A data-driven centrifugal model stage one-dimensional design method

Abstract

This application relates to the field of centrifugal compressors, and more particularly to a data-driven one-dimensional design method for centrifugal model-level centrifugal compressors, comprising the following steps: S1, establishing a centrifugal model-level geometric and performance dataset, the dataset including design parameters, geometric parameters, and performance parameters; S2, performing correlation analysis on the parameters in the dataset to determine design parameters strongly correlated with geometric and performance parameters, and based on this, determining the characteristic parameters and target values ​​of the prediction model; S3, based on the correlation analysis results, training multiple correlation models using machine learning methods, including a meridional parameter prediction model, a blade installation angle prediction model, a performance prediction model, and a performance curve prediction model; S4, inputting the centrifugal model-level design parameters into the trained correlation models, outputting the corresponding geometric and performance parameters to complete the one-dimensional design at the centrifugal model level. This application achieves rapid and accurate design at the centrifugal model level.

Description

Technical Field

[0001] This application relates to the field of centrifugal compressors, and in particular to a data-driven centrifugal model-level one-dimensional design method. Background Technology

[0002] Centrifugal compressors, as core equipment in key industrial sectors such as energy, chemical, and metallurgy, undertake the important task of gas compression and transportation, and their performance directly affects the efficiency and stability of the entire process. The centrifugal model stage, as the core building block of the centrifugal compressor, directly determines the overall capability and performance level of the compressor product through its parameter coverage and performance characteristics. Therefore, the optimized design of the centrifugal model stage is crucial for enhancing the market competitiveness of centrifugal compressors.

[0003] One-dimensional design, as a fundamental step in centrifugal model-level development, directly impacts the development cycle and performance of new centrifugal compressor products. It not only helps optimize performance, accelerate design iterations, and realize digital processes, but also enables rapid prediction and preliminary design while meeting industry compliance and standardization requirements. However, current centrifugal model-level one-dimensional design software is mostly based on the fundamental principles of centrifugal compressors, combining various loss models and empirical coefficients. This method heavily relies on the designer's experience, and the design results often deviate significantly from actual performance. Multiple iterative calculations using numerical simulation methods are frequently necessary, which is not only time-consuming and labor-intensive but also makes it difficult to guarantee a high first-time success rate, becoming a technical bottleneck restricting the rapid development of new centrifugal compressor products. Summary of the Invention

[0004] To achieve rapid and accurate centrifuge model-level design, this application provides a data-driven one-dimensional centrifuge model-level design method.

[0005] This application provides a data-driven one-dimensional design method for centrifugal models, which adopts the following technical solution: A data-driven, one-dimensional centrifugal model-level design method includes the following steps: S1. Establish a geometric and performance dataset at the centrifugal model level, which includes design parameters, geometric parameters, and performance parameters; S2. Perform correlation analysis on the parameters in the dataset to determine the design parameters that are strongly correlated with the geometric and performance parameters, and determine the characteristic parameters and target values ​​of the prediction model based on this. S3. Based on the correlation analysis results, multiple correlation models are trained using machine learning methods. The correlation models include a meridional parameter prediction model, a blade installation angle prediction model, a performance prediction model, and a performance curve prediction model. S4. Input the design parameters at the centrifugal model level into the trained associated model, and output the corresponding geometric parameters and performance parameters to complete the one-dimensional design at the centrifugal model level.

[0006] By adopting the above technical solutions and establishing a comprehensive dataset covering design parameters, geometric parameters, and performance parameters, a reliable data foundation is provided for subsequent model training, ensuring that the correlation model can accurately capture the intrinsic relationship between design parameters and geometry and performance. In the correlation analysis stage, Pearson correlation coefficients are used to screen strongly correlated design parameters, effectively eliminating redundant features that interfere with the model, improving training efficiency and avoiding the negative impact of irrelevant information on prediction accuracy. Correlation models are trained separately for meridional parameters, blade installation angles, performance, and performance curves, enabling rapid prediction of geometric dimensions (such as meridional parameters and blade inlet / outlet installation angles) and core performance (such as variable efficiency, pressure ratio, and surge margin) across all dimensions in centrifugal model-level design. Finally, by inputting design parameters, geometric parameters and performance results can be output simultaneously, compressing multi-parameter iterative calculations that originally required hours or even days to be completed within one second, significantly shortening the design cycle and reducing R&D costs. With the continuous accumulation of model-level data across different parameter ranges, the model can be continuously optimized through iterative training, improving prediction accuracy and forming a positive cycle of data accumulation, model evolution, and design optimization, providing scalable technical support for efficient and accurate centrifugal model-level design.

[0007] Preferably, the correlation analysis is as follows: Using the Pearson correlation coefficient, parameters with correlation coefficients greater than 0.5 or less than -0.5 were selected to identify design parameters that are strongly correlated with model-level geometric and performance parameters, thereby determining the characteristic parameters and target values ​​of each prediction model.

[0008] By adopting the above technical solutions, on the one hand, the subjective bias in traditional experience-based feature selection is objectively eliminated. A clear statistical and quantitative standard is used to define the degree of correlation between parameters, ensuring that the selected feature parameters have a real and significant causal relationship with the target value (geometric or performance parameters). This avoids irrelevant or weakly correlated parameters from being mixed into the model training process, reducing noise interference from the source. On the other hand, the feature dimension of the model input is significantly reduced, retaining only the strongly correlated parameters that have the most critical impact on the target value. This improves the computational efficiency of model training and avoids overfitting caused by redundant features, significantly enhancing the model's generalization ability to new data. Simultaneously, by clarifying the mapping logic between model input and output, engineers can intuitively understand which design parameters play a dominant role in geometric dimensions (such as meridional parameters, blade installation angle) or performance indicators (such as variable efficiency, surge margin) through the selected strongly correlated parameters. This provides clear directional guidance for subsequent design optimization. This quantitative screening mechanism ensures the effectiveness of the associated model training data, enabling the model to more accurately capture the inherent laws between design parameters and geometry / performance.

[0009] Preferably, the machine learning method includes linear regression and artificial neural networks, and the machine learning method trains the model by minimizing the mean squared error between the predicted value and the actual value.

[0010] By adopting the above technical solutions, linear regression excels at capturing the linear correlation between design parameters and geometry / performance, quickly establishing basic mapping relationships and providing stable initial predictions; artificial neural networks, on the other hand, possess powerful nonlinear fitting capabilities, capable of uncovering complex implicit correlation patterns between parameters, compensating for the insufficient representation of nonlinear relationships by linear models. The combination of the two enables the correlation model to cover a wide range of parameter correlation types while maintaining high accuracy in complex scenarios; by using the minimization of mean squared error as the training objective, the deviation between the model's predicted values ​​and the actual values ​​in the dataset is directly quantified and minimized, forcing the model to actively learn the true patterns in the data rather than surface noise, significantly improving the accuracy of the prediction results; at the same time, it enhances the model's generalization ability to new input data, regardless of whether the parameters of the design centrifugal model are in the common range or marginal interval of the training data, the model can output prediction results that highly match the actual situation.

[0011] Preferably, when training the meridional parameter prediction model, the flow coefficient, pressure ratio, machine Mach number, D4 / D2 and hub ratio are used as feature parameters, and the meridional size parameter is used as the target value. Among them, at least one of b2 / D2, b5 / D2, b6 / D2, D5 / D2, D6 / D2, and D7s / D2.

[0012] By adopting the above technical solution, the selected flow coefficient, pressure ratio, machine Mach number, and hub ratio are all parameters that are strongly correlated with meridional dimensions and are frequently used in the design. This not only eliminates the interference of redundant features but also ensures the true correlation between the model input and meridional geometry. The model's targeted learning of these parameters enables it to accurately capture the inherent laws of how design parameters affect meridional dimensions, and the prediction results are more in line with actual geometric requirements. At the same time, training with meridional dimensions as the target value allows the model output to directly correspond to the most critical geometric inputs in the design. Without additional transformation or verification of intermediate variables, the predicted impeller outlet diameter ratio, blade height ratio, etc., can be directly used... The design of subsequent blade installation angles and performance curves significantly shortens the one-dimensional design process cycle. The training strategy focusing on core geometric parameters avoids the model's ability to fit meridional dimensions weakened by learning non-critical information in a scattered manner. Whether in the model-level under normal operating conditions or in edge scenarios of parameter range, it can quickly output accurate meridional geometry predictions, laying a stable and reliable geometric foundation for the entire centrifugal model-level one-dimensional design. It realizes a design closed loop of accurate meridional dimension prediction, reduced subsequent adjustment and trial and error, and guaranteed overall performance. Especially in the development of centrifugal model-level with high parameter density and short cycle, it can effectively reduce R&D costs and accelerate the product launch.

[0013] Preferably, a third-order polynomial model is established based on the target value, and the coefficients of the polynomial model are determined by K-fold cross-validation and least squares method with the goal of minimizing the mean square error. The flow coefficient = Machine Mach number = Wheel hub ratio = Pressure ratio = ; Among them, Q v U is the inlet volumetric flow rate, D2 is the impeller outlet diameter, u2 is the impeller outlet circumferential velocity, and a is the speed of sound of the gas under the current conditions.

[0014] By adopting the above technical solution, the nonlinear relationship between characteristic parameters such as flow coefficient and pressure ratio and meridional dimension target values ​​is accurately captured through a third-order polynomial model. This avoids the inadequacy of linear models in representing complex laws and prevents overfitting of high-order polynomials. Combined with K-fold cross-validation, the data is repeatedly divided into training / test sets and the optimal model is selected, effectively solving the problem of model overfitting to a single batch of data and ensuring that the model maintains stable generalization ability on model-level data with different parameter ranges. The least squares method with the goal of minimizing the mean square error directly quantifies and minimizes the deviation between the predicted value and the actual geometric dimensions. This makes the meridional parameters such as the impeller outlet diameter ratio and blade height ratio output by the model highly consistent with the actual design requirements. The meridional parameter prediction model can accurately reproduce the influence of design parameters on meridional geometry and quickly output reliable geometric prediction results. There is no need to adjust the meridional dimensions through multiple trial calculations. The model output can be directly used for the design of subsequent blade installation angles and performance curves, which greatly shortens the determination time of meridional geometry and reduces the performance discrepancy caused by geometric dimension deviations. In the development of models with high parameter complexity, the trial and error cost is effectively reduced.

[0015] Preferably, when training the blade installation angle prediction model, the flow coefficient, pressure ratio, surge margin, blockage margin, hub ratio, and multiple geometric ratios are used as characteristic parameters, specifically: D2, D0s / D2, b2 / D2, b4 / D2, b5 / D2, b6 / D2, D4 / D2, D6 / D2, D7s / D2, and L / D2. The target value is defined as at least one of the following: impeller blade inlet installation angle, impeller blade outlet installation angle, diffuser blade inlet installation angle, diffuser blade outlet installation angle, reflux condenser blade inlet installation angle, and reflux condenser blade outlet installation angle. Specifically: β 1h β 1s β 2h β 2s β3, β4, β5, β6.

[0016] By adopting the above technical solution, the selected characteristic parameters include aerodynamic performance indicators such as flow coefficient, pressure ratio, surge margin, and clogging margin, which directly reflect the operational requirements and boundaries at the model level. They also cover various geometric dimensional parameters such as hub ratio, D2 (impeller outlet diameter), and b2 / D2 (impeller outlet relative width), which directly determine the spatial constraints of the impeller / flow channel. This allows the model to fully capture the inherent logic of aerodynamic requirements, geometric constraints, and installation angle adaptation. Among these, the flow coefficient and pressure ratio determine the acceleration requirements of the airflow, and the installation angle is used to guide the airflow to conform to the blade flow channel. The surge margin and clogging margin limit the boundaries of the installation angle, avoiding flow separation or clogging caused by improper angles. The target value directly anchors the inlet and outlet installation angles of the impeller / diffuser / return valve. These parameters are the core aerodynamic design variables for controlling the airflow direction and improving energy conversion efficiency. The model's targeted learning of these parameters enables the output installation angle to accurately match the comprehensive requirements of flow, pressure, and stability.

[0017] Preferably, when training the performance prediction model, the flow coefficient, machine Mach number, energy head coefficient, pressure ratio, surge margin, and hub ratio are used as characteristic parameters, and the model-level variable efficiency is used as the target value.

[0018] By adopting the above technical solution, the selected flow coefficient, machine Mach number, energy head coefficient, pressure ratio, surge margin, and hub ratio cover aerodynamic flow, energy conversion, operational stability, and geometric constraints. This enables the model to comprehensively learn how design parameters work together to address the core issue of variable efficiency. For example, the flow coefficient and pressure ratio determine the acceleration and expansion of the airflow, the energy head coefficient reflects the energy conversion efficiency, the surge margin limits the operating boundary to avoid a sudden drop in efficiency, and the hub ratio indirectly affects the airflow organization within the flow channel through geometric constraints. The training direction with variable efficiency as the target value allows the model output to directly point to the core performance indicators at the centrifugal model level. Efficiency predictions under design conditions can be quickly obtained without complex 3D simulations or experimental verification, significantly shortening the performance evaluation cycle.

[0019] Preferably, training the performance curve prediction model includes: Train a flow coefficient-variable efficiency curve prediction model by fitting curve parameters D, G, and H, and then use an artificial neural network to predict these parameters. Train a flow coefficient-energy head coefficient curve prediction model by fitting curve parameters kdf and Cs, and then use an artificial neural network to predict these parameters. For the flow coefficient-energy head coefficient curve, the following method given by Casey and Schlegel is adopted:

[0020] In this expression, k df Cs represents the coefficient of friction of the disk, and Cs is the sliding velocity. For flow coefficient, The design point flow coefficient.

[0021] By adopting the above technical solutions, the originally implicit curve morphology is transformed into explicit parameter target values, enabling the artificial neural network to focus on high-order mapping learning between design parameters and curve parameters. This significantly improves the model's ability to represent complex surface relationships. It retains the physical insights of classic theories such as Casey and Schlegel into the energy head coefficient curve, while also enhancing its adaptability to differences in data at different model levels through machine learning. Ultimately, the model can not only quickly output flow-variable efficiency curves and flow-energy head coefficient curves that conform to physical laws, but also accurately predict key curve parameters, providing engineers with intuitive evidence to assess performance margins under design conditions and to judge surge and blockage boundaries.

[0022] Preferably, in the training of the flow coefficient-variable efficiency curve prediction model, the curve is divided into two segments: one below the peak efficiency point and the other above the peak efficiency point, which are modeled separately. For flow rates below the peak efficiency point, the polytropic efficiency is expressed by the following formula: , For traffic volumes exceeding peak efficiency, the formula is further modified to account for the possibility that efficiency may differ from zero when maximum traffic is reached. The formula is as follows: .

[0023] By adopting the above technical solution, when the efficiency point is higher than the peak efficiency point, the modified formula incorporates parameters such as G and H to specifically describe the efficiency decay characteristics caused by flow separation or blockage under the maximum flow rate. This avoids fitting the entire curve with a single model. The curve parameters D, G, and H are pre-fitted by nonlinear least squares method and then used as the prediction target of artificial neural network. This not only retains the prior law constraints of physical formula, but also enhances the adaptability to the differences in data at different model levels through machine learning.

[0024] Preferably, the model is trained using the K-fold cross-validation method, in which 80% of the samples are randomly selected as the training set and 20% of the samples are selected as the test set, and multiple training and evaluations are performed to select the optimal model.

[0025] By employing the aforementioned technical solution, the dataset is randomly divided into an 80% training set and a 20% test set, and then trained and evaluated multiple times. Different batches of training / test subsets cover different distribution characteristics of the data, forcing the model to learn the general patterns in the data rather than the local noise of specific subsets, significantly reducing the risk of overfitting. By comprehensively comparing the model's performance on the test set under each partition, the optimal model that maintains high accuracy in most scenarios is selected, rather than relying on the accidental results of a single partition, ensuring the model's strong adaptability to new input data. In centrifugal model-level design, this validation method enables the associated model to accurately capture the correlation between design parameters and geometry / performance in the training data, and to still output highly consistent prediction results when facing parameter ranges not involved in training, significantly reducing design bias caused by insufficient model generalization ability. Simultaneously, the multiple validation processes enhance the credibility of model performance evaluation, allowing engineers to clearly understand the performance boundaries of the model on different data subsets, providing more reliable tool support for subsequent design optimization.

[0026] In summary, this application includes at least one of the following beneficial technical effects: By establishing a comprehensive dataset covering design parameters, geometric parameters, and performance parameters, a reliable data foundation is provided for subsequent model training, ensuring that the correlation model can accurately capture the intrinsic relationship between design parameters and geometry and performance. In the correlation analysis stage, Pearson correlation coefficients are used to screen strongly correlated design parameters, effectively eliminating redundant features that interfere with the model. This improves training efficiency and avoids the negative impact of irrelevant information on prediction accuracy. Correlation models are trained separately for meridional parameters, blade installation angles, performance, and performance curves, enabling rapid prediction of geometric dimensions (such as meridional parameters and blade inlet / outlet installation angles) and core performance (such as variable efficiency, pressure ratio, and surge margin) across all dimensions in centrifugal model-level design. Finally, geometric parameters and performance results can be output simultaneously by inputting design parameters, compressing multi-parameter iterative calculations that originally required hours or even days to be completed within one second, significantly shortening the design cycle and reducing R&D costs. With the continuous accumulation of model-level data across different parameter ranges, the model can be continuously optimized through iterative training, improving prediction accuracy and forming a positive cycle of data accumulation, model evolution, and design optimization. This provides scalable technical support for efficient and accurate centrifugal model-level design. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the data-driven centrifugal model-level one-dimensional design method in an embodiment of this application. Figure 2 This is a schematic diagram illustrating the meridional parameters at the centrifugal model level; Figure 3 This is a schematic diagram illustrating the blade angles of a centrifugal model. Detailed Implementation

[0028] The following is in conjunction with the appendix Figure 1-3 This application will be described in further detail.

[0029] This application discloses a data-driven one-dimensional centrifuge model-level design method. The data-driven one-dimensional centrifuge model-level design method includes the following steps: S1. Establish a centrifugal model-level geometry and performance dataset, which includes design parameters, geometric parameters, and performance parameters.

[0030] The design parameters include flow coefficient, machine Mach number, energy head coefficient, hub ratio, and length-to-diameter ratio. The geometric parameters include b2 / D2, b5 / D2, b6 / D2, D4 / D2, D5 / D2, D6 / D2, D7s / D2, impeller blade inlet installation angle, impeller blade outlet installation angle, diffuser blade inlet installation angle, diffuser blade outlet installation angle, return flow vane inlet installation angle, and return flow vane outlet installation angle. The performance parameters include blade multivariable efficiency, pressure ratio, surge margin, and clogging margin.

[0031] Flow coefficient = , Among them, Q v U is the inlet volumetric flow rate, D2 is the impeller outlet diameter, and u2 is the impeller outlet circumferential velocity.

[0032] Machine Mach number = , where a is the speed of sound of the gas in its current state.

[0033] Energy head coefficient = ; Where Cp is the specific heat capacity at constant pressure, and ΔT is the total temperature rise of the gas as it passes through the model stage.

[0034] Wheel hub ratio = .

[0035] Aspect Ratio = .

[0036] Variable efficiency = = The ratio of the variable compression work required to increase the pressure from P1 to P7 to the actual work consumed.

[0037] Pressure ratio =

[0038] Surge margin = ,in: For surge point flow rate, For the working point flow rate.

[0039] Congestion margin = : The flow rate at the congestion point.

[0040] S2. Perform correlation analysis on the parameters in the dataset to identify design parameters that are strongly correlated with geometric and performance parameters, and determine the characteristic parameters and target values ​​of the prediction model based on this.

[0041] Specifically, the correlation analysis is as follows: Using the Pearson correlation coefficient, parameters with correlation coefficients greater than 0.5 or less than -0.5 were selected to identify design parameters that are strongly correlated with model-level geometric and performance parameters, thereby determining the characteristic parameters and target values ​​of each prediction model.

[0042] On the one hand, it objectively eliminates the subjective bias in traditional experience-based feature selection, defining the degree of correlation between parameters with clear statistical quantification standards. This ensures that the selected feature parameters have a real and significant causal relationship with the target value (geometric or performance parameters), avoiding irrelevant or weakly correlated parameters from being mixed into the model training process, thus reducing noise interference from the source. On the other hand, it significantly reduces the feature dimension of the model input, retaining only the strongly correlated parameters that have the most critical impact on the target value. This not only improves the computational efficiency of model training but also avoids overfitting caused by redundant features, significantly enhancing the model's generalization ability to new data. At the same time, it clarifies the mapping logic between model input and output. Engineers can intuitively understand which design parameters play a dominant role in geometric dimensions (such as meridional parameters, blade installation angle) or performance indicators (such as variable efficiency, surge margin) through the selected strongly correlated parameters, providing clear directional guidance for subsequent design optimization. This quantitative screening mechanism ensures the effectiveness of the associated model training data, enabling the model to more accurately capture the inherent laws between design parameters and geometry / performance.

[0043] S3. Based on the correlation analysis results, multiple correlation models are trained using machine learning methods. The correlation models include a meridional parameter prediction model, a blade installation angle prediction model, a performance prediction model, and a performance curve prediction model.

[0044] Machine learning methods include linear regression and artificial neural networks. These methods train the model by minimizing the mean squared error between the predicted and actual values.

[0045] Linear regression excels at capturing the linear relationship between design parameters and geometry / performance, quickly establishing basic mapping relationships and providing stable initial predictions; artificial neural networks, on the other hand, possess powerful nonlinear fitting capabilities, capable of uncovering complex implicit correlation patterns between parameters, compensating for the shortcomings of linear models in representing nonlinear relationships. The combination of the two enables the correlation model to cover a wide range of parameter correlation types while maintaining high accuracy in complex scenarios; by using the minimization of mean squared error as the training objective, the deviation between the model's predicted values ​​and the actual values ​​in the dataset is directly quantified and minimized, forcing the model to actively learn the true patterns in the data rather than surface noise, significantly improving the accuracy of the prediction results.

[0046] Meanwhile, the combined use of these two methods enhances the model's generalization ability to new input data. Regardless of whether the parameters of the designed centrifugal model fall within the common range or marginal interval of the training data, the model can output predictions that highly match the actual situation. Furthermore, the complementarity of the two methods reduces the risk of overfitting by a single model: linear regression serves as a baseline framework that constrains the model's complexity, while neural networks supplement nonlinear details within a limited range. This allows the associated model to maintain simplicity while possessing sufficient flexibility, ultimately achieving the technical effect of rapid training, accurate prediction, and wide applicability. This provides crucial support for the efficiency and reliability of one-dimensional design at the centrifugal model level.

[0047] When training the meridional parameter prediction model, the flow coefficient, pressure ratio, machine Mach number and hub ratio are used as characteristic parameters, and the meridional size parameters are used as target values; among them, the meridional size parameters include at least one of the impeller outlet diameter ratio, blade height ratio and flow channel diameter ratio.

[0048] The selected flow coefficient, pressure ratio, machine Mach number, and hub ratio are all parameters strongly correlated with meridional dimensions and frequently used in design. This eliminates interference from redundant features and ensures a true correlation between the model input and meridional geometry. For example, the impeller outlet diameter ratio directly determines the matching between flow rate and pressure ratio, the blade height ratio affects the surge margin boundary, and the flow channel diameter ratio is related to the energy conversion efficiency of the internal flow channel. The model's targeted learning of these parameters enables it to accurately capture the intrinsic laws of how design parameters affect meridional dimensions, resulting in predictions that better match actual geometric requirements. Furthermore, training with meridional dimensions as the target value ensures that the model output directly corresponds to the most critical geometric inputs in the design, eliminating the need for additional transformations or validation of intermediate variables. The predicted impeller outlet diameter ratio and blade height ratio can be directly used for the design of subsequent blade installation angles and performance curves, significantly shortening the process cycle of one-dimensional design. The training strategy that focuses on core geometric parameters avoids the model's ability to fit meridional dimensions weakened by learning non-critical information in a scattered manner. Whether it is the model level under normal operating conditions or the edge scenarios of parameter range, it can quickly output accurate meridional geometry predictions, laying a stable and reliable geometric foundation for the entire centrifugal model-level one-dimensional design. It realizes a design closed loop of accurate meridional dimension prediction, reduced subsequent adjustment and trial and error, and guaranteed overall performance. Especially in the development of centrifugal model level with high parameter density and short cycle, it can effectively reduce R&D costs and accelerate the product launch.

[0049] In an optional embodiment, a third-order polynomial model is established based on the target value, and the coefficients of the polynomial model are determined by K-fold cross-validation and least squares method with the goal of minimizing the mean square error.

[0050] The model accurately captures the nonlinear relationship between characteristic parameters such as flow coefficient and pressure ratio and the target value of meridional dimensions using a third-order polynomial model. This avoids the inadequacy of linear models in representing complex patterns and prevents overfitting of high-order polynomials. Combined with K-fold cross-validation, the data is repeatedly divided into training / test sets, and the optimal model is selected to effectively solve the problem of overfitting the model to a single batch of data. This ensures that the model maintains stable generalization ability on model-level data with different parameter ranges. The least squares method, which aims to minimize the mean square error, directly quantifies and minimizes the deviation between the predicted value and the actual geometric dimensions. This makes the meridional parameters such as the impeller outlet diameter ratio and blade height ratio output by the model highly consistent with the actual design requirements. The meridional parameter prediction model can accurately reproduce the influence of design parameters on meridional geometry and quickly output reliable geometric prediction results. It eliminates the need for multiple trial calculations to adjust the meridional dimensions. The model output can be directly used for the design of subsequent blade installation angles and performance curves, significantly shortening the determination time of meridional geometry and reducing performance discrepancies caused by geometric dimension deviations. In the development of models with high parameter complexity, this effectively reduces trial and error costs.

[0051] When training the blade installation angle prediction model, the characteristic parameters are the flow coefficient, pressure ratio, surge margin, clogging margin, hub ratio, and multiple geometric ratios, specifically: D2, D0s / D2, b2 / D2, b4 / D2, b5 / D2, b6 / D2, D4 / D2, D6 / D2, D7s / D2, and L / D2. The target value is at least one of the following: impeller blade inlet installation angle, impeller blade outlet installation angle, diffuser blade inlet installation angle, diffuser blade outlet installation angle, return flow vane inlet installation angle, and return flow vane outlet installation angle. Specifically: β 1h β 1s β 2h β 2s β3, β4, β5, β6.

[0052] The selected characteristic parameters include aerodynamic performance indicators such as flow coefficient, pressure ratio, surge margin, and clogging margin, which directly reflect the operational requirements and boundaries at the model level. They also cover various geometric parameters such as hub ratio, D2 (impeller outlet diameter), and b2 / D2, which directly determine the spatial constraints of the impeller / flow channel. This allows the model to fully capture the inherent logic of aerodynamic requirements, geometric constraints, and installation angle adaptation. Among these, the flow coefficient and pressure ratio determine the acceleration requirements of the airflow, and the installation angle is used to guide the airflow to conform to the blade flow channel. The surge margin and clogging margin limit the boundaries of the installation angle to avoid flow separation or clogging caused by improper angles. The target values ​​directly anchor the inlet and outlet installation angles (β1h, β1s, β2h, etc.) of the impeller / diffuser / return valve. These parameters are the core aerodynamic design variables for controlling the airflow direction and improving energy conversion efficiency. The model's targeted learning of these parameters enables the output installation angle to accurately match the comprehensive requirements of flow, pressure, and stability. This training strategy, which involves inputting all factors and outputting core aerodynamic targets, avoids the mismatch between the installation angle and impeller size caused by ignoring geometric constraints. It also prevents focusing solely on aerodynamic parameters while neglecting structural feasibility. Ultimately, it achieves the design effect of accurately predicting the installation angle, reducing manual adjustments and trial and error, and ensuring the rationality of airflow organization. This significantly improves the aerodynamic performance and operational stability of the model, while providing accurate basic inputs for subsequent performance prediction models and curve training, thus enhancing the coherence and reliability of the entire one-dimensional design process.

[0053] When training the performance prediction model, the flow coefficient, machine Mach number, energy head coefficient, pressure ratio, surge margin, and hub ratio are used as characteristic parameters, and the model-level polyvariable efficiency is used as the target value.

[0054] The selected flow coefficient, machine Mach number, energy head coefficient, pressure ratio, surge margin, and hub ratio comprehensively cover aerodynamic flow (flow rate, velocity field), energy conversion (energy head, pressure ratio), operational stability (surge margin), and geometric constraints (hub ratio). This allows the model to fully learn how design parameters work together to address the core issue of variable efficiency. For example, the flow coefficient and pressure ratio determine the acceleration and expansion of the airflow, the energy head coefficient reflects the energy conversion efficiency, the surge margin limits the operating boundary to avoid a sudden drop in efficiency, and the hub ratio indirectly affects the airflow organization within the flow channel through geometric constraints. The training direction with variable efficiency as the target value allows the model output to directly point to the core performance indicators at the centrifugal model level. It can quickly obtain the efficiency prediction value under the design conditions without the need for complex 3D simulation or experimental verification, significantly shortening the performance evaluation cycle.

[0055] Meanwhile, this mapping relationship between all-factor features and core performance avoids the efficiency prediction bias caused by neglecting some key parameters (such as the geometric influence of the hub ratio) in traditional methods. The variable efficiency output by the model is closer to the actual operating value, providing a reliable performance benchmark for subsequent performance curve prediction and design optimization. In addition, combined with the training objective of minimizing the mean square error, the model can accurately fit the nonlinear relationship between each parameter and variable efficiency. Whether it is a model at the standard parameter range or a new design after parameter adjustment, it can output high-confidence efficiency prediction results, significantly improving the first-time success rate of the design and reducing the cost of repeated modifications due to efficiency discrepancies. Ultimately, it realizes a design closed loop of rapid prediction of core performance, guiding design optimization, and ensuring efficiency targets are met, enhancing the engineering practicality of centrifugal model-level one-dimensional design methods.

[0056] Training performance curve prediction models include: Train a flow coefficient-variable efficiency curve prediction model by fitting curve parameters D, G, and H, and then use an artificial neural network to predict these parameters. Train the flow coefficient-energy head coefficient curve prediction model, and fit the curve parameter k df and C s And use artificial neural networks to predict these parameters; For the flow coefficient-energy head coefficient curve, the following method given by Casey and Schlegel is adopted:

[0057] In this expression, k df Cs represents the coefficient of friction of the disk, and Cs is the sliding velocity. For flow coefficient, The design point flow coefficient.

[0058] Below the peak flow rate, the focus is on flow organization efficiency, while above the peak flow rate, the efficiency degradation characteristics at maximum flow rate must be considered to avoid a coarse fit of the entire curve by a single model; instead, the curve parameters (D, G, H, or k) are pre-fitted using a nonlinear least squares method. df C s This process feeds back into the dataset, transforming the previously implicit curve morphology into explicit parameter target values. This allows the artificial neural network to focus on learning the higher-order mapping between design parameters and curve parameters, significantly improving the model's ability to represent complex surface relationships. It retains the physical insights of classic theories such as Casey and Schlegel into the energy head coefficient curve, while also enhancing its adaptability to differences in data at different model levels through machine learning. Ultimately, the model can not only quickly output flow-variable efficiency curves and flow-energy head coefficient curves that conform to physical laws, but also accurately predict key curve parameters, such as the location of the peak efficiency point, the efficiency decay rate at the maximum flow, and the slope of the energy head coefficient as a function of flow. This provides engineers with intuitive evidence to assess the performance margin under design conditions and to determine surge and blockage boundaries.

[0059] In training the flow coefficient-variable efficiency curve prediction model, the curve is divided into two segments: one below the peak efficiency point and the other above the peak efficiency point, which are modeled separately. For flow rates below the peak efficiency point, the polytropic efficiency is expressed by the following formula: , For traffic volumes exceeding peak efficiency, the formula is further modified to account for the possibility that efficiency may differ from zero when maximum traffic is reached. The formula is as follows: .

[0060] Below the peak efficiency point, the formula focuses on the efficiency gain mechanism of airflow conforming to the blade channel, capturing the positive improvement law of flow rate-efficiency through the correlation between geometric and flow parameters such as D and D1. Above the peak efficiency point, the modified formula incorporates parameters such as G and H to specifically describe the efficiency decay characteristics caused by flow separation or blockage at maximum flow rate, avoiding the fitting of a single model to the entire curve. The curve parameters D, G, and H are pre-fitted by nonlinear least squares method and then used as the prediction target of artificial neural network. This not only retains the prior law constraints of physical formula, but also enhances the adaptability to the differences in data at different model levels through machine learning.

[0061] The combination of physical deconstruction and data learning enables the model to output efficiency curves that closely resemble actual flow. Engineers can quickly obtain key information such as peak efficiency locations and efficiency decay rates without relying on time-consuming 3D simulations or experiments, accurately assessing the performance margin and operational stability of design conditions (such as surge and blockage boundaries). Simultaneously, the parameterized curve model enhances the interpretability of predictions. Engineers can understand the impact of design variables on the efficiency curve by adjusting parameters such as D, G, and H, providing a clear direction for subsequent optimization. Ultimately, this method significantly shortens the performance curve evaluation cycle and reduces design iterations caused by curve deviations.

[0062] S4. Input the design parameters at the centrifugal model level into the trained associated model, and output the corresponding geometric parameters and performance parameters to complete the one-dimensional design at the centrifugal model level.

[0063] The model was trained using K-fold cross-validation, in which 80% of the samples were randomly selected as the training set and 20% as the test set. The model was then trained and evaluated multiple times to select the optimal model.

[0064] The dataset is randomly divided into an 80% training set and a 20% test set, and then trained and evaluated multiple times. Different batches of training / test subsets cover different distribution characteristics of the data, forcing the model to learn the general patterns in the data rather than the local noise of specific subsets, significantly reducing the risk of overfitting. By comprehensively comparing the model's performance on the test set under each partition (such as mean squared error), the optimal model that can maintain high accuracy in most scenarios is selected, rather than relying on the accidental results of a single partition, ensuring the model's strong adaptability to new input data. In centrifugal model-level design, this validation method enables the associated model to accurately capture the correlation between design parameters and geometry / performance in the training data, and to still output prediction results that are highly consistent with reality when facing parameter ranges not involved in training (such as aspect ratio or flow coefficient in new model-level models), greatly reducing design bias caused by insufficient model generalization ability. At the same time, the multiple validation processes also enhance the credibility of model performance evaluation. Engineers can clearly know the performance boundaries of the model on different data subsets, providing more reliable tool support for subsequent design optimization.

[0065] The implementation principle of this application embodiment is as follows: By establishing a comprehensive dataset covering design parameters, geometric parameters, and performance parameters, a reliable data foundation is provided for subsequent model training, ensuring that the correlation model can accurately capture the intrinsic relationship between design parameters and geometry and performance. In the correlation analysis stage, Pearson correlation coefficient is used to screen strongly correlated design parameters, effectively eliminating the interference of redundant features on the model, which not only improves training efficiency but also avoids the negative impact of irrelevant information on prediction accuracy. Correlation models are trained separately for meridional parameters, blade installation angles, performance, and performance curves to achieve rapid prediction of geometric dimensions (such as meridional parameters and blade inlet / outlet installation angles) and core performance (such as variable efficiency, pressure ratio, and surge margin) in centrifugal model-level design. Finally, geometric parameters and performance results can be output simultaneously by inputting design parameters, compressing the multi-parameter iterative calculation that originally required several hours or even days to be completed within 1 second, significantly shortening the design cycle and reducing R&D costs. With the continuous accumulation of model-level data in different parameter ranges, the model can be continuously optimized through iterative training, and the prediction accuracy will be improved accordingly, forming a positive cycle of data accumulation-model evolution-design optimization, providing scalable technical support for efficient and accurate centrifugal model-level design.

[0066] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A data-driven, centrifugal model-level one-dimensional design method, characterized in that, Including the following steps: S1. Establish a geometric and performance dataset at the centrifugal model level, which includes design parameters, geometric parameters, and performance parameters; S2. Perform correlation analysis on the parameters in the dataset to determine the design parameters that are strongly correlated with the geometric and performance parameters, and determine the characteristic parameters and target values ​​of the prediction model based on this. S3. Based on the correlation analysis results, multiple correlation models are trained using machine learning methods. The correlation models include a meridional parameter prediction model, a blade installation angle prediction model, a performance prediction model, and a performance curve prediction model. S4. Input the design parameters at the centrifugal model level into the trained associated model, and output the corresponding geometric parameters and performance parameters to complete the one-dimensional design at the centrifugal model level.

2. The data-driven centrifugal model-level one-dimensional design method according to claim 1, characterized in that, The correlation analysis is as follows: Using the Pearson correlation coefficient, parameters with correlation coefficients greater than 0.5 or less than -0.5 were selected to identify design parameters that are strongly correlated with model-level geometric and performance parameters, thereby determining the characteristic parameters and target values ​​of each prediction model.

3. The data-driven centrifugal model-level one-dimensional design method according to claim 2, characterized in that, The machine learning method includes linear regression and artificial neural networks, and the machine learning method trains the model by minimizing the mean squared error between the predicted value and the actual value.

4. The data-driven centrifugal model-level one-dimensional design method according to claim 3, characterized in that, When training the meridian parameter prediction model, the flow coefficient, pressure ratio, machine Mach number and hub ratio are used as feature parameters, and the meridian size parameter is used as the target value. The meridional dimension parameters include b2 / D2, b5 / D2, b6 / D2, D5 / D2, D6 / D2, and D7s / D2. At least one of them.

5. The data-driven centrifugal model-level one-dimensional design method according to claim 4, characterized in that, A third-order polynomial model is established based on the target value. The coefficients of the polynomial model are determined by K-fold cross-validation and least squares method with the goal of minimizing the mean square error. The flow coefficient = Machine Mach number = Wheel hub ratio = Pressure ratio = ; Among them, Q v U is the inlet volumetric flow rate, D2 is the impeller outlet diameter, u2 is the impeller outlet circumferential velocity, and a is the speed of sound of the gas under the current conditions.

6. The data-driven centrifugal model-level one-dimensional design method according to claim 3, characterized in that, When training the blade installation angle prediction model, the flow coefficient, pressure ratio, surge margin, clogging margin, hub ratio, and multiple geometric ratios are used as characteristic parameters, specifically: D2, D0s / D2, b2 / D2, b4 / D2, b5 / D2, b6 / D2, D4 / D2, D6 / D2, D7s / D2, and L / D2. The target value is defined as at least one of the following: impeller blade inlet installation angle, impeller blade outlet installation angle, diffuser blade inlet installation angle, diffuser blade outlet installation angle, reflux condenser blade inlet installation angle, and reflux condenser blade outlet installation angle. Specifically: β 1h β 1s β 2h β 2s β3, β 4、 β5, β6.

7. The data-driven centrifugal model-level one-dimensional design method according to claim 3, characterized in that, When training the performance prediction model, the flow coefficient, machine Mach number, energy head coefficient, pressure ratio, surge margin and hub ratio are used as characteristic parameters, and the model-level polyvariable efficiency is used as the target value.

8. The data-driven centrifugal model-level one-dimensional design method according to claim 3, characterized in that, Training the performance curve prediction model includes: Train a flow coefficient-variable efficiency curve prediction model by fitting curve parameters D, G, and H, and then use an artificial neural network to predict these parameters. Train the flow coefficient-energy head coefficient curve prediction model, and fit the curve parameter k df And Cs, and use artificial neural networks to predict these parameters; The following method is used for the flow coefficient-energy head coefficient curve: In this expression, k df Cs represents the coefficient of friction of the disk, and Cs is the sliding velocity. For flow coefficient, The design point flow coefficient.

9. The data-driven centrifugal model-level one-dimensional design method according to claim 8, characterized in that, In the training of the flow coefficient-variable efficiency curve prediction model, the curve is divided into two segments: one below the peak efficiency point and the other above the peak efficiency point, which are modeled separately. For flow rates below the peak efficiency point, the polytropic efficiency is expressed by the following formula: ， For traffic volumes exceeding peak efficiency, the formula is further modified to account for the possibility that efficiency may differ from zero when maximum traffic is reached. The formula is as follows: 。 10. The data-driven centrifugal model-level one-dimensional design method according to claim 1, characterized in that, The model was trained using K-fold cross-validation, in which 80% of the samples were randomly selected as the training set and 20% as the test set. The model was then trained and evaluated multiple times to select the optimal model.

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