A method for optimizing model coefficients of one-dimensional calculation program for multi-stage axial flow compressor based on ensemble Kalman filter algorithm

Abstract

The present invention discloses a method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm, which is applied to the field of aerodynamic design of multi-stage axial flow compressors. The method comprises: obtaining the flow field parameters of each stage of the multi-stage axial flow compressor based on three-dimensional numerical calculation; sampling the model coefficients of the one-dimensional calculation program for each stage in the multi-stage axial flow compressor based on a Latin hypercube sampling method, and starting from the first stage, performing one-dimensional calculations step by step based on the determined model coefficients and the coefficient sampling results of each stage, calculating the Kalman gain of each stage, and correcting the one-dimensional calculation results using the flow field parameters of the corresponding stage until the mean difference between the one-dimensional calculation results before and after the correction is less than a preset threshold value, and using the model coefficients in the corrected one-dimensional calculation results as the one-dimensional calculation program model coefficients of the current stage. The present invention effectively improves the calculation accuracy of the one-dimensional calculation program and is of great significance for the design and application of compressors.

Description

Technical Field

[0001] The present invention relates to the field of aerodynamic design of multi-stage axial flow compressors, and in particular to a method for optimizing model coefficients of a one-dimensional calculation program of a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm. Background Art

[0002] Since the concept of multi-stage axial flow compressors was proposed, researchers have conducted research on axial flow compressors and their design methods. Compressor aerodynamic design technology has a long history. In the early 20th century, compressor aerodynamic design was mainly based on one-dimensional flow. In the 1950s, the flow calculation program developed based on the two types of flow surface theory (S1 and S2 flow surfaces) was widely used in compressor aerodynamic design. Later, by introducing empirical models based on a large amount of test data statistics, the design level of the S1 and S2 flow surface programs was further improved. In recent decades, compressor design methods have developed from quasi-three-dimensional design theory to full three-dimensional flow field optimization design. The current mature design methods are generally: first perform one-dimensional program calculations, then perform flow design program calculations and blade shaping calculations, flow S2 direct problem analysis, quasi-three-dimensional and full three-dimensional CFD calculation analysis.

[0003] As the foundation of compressor design, the reliability of one-dimensional calculations directly impacts subsequent compressor design work, making it difficult to correct problems in the one-dimensional design during subsequent design steps. Currently used one-dimensional calculation programs are older, and the models they use are based on compressor test data from that era. This has limitations for current high-efficiency, high-load compressor design calculations. Re-initiating experimental research on a large number of compressors and revising the models in the one-dimensional programs would clearly be prohibitively expensive.

[0004] Multi-stage compressor design methods based on full 3D simulation technology have significantly improved compressor aerodynamic design and have been widely used in recent years. However, within the flow environment of a multi-stage compressor, fluid mechanics issues dominated by viscosity and separation limit simulation accuracy. Due to the limitations of turbulence models and conservation equations at the static-dynamic interface, computational errors can be amplified nonlinearly at each stage during 3D simulation of a multi-stage compressor. This limits the application of full 3D design in the design of multi-stage compressors, especially high-load multi-stage compressors.

[0005] To this end, how to provide a multi-stage axial flow compressor one-dimensional calculation program model coefficient optimization method based on the ensemble Kalman filter algorithm that can effectively improve the calculation accuracy of the one-dimensional calculation program at a relatively low cost and solve the limitations in the subsequent high-efficiency and high-load multi-stage compressor design application is an issue that technical personnel in this field urgently need to solve. Summary of the Invention

[0006] In view of this, the present invention proposes a method for optimizing the model coefficients of a one-dimensional calculation program of a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm comprises:

[0009] Step 1: Perform three-dimensional numerical calculations based on the three-dimensional simulation model of the multi-stage axial flow compressor to obtain the flow field parameters of each stage of the multi-stage axial flow compressor;

[0010] Step 2: Based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled. Starting from the first stage, based on the determined one-dimensional calculation program model coefficients and the coefficient sampling results of each stage, one-dimensional calculations are performed stage by stage, and the Kalman gain of each stage is calculated. The one-dimensional calculation results are corrected using the flow field parameters of the corresponding stage until the mean difference between the one-dimensional calculation results before and after the correction is less than a preset threshold. The model coefficients in the corrected one-dimensional calculation results are used as the one-dimensional calculation program model coefficients of the current stage.

[0011] Step 3: After determining the one-dimensional calculation program model coefficients for all stages, complete the one-dimensional calculation program model coefficient optimization for the multi-stage axial flow compressor.

[0012] Optionally, in step 1, a three-dimensional numerical calculation is performed based on a three-dimensional simulation model of the multi-stage axial flow compressor to obtain the flow field parameters of each stage of the multi-stage axial flow compressor, specifically:

[0013] A three-dimensional simulation is performed based on the turbulence model and transition model of a multi-stage axial flow compressor. The circumferentially averaged three-dimensional data are then used to obtain the flow field parameters at the mid-diameter of each blade stage after circumferential averaging.

[0014] Optionally, in step 1, the flow field parameters include: temperature, pressure and airflow angle parameters.

[0015] Optional airflow angle parameters, including: compression ratio, efficiency, lagging angle, and angle of attack.

[0016] Optionally, in step 2, based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled, specifically:

[0017] The one-dimensional calculation program model coefficients of each level are sampled within the upper and lower preset ranges thereof; wherein the number of one-dimensional calculation program model coefficient groups contained in each level is the product of the current level number and the number of blade rows of each level; each group of one-dimensional calculation program model coefficients corresponds to a one-dimensional calculation result.

[0018] Optionally, in step 2, the one-dimensional calculation program model includes: a lagging angle calculation model, a rim work calculation model, and an efficiency calculation model.

[0019] Optionally, in step 2, the calculation of the Kalman gain is as follows:

[0020] Calculate the sample covariance matrix and error covariance matrix;

[0021] The calculation of the sample covariance matrix is ​​as follows:

[0022]

[0023] Where P is the sample covariance matrix; l is the number of samples, l = ab; a is the current level; b is the number of blade rows; is the result of the i-th one-dimensional calculation in the current series; The average value of the one-dimensional calculation results of the current series;

[0024] The error covariance matrix is ​​calculated as follows:

[0025]

[0026] Where R is the error covariance matrix; W is the observation noise set, W = (w 1 ,w 2 ,…,w l ); w is the observation noise;

[0027] Based on the sample covariance matrix and the error covariance matrix, the Kalman gain is calculated as follows:

[0028] K=PH T (HPH T +R) -1 ;

[0029] Among them, K is the Kalman gain; H is the observation matrix.

[0030] Optionally, in step 2, based on the Kalman gain, the flow field parameters of the corresponding stage are used to correct the one-dimensional calculation results as follows:

[0031]

[0032] in, is the corrected one-dimensional calculation result of the i-th in the current series; is the i-th one-dimensional calculation result in the current series; K is the Kalman gain; y exp is the flow field parameter of the corresponding stage; w i is the observation noise of the i-th one-dimensional calculation result in the current series; H is the measurement matrix.

[0033] Through the above technical solutions, it can be seen that compared with the prior art, the present invention proposes a method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm. The target parameters of the one-dimensional calculation are obtained through three-dimensional numerical calculation, and a one-dimensional calculation program model data set is generated using the Latin hypercube sampling method to provide a data basis for the ensemble Kalman algorithm. Based on the target parameters, the ensemble Kalman algorithm is used for iterative calculation to optimize the model coefficients starting from the first stage, and the optimal one-dimensional calculation program model coefficient values ​​are obtained step by step. The influence of different compressor stages on the prediction results is fully considered, and a step-by-step analysis and optimization method is adopted to achieve the effective improvement of the calculation accuracy of the one-dimensional calculation program at a relatively low cost, thereby solving the limitations in the subsequent design and application of high-efficiency and high-load multi-stage compressors. This is of great significance for the future design and application of compressors. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0035] Figure 1 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0037] Example 1:

[0038] Embodiment 1 of the present invention discloses a method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm, comprising:

[0039] Step 1: Perform three-dimensional numerical calculation based on the three-dimensional simulation model of the multi-stage axial flow compressor to obtain the flow field parameters of each stage of the multi-stage axial flow compressor.

[0040] Based on the three-dimensional simulation model of the multi-stage axial flow compressor, three-dimensional numerical calculations are performed to obtain the flow field parameters of each stage of the multi-stage axial flow compressor, specifically:

[0041] Three-dimensional simulation calculations are performed based on the turbulence model and transition model of a multi-stage axial flow compressor, and the circumferential average calculation of the three-dimensional data is performed to obtain the average values ​​of each parameter on the meridian plane. The flow field parameters at the mid-length of each blade stage after circumferential averaging are obtained.

[0042] Flow field parameters, including temperature, pressure and airflow angle parameters.

[0043] Airflow angle parameters, including: compression ratio, efficiency, lagging angle, and angle of attack.

[0044] Step 2: Based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled, and starting from the first stage, based on the determined one-dimensional calculation program model coefficients, according to the coefficient sampling results of each stage, one-dimensional calculation is performed stage by stage, the Kalman gain of each stage is calculated, and the one-dimensional calculation results are corrected using the flow field parameters of the corresponding stage until the mean difference between the one-dimensional calculation results before and after the correction is less than the preset threshold value, and the model coefficients in the corrected one-dimensional calculation results are used as the one-dimensional calculation program model coefficients of the current stage.

[0045] Taking a certain level as an example, when performing one-dimensional calculations at this level, the one-dimensional calculation program model coefficients of the level before this level have been determined, so the one-dimensional calculation program model coefficients of these levels will not change. On the basis of these determined one-dimensional calculation program model coefficients, the one-dimensional calculation of the current level is performed according to the coefficient sampling results of this level.

[0046] Based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled, specifically:

[0047] The one-dimensional calculation program model coefficients of each level are sampled within the upper and lower preset ranges of the same; the number of one-dimensional calculation program model coefficient groups contained in each level is the product of the current level and the number of blade rows at each level. Assuming that the current level is the mth level and the number of blade rows at each level is 2, there are 2m groups of one-dimensional calculation program model coefficients; each group of one-dimensional calculation program model coefficients corresponds to a one-dimensional calculation result, and these one-dimensional calculation results together constitute the one-dimensional calculation result of the current level.

[0048] One-dimensional calculation program model, including: lagging angle calculation model, rim work calculation model, efficiency calculation model, etc.

[0049] Taking the backward angle calculation model as an example, its expression is as follows:

[0050]

[0051] Where, δ is the lagging angle; is the maximum curvature position; B 2k is the geometric outlet angle; x dContains the correction factor reserved for the user; b t is the consistency; θ is the blade bending angle.

[0052] Among them, "0.92," "-0.002," "0.18," "1," and "-0.002" are all optimizable one-dimensional calculation program model coefficients. Taking "0.92" as an example, sampling is performed within its upper and lower preset ranges. In this embodiment of the present invention, the upper and lower preset ranges are set at 20 percent, meaning the sampling range is 0.736-1.104.

[0053] The calculation of Kalman gain is as follows:

[0054] Calculate the sample covariance matrix and error covariance matrix;

[0055] The calculation of the sample covariance matrix is ​​as follows:

[0056]

[0057] Where P is the sample covariance matrix; l is the number of samples, l = an; a is the current level; b is the number of blade rows; is the result of the i-th one-dimensional calculation in the current series; The average value of the one-dimensional calculation results of the current series;

[0058] The error covariance matrix is ​​calculated as follows:

[0059]

[0060] Where R is the error covariance matrix; W is the observation noise set, W = (w 1 ,w 2 ,…,w l ); w is the observation noise;

[0061] Based on the sample covariance matrix and the error covariance matrix, the Kalman gain is calculated as follows:

[0062] K=PH T (HPH T +R) -1 ;

[0063] Among them, K is the Kalman gain; H is the observation matrix.

[0064] Based on the Kalman gain, the flow field parameters of the corresponding stage are used to correct the one-dimensional calculation results as follows:

[0065]

[0066] in, is the corrected one-dimensional calculation result of the i-th in the current series; is the i-th one-dimensional calculation result in the current series; K is the Kalman gain; y exp is the flow field parameter of the corresponding stage; w i is the observation noise of the i-th one-dimensional calculation result in the current series; H is the measurement matrix.

[0067] Step 3: After determining the one-dimensional calculation program model coefficients for all stages, complete the one-dimensional calculation program model coefficient optimization for the multi-stage axial flow compressor.

[0068] The embodiment of the present invention discloses a method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm. The target parameters of the one-dimensional calculation are obtained through three-dimensional numerical calculation, and a one-dimensional calculation program model data set is generated using the Latin hypercube sampling method to provide a data basis for the ensemble Kalman algorithm. Based on the target parameters, the ensemble Kalman algorithm is used for iterative calculation to optimize the model coefficients starting from the first stage, and the optimal one-dimensional calculation program model coefficient values ​​are obtained step by step. The influence of different compressor stages on the prediction results is fully considered, and a step-by-step analysis and optimization method is adopted to achieve the effective improvement of the calculation accuracy of the one-dimensional calculation program at a relatively low cost, thereby solving the limitations in the subsequent design and application of high-efficiency and high-load multi-stage compressors. This method is of great significance for the future design and application of compressors.

[0069] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0070] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm, characterized in that: include: Step 1: Perform three-dimensional numerical calculations based on the three-dimensional simulation model of the multi-stage axial flow compressor to obtain the flow field parameters of each stage of the multi-stage axial flow compressor; Step 2: Based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled, and starting from the first stage, based on the determined one-dimensional calculation program model coefficients and according to the coefficient sampling results of each stage, one-dimensional calculation is performed stage by stage, the Kalman gain of each stage is calculated, and the one-dimensional calculation results are corrected using the flow field parameters of the corresponding stage until the mean difference of the one-dimensional calculation results before and after the correction is less than a preset threshold, and the model coefficients in the corrected one-dimensional calculation results are used as the one-dimensional calculation program model coefficients of the current stage; Step 3: After determining the one-dimensional calculation program model coefficients of all stages, the one-dimensional calculation program model coefficients of the multi-stage axial flow compressor are optimized.

2. The method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 1, a three-dimensional numerical calculation is performed based on the three-dimensional simulation model of the multi-stage axial flow compressor to obtain the flow field parameters of each stage of the multi-stage axial flow compressor, specifically: A three-dimensional simulation is performed based on the turbulence model and transition model of a multi-stage axial flow compressor. The circumferentially averaged three-dimensional data are then used to obtain the flow field parameters at the mid-diameter of each blade stage after circumferential averaging.

3. The method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 1, the flow field parameters include temperature, pressure and airflow angle parameters.

4. The method for optimizing the model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 3, characterized in that: The airflow angle parameters include: compression ratio, efficiency, lagging angle, and angle of attack.

5. The method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 2, based on the Latin hypercube sampling method, the one-dimensional calculation program model coefficients of each stage in the multi-stage axial flow compressor are sampled, specifically: The one-dimensional calculation program model coefficients of each level are sampled within the upper and lower preset ranges thereof; wherein the number of one-dimensional calculation program model coefficient groups contained in each level is the product of the current level number and the number of blade rows of each level; each group of one-dimensional calculation program model coefficients corresponds to a one-dimensional calculation result.

6. The method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 2, the one-dimensional calculation program model includes: a lagging angle calculation model, a rim work calculation model, and an efficiency calculation model.

7. The method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 2, the calculation of the Kalman gain is specifically as follows: Calculate the sample covariance matrix and error covariance matrix; The sample covariance matrix is ​​calculated as follows: Where P is the sample covariance matrix; l is the number of samples, l = ab; a is the current level; b is the number of blade rows; is the result of the i-th one-dimensional calculation in the current series; The average value of the one-dimensional calculation results of the current series; The error covariance matrix is ​​calculated as follows: Where R is the error covariance matrix; W is the observation noise set, W = (w 1 ,w 2 ,…,w l ); w is the observation noise; Based on the sample covariance matrix and the error covariance matrix, the Kalman gain is calculated as follows: K=PH T (HPH T +R) -1 ; Among them, K is the Kalman gain; H is the observation matrix.

8. The method for optimizing model coefficients of a one-dimensional calculation program for a multi-stage axial flow compressor based on an ensemble Kalman filter algorithm according to claim 1, characterized in that: In step 2, based on the Kalman gain, the flow field parameters of the corresponding stage are used to correct the one-dimensional calculation results as follows: in, is the corrected one-dimensional calculation result of the i-th in the current series; is the i-th one-dimensional calculation result in the current series; K is the Kalman gain; y exp is the flow field parameter of the corresponding stage; w i is the observation noise of the i-th one-dimensional calculation result in the current series; H is the measurement matrix.

Images