evaluation is carried out at the position;
repeating the above until the number of iterations reaches the maximum iteration number iter max General iter max ＝8||I j ||；
And selecting a sample with the optimal sample value from the evaluated samples in the subspace as an optimization result.
2. The method for efficiently designing and optimizing the ultra-large variable impeller machinery according to claim 1, wherein a design space is established, a plurality of sections of a three-dimensional blade object are taken as characteristic sections of a model, and a plurality of design parameters are selected to adjust the bending and twisting states of the three-dimensional blade during stacking.
3. The method for efficiently designing and optimizing the ultra-large variable impeller machine according to claim 1, wherein the r sub-problem optimization results are arranged and combined:
obtain a composition comprising 2 r -potential combined sample set X of r-2 samples p combine And uses a global modelObtaining predictive value of all potential combination samples +.>And the sum of Euclidean distances dist (X) of each potential combined sample and the existing sample p combine )；
Obtaining X by ascending order based on the predicted value sort predict The distance sum is used as the basis to obtain X by ascending order sort dist ；
Sequentially selecting N from two sequences combine Samples, typically N combine ＝||I j ||/2
The selected samples are evaluated.
4. An ultra-large variable impeller machine efficient design optimization system, comprising:
the design space building module is used for taking the impeller mechanical part as a design object to obtain adjustment parameters of the three-dimensional blade;
the stage efficiency value obtaining module is used for obtaining a plurality of sample coordinates with more uniform distribution in the established design space by using an LHS method, and performing performance evaluation on the sample coordinates to obtain stage efficiency values of the plurality of design samples;
a fitting model building module for building a PCE fitting model by using the obtained sample coordinates and sample valuesAfter modeling, carrying out level efficiency evaluation on the coordinates of the model prediction optimal value, and adding the coordinates and the evaluation result into a data list;
the decomposition module is used for selecting the value with the highest level efficiency in all samples as a core point, decomposing the high-dimensional global problem into r low-dimensional problems, and recording the determined decomposition parameters { x } * ,I}；
An optimized search module for synchronously and parallelly completing operations for r low-dimensional problems: complete independent optimization search is completed in the sub-problem space by using a multi-fidelity agent model HK model and a maximum expected lifting point-adding criterion, and the optimization result is x best,j ；
A model updating module for updating the global PCE model by using all the evaluated samplesCalculation model->The minimum predicted value coordinates of (2) are added into the data set after the coordinates are evaluated;
the evaluation module is used for arranging and combining the r sub-problem optimization results and screening N according to the global model combine Evaluating each sample; repeating the above until the algorithm meets the stop condition;
the high-dimensional global problem decomposition is specifically as follows:
finding the sample with the smallest evaluation value in all the evaluated samples, and marking the sample as x * ；
Randomly determining subspace variable allocation method I, i= { I 1 ,I 2 ,I 3 ,...,I r Dividing the variables into
The coordinates in the subspace and the coordinates in the high-dimensional global space have the following one-to-one correspondence: let the partial sitting mark be x local Global sitting is marked x global Has x local ∈S j ，x global ∈S；
x global ＝[x 1 g ,x 2 g ,x 3 g ,...,x D g ]
Without taking into account the adjustment of the boundaries of the subspaces, there are subspacesThe variables corresponding to each subspace have the following relationship without considering subspace overlapping and pruning the variables:
operations are completed in parallel and synchronously for r low-dimensional problems:
in subspaceWherein Latin hypercube algorithm is used for initial dotting, and the number of the initial dotting is N l j,ini General N l j,ini ＝2||I j ||；
Establishing a multi-fidelity proxy model in a subspace, wherein a high-fidelity source is a sample adding point in the subspace, and a low-fidelity source is a part of the global model located in the subspace; the model is built as follows:
for already built modelsThe EI value of the system in the subspace range is calculated, the coordinate position with the largest EI value in the subspace range is obtained through searching, and point addition evaluation is carried out at the position;
repeating the above until the number of iterations reaches the maximum iteration number iter max General iter max ＝8||I j ||；
And selecting a sample with the optimal sample value from the evaluated samples in the subspace as an optimization result.
5. The use of an oversized variable impeller machine efficient design optimization system of claim 4 for an impeller machine efficient design.
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