Intelligent prediction method and device for supporting rigidity of turbomachinery

Abstract

The invention provides an intelligent prediction method and device for the supporting rigidity of turbomachinery, and belongs to the technical field of mechanical structures.The method comprises the steps that a reduced finite element model is established based on a real turbomachinery foundation supporting model; using a Latin hypercube sampling method to construct a data sample set for reducing the support stiffness and the damping ratio of the finite element model; performing finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in the vertical and horizontal directions; according to the data sample set and the dynamic stiffness curves of the supporting structure in the vertical and horizontal directions, constructing an intelligent prediction model of the supporting stiffness of the turbomachinery; and utilizing the intelligent prediction model for the supporting rigidity of the turbomachinery to intelligently predict the supporting rigidity of the turbomachinery. The method can accurately capture the characteristics of a complex dynamic system, provides more reliable technical support and decision basis, optimizes equipment management and maintenance, improves the overall performance of the turbomachinery, and prolongs the service life of the turbomachinery.

Description

Background Art

[0002] As a key power equipment in industrial production, the operating stability and safety of turbine machinery are directly related to the efficiency and reliability of the entire system. The support stiffness of turbine machinery is an important parameter to measure the structural stability of the equipment. Its influencing factors are complex, including various physical properties such as support stiffness and damping ratio. In practical applications, turbine machinery may face complex and changeable working conditions during operation. The reasonable prediction of support stiffness is crucial for the evaluation and maintenance of the equipment's operating status.

[0003] In the prior art, traditional finite element analysis methods are often used to analyze and predict the support stiffness of turbine machinery. These methods usually require a large amount of experimental data and complex calculation processes to obtain key parameters and dynamic stiffness curves. However, with the increasing complexity of industrial equipment, traditional methods have significant defects in the following aspects: First, the accuracy of the finite element model depends on high-precision parameter input. However, under actual operating conditions, the diversity and uncertainty of the input data are often difficult to fully cover, resulting in insufficient reliability of the prediction results; second, for multi-variable dynamic response analysis, the calculation efficiency of traditional methods is low and it is difficult to meet real-time requirements, especially when dealing with complex changes in support stiffness and damping ratio; third, when dealing with support stiffness calculations in different directions (such as vertical and horizontal directions), the existing technology often cannot take into account both global and local characteristics, resulting in limited accuracy of the analysis results.

[0004] In addition, for the prediction of turbine machinery support stiffness, the existing technology has not yet achieved the best balance between model simplification and data sampling, and there are usually problems such as excessive consumption of computing resources and insufficient data coverage. Limited sample data cannot fully express the complex changes in support stiffness and damping ratio, which in turn limits the generalization ability of the prediction model. At the same time, in the absence of in-depth mining of nonlinear features, it is difficult to further improve the prediction accuracy, especially in actual applications under multiple working conditions, where prediction deviations are prone to occur, affecting the long-term stable operation of the equipment. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the present invention provides a method and device for intelligently predicting the support stiffness of a turbine machinery.

[0006] According to a first aspect of an embodiment of the present invention, a method for intelligently predicting support stiffness of a turbomachinery is provided, the method comprising: Based on the real turbomachinery foundation support model, a reduced finite element model is established; Using a Latin hypercube sampling method, a data sample set of support stiffness and damping ratio of the reduced finite element model is constructed; Performing finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in vertical and horizontal directions; Constructing a turbomachinery support stiffness intelligent prediction model based on the data sample set and the dynamic stiffness curves of the support structure in vertical and horizontal directions; The turbine machinery support stiffness intelligent prediction model is used to perform turbine machinery support stiffness intelligent prediction.

[0007] In some exemplary embodiments of the present invention, based on the above-mentioned solution, using the turbine machinery support stiffness intelligent prediction model to perform turbine machinery support stiffness intelligent prediction includes: Perform multi-scale feature extraction and conversion on the newly input support stiffness and damping ratio data to obtain the conversion result; Performing a transformation operation on the transformation result to obtain a multi-scale feature vector; Performing feature fusion on the multi-scale feature vectors to obtain an intelligent prediction result of the turbomachinery support stiffness; Wherein, the intelligent prediction result of the turbomachinery support stiffness includes the dynamic stiffness curves of the support structure in the vertical and horizontal directions.

[0008] In some exemplary embodiments of the present invention, based on the above scheme, multi-scale feature extraction and conversion are performed on the newly input support stiffness and damping ratio data, and the conversion results obtained include: Extracting different scale features of the newly input support stiffness and damping ratio data; The feature extraction results of each scale of the newly input support stiffness and damping ratio data are converted into a new representation by utilizing nonlinear changes of multiple activation functions; The new representation is subjected to weighted summation and nonlinear transformation to obtain a transformation result.

[0009] In some exemplary embodiments of the present invention, based on the aforementioned scheme, using nonlinear changes of multiple activation functions, converting the feature extraction results of each scale of the newly input support stiffness and damping ratio data into a new representation includes: ; in, The new representation formed by the representation transformation, is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n Layer l The weight of the neuron, is the corresponding bias, Indicates The B-spline basis functions are The value of N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale The grid size below, Representation scale The spline degree of the B-spline curve below.

[0010] In some exemplary embodiments of the present invention, based on the above scheme, the conversion result is converted to obtain a multi-scale feature vector include: ; in, Indicated in The conversion result obtained by scale is , is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n The weight of the second neuron in the layer, is the corresponding bias, Indicates The B-spline basis functions are The value of N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale The grid size below, Representation scale The spline degree of the B-spline curve below.

[0011] In some exemplary embodiments of the present invention, based on the above scheme, the multi-scale feature vector is subjected to feature fusion to obtain the intelligent prediction result of the turbomachinery support stiffness, including: ; in, It represents the intelligent prediction result of turbomachinery support stiffness. represents the weight of the fusion layer, represents the multi-scale feature vector, Represents the bias of the fusion layer.

[0012] In some exemplary embodiments of the present invention, based on the above scheme, the loss function of the turbomachinery support stiffness intelligent prediction model is include: ; in, represents the number of samples, represents the loss function used to measure the difference between the predicted value and the true value, Represents the network model, Representation scale s Next input m The characteristics of the samples, Indicates the corresponding true value.

[0013] According to a second aspect of an embodiment of the present invention, there is provided a device based on the above-mentioned turbomachinery support stiffness intelligent prediction method, comprising: Model building module for building reduced finite element models based on real turbomachinery foundation support models; A sample set construction module, used to construct a data sample set of support stiffness and damping ratio of the reduced finite element model by using a Latin hypercube sampling method; A curve generating module, used for performing finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the supporting structure in vertical and horizontal directions; A prediction model generation module, used for constructing a turbomachinery support stiffness intelligent prediction model based on the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions; A prediction module is implemented to perform intelligent prediction of turbine machinery support stiffness using the turbine machinery support stiffness intelligent prediction model.

[0014] According to a third aspect of an embodiment of the present invention, there is provided an electronic device, comprising: a processor; and a memory, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the processor, the method for intelligently predicting the support stiffness of turbine machinery in the first aspect is implemented.

[0015] According to a fourth aspect of an embodiment of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for intelligently predicting support stiffness of a turbine machinery in the first aspect.

[0016] The technical solution provided by the embodiments of the present invention may have the following beneficial effects: In the embodiments of the present invention, by combining finite element analysis, data sampling technology and intelligent prediction models, the characteristics of complex dynamic systems can be accurately captured, more reliable technical support and decision-making basis can be provided, and equipment management and maintenance can be optimized, thereby improving the overall performance and service life of turbine machinery.

[0017] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0019] Figure 1 A schematic diagram showing a system architecture of an exemplary application environment in which a method and device for intelligently predicting support stiffness of a turbomachinery according to an embodiment of the present invention can be applied; Figure 2 A schematic diagram of a process flow of a turbomachinery support stiffness intelligent prediction method according to some embodiments of the present invention is shown; Figure 3 (a) schematically shows a dynamic stiffness curve in the vertical direction according to some embodiments of the present invention; Figure 3 (b) schematically shows a dynamic stiffness curve in the horizontal direction according to some embodiments of the present invention; Figure 4 Schematically showing a schematic diagram of the structure of a multi-scale Kolmogorov-Arnold network according to some embodiments of the present invention; Figure 5 (a) schematically shows a schematic diagram of the loss change of each model under vertical training data according to some embodiments of the present invention; Figure 5 (b) schematically shows a schematic diagram of the loss change of each model under horizontal training data according to some embodiments of the present invention; Figure 6 (a) schematically shows the R of CNN, ResNet, KAN at various scales and MKAN in the prediction of dynamic stiffness of a vertical test set according to some embodiments of the present invention. 2 Schematic diagram of coefficient indicators; Figure 6 (b) schematically shows the MAE index of CNN, ResNet, KAN and MKAN at various scales in the dynamic stiffness prediction of the vertical test set according to some embodiments of the present invention; Figure 6 (c) schematically shows the RMSE indicators of CNN, ResNet, KAN and MKAN at various scales in the prediction of dynamic stiffness of a vertical test set according to some embodiments of the present invention; Figure 7 (a) schematically shows a schematic diagram of prediction results of a convolutional neural network CNN in Experiment 1 according to some embodiments of the present invention; Figure 7 (b) schematically shows a schematic diagram of prediction results of the residual network ResNet in Experiment 1 according to some embodiments of the present invention; Figure 7 (c) to Figure 7 (e) schematically shows a schematic diagram of prediction results of the novel neural network architecture KAN at different grid sizes in Experiment 1 according to some embodiments of the present invention; Figure 7(f) schematically shows a schematic diagram of prediction results of a multi-scale Kolmogorov-Arnold network MKAN in Experiment 1 according to some embodiments of the present invention; in the figure, True represents a true value; Figure 8 (a) schematically shows the R of CNN, ResNet, KAN at various scales and MKAN in the prediction of dynamic stiffness of a horizontal test set according to some embodiments of the present invention. 2 coefficient; Figure 8 (b) schematically shows the MAE of CNN, ResNet, KAN and MKAN at various scales in the dynamic stiffness prediction of the horizontal test set according to some embodiments of the present invention; Figure 8 (c) schematically shows the RMSE of CNN, ResNet, KAN and MKAN at various scales in the prediction of dynamic stiffness of a horizontal test set according to some embodiments of the present invention; Fig. 9 (a) schematically shows a schematic diagram of prediction results of a convolutional neural network CNN in Experiment 2 according to some embodiments of the present invention; Fig. 9 (b) schematically shows a schematic diagram of prediction results of the residual network ResNet in Experiment 2 according to some embodiments of the present invention; Fig. 9 (c) to Fig. 9 (e) schematically shows the prediction results of the novel neural network architecture KAN at different grid sizes in Experiment 2 according to some embodiments of the present invention; Fig. 9 (f) schematically shows a schematic diagram of prediction results of a multi-scale Kolmogorov-Arnold network MKAN in Experiment 2 according to some embodiments of the present invention; in the figure, True represents a true value; Fig.10 A schematic diagram of a turbomachinery support stiffness intelligent prediction device according to some embodiments of the present invention is schematically shown; Fig.11 A schematic diagram schematically shows a structure of a computer system of an electronic device according to some embodiments of the present invention; Fig.12 A schematic diagram of a computer-readable storage medium according to some embodiments of the present invention is schematically shown. DETAILED DESCRIPTION

[0020] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0021] The terms used in the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the" and "the" used in the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0022] It should be understood that although the terms first, second, third, etc. may be used in the present invention to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present invention, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0023] Figure 1 A schematic diagram of a system architecture of an exemplary application environment of a method and device for intelligently predicting support stiffness of a turbine machinery according to an embodiment of the present invention is shown.

[0024] like Figure 1 As shown, the system architecture 100 may include one or more terminal devices such as a desktop computer 101, a portable computer 102, a smart phone 103, a network 104, and a server 105. The network 104 is used to provide a medium for a communication link between the terminal device and the server 105. The network 104 may include various connection types, such as wired or wireless communication links or optical fiber cables, etc. The terminal device may be various electronic devices with data processing functions, and the electronic device has a display screen, which is used to display the intelligent prediction results of the turbine machinery support stiffness to the user, including but not limited to the above-mentioned desktop computers, portable computers, smart phones, etc. It should be understood that Figure 1 The number of terminal devices, networks and servers in the embodiment is only for illustration. According to the implementation requirements, there may be any number of terminal devices, networks and servers. For example, the server 105 may be a sub-server cluster composed of multiple sub-servers.

[0025] The turbine machinery support stiffness intelligent prediction method provided in the embodiment of the present invention can generally be executed by a terminal device, and accordingly, the turbine machinery support stiffness intelligent prediction device is generally set in the terminal device. However, it is easy for a person skilled in the art to understand that the turbine machinery support stiffness intelligent prediction method provided in the embodiment of the present invention can also be executed by the server 105, and accordingly, the turbine machinery support stiffness intelligent prediction device can also be set in the server 105, which is not particularly limited in this exemplary embodiment.

[0026] In addition, it should be understood that the intelligent prediction method for turbine machinery support stiffness of the embodiment of the present invention can be configured as a software module. In some implementation scenarios, the intelligent prediction scheme for turbine machinery support stiffness of the present invention can be deployed separately to achieve the generation of different prediction contents. In other implementation scenarios, the intelligent prediction scheme for turbine machinery support stiffness of the present invention can be deployed in other software as a functional module of the software, such as deployed in the analysis software of turbine machinery support stiffness. The present invention does not impose any special restrictions on the application of the intelligent prediction method for turbine machinery support stiffness.

[0027] Next, the embodiments of the present invention are described in detail.

[0028] like Figure 2 As shown, Figure 2 1 is a flow chart of a method for intelligently predicting support stiffness of a turbomachinery according to an exemplary embodiment of the present invention, comprising the following steps: S210: Establish a reduced finite element model based on the real turbomachinery foundation support model; S220: constructing a data sample set of support stiffness and damping ratio of the reduced finite element model by using a Latin hypercube sampling method; S230: Perform finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in vertical and horizontal directions; S240: constructing a turbomachinery support stiffness intelligent prediction model according to the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions; S250: Using the turbine machinery support stiffness intelligent prediction model to perform turbine machinery support stiffness intelligent prediction.

[0029] In S210, a reduced finite element model is established based on the actual turbomachinery foundation support model.

[0030] The turbine machinery foundation support model refers to a mathematical or physical model of the foundation structure used to support the turbine machinery. It usually describes how the foundation bears the load (such as vibration, pressure, temperature change, etc.) generated by the turbine machinery during operation. In the implementation of the present invention, the turbine machinery foundation support model focuses on the support effect and support stiffness of the foundation on the turbine machinery. Support stiffness refers to the ability of the foundation to resist displacement when subjected to load. The support performance of the foundation is very important to the stability and operation effect of the turbine machinery.

[0031] The turbomachinery foundation support model can be established by measuring the deformation and stress of the foundation and combining it with the principles of structural mechanics.

[0032] Reduced finite element model refers to reducing the degrees of freedom (DOF) of the original finite element model through certain techniques, thereby reducing the amount of calculation. Reduced finite element model can be established by modal reduction, principal component analysis reduction or hypothetical element method reduction.

[0033] In an embodiment of the present invention, establishing a reduced finite element model based on a real turbomachinery foundation support model further includes: Add master nodes at six constraint locations of the foundation base of the real turbine machinery foundation support model; A reduced finite element model is established based on the turbine machinery foundation support model after adding the main nodes.

[0034] Here, the six constraint positions refer to the support positions of the turbine machinery foundation base. These positions correspond to the fixed points of the foundation, and the foundation is connected to the surrounding environment (such as the ground, foundation) through these constraint points. These constraints are usually rigid supports (such as fixed supports, hinged supports, etc.), which limit the freedom of the foundation in specific directions. Adding master nodes to the six constraint positions of the foundation base means setting nodes at these constraint positions, which are responsible for bearing the constraint conditions. For a three-dimensional structure, there are usually six degrees of freedom (three translational degrees of freedom (displacement in the X, Y, and Z directions), and three rotational degrees of freedom (rotation around the X, Y, and Z axes)) to describe the movement of the nodes.

[0035] By adding master nodes, the displacement and rotation behavior of the turbine machinery foundation can be controlled and its mechanical model can be established.

[0036] On this basis, a reduced finite element model is established. When establishing the reduced finite element model, the geometric model of the foundation base can be created first, the main nodes can be set at the six constraint positions of the foundation, and then the element type can be selected (it can be a beam element, shell element, solid element, etc.), and the material properties can be defined.

[0037] By establishing a realistic turbine machinery foundation support model, the key features of the turbine machinery foundation support can be retained, while ensuring the calculation accuracy, the resources and time required for calculation can be reduced, and an efficient data basis can be provided for subsequent predictive analysis; on this basis, the reduced finite element method is used to simplify the calculation, which can effectively reduce the calculation complexity and improve the calculation efficiency.

[0038] In S220, a Latin hypercube sampling method is used to construct a data sample set of support stiffness and damping ratio of the reduced finite element model.

[0039] Latin Hypercube Sampling (LHS) is an efficient statistical sampling method for uniformly extracting samples in multidimensional space. Compared with traditional random sampling methods, LHS can ensure uniform distribution within the range of values ​​of each variable and avoid the phenomenon of samples being concentrated in a certain area. The LHS method can fully explore the parameter space of different variables in the reduced finite element model.

[0040] Support stiffness is a physical quantity that describes the resistance of the support system to external forces or deformations. It is usually expressed as the force required per unit displacement. Support stiffness can be defined in different directions (such as horizontal and vertical directions), and the commonly used units are N / m or N·m / rad (for rotational stiffness). Damping ratio is a dimensionless parameter that describes the vibration attenuation ability of the system, and is usually defined as the ratio of the actual damping of the structure to the critical damping. It is closely related to the vibration attenuation, energy consumption and other characteristics of the system, and is usually expressed as a percentage. The damping ratio ranges from 0% (no damping) to 5%-10% (high damping).

[0041] Using the Latin hypercube sampling method, the process of constructing a data sample set of support stiffness and damping ratio of the reduced finite element model may be: Based on actual design requirements, material properties or existing experimental data, define the range of support stiffness and damping ratio. For example, the support stiffness can be 1000 N / m to 5000 N / m; the damping ratio range is 0.01 (1%) to 0.05 (5%).

[0042] Divide the parameter space. Divide the range of each parameter into several equal intervals, and then randomly select a value from each interval. Assuming that N samples are to be generated, the interval of each parameter will be divided into N sub-intervals, and a sample point will be randomly selected from each sub-interval.

[0043] Generate samples. Use the Latin hypercube sampling method to uniformly select a sample point from each interval. For example, if there are N samples, then N samples are drawn from the range of 1000 N / m to 5000 N / m, and N samples are drawn from the range of 0.01 (1%) to 0.05 (5%). Ensure independent random sampling during the sampling process.

[0044] The data sample set is formed by combining N results extracted from the range of support stiffness and N results extracted from the range of damping ratio. In the present invention, N=100.

[0045] In S230, finite element analysis is performed on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in vertical and horizontal directions.

[0046] Dynamic stiffness describes the stiffness characteristics of a structure when it is subjected to dynamic loads (such as vibration and impact). Dynamic stiffness is frequency-dependent, that is, the stiffness value of the supporting structure will be different at different frequencies. The dynamic stiffness curve is a graph with frequency as the horizontal axis and dynamic stiffness as the vertical axis.

[0047] In finite element analysis software, support stiffness and damping ratio can be applied as constraints on base nodes or contact surfaces.

[0048] On this basis, in order to obtain the dynamic stiffness curve, the frequency sweep method can be used to apply dynamic loads (such as sinusoidal excitation, impact load or random vibration) at different frequencies of the support structure. Then, according to the applied dynamic load and support conditions, the dynamic response of the support structure at different frequencies is solved. The dynamic stiffness is calculated based on the response results. Then the curve of dynamic stiffness changing with frequency is plotted, refer to Figure 3 (a) and Figure 3 (b) shown.

[0049] Here, the dynamic stiffness can be calculated as: ; in, is the dynamic stiffness, is at frequency The force applied under is the displacement response at this frequency.

[0050] Finite element analysis is performed on each data sample in the data sample set to generate the dynamic stiffness curves of the support structure in the vertical and horizontal directions. In fact, the dynamic response of the support structure is simulated by the finite element model, and the dynamic stiffness of each sample at different frequencies is calculated. This process includes defining the model, applying loads, performing frequency response analysis, calculating dynamic stiffness, and generating dynamic stiffness curves.

[0051] In S240, a turbomachinery support stiffness intelligent prediction model is constructed based on the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions.

[0052] Here, the data sample set can be used as input data for some machine learning models, and the dynamic stiffness curves of the supporting structure in the vertical and horizontal directions can be used as output data to train the machine learning model. The trained machine learning model is the intelligent prediction model of turbine machinery support stiffness.

[0053] The present invention does not limit the specific structure of the machine learning model. For example, in some embodiments, the machine learning model can be a deep neural network, a convolutional neural network, a long short-term memory network, etc.

[0054] In the embodiment of the present invention, the machine learning model is a multi-scale Kolmogorov-Arnold network (MKAN) model, and the model structure is referenced Figure 4 shown.

[0055] In S250, using the turbine machinery support stiffness intelligent prediction model to perform turbine machinery support stiffness intelligent prediction includes: Perform multi-scale feature extraction and conversion on the newly input support stiffness and damping ratio data to obtain the conversion result; Performing a transformation operation on the transformation result to obtain a multi-scale feature vector; Performing feature fusion on the multi-scale feature vectors to obtain an intelligent prediction result of the turbomachinery support stiffness; Wherein, the intelligent prediction result of the turbomachinery support stiffness includes the dynamic stiffness curves of the support structure in the vertical and horizontal directions.

[0056] Multi-scale feature extraction and transformation can effectively capture the global characteristics and local details in the input data, ensuring that features of different scales are fully characterized. It can more comprehensively reflect the changing laws of support stiffness and damping ratio, providing rich basic information for subsequent feature processing. In addition, multi-scale feature extraction can enhance the generalization ability of the model and adapt it to different working conditions.

[0057] The conversion results are further converted into multi-scale feature vectors to achieve structured representation of complex data. This process effectively maps the original features into a high-dimensional feature space, helps to reveal the deep connections between data, and improves the model's ability to capture nonlinear relationships, thus providing a more accurate data foundation for intelligent prediction.

[0058] Feature fusion can integrate key information in multi-scale features, eliminate redundancy, enhance the integrity and stability of feature expression, help improve the accuracy and robustness of the prediction model, and enable the model to fully utilize the synergy of features at different scales to generate more reliable prediction results.

[0059] By generating dynamic stiffness curves of the support structure in the vertical and horizontal directions, the dynamic characteristics of the turbomachinery support stiffness can be fully displayed. These curves provide an important basis for monitoring and analyzing the operating status of the equipment, helping to detect abnormalities in a timely manner and improve the safety and stability of equipment operation. In addition, these results can also be used to optimize design, formulate maintenance strategies and improve operating performance.

[0060] In some implementations, multi-scale feature extraction and conversion are performed on the newly input support stiffness and damping ratio data to obtain conversion results including: Extracting different scale features of the newly input support stiffness and damping ratio data; The feature extraction results of each scale of the newly input support stiffness and damping ratio data are converted into a new representation by utilizing nonlinear changes of multiple activation functions; The new representation is subjected to weighted summation and nonlinear transformation to obtain a transformation result.

[0061] Here, the feature extraction results of each scale of the newly input support stiffness and damping ratio data are converted into a new representation by utilizing the nonlinear changes of multiple activation functions, which can be understood as follows: For a set of input data , at each scale In the feature extraction process, the first layer of neurons in MKAN converts each input Through the nonlinear changes of multiple activation functions, it is transformed into a new representation. Specifically, for the Input , through the The processing of neurons can be obtained ,Right now: ; in, The new representation formed by the representation transformation, is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n Layer l The weight of the neuron, is the corresponding bias, Indicates The B-spline basis functions are The value of , N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale s The grid size below, Representation scale s The spline degree of the B-spline curve below.

[0062] The conversion result is converted to obtain a multi-scale feature vector including: By forming a univariate continuous function of the input data , and Through nonlinear mapping, it is transformed into a new feature space. Furthermore, the second layer grid is the output of the first layer Perform weighted summation and nonlinear transformation to obtain : ; After multi-scale feature extraction, the input data is converted into a multi-scale feature vector through a concatenation operation, which is expressed as follows: ; in, Indicated in The conversion result obtained by scale is , is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n The weight of the second neuron in the layer, is the corresponding bias, Indicates The B-spline basis functions are The value of , N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale s The grid size below, Representation scale s The spline degree of the B-spline curve below.

[0063] Finally, the multi-scale features are summed up by nonlinear weighted summation. By performing feature fusion, we can get the final output : ; in, It represents the intelligent prediction result of turbomachinery support stiffness. represents the weight of the fusion layer, represents the multi-scale feature vector, Represents the bias of the fusion layer.

[0064] Combining the above formula with the Kolmogorov-Arnold theorem, we can get the approximate principle of MKAN as follows: ; On this basis, the present invention designs the loss function of the intelligent prediction model of turbine machinery support stiffness include: ; in, represents the number of samples, represents the loss function used to measure the difference between the predicted value and the true value, Represents the network model, Representation scale s Next input mThe characteristics of the samples, Indicates the corresponding true value.

[0065] Based on the above technical solution, the present invention also verifies the intelligent prediction model of turbomachinery support stiffness, including: Different models were compared, including Convolutional Neural Network (CNN), Residual Network (ResNet), and a novel neural network architecture (Kolmogorov-Arnold Networks, KAN). The KAN model was tested at three different scales, which correspond to the scales used in the MKAN model, with grid sizes of 5, 10, and 20. The mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R 2 ) to verify the results. All three models use Adam optimizer for parameter optimization. The training process is repeated 500 times, with a learning rate of 0.001 and a batch size of 16.

[0066] MAE, RMSE, R 2 The formula for the coefficient of determination is: ; ; ; in, Indicates the number of training batches. Represents the true value of a batch of samples, Represents the predicted value of a batch of samples, Indicates samples, Represents the total number of samples.

[0067] The loss during training reflects the convergence ability of the model. Figure 5 This is the change in loss of the experimental model under vertical and horizontal training data. Figure 5 (a) and Figure 5As shown in (b), the convergence and stability of the MKAN model are significantly better than those of other models, with lower loss values. Specifically, the loss curve of the MKAN model shows a rapid decline and stabilizes in fewer iterations, eventually reaching the lowest loss value. This shows that MKAN has enhanced feature learning and optimization capabilities during training. In contrast, the ResNet model exhibits a higher initial loss and a slower rate of decline. Although it eventually stabilizes, its final loss is still significantly greater than that of the MKAN model, indicating that its ability to capture data features is weaker. The CNN model performs slightly better than ResNet; however, its final loss is still significantly higher than that of MKAN, indicating that its generalization performance is relatively limited. Although the KAN model shows faster convergence in the vertical direction, it does not exceed MKAN, which strengthens the assertion that multi-scale extraction enhances feature capture. In addition, although the KAN model converges quickly in the vertical direction, its training process lacks smoothness, especially in the horizontal direction, where a large peak appears, indicating a certain instability.

[0068] For the prediction of dynamic stiffness in the vertical direction, the present invention first evaluates the overall generalization of the model. Figure 6 is the evaluation factor of each model in the verification experiment in any vertical direction. Figure 6 As shown in (a), MKAN outperforms other models with higher consistency and stability, with R 2 The scores remain high. Figure 6 As can be seen in (b), MKAN maintains the lowest MAE value, reflecting its ability to minimize prediction error. KAN also achieves low error values ​​in most cases, but lags slightly behind MKAN in some areas. In contrast, ResNet and CNN have higher MAE values, and the errors of some data points are significantly larger. Figure 6 (c) It can be seen that MKAN can obtain the lowest RMSE value in all test data, further confirming its superior error control ability. Although KAN is better than ResNet and CNN, it still lags behind MKAN.

[0069] The prediction results are quantitatively evaluated and summarized as shown in Table 1, which gives the average evaluation factors of the prediction results of each model in the validation experiment in any vertical direction. It is obvious that the MKAN model outperforms other models in all evaluation indicators. Specifically, its Average Coefficient of Determination (Mean R2 score) score is 0.963401, which is 9.17%, 3.98%, 4%, 2.02% and 3.74% higher than ResNet, CNN and KAN at different grid sizes, respectively. In terms of Mean Absolute Error (Mean MAE), the MKAN model has the lowest error of 0.025573, which is 49.44% lower than the ResNet model, 39.66% lower than the CNN model, and 30.78%, 16.58% and 32.24% lower than the KAN model at different grid sizes. This shows that MKAN significantly reduces the prediction error and more accurately estimates the true value in the real prediction scenario. In terms of Mean Root Mean Square Error (MeanRMSE), MKAN achieves an error of 0.037957, which is 48.92%, 37.51%, 31.78%, 21.33%, and 29.59% lower than ResNet, CNN, and KAN models with different grid sizes, respectively. The significant reduction in RMSE indicates that MKAN provides better error control, especially when dealing with large deviations, and maintains higher prediction stability over a wide range of data.

[0070] Table 1 Schematic diagram of average evaluation factors of each vertical direction verification experiment

[0071] In addition, the present invention uses specific sample predictions to accurately evaluate the effectiveness and superiority of the network model. Figure 7 is the prediction result of each model in Experiment 1. Figure 7 In (a), the CNN prediction results show obvious deviations, especially in the mid- and high-frequency bands, and cannot accurately capture the dynamic stiffness characteristics, especially the peak value. Figure 7 (b) provides improved performance, especially in the range of 0.6 to 0.8, but errors still exist, especially when capturing peaks. Figure 7(c)-(e) show the performance of the KAN model with different mesh sizes. They perform well in the low-frequency band and some mid-frequency bands; however, they deviate from the true value in the high-frequency region. It has been observed that using a finer mesh does not enhance the generalization of the model; instead, it only improves the accuracy in a specific fitting region. Moreover, this is accompanied by an increase in local noise. In contrast, Figure 7 As shown in (f), the MKAN model shows good fitting ability in the entire frequency band. It is worth noting that MKAN can accurately capture the dynamic stiffness curve and identify multiple frequency peaks.

[0072] Evaluate the dynamic stiffness data in the horizontal direction. Figure 8 The prediction performance of each model is compared. Obviously, the performance of MKAN is significantly better than other models. 2 In terms of coefficients, MKAN consistently provides the best performance in all sample experiments, while achieving the lowest levels of MAE and RMSE in almost all cases. This highlights MKAN's superior ability to comprehensively capture complex patterns in the input data.

[0073] The present invention calculates the statistical averages of the evaluation indicators of all sample data sets, as shown in Table 2. From these results, it can be seen that the MKAN model outperforms other models in all indicators. 2 The score reaches 0.994681, which is about 7.17% higher than ResNet, 2.99% higher than CNN, and 1.57%, 1.09%, and 1.03% higher than KAN. In terms of average MAE, MKAN has the smallest error of 0.008656, which is 81.46% lower than ResNet, 74.51% lower than CNN, and 60.15%, 57.24%, and 57.10% lower than the three-parameter KAN, respectively. Similarly, for average RMSE, MKAN performs well with an error of 0.015608, which is 77.10% lower than ResNet, 67.75% lower than CNN, and 52.06%, 46.00%, and 46.45% lower than the three-parameter KAN, respectively. In summary, these results once again verify the superiority and effectiveness of the MKAN model for dynamic stiffness prediction.

[0074] Table 2 Schematic diagram of average evaluation factors of verification experiments in each horizontal direction

[0075] In addition, the present invention also examines specific experimental cases to evaluate the effectiveness of the network model predictions. Fig. 9The prediction results of each model in Experiment 2. The CNN model effectively captures the overall trend of the dynamic stiffness in most frequency ranges. However, it shows significant deviations, especially in the higher frequency range from 0.7 to 1.0. The ResNet model shows superior performance in the frequency range of 0.4 to 0.8. However, it still shows inaccuracies in the higher frequency range, especially around 0.9. For the three grid sizes, the KAN model shows effective performance in the frequency range of 0.3 to 0.7. However, it shows deviations in all high-frequency bands, especially from 0.9 to 1.0. In contrast, the MKAN model outperforms the other models and maintains a high degree of consistency with the true value in almost all frequency intervals. It accurately captures the fluctuation characteristics, especially in the higher frequency region. Overall, the MKAN model shows excellent performance in the entire frequency range, with excellent prediction accuracy and adaptability to dynamic characteristics, while the other models show limitations in the high-frequency range.

[0076] According to a second aspect of an embodiment of the present invention, there is also provided a turbomachinery support stiffness intelligent prediction device, referring to Fig.10 As shown, the turbomachinery support stiffness intelligent prediction device 1000 comprises: A model building module 1010 is used to build a reduced finite element model based on a real turbomachinery foundation support model; A sample set construction module 1020 is used to construct a data sample set of support stiffness and damping ratio of the reduced finite element model by using a Latin hypercube sampling method; The curve generating module 1030 is used to perform finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the supporting structure in vertical and horizontal directions; A prediction model generation module 1040, configured to construct an intelligent prediction model for support stiffness of a turbomachinery according to the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions; The prediction module 1050 is implemented to perform intelligent prediction of the support stiffness of the turbine machinery by using the intelligent prediction model of the support stiffness of the turbine machinery.

[0077] It should be noted that, although several modules and submodules of the turbomachinery support stiffness intelligent prediction device are mentioned in the above detailed description, this division is not mandatory. In fact, according to an embodiment of the present invention, the features and functions of two or more modules or submodules described above can be embodied in one module or unit. Conversely, the features and functions of one module or submodule described above can be further divided into multiple modules or submodules to be embodied.

[0078] In addition, in an exemplary embodiment of the present invention, an electronic device capable of implementing the above-mentioned method for intelligent prediction of turbomachinery support stiffness is also provided.

[0079] Those skilled in the art will appreciate that various aspects of the present invention may be implemented as systems, methods or program products. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: complete hardware embodiments, complete software embodiments (including firmware, microcode, etc.), or embodiments combining hardware and software aspects, which may be collectively referred to herein as "circuits", "modules" or "systems".

[0080] Refer to the following Fig.11 1100 according to this embodiment of the present invention will be described. Fig.11 The electronic device 1100 shown is merely an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0081] like Fig.11 As shown, the electronic device 1100 is in the form of a general computing device. The components of the electronic device 1100 may include but are not limited to: the at least one processing unit 1110, the at least one storage unit 1120, a bus 1130 connecting different system components (including the storage unit 1120 and the processing unit 1110), and a display unit 1140.

[0082] The storage unit stores program codes, which can be executed by the processing unit 1110, so that the processing unit 1110 performs the steps of various exemplary embodiments of the present invention described in the above “Exemplary Method” section. For example, the processing unit 410 can perform the following steps: Figure 2 As shown in S210, a reduced finite element model is established based on a real turbine machinery foundation support model; S220, a data sample set of support stiffness and damping ratio of the reduced finite element model is constructed using the Latin hypercube sampling method; S230, a finite element analysis is performed on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in the vertical and horizontal directions; S240, a turbine machinery support stiffness intelligent prediction model is constructed based on the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions; S250, the turbine machinery support stiffness intelligent prediction model is used to perform turbine machinery support stiffness intelligent prediction.

[0083] The storage unit 1120 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 1121 and / or a cache memory unit 1122 , and may further include a read-only memory unit (ROM) 1123 .

[0084] The storage unit 1120 may also include a program / utility 1124 having a set (at least one) of program modules 1125, such program modules 1125 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0085] Bus 1130 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0086] The electronic device 1100 may also communicate with one or more external devices 1170 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 1100, and / or communicate with any device that enables the electronic device 1100 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed through an input / output (I / O) interface 1150. In addition, the electronic device 1100 may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) through a network adapter 1160. As shown, the network adapter 1160 communicates with other modules of the electronic device 1100 through a bus 1130. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the electronic device 1100, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0087] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the exemplary embodiments described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the embodiment of the present invention can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiment of the present invention.

[0088] In an exemplary embodiment of the present invention, a computer-readable storage medium is also provided, on which a program product capable of implementing the above method of the present invention is stored. In some possible embodiments, various aspects of the present invention can also be implemented in the form of a program product, which includes a program code, and when the program product is run on a terminal device, the program code is used to enable the terminal device to perform the steps of various exemplary embodiments of the present invention described in the above "Exemplary Method" section of the present invention.

[0089] refer to Fig.12 As shown, a program product 1200 for implementing the above-mentioned intelligent prediction method for foundation stiffness of a turbomachinery according to an embodiment of the present invention is described, which can adopt a portable compact disk read-only memory (CD-ROM) and include program code, and can be run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto. In the present invention, the readable storage medium can be any tangible medium containing or storing a program, and the program can be used by or in combination with an instruction execution system, an apparatus or a device.

[0090] The program product may use any combination of one or more readable storage media. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0091] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0092] In addition, the above-mentioned figures are only schematic illustrations of the processes included in the method according to an exemplary embodiment of the present invention, and are not intended to be limiting. It is easy to understand that the processes shown in the above-mentioned figures do not indicate or limit the time sequence of these processes. In addition, it is also easy to understand that these processes can be performed synchronously or asynchronously, for example, in multiple modules.

[0093] Through the description of the above embodiments, it is easy for those skilled in the art to understand that the exemplary embodiments described here can be implemented by software, or by software combined with necessary hardware. Therefore, the technical solution according to the embodiment of the present invention can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to execute the method according to the embodiment of the present invention.

[0094] Other embodiments of the invention will readily occur to those skilled in the art after considering the specification and practicing the invention disclosed herein. The invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0095] It should be understood that the present invention is not limited to the exact construction that has been described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for intelligent prediction of turbomachinery support stiffness, characterized in that: include: Based on the real turbomachinery foundation support model, a reduced finite element model is established; Using a Latin hypercube sampling method, a data sample set of support stiffness and damping ratio of the reduced finite element model is constructed; Performing finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the support structure in vertical and horizontal directions; Constructing a turbomachinery support stiffness intelligent prediction model based on the data sample set and the dynamic stiffness curves of the support structure in vertical and horizontal directions; The turbine machinery support stiffness intelligent prediction model is used to perform turbine machinery support stiffness intelligent prediction.

2. The method for intelligent prediction of turbomachinery support stiffness according to claim 1, characterized in that: Using the turbine machinery support stiffness intelligent prediction model to perform turbine machinery support stiffness intelligent prediction includes: Perform multi-scale feature extraction and conversion on the newly input support stiffness and damping ratio data to obtain the conversion result; Performing a transformation operation on the transformation result to obtain a multi-scale feature vector; Performing feature fusion on the multi-scale feature vectors to obtain an intelligent prediction result of the turbomachinery support stiffness; Wherein, the intelligent prediction result of the turbomachinery support stiffness includes the dynamic stiffness curves of the support structure in the vertical and horizontal directions.

3. The intelligent prediction method for turbomachinery support stiffness according to claim 2, characterized in that: The newly input support stiffness and damping ratio data are subjected to multi-scale feature extraction and conversion, and the conversion results include: Extracting different scale features of the newly input support stiffness and damping ratio data; The feature extraction results of each scale of the newly input support stiffness and damping ratio data are converted into a new representation by utilizing nonlinear changes of multiple activation functions; The new representation is subjected to weighted summation and nonlinear transformation to obtain a transformation result.

4. The method for intelligent prediction of turbomachinery support stiffness according to claim 3, characterized in that: Using nonlinear changes of multiple activation functions, the feature extraction results of each scale of the newly input support stiffness and damping ratio data are converted into a new representation including: ； in, The new representation formed by the representation transformation, is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n Layer l The weight of the neuron, is the corresponding bias, Indicates The B-spline basis functions are The value of N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale The grid size below, Representation scale The spline degree of the B-spline curve below.

5. The method for intelligent prediction of turbomachinery support stiffness according to claim 2, characterized in that: The transformation result is transformed to obtain a multi-scale feature vector include: ； in, Indicated in The conversion result obtained by scale is , is the activation function and , Indicates the newly entered support stiffness and damping ratio data for the connection No. n The weight of the second neuron in the layer, is the corresponding bias, Indicates The B-spline basis functions are The value of N is the number of B-spline basis functions, are the control points of the spline basis function, Representation scale The grid size below, Representation scale The spline degree of the B-spline curve below.

6. The intelligent prediction method for turbomachinery support stiffness according to claim 2, characterized in that: The multi-scale feature vectors are subjected to feature fusion to obtain the intelligent prediction results of the turbomachinery support stiffness, including: ； in, It represents the intelligent prediction result of turbomachinery support stiffness. represents the weight of the fusion layer, represents the multi-scale feature vector, Represents the bias of the fusion layer.

7. The method for intelligent prediction of turbomachinery support stiffness according to any one of claims 1 to 6, characterized in that: The loss function of the intelligent prediction model for turbomachinery support stiffness include: ； in, represents the number of samples, represents the loss function used to measure the difference between the predicted value and the true value, Represents the network model, Representation scale s Next input m The characteristics of the samples, Indicates the corresponding true value.

8. A device based on the turbomachinery support stiffness intelligent prediction method according to any one of claims 1 to 7, characterized in that: include: Model building module for building reduced finite element models based on real turbomachinery foundation support models; A sample set construction module, used to construct a data sample set of support stiffness and damping ratio of the reduced finite element model by using a Latin hypercube sampling method; A curve generating module, used for performing finite element analysis on each data sample in the data sample set to generate dynamic stiffness curves of the supporting structure in vertical and horizontal directions; A prediction model generation module, used for constructing a turbomachinery support stiffness intelligent prediction model based on the data sample set and the dynamic stiffness curves of the support structure in the vertical and horizontal directions; A prediction module is implemented to perform intelligent prediction of turbine machinery support stiffness using the turbine machinery support stiffness intelligent prediction model.

9. An electronic device, characterized in that: include: processor; as well as A memory having computer-readable instructions stored thereon, wherein the computer-readable instructions, when executed by the processor, implement the method for intelligent prediction of support stiffness of a turbomachinery according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the method for intelligently predicting the support stiffness of a turbomachinery according to any one of claims 1 to 7 is implemented.

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