Impeller machine design optimization method and system based on dimension similarity principle

Abstract

The invention provides a turbomachine design optimization method and system based on a dimension similarity principle. The method comprises the steps that a dimension matrix is established based on turbomachine flow field physical quantity parameters, a constraint equation is solved, a standard orthogonal basis of scaling parameters is obtained, and the scaling parameters are generated; generating enhanced data samples based on the scaling parameters and training a neural network; and training geometric parameters, working condition parameters and space coordinates of the target turbomachinery based on the trained neural network to complete optimization. According to the method, through combination of the deep learning model and the dimension similar data enhancement method, high-accuracy physical field prediction can be obtained under the condition of few samples, so that the iterative design period of engineering fields such as turbomachinery can be remarkably shortened. The method has obvious advantages in generalization ability of cross-working-condition and cross-design-variable combination, the dependence on massive numerical simulation data is effectively reduced, and the overall efficiency of optimization design is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the field of power machinery, and in particular relates to an impeller machinery design optimization method and system based on the dimensional similarity principle. Background Art

[0002] As a core power device in fields such as energy and aviation, the optimization design of turbomachinery is a complex multidisciplinary problem involving aerodynamics and heat transfer intensity. Traditional design methods rely primarily on computational fluid dynamics (CFD) simulation and experimental verification, but these methods have significant limitations. First, CFD simulation requires high-precision meshing and long iterative calculations. This is particularly true for multi-condition, high-dimensional parameter optimization, which consumes enormous computing resources, with a single simulation taking hours or even days. Second, while optimization techniques based on surrogate models and evolutionary algorithms accelerate design space exploration, their accuracy is limited by the number of samples and they struggle to directly process relevant flow field information.

[0003] Existing deep learning-based physical field prediction models often use fully supervised learning, relying on large amounts of labeled data and resulting in significant prediction errors for out-of-distribution (OoD) samples. For example, changes in operating parameters in turbine design (such as speed and fluid properties) can easily lead to a decrease in model generalization ability, necessitating repeated retraining. Summary of the Invention

[0004] The object of the present invention is to provide a turbomachinery design optimization method and system based on the principle of dimensional similarity to solve the above problems.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a turbomachinery design optimization method based on the dimensional similarity principle, comprising:

[0007] A dimensional matrix is ​​established based on the physical parameters of the impeller machinery flow field, and the standard orthogonal basis of the scaling parameters is obtained by solving the constraint equations to generate the scaling parameters;

[0008] Generate augmented data samples based on the scaling parameters and train the neural network:

[0009] Based on the trained neural network, the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery are trained to complete the optimization.

[0010] Furthermore, the row vectors of the dimensional matrix correspond to the dimensional coefficients of each physical field, and the column vectors correspond to the four basic dimensions of mass, length, time and temperature.

[0011] Further, specific:

[0012] The analysis of the turbomachinery flow physics field is based on the Navier-Stokes equations, in which the six basic physical quantities involve four basic dimensions. The matrix S describing the basic dimensions of each physical field is as follows:

[0013]

[0014] Among them, each row of the matrix represents the dimensional coefficient of a physical field, M, L, t, T, representing the four basic dimensions of mass, length, time and temperature respectively.

[0015] Furthermore, the step of obtaining a standard orthogonal basis of the scaling parameters by solving the constraint equations and generating the scaling parameters includes:

[0016] By solving the constraint equations of the physical constants in the Navier-Stokes equations, we obtain the standard orthogonal basis of the scaling parameters. Based on the joint Gaussian distribution random sampling, we generate a set of scaling coefficients that meet the physical laws. Specifically,

[0017] For any multi-physics field sample, a reasonable similarity transformation is performed by scaling the dimensional coefficients. The dimensional scaling coefficient is set to α. At this time, the boundary conditions of the original equation also need to be scaled accordingly to maintain consistency. The uniform scaling of all physical quantities U is:

[0018]

[0019] Among them, U is the physical field related to the design object, S u Represents the dimensional matrix corresponding to the physical location; in the Navier-Stokes equation, the universal gas constant R g The dynamic viscosity coefficient μ of the working fluid should remain constant before and after the similarity transformation; the parameter α satisfies the following constraint equation.

[0020]

[0021] First solve the constraint formula S C α=0, we get its standard orthogonal basis V, through α=eV T To arbitrarily generate a dimensional scaling coefficient α with physical significance, and e is the base coefficient used to construct the parameter α, which conforms to the joint Gaussian distribution e = N (μ, ∑) by default; when selecting the specific dimensional scaling coefficient, it is necessary to randomly sample from the distribution to obtain the specific coefficient.

[0022] Furthermore, generating enhanced data samples based on the scaling parameters and training a neural network includes:

[0023] The original input and output data are denormalized, and the physical field parameters are similarly mapped using scaling coefficients to generate enhanced sample pairs that satisfy dimensional similarity. The enhanced sample pairs are input into a neural network containing a self-supervisory mechanism, and associated samples are generated by constructing two sets of scaling coefficients A and B that do not satisfy the constraints. A loss function based on dimensional similarity constraints is established, and the loss function achieves network training by comparing the dimensional consistency between the predicted outputs of the enhanced samples corresponding to the scaling coefficients A and B.

[0024] Further, specific:

[0025] The scaling factor is constructed as follows:

[0026] A=e d 1,B=e d 1+e f ·v

[0027]

[0028] Here d and e f are two random vectors used to construct augmented data, which are normally distributed, and the standard deviation of the specific distribution is given by the user. (A) and X (B) These are the two new input samples finally generated.

[0029] After obtaining the predicted output values ​​of the two samples through forward inference of the model, the loss function is established using the following formula:

[0030]

[0031] Among them, λ is the weighting coefficient of dimensional similarity loss and full supervision loss.

[0032] After determining the loss function expression based on dimensional similarity, the specific training process of the network is expressed as follows:

[0033]

[0034] in Represents the loss function defined during training.

[0035] Furthermore, the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery are input into the trained neural network, and the predicted physical field data are output. After denormalization, the predicted value of the performance index is calculated, and the optimized design of the impeller machinery across working conditions is achieved by iteratively adjusting the geometric parameters and operating parameters.

[0036] In a second aspect, the present invention provides an impeller machinery design optimization system based on the dimensional similarity principle, comprising:

[0037] A parameter collection module is used to establish a dimensional matrix based on the physical quantity parameters of the impeller machinery flow field, obtain the standard orthogonal basis of the scaling parameters by solving the constraint equations, and generate the scaling parameters;

[0038] A training module, configured to generate augmented data samples based on the scaling parameters and train a neural network:

[0039] The output module is used to train the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery based on the trained neural network to complete the optimization.

[0040] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the impeller machinery design optimization method based on the principle of dimensional similarity are implemented.

[0041] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the impeller machinery design optimization method based on the dimensional similarity principle.

[0042] Compared with the prior art, the present invention has the following technical effects:

[0043] This method achieves mechanism-driven augmentation of physical field data by constructing a dimensional matrix and corresponding scaling constraint equations. Compared to traditional sample generation methods that rely on statistical distributions, the samples generated by this method strictly adhere to the dimensional invariance of physical laws (such as the NS equations). Tests have shown that in high-dimensional scenarios such as turbine design, this method can reduce the prediction error of out-of-distribution (OoD) samples by an order of magnitude.

[0044] This paper proposes a universal self-supervised learning architecture that embeds dimensional similarity constraints into the loss function design. A dynamic constraint mechanism automatically adjusts the distribution of scaling factors, suppressing the risk of high-dimensional training crashes. This framework overcomes the limitations of traditional physics-driven models (such as PINN) that rely on equation embedding. This dimensional analysis method does not require an explicit format for specific physical equations, making it more suitable for black-box engineering design scenarios with unknown or complex mechanisms, enhancing the model's application value in real-world engineering scenarios.

[0045] By combining a deep learning model with a dimensionally similar data augmentation method, this method achieves highly accurate physical field predictions even with relatively few samples, significantly shortening the iterative design cycle in engineering fields such as turbomachinery. This method demonstrates significant advantages in generalization across operating conditions and design variable combinations, effectively reducing reliance on massive amounts of numerical simulation data and significantly improving the overall efficiency of design optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of an embodiment of the present invention.

[0047] Figure 2 Schematic diagram of the data enhancement method in network weight training of the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described below with reference to the accompanying drawings:

[0049] 1. Data enhancement based on similar dimensions

[0050] Constructing a physical dimension matrix: First, analyze the relationship between the input and output dimensions of the design object problem to facilitate subsequent data enhancement. The analysis of the impeller machinery flow physical field is generally based on the Navier-Stokes (NS) equations, in which the six basic physical quantities involve four basic dimensions. The matrix S describing the basic dimensions of each physical field is as follows:

[0051]

[0052] Each row of the matrix represents a dimensional coefficient of a physical field, for example [P] = ML -1 t -2 M, L, t, and T represent the four basic dimensions of mass, length, time, and temperature respectively.

[0053] Generate scaling parameters: For any multi-physics field sample, a reasonable similarity transformation can be performed by scaling the dimensional coefficient. Set the dimensional scaling coefficient to α. As long as the scaling coefficient of each physical quantity in the multi-physics field sample satisfies the same dimensional change, the solution obtained by the similarity transformation will still satisfy the original equation. At this time, the boundary conditions of the original equation also need to be scaled accordingly to maintain consistency. Take pressure P as an example: It is known that the dimensional matrix of pressure P is, S P =[1-1-20], α contains the components representing the size of each dimension to be scaled, that is, α = [α [M] α [L] α [t] α [T] ] T , then the scaling ratio of the physical quantity P is Scaling all physical quantities U uniformly is:

[0054]

[0055] Among them, U is the physical field related to the design object, S uRepresents the dimensional matrix corresponding to the physical location. In dimensional similarity transformations, the parameter α cannot be chosen arbitrarily; to ensure the physical meaning of the solution, certain constraints must be met. When performing dimensional scaling, the physical constants involved must remain constant. In the Navier-Stokes equations, the universal gas constant and the dynamic viscosity of the working fluid must remain constant before and after the similarity transformation. Therefore, the parameter α must satisfy the following constraint equation.

[0056]

[0057] Therefore, we need to first solve the constraint formula S C α=0, and its standard orthogonal basis V is obtained, which can be obtained by α=eV T To arbitrarily generate a physically meaningful dimensional scaling coefficient α, e is the base coefficient used to construct the parameter number α, which defaults to a joint Gaussian distribution e = N(μ,∑). When selecting a specific dimensional scaling coefficient, it is necessary to randomly sample from the distribution to obtain the specific coefficient.

[0058] Generate enhanced data samples: For an end-to-end physical field prediction problem, make sure that the input and output (X, Y) satisfy a deterministic physical relationship Y = F(X). Based on the information of (X, Y) and F(·), we can obtain the dimension matrix S of the three: X 、S Y and S C As long as an arbitrary set of parameters α is generated according to the coefficient generation method in the previous step, the input can be similarly mapped to a new and reasonable data. In the actual training process, the network often normalizes the input and output data when learning the physical field. However, normalization of physical quantity parameters will destroy the dimensional similarity relationship, so denormalization must be performed first. The complete similarity mapping function can be expressed as follows:

[0059]

[0060] A pair of known input and output (X, Y) is similarly mapped to obtain a set of new sample pairs (X * ,Y * ), and ensure that this new set of sample pairs still satisfies the physical mapping relationship F(·).

[0061] X * =sim(X,α;S x ),Y * =sim(Y,α;S Y ),Y * =F(X * )

[0062] 2. Establishment and training of neural networks

[0063] The present invention directly applies the data augmentation method established in the previous step to fully supervised training, thereby improving the diversity of training data without increasing the amount of data and without the need for. In order to make the generated self-supervised samples uniformly distributed in the boundary condition space, it is necessary to construct two scaling factors A and B. The input X of the two data augmented samples can be obtained based on the scaling factors A and B. (A) and X (B) The specific scaling factor is constructed as follows:

[0064] A=e d 1,B=e d 1+e f ·v

[0065]

[0066] It is worth noting that since parameters A and B do not satisfy the constraint S C α=0, so the physical field F(X (A) ) and F(X (B) ) cannot be obtained through a simple dimensional similarity mapping, but the two satisfy dimensional similarity. After obtaining the predicted output values ​​of the two samples through forward inference of the model, the loss function can be established using the following formula.

[0067]

[0068] After determining the loss function expression based on dimensional similarity, the specific training process of the network is expressed as follows:

[0069]

[0070] 3. Carry out optimization design tasks based on the network

[0071] For a specific power mechanical equipment under specific working conditions, the trained network can be used to Predict its physical field. After inputting the geometric parameters x, device state parameters α and predicted coordinates g, input them into the trained network to obtain the predicted physical field output Then denormalize it to get the predicted physical field tensor data of the real scale Based on the obtained physical field tensor data, the predicted values ​​of the required performance indicators can be obtained through explicit calculations

[0072] See also Figures 1 to 2 A specific implementation case of a turbomachinery design optimization method and system based on the principle of dimensional similarity in the first-stage high-pressure turbine of the GE-E3 is presented. The implementation process includes geometric parameter modeling, boundary condition sampling, CFD calculation verification, and data set construction. The specific steps are as follows:

[0073] 1. Dataset Preparation Process

[0074] Geometric space and boundary condition sampling:

[0075] The geometric model of the GE-E3 first-stage high-pressure turbine consists of four components: the stationary blades (S1), the rotating blades (R1), the endwall, and the casing. The stationary blades S1 have 46 blades, while the rotating blades R1 have 76 blades. The rotor blade tip clearance is 0.3 mm.

[0076] In geometric modeling, five parameters were assigned to each of the root, midpoint, and tip sections of each row of blades (a total of 15 parameters) to control the profile, and three parameters were used to describe the three-dimensional stacked shape of the blades. This method accurately describes the spatial configuration of the turbine's stator and rotor blades. Ultimately, a total of 36 geometric parameters were used for both rows of blades.

[0077] In addition, according to the actual operating conditions, the sampling range of boundary conditions such as inlet and outlet pressure, temperature and flow rate is set, and constraints are imposed in combination with the principle of dimensional similarity to ensure that the generated samples meet both engineering feasibility and reasonable distribution requirements for subsequent flow field prediction.

[0078] Working condition design variable definition table

[0079]

[0080]

[0081] Numerical simulation and flow field extraction: After completing the sampling of geometry and boundary conditions, CFD software is used to perform steady-state numerical simulation of a single-channel flow channel for each group of samples. In order to ensure the accuracy of the simulation, this embodiment selects a reasonable turbulence model and controls the grid density and convergence requirements. After obtaining the flow field calculation results, the meridian flow field data corresponding to each group of samples is extracted, mainly including pressure, temperature, velocity (including three components) and other auxiliary physical quantities. The meridian data is used as a training sample for input and output in the subsequent deep learning model.

[0082] 2. Determination of dimensional analysis parameters

[0083] Determine the dimensional matrices of input and output: In this embodiment, the working condition dimensions of the input parameters are 5 in total, and the output is 6 physical quantities included in the NS equation. The dimensional matrices of the input and output can be listed separately.

[0084]

[0085] Considering the constraints of the NS equation and the current geometric conditions, that is, keeping the flow channel geometry L fixed (not arbitrarily scalable), and ignoring the constraint on the viscosity coefficient in the high Reynolds number range, the constraints will be adjusted according to the specific needs of this embodiment. Finally, a separate dimensional constraint is added to the length L, and the viscosity coefficient constraint is removed. The resulting dimensional constraint equation can be expressed as

[0086]

[0087] In this embodiment, the training set distribution variance of 5% is selected as e f With e d The default variance of ensures that the actual scaling range of the physical quantity does not deviate too much from this numerical range.

[0088] 3. Construction and training of deep learning models

[0089] Network Structure and Pre-training: This example uses a convolutional neural network with a UNet structure to perform physical field prediction. The specific network structure is shown in the table below. The network is pre-trained in a fully supervised manner using all training data to obtain a baseline model.

[0090] Network Module Output scale Input 4096×(28+2) Conv2d+ResBlock 4096×30 Conv2d×2 4096×64 ResBlock+MaxPool2d+Conv2d×2 64×32×32 ResBlock+MaxPool2d+Conv2d×2 128×16×16 ResBlock+MaxPool2d+Conv2d×2 256×8×8 ResBlock+MaxPool2d+Conv2d×2 512×4×4 ConvTranspose2d+(Conv2d×3)+ResBlock 512×8×8 ConvTranspose2d+(Conv2d×3)+ResBlock 256×16×16 ConvTranspose2d+(Conv2d×3)+ResBlock 128×32×32 ConvTranspose2d+(Conv2d×3)+ResBlock 4096×64 Conv2d+ResBlock 4096×5 Interp2dUpsample+Conv2d 4096×5

[0091] Self-supervised learning and data enhancement: Based on the above baseline model, a dimensionally similar data enhancement strategy is introduced: random scaling that satisfies the dimensionally similar constraint is applied to some samples (i.e., the e obtained in step 1). f With e d ), thereby generating new input values; dimensional similarity loss is added during the training process to ensure that the predicted physical field meets dimensional consistency and improve the generalization ability of the network.

[0092] Hyperparameter Settings: During the fine-tuning training phase, the fully supervised learning and self-supervised learning processes in this embodiment use the same optimizer and hyperparameter configuration. Specifically, the Adaw optimizer is used for optimization. The fully supervised process has an iteration cycle of 500 and a learning rate fixed at 1e-4, while the self-supervised learning process has an iteration cycle of 500 and a learning rate fixed at 1e-5.

[0093] Analysis of example results: Under the same network structure, compared with the network training results of fully supervised learning with 1000 iteration cycles, the L2 error of the present invention in the prediction of the GE-E3 first-stage turbine physical field is reduced from 9e-3 to 2e-3, proving the effectiveness of the method of the present invention.

[0094] In one embodiment of the present invention, a turbomachinery design optimization system based on the dimensional similarity principle is provided, which can be used to implement the above-mentioned turbomachinery design optimization method based on the dimensional similarity principle. Specifically, the system includes:

[0095] A parameter collection module is used to establish a dimensional matrix based on the physical quantity parameters of the impeller machinery flow field, obtain the standard orthogonal basis of the scaling parameters by solving the constraint equations, and generate the scaling parameters;

[0096] A training module, configured to generate augmented data samples based on the scaling parameters and train a neural network:

[0097] The output module is used to train the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery based on the trained neural network to complete the optimization.

[0098] The module division in the embodiments of the present invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in various embodiments of the present invention may be integrated into a single processor, exist physically as separate modules, or two or more modules may be integrated into a single module. The integrated modules may be implemented in either hardware or software functional modules.

[0099] In another embodiment of the present invention, a computer device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of a turbomachinery design optimization method based on the principle of dimensional similarity.

[0100] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device for storing programs and data. It is understandable that the computer-readable storage medium here can include both built-in storage media in the computer device and, of course, extended storage media supported by the computer device. The computer-readable storage medium provides a storage space that stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the impeller machinery design optimization method based on the dimensional similarity principle in the above embodiment.

[0101] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0102] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0103] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0104] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A turbomachinery design optimization method based on the principle of dimensional similarity, characterized in that: include: A dimensional matrix is ​​established based on the physical parameters of the impeller machinery flow field, and the standard orthogonal basis of the scaling parameters is obtained by solving the constraint equations to generate the scaling parameters; Generate augmented data samples based on the scaling parameters and train the neural network: Based on the trained neural network, the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery are trained to complete the optimization.

2. The impeller machinery design optimization method based on the dimensional similarity principle according to claim 1 is characterized in that: The row vectors of the dimensional matrix correspond to the dimensional coefficients of each physical field, and the column vectors correspond to the four basic dimensions of mass, length, time and temperature.

3. The impeller machinery design optimization method based on the dimensional similarity principle according to claim 2 is characterized in that: Specifically: The analysis of the turbomachinery flow physics field is based on the Navier-Stokes equations, in which the six basic physical quantities involve four basic dimensions. The matrix S describing the basic dimensions of each physical field is as follows: Among them, each row of the matrix represents the dimensional coefficient of a physical field, M, L, t, T, representing the four basic dimensions of mass, length, time and temperature respectively.

4. The impeller machinery design optimization method based on dimensional similarity principle according to claim 1 is characterized in that: The step of obtaining a standard orthogonal basis of scaling parameters by solving the constraint equations and generating the scaling parameters comprises: By solving the constraint equations of the physical constants in the Navier-Stokes equations, we obtain the standard orthogonal basis of the scaling parameters. Based on the joint Gaussian distribution random sampling, we generate a set of scaling coefficients that meet the physical laws. Specifically, For any multi-physics field sample, a reasonable similarity transformation is performed by scaling the dimensional coefficients. The dimensional scaling coefficient is set to α. At this time, the boundary conditions of the original equation also need to be scaled accordingly to maintain consistency. The uniform scaling of all physical quantities U is: Among them, U is the physical field related to the design object, S u Represents the dimensional matrix corresponding to the physical location; in the Navier-Stokes equation, the universal gas constant R g The dynamic viscosity coefficient μ of the working fluid should remain constant before and after the similarity transformation; the parameter α satisfies the following constraint equation; S C α＝0 First solve the constraint formula S C α=0, we get its standard orthogonal basis V, through α=eV T To arbitrarily generate a dimensional scaling coefficient α with physical significance, and e is the base coefficient used to construct the parameter α, which conforms to the joint Gaussian distribution e = N (μ, ∑) by default; when selecting the specific dimensional scaling coefficient, it is necessary to randomly sample from the distribution to obtain the specific coefficient.

5. The impeller machinery design optimization method based on dimensional similarity principle according to claim 4 is characterized in that: Generating augmented data samples based on the scaling parameters and training a neural network, comprising: The original input and output data are denormalized, and the physical field parameters are similarly mapped using scaling coefficients to generate enhanced sample pairs that satisfy dimensional similarity. The enhanced sample pairs are input into a neural network containing a self-supervisory mechanism, and associated samples are generated by constructing two sets of scaling coefficients A and B that do not satisfy the constraints. A loss function based on dimensional similarity constraints is established, and the loss function achieves network training by comparing the dimensional consistency between the predicted outputs of the enhanced samples corresponding to the scaling coefficients A and B.

6. The impeller machinery design optimization method based on dimensional similarity principle according to claim 5 is characterized in that: Specifically: The scaling factor is constructed as follows: A=e d ·1,B=e d ·1+e f ·v After obtaining the predicted output values ​​of the two samples through forward inference of the model, the loss function is established using the following formula: After determining the loss function expression based on dimensional similarity, the specific training process of the network is expressed as follows:

7. The impeller machinery design optimization method based on dimensional similarity principle according to claim 1, characterized in that: The geometric parameters, operating parameters and spatial coordinates of the target impeller machinery are input into the trained neural network, and the predicted physical field data are output. After denormalization, the predicted value of the performance index is calculated. By iteratively adjusting the geometric parameters and operating parameters, the optimized design of the impeller machinery across working conditions is achieved.

8. A turbomachinery design optimization system based on the principle of dimensional similarity, characterized in that: include: A parameter collection module is used to establish a dimensional matrix based on the physical quantity parameters of the impeller machinery flow field, obtain the standard orthogonal basis of the scaling parameters by solving the constraint equations, and generate the scaling parameters; A training module, configured to generate augmented data samples based on the scaling parameters and train a neural network: The output module is used to train the geometric parameters, operating parameters and spatial coordinates of the target impeller machinery based on the trained neural network to complete the optimization.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the processor implements the steps of the impeller machinery design optimization method based on the dimensional similarity principle as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the impeller machinery design optimization method based on the dimensional similarity principle as claimed in any one of claims 1 to 7 are implemented.

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