Annealing optimization algorithm during impeller parameter sensitivity analysis and response surface mismatch
By using impeller parameter sensitivity analysis and annealing optimization algorithm under response surface misfit, the problem of lack of theoretical support for impeller optimization is solved, and more efficient and reliable impeller performance optimization is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-16
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies struggle to accurately quantify the interaction between impeller aerodynamics and fluid dynamics, resulting in a lack of theoretical support for impeller optimization methods. Furthermore, response surface optimization methods suffer from insufficient accuracy and reliability in practical applications.
We employ impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit. By using sensitivity analysis to screen effective design variables and construct a reliable response surface, we can optimize the response surface using simulated annealing algorithm, thereby avoiding blind optimization and improving computational efficiency and logical reliability.
Without increasing the need for specialized knowledge, the computational efficiency and optimization logic reliability of impeller optimization are improved, resulting in more accurate impeller performance optimization.
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Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of centrifugal compressors, and relates to an impeller parameter sensitivity analysis and annealing optimization algorithm in response surface misfit. BACKGROUND
[0002] Centrifugal compressors are an important classification of compressors, and are widely used in the fields of aviation, ships, chemical industry and the like as process machinery. Looking forward to 2035, the requirement of making decisive progress in high-quality energy development and basically building a modern energy system, performance optimization, cost reduction and efficiency improvement of centrifugal compressors are of great significance to energy saving and emission reduction and healthy development of the energy system.
[0003] Centrifugal impellers are the most important elements in the flow passage components of centrifugal compressors. The most core and important step of optimizing the performance of centrifugal compressors is to optimize the flow and work performance of centrifugal impellers. However, researches on aerodynamics and fluid mechanics of centrifugal impellers show that the movement of gas medium in the impeller and the interaction mode with the impeller blades are difficult to be quantitatively expressed and predicted by accurate mathematical formulas, which makes the design and use of impeller optimization methods lack absolute and recognized theoretical support.
[0004] Under such a background, many researchers and practitioners have constructed parameterized impeller optimization methods, and through constructing response surfaces and using approximation models, the optimization problem of the impeller is converted into a statistical problem between input parameters and output performance. Through the intermediate approximation model based on enough sampling points, a statistical method is used to explain the "black box" problem between the design parameters of the impeller and the performance.
[0005] Such optimization logic solves the optimization problem in the design process of air compressors to a certain extent. Especially when enterprises do not have personnel who can completely analyze the internal flow phenomena and aerodynamic laws of the impeller, this method provides a shortcut to bypass the research of computational fluid dynamics and directly optimize. However, with the gradual popularization and application of this method, its drawbacks gradually emerge, and the application scene and optimization accuracy are gradually found to be not as extensive and reliable as expected.
[0006] Therefore, an impeller parameter sensitivity analysis and annealing optimization algorithm in response surface misfit is designed to overcome the above problems. SUMMARY
[0007] The purpose of the present application is to overcome the deficiencies of the prior art and provide an impeller parameter sensitivity analysis and annealing optimization algorithm in response surface misfit. The present application provides a method for extracting effective design variables, avoiding blind optimization, improving calculation efficiency and improving the reliability of the optimization logic without increasing the need for professional knowledge in the process of designing and optimizing the impeller as much as possible.
[0008] The application is implemented by the following technical scheme: a centrifugal impeller parameter sensitivity analysis and annealing optimization algorithm in response surface misfit, the algorithm specifically comprises: 1) sensitivity analysis of impeller parameter change on compressor performance change; 2) analysis of reliability of impeller optimization response surface construction; 3) annealing algorithm optimization method of impeller parameters; The specific method of sensitivity analysis of impeller parameter change on compressor performance change is as follows: S11, determine the geometric characteristic parameters of the centrifugal compressor impeller to be optimized, and construct a parameterized model; S12, determine the output parameters of the optimized impeller; S13, determine the upper and lower limits of the optimization process of the geometric characteristic parameters of the centrifugal compressor impeller to be optimized; S14, construct a sensitivity analysis test sample, and adopt Box-Behnken design to construct the sensitivity analysis test sample; S15, impeller parameter sensitivity analysis; S16, build a zone different from the traditional input variable upper and lower limit interval in S13.
[0009] As preferred: the specific content of the geometric characteristic parameters in step 11) includes at least: five or more control point coordinates of the Bezier curve of the hub profile and the slope or radius of the corresponding coordinates; the setting angle of five or more control points of the Bezier curve of the profile located at the hub and the rim two span sections of the blade; the closed impeller should also include five or more control point coordinates of the Bezier curve of the shroud profile and the slope or radius of the corresponding coordinates; the number of main blades; the impeller containing splitter blades should also include the number of splitter blades and the flow direction starting setting point of the splitter blades; some specialized designs can also include the blade tail inclination angle, the back bending angle, the thickness variation curve of the blade, and the attack angle of the blade leading edge.
[0010] As preferred: the specific analysis method of the sensitivity analysis in step 15) is as follows: The first step is to normalize the input independent variable, i.e. the impeller design parameter, and the dependent variable, i.e. the target performance parameter, wherein the impeller design parameter is normalized to the [-1, 1] interval, and the efficiency is normalized to the [0, 1] interval; The second step: the input and output uncertainty is quantified in the form of probability distribution by adopting the sensitivity analysis method based on variance, and the output variance is decomposed into the part attributable to the input variable and the variable combination; Third step: the correlation coefficient between each design parameter as input and target output can be obtained, the coefficient has positive and negative values, positive and negative values represent increasing or reducing the influence of input on output, the higher the absolute value of sensitivity correlation coefficient, the more significant the change of this design parameter will affect the efficiency.
[0011] As preferred: the specific construction method in step 16) is: 1) The determination method of the upper and lower limits of the parameter optimization process is based on the results of sensitivity analysis, first filter or screen the input variables that have no significant correlation with the output variable, thereby reducing the number of parameters to be analyzed and reducing the calculation cost, 2) Sort the absolute values of sensitivity correlation coefficients from large to small, thereby obtaining the strength order of the influence of structural parameters on performance, and rearrange the input parameters according to the order: Where Cor is the correlation coefficient of sensitivity, and the fitting equation of the output parameter is shown in equation 1): 1) Where x1, x2, x3, etc. refer to variables, a, b, c refer to correlation coefficients, and alpha, beta refer to the order of variables; 3) Find the upper and lower limit interval of variable x1, keep the default values of other input parameters unchanged, approach the default value from the design extreme value of variable x1, and determine the upper and lower limits after reaching the allowable value of topology and computational fluid dynamics (CFD) grid; 4) Respectively take the upper and lower limits of variable x1 as constraints, find the upper and lower limit interval of variable x2, and approach the default value from the design extreme value using the same method, and determine the upper and lower limits after reaching the allowable value of topology and computational fluid dynamics (CFD) grid; 5) Further determine the upper and lower limits of variables x3 to xi, but the calculation amount will further increase, and a certain number of variables with higher sensitivity correlation coefficients can be selected within the required optimization accuracy.
[0012] As preferred: the specific analysis method for analyzing the reliability of impeller optimization response surface construction in step 2) is: S21. Misfit test for sensitivity analysis response surface construction; S22. Parameters to be monitored for misfit test; S23. Results and evaluation criteria of misfit test; Where the misfit test in S21 needs to meet the following conditions before it can be performed: Condition 1: The fitting equation for the output parameters described in S16 does not include all variables and all combinations of variables of all orders. In sensitivity analysis, there will almost certainly be some variables or combinations of variables of all orders that are not significantly correlated with the output variable and will be filtered out. Condition 2: Repeatability testing is required. Combining the Box-Behnken experimental design described in S14 and appropriately increasing the central sample, after filtering out some variables due to low sensitivity and relevance, “repeatability testing” will almost certainly occur.
[0013] As a preferred embodiment: in s22 The parameters of interest in the fit test include Mean Square Lack of Fit (MSLF), Mean Square Pure Error (MSPE), F-test value, and P-value, where the F-value is obtained from Equation 2): 2) In the formula, m is the number of levels of the independent variable, and n is the total number of observations; The P-value is determined by referencing the F-distribution with m-2 degrees of freedom in the numerator and nm degrees of freedom in the denominator.
[0014] As a preferred option, the results and evaluation criteria of the lack-of-fit test in s23 are as follows: The results of the lack-of-fit test are determined by comparing the P-value with the significance level α, which is usually set to 0.05. If P > α, the lack-of-fit test term is considered insignificant, indicating that the fitted equation can express the relationship between the input and output parameters well. If P < α, the lack-of-fit test term is significant, and the reliability of the fitted equation in expressing the relationship between the input and output parameters is poor. When the fitted equation can express the relationship between the input and output parameters well, it indicates that the response surface constructed by the sensitivity analysis is reliable and can be optimized based on the above statistical analysis to achieve impeller parameter optimization. Subsequently, optimization algorithms such as Kriging, genetic algorithms, and evolutionary algorithms can be used to optimize the response surface and complete impeller optimization. When the fitted equation cannot express the relationship between the input and output parameters well, it indicates that the reliability of the response surface constructed by the sensitivity analysis is poor. In this case, if response surface optimization is continued, it is difficult to achieve optimization. At this time, the annealing algorithm optimization method for impeller parameters needs to be adopted.
[0015] As a preferred option: the annealing algorithm optimization method for the impeller parameters is based on a simulated annealing algorithm for the impeller parameters. Simulated annealing simulates industrial annealing, where the metal is first heated and then slowly cooled to allow the internal molecules of the metal to arrange themselves more tightly, resulting in the lowest internal energy of the metal particles and thus improving the metal's performance. The annealing algorithm optimization method for the impeller parameters sets the output parameter, i.e., efficiency, as the "internal energy of the metal particles," and "temperature" as the optimization control parameter. The impeller parameters are then used as the "molecular arrangement" for optimization, ultimately achieving the desired result. The specific method is as follows: S31. The values of the input variables continue the upper and lower limits of the parameters determined in S16, i.e., the parameter range of the optimization process. The output variable, i.e., the efficiency, has a better value magnitude than a worse value, and its sign is opposite to that of the internal energy in the annealing process. During the optimization process, the values of some input variables will be changed, also known as adding perturbations. If the output variable is better after the perturbation, there is a 100% probability of accepting the perturbation. If the output variable is worse after the perturbation, there is a probability P of accepting the perturbation. The method for calculating P is as follows: 3) In the formula, η is the output variable, i.e., efficiency; T is the temperature; k is a constant. In order to keep P within a reasonable range, the constant k and the global temperature T should be adjusted around the amplitude of Δη, and the larger η (the negative number of the efficiency value) is, the higher the global temperature. S32. Optimization Results and Verification: After global optimization based on S31, the optimal solution of the algorithm can be obtained. At this time, the corresponding input parameter values are recorded, the impeller is optimized by parameterization modeling, and the optimized impeller is studied by computational fluid dynamics or experimental methods to solve and verify its optimization effect.
[0016] The beneficial effects of this invention are as follows: Based on the aforementioned background technology, this invention provides a method for impeller parameter sensitivity analysis and annealing optimization algorithm design when response surface misfits. Under the premise of minimizing the need for professional knowledge in the impeller design and optimization process, this invention provides a method for extracting effective design variables, avoiding blind optimization, improving computational efficiency, and enhancing the reliability of optimization logic. Attached Figure Description
[0017] Figure 1 Experimental quantity diagram centered on the sample; Figure 2 To construct a process diagram; Figure 3 A graph showing the output efficiency values of the test samples; Figure 4 The response surface plot constructed for the input parameters; Figure 5 This is a diagram of the heating process; Figure 6 The diagram shows the process of finding the optimal cooling method. Detailed Implementation
[0018] To enable those skilled in the art to more clearly understand the purpose, technical solution, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0019] In the description of this invention, it should be understood that the orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "inner", "outer", "lateral", and "vertical" is based on the orientation or positional relationship shown in the accompanying drawings and is only for the convenience of describing this invention, and is not intended to indicate or imply that the device or component referred to must have a specific orientation, and therefore should not be construed as a limitation of this invention.
[0020] The invention will now be described in detail with reference to the accompanying drawings: Figure 1 As shown, an annealing optimization algorithm for impeller parameter sensitivity analysis and response surface misfit is presented. The algorithm specifically includes: 1) Sensitivity analysis of impeller parameter changes on compressor performance changes; 2) Reliability analysis of impeller optimization response surface construction; 3) Annealing algorithm optimization method for impeller parameters; The specific method for sensitivity analysis of the impact of impeller parameter changes on compressor performance is as follows: S11. Determine the geometric characteristic parameters of the centrifugal compressor impeller to be optimized and construct a parameterized model; S12. Determine the output parameters for optimizing the impeller; Typically, the total pressure-to-total pressure adiabatic efficiency or variable efficiency is used from the impeller inlet to the impeller outlet. In addition, flow rate limits and lower pressure ratio limits should be set. This is because changes in impeller design parameters will simultaneously affect performance parameters such as efficiency, pressure ratio, and flow rate, including both positive and negative effects. Although parameters such as flow rate and pressure ratio are not the target parameters for seeking higher values, excessively low values will not meet the usage requirements.
[0021] S13. Determine the upper and lower limits of the optimization process for the geometric characteristic parameters of the centrifugal compressor impeller to be optimized; Determine the upper and lower limits of the optimization process for the geometric characteristic parameters of the centrifugal compressor impeller to be optimized. Typical optimization processes are based on initial parameters, using certain proportions or amplitudes to limit the upper and lower limits of the optimization process. Taking NRECConcepts' recommended values as an example, the adjustment range for the control point parameters of the impeller disk and cover is ±8%, the blade placement angle is ±15°, and the angle of attack is 0-5°. Using the recommended values can handle local optimization in most cases, but cannot achieve global optimization.
[0022] S14. Construct the sensitivity analysis test sample using the Box-Behnken design; Because impellers have numerous design parameters, using sample design methods such as central composite designs would significantly increase the sample size, making data acquisition much more difficult. However, the Box-Behnken design method can effectively control the sample size. This is because the Box-Behnken design positions each sample point at the edge center of a polyhedron of the variable, possessing approximate rotational properties, which can equivalently guarantee the prediction accuracy of the variable on a sphere centered at the design center. For example, for a Box-Behnken experimental design with 3 variables and 2 levels, a total of 12+ central samples are required. Figure 1 As shown. On the other hand, the number of central samples can be increased to improve the sample base in the subsequent experimental result fitting process, thereby improving the fitting accuracy. Finally, using the impeller design parameters described in S11 as variables, experimental samples are constructed, an appropriate number of central samples is increased, and the sample experiment is completed using the CFD method.
[0023] S15. Impeller parameter sensitivity analysis.
[0024] S16. Establish upper and lower limit intervals for input variables that differ from the traditional ones in S13.
[0025] The specific contents of the geometric feature parameters in step 11) are as follows: at least the coordinates of more than five control points of the Bézier curve of the hub profile and the slope or radius of the corresponding coordinates; the placement angle of more than five control points of the Bézier curve of the blade profile located at the two span sections of the hub and the rim; for closed impellers, the coordinates of more than five control points of the Bézier curve of the shroud profile and the slope or radius of the corresponding coordinates should also be included; the number of main blades; for impellers containing split blades, the number of split blades and the starting placement point of the split blade flow direction should also be included; some specialized designs may also include the blade tail tilt angle, backbend angle, blade thickness variation curve, blade leading edge angle of attack, etc.
[0026] The specific analytical method for sensitivity analysis in step 15) is as follows: The first step is to normalize the input independent variables, i.e., the impeller design parameters, and the dependent variable, i.e., the target performance parameters. The impeller design parameters are normalized to the [-1, 1] interval, and the efficiency is normalized to the [0, 1] interval. Then, a variance-based sensitivity analysis method is used to quantify the uncertainty of the input and output in the form of a probability distribution, and the output variance is decomposed into parts attributable to the input variables and combinations of variables. From this, the correlation coefficient between each design parameter as input and the target output can be obtained. This coefficient has positive and negative values, representing the impact of increasing or decreasing the input on the output, respectively. The higher the absolute value of the sensitivity correlation coefficient, the more significantly changing this design parameter will affect the efficiency. The second step is to use a variance-based sensitivity analysis method to quantify the uncertainty of input and output in the form of a probability distribution, and decompose the output variance into parts that can be attributed to input variables and combinations of variables. The third step is to obtain the correlation coefficient between each design parameter used as input and the target output. This coefficient has positive and negative values, which represent the impact of increasing or decreasing the input on the output. The higher the absolute value of the sensitivity correlation coefficient, the more significantly changing this design parameter will affect efficiency.
[0027] The specific construction method in step 16) is as follows: 1) The method for determining the upper and lower limits of the parameter optimization process is based on the results of sensitivity analysis. Input variables that are not significantly correlated with the output variables are first filtered or screened, thereby reducing the number of parameters that need to be analyzed and decreasing computational costs. 2) Sort the input parameters by the absolute value of their sensitivity correlation coefficients from largest to smallest. This ranking determines the strength of the structural parameters' impact on performance. Rearrange the input parameters according to this ranking. Where Cor is the correlation coefficient of sensitivity, the fitting equation for the output parameters is shown in Equation 1): 1) Where x1, x2, x3, etc. refer to variables, a, b, c refer to correlation coefficients, and the Roman letters α and β refer to the order of variables; It can be observed that the fitting equation includes both linear combinations of single variables of various orders and linear combinations of multiple variables of various orders, ultimately forming a relatively complex fitting formula. Furthermore, generally, the higher the order of the input variables and their combinations, the higher the accuracy and generalization of the fitting equation. Additionally, earlier input variables have a greater impact on the output parameters, and therefore require more consideration of the reasonable upper and lower limits of the input variables to better find the global optimum. 3) Find the upper and lower limit range of variable x1, keep the default values of other input parameters unchanged, and approximate variable x1 from the design extreme value to the default value. After reaching the allowable value of the topology and computational fluid dynamics (CFD) mesh, determine the upper and lower limits. 4) Using the upper and lower limits of variable x1 as constraints, find the upper and lower limit intervals of variable x2. Use the same method to approximate the design extreme value to the default value, and determine the upper and lower limits after reaching the allowable values of the topology and computational fluid dynamics (CFD) mesh. 5) Further determine the upper and lower limits of variables x3 to xi, but this will further increase the computational burden. Within the required optimization accuracy range, appropriately select several variables with high sensitivity correlation coefficients. The construction process is as follows: Figure 2 As shown.
[0028] Sensitivity analysis, as described in S15, still has significant limitations because: S171, the independence between input variables affects the reliability of sensitivity analysis results. In impeller optimization parameters, changes in parameters at control points, such as blade profile control points, further affect the aerodynamics of other control points, thus altering efficiency output. However, this independence is difficult to quantify, assess, or simply attribute. Therefore, the lack of prior independence between parameters significantly reduces the reliability of sensitivity analysis results. S172, the accuracy of sensitivity analysis also depends on the order of the fitted relationship. However, even using high-order relationships to describe the relationship between output variables and input variables of different orders, it is often impossible to accurately describe their relationship. This is because: for a given type of centrifugal impeller, the relationship between impeller parameters and its performance can be functional, discontinuous, or chaotic, stemming from the complex aerodynamics within the impeller. Therefore, for some impeller structures, their structural parameters (within a certain range) may establish a reliable functional relationship with performance, but for many other impeller structures, this functional relationship established through sensitivity analysis is unreliable. Therefore, the first step is to determine whether a reliable response surface between input and output variables can be constructed using sensitivity analysis for impeller optimization. The second step is to explore how to further complete the optimization if the response surface cannot be relied upon.
[0029] The specific analysis method for the reliability analysis of the impeller optimized response surface construction in step 2) is as follows: S21. Lack of fit test for response surface construction in sensitivity analysis. S22. Parameters of interest in the lack-of-fit test; S23. Results and Evaluation Criteria of the Lack of Fit Test; Based on the limitations of sensitivity analysis described in S17, and combined with impeller optimization experience, sensitivity analysis and response surface optimization can handle impeller optimization tasks in many scenarios, but are less effective in others. According to aerodynamic and CFD methods, this phenomenon arises because parameter changes in different impeller structures affect internal flow characteristics in different ways, and currently there is no sufficiently reliable theoretical method to explain or judge the reliability of the response surface construction. Therefore, a statistical lack of fit test is used to verify the reliability of the response surface construction.
[0030] The lack-of-fit test in S21 can only be performed if certain conditions are met: Condition 1: The fitting equation for the output parameters described in S16 does not include all variables and all combinations of variables of all orders. In sensitivity analysis, there will almost certainly be some variables or combinations of variables of all orders that are not significantly correlated with the output variable and will be filtered out. Condition 2: Repeatability testing is required. Combining the Box-Behnken experimental design described in S14 and appropriately increasing the central sample, after filtering out some variables due to low sensitivity and relevance, “repeatability testing” will almost certainly occur.
[0031] In s22 The parameters of interest in the fit test include Mean Square Lack of Fit (MSLF), Mean Square Pure Error (MSPE), F-test value, and P-value, where the F-value is obtained from Equation 2): 2) In the formula, m is the number of levels of the independent variable, and n is the total number of observations; The P-value is determined by referencing the F-distribution with m-2 degrees of freedom in the numerator and nm degrees of freedom in the denominator.
[0032] The results and evaluation criteria of the lack-of-fit test in s23 are as follows: The results of the lack-of-fit test are determined by comparing the P-value with the significance level α, which is usually set to 0.05. If P > α, the lack-of-fit test term is considered insignificant, indicating that the fitted equation can express the relationship between the input and output parameters well. If P < α, the lack-of-fit test term is significant, and the reliability of the fitted equation in expressing the relationship between the input and output parameters is poor. When the fitted equation can express the relationship between the input and output parameters well, it indicates that the response surface constructed by the sensitivity analysis is reliable and can be optimized based on the above statistical analysis to achieve impeller parameter optimization. Subsequently, optimization algorithms such as Kriging, genetic algorithms, and evolutionary algorithms can be used to optimize the response surface and complete impeller optimization. When the fitted equation cannot express the relationship between the input and output parameters well, it indicates that the reliability of the response surface constructed by the sensitivity analysis is poor. In this case, if response surface optimization is continued, it is difficult to achieve optimization. At this time, the annealing algorithm optimization method for impeller parameters needs to be used.
[0033] The annealing algorithm optimization method for impeller parameters is based on a simulated annealing algorithm for impeller parameters. Simulated annealing simulates industrial annealing, where the metal is first heated and then slowly cooled to allow the internal molecules of the metal to arrange themselves more tightly, resulting in the lowest internal energy of the metal particles and thus improving the metal's performance. The annealing algorithm optimization method for impeller parameters sets the output parameter, i.e., efficiency, as the "internal energy of metal particles," and "temperature" as the optimization control parameter. The impeller parameters are then used as the "molecular arrangement" for optimization, ultimately achieving the desired result. The specific method is as follows: S31. The values of the input variables continue the upper and lower limits of the parameters determined in S16, i.e., the parameter range of the optimization process. The output variable, i.e., the efficiency, has a better value magnitude than a worse value, and its sign is opposite to that of the internal energy in the annealing process. During the optimization process, the values of some input variables will be changed, also known as adding perturbations. If the output variable is better after the perturbation, there is a 100% probability of accepting the perturbation. If the output variable is worse after the perturbation, there is a probability P of accepting the perturbation. The method for calculating P is as follows: 3) In the formula, η is the output variable, i.e., efficiency; T is the temperature; k is a constant. In order to keep P within a reasonable range, the constant k and the global temperature T should be adjusted around the amplitude of Δη, and the larger η (the negative number of the efficiency value) is, the higher the global temperature. S32. Optimization Results and Verification: After global optimization based on S31, the optimal solution of the algorithm can be obtained. At this time, the corresponding input parameter values are recorded, the impeller is optimized by parameterization modeling, and the optimized impeller is studied by computational fluid dynamics or experimental methods to solve and verify its optimization effect. Example
[0034] 1. Conduct a sensitivity analysis on the impact of impeller parameter changes on compressor performance.
[0035] Complete S11-S13. This embodiment uses the first stage of a certain type of centrifugal air compressor as the optimization object. The optimization structure focuses on the impeller, while requiring no change to the impeller outlet diameter to avoid the possibility of modifying other structures, changing the inlet guide vane structure, changing the suction inlet structure, or changing the diffuser form. Considering the manufacturing process, the number of impeller blades and the form of the splitter blades will not be further changed. Therefore, the impeller geometric parameters used as input variables in the optimization process mainly include some control points of the profile of the rim and hub, and some control points of the span section of the blades. On the other hand, the optimization goal is to achieve the highest possible efficiency, which is taken as the efficiency from the suction inlet to the diffuser outlet. The upper and lower limits of the adjustment of the geometric parameter input variables adopt the default recommended values. The input and output parameters, default values, and upper and lower limits of the optimization values are shown in Table 1: Table 1 Complete S14, using a Box-Behnken design for the experimental sample, adding an appropriate number of center samples, for a total sample size of 91. The output efficiency values for each experimental sample are as follows: Figure 3 As shown.
[0036] Complete the impeller parameter sensitivity analysis for S15. The sensitivity correlation coefficients between each input and output parameter are shown in Table 2. The correlation coefficient table clearly identifies the design parameters with the greatest impact on efficiency. Furthermore, it allows for the elimination of design parameters with smaller correlation coefficients—those with less impact on efficiency—during subsequent design optimization, simplifying the optimization calculation. For simplicity, S16 is skipped.
[0037] Table 2 2. Complete the reliability analysis of the impeller optimized response surface construction.
[0038] Complete sections S21-S24. The response surface fitting equations constructed through sensitivity analysis are shown below. The response surfaces constructed from the two input parameters with the highest correlation coefficients are as follows: Figure 4 As shown. The fit test yielded the following parameters: F-value = 50485.39, P-value < 0.0001. α=0.05, showing significant significance. This means that the response surface fitting equation cannot accurately represent the relationship between the actual impeller design parameters and their performance. Further optimization based on the response surface fitting equation was performed, and a globally optimal design was obtained. The design parameters were then parametrically modeled, and CFD numerical simulations were conducted on the optimal response surface solution. The efficiency of the CFD solution was 89.4%, while the response surface prediction result was 91.0%. In the field of statistics, such errors are acceptable, even for some impellers with poor initial designs. However, for some demanding situations requiring a high level of optimization, such as this example, optimization can be considered a failure, and the response surface fitting method cannot complete the optimization task. The fundamental reason is that the statistical fitting model's representation of the physical phenomena between the actual input and output, even within a given range, remains unreliable. Therefore, the annealing optimization algorithm described in this invention was further employed for optimization.
[0039] 3. Complete the annealing algorithm optimization for impeller parameters.
[0040] Complete S31 and S32. The optimization process employs a CFD method with fewer iterations and fewer grid cells to ensure high optimization efficiency while sacrificing a small amount of numerical simulation accuracy. The first step is to simulate the heating process, specifically the heating process of metal during industrial annealing. This process involves modifying the input variables to find the combination of variables with the highest efficiency (i.e., the worst-performing model). The worse the initial model performance during the heating process, the easier it is for the optimization process to escape local optima. Figure 5 For the heating process, after finding the local worst model, the temperature is increased from that location and then cooled down to find the optimal model. Figure 6 This is the cooling optimization process. After a perturbation is introduced, i.e., after adjusting the input parameters, if the efficiency value increases (or decreases as the inverse of efficiency for the algorithm), the perturbation is accepted; if the efficiency value decreases, then according to Equation 3), and based on the current temperature, the perturbation is accepted probabilistically, and a new local worst-case model is reached. As the temperature decreases, the probability of accepting perturbations that reduce the performance decreases synchronously. After the temperature drops to 0, only perturbations that increase efficiency are accepted, meaning only optimizations are accepted. The total number of iterations in this example is 298. The corresponding parameters of the algorithm can be modified according to computing power and optimization requirements. If, after several optimizations following a temperature drop to 0, a better model is still not found after a certain number of optimizations, then this optimization is considered the globally optimal model.
[0041] Complete S33. Verify the reliability of the globally optimal model. Parametric modeling was performed using the design parameters of the globally optimal model. High-accuracy CFD mesh generation and iterative solution were applied to the impeller model, achieving an efficiency of 91.0%. This represents a 1% optimization compared to the input model, completing impeller optimization. The 1% efficiency improvement in this instance is because the input model was already a relatively excellent design with high initial efficiency, and conventional optimization methods had limited effect. Therefore, the optimization method described in this patent was developed and used to achieve further optimization. For some input models with poor performance, significant efficiency improvements can be achieved.
[0042] The specific embodiments described herein are merely illustrative of the principles and effects of the invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this invention should still be covered by the claims of this invention.
Claims
1. An annealing optimization algorithm for impeller parameter sensitivity analysis and response surface misfit, characterized in that: The algorithm specifically includes: 1) Sensitivity analysis of impeller parameter changes on compressor performance changes; 2) Reliability analysis of impeller optimization response surface construction; 3) Annealing algorithm optimization method for impeller parameters; The specific method for sensitivity analysis of the impact of impeller parameter changes on compressor performance is as follows: S11: Determine the geometric characteristic parameters of the centrifugal compressor impeller to be optimized and construct a parameterized model; S12. Determine the output parameters for optimizing the impeller; S13. Determine the upper and lower limits of the optimization process for the geometric characteristic parameters of the centrifugal compressor impeller to be optimized; S14. Construct the sensitivity analysis test sample using the Box-Behnken design; S15. Impeller parameter sensitivity analysis; S16. Establish upper and lower limit intervals for input variables that differ from the traditional ones in S13.
2. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 1, characterized in that: The specific contents of the geometric feature parameters in step 11) are as follows: at least the coordinates of more than five control points of the Bézier curve of the hub profile and the slope or radius of the corresponding coordinates; the placement angle of more than five control points of the Bézier curve of the blade profile located at the two span sections of the hub and the rim; for closed impellers, the coordinates of more than five control points of the Bézier curve of the shroud profile and the slope or radius of the corresponding coordinates should also be included; the number of main blades; for impellers containing split blades, the number of split blades and the starting placement point of the split blade flow direction should also be included; some specialized designs may also include the blade tail tilt angle, backbend angle, blade thickness variation curve, and blade leading edge angle of attack.
3. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 1, characterized in that: The specific analytical method for sensitivity analysis in step 15) is as follows: The first step is to normalize the input independent variables, namely the impeller design parameters, and the dependent variables, namely the target performance parameters. The impeller design parameters are normalized to the interval [-1,1], and the efficiency is normalized to the interval [0,1]. The second step is to use a variance-based sensitivity analysis method to quantify the uncertainty of input and output in the form of a probability distribution, and decompose the output variance into parts that can be attributed to input variables and combinations of variables. The third step is to obtain the correlation coefficient between each design parameter used as input and the target output. This coefficient has positive and negative values, which represent the impact of increasing or decreasing the input on the output. The higher the absolute value of the sensitivity correlation coefficient, the more significantly changing this design parameter will affect efficiency.
4. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 1, characterized in that: The specific construction method in step 16) is as follows: 1) The method for determining the upper and lower limits of the parameter optimization process is based on the results of sensitivity analysis. Input variables that are not significantly correlated with the output variables are first filtered or screened, thereby reducing the number of parameters that need to be analyzed and decreasing computational costs. 2) Sort the input parameters by the absolute value of their sensitivity correlation coefficients from largest to smallest. This ranking determines the strength of the structural parameters' impact on performance. Rearrange the input parameters according to this ranking. Where Cor is the correlation coefficient of sensitivity, the fitting equation for the output parameters is shown in Equation 1): 1） Where x1, x2, x3, etc. refer to variables, a, b, c refer to correlation coefficients, and the Roman letters α and β refer to the order of variables; 3) Find the upper and lower limit range of variable x1, keep the default values of other input parameters unchanged, and approximate variable x1 from the design extreme value to the default value. After reaching the allowable value of the topology and computational fluid dynamics (CFD) mesh, determine the upper and lower limits. 4) Using the upper and lower limits of variable x1 as constraints, find the upper and lower limit intervals of variable x2. Use the same method to approximate the design extreme value to the default value, and determine the upper and lower limits after reaching the allowable values of the topology and computational fluid dynamics mesh. 5) Further determine the upper and lower limits of variables x3 to xi, but the amount of calculation will increase further. Within the required optimization accuracy range, select several variables with higher sensitivity correlation coefficients.
5. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 1, characterized in that: The specific analysis method for the reliability analysis of the impeller optimized response surface construction in step 2) is as follows: S21. Lack of fit test for the response surface constructed for sensitivity analysis; S22. Parameters of interest in the lack-of-fit test; S23. Results and evaluation criteria of the lack-of-fit test; The lack-of-fit test in S21 can only be performed if certain conditions are met: Condition 1: The fitting equation for the output parameters described in S16 does not include all variables and all combinations of variables of all orders. In sensitivity analysis, there will almost certainly be some variables or combinations of variables of all orders that are not significantly correlated with the output variable and will be filtered out. Condition 2: Repeatability testing is required. Combining the Box-Behnken experimental design described in S14 and appropriately increasing the central sample, after filtering out some variables due to low sensitivity and correlation, "repeatability testing" will almost certainly occur.
6. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 5, characterized in that... In s22 The parameters of interest in the lack-of-fit test include mean square of lack-of-fit (MSLF), mean square of pure error (MSPE), F-value, and P-value, where the F-value is obtained from equation 2): 2） In the formula, m is the number of levels of the independent variable, and n is the total number of observations; The P-value is determined by referencing the F-distribution with m-2 degrees of freedom in the numerator and nm degrees of freedom in the denominator.
7. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 5, characterized in that... The results and evaluation criteria of the lack-of-fit test in s23 are as follows: The results of the lack-of-fit test are determined by comparing the P-value with the significance level α, which is usually set to 0.
05. If P > α, the lack-of-fit test term is considered insignificant, indicating that the fitted equation can express the relationship between the input and output parameters well. If P < α, the lack-of-fit test term is significant, and the reliability of the fitted equation in expressing the relationship between the input and output parameters is poor. When the fitted equation can express the relationship between the input and output parameters well, it indicates that the response surface constructed by the sensitivity analysis is reliable and can be optimized based on the above statistical analysis to achieve impeller parameter optimization. Subsequently, optimization algorithms such as Kriging, genetic algorithms, and evolutionary algorithms can be used to optimize the response surface and complete impeller optimization. When the fitted equation cannot express the relationship between the input and output parameters well, it indicates that the reliability of the response surface constructed by the sensitivity analysis is poor. In this case, if response surface optimization is continued, it is difficult to achieve optimization. At this time, the annealing algorithm optimization method for impeller parameters needs to be used.
8. The impeller parameter sensitivity analysis and annealing optimization algorithm for response surface misfit as described in claim 1 or 6, characterized in that... The annealing algorithm optimization method for impeller parameters is based on a simulated annealing algorithm for impeller parameters. Simulated annealing simulates industrial annealing, where the metal is first heated and then slowly cooled to allow the internal molecules of the metal to arrange themselves more tightly, resulting in the lowest internal energy of the metal particles and thus improving the metal's performance. The annealing algorithm optimization method for impeller parameters sets the output parameter, i.e., efficiency, as the "internal energy of metal particles," and "temperature" as the optimization control parameter. The impeller parameters are then used as the "molecular arrangement" for optimization, ultimately achieving the desired result. The specific method is as follows: S31. The values of the input variables continue the upper and lower limits of the parameters determined in S16, i.e., the parameter range of the optimization process. The output variable, i.e., the efficiency, has a better value magnitude than a worse value, and its sign is opposite to that of the internal energy in the annealing process. During the optimization process, the values of some input variables will be changed, also known as adding perturbations. If the output variable is better after the perturbation, there is a 100% probability of accepting the perturbation. If the output variable is worse after the perturbation, there is a probability P of accepting the perturbation. The method for calculating P is as follows: 3） In the formula, η is the output variable, i.e., efficiency; T is the temperature; k is a constant. In order to keep P within a reasonable range, the constant k and the global temperature T should be adjusted around the amplitude of Δη, and the larger η is, the higher the global temperature. S32. Optimization Results and Verification: After global optimization based on S31, the optimal solution of the algorithm can be obtained. At this time, the corresponding input parameter values are recorded, the impeller is optimized by parameterization modeling, and the optimized impeller is studied by computational fluid dynamics or experimental methods to solve and verify its optimization effect.