Disc temperature and stress prediction method and system based on data-driven agent model

Abstract

The application discloses a disc temperature and stress prediction method and system based on a data-driven agent model, relates to the technical field of aero-engine part test, and has the technical scheme as follows: advanced data modeling technology is introduced, a high-precision data-driven agent model is constructed, and a multi-physical field coupling analysis method is deeply fused, so that a zero-dimensional simplified model for disc temperature prediction, a high-fidelity three-dimensional physical field simulation model and a disc stress field distribution model are effectively integrated. The method can not only accurately capture the temperature change of key positions of the disc, but also comprehensively reflect the spatial distribution characteristics of the temperature field inside the heater, and accurately predict the stress distribution of the disc under the working state. The method is especially suitable for rapid and accurate analysis and evaluation of the temperature and stress state of the disc of an aero-engine under an extreme high-temperature and high-speed operating environment.

Description

Technical Field

[0001] This invention relates to the field of testing technology for aero-engine components, and more specifically, to a method and system for predicting wheel temperature and stress based on a data-driven proxy model. Background Technology

[0002] Aero-engines are the core power source of aviation equipment, and their reliability and performance directly determine the operational safety and combat effectiveness of aviation equipment. As a core load-bearing component of the aero-engine, the rotor disc undertakes critical functions such as torque transmission and blade fixing. Its structural strength and thermal stability are the core guarantee for the safe operation of the engine throughout its entire life cycle. Therefore, rotor disc strength testing is an indispensable key link in engine research and development, type approval, and maintenance. In rotor disc strength testing, temperature is a core critical parameter affecting the accuracy and safety of test results. On the one hand, the mechanical properties of the rotor disc material (such as strength, toughness, and fatigue life) are highly sensitive to temperature. The stress characteristics and failure mechanisms of the rotor disc differ significantly under different temperature conditions. Precise temperature control is a prerequisite for ensuring that the test results conform to actual operating conditions and support design verification. On the other hand, rotor disc testing needs to simulate temperature environments under extreme conditions such as high altitude and high speed. The rationality of temperature control directly affects whether the test piece will fail prematurely due to local overheating or abnormal temperature gradients, or even cause damage to test equipment or safety accidents.

[0003] However, the existing temperature control technology in the strength test of the wheel faces many prominent pain points: (1) The wheel has a complex structure and large heat capacity, and has the inherent characteristics of slow heating and strong thermal inertia. Traditional temperature control relies on the experience judgment of the test personnel or simple open-loop control logic, and lacks accurate prediction of temperature change trend. This makes it easy for problems such as temperature control lag and excessive overshoot to occur during the test. If the heating rate is not properly controlled, the test cycle will be extended. If the temperature is overshooted, it may cause irreversible damage to the wheel material performance, directly leading to test failure and increasing test costs. (2) The traditional wheel development model is highly dependent on physical test to verify the temperature control scheme. The manufacturing cost of a single wheel test piece is high, the test process requires a lot of energy and time, and the high temperature simulation under extreme working conditions has significant safety risks (such as wheel thermal fatigue cracking and heating system runaway). At the same time, the irreversibility of physical test means that a complete test must be carried out again for each parameter adjustment, resulting in many repetitive operations and extremely low R&D iteration efficiency. (3) Existing digital twin technology applications in the field of aero-engines mostly focus on one-way data mapping from "physical to virtual", that is, driving virtual model simulation through physical test data, but cannot achieve real-time guidance and dynamic feedback of virtual model prediction results to physical tests. The virtual model and physical test are in a "disconnected" state, and the model parameters cannot be updated online according to real-time test data, which causes the prediction results to gradually deviate from reality as the test progresses, making it difficult to support the dynamic optimization of temperature control schemes, and restricting the speed of design iteration and the accuracy of operation and maintenance. (4) A large amount of test data such as temperature and power will be generated during the wheel test, but existing technologies lack effective data fusion and modeling methods. Historical test data and simulation data are not fully reused, which means that the layout of measurement points and parameter settings for each test need to be explored again, which cannot provide a scientific basis for test scheme design, further aggravating the problems of long test cycles and high costs.

[0004] Therefore, researching and designing a data-driven proxy model-based method and system for predicting wheel temperature and stress that can overcome the above-mentioned defects is a problem that we urgently need to solve. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for predicting the temperature and stress of aero-engine rotor disks based on a data-driven proxy model. This system enables core functions such as online high-precision prediction of aero-engine rotor disk temperature and multi-physics field coupling control simulation of temperature and stress fields under complex operating conditions. By constructing a precise prediction model that combines data-driven and mechanism-based approaches, and a highly integrated intelligent temperature and stress control system, the system optimizes the real-time online dynamic adjustment of control strategies. This effectively reduces the high costs and potential safety risks associated with traditional physical experiments, significantly improves the rapid iteration capability of aero-engine rotor disks during the R&D phase, and enhances the accuracy of fault warning and health management during the operation and maintenance phase. Ultimately, this invention successfully solves the challenges of precise temperature control and lifespan assurance of rotor disks under extreme service environments.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution: Firstly, a method for predicting disk temperature and stress based on a data-driven proxy model is provided, including the following steps: A surrogate model for the temperature performance of a roulette wheel and a reduced-order model for the temperature field of a roulette wheel are constructed. The surrogate model for the temperature performance of a roulette wheel uses a multi-fidelity data fusion algorithm and takes the temperature of the heating wire as input to predict the temperature of key parts of the roulette wheel. The reduced-order model for the temperature field of a roulette wheel uses the orthogonal decomposition method to reduce the dimensionality of the field data and combines it with the response surface algorithm to predict the temperature distribution inside the heater. Using the temperature of the heating wire as input, a reduced-order model of the wheel stress field is constructed by the orthogonal decomposition method and the Kriging algorithm to predict the stress distribution of the wheel. By mapping the wheel temperature performance proxy model, the wheel temperature field reduced-order model, and the wheel stress field reduced-order model through input and output ports, a virtual test system is constructed, which supports joint operation and outputs temperature and stress simulation results; Through virtual-real interaction, the virtual experimental system uses the Modbus protocol to import physical test data in real time, establishes a virtual-real mapping relationship, and enables the virtual experimental system to dynamically predict the temperature field and stress field based on real-time data, and guide the adjustment of physical test parameters.

[0007] Furthermore, the construction process of the wheel temperature performance proxy model includes: A low-fidelity proxy model is established using low-fidelity data, where the low-fidelity data is the simulation data of the wheel temperature. Substitute the high-fidelity data input variables into the low-fidelity proxy model to obtain the high-fidelity prediction output variables, wherein the high-fidelity data is the historical test data of the wheel heating. Calculate the difference between the output variable of the high-fidelity data and the high-fidelity predicted output variable, and establish an error proxy model; The low-fidelity proxy model and the error proxy model are combined to form the fused wheel temperature performance proxy model.

[0008] Furthermore, the multi-fidelity data fusion algorithm is implemented through Gaussian process regression; The covariance function of the Gaussian process regression is any one of the radial basis function kernel, Matérn kernel, rational quadratic kernel, sine square kernel, and dot product kernel, and the model fit is improved through parameter optimization.

[0009] Furthermore, the construction process of the reduced-order model of the disk temperature field includes: The temperature field data was analyzed from the 3D simulation software and converted into CSV format. The field data sample set is subjected to feature orthogonal decomposition to extract the optimal orthogonal basis, and the number of basis is adaptively determined according to the energy threshold. The field variable characteristics of the low-dimensional orthogonal basis are trained using response surface methodology, kriging algorithm, or neural network algorithm to obtain the reduced-order model of the roulette temperature field.

[0010] Furthermore, the process of constructing the reduced-order model of the disk stress field includes: Extract field variable information containing displacement, stress, and strain data from structural simulation software; Based on the field variable information, the model is trained by combining the orthogonal eigenvalue decomposition method with the Kriging algorithm, wherein the covariance function is selected as the radial basis function, and the rank of the orthogonal eigenvalue decomposition method is adaptively adjusted. By comparing simulation and prediction results using random grid nodes to control the relative error within a set range, a reduced-order model of the wheel stress field is obtained.

[0011] Furthermore, the construction process of the virtual testing system includes: The model can be configured and designed through a graphical interface, and users can connect the model's input and output ports by dragging and dropping. Supports simultaneous visualization of temperature field and stress field data.

[0012] Furthermore, the real-time acquisition of physical experimental data using the Modbus protocol includes: Configure the IP address and port number to ensure that the computer system and the PLC control system of the wheel test are in the same network environment, and establish a data transmission channel for the temperature and stress data of the wheel heating wire; Define register types, including input registers, holding registers, coil registers, and discrete input registers; Set the register address according to the storage mapping rules of the roulette test PLC; Configure the number and layout of registers. Based on the characteristics of the roulette test data, the number of registers is set to 1 to represent integer data and 2 to represent floating-point data. The layout mode adopts either high byte first or low byte first to adapt to the transmission of roulette parameters. The data conversion methods include range mapping or linear conversion. Range mapping is based on the upper and lower limits of the wheel sensor encoding to convert the range, while linear conversion adjusts the wheel temperature data by setting a coefficient.

[0013] Furthermore, the input register is configured as read-only data to store the raw data collected by the sensor in real time; The holding register is configured as a read-write data type to store intermediate calculation results of the system. The coil register is configured as a Boolean type and stores the switching status of the reaction device and control commands. The discrete input register is configured as a read-only Boolean type to store digital input signals.

[0014] Furthermore, the process of establishing the virtual-real mapping relationship includes: The transfer program obtains the real-time channel table of the physical test through the Modbus protocol, filters the channels, generates a real-time connection channel table, and transmits it to the digital test terminal through shared memory. The digital test terminal provides a graphical interface, allowing users to bind real-time connection channels to digital twin model ports one-to-one through operation; The system automatically verifies the bound mapping relationship, checks for port conflicts and data type mismatches, and ensures the accuracy of data transmission. During the trial operation, users can modify and update the mapping relationship in real time according to equipment replacement or data collection point changes.

[0015] Secondly, a data-driven proxy model-based system for predicting wheel temperature and stress is provided, including: The temperature prediction module is configured to construct a wheel temperature performance proxy model and a wheel temperature field reduction model. The wheel temperature performance proxy model uses a multi-fidelity data fusion algorithm, with the heating wire temperature as input, to predict the temperature of key parts of the wheel. The wheel temperature field reduction model uses the feature orthogonal decomposition method to reduce the dimensionality of the field data and combines it with the response surface algorithm to predict the temperature distribution inside the heater. The stress prediction module is configured to take the heating wire temperature as input, construct a reduced-order model of the wheel stress field using the orthogonal decomposition method and the Kriging algorithm, and predict the stress distribution of the wheel. The virtual integration module is configured to map the wheel temperature performance proxy model, the wheel temperature field reduced-order model, and the wheel stress field reduced-order model through input and output ports to construct a virtual test system, which supports joint operation and outputs temperature and stress simulation results; The virtual-real interaction module is configured to connect to physical test data in real time via the Modbus protocol through virtual-real interaction, establish a virtual-real mapping relationship, and enable the virtual test system to dynamically predict the temperature field and stress field based on real-time data, and guide the adjustment of physical test parameters.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for predicting wheel temperature and stress based on a data-driven surrogate model. By introducing advanced data modeling technology, a high-precision data-driven surrogate model is constructed, and multi-physics coupling analysis methods are deeply integrated. This effectively combines a zero-dimensional simplified model for wheel temperature prediction, a high-fidelity three-dimensional physics simulation model, and a wheel stress field distribution model. This method not only accurately captures temperature changes in key parts of the wheel but also comprehensively reflects the spatial distribution characteristics of the temperature field inside the heater, while accurately predicting the stress distribution of the wheel under operating conditions. Furthermore, this method supports real-time dynamic optimization and adjustment of test parameters, significantly improving the adaptability and controllability of the test process. This method provides important technical support for the efficient implementation of aero-engine wheel strength tests, helps to significantly reduce test costs, and enhances the safety and reliability of the test process. It is particularly suitable for the rapid and accurate analysis and evaluation of wheel temperature and stress state in aero-engines operating under extreme high-temperature and high-speed environments.

[0017] 2. This invention systematically collects and organizes historical experimental data and utilizes advanced modeling techniques to deeply analyze and model the complex relationship between parameters and experimental results, successfully constructing an efficient and accurate parameter-result mapping model. Before conducting a new experiment, researchers only need to input initial experimental parameters, and the model can quickly and accurately predict the possible results based on existing data, thus directly recommending the optimal parameter combination to the experimenters, significantly reducing unnecessary experimentation and avoiding resource waste. In contrast, traditional physics experiments typically rely on a "trial and error" approach, requiring researchers to repeatedly adjust parameters and conduct numerous experiments to gradually approach the ideal result. This process is not only inefficient but also prolongs the entire research and development cycle. This invention, through an intelligent data-driven method, effectively improves the overall efficiency of experiments, significantly shortens the time required for experimental design and parameter control, and provides strong technical support for research and development in related fields.

[0018] 3. This invention utilizes a high-precision prediction model built upon extensive physical experimental data. This model accurately captures the complex influence of multi-parameter changes on experimental results, significantly improving the reliability and practicality of predictions. During the experiment, the model dynamically analyzes and predicts the evolution trend of subsequent experimental results based on real-time collected multi-dimensional experimental data (such as key parameters like temperature, pressure, and stress), and can issue timely warnings for various potential risks (such as material cracking and structural instability). Experimenters can react quickly to the model's predictions and analytical suggestions, promptly optimizing and adjusting control strategies (such as precisely controlling the heating rate and setting appropriate pressure thresholds), thereby effectively avoiding experimental failures and improving the success rate and resource utilization efficiency.

[0019] 4. This invention establishes a systematic experimental data management method and modeling process, effectively integrating physical experimental data that was originally scattered across different stages and sources, thereby transforming it into a structured knowledge asset. This asset not only facilitates storage and retrieval but also provides a reliable data foundation for subsequent model construction and optimization. With the continuous addition of new experimental data, the predictive model can be continuously iterated and optimized, significantly improving its accuracy and generalization ability. This process forms a self-reinforcing closed-loop mechanism: a virtuous cycle of "data-driven model optimization, model-guided experimental design, experiments generating new data, and new data further improving the model," continuously driving technological advancements and enhancing application effectiveness. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the training and prediction of the midfield order reduction model in Embodiment 1 of the present invention; Figure 2 This is a flowchart of the zero-dimensional performance model training process in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the mesh generation of the convective heat transfer model in Embodiment 1 of the present invention. a is a diagram from the inlet end view and b is a diagram from the outlet end view. Figure 4 This is a flowchart of the simulation result extraction in Embodiment 1 of the present invention; Figure 5 This is a diagram showing the predicted temperature field at the center section of the disk simulation in Embodiment 1 of the present invention. Figure 6 This is a graph showing the predicted temperature field at the center section of the reduced-order model of the roulette wheel field in Embodiment 1 of the present invention. Figure 7 These are comparison charts showing the verification results of the wheel stress field model prediction in Embodiment 1 of the present invention. a is a simulation chart of the temperature displacement distribution at 300℃, b is a predicted chart of the temperature displacement distribution at 300℃, c is a simulation chart of the equivalent stress distribution at 300℃, d is a predicted chart of the equivalent stress distribution at 300℃, e is a simulation chart of the equivalent strain distribution at 300℃, and f is a predicted chart of the equivalent strain distribution at 300℃. Figure 8 This is a schematic diagram of the construction of the roulette virtual test system in Embodiment 1 of the present invention; Figure 9 This is a flowchart of the Modbus connection configuration in Embodiment 1 of the present invention; Figure 10 This is a diagram of the physical channel addition configuration interface in Embodiment 1 of the present invention; Figure 11 This is a schematic diagram of register type configuration in Embodiment 1 of the present invention; Figure 12 This is a schematic diagram of the range mapping setting in Embodiment 1 of the present invention; Figure 13 This is a schematic diagram of the linear transformation setup in Embodiment 1 of the present invention; Figure 14 This is a schematic diagram illustrating the construction principle of virtual-real mapping in Embodiment 1 of the present invention; Figure 15 The diagram shows the predicted results of the wheel temperature / stress-strain information in Embodiment 1 of the present invention. a is the predicted result of the wheel stress distribution, b is the predicted result of the temperature inside the wheel heating cavity, and c is the predicted result of the temperature at the measuring point by the wheel temperature performance proxy model. Figure 16 This is a system block diagram in Embodiment 2 of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0022] Example: A method for predicting wheel temperature and stress based on a data-driven proxy model is implemented through the following steps.

[0023] Step 1: Construct a proxy model for the temperature performance of the wheel.

[0024] In the strength test of a rotating disk, to simulate the thermal load under high-speed rotation, the disk is usually heated before the high-speed rotation test. This invention takes disk temperature as the research object and achieves rapid prediction of multi-dimensional information about disk temperature by establishing a performance surrogate model for temperature prediction and a field order reduction model.

[0025] Based on experimental and simulation data, a surrogate model for predicting wheel temperature was trained, using the heating wire temperature as input and the temperatures of the wheel's center and rim as outputs. Since the experimental and simulation data have different confidence levels, a multi-fidelity data fusion algorithm was employed to train the model when both types of data were used simultaneously. This resulted in a surrogate model capable of predicting the temperature at specified measuring points on the wheel.

[0026] Multi-fidelity data fusion algorithms are advanced modeling methods that effectively integrate data from different sources, of varying quality and resolution. Through techniques such as Gaussian process regression, a more complete and accurate model is ultimately constructed. The algorithm's execution logic includes the following four key steps: First, a low-fidelity surrogate model is established using low-fidelity data, such as roulette wheel temperature simulation data, as the basis for subsequent processing. Second, input variables from high-fidelity data, such as historical roulette wheel heating test data, are substituted into the low-fidelity surrogate model to obtain high-fidelity predicted output variables. Next, the actual output variables from the high-fidelity data are compared with the obtained high-fidelity predicted output variables, their differences are calculated, and an error surrogate model is established based on these differences. Finally, the low-fidelity surrogate model and the error surrogate model are combined to form a comprehensive fusion model, improving the overall accuracy and reliability of the prediction.

[0027] When training a surrogate model using Gaussian processes, it is necessary to comprehensively consider the spatial correlations and dynamic changes in the temporal dimension inherent in the data. Specifically, spatial correlations manifest as the mutual influence of temperature between different measurement points, while temporal dynamics reflect the evolution of temperature over time. To effectively capture these two types of features, it is necessary to appropriately select and define the form of the covariance function, and use this function to mathematically express the dependencies between variables.

[0028] During the model building phase, one of several kernel functions can be used to construct the covariance structure. For example, the radial basis function kernel can effectively describe smooth spatial variations, the Matérn kernel can flexibly adjust the smoothness to adapt to different scenarios, the rational quadratic kernel is suitable for multi-scale modeling, the sine square kernel can capture periodic variation patterns, and the dot product kernel is often used to construct nonlinear mappings related to input features. By combining the characteristics of these kernel functions, the spatiotemporal distribution of the temperature field can be characterized more precisely.

[0029] During training, maximum likelihood estimation or Bayesian methods are used to iteratively optimize the hyperparameters in the covariance function, thereby enabling the model to better fit the distribution characteristics of the observed data. This optimization process helps improve the accuracy of the surrogate model in the roulette wheel temperature prediction task, while enhancing its generalization ability, allowing it to maintain stable prediction performance even when faced with unknown data.

[0030] Radial basis function kernel: a fixed kernel, also known as a "squared exponent" kernel. The parameter can be either a scalar (an isotropic variant of the kernel) or a parameter related to the input. (The anisotropic variant of the kernel) has vectors of the same number of dimensions. This kernel, as a Gaussian process of covariance function, has mean squared deviation derivatives of all orders, and is therefore very smooth. This kernel It can be defined as: ; in, and These represent different heating temperature points of the heating wire. The length scale parameter, determined based on the number of training point samples (i.e., the heating temperature data of the heating wire), controls the smoothness of the function. This represents the distance between two sample points.

[0031] Radial basis functions (RBFs) are a distance-based surrogate modeling method that approximates complex systems by constructing a network of RBFs. Their advantage lies in their strong ability to capture local features, but they are sensitive to parameter selection. Advantages: Strong ability to capture local features. Disadvantages: Sensitive to parameter selection. Applications: Suitable for applications with high requirements for local features, such as image processing and pattern recognition.

[0032] Matérn kernel: A fixed kernel, it is a generalization of the radial basis function kernel, with additional parameters that determine the smoothness of the function and can better adapt to the associative properties of the underlying functions. This kernel can be defined as: ; in, The variance parameter reflects the degree of fluctuation in the correlation between the heating wire temperature and the disk surface temperature. It is learned from the sample data of heating temperature points through maximum likelihood estimation. The solution with the minimum fitting error and the maximum likelihood function value is obtained through a numerical optimization algorithm (gradient descent). The optimal value; The smoothness parameter indicates the order of differentiability of the model's predicted values. The larger the value, the smoother the function. Usually, values ​​of 1.5, 2.5, and 3.5 are used. Based on experimental experience, the change in wheel temperature with heating wire temperature is a continuous and gradual process, so 2.5 can be used in this invention. The scaling factor is used to perform a second scaling on the normalized distance between sample points. It is an additional scale adjustment parameter of the Matérn kernel and is also determined through maximum likelihood estimation optimization. For gamma function, This is a modified Bessel function of the second type.

[0033] The Matérn kernel has several parameters, including a distance scale parameter (length_scale) and a smoothness parameter (ν). These parameters can be adjusted based on the characteristics of the dataset to adapt to different data distributions and patterns. However, this also means that choosing the appropriate parameter values ​​may require more trial and error. Inappropriate parameter selection can lead to poor model performance.

[0034] Rational quadratic kernel: A non-fixed kernel, viewed as a scale mixture of radial basis function kernels at different feature scales. It only supports scalar isotropic variables. This kernel can be defined as: ; in, The shape parameter controls the mixing ratio of the rational quadratic kernel across different feature scales, typically taking values ​​between (0.1, 10). This kernel function can be used when there are small-scale local high temperature gradients at the wheel temperature sample points, while the overall display exhibits large-scale temperature gradient characteristics.

[0035] This kernel function exhibits good performance across various data distributions and feature spaces, making it widely applicable for handling complex problems. However, when dealing with certain special datasets or feature spaces, the rational quadratic kernel function may experience numerical stability issues. This could be due to special functions in its mathematical form or improper parameter settings. Therefore, special attention must be paid to numerical stability and computational accuracy when using it.

[0036] Sine square kernel: Can model periodic functions. Only supports scalar isotropic variables. This kernel can be defined as: ; in, This is a period parameter that controls the period length of the sine function. The larger the value, the longer the cycle. In this invention, if the effect of the heating wire temperature on the wheel temperature changes periodically, this kernel function can be used during training, and the cycle can be determined based on the change period. Size.

[0037] The sine square kernel function may have advantages such as nonlinear mapping capabilities and parameter tuning, but it also has disadvantages such as parameter sensitivity, computational complexity, and interpretability. However, since the sine square kernel function is not one of the most widely used kernel functions, these advantages and disadvantages may require further analysis and verification based on specific implementations and application scenarios.

[0038] Dot product kernel: A non-fixed kernel. It can be obtained by adding a prior that follows a normal distribution to the correlation coefficient or bias of a linear regression. This kernel can be defined as: ; in, The bias function provides a globally constant basic covariance value for the kernel function. The initial value is estimated based on experience. In combination with the actual situation of this invention, it can be set as the initial value of the wheel temperature, and then internal optimization is performed based on the maximum likelihood estimation. It is the dot product of vectors.

[0039] The dot product is simple and efficient, and the dot product kernel function works well when the data is linearly separable in the original space or in a space after a simple transformation. It does not introduce additional nonlinear transformations, thus preserving the original linear relationship of the data. However, it also has drawbacks such as limited nonlinear processing capabilities, sensitivity to feature scaling, potential for overfitting, and limited applicability.

[0040] Step 2: Construct a reduced-order model of the wheel temperature field.

[0041] The reduced-order model of a physical field can be viewed as a collection of surrogate models for field variables at grid nodes within the modeling object. Training a single grid node's field variable model can employ algorithms similar to those used for training performance surrogate models, directly learning the relationship between the node's input variables and field variables. The difference in field modeling lies in the fact that, to improve the computational efficiency of model training and subsequent prediction efficiency, the POD (Orthogonal Eigenvalue Decomposition) method is used to reduce the order of the field data before training the reduced-order model. This effectively reduces the degrees of freedom of the physical problem while maintaining a high approximation, thereby significantly reducing computation time and data storage space. The technical approach is as follows: the grid is reduced in order using POD, and then the model is trained using Kriging or response surface algorithms. The final reduced-order model is a combination of POD basis functions and a low-dimensional surrogate model. When performing predictions using the reduced-order model, the low-dimensional surrogate model can quickly obtain low-dimensional field variable information. This low-dimensional field variable information is then linearly combined with the POD function to reconstruct the complete high-dimensional flow field solution.

[0042] like Figure 1 As shown, the training of the field reduction model consists of three steps: extraction of field variable data, orthogonal decomposition (POD) of field data, and training of the characteristic model of low-dimensional orthogonal basis field variables.

[0043] ① Extraction of field variable data.

[0044] The training data for the physics field order reduction model is 3D simulation result data, which typically comes from different simulation software and has various data formats. It is necessary to parse the simulation software result files according to their format, extract the field variable information needed for training the order reduction model, and convert the extracted data into CSV format for easy data reading during the next stage of model training.

[0045] ②POD (Orthogonal Decomposition of Characteristics) method.

[0046] The core idea of ​​POD is to obtain an approximate state of the flow field parameters through the linear superposition of a series of special basis functions. Assume... Given a known physical field, such as the temperature field of the heating cavity calculated above, it can represent the temperature distribution in the flow field under the current calculation conditions. In POD, this can be called a sample or snapshot. Assuming a sample... Consisting of N (number of grids) data, M samples are taken to form a sample set. , which is an N×M matrix.

[0047] The essence of the POD method is to extract the characteristics of the sample set and find a set of optimal orthogonal bases. , so that the physical field of the sample can be expressed as , all form an optimal orthogonal matrix , and there is , which is a matrix of the same order as U. The optimal orthogonal bases are required to satisfy that the average value of the projections of all samples on this set of bases is the largest. It can be expressed as: ; where the matrix is the matrix composed of the eigenvectors of matrix C, that is, it satisfies: ; Each element in matrix C is obtained from the sample set and is: ; From the definition of matrix C, it can be seen that C is an M×N real symmetric matrix, and all its diagonal elements are non-negative numbers. Therefore, all its eigenvalues are real numbers.

[0048] Thus, the problem of solving the optimal orthogonal bases becomes the problem of solving the eigenvalues and eigenvectors of matrix C. The obtained eigenvectors are sorted in descending order according to the corresponding eigenvalues. The magnitude of the eigenvalues can represent the proportion of the energy occupied by the corresponding orthogonal bases in the samples, that is, the flow field energy in the k-th optimal orthogonal basis direction accounts for the proportion of the total energy ( is the eigenvalue); Therefore, if necessary, some bases with relatively small energy can be ignored according to the energy occupied by each orthogonal basis, reducing the number of bases, so that the sample vectors can be reconstructed by Equation , where L is the number of orthogonal bases used, and L<M. After calculating the optimal orthogonal bases, the coefficient vector corresponding to each sample can be obtained by the inner product of the corresponding orthogonal basis and the sample: ; Among them, the superscript t represents the t-th sample. From the above analysis, it can be seen that if L = M, that is, all bases are retained and no energy is ignored, the sample values reconstructed by POD are exactly the same as the original sample values; if L < M, that is, (M - L) groups of bases are ignored, there are differences between the reconstructed sample values and the original sample values, and the error magnitude can be controlled by the total sum of the energy occupied by the used orthogonal bases.

[0049] In this invention, the POD algorithm is encapsulated. Taking the extracted Fluent full-scale simulation result set as the training data, the prediction accuracy of the reduced-order model is adjusted by adjusting the number of orthogonal basis vectors and the proxy model training algorithm. The setting of the number of basis vectors has a great impact on the prediction accuracy of the reduced-order model. Therefore, an energy threshold judgment is set inside the encapsulated algorithm to help designers perform self-adaptation when the value of the rank is not clear. The so-called energy threshold refers to the proportion of the first L modes in the total energy, that is: .

[0050] When the cumulative energy ratio of the first L modes meets the threshold requirement, setting the rank to L can ensure that the obtained energy meets the requirement. In the encapsulated algorithm, the default = 0.99. That is to say, self-adaptation represents capturing 99% of the energy. However, a relatively high accuracy requirement will reduce the speed-up advantage brought by reducing the order to a certain extent. Therefore, the selection of the rank needs to be comprehensively considered by designers.

[0051] ③ Training of the low-dimensional orthogonal basis field variable characteristic model.

[0052] As Figure 2 shown, for each low-dimensional orthogonal basis, the field variable characteristic model is trained, and the corresponding modeling data table is extracted from the physical field data. The table contains the input and output parameters of the modeling object. The correlation between the input parameters and the output parameters is fitted, interpolated or learned through statistical and machine learning algorithms, and finally a black-box model representing a certain performance is formed. The algorithms for realizing the encapsulated model training in this invention include the response surface algorithm, the Kriging algorithm, and the neural network algorithm.

[0053] The response surface algorithm uses a multiple regression equation to fit the functional relationship between the factor coefficients and the response values. At the same time, the relationship between the factors and the response values is fitted through polynomial regression to seek the optimal process parameters, which is a statistical method for solving multi-variable problems. A response surface is fitted through a series of deterministic "experimental data" to simulate the real limit state surface. Its basic idea is to assume an analytical expression including some unknown parameters between the limit state function and the basic variables to replace the actual structure limit state function that cannot be clearly expressed.

[0054] ; in, represents the predicted response value of the response surface algorithm, which in the modeling case represents the predicted value of the disk temperature under other heating wire temperatures; i,j represent the order of the response surface algorithm, which determines the order of the response surface fitting function. This is the dependent variable parameter, which in the modeling case is the heating temperature of the heating wire; To represent the number of parameters for the dependent variable, in this case k=1. The coefficients are used for training and learning based on sample data of roulette heating points in a certain dimension.

[0055] The Kriging (KG) model is an interpolation model based on unbiased estimation. It can be defined as a combination of a global trend and a stochastic process. By constructing a random field model and solving its covariance matrix, it can predict and simulate unknown data. It first considers the variation distribution of spatial attributes across spatial locations, determining the distance range that influences the value of a point to be interpolated, and then uses sampling points within this range to estimate the attribute value of the point to be interpolated. When predicting the response to new data, the Kriging model automatically selects the training data most similar to the new data. It implements a certain degree of regularization, which can avoid overfitting. Theoretically, it can be used for any type of data (regression / classification) and inputs of any dimension, achieving true integrated learning. The kernel function has hyperparameters, and the optimal values ​​of these hyperparameters can be found through methods such as maximum a posteriori estimation. The accuracy of the hyperparameters will affect the model performance. The kernel functions that can be used in the Kriging algorithm are described in the kernel section of the roulette wheel temperature performance proxy model.

[0056] Neural network algorithms are interconnected network structures based on artificial neurons that perform complex computational tasks by simulating information processing in biological nervous systems. These networks consist of a large number of simple processing units (i.e., neurons). Each neuron receives input signals from other neurons and generates output signals through mechanisms such as weighted summation and activation functions. The entire network learns the mapping relationship between input and output by adjusting the connection weights (also called parameters) between neurons, thereby achieving specific functions.

[0057] To meet the requirements for building a wheel temperature field model, a process of data preparation → model training → model validation was adopted to determine the final reduced-order model of the wheel test temperature field.

[0058] ① Data preparation.

[0059] Data preparation for the temperature field reduction model requires obtaining thermal simulation data from the wheel test. By simulating radiation and convection heat transfer during the wheel heating process, the temperature distribution data inside the heating furnace is obtained, and temperature field change data under different heating conditions is accumulated through batch simulation calculations.

[0060] This invention simplifies the model of the heating cavity and performs mesh generation and steady-state simulation calculations based on the simplified model. For example... Figure 3 As shown, to consider the impact of convective heat transfer on the temperature field inside the wheel heater, the original gap in the model was retained at the orifice cover as the inlet, and an opening was made on the base as the outlet with a diameter of 50 mm. Fluent meshing was used for mesh generation, employing a polyhedral mesh, resulting in a final mesh size of approximately 300 W. Wheel heating simulations were conducted within a range of 200℃-900℃ by varying the temperature of the heating wire inside the furnace, with a temperature interval of 50℃. The inlet temperature of the gap was set to the ambient temperature of the external furnace, and the inlet velocity was 5 m / s. Finally, 15 sets of simulation data were obtained as training data for the subsequent order reduction model.

[0061] like Figure 4 As shown, the temperature field simulation of the wheel was performed using Fluent software. The simulation results are in .cas and .dat formats. The .cas file mainly stores grid node information, while the .dat file mainly stores field variable information.

[0062] This invention employs the VTK library to extract Fluent calculation results. The VTK library parses the simulation result file set into an internal data model, which is a hierarchical data structure. The core components are a geometric mesh and the field variable data attached to it. The mesh information contains the three-dimensional coordinates of all nodes in space, defining the geometry of the flow field; while the field variable data contains a series of physical quantities, such as pressure and temperature, for each node or mesh cell. Training the reduced-order model essentially involves learning the relationship between the simulated variable boundary conditions and the field variables. Therefore, in subsequent data extraction, data can be extracted according to the names of the field variables as needed, making the extracted information more targeted and reducing the computational burden of model training. Finally, through data transcoding, the originally unreadable binary text is converted into .csv format, supporting the subsequent training of the reduced-order physical field model.

[0063] One simulation calculation result corresponds to one .csv extraction result. To support the training of the physical field reduced-order model, the final extracted data results are still saved in the form of a folder.

[0064] ② Training of the reduced-order model of the roulette temperature field.

[0065] The roulette wheel physics field order reduction model was trained using data extracted during the data preparation phase. The POD+response surface algorithm described above was employed, with the response surface order set to 3 and the POD rank adaptively adjusted. The final trained model can be used to predict the temperature distribution within a heater under different heating wire temperatures.

[0066] ③ Validation of the reduced-order model of the temperature field of the roulette wheel.

[0067] The reduced-order model was validated using a 215℃ heating wire temperature as input. Simulation calculations and field-reduced-order model predictions were performed separately, and the results are compared below. Figure 5 and Figure 6 As shown in the cloud map, the temperature distribution trend inside the disc heater is consistent.

[0068] Ten grid nodes from the random results were compared, and the comparison results are shown in Table 1. The prediction error of the random nodes was calibrated to within 5%.

[0069] Table 1 Comparison of simulated wheel temperatures

[0070] Step 3: Construct a reduced-order model of the disk stress field.

[0071] The technical approach for constructing the reduced-order model of the roulette stress field is consistent with that for the simulation of the roulette temperature field, proceeding in steps of "data preparation → model training → model verification".

[0072] ① Data preparation for stress field order reduction model.

[0073] The stress field reduced-order model was constructed based on stress simulation data. Considering the high-temperature, high-pressure, and high-speed rotational working environment of the engine disk, the disk strength test is usually performed after heating to test the stress distribution of the disk under specific conditions. The stress data was first obtained based on temperature field data of 200-900℃ obtained from Fluent calculations. A systematic simulation analysis was conducted on the thermo-structural coupling response of the 1Cr11Ni2W2MoV (GH961) material disk at 10000 rpm. The final structural simulation data is in .rst format, containing displacement, stress, and strain data. The displacement data includes displacements in the X, Y, and Z directions and the displacement vector sum. The stress data includes normal stresses in the X, Y, and Z directions, shear stresses in the three coordinate planes, and equivalent stresses. The strain data includes linear strains in the X, Y, and Z directions, shear strains in the three coordinate planes, and equivalent strains.

[0074] Extracting structural simulation data also requires customized parsing for the .rst format results. The ansys-mapdl-reader library is used to read the structural simulation results, and displacement, stress, and strain data are extracted according to the internal data organization rules. A script is then written to write the located valid data into a CSV file according to a specific pattern, which serves as the final training data for the reduced-order model.

[0075] ② Training of stress field order reduction model.

[0076] Simulation data at 200℃, 400℃, 600℃, and 800℃ were input, and training data for the reduced-order model was obtained through data extraction. The POD+Kriging algorithm was used for model training, the covariance function was selected as the radial basis function, and the rank of POD was adaptively adjusted. The final trained model can be used to predict the stress and strain distribution of the wheel at different heating temperatures.

[0077] ③ Validation of the stress field order reduction model.

[0078] The stress reduction model for the wheel disk was validated by predicting the stress-strain field at a heating temperature of 300℃ and comparing it with the original simulation results at the same temperature. Data from ten randomly selected grid nodes were used to compare the displacement, stress, and strain parameters of each node. Table 2 shows the relative errors obtained based on these comparison parameters. It can be seen that the average errors for displacement, stress, and strain are within 5%, with a maximum error of 5.71% for displacement, 2.95% for equivalent stress, and 2.29% for equivalent strain. The randomness of the grid selection led to relatively large error fluctuations at some nodes, but the overall error level remained within acceptable limits, validating the accuracy and reliability of the stress reduction model in predicting the stress-strain distribution of the wheel disk.

[0079] Table 2 Comparison of prediction errors of the reduced-order model for the stress field of the wheel disk

[0080] With a large number of grid nodes, some misalignment of individual nodes is normal. This can be seen by comparing the predicted contour plots from the field model with the simulated contour plots. Figure 7 As shown, the two models are highly consistent in terms of overall stress and displacement distribution trends, especially in stress concentration areas such as the blade root and tip, where the predicted contour maps accurately capture the high stress gradient characteristics in the simulation results. Furthermore, a comparison of the displacement field contour maps reveals that the reduced-order model's prediction of the spatial distribution of blade elastic deformation is consistent with the simulation results, particularly capturing important deformation characteristics at key deformation locations such as blade tip deflection, thus verifying the model's reliability in predicting structural deformation.

[0081] Step 4: Construct a virtual roulette wheel testing system.

[0082] The construction of the roulette virtual testing system aims to integrate the aforementioned reduced-order temperature and stress field models into an integrated, interactive simulation environment. This system requires a user-friendly graphical user interface (GUI) that allows users to establish data interaction relationships between different models through simple drag-and-drop operations, and to achieve model configuration design through connections, thereby quickly building the roulette virtual testing system. Figure 8 As shown.

[0083] The above-mentioned wheel virtual test system takes the real-time temperature data of the heating wire as input. It can predict the temperature of a specific measuring point through the wheel temperature performance proxy model, predict the distribution of the temperature field in the heating cavity through the wheel temperature field reduced-order model, and predict the stress distribution on the wheel surface through the wheel stress field reduced-order model.

[0084] Step 5: Experiment with virtual-real interaction development using the roulette wheel.

[0085] The core of developing a virtual-real interactive roulette wheel test lies in achieving deep integration and real-time interaction between the virtual simulation model and the actual physical experiment. Specifically, this solution requires building an efficient data communication bridge to ensure the virtual testing system can receive sensor data from the actual experiment in real time, such as the actual temperature of the heating wire. Simultaneously, the virtual testing system must have rapid response capabilities, able to immediately make predictions based on the received real-time data using pre-built reduced-order temperature and stress field models, and provide the prediction results (such as temperature field distribution, stress and strain distribution, etc.) to the test personnel in an intuitive and visual form.

[0086] Therefore, virtual-real interaction mainly includes two parts. First, it enables virtual-real data communication to ensure that real-time data can be transmitted to the virtual test site. Second, it needs to provide a virtual-real mapping construction function to support the construction of the mapping relationship between real-time data channels and virtual model ports, ensuring the accuracy and uniqueness of virtual-real data interaction.

[0087] (1) Virtual and real data communication.

[0088] like Figure 9 As shown, the wheel strength test data is stored in the PLC control system and communicates using the Modbus protocol. A real-time data transfer program was also developed for this communication protocol, connecting to the motor control system and equipment control system by configuring the IP address and port number. Request frames are sent to the target device via the network, and the corresponding data frames returned by the target device are monitored in real time. The Modbus communication protocol specifies the structure of the returned data; data parsing and reception can be performed according to the standard.

[0089] like Figure 10 As shown, during deployment, it is necessary to ensure that the system and the PLC are in the same network environment. Then, a basic data transmission channel is established by matching the communication ports of the system and the PLC acquisition program. After that, the physical channel is decoded and defined according to the PLC's own storage rules, thereby realizing the addition of real-time channels.

[0090] like Figure 11As shown, the register types are as follows: Based on the data storage characteristics of the wheel test, the Modbus subsystem needs to be configured with four key register types: Input registers, which are read-only and store raw data collected in real time by sensors, such as real-time data collected by the wheel temperature sensor; Holding registers, which are read-write and store system configuration parameters and intermediate calculation results, such as the maximum and minimum speeds of the wheel; Coil registers, which are Boolean and reflect the on / off status of the equipment and control commands, such as manual and automatic mode switching commands; Discrete input registers, which are read-only Boolean and store the status of digital input signals, such as the valve opening status.

[0091] Register Addresses: Register address configuration must strictly follow the PLC's internal storage mapping rules. For example, input registers are numbered consecutively starting from 30001, holding registers start from 40001, coil registers are based on 00001, and discrete input registers are assigned from 10001. Each register address corresponds to a unique physical quantity or control signal. For example, input register 30012 may correspond to data from a wheel radial vibration sensor, and holding register 40025 stores test temperature threshold parameters.

[0092] Register Quantity and Layout: The number and layout of registers determine the data type of the physical channel and whether it includes signed data. The number of data items has only two options: 1 for integer and 2 for floating-point. Register layout has two modes: high-byte first (HTF) and low-byte first (LTF). For example, if a holding register uses a HTF layout, the test temperature threshold parameter stored in register 40025 will have its high-order byte sent first during data transmission. By properly configuring the number and layout of registers, the digital twin system can accurately interpret various types of data from the PLC.

[0093] like Figure 12 and Figure 13 As shown, the data conversion methods are for decoding and include two approaches: range mapping and linear conversion. Range mapping requires knowledge of the upper and lower limits of the encoding and the range, and performs corresponding conversions based on these two ranges. Linear conversion involves coefficient conversion based on the original code, and the coefficients can be set manually.

[0094] (2) Construction of virtual-real mapping.

[0095] like Figure 14As shown, after implementing the real-time data transfer to the virtual terminal, a virtual-real mapping needs to be established to meet the application requirements of virtual-real interaction. Virtual-real mapping essentially establishes the data transmission relationship between the real-time data channel and the virtual terminal's digital twin model port, and delivers real-time data to the corresponding port according to the predetermined data flow during the experiment. The core of constructing the virtual-real mapping relationship is the transmission of channel table information. In this project, the acquisition program obtains the real-time channel table of the experiment through the Modbus protocol, filters the channels in the acquisition program, generates a real-time data transfer channel table, and then transmits it to the digital experimental terminal via shared memory. The user specifies the mapping relationship between the real-time data transfer channel and the model port.

[0096] On the digital test platform, the mapping configuration interface provides an intuitive graphical interface, allowing users to easily bind real-time connection channels to digital twin model ports one-to-one. After configuration, the system verifies the validity of the mapping relationship, checking for port conflicts or data type mismatches. Once verified, during test operation, real-time data will be accurately transmitted to the corresponding ports of the digital twin model according to the established virtual-real mapping relationship, providing data support for the model's real-time operation. Furthermore, to ensure the stability and reliability of the virtual-real mapping, the system also features dynamic adjustment capabilities. When equipment is replaced or data acquisition points change during the test, users can promptly modify and update the mapping relationship on the digital test platform, ensuring continuous and normal virtual-real interaction.

[0097] Based on the functions of the digital twin platform developed above, and in conjunction with the digital twin model, the following online prediction function for the strength test characteristics of the roulette wheel can be achieved. The specific steps are as follows: First, using the surrogate model training function, the experimental data is used as training data to train the wheel temperature performance surrogate model, which supports the prediction of temperature at specific measuring points; Secondly, using the physical field order reduction model training function, the simulation data of the flow field inside the heating cavity of the wheel and the simulation data of the thermal stress of the wheel are used as training data to extract effective temperature field and stress-strain field information, and train the wheel temperature field and stress field models. These models support the prediction of field information. Then, by utilizing the experimental system building function, virtual models of different dimensions are combined into a digital experimental system, supporting joint calculation of the models to ensure real-time prediction and comparison of multi-dimensional information during the virtual experiment. Next, by utilizing the real-time data import and virtual-real mapping functions, the real-time data of the wheel test in this project will be imported and mapped. The real-time channel data required for the virtual test will be imported to the virtual end and associated with the corresponding model input end, supporting the online prediction of wheel strength test temperature and stress-strain. Finally, by utilizing the model's predictive capabilities and appropriate visualization methods, online prediction of disk temperature and stress-strain information is achieved. The prediction results are then displayed in multiple dimensions using various visualization techniques, making it convenient for experimenters to intuitively obtain experimental information.

[0098] like Figure 15 As shown, testers can plan subsequent test steps in advance based on the predicted results of the digital test, such as whether to adjust the heating wire temperature or change the test duration, in order to optimize the test process and improve test efficiency. Throughout the entire process, digital and physical tests are closely integrated to form a closed-loop system of virtual and real interaction, ensuring the safety, controllability, and efficiency of the test process.

[0099] Example 2: A wheel temperature and stress prediction system based on a data-driven proxy model. This system is used to implement the wheel temperature and stress prediction method based on a data-driven proxy model described in Example 1, such as... Figure 16 As shown, it includes a temperature prediction module, a stress prediction module, a virtual integration module, and a virtual-real interaction module.

[0100] The system includes the following modules: a temperature prediction module, configured to construct a proxy model for the wheel's temperature performance and a reduced-order model for the wheel's temperature field; the proxy model employs a multi-fidelity data fusion algorithm, using the heating wire temperature as input, to predict the temperature of key parts of the wheel; and the reduced-order model uses a characteristic orthogonal decomposition method to reduce the dimensionality of the field data, combined with a response surface methodology to predict the temperature distribution within the heater. A stress prediction module, configured to use the heating wire temperature as input, constructs a reduced-order model of the wheel's stress field using a characteristic orthogonal decomposition method and a Kriging algorithm to predict the wheel's stress distribution. A virtual integration module, configured to map the proxy model, the reduced-order model, and the reduced-order model through input / output ports to construct a virtual experimental system, supporting joint operation and outputting temperature and stress simulation results. A virtual-real interaction module, configured to use the Modbus protocol to connect to physical experimental data in real time via virtual-real interaction, establishing a virtual-real mapping relationship, enabling the virtual experimental system to dynamically predict the temperature and stress fields based on real-time data and guide the adjustment of physical experimental parameters.

[0101] Working Principle: This invention addresses several technical challenges in traditional wheel strength testing, including insufficient data utilization, disconnect between the model and actual operating conditions, and reliance on operator subjective experience for test control. It proposes an innovative solution. By constructing a big data-driven intelligent agent model, this invention achieves accurate online real-time prediction of the temperature field distribution and stress state during wheel operation. This provides a scientific and objective basis for controlling the physical testing process, significantly reducing repetitive tests caused by blind operation or lack of experience, and improving the overall efficiency and reliability of the results.

[0102] The digital twin platform developed in this invention is highly integrated, fully covering the entire process from data acquisition and preprocessing, surrogate model training and optimization, online real-time predictive analysis, to multi-dimensional visualization and guidance for dynamic adjustment of test parameters. The platform design balances user-friendliness with functional completeness, featuring a logical interface layout and clear interactive logic. Test personnel can intuitively grasp key information such as temperature changes at critical measuring points of the wheel, the internal temperature gradient distribution of the heater, and the prediction of the system's steady-state temperature through the platform's built-in two-dimensional temperature-time curve control and high-definition temperature field cloud map. Without requiring professional modeling, simulation, or numerical calculation background, users can quickly determine the current test status and make decisions such as whether to adjust the target temperature based on the prediction results provided by the system. This platform has good versatility and adaptability, and can be widely applied to wheel strength tests of different specifications and under different test conditions, significantly reducing the entry barrier and operational difficulty of the technology.

[0103] This invention represents a significant breakthrough compared to existing digital twin systems, which mostly achieve a one-way mapping from physical to digital. It realizes deep bidirectional coupling and real-time interaction between the physical and digital experimental systems. Leveraging efficient real-time data acquisition and communication mechanisms, various sensor data, such as temperature, power, and rotational speed, collected during physical experiments can be synchronized to the digital twin platform in real time. This data drives the online updates and continuous training of the proxy model, ensuring the model can dynamically respond to changes in actual conditions. Simultaneously, predictions generated on the digital side using ultra-real-time computing capabilities, including temperature evolution trends and abnormal state warnings, can be instantly fed back to the physical experiment side. This provides precise guidance and safety margin assessments for adjusting experimental parameters, forming a complete closed loop of "physical experiment data acquisition → dynamic model update → prediction result guidance → physical experiment feedback optimization." This mechanism ensures that the digital model and the physical entity maintain a high degree of consistency, mutually verifying and evolving collaboratively, greatly enhancing the real-time performance, adaptability, and accuracy of temperature control schemes.

[0104] To balance model accuracy and computational resource consumption, this invention employs an advanced multi-fidelity data fusion algorithm to train a proxy model of the roulette wheel's temperature performance. It then combines intrinsic orthogonal decomposition (POD) and response surface modeling methods to construct an efficient reduced-order model of the roulette wheel's temperature field. Under the premise of strictly controlling the prediction error to no more than 5% and maintaining consistency between the temperature distribution pattern and high-precision simulation results, this model structure significantly reduces the complexity of numerical calculations and the demand for hardware computing power. Furthermore, relying on ultra-real-time simulation technology, the digital experiment progresses much faster than the physical experiment, enabling the output of temperature prediction results and potential risk warnings several times earlier, effectively avoiding time delays and repetitive operations caused by waiting for data or human error in physical experiments. Compared with traditional experimental and simulation methods, this invention achieves significant improvements in the response speed of temperature prediction and the control efficiency of the experimental process, thereby shortening the overall cycle of the roulette wheel strength test and reducing the overall cost.

[0105] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0106] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0107] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0108] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0109] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for wheel disc temperature and stress prediction based on data-driven surrogate model, characterized in that, Includes the following steps: A surrogate model for the temperature performance of a roulette wheel and a reduced-order model for the temperature field of a roulette wheel are constructed. The surrogate model for the temperature performance of a roulette wheel uses a multi-fidelity data fusion algorithm and takes the temperature of the heating wire as input to predict the temperature of key parts of the roulette wheel. The reduced-order model for the temperature field of a roulette wheel uses the orthogonal decomposition method to reduce the dimensionality of the field data and combines it with the response surface algorithm to predict the temperature distribution inside the heater. Using the temperature of the heating wire as input, a reduced-order model of the wheel stress field is constructed by the orthogonal decomposition method and the Kriging algorithm to predict the stress distribution of the wheel. By mapping the wheel temperature performance proxy model, the wheel temperature field reduced-order model, and the wheel stress field reduced-order model through input and output ports, a virtual test system is constructed, which supports joint operation and outputs temperature and stress simulation results; Through virtual-real interaction, the virtual experimental system uses the Modbus protocol to import physical test data in real time, establishes a virtual-real mapping relationship, and enables the virtual experimental system to dynamically predict the temperature field and stress field based on real-time data, and guide the adjustment of physical test parameters.

2. The method for predicting disk temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The construction process of the disk temperature performance proxy model includes: A low-fidelity proxy model is established using low-fidelity data, where the low-fidelity data is the simulation data of the wheel temperature. Substitute the high-fidelity data input variables into the low-fidelity proxy model to obtain the high-fidelity prediction output variables, wherein the high-fidelity data is the historical test data of the wheel heating. Calculate the difference between the output variable of the high-fidelity data and the high-fidelity predicted output variable, and establish an error proxy model; The low-fidelity proxy model and the error proxy model are combined to form the fused wheel temperature performance proxy model.

3. The method for predicting wheel temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The multi-fidelity data fusion algorithm is implemented through Gaussian process regression. The covariance function of the Gaussian process regression is any one of the radial basis function kernel, Matérn kernel, rational quadratic kernel, sine square kernel, and dot product kernel, and the model fit is improved through parameter optimization.

4. The method for predicting wheel temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The process of constructing the reduced-order model of the roulette wheel temperature field includes: The temperature field data was analyzed from the 3D simulation software and converted into CSV format. The field data sample set is subjected to feature orthogonal decomposition to extract the optimal orthogonal basis, and the number of basis is adaptively determined according to the energy threshold. The field variable characteristics of the low-dimensional orthogonal basis are trained using response surface methodology, kriging algorithm, or neural network algorithm to obtain the reduced-order model of the roulette temperature field.

5. The method for predicting disk temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The process of constructing the reduced-order model of the disk stress field includes: Extract field variable information containing displacement, stress, and strain data from structural simulation software; Based on the field variable information, the model is trained by combining the orthogonal eigenvalue decomposition method with the Kriging algorithm, wherein the covariance function is selected as the radial basis function, and the rank of the orthogonal eigenvalue decomposition method is adaptively adjusted. By comparing simulation and prediction results using random grid nodes to control the relative error within a set range, a reduced-order model of the wheel stress field is obtained.

6. The method for predicting disk temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The construction process of the virtual testing system includes: The model can be configured and designed through a graphical interface, and users can connect the model's input and output ports by dragging and dropping. Supports simultaneous visualization of temperature field and stress field data.

7. The method for predicting wheel temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The method of using the Modbus protocol to import physical experimental data in real time includes: Configure the IP address and port number to ensure that the computer system and the PLC control system of the wheel test are in the same network environment, and establish a data transmission channel for the temperature and stress data of the wheel heating wire; Define register types, including input registers, holding registers, coil registers, and discrete input registers; Set the register address according to the storage mapping rules of the roulette test PLC; Configure the number and layout of registers. Based on the characteristics of the roulette test data, the number of registers is set to 1 to represent integer data and 2 to represent floating-point data. The layout mode adopts either high byte first or low byte first to adapt to the transmission of roulette parameters. The data conversion methods include range mapping or linear conversion. Range mapping is based on the upper and lower limits of the wheel sensor encoding to convert the range, while linear conversion adjusts the wheel temperature data by setting a coefficient.

8. The method for predicting wheel temperature and stress based on a data-driven proxy model according to claim 7, characterized in that, The input register is configured as a read-only data type to store the raw data collected by the sensor in real time; The holding register is configured as a read-write data type to store intermediate calculation results of the system. The coil register is configured as a Boolean type and stores the switching status of the reaction device and control commands. The discrete input register is configured as a read-only Boolean type to store digital input signals.

9. The method for predicting wheel temperature and stress based on a data-driven proxy model according to claim 1, characterized in that, The process of establishing the virtual-real mapping relationship includes: The transfer program obtains the real-time channel table of the physical test through the Modbus protocol, filters the channels, generates a real-time connection channel table, and transmits it to the digital test terminal through shared memory. The digital test terminal provides a graphical interface, allowing users to bind real-time connection channels to digital twin model ports one-to-one through operation; The system automatically verifies the bound mapping relationship, checks for port conflicts and data type mismatches, and ensures the accuracy of data transmission. During the trial operation, users can modify and update the mapping relationship in real time according to equipment replacement or data collection point changes.

10. A wheel temperature and stress prediction system based on a data-driven surrogate model, characterized in that, include: The temperature prediction module is configured to construct a wheel temperature performance proxy model and a wheel temperature field reduction model. The wheel temperature performance proxy model uses a multi-fidelity data fusion algorithm, with the heating wire temperature as input, to predict the temperature of key parts of the wheel. The wheel temperature field reduction model uses the feature orthogonal decomposition method to reduce the dimensionality of the field data and combines it with the response surface algorithm to predict the temperature distribution inside the heater. The stress prediction module is configured to take the heating wire temperature as input, construct a reduced-order model of the wheel stress field using the orthogonal decomposition method and the Kriging algorithm, and predict the stress distribution of the wheel. The virtual integration module is configured to map the wheel temperature performance proxy model, the wheel temperature field reduced-order model, and the wheel stress field reduced-order model through input and output ports to construct a virtual test system, which supports joint operation and outputs temperature and stress simulation results; The virtual-real interaction module is configured to connect to physical test data in real time via the Modbus protocol through virtual-real interaction, establish a virtual-real mapping relationship, and enable the virtual test system to dynamically predict the temperature field and stress field based on real-time data, and guide the adjustment of physical test parameters.

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