A full-working-condition high-efficiency running centrifugal pump impeller optimization method and system

Abstract

This invention discloses a method and system for optimizing the impeller of a centrifugal pump operating efficiently under all conditions. The method includes: defining the geometric design variables and feasible region of the centrifugal pump impeller and generating an initial impeller geometry sample set; performing high-fidelity computational fluid dynamics numerical simulation and extracting the flow field physical field feature data and corresponding operating parameters for each operating condition; preprocessing the geometric design variables, flow field physical field feature data, and corresponding operating parameters, and fusing them into a unified multimodal feature representation; constructing a deep multimodal neural network model and training it; constructing a comprehensive optimization function, integrating manufacturing constraints, and outputting the impeller geometric parameter combination; performing three-dimensional model reconstruction and engineering feasibility verification, and generating a manufacturing data file. This method constructs a high-fidelity, highly generalized performance prediction surrogate model, significantly improving the model's accuracy and physical consistency in capturing the nonlinear relationship between small changes in impeller geometry and complex flows.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery technology, and in particular to a method and system for optimizing the impeller of a centrifugal pump that operates efficiently under all conditions. Background Technology

[0002] With the increasing demands for energy efficiency and intelligence in the industrial sector, centrifugal pumps, as core power equipment in fluid transport systems, directly impact the energy consumption, reliability, and maintenance costs of the entire industrial system. They hold an irreplaceable position in key scenarios such as petrochemicals, power energy, municipal water services, and high-end manufacturing. Driven by the "dual-carbon" goals and the upgrading of intelligent manufacturing, users urgently need centrifugal pumps to maintain high efficiency, low fluctuations, and strong stability across a wide flow range, rather than simply performing well under a single design condition. The impeller, as the core component for energy conversion in a centrifugal pump, has a highly coupled three-dimensional geometry and internal complex turbulent flow field, determining the pump's overall hydraulic performance, cavitation characteristics, vibration noise, and lifespan. However, existing impeller optimization technologies remain constrained by traditional engineering paradigms, making it difficult to support the practical needs of efficient operation across all operating conditions.

[0003] In existing technologies, the centrifugal pump impeller optimization method based on deep multimodal fusion aims to overcome the limitations of single-point operating condition dependence, single-source data modeling, and black-box optimization. It systematically integrates multi-source heterogeneous information such as impeller geometric parameters, high-dimensional flow field physics, dynamic operating conditions, and multi-dimensional performance indicators to construct an intelligent collaborative optimization system with physical consistency, strong generalization ability, and engineering feasibility. This method is based on high-precision NURBS parametric modeling, combined with high-fidelity CFD simulation, measured operating data, and an advanced deep learning architecture. It establishes a nonlinear mapping mechanism from microscopic geometric perturbations to macroscopic full-condition performance response. Its core lies in using a cross-modal attention mechanism to drive deep interaction of multimodal features, thereby accurately capturing the intrinsic correlation between impeller structural evolution and flow performance, and achieving proactive design and collaborative control of performance across the entire flow domain.

[0004] However, the aforementioned existing technologies suffer from four major contradictions in intelligent optimization of centrifugal pump impellers across all operating conditions: First, mainstream optimization methods generally focus on the design operating condition or a few fixed flow points, lacking joint modeling and coordinated constraints on efficiency flatness, head stability, required net positive suction head (NPSH), and flow uniformity across the entire operating range. This leads to a sharp drop in efficiency and severe pressure pulsation during actual variable load operation, and may even induce stall or surge. Second, traditional surrogate models (such as Kriging, RBF, and SVR) are severely inadequate in expressing high-dimensional, nonlinear, and strongly coupled flow field characteristics, making it difficult to accurately reflect the complex turbulent structural evolution caused by minute geometric changes in the blades, resulting in low prediction accuracy. First, the extrapolation capability is limited. Second, current deep learning-based optimization schemes mostly use single-modal inputs (such as only geometric parameters or only CFD results), failing to effectively integrate multi-dimensional information such as structure, flow field, operating conditions, and performance. This results in poor model generalization, weak physical interpretability, sharp performance drops under varying operating conditions, and optimization results often violate the basic laws of fluid mechanics. Finally, most optimization processes treat manufacturing feasibility as a post-processing step, failing to embed key process constraints such as minimum blade thickness, maximum torsion angle, and machinable fillet radius into the optimization feasible region or objective function. As a result, although the generated "optimal" impeller performs well in simulation, it loses its engineering value because it cannot be manufactured, assembled, or put into service. These technical bottlenecks severely restrict the improvement of energy efficiency and intelligent operation and maintenance of centrifugal pumps under complex dynamic operating conditions. Summary of the Invention

[0005] The main objective of this invention is to provide a method and system for optimizing the impeller of a centrifugal pump that operates efficiently under all conditions, in order to solve the technical problems that cannot be processed, assembled, or put into service in the prior art.

[0006] To achieve the above objectives, this invention provides a method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions, the method comprising: S10, based on parametric modeling technology, defines the geometric design variables and feasible domain of the centrifugal pump impeller, and generates an initial impeller geometry sample set covering the design space; S20, based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation, and extract the flow field physical field characteristic data and corresponding operating parameters under each working condition; S30, preprocess the geometric design variables, the flow field physical field characteristic data and the corresponding operating parameters, and fuse the preprocessed data into a unified multimodal feature representation through an encoding network; S40, Construct a deep multimodal neural network model and train the deep multimodal neural network model; S50, based on the trained deep multimodal neural network model, constructs a comprehensive optimization function, integrates manufacturing constraints, and uses a Bayesian optimization algorithm to perform global optimization within the feasible domain of the geometric design variables, outputting the impeller geometric parameter combination; S60, based on the output impeller geometric parameter combination, performs three-dimensional model reconstruction and engineering feasibility verification, and generates manufacturing data files that can be directly used for CNC machining or 3D printing.

[0007] Optionally, the geometric design variables include the blade inlet angle β1, the blade outlet angle β2, the blade wrap angle φ, the number of blades Z, the hub diameter Dh, the hub cover diameter Ds, and the blade thickness distribution function f(t).

[0008] Optionally, step S20 includes the following steps: S210, based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation based on the Reynolds-averaged Navier-Stokes equations and the shear stress transport k-ω turbulence model; S220 extracts the flow field physical field characteristic data and corresponding operating parameters for each operating condition.

[0009] Optionally, the flow field physical field characteristic data includes scalar and vector field data of pressure field, velocity field, turbulent kinetic energy, and turbulent dissipation rate, and the corresponding operating parameters include secondary flow intensity, flow separation region area, and entropy production rate distribution.

[0010] Optionally, step S40 includes the following steps: S410 selects a basic network architecture based on attention mechanisms and graph neural networks; S420, Based on the aforementioned basic network architecture, design the network structure of the deep multimodal neural network model; S430, construct a deep multimodal neural network model; S440, using the multimodal feature representation as input, and the flow field physical field feature data and corresponding operating parameters under each operating condition as supervision labels, learns the nonlinear mapping relationship from impeller geometry and operating condition to full operating condition performance index, thereby training the deep multimodal neural network model.

[0011] Optionally, the comprehensive optimization function F is defined as follows: F=w1·(1-ηavg)+w2·ση+w3·(1 / Hopt)+w4·NPSHr Where w1, w2, w3, and w4 are all weighting coefficients, ηavg is the average efficiency under all operating conditions, ση is the standard deviation of efficiency under all operating conditions, Hopt is the design head under operating conditions, and NPSHr is the required net positive suction head. Optionally, the manufacturing constraints include minimum blade thickness tmin, maximum blade twist angle θmax, and minimum fillet radius rmin.

[0012] Furthermore, to achieve the above objectives, this application also provides a centrifugal pump impeller optimization device for high-efficiency operation under all working conditions, the device comprising: The parametric modeling and design space generation module is used to construct a three-dimensional parametric model of the impeller based on a non-uniform rational B-spline surface, define geometric design variables and their constraint boundaries, and generate an initial design sample set. The multi-condition computational fluid dynamics simulation and flow field feature extraction module is used to perform high-fidelity computational fluid dynamics simulation on each impeller model in the initial design sample set within a preset full-condition flow range, and extract multi-dimensional flow field physical field data characterizing the flow characteristics. The multimodal data fusion and feature encoding module is used to receive the geometric design variables, the multidimensional flow field physical field data and operating parameters, and also to generate a unified-dimensional multimodal feature vector through heterogeneous data alignment and feature transformation. The deep multimodal performance prediction model module is used to construct a deep network based on attention mechanism and graph neural network, and to interactively fuse and nonlinearly map the multimodal feature vectors to output the performance prediction index of the impeller under all working conditions. It is also used to decode through a multilayer perceptron to output the performance prediction index vector under all working conditions. The multi-objective optimization and constraint processing module is used to construct a comprehensive performance objective function covering all working conditions based on the performance prediction index, and integrate manufacturing process constraints to drive the global optimization algorithm to search for impeller geometric parameters. The engineering feasibility verification and output module is used to perform three-dimensional model reconstruction, mesh independence verification and interference check on the impeller geometric parameters, and generate engineering drawings and process documents that can be directly used for manufacturing.

[0013] Optionally, in the parametric modeling and design space generation module, the constraint boundaries of the geometric design variables include β1, β2 and Z, wherein the value range of β1 is 15° to 30°, the value range of β2 is 20° to 40°, and the value range of Z is 5 to 9.

[0014] Optionally, in the deep multimodal performance prediction model module, the full-condition performance prediction index vector includes the design condition efficiency ηopt, the full-condition average efficiency ηavg, the full-condition efficiency standard deviation ση, the design condition head Hopt, and the required net positive suction head NPSHr.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: The centrifugal pump impeller optimization method provided in this application embodiment deeply integrates multimodal data of geometry, flow field, operating conditions and performance, and uses a network framework based on attention mechanism for feature interaction to construct a high-fidelity and strong generalization performance prediction proxy model, which significantly improves the model's accuracy and physical consistency in capturing the nonlinear relationship between impeller geometric micro-variations and complex flow.

[0016] This application innovatively incorporates multiple performance indicators (such as average efficiency, efficiency standard deviation, head, and net positive suction head) across the entire operating flow range into the optimization objective function, thereby achieving proactive design of the impeller's "high-efficiency zone" width and stability, effectively solving the problem of sharp performance drop under varying operating conditions in traditional methods.

[0017] The embodiments of this application explicitly integrate manufacturing process constraints such as minimum blade thickness, maximum twist angle, and minimum fillet radius in the optimization cycle, ensuring that the optimized impeller design not only has excellent simulation performance, but also good engineering feasibility and manufacturability. Attached Figure Description

[0018] Figure 1 A flowchart illustrating the method for optimizing the impeller of a centrifugal pump operating efficiently under all conditions, as provided in the embodiments of this application; Figure 2 This is a schematic diagram of the core principle framework of the deep multimodal performance prediction model provided in the embodiments of this application; Figure 3 This is a logical flowchart of the parametric modeling and design space generation, multi-condition computational fluid dynamics simulation and flow field feature extraction provided in the embodiments of this application; Figure 4 This is a schematic diagram of the multi-level interaction and data flow of the multimodal data fusion and feature encoding, and the deep multimodal performance prediction model provided in the embodiments of this application; Figure 5 This is a logical flowchart of the multi-objective optimization and constraint processing, engineering feasibility verification and output provided in the embodiments of this application; Figure 6 A structural block diagram of the centrifugal pump impeller optimization device for high-efficiency operation under all working conditions provided in the embodiments of this application.

[0019] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0020] It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the application. Rather, these embodiments are provided to make the disclosure more thorough and complete, and to fully convey the scope of the disclosure to those skilled in the art.

[0021] To address the aforementioned technical problems, this application provides a method for optimizing the impeller of a centrifugal pump operating efficiently under all conditions, such as... Figure 1 As shown, the method may include the following steps: S10, based on parametric modeling technology, defines the geometric design variables and feasible domain of the centrifugal pump impeller, and generates an initial impeller geometry sample set covering the design space.

[0022] The geometric design variables include the blade inlet angle β1, the blade outlet angle β2, the blade wrap angle φ, the number of blades Z, the hub diameter Dh, the hub cover diameter Ds, and the blade thickness distribution function f(t).

[0023] Specifically, an initial impeller geometry sample set covering the design space is generated through Latin hypercube sampling. The steps for generating the sample set are as follows: Stratification: Divide the value range of each design variable into N intervals evenly, where N is the required number of samples; Random sampling: Randomly select a value within each interval of each design variable; Permutation and combination: Arrange and combine the sampled values ​​of different design variables to form N sample points; The sample points generated by the above process are combined into an initial impeller geometry sample set.

[0024] In this embodiment, the feasible region refers to the range of values ​​that the design variables can take. These ranges define a multidimensional space where each point represents a set of possible design solutions. For the geometric design variables of a centrifugal pump impeller, the feasible region is typically determined based on the following factors: Physical constraints: The values ​​of design variables must be physically feasible. For example, the impeller diameter cannot be infinitely large and must fit the pump housing and system layout.

[0025] Performance requirements: The design must meet certain performance standards, such as efficiency, head, and flow rate requirements. Some designs may be numerically feasible but fail to meet performance requirements and are therefore excluded from the feasible region.

[0026] Manufacturing constraints: The design must take into account manufacturing feasibility, including material availability, processing capabilities, and cost-effectiveness.

[0027] Operating conditions: The design must be adapted to the operating environment, such as temperature, pressure and media characteristics.

[0028] S20, based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation within the full operating range from 0.6 times to 1.4 times the design flow rate, and extract the flow field physical field characteristic data and corresponding operating parameters for each operating condition.

[0029] In an exemplary embodiment, step S20 may include the following steps: S210, based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation based on the Reynolds-averaged Navier-Stokes equations and the shear stress transport k-ω turbulence model; S220 extracts the flow field physical field characteristic data and corresponding operating parameters for each operating condition.

[0030] The flow field physical field characteristic data includes scalar and vector field data of pressure field, velocity field, turbulent kinetic energy, and turbulent dissipation rate, and the corresponding operating parameters include secondary flow intensity, flow separation region area, and entropy production rate distribution.

[0031] S30, the geometric design variables, the flow field physical field characteristic data and the corresponding operating parameters are preprocessed, and the preprocessed data are fused into a unified multimodal feature representation through an encoding network.

[0032] Specifically, preprocessing includes standardization and feature alignment. Standardization can be achieved using Z-score standardization (which transforms the data into a distribution with a mean of 0 and a standard deviation of 1) or Min-Max standardization (which linearly maps the data to the [0, 1] interval). Feature alignment uses interpolation or resampling methods to align data from different modalities in time and space.

[0033] S40, Construct a deep multimodal neural network model and train the deep multimodal neural network model.

[0034] In an exemplary embodiment, step S40 may include the following steps: S410 selects a basic network architecture based on attention mechanisms and graph neural networks; S420, Based on the aforementioned basic network architecture, design the network structure of the deep multimodal neural network model; S430, construct a deep multimodal neural network model; S440, using the multimodal feature representation as input, and the flow field physical field feature data and corresponding operating parameters under each operating condition as supervision labels, learns the nonlinear mapping relationship from impeller geometry and operating condition to full operating condition performance index, thereby training the deep multimodal neural network model.

[0035] S50, based on the trained deep multimodal neural network model, constructs a comprehensive optimization function with the objectives of maximizing average efficiency under all working conditions, minimizing efficiency fluctuations, meeting head requirements, and achieving excellent cavitation performance. It also integrates manufacturing constraints and uses a Bayesian optimization algorithm to perform global optimization within the feasible domain of the geometric design variables, outputting the impeller geometric parameter combination. Specifically, the comprehensive optimization function F is defined as follows: F=w1·(1-ηavg)+w2·ση+w3·(1 / Hopt)+w4·NPSHr Where w1, w2, w3, and w4 are all weighting coefficients, ηavg is the average efficiency under all operating conditions, ση is the standard deviation of efficiency under all operating conditions, Hopt is the design head under operating conditions, and NPSHr is the required net positive suction head. Furthermore, the manufacturing constraints include minimum blade thickness tmin, maximum blade twist angle θmax, and minimum fillet radius rmin.

[0036] S60, based on the output impeller geometric parameter combination, performs three-dimensional model reconstruction and engineering feasibility verification, and generates manufacturing data files that can be directly used for CNC machining or 3D printing.

[0037] Next, taking a specific scenario of energy-saving renovation of a secondary water supply pump station in a municipal water supply network as an example, the steps of the above embodiments will be elaborated and described in detail with data to demonstrate the completeness, operability and significant technical effects of the method of the present invention.

[0038] A city's water supply company's secondary booster pump station relies on multi-stage centrifugal pumps, the core equipment of which requires variable frequency drive (VFD) adjustments based on peak and off-peak water usage throughout the year. The operating flow rate frequently varies between 0.7 and 1.3 times the design flow rate. The existing impeller is an early design; while its efficiency is acceptable at the design point, it drops by more than 8% under low load conditions, resulting in low overall operating efficiency and high electricity costs throughout the year. The project aims to apply the method of this invention to design a new impeller that significantly expands the high-efficiency operating range and reduces average energy consumption across all operating conditions, without reducing the design head.

[0039] In step S10, the project team first clarified the basic design parameters of the target pump: a design flow rate of 300 cubic meters per hour, a design head of 80 meters, a rotational speed of 2950 revolutions per minute, and the conveying medium being ambient temperature clean water. Based on this, parametric modeling technology was used to precisely define the geometric design variables of the impeller. In addition to the seven main variables described in Example 1, considering the high cavitation performance requirements of the first-stage impeller of this multi-stage pump, additional blade inlet angle of attack correction coefficients and blade leading edge profile parameters were added as design variables to more precisely control the inlet flow state. The feasible domains of all nine variables were determined after repeated calibration based on the original impeller measurement dimensions and the accuracy and stroke of existing processing equipment. Using the optimal Latin hypercube sampling method, an initial impeller geometry sample set containing 180 samples was generated within this 9-dimensional design space, fully ensuring the breadth and uniformity of the design space exploration.

[0040] Step S20: For these 180 samples, high-fidelity computational fluid dynamics simulations were performed at 7 operating points within a full operating range from 0.65 to 1.35 times the design flow rate. The simulation used a coupled solver, and the medium properties were set as clean water. To ensure the reliability of the simulation results as the "gold standard," each simulation case underwent rigorous mesh independence verification before submission: three sets of meshes (coarse, medium, and fine) were used for simulation. When the difference in key indicators (such as efficiency and head) between the medium and fine meshes was less than 0.5%, the results of the medium mesh were considered reliable. After the simulation, not only were the fundamental physical fields such as the pressure field and velocity field extracted globally, but special attention was also paid to extracting depth feature data closely related to cavitation initiation and flow separation, such as the low-pressure zone volume in the impeller inlet region, the momentum thickness distribution of the boundary layer on the blade suction surface, and the location of the vortex core within the blade passage, under each operating condition. This formed a set of highly dimensional and information-rich flow field feature datasets.

[0041] Step S30 involves data fusion and encoding. Geometric variables are encoded as 9-dimensional vectors. The flow field feature data exceeds one million dimensions; principal component analysis (PCA) is used for dimensionality reduction, retaining the top 80 principal components with a cumulative contribution rate exceeding 95% as flow field feature vectors. This significantly reduces data dimensionality while preserving most of the information. Operating parameters, namely flow rate and rotational speed, are encoded as 2-dimensional vectors. A three-layer projection network is used to uniformly map the dimensions of the geometric, flow field, and operating condition feature vectors to 256 dimensions, and then concatenates them to generate the final unified multimodal feature representation.

[0042] Step S40: Construct and train a deep multimodal neural network model. The model architecture adopts a hybrid network with a graph attention network as the backbone and residual connections to alleviate the gradient vanishing problem in deep network training. During training, the simulation data of 180 samples is divided into training, validation, and test sets in an 8:1:1 ratio. An adaptive moment estimation algorithm is used as the optimizer, with an initial learning rate set to 0.001 and dynamically adjusted using a cosine annealing strategy. During training, in addition to the mean squared error loss function, a physical consistency constraint loss based on the pump's fundamental energy equation is introduced. For example, it requires that the predicted head, flow rate, and efficiency satisfy an approximate relationship to improve the model's physical interpretability and generalization ability outside the training data distribution. After sufficient training, the model's mean absolute error in predicting the average efficiency under all operating conditions on an independent test set is less than 0.4%, and the prediction error in predicting the required net positive suction head (NPSH) is less than 0.3%, fully meeting the accuracy requirements of engineering optimization for surrogate models.

[0043] Step S50: Automated global optimization is performed based on the comprehensive optimization function. The definition of the comprehensive optimization function has been shown in the above embodiment and will not be repeated here. The design head requirement is 80 meters, and is a penalty factor. When the predicted head is lower than 78 meters, this factor generates a large penalty value to ensure that the head meets the basic requirement. In addition to the constraints described in Embodiment 1, the manufacturing constraints also include a "minimum passivation thickness at the blade exit edge" constraint to adapt to silt wear during long-term operation. The optimization algorithm adopts Bayesian optimization, using a pre-trained high-precision neural network model as a surrogate model, with the expected improvement as the acquisition function, to perform efficient search within the 9-dimensional design space. The Bayesian optimization algorithm models the objective function through a Gaussian process and achieves a balance between exploration and utilization. After 250 iterations, the algorithm finds an optimal solution on the Pareto front. The predicted performance corresponding to this solution is: a 1.2% increase in design point efficiency, a 2.5% increase in average efficiency under all operating conditions, a 40% reduction in the standard deviation of efficiency under all operating conditions, and a 0.5% reduction in required net positive suction head (NPSH).

[0044] Specifically, the steps for Gaussian process modeling are as follows: A Gaussian process is a nonparametric Bayesian method used for regression and classification. It probabilistically models the objective function. A Gaussian process is defined by the mean function m(x) and the covariance function (also known as the kernel function) k(x,x′), i.e., f(x). GP(m(x),k(x,x′)).

[0045] Step S60 involves engineering implementation and effect verification. The optimized parameters are reconstructed in three dimensions, and machining code is generated. The new impeller is manufactured using stainless steel precision casting. It is assembled into the original pump for actual testing. Performance test results show that under the design flow rate of 300 cubic meters per hour, the efficiency reaches 86.5%, an improvement of 1.1% compared to the original impeller; under a low load of 210 cubic meters per hour, the efficiency reaches 83.2%, an improvement of 3.8% compared to the original impeller; and the efficiency curve becomes significantly flatter across the entire test flow range. Based on simulation calculations using the pump house's annual operating data, it is estimated that the application of the new impeller will save 4.7% of electricity annually, demonstrating significant economic benefits. This case fully demonstrates the effectiveness and engineering practical value of the method of this invention in the synergistic optimization of performance under all operating conditions.

[0046] In the above exemplary embodiments, by deeply fusing multimodal data of geometry, flow field, operating conditions and performance, and using a network framework based on attention mechanism for feature interaction, a high-fidelity and strong generalization performance prediction proxy model is constructed, which significantly improves the model's accuracy and physical consistency in capturing the nonlinear relationship between impeller geometry micro-variation and complex flow.

[0047] The above embodiments innovatively incorporate multiple performance indicators (such as average efficiency, efficiency standard deviation, head, and net positive suction head) within the full operating flow range (0.6Qopt to 1.4Qopt) into the optimization objective function, realizing the proactive design of the impeller's "high-efficiency zone" width and stability, and effectively solving the problem of sharp performance drop under varying operating conditions in traditional methods.

[0048] The above embodiments explicitly integrate manufacturing process constraints such as minimum blade thickness, maximum twist angle, and minimum fillet radius in the optimization cycle, ensuring that the optimized impeller design not only has excellent simulation performance, but also good engineering feasibility and manufacturability.

[0049] Based on the above embodiments, refer to Figure 6 Another embodiment of this application also provides a centrifugal pump impeller optimization device for high-efficiency operation under all operating conditions, which may include the following modules: The parametric modeling and design space generation module is used to construct a three-dimensional parametric model of the impeller based on a non-uniform rational B-spline surface, define geometric design variables and their constraint boundaries, and generate an initial design sample set. This initial design sample set is generated within the design space through Latin hypercube sampling; the specific generation steps have been described in detail in the above embodiments and will not be repeated here. The number of samples N satisfies N≥10×k, where k is the dimension of the design variables. The multi-condition computational fluid dynamics simulation and flow field feature extraction module is used to perform high-fidelity computational fluid dynamics simulation on each impeller model in the initial design sample set within a preset full-condition flow range, and extract multi-dimensional flow field physical field data characterizing the flow characteristics. The multimodal data fusion and feature encoding module is used to receive the geometric design variables, the multidimensional flow field physical field data and operating parameters, and also to generate a unified-dimensional multimodal feature vector through heterogeneous data alignment and feature transformation. The deep multimodal performance prediction model module is used to construct a deep network based on attention mechanism and graph neural network, and to interactively fuse and nonlinearly map the multimodal feature vectors to output the performance prediction index of the impeller under all working conditions. It is also used to decode through a multilayer perceptron to output the performance prediction index vector under all working conditions. The multi-objective optimization and constraint processing module is used to construct a comprehensive performance objective function covering all working conditions based on the performance prediction index, and integrate manufacturing process constraints to drive the global optimization algorithm to search for impeller geometric parameters. The engineering feasibility verification and output module is used to perform three-dimensional model reconstruction, mesh independence verification and interference check on the impeller geometric parameters, and generate engineering drawings and process documents that can be directly used for manufacturing.

[0050] In the parametric modeling and design space generation module, the constraint boundaries of the geometric design variables include β1, β2 and Z, wherein the value range of β1 is 15° to 30°, the value range of β2 is 20° to 40°, and the value range of Z is 5 to 9.

[0051] Furthermore, in the deep multimodal performance prediction model module, the full-condition performance prediction index vector includes the design condition efficiency ηopt, the full-condition average efficiency ηavg, the full-condition efficiency standard deviation ση, the design condition head Hopt, and the required net positive suction head NPSHr.

[0052] The workflow of each module in the above embodiments will be described in detail below: First, the parametric modeling and design space generation module begins operation. The core of this module is to establish a high-precision, fully parametric 3D geometric model of the impeller. This module employs non-uniform rational B-spline surface technology, using blade profiles, hub profiles, shroud profiles, and blade wrap angles as the basic control framework to construct the 3D solid model of the impeller.

[0053] Based on this model, the parametric modeling and design space generation module defines seven core geometric design variables: blade inlet angle, used to optimize the angle of attack of fluid entering the impeller and reduce inlet impact and backflow losses; blade outlet angle, which directly affects the pump's head characteristics and the uniformity of outlet flow; blade wrap angle, which determines the degree of fluid turning and the work path within the flow channel; number of blades, affecting the number of flow channel segments and the load per blade; hub diameter and wheel cover diameter, which together define the radial dimension range of the flow channel inlet and outlet; and a parametric blade thickness distribution function, used to accurately describe the thickness variation of the blade from the inlet edge to the outlet edge, and from the pressure surface to the suction surface, to meet strength and flow requirements. Each design variable has strict numerical constraints based on industry hydraulic design standards, material mechanical properties, and the technological capabilities of five-axis CNC machining centers. For example, the blade inlet angle is limited to a range of 15 to 30 degrees, the blade outlet angle to a range of 20 to 40 degrees, and the number of blades to a range of 5 to 9. These boundaries collectively define a high-dimensional, continuous, and bounded geometric design space.

[0054] To systematically explore the design space, the parametric modeling and design space generation module employs the optimal Latin hypercube sampling method to generate an initial design sample set with excellent space-filling characteristics within the multidimensional space bounded by the aforementioned constraint boundaries. The sampling strategy follows an engineering rule of thumb: the total number of samples should be no less than 10 times the dimension of the design variables. Assuming that the aforementioned seven main geometric variables are considered in this embodiment, the initial sample set is set to 100. The sampling process ensures that each design variable is uniformly sampled within its value range, and that the projection of all sample points in the multidimensional space is uniformly distributed, avoiding overly dense or sparse samples in local areas. For each sampling point, i.e., a specific combination of geometric parameters, the module automatically calls the built-in computer-aided design kernel to generate the corresponding impeller 3D solid model file in real time and stores it in a standard format, providing accurate geometric input for subsequent simulation analysis. See also... Figure 3 This process clearly demonstrates the logical chain from parameter definition and spatial sampling to 3D model generation.

[0055] Subsequently, the multi-condition computational fluid dynamics simulation and flow field feature extraction module performed a comprehensive fluid dynamics performance evaluation on the aforementioned 100 initial impeller samples. This module pre-defined a typical full-condition flow range covering the pump's actual operating conditions, from 0.6 times the design flow rate to 1.4 times the design flow rate. For each impeller sample, the module selected at least five representative operating points within this flow range for high-fidelity numerical simulations, typically including points at 0.6, 0.8, 1.0, 1.2, and 1.4 times the design flow rate. The simulation was based on the Reynolds-averaged Navier-Stokes governing equations and employed a shear stress transport turbulence model to accurately capture the complex turbulent flow, flow separation, and vortex structures within the impeller. The calculations included the complete inlet extension, impeller flow channel, volute, and outlet extension. A high-quality structured hexahedral mesh was used, with multi-layered refinement in the near-wall region to meet the wall resolution requirements of the turbulence model and ensure the accuracy of the simulation results.

[0056] After the simulation converges, the multi-condition computational fluid dynamics simulation and flow field feature extraction module does not merely record macroscopic performance indicators such as efficiency and head, but delves into the internal flow field to extract multi-dimensional, high-resolution raw data of the flow field physics. This data constitutes a "fingerprint" characterizing the complex flow properties inside the impeller, including: the static pressure scalar field, three-dimensional velocity vector field, turbulent kinetic energy scalar field, and turbulent dissipation rate scalar field on all grid nodes throughout the computational domain. Furthermore, through specialized post-processing algorithms, the module further extracts more engineering-physically significant derived features from the raw field data: for example, by calculating the velocity moment at the mid-section of the impeller channel, the intensity of the secondary flow within the impeller channel is quantified; by identifying regions where the velocity direction is opposite to the mainstream direction, the area of ​​the flow separation region is marked and calculated; based on entropy production theory, the local entropy production rate distribution cloud map caused by viscous friction and turbulent dissipation within the impeller channel is calculated to accurately assess flow losses. All these flow field data, along with the corresponding operating parameters, are structured and stored in a high-performance database. See also Figure 3 This module completes the entire process from geometric model input, multi-condition simulation settings, numerical solution calculation to flow field feature extraction and storage.

[0057] Next, the multimodal data fusion and feature encoding module is responsible for processing the heterogeneous data from the first two modules. This module receives three types of data input: first, numerical vectors of geometric design variables from the parametric modeling module; second, multi-dimensional flow field physical field data from the simulation module; and third, operating parameters characterizing the operating conditions. These three types of data differ in dimension, scale, and physical meaning, and must be aligned and deeply fused. The module first performs data standardization to eliminate the influence of different physical scales. For geometric design variables, they are directly encoded into a fixed-length numerical vector. For high-dimensional, unstructured flow field data, the module uses a lightweight 3D convolutional neural network for automatic feature extraction. This network takes the flow field physical field data as input and, through multiple 3D convolutional and pooling layers, gradually abstracts feature maps that characterize key physical phenomena such as flow instability, separation vortices, and high-loss regions, ultimately flattening them into a fixed-dimensional flow field feature vector. The operating parameters are directly encoded into a two-dimensional vector. Thus, the three modalities of data are transformed into three feature vectors with different dimensions.

[0058] To achieve deep interaction, the module uses a shared fully connected projection layer to map the three feature vectors of different dimensions into a unified feature semantic space with the same dimensions. The weights of the projection layer are learned and optimized during model training, aiming to align features from different modalities in a unified semantic space, enabling effective comparison and fusion of information on geometry, internal flow details, and external operating conditions. The projected features are then concatenated to generate a unified multimodal feature vector. This vector deeply integrates geometric information, internal flow details, and external operating condition information, providing a comprehensive and consistent data foundation for subsequent performance prediction. See also... Figure 4 This process demonstrates the data flow path of heterogeneous data being encoded, projected, and finally fused into a unified feature representation.

[0059] The deep multimodal performance prediction model module is the intelligent core of the entire system. Its task is to establish a precise and rapid nonlinear mapping relationship from multimodal characteristics of "geometry-flow field-operating conditions" to "full-condition performance indicators," replacing time-consuming computational fluid dynamics simulations and providing millisecond-level speed for optimization iterations. See also... Figure 2This module constructs a deep network model based on an attention mechanism and a graph neural network. The network treats each feature element in the generated multimodal feature vector as a graph node. The connections between nodes are not fully connected, but dynamically constructed based on the physical correlation or cosine similarity between features. For example, a strong connection is established between a geometric feature node representing the blade outlet angle and a flow field feature node representing the uniformity of the velocity field near the impeller outlet; similarly, a connection is established between a node representing a specific flow condition and a node representing the pressure distribution characteristics inside the impeller under that condition.

[0060] The core computational layer of the network is the cross-modal attention layer. For each pair of connected nodes in the graph, the attention mechanism calculates an attention coefficient to quantify the degree of attention the target node pays to each neighbor node when aggregating its neighbor information. The calculation of the attention coefficient follows a standardized process: First, the features of the target node and its neighbor nodes are mapped using a shared linear transformation matrix; then, the two mapped feature vectors are concatenated and a scalar attention score is calculated using a single-layer feedforward neural network; finally, a function is used to normalize the attention scores of all neighbors of the target node to obtain the final attention coefficient. This coefficient is dynamic and related to the input feature content. Through the stacking of multiple layers of such graph attention networks, the features of each node iteratively aggregate the information of its neighbor nodes, thereby achieving deep interaction and information complementarity between geometric features, flow field features, and operating condition features. After multiple layers of information transmission and aggregation, the updated features of all nodes are collected and fed into a multilayer perceptron for decoding, ultimately outputting a performance prediction index vector. This vector includes five key performance indicators: design operating efficiency, average efficiency across the entire operating range, standard deviation of efficiency across the entire operating range, design operating head, and required net positive suction head (NPSH).

[0061] Training the deep network model is a supervised learning process. The training data comes from the aforementioned steps: 100 initial samples and real performance data obtained from computational fluid dynamics simulations under full operating conditions are used as supervision labels. The loss function is defined as the mean squared error between the predicted performance index vector and the real simulation performance index vector. All parameters in the network are optimized using the backpropagation algorithm, enabling the model to autonomously learn from massive amounts of data how minute changes in impeller geometry affect macroscopic external properties through complex internal flow field responses. After training, the model becomes a high-fidelity surrogate model, with prediction accuracy comparable to computational fluid dynamics simulations, but with a single evaluation time reduced from hours to milliseconds, providing crucial speed assurance for subsequent optimization iterations.

[0062] The multi-objective optimization and constraint handling module performs global optimization based on a pre-trained deep network model. This module first constructs a comprehensive performance objective function, aiming to simultaneously optimize multiple competing and even contradictory performance indicators. The objective function is defined as a weighted sum of four sub-objectives: 1) maximizing the average efficiency under all operating conditions; 2) minimizing the standard deviation of the efficiency under all operating conditions to ensure stability under different flow rates; 3) meeting the design head requirements; and 4) minimizing the required net positive suction head (NPSH) to improve the pump's cavitation resistance. Mathematically, the maximization problem is transformed into a minimization problem by taking the reciprocal or a negative sign, ultimately forming a scalarized comprehensive objective function. The weight coefficients of each sub-objective are set by engineers with at least 10 years of experience in weight coefficient evaluation, based on the priority of the specific engineering project.

[0063] The entire optimization process must be conducted under strict manufacturing process and engineering feasibility constraints. These constraints are explicitly and seamlessly integrated into the optimization algorithm, including: minimum blade thickness constraints to ensure sufficient structural strength to withstand fluid loads during operation; maximum blade torsion angle constraints to prevent difficulties in five-axis CNC machining or defects during precision casting due to excessive distortion of the blade's three-dimensional shape; and minimum fillet radius constraints at the connection between the blade and the hub / cover to prevent stress concentration and ensure the accessibility of machining tools. The module employs an improved non-dominated sorting genetic algorithm as the optimization engine. This algorithm uses the aforementioned deep multimodal performance prediction model as a fast evaluation tool, the feasible region of geometric design variables as the search space, and minimizes the comprehensive objective function as the guide, evolving in parallel a population consisting of hundreds of design schemes. In each generation of evolution, the algorithm generates new design scheme offspring through genetic operations such as selection, crossover, and mutation, quickly predicts their performance using a surrogate model, and performs non-dominated sorting and crowding calculation on all schemes based on the objective function value and the degree of constraint violation, selecting excellent individuals to enter the next generation. After hundreds of generations of iterative evolution, the algorithm eventually converges to a Pareto optimal solution set. Each solution in this set, under the current constraints, cannot be further optimized on one objective without compromising other objectives. Engineers can then select a final optimal combination of impeller geometry parameters from this solution set based on practical engineering preferences. See also... Figure 5 This module clearly depicts the complete process from defining the objective and constraints, iterative evolution of the optimization algorithm, to outputting the optimal parameter set.

[0064] Finally, the engineering feasibility verification and output module is responsible for transforming the optimal parameter combination obtained in the "digital world" into a manufacturable and assemblable physical part in the "physical world." The module first receives the optimal geometric parameter combination and drives the computer-aided design software kernel to automatically reconstruct the corresponding 3D solid model. Subsequently, a series of rigorous engineering verifications are performed on this 3D model: first, mesh independence verification, using three sets of meshes with different densities to verify the model through computational fluid dynamics simulation, confirming that its key performance prediction results do not change significantly with further mesh refinement, thus ensuring the numerical reliability of the optimization results; second, static and dynamic interference checks, importing the impeller model into a complete pump assembly model containing components such as the pump casing, sealing ring, shaft, and bearings, checking for interference risks between the impeller in a static assembly state and under dynamic factors such as thermal expansion and stress deformation. After all verifications pass, the module automatically generates 2D engineering drawings conforming to national or international standards, including all necessary dimensions, dimensional and geometric tolerances, surface roughness requirements, and necessary sectional views and enlarged details. Simultaneously, the module outputs a 3D model file and a detailed process instruction manual. This manual clearly outlines the machining steps, recommended tool types and specifications, cutting parameters, and methods and key points for detecting critical dimensions. These output files can be directly transferred to CNC machining centers or additive manufacturing equipment used for 3D printing to initiate the physical manufacturing process.

[0065] In the description of this application, it should be noted that the terms "first", "second", and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0066] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0067] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the coupling or direct coupling or communication connection shown or discussed may be through some communication interface; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0068] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0069] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0070] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0071] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the technical scope disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the protection scope of this application. Therefore, the protection scope of this application should be determined by the protection scope of the claims.

[0072] Furthermore, although the operations of the method of this application are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

Claims

1. A method for optimizing the impeller of a centrifugal pump operating efficiently under all conditions, characterized in that, The method includes the following steps: S10, based on parametric modeling technology, defines the geometric design variables and feasible domain of the centrifugal pump impeller, and generates an initial impeller geometry sample set covering the design space; S20, based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation, and extract the flow field physical field characteristic data and corresponding operating parameters under each working condition; S30, preprocess the geometric design variables, the flow field physical field characteristic data and the corresponding operating parameters, and fuse the preprocessed data into a unified multimodal feature representation through an encoding network; S40, Construct a deep multimodal neural network model and train the deep multimodal neural network model; S50, based on the trained deep multimodal neural network model, constructs a comprehensive optimization function, integrates manufacturing constraints, and uses a Bayesian optimization algorithm to perform global optimization within the feasible domain of the geometric design variables, outputting the impeller geometric parameter combination; S60, based on the output impeller geometric parameter combination, performs three-dimensional model reconstruction and engineering feasibility verification, and generates manufacturing data files that can be directly used for CNC machining or 3D printing.

2. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 1, characterized in that, The geometric design variables include blade inlet angle β1, blade outlet angle β2, blade wrap angle φ, number of blades Z, hub diameter Dh, hub cover diameter Ds, and blade thickness distribution function f(t).

3. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 1, characterized in that, Step S20 includes the following steps: S210, Based on each sample in the initial impeller geometry sample set, perform high-fidelity computational fluid dynamics numerical simulation based on the Reynolds-averaged Navier-Stokes equations and the shear stress transport k-ω turbulence model; S220 extracts the physical field characteristics of the flow field and the corresponding operating parameters for each operating condition.

4. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 3, characterized in that, The physical field characteristic data of the flow field includes scalar and vector field data of pressure field, velocity field, turbulent kinetic energy, and turbulent dissipation rate. The corresponding operating parameters include secondary flow intensity, flow separation region area, and entropy production rate distribution.

5. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 1, characterized in that, Step S40 includes the following steps: S410 selects a basic network architecture based on attention mechanisms and graph neural networks; S420, Based on the aforementioned basic network architecture, design the network structure of the deep multimodal neural network model; S430, construct a deep multimodal neural network model; S440, using the multimodal feature representation as input, and the flow field physical field feature data and corresponding operating parameters under each operating condition as supervision labels, learns the nonlinear mapping relationship from impeller geometry and operating condition to full operating condition performance index, thereby training the deep multimodal neural network model.

6. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 1, characterized in that, The comprehensive optimization function F is defined as follows: F=w1·(1-ηavg)+w2·ση+w3·(1 / Hopt)+w4·NPSHr Where w1, w2, w3, and w4 are all weighting coefficients, ηavg is the average efficiency under all operating conditions, ση is the standard deviation of efficiency under all operating conditions, Hopt is the design head under operating conditions, and NPSHr is the required net positive suction head.

7. The method for optimizing the impeller of a centrifugal pump operating at high efficiency under all conditions according to claim 1, characterized in that, The manufacturing constraints include minimum blade thickness tmin, maximum blade twist angle θmax, and minimum fillet radius rmin.

8. A centrifugal pump impeller optimization device for high-efficiency operation under all working conditions, characterized in that, include: The parametric modeling and design space generation module is used to construct a three-dimensional parametric model of the impeller based on a non-uniform rational B-spline surface, define geometric design variables and their constraint boundaries, and generate an initial design sample set. The multi-condition computational fluid dynamics simulation and flow field feature extraction module is used to perform high-fidelity computational fluid dynamics simulation on each impeller model in the initial design sample set within a preset full-condition flow range, and extract multi-dimensional flow field physical field data characterizing the flow characteristics. The multimodal data fusion and feature encoding module is used to receive the geometric design variables, the multidimensional flow field physical field data and operating parameters, and also to generate a unified-dimensional multimodal feature vector through heterogeneous data alignment and feature transformation. The deep multimodal performance prediction model module is used to construct a deep network based on attention mechanism and graph neural network, and to interactively fuse and nonlinearly map the multimodal feature vectors to output the performance prediction index of the impeller under all working conditions. It is also used to decode through a multilayer perceptron to output the performance prediction index vector under all working conditions. The multi-objective optimization and constraint processing module is used to construct a comprehensive performance objective function covering all working conditions based on the performance prediction index, and integrate manufacturing process constraints to drive the global optimization algorithm to search for impeller geometric parameters. The engineering feasibility verification and output module is used to perform three-dimensional model reconstruction, mesh independence verification and interference check on the impeller geometric parameters, and generate engineering drawings and process documents that can be directly used for manufacturing.

9. The centrifugal pump impeller optimization system for all operating conditions as described in claim 8, characterized in that, In the parametric modeling and design space generation module, the constraint boundaries of the geometric design variables include β1, β2 and Z, wherein the value range of β1 is 15° to 30°, the value range of β2 is 20° to 40°, and the value range of Z is 5 to 9.

10. The centrifugal pump impeller optimization system for all operating conditions as described in claim 8, characterized in that, In the deep multimodal performance prediction model module, the full-condition performance prediction index vector includes the design condition efficiency ηopt, the full-condition average efficiency ηavg, the full-condition efficiency standard deviation ση, the design condition head Hopt, and the required net positive suction head NPSHr.

Images