Mechanical rotating body deformation amount prediction method and system based on PINN and multi-physical field coupling

Abstract

The application provides a mechanical rotating body deformation prediction method and system based on PINN and multi-physical field coupling, and relates to the field of industrial intelligent computing model. The method firstly fuses multi-physical field data such as thermal expansion, pressure, wear and elastic deformation to construct a dynamic equivalent radius model reflecting the real geometric state of the mechanical rotating body; secondly, a time-varying constraint physical information neural network solver is designed to fuse the mechanical mechanism and data driving; finally, the multi-component coupling effect of the mechanical system is solved, the rotating body deformation prediction value is fused, and the comprehensive deformation of the rotating body under complex load is obtained. In general, the method can improve the accuracy and real-time performance of the rotating body deformation calculation, improve the accuracy of the external load and displacement calculation, thereby improve the workpiece deformation prediction accuracy, and provide core theoretical support for high-precision industrial processes.

Description

Technical Field

[0001] This invention relates to the field of industrial intelligent computing models, and in particular to a method and system for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling. Background Technology

[0002] In many industrial applications, especially in scenarios involving the dynamic deformation of mechanical components, accurate prediction of component deformation under complex loads is crucial for ensuring product quality and production efficiency. Traditional methods, such as the Hitchcock model, neglect the nonlinearity of pressure distribution in mechanical components and fail to consider the coupling effects of multi-component deformation, making them only applicable to simple working conditions. The Shohet model has a computational delay exceeding 10 minutes, limiting its application to offline use. The finite element method relies on finite element calibration, and setting complex contact boundary conditions is difficult. Most existing computational models fail to meet real-time and accuracy requirements due to the lack of multi-physics dynamic coupling and efficient computational methods. Therefore, a real-time deformation prediction computational method for rotating mechanical bodies that can efficiently achieve multi-physics coupling is needed. Summary of the Invention

[0003] Purpose of the invention: To solve the above problems, this invention fully utilizes the data-driven PINN intelligent model, incorporates multi-source physical constraints, calculates the coupling effect between working parts and supporting parts, and proposes a method and system for predicting the deformation of mechanical rotating bodies based on PINN and multi-physics coupling. This method can achieve efficient prediction of the deformation of mechanical parts under complex loads and is particularly suitable for calculating the deformation of mechanical rotating bodies. In particular, it solves the real-time and accuracy bottleneck problems caused by the neglect of dynamic coupling effects in traditional calculation models.

[0004] In a first aspect, the present invention proposes a method for predicting the deformation of a mechanical rotating body based on PINN coupled with multiphysics, comprising the following steps:

[0005] A pressure sensor is installed on the surface of the bearing component of the rotating body to collect the original pressure signal; a distributed temperature sensor is laid in the internal cavity of the rotating body to collect the temperature of the cooling water channel and reconstruct it into the effective temperature field of the rotating body surface.

[0006] By integrating the original pressure signal and the effective temperature field on the surface of the rotating body, the dynamic equivalent radius is calculated.

[0007] A time-varying constraint PINN is constructed as a predictor of the deformation of the body of revolution. The dynamic equivalent radius is used as one of the input parameters of the predictor of the deformation of the body of revolution. The preset physical constraints are embedded into the learning process of the predictor of the deformation of the body of revolution. The predicted value of the deformation of the body of revolution is output by the predictor of the deformation of the body of revolution.

[0008] Solve for the coupling effect of multiple components in the mechanical system, and integrate the predicted values ​​of the deformation of the rotating body to obtain the comprehensive deformation of the rotating body under complex loads.

[0009] In a further embodiment of the first aspect, a pressure sensor is installed on the surface of the bearing component of the rotating body, the pressure sensor acquires the raw pressure signal, and Kalman filtering is used to eliminate high-frequency hydraulic vibration noise:

[0010]

[0011] In the formula, The signal is the original pressure signal after Kalman filtering; x is the axial position coordinate of the rotating body; t is the time variable, the start-up time. ; p is the time index; The sampling interval; The time constant of the hydraulic system; This represents the original pressure signal at the axial position x and time t of the rotating body.

[0012] In a further embodiment of the first aspect, distributed temperature sensors are installed in the internal cavities of the rotating body to collect the temperature of the cooling water channels. And reconstructed into the effective temperature field of the surface of the rotating body. :

[0013]

[0014] In the formula, The heat flux density of the cooling water; Let the radius be the surface radius of the body of revolution; Radius of the cooling water channel; Thermal conductivity; denoted as the thermal diffusivity of the rotating material.

[0015] In a further embodiment of the first aspect, the original pressure signal after Kalman filtering is fused. Effective temperature field on the surface of the rotating body Calculate the dynamic equivalent radius :

[0016]

[0017] In the formula, The nominal radius of the rotating body in its cold state; The coefficient of thermal expansion of the rotating body material; The temperature is the 30-second moving average. The wear depth; The wear distribution is Gaussian. This represents the elastic deformation component.

[0018] In a further embodiment of the first aspect, the wear depth The following formula is used to calculate:

[0019]

[0020] In the formula, As the baseline wear rate, For real-time external loads, by Obtained by integral calculation; As the reference external load, The material hardening index;

[0021] Gaussian wear distribution The following formula is used to calculate:

[0022]

[0023] In the formula, This is the location of the wear center; For wear distribution bandwidth;

[0024] The elastic deformation component The original pressure signal after Kalman filtering Solving by integration yields:

[0025]

[0026] In the formula, s is the integral position variable, d is the contact half-width, v is Poisson's ratio, and E is the elastic modulus.

[0027] In a further embodiment of the first aspect, the time-varying constraint PINN includes an input layer, a data constraint layer, a physical constraint layer, and an output layer;

[0028] The input layer accepts a five-dimensional vector. ;

[0029] in, The average pressure in the contact area; The effective temperature field on the surface of the rotating body; Effective viscosity for lubrication; For process speed; For dynamic equivalent radius; Indicates the transpose operation;

[0030] The data-driven layer consists of four gated physical units, and the output of the fourth gated physical unit is passed as input to the physical constraint layer.

[0031] The physical constraint terms consist of elastic constraints, thermal constraints, boundary constraints, and rheological constraints. :

[0032]

[0033] In the formula, This represents the deformation of the body of revolution. For the Laplace operator; For time-varying weights; Where is the thermal diffusivity; L is the transverse length of the rotating body; For constraint strength; The yield strength of the material is given by A; A, P, and B are the experimentally calibrated rheological parameters of the material; and T is the temperature field distribution on the surface of the rotating body. Strain rate;

[0034] The output layer predicts the output, yielding the predicted value of the deformation of the rotating body:

[0035]

[0036] In the formula, This is the predicted value of the deformation of the rotating body. , For position The elastic deformation of the rotating body at that point; This is the output of the fourth-layer gated physical unit, which contains data-driven features and physical constraint information; , These are the weights and biases for the output layer.

[0037] In a further embodiment of the first aspect, the solution of the multi-component coupling effect of the mechanical system specifically includes:

[0038] Measured pressure distribution Perform a Fast Fourier Transform to obtain the spatial spectrum. :

[0039]

[0040] In the formula, The pressure is in the frequency domain; N is the number of pressure sensors. This is the actual measured pressure; Here are the coordinates of the axial measurement point, and n is the coordinate index. is the spatial step size, L is the transverse length of the body of revolution; k is the harmonic order of axial deformation.

[0041] From the spatial spectrum Calculate the frequency domain response of the support component :

[0042]

[0043] In the formula, For the frequency response characteristics of the supporting components, , For surface roughness attenuation, , Poisson's ratio for the supporting components; The elastic modulus of the supporting component; This refers to the amount of wear. ; This is the wear influence coefficient; Roughness factor;

[0044] Frequency domain response of the support components Perform iterative coupling of the working component and the support component until the continuity is satisfied. The cumulative error of the next iteration is less than the error threshold. The deformation iteration values ​​of the working parts are obtained. .

[0045] In a further embodiment of the first aspect, thermal deformation and physical reference values ​​are calculated, and the predicted value of the deformation of the rotating body output by PINN is fused to obtain the comprehensive deformation of the working part.

[0046] The thermal deformation Calculated using the following formula:

[0047]

[0048] In the formula, This represents the temperature change, specifically the difference between the current temperature and the reference temperature. This is the thermal convexity coefficient; This is the thermal inertia compensation factor; The nominal radius of the rotating body in its cold state; The coefficient of thermal expansion of the rotating body material;

[0049] By combining frequency domain and physical domain information, a physical reference is obtained. ,at the same time Predicted values ​​of deformation of rotating bodies The error between them satisfies the condition At that time, the physical constraint layer is triggered to update in real time:

[0050]

[0051] In the formula, ; The deformation caused by the mechanical load output by the coupled iteration;

[0052] Fusion and Obtain the comprehensive deformation amount :

[0053]

[0054] In the formula, These are the weighting coefficients; This represents the number of hours the machine has been running.

[0055] A second aspect of the present invention provides a system for predicting the deformation of a rotating body, which can automatically execute the method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling disclosed in the first aspect and its further embodiments. The prediction system specifically includes:

[0056] A pressure sensor is installed on the surface of the bearing component of the rotating body, and the original pressure signal is collected by the pressure sensor.

[0057] A distributed temperature sensor is installed in the internal cavity of the rotating body. The temperature of the cooling water channel is collected by the distributed temperature sensor and reconstructed into an effective temperature field on the surface of the rotating body.

[0058] The calculation module is used to fuse the original pressure signal and the effective temperature field of the rotating body surface to calculate the dynamic equivalent radius;

[0059] A rotational body deformation predictor based on time-varying constraint PINN; the dynamic equivalent radius is used as one of the input parameters of the rotational body deformation predictor, and the preset physical constraints are embedded into the learning process of the rotational body deformation predictor, and the rotational body deformation predictor outputs the predicted value of the rotational body deformation.

[0060] The final result output module is used to solve the coupling effect of multiple components in the mechanical system, and integrate the predicted value of the deformation of the rotating body to obtain the comprehensive deformation of the rotating body under complex loads.

[0061] Beneficial Effects: The proposed method for predicting the deformation of rotating bodies integrates PINN with multi-domain physical constraints to predict the deformation, overcoming the limitations of traditional data-driven models that lack mechanistic constraints. Real-time updates of the equivalent radius using multi-source data such as thermal expansion, pressure, wear, and elastic deformation significantly improve the accuracy of multi-physics coupling. The fusion of the physical benchmark obtained from the coupled response with PINN deformation prediction enhances the anti-drift capability of the deformation prediction method. Dynamic self-learning updates improve the model's generalization ability and adaptability to complex working conditions. In summary, this method greatly improves the accuracy and real-time performance of calculating the deformation of rotating bodies, enhances the accuracy of external load and displacement calculations, thereby improving workpiece deformation accuracy and significantly reducing processing costs. It provides core theoretical support for high-precision industrial processes and can be applied to deformation prediction in industrial equipment such as rotating machinery, pressure vessels, and transmission systems. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0063] Figure 1 This is a flowchart of the method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling in the embodiment.

[0064] Figure 2 This is a schematic diagram of the time-varying constraint PINN in the embodiment. Detailed Implementation

[0065] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0066] This invention fully utilizes the data-driven PINN intelligent model, incorporates multi-source physical constraints, and calculates the coupling effect between working and supporting components. It proposes a method for predicting the deformation of rotating mechanical bodies based on PINN and multi-physics coupling. Specifically, firstly, it fuses multi-physics data such as thermal expansion, pressure, wear, and elastic deformation in real time to construct a dynamic equivalent characteristic model reflecting the true geometric state of the mechanical components. Secondly, it designs a time-varying constraint PINN solver, integrating mechanical mechanisms with data-driven approaches. Finally, it solves for the coupling effect of multiple components in the mechanical system, fusing the predicted deformation value and the physical reference value to obtain the comprehensive deformation of the mechanical components, thereby contributing to the efficient and accurate control of component deformation precision.

[0067] The following section, in conjunction with the accompanying drawings, provides a detailed explanation of this scheme.

[0068] A method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling, the process of which is as follows: Figure 1 As shown.

[0069] Step 1: Construct a dynamic equivalent feature model based on multi-source sensor data and calculate the dynamic equivalent radius. High-precision pressure sensors are installed on the surface of the bearing components of the rotating body. The sensors acquire the raw pressure signals, and Kalman filtering is used to eliminate high-frequency hydraulic vibration noise.

[0070]

[0071] in, The load pressure signal is processed by Kalman filtering; x is the axial position coordinate of the rotating body (width direction); t is the time variable (starting time of the mechanical system). p is the time index; The sampling interval is 0.5ms. The hydraulic system time constant (value is 5ms); The pressure signal at position x and time t;

[0072] Distributed fiber optic temperature sensors are deployed within the internal cavity of the rotating body. The surface temperature of the rotating body is retrieved via Raman scattering for temperature field reconstruction, thereby reducing surface temperature errors.

[0073]

[0074] in, The effective temperature field on the surface of the component; This refers to the temperature of the cooling water channels; The heat flux density of the cooling water; Let the radius be the surface radius of the body of revolution; Radius of the cooling water channel; Thermal conductivity (value is given) ); This is the thermal diffusivity (material constant) of the rotating material.

[0075] Fusion , Based on multi-source sensor data, the dynamic equivalent radius is calculated as follows:

[0076]

[0077] in, For dynamic equivalent radius; The nominal radius of the rotating body in its cold state (reference value); The coefficient of thermal expansion of the rotating body material (taken as for forged steel rotating bodies) is . ); The temperature is the 30-second moving average. For wear depth, The baseline wear rate (calibrated value) ), For real-time external loads, by Integral calculation yields , The reference external load is 2000kN. The material hardening index (value 1.7). The wear distribution is Gaussian. The location of the wear center (measured by an eddy current sensor); The wear distribution bandwidth (calibrated value 100mm); The elastic deformation component is obtained by filtering the pressure signal. The integral solution is used to prevent oscillation distortion, thereby improving the calculation accuracy of the elastic deformation component. s is the integral position variable, d is the contact half-width, v is Poisson's ratio (the ratio of the material's transverse strain to its longitudinal strain; v=0.3 when the rotating body is forged steel), and E is the elastic modulus (210 GPa for forged steel).

[0078] Step Two: As Figure 2 The time-varying constrained PINN rotational body deformation predictor is constructed as shown, and the result obtained in step one is used to predict the deformation amount. (simplified to) As one of the input parameters of PINN, physical constraints are embedded into the learning process of PINN to realize the fusion of mechanism and data calculation, break through the limitation of traditional data-driven models that lack physical constraints, and improve generalization ability.

[0079] PINN consists of an input layer, a data constraint layer, a physical constraint layer, and an output layer. First, the PINN input layer accepts a five-dimensional vector:

[0080]

[0081] in, The average pressure in the contact area, ; The result obtained in equation (2) ; For effective lubrication viscosity, Based on viscosity (value) ), Pressure influence coefficient (value) ), Temperature influence coefficient (value) ), The change in temperature , This is the initial startup temperature. The process temperature at time t; The process speed.

[0082] The data-driven layer consists of four gated physical units (GPU-cells), and the structure of each GPU-cell is as follows:

[0083]

[0084] Where m is the number of training iterations. To control the percentage of historical states retained, use the forget gate. , for The trainable weight matrix and bias vector in the middle. It is the sigmoid activation function; To reset the gate and control the proportion of new information fusion, , for The trainable weight matrix and bias vector; To generate new candidate states, For Hadamard product, , for The trainable weight matrix and bias vector; The new state is obtained by fusing historical states with new candidate states and injecting physical constraints. For physical constraints, For time-varying constraint strength coefficients, design The performance decays with each training round m, initially enhancing physical constraints and later releasing data-driven capabilities.

[0085] The output of the fourth GUP-cell is passed as input to the physical constraint layer. The physical constraints consist of four terms: elastic constraints, thermal constraints, boundary constraints, and rheological constraints. The calculation is as follows:

[0086]

[0087] Among them, the elastic constraint term forces the rotating body to satisfy Hertzian contact theory, and the v, E, and P parameters are the same as above. This represents the deformation of the body of revolution. The Laplace operator (second derivative in space); the thermal constraint term couples the temperature field and the deformation field. For time-varying weights, , Where is the thermal diffusivity, , Thermal conductivity, The density of the material to be manufactured (such as sheet metal). Let L be the specific heat capacity of the material to be processed; the boundary constraint term ensures that the transverse boundary conditions are satisfied during machining (such as rolling), and L is the transverse length of the body of revolution; the material rheological constraint is coupled with the plastic behavior of the workpiece material. The constraint strength is 0.2. Let A be the material's yield strength, p be the experimentally calibrated material rheological parameters, and T be the temperature field distribution on the surface of the rotating body. For strain rate, h is the instantaneous thickness of the workpiece (measured by an online thickness gauge).

[0088] The output layer predicts the output, yielding the predicted values ​​for the deformation of the body of revolution.

[0089]

[0090] in, This is the predicted value of the deformation of the rotating body. , For position The elastic deformation of the rotating body at that point; This is the output of the fourth-layer GPU-cell, which contains data-driven features and physical constraint information; , These are the weights and biases for the output layer.

[0091] Next, the loss function in optimized equation (8) is used to pre-train PINN using the Finite Element Method (FEM). After pre-training, an initial model for deformation prediction is obtained. The pre-training loss function is designed as follows:

[0092]

[0093] in, For pre-training loss; N is the batch size (e.g., 128). Let be the deformation predicted by the network in the i-th batch; The reference deformation is calculated for the i-th batch of FEM. For time-varying weighting functions, , The maximum number of training steps, This represents the current number of training steps. The residuals of the four physical constraints are: The four physical constraints Norm sum of squares , These refer to elastic constraints, thermal constraints, boundary constraints, and rheological constraints, respectively.

[0094] Next, by monitoring the industrial process online and compensating for model drift in real time, an adaptive deformation prediction model is obtained. Specifically, when the prediction error reaches the maximum allowable error threshold in the industry for M consecutive times (e.g., 50), the model is optimized. (If taken) When, that is At that time, freeze the network parameters of the first three units of the GPU-cell, and only adjust the weights of the physical constraint layer. Adaptive online updates are performed to accommodate changes in the state of the rotating body, resulting in a drift compensation model for the trained model, thus solving the over-constraint problem of traditional PINN under transient conditions.

[0095]

[0096] Where M is the size of the sliding window; The actual deformation was measured using a laser rangefinder. is the regularization coefficient (which can be taken as 0.1). The regularization term is used to prevent excessive deviation from the initial state of the body of revolution. These are the initial weights for pre-training; These are network weight parameters; For adaptive weights.

[0097] Step 3: The frequency domain-physics hybrid solver enables efficient calculation of the coupling effect of multiple components. It then integrates the deformation prediction value output by PINN in Step 2 to output the comprehensive deformation of the mechanical working parts, which can reflect the real deformation state under complex loads and directly determine the final displacement control accuracy.

[0098] First, the measured pressure distribution Perform a Fast Fourier Transform to obtain the spatial spectrum. :

[0099]

[0100] in, The pressure is in the frequency domain; N is the number of pressure sensors. This is the actual measured pressure; Here are the coordinates of the axial measurement point, and n is the coordinate index. L is the spatial step size, and k is the order of the axial deformation harmonics.

[0101] Secondly, by Calculate the frequency domain response of the mechanical support components:

[0102]

[0103]

[0104]

[0105] Where k is the same as above; The frequency domain response of the support component under deformation; Frequency response characteristics of the supporting components; For surface roughness attenuation; The Poisson's ratio for the supporting component is 0.3. The elastic modulus of the supporting component (value is 210 GPa). This refers to the amount of wear. ; Wear influence coefficient (value) ); This is the roughness factor (value 0.02).

[0106] Then, from the frequency domain response The coupling iteration between the working component and the supporting component is performed as follows:

[0107] Calculate the contact pressure:

[0108]

[0109] in, Let be the contact pressure between the working component and the supporting component during the m-th iteration. Hertzian contact stiffness coefficient (values) ), Let m be the deformation of the working component in the m-th iteration; Let be the deformation of the support component in the m-th iteration, expressed by the domain response. Converted into spatial deformation via inverse FFT; This is the change in the equivalent radius. .

[0110] The support component has been deformed and updated as follows:

[0111]

[0112] Among them, L, k, As above, F is the Fast Fourier Transform operator; This represents the contact pressure between the working component and the supporting component during the m-th iteration. The lateral deformation coefficient of the supporting component material (also known as Poisson's ratio, with a value of 0.3); This is the elastic modulus (e.g., 210 GPa).

[0113] The working parts are deformed and updated using equation (15). A closed loop is formed with the deformation of the supporting components:

[0114]

[0115] in, For time-varying constrained PINN output, The Poisson's ratio for the working part is 0.3. The elastic modulus is 210 GPa.

[0116] Through adaptive relaxation acceleration based on operating conditions, the deformation iteration of the rotating body converges rapidly until the cumulative error of Z consecutive iterations is less than a certain error threshold. ,Right now Finally, the deformation value of the working part is obtained:

[0117]

[0118] in, This is the acceleration factor for iterative convergence. The base weight (its value is adjusted according to the production status, such as 0.8 for the first hour after startup, 0.4 for the specification change stage, 0.6 for steady-state rolling, and 0.7 for high-speed rolling). As an acceleration factor, This is the convergence threshold (e.g., 0.001 mm). This is the current calculated value. The value from the previous iteration. This is the value for the next working part deformation iteration.

[0119] Step 4: Integrate PINN predicted values ​​with physical baseline values ​​to output the final deformation prediction. By calculating thermal deformation and physical baseline values, and integrating PINN predicted values, the comprehensive dynamic deformation value of the working part is output.

[0120] The thermal deformation is calculated as follows:

[0121]

[0122] in, The temperature change is the difference between the current temperature and the reference temperature. The thermal convexity coefficient (e.g., taking...) ), For thermal inertia compensation factor (e.g., take...) ).

[0123] By combining frequency domain and physical domain information, a physical reference is obtained. ,at the same time Compared with PINN predicted value The error between them satisfies the condition hour( For the error threshold, if it can be taken as... This will be used to trigger real-time updates of the PINN physical constraint layer.

[0124]

[0125] in, For boundary decay function, ; The deformation caused by the mechanical load output by the coupled iteration. .

[0126] Fusion PINN Predictions and coupling effect physical reference value The system predicts the total deformation of the rotating body. The input is fed into the mechanical control system to adjust the position of the rotating body in real time, so as to ensure the deformation accuracy of the component and at the same time alleviate the problem of slow iterative convergence of large support components.

[0127]

[0128] in, These are the weighting coefficients. This represents the number of hours the machine has been running.

[0129] The technical process of the mechanical rotating body deformation prediction method based on PINN and multiphysics coupling disclosed in the above embodiments can be implemented in whole or in part through software, hardware, firmware or other arbitrary combinations.

[0130] When implemented in hardware, the above embodiments can, in whole or in part, compile the working logic and calculation process into software and run it on a rotating body deformation prediction system. In this embodiment, the system consists of a pressure sensor, a distributed temperature sensor, a calculation module, a rotating body deformation predictor, and a final result output module.

[0131] A pressure sensor is mounted on the surface of the bearing component of the rotating body, and the original pressure signal is acquired by the pressure sensor.

[0132] Distributed temperature sensors are laid in the internal cavity of the rotating body. The temperature of the cooling water channel is collected by the distributed temperature sensors and reconstructed into an effective temperature field on the surface of the rotating body.

[0133] The calculation module is used to fuse the original pressure signal and the effective temperature field of the rotating body surface to calculate the dynamic equivalent radius;

[0134] The rotational body deformation predictor is built based on the time-varying constraint PINN. The dynamic equivalent radius is used as one of the input parameters of the rotational body deformation predictor, and the preset physical constraints are embedded into the learning process of the rotational body deformation predictor. The rotational body deformation predictor outputs the predicted value of the rotational body deformation.

[0135] The final output module is used to solve the coupling effect of multiple components in the mechanical system, integrate the predicted value of the deformation of the rotating body, and obtain the comprehensive deformation of the rotating body under complex loads.

[0136] Preferably, the time-varying constraint PINN comprises an input layer, a data constraint layer, a physical constraint layer, and an output layer. The input layer accepts a five-dimensional vector consisting of the average pressure in the contact area, the effective temperature field of the rotating body surface, the effective lubrication viscosity, the process velocity, and the dynamic equivalent radius. The data-driven layer consists of four gated physical units, with the output of the fourth gated physical unit being passed as input to the physical constraint layer; the physical constraint terms consist of elastic constraints, thermal constraints, boundary constraints, and rheological constraints. The output layer predicts the output, obtaining the predicted value of the rotating body's deformation.

[0137] The final output module is used to solve the coupling effect of multiple components in the mechanical system, integrate the predicted value of the deformation of the rotating body, and obtain the comprehensive deformation of the rotating body under complex loads.

[0138] When the above-mentioned rotating body deformation prediction system is run, it can automatically execute the technical process of the mechanical rotating body deformation prediction method based on PINN and multi-physics coupling disclosed in the above embodiments, which will not be elaborated here.

[0139] When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. If the above methods are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of this application are not limited to any specific hardware, software, or firmware, or any combination of hardware, software, and firmware.

[0140] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling, characterized in that, Includes the following steps: A pressure sensor is installed on the surface of the bearing component of the rotating body to collect the original pressure signal; a distributed temperature sensor is laid in the internal cavity of the rotating body to collect the temperature of the cooling water channel and reconstruct it into the effective temperature field of the rotating body surface. By integrating the original pressure signal and the effective temperature field on the surface of the rotating body, the dynamic equivalent radius is calculated. A time-varying constraint PINN is constructed as a predictor of the deformation of the body of revolution. The dynamic equivalent radius is used as one of the input parameters of the predictor of the deformation of the body of revolution. The preset physical constraints are embedded into the learning process of the predictor of the deformation of the body of revolution. The predicted value of the deformation of the body of revolution is output by the predictor of the deformation of the body of revolution. The time-varying constraint PINN includes an input layer, a data-driven layer, a physical constraint layer, and an output layer. The input layer accepts a five-dimensional vector. ; in, The average pressure in the contact area; The effective temperature field on the surface of the rotating body; Effective viscosity for lubrication; For process speed; For dynamic equivalent radius; Indicates the transpose operation; The data-driven layer consists of four gated physical units, and the output of the fourth gated physical unit is passed as input to the physical constraint layer. The physical constraint terms consist of elastic constraints, thermal constraints, boundary constraints, and rheological constraints. : In the formula, This represents the deformation of the body of revolution. For the Laplace operator; For time-varying weights; Where is the thermal diffusivity; L is the transverse length of the rotating body; For constraint strength; The yield strength of the material is given by A; A, P, and B are the experimentally calibrated rheological parameters of the material; and T is the temperature field distribution on the surface of the rotating body. Strain rate; The output layer predicts the output, yielding the predicted value of the deformation of the rotating body: In the formula, This is the predicted value of the deformation of the rotating body. , For position The elastic deformation of the rotating body at that point; This is the output of the fourth-layer gated physical unit, which contains data-driven features and physical constraint information; , The weights and biases of the output layer; Solve for the coupling effect of multiple components in the mechanical system, and integrate the predicted values ​​of the deformation of the rotating body to obtain the comprehensive deformation of the rotating body under complex loads.

2. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling as described in claim 1, characterized in that, A pressure sensor is installed on the surface of the bearing component of the rotating body. The original pressure signal is collected by the pressure sensor, and high-frequency hydraulic vibration noise is eliminated by Kalman filtering. In the formula, The signal is the original pressure signal after Kalman filtering; x is the axial position coordinate of the rotating body; t is the time variable, the start-up time. ; p is the time index; The sampling interval; The time constant of the hydraulic system; This represents the original pressure signal at the axial position x and time t of the rotating body.

3. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling as described in claim 1, characterized in that, Distributed temperature sensors are installed in the internal cavities of the rotating body to collect the temperature of the cooling water channels. And reconstructed into the effective temperature field of the surface of the rotating body. : In the formula, The heat flux density of the cooling water; Let the radius be the surface radius of the body of revolution; Radius of the cooling water channel; Thermal conductivity; denoted as the thermal diffusivity of the rotating material.

4. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling as described in claim 1, characterized in that, The original pressure signal after Kalman filtering is fused together. Effective temperature field on the surface of the rotating body Calculate the dynamic equivalent radius : In the formula, The nominal radius of the rotating body in its cold state; The coefficient of thermal expansion of the rotating body material; The temperature is the 30-second moving average. The wear depth; The wear distribution is Gaussian. This represents the elastic deformation component.

5. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling according to claim 4, characterized in that, The wear depth The following formula is used to calculate: In the formula, As the baseline wear rate, For real-time external loads, by Obtained by integral calculation; As the reference external load, The material hardening index; Gaussian wear distribution The following formula is used to calculate: In the formula, This is the location of the wear center; For wear distribution bandwidth; The elastic deformation component The original pressure signal after Kalman filtering Solving by integration yields: In the formula, s is the integral position variable, d is the contact half-width, v is Poisson's ratio, and E is the elastic modulus.

6. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling according to claim 1, characterized in that, The solution to the multi-component coupling effect of the mechanical system specifically includes: Measured pressure distribution Perform a Fast Fourier Transform to obtain the spatial spectrum. : In the formula, The pressure is in the frequency domain; N is the number of pressure sensors. This is the actual measured pressure; Here are the coordinates of the axial measurement point, and n is the coordinate index. is the spatial step size, L is the transverse length of the body of revolution; k is the harmonic order of axial deformation. From the spatial spectrum Calculate the frequency domain response of the support component : In the formula, For the frequency response characteristics of the supporting components, , For surface roughness attenuation, , Poisson's ratio for the supporting components; The elastic modulus of the supporting component; This refers to the amount of wear. ; This is the wear influence coefficient; Roughness factor; Frequency domain response of the support components Perform iterative coupling of the working component and the support component until the continuity is satisfied. The cumulative error of the next iteration is less than the error threshold. The deformation iteration values ​​of the working parts are obtained. .

7. The method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling as described in claim 6, characterized in that, Calculate thermal deformation and physical reference values, and integrate the predicted deformation values ​​of the rotating body output by PINN to obtain the comprehensive deformation of the working part; The thermal deformation Calculated using the following formula: In the formula, This represents the temperature change, specifically the difference between the current temperature and the reference temperature. This is the thermal convexity coefficient; This is the thermal inertia compensation factor; The nominal radius of the rotating body in its cold state; The coefficient of thermal expansion of the rotating body material; By combining frequency domain and physical domain information, a physical reference is obtained. ,at the same time Predicted values ​​of deformation of rotating bodies The error between them satisfies the condition At that time, the physical constraint layer is triggered to update in real time: In the formula, ; The deformation caused by the mechanical load output by the coupled iteration; Fusion and Obtain the comprehensive deformation amount : In the formula, These are the weighting coefficients; This represents the number of hours the machine has been running.

8. A system for predicting the deformation of a rotating body, used to execute the method for predicting the deformation of a mechanical rotating body based on PINN and multiphysics coupling as described in any one of claims 1 to 7, characterized in that, include: A pressure sensor is installed on the surface of the bearing component of the rotating body, and the original pressure signal is collected by the pressure sensor. A distributed temperature sensor is installed in the internal cavity of the rotating body. The temperature of the cooling water channel is collected by the distributed temperature sensor and reconstructed into an effective temperature field on the surface of the rotating body. The calculation module is used to fuse the original pressure signal and the effective temperature field of the rotating body surface to calculate the dynamic equivalent radius; A rotational body deformation predictor based on time-varying constraint PINN; the dynamic equivalent radius is used as one of the input parameters of the rotational body deformation predictor, and the preset physical constraints are embedded into the learning process of the rotational body deformation predictor, and the rotational body deformation predictor outputs the predicted value of the rotational body deformation. The final result output module is used to solve the coupling effect of multiple components in the mechanical system, and integrate the predicted value of the deformation of the rotating body to obtain the comprehensive deformation of the rotating body under complex loads.

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