Ultrasonic digital-analog fusion tilting pad thrust bearing state monitoring method and system

Abstract

This invention discloses a method and system for monitoring the condition of tilting bearing pads in thrust bearings using ultrasonic numerical-model fusion, belonging to the field of intelligent monitoring technology for sliding bearings. It aims to solve the problems of long computation time, sparse monitoring data, and large model prediction bias in existing technologies. The method includes: constructing a thermo-elastic-fluid coupled simulation dataset; training a deep operator network with physical constraints; establishing a fast mapping surrogate model; acquiring signals through an ultrasonic sensor array; calculating the oil film thickness and inverting the geometric and thermal deformation parameters of the tilting bearing pads; updating the input state of the surrogate model based on ensemble Kalman filtering data assimilation and fusing the inversion results; and reconstructing the overall pressure and temperature distribution to achieve condition monitoring and fault early warning. This invention balances computational efficiency, physical consistency, and generalization ability, achieving real-time and accurate monitoring and ensuring reliable equipment operation.

Description

Technical Field

[0001] This invention belongs to the field of intelligent monitoring and operation and maintenance support technology for sliding bearings, specifically relating to a method and system for monitoring the condition of tilting pad thrust bearings using ultrasonic digital-analog fusion. Background Technology

[0002] As a core support component of high-end equipment such as heavy-duty gas turbines, large centrifugal compressors, nuclear main pumps, and large pumping station units, the load-bearing capacity and operational stability of tilting pad thrust bearings are crucial to the safety and lifespan of the entire system. Under complex service conditions such as high speed, heavy load, and variable operating conditions, the lubricating oil film inside the tilting pad thrust bearing will exhibit a significant thermo-elasto-hydrodynamic coupling effect, manifested as the interaction between the oil film pressure field, temperature field, and the thermoelastic deformation of the tilting pad and base. Therefore, accurately characterizing and monitoring key performance indicators such as minimum oil film thickness, contact safety margin, efficiency, and tilting pad temperature distribution online is a necessary prerequisite for ensuring long-term reliable operation of equipment and avoiding unexpected downtime accidents.

[0003] Currently, for real-time thermo-elasto-fluidic analysis of tilting pad thrust bearings, existing research typically employs numerical simulation methods based on fluid lubrication equations, energy equations, and structural mechanics equations. These methods aim to obtain the full-field distribution of pressure, temperature, and tilting pad deformation within the oil film. While such high-fidelity mechanistic models offer unparalleled advantages in bearing design and theoretical analysis, deeply revealing the underlying physical laws behind physical phenomena, their solution process involves complex nonlinear iterations and requires enormous computational resources, often taking hours or even longer. This makes it difficult to meet the real-time or near-real-time online monitoring requirements of tilting pad thrust bearings in practical engineering. In engineering practice, existing technologies mostly indirectly monitor the operating status of tilting pad thrust bearings by deploying a limited number of temperature, vibration, or pressure sensors, and combine this with empirical thresholds or simple statistical analysis for fault warning. However, such discrete sensor data can only provide information on local measurement points of the tilting pad thrust bearing, and cannot directly reflect the global distribution of the oil film pressure field, temperature field, and thermoelastic deformation field of the tilting pad. In particular, it is difficult to capture local high temperature points or extremely thin film points that exist in the sensor measurement blind zone, thus limiting the accurate identification and prediction of potential dangerous areas.

[0004] In recent years, the application of digital twin technology in rotating machinery and bearing systems has attracted increasing attention. It aims to achieve real-time perception, prediction, and optimization of operating conditions by constructing virtual mappings of physical entities. However, current digital twin systems used in tilting pad thrust bearings, if relying solely on pure mechanistic models for online monitoring, are prone to continuous deviations between virtual model predictions and actual bearing operating conditions. This is because factors such as changes in lubricating oil properties, uncertainties in boundary conditions, assembly tolerances, and wear evolution during actual operation are difficult for the model to fully and accurately capture for parameter updates. While traditional data-driven methods or deep learning proxy models can improve computational efficiency to some extent, these models are typically trained on offline operating data, lacking sufficient consideration of complex thermo-elastic-fluid coupling mechanisms and having limited generalization ability to actual operating condition changes and structural parameter disturbances. More importantly, existing technologies generally lack an effective unified framework that deeply integrates mechanistic models, data-driven models, and real-time monitoring data, making it difficult to adaptively correct and calibrate inherent uncertainties or real-time deviations in mechanistic models.

[0005] In summary, the current field of thermo-elasto-fluidic state monitoring for tilting pad thrust bearings faces at least the following pressing technical challenges: First, how to achieve efficient calculation and online prediction of the pressure, temperature, and deformation state within the bearing under the premise of fully considering the complex thermo-elasto-fluidic coupling mechanism; second, how to effectively integrate the mechanism model with sparse monitoring data from actual operation to construct a unified framework capable of dynamically correcting the model's state or parameters, thereby significantly improving the overall prediction accuracy and robustness; and third, how to ensure the model's stability, generalization ability, and physical consistency under multi-condition, highly nonlinear, and parameter uncertain environments to meet the requirements of high reliability and high safety in engineering applications.

[0006] Therefore, there is an urgent need in this field to propose an intelligent monitoring method and system for the thermo-elasto-fluidic state of tilting pad thrust bearings, which takes into account both physical mechanisms and data-driven advantages, in order to solve the shortcomings of existing technologies in terms of computational efficiency, model accuracy, and virtual-real fusion capabilities. Summary of the Invention

[0007] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing an ultrasonic digital-analog fusion method and system for monitoring the condition of tilting pad thrust bearings. This method achieves efficient solution of the thermo-elastic-fluid field through physical information deep operator learning technology, and combines ultrasonic geometric inversion and ensemble Kalman filtering data assimilation technology to establish a digital twin with adaptive correction capabilities. This enables real-time and accurate monitoring of the pressure, temperature, and deformation state of the tilting pad thrust bearing across the entire field. This addresses the technical problems in existing technologies where high-fidelity mechanism models for tilting pad thrust bearings are computationally expensive and difficult to meet online monitoring requirements, while purely data-driven models lack physical constraints and have poor adaptability to changes in operating conditions and parameter drift. Furthermore, existing monitoring methods can only acquire sparse measurement point information and cannot achieve full-field condition perception.

[0008] The present invention adopts the following technical solution:

[0009] A method for monitoring the condition of a tilting pad thrust bearing using ultrasonic digital-analog fusion, comprising the following steps:

[0010] S1. Construct a physical information deep operator network and establish a mapping proxy model from working parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing;

[0011] S2. Collect real-time ultrasonic reflection echo signals from the back of the tilting bearing in the tilting pad thrust bearing, and calculate the oil film thickness measurement values ​​at multiple points; based on the preset parameterized oil film thickness model and the multi-point oil film thickness measurement values, obtain the geometric attitude parameters and thermal deformation parameters of the tilting bearing at the current moment through geometric inversion optimization identification;

[0012] S3. Using the geometric attitude parameters and thermal deformation parameters identified in S2 as observation vectors, and using the mapping proxy model established in S1, the physical field state is predicted based on the input state vector of the previous moment as the background field. The Kalman gain is calculated by assimilating the Kalman filter data, and the input state vector of the current moment is updated.

[0013] S4. Input the current input state vector obtained by updating S3 into the mapping proxy model established in S1 to reconstruct the pressure distribution and temperature distribution of the tilting pad thrust bearing in the entire field; perform state monitoring and fault early warning based on the reconstructed pressure distribution and temperature distribution.

[0014] Preferably, in S1, the construction process of the mapping proxy model includes:

[0015] Based on the thermo-elastic-fluid dynamic characteristics of tilting pad thrust bearings, a thermo-elastic-fluid dynamic simulation dataset is generated using Latin hypercube sampling within a preset operating space. The operating parameters include the bearing spindle speed, specific pressure load, inlet oil temperature, and basic viscosity of the lubricating oil. The simulation dataset includes the full-field oil film pressure distribution and temperature distribution of the tilting pad thrust bearing.

[0016] The physical information deep operator network is trained using the simulation dataset. The loss function of the physical information deep operator network includes a data-driven error term and a physical equation residual term.

[0017] Preferably, the physical information deep operator network adopts a dual-tower structure, including a branch network and a backbone network; the branch network is used to perform feature encoding on the input working condition parameter vector and output a working condition feature vector; the backbone network is used to perform position encoding on the input spatial coordinates in polar coordinates and output a spatial basis function vector; the predicted field value is obtained by the dot product operation between the output of the branch network and the output of the backbone network.

[0018] Both the branch network and the backbone network adopt a fully connected neural network, which contains 3 hidden layers, each with 100 neurons, and the activation function is the Tanh function.

[0019] Preferably, the physical equation residuals include at least the Reynolds equation residuals, the energy equation residuals, and the boundary condition residuals; the physical equation residuals are obtained by calculating the partial derivatives of the network output with respect to spatial coordinates using automatic differentiation techniques, and then substituting them into the generalized Reynolds equation and the energy equation.

[0020] The expression for the loss function is:

[0021]

[0022] in, Data-driven error; The residuals of the Reynolds equation; The residuals of the energy equation; λ1, λ2, and λ3 are the boundary condition residuals; λ1, λ2, and λ3 are the weighting coefficients.

[0023] Preferably, in S2, the ultrasonic reflected echo signal is acquired by an ultrasonic sensor array arranged on the back of the tilting bearing; the ultrasonic sensor array is arranged as follows:

[0024] Three ultrasonic sensors are arranged on the back of the tilting bearing near the oil inlet and oil outlet edges;

[0025] The calculation method for the multi-point oil film thickness measurement value is as follows:

[0026] The local oil film thickness at each ultrasonic sensor measuring point is obtained by calculating the ultrasonic reflected echo signal using a resonance model or a spring model.

[0027] Preferably, in S2, the expression for the parameterized oil film thickness model is:

[0028]

[0029] in, For the oil film thickness at any location, Polar radius, Polar angle; This is the reference value for the film thickness at the tilting bearing support point; For the radial tilt angle and circumferential dip angle The resulting change in film thickness; This represents the amount of thermal arching deformation.

[0030] Preferably, in S3, the input state vector is an augmented state vector X. t The augmented state vector X t From the physical field state vector X state and the unknown model parameter vector X to be identified param Composition; the physical field state vector X state This includes the discretized full-field pressure vector and full-field temperature vector; the unknown model parameter vector X param This includes lubricating oil viscosity correction factor and load correction factor;

[0031] The initialization process for the Kalman filter data assimilation of the set is as follows:

[0032] The Monta Carlo sampling method is used to generate a sample containing... M c The initial state set of samples is used to introduce Gaussian random perturbations into the parameter part of each sample in the initial state set within a preset error range, forming an initial probability distribution that characterizes the uncertainty of the system.

[0033] Preferably, in S3, the ensemble Kalman filter data assimilation further includes constructing an observation operator, which is used to extract geometric feature prediction values ​​from the physical field state of the background field. The geometric feature prediction values ​​include the radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient of the tiltable bearing.

[0034] The Kalman gain is calculated as follows:

[0035]

[0036] in, for The Kalman gain matrix at time 10:00. For the prediction error covariance matrix, To observe the transpose of the operator matrix, R is the observation prediction error covariance matrix; R is the observation noise covariance matrix;

[0037] The update formula for the input state vector is:

[0038]

[0039] in, for Time of the first The analysis state vector of each sample, for Time of the first The predicted state vector of each sample. for The observation vector at time t, For the first The observational perturbation noise corresponding to each sample The observation operator matrix.

[0040] Preferably, in S4, the condition monitoring includes lifetime prediction based on the Pamgren-Miner linear cumulative damage theory, specifically:

[0041] Using the reconstructed full-field pressure distribution as an alternating stress source, the fatigue damage increment of the Babbitt alloy liner on the surface of the tilting bearing is calculated in real time, and the total historical accumulated damage is updated. The total historical accumulated damage is used as the fatigue damage accumulation.

[0042] The fault early warning system adopts a multi-dimensional hierarchical strategy:

[0043] When the instantaneous physical extreme values ​​in the reconstructed pressure and temperature distributions exceed the safety threshold, an emergency fault warning is triggered.

[0044] When the accumulated fatigue damage exceeds a preset lifespan threshold, a durability failure warning is triggered.

[0045] Secondly, embodiments of the present invention provide an ultrasonic digital-analog fusion-based tilting pad thrust bearing condition monitoring system, comprising:

[0046] The module is used to build a deep operator network for physical information and establish a mapping proxy model from working parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing;

[0047] The inversion module is used to acquire real-time ultrasonic reflection echo signals from the back of the tilting bearing in the tilting pad thrust bearing, and calculate multi-point oil film thickness measurements. Based on the preset parameterized oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tilting bearing at the current moment are obtained through geometric inversion optimization identification.

[0048] The update module is used to use the geometric attitude parameters and thermal deformation parameters as observation vectors, use the mapping proxy model to predict the physical field state based on the input state vector of the previous moment as the background field, calculate the Kalman gain by assimilating the Kalman filter data, and update the input state vector at the current moment.

[0049] The early warning module is used to input the updated input state vector into the mapping proxy model to reconstruct the pressure and temperature distribution of the tilting pad thrust bearing in the entire field; and to perform state monitoring and fault early warning based on the reconstructed pressure and temperature distribution.

[0050] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described ultrasonic digital-analog fusion method for monitoring the condition of tilting tile thrust bearings.

[0051] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described ultrasonic digital-analog fusion method for monitoring the condition of tilting tile thrust bearings.

[0052] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described ultrasonic digital-analog fusion method for monitoring the condition of tilting tile thrust bearings.

[0053] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, wherein when the computer program is executed by the electronic device, it implements the steps of the above-described ultrasonic digital-analog fusion method for monitoring the condition of tilting tile thrust bearings.

[0054] Compared with the prior art, the present invention has at least the following beneficial effects:

[0055] An ultrasonic-based numerical-analog fusion method for monitoring the condition of tilting pad thrust bearings is presented. This method, for the first time, organically integrates a Physical-Informed Deep Operator Network (PI-DeepONet), ultrasonic-based geometric inversion, and Ensemble Kalman Filter (EnKF) data assimilation, forming a complete technical closed loop. This method fundamentally solves the problems of traditional high-fidelity mechanism models being computationally too time-consuming for online application, and purely data-driven models lacking physical constraints and exhibiting poor generalization ability. Geometric inversion in step S2 provides realistic geometric observations. Step S3 utilizes EnKF to deeply fuse the observations with the theoretical predictions of PI-DeepONet, achieving adaptive online correction of input parameters and internal states, ensuring continuous synchronization between the digital twin and the physical entity. Finally, step S4 achieves high-precision, high-efficiency reconstruction of the full-field pressure / temperature of the tilting pad thrust bearing from sparse point measurements, laying the foundation for intelligent early warning based on full-field conditions. This innovative monitoring method combines physical consistency, real-time computation, and adaptability.

[0056] Furthermore, a training dataset is generated using Latin hypercube sampling within a predefined operating space, ensuring uniform and efficient coverage of the multidimensional complex operating space by the samples. This lays a comprehensive and high-quality data foundation for the mapping proxy model. The loss function of the mapping proxy model explicitly includes both data-driven error terms and physical equation residual terms. The mapping proxy model not only learns data mapping relationships but is also forced to satisfy underlying physical laws such as fluid lubrication and heat transfer. This significantly improves the extrapolation prediction ability and physical rationality of the prediction results under operating conditions not covered by the training data, avoiding the absurd outputs of pure black-box models. This is a core technical feature ensuring the generalization and reliability of the mapping proxy model.

[0057] Furthermore, a branch network is used to handle changing operating parameters, while the backbone network handles fixed spatial coordinates. Finally, a dot product operation is used to synthesize the overall prediction. This dual-tower structure decouples the parameter space from the physical space, enabling the network to learn a continuous operator from arbitrary input parameters to an output at any spatial point, rather than a discrete mapping. PI-DeepONet possesses greater generalization flexibility, easily handling the requirements of different grid resolutions, and is computationally more efficient. The use of a fully connected Tanh network with three hidden layers ensures effective learning of complex nonlinear mappings.

[0058] Furthermore, by simultaneously incorporating the Reynolds equation residuals, energy equation residuals, and boundary condition residuals into the loss function, a complete physical constraint system is formed, ensuring that the predictions of the mapped surrogate model strictly adhere to the core governing equations of fluid lubrication and heat transfer, as well as the actual boundary conditions. Automatic differentiation techniques are used to calculate the partial derivatives of the network output with respect to spatial coordinates and to compute the residuals, avoiding the dependence on grids inherent in traditional numerical methods and making computation more convenient. This makes the mapped surrogate model a differentiable physical simulator, with its predictions having a solid physical basis, significantly improving prediction confidence and model reliability in sparse data regions or under extreme conditions.

[0059] Furthermore, three sensors are strategically placed on the oil inlet and outlet edges of each tilting bearing. This arrangement strategically covers the critical area for oil film formation, enabling the acquisition of key information reflecting the overall tilt and deformation morphology of the tilting bearing with a minimal number of sensors, thus balancing cost and efficiency. Using a resonance model or spring model to calculate the film thickness from the ultrasonic echo signal, online measurement of oil film thickness with micron-level accuracy can be achieved.

[0060] Furthermore, the thermal arching deformation is introduced and characterized by a parabolic function, accurately reflecting the physical reality of non-uniform thermal expansion of the tilting bearing pads due to temperature gradients during operation, thus compensating for the inversion error caused by neglecting thermal deformation in traditional models. With the goal of minimizing the sum of squared errors between measured and calculated film thickness, the Levenberg-Marquardt (LM) optimization algorithm is used to solve for the geometric parameter vector in reverse. This algorithm has fast convergence speed and high solution accuracy, and can accurately identify key parameters such as fulcrum film thickness, tilt angle, and thermal arching deformation coefficient, providing accurate observation vectors for data assimilation.

[0061] Furthermore, the augmented state vector simultaneously includes both the physical field state vector and the unknown model parameter vector, solving the problem of one-sidedness caused by traditional methods that only estimate states or parameters. It can simultaneously correct key parameters such as overall pressure, temperature distribution, lubricating oil viscosity, and load, ensuring a high degree of consistency between the unknown model and the actual operating state. Monta Carlo sampling is used to generate the initial state set, and Gaussian random perturbations are introduced to fully characterize the system's uncertainties. This provides a reasonable initial probability distribution for ensemble Kalman filtering, ensuring the stability and convergence of the subsequent data assimilation process.

[0062] Furthermore, the observation operator can accurately extract geometric feature predictions from the physical field state, achieving dimensional matching between the background field and the observation vector, providing crucial support for Kalman gain calculation. The Kalman gain formula quantifies the weighted relationship between the observed data and the predicted state, while the state update formula introduces observation perturbation noise, effectively avoiding the filter divergence problem caused by excessively rapid contraction of the ensemble variance, thus ensuring the stability of the state update. It adheres to the core principles of ensemble Kalman filtering and is optimized for the monitoring scenario of tilting tile thrust bearings, guaranteeing the accuracy and robustness of the input state vector update.

[0063] Furthermore, based on the Palmgren-Miner linear cumulative damage theory, life prediction can calculate the fatigue damage increment of the Babbitt alloy liner in real time, predicting the progressive failure risk of tilting pad thrust bearings in advance, thus overcoming the limitations of traditional methods that only focus on instantaneous failures. The multi-dimensional, graded early warning strategy simultaneously monitors instantaneous physical extremes and cumulative fatigue damage, triggering early warnings for both sudden failures and durability failures. This achieves dual protection against both sudden failures and long-term degradation of tilting pad thrust bearings, significantly improving the proactiveness and reliability of equipment operation and maintenance, and reducing losses caused by unexpected downtime.

[0064] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0065] In summary, this invention ensures the extrapolation capability of the physical information deep operator network through physical information deep learning, achieves precise synchronization between virtual and real data and parameter self-correction through geometric inversion and EnKF data assimilation, and ultimately realizes real-time, high-precision reconstruction of the entire field state of tilting pad thrust bearings and predictive early warning based on failure mechanisms, thus completely solving the shortcomings of traditional methods in terms of computational efficiency, model accuracy and virtual-real fusion capability.

[0066] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the process of a digital twin method for tilting pad thrust bearings based on ultrasonic oil film thickness monitoring and digital-analog fusion driving according to the present invention.

[0068] Figure 2 This is a schematic diagram of the physical information deep operator network architecture of the present invention;

[0069] Figure 3 Schematic diagram of a tilting pad thrust bearing structure;

[0070] Figure 4 A schematic diagram illustrating the thermal arching deformation and geometric parameters of a tilting bearing;

[0071] Figure 5 This is a schematic diagram illustrating the principle of closed-loop flow of virtual and real data in this invention.

[0072] Figure 6 This is a block diagram showing the module composition of the intelligent bearing monitoring system.

[0073] Figure 7 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0074] Figure 8 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0075] Among them, 1. Thrust plate; 2. Liner; 3. Tilting bearing; 4. Rotating base; 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic equipment; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0078] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0079] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0080] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0081] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0082] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0083] This invention provides a method for monitoring the condition of tilting pad thrust bearings using ultrasonic digital-analog fusion, aiming to solve the problem encountered in constructing a digital twin system for tilting pad thrust bearings where real-time computation and adaptive parameter correction cannot be simultaneously achieved in thermo-elasto-hydrodynamic multiphysics calculations. First, a Physical Information Deep Operator Network (PI-DeepONet) is constructed as a surrogate model for rapid multiphysics solution. A geometric inversion optimizer is built using sparse ultrasonic measurement data to identify the tilting pad bearing's attitude and thermal deformation characteristics. A data assimilation framework based on ensemble Kalman filtering is established to fuse the inversion results and correct the input parameters of the surrogate model in real time, achieving reconstruction of the full-field pressure and temperature distribution. This invention achieves real-time, high-precision reconstruction of the full-field state of tilting pad thrust bearings under complex operating conditions, significantly improving the monitoring system's virtual-real fusion capability and early warning reliability.

[0084] Please see Figure 1 This invention discloses a method for monitoring the condition of tilting pad thrust bearings using ultrasonic digital-analog fusion, comprising two stages: offline modeling and online monitoring. The specific steps are as follows:

[0085] S1. Construct a thermal-elastic-fluid coupling dynamic simulation dataset for tilting pad thrust bearings, train a physical information deep operator network (PI-DeepONet), and establish a mapping proxy model from the working parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing; the loss function of the physical information deep operator network includes a data-driven error term and a physical equation residual term.

[0086] S101. Construct a thermal-elastic-fluid coupling dynamics simulation dataset for tiltable pad thrust bearings;

[0087] Based on the thermo-elastic-fluid dynamics simulation program for tilting pad thrust bearings, Latin hypercube sampling is performed within a preset operating space to generate 2000 sets of steady-state training samples. The operating parameter vector u includes the tilting pad thrust bearing spindle speed, specific pressure load, inlet oil temperature, and lubricating oil base viscosity; the output space corresponds to the full-field oil film pressure distribution. and temperature distribution .

[0088] S102. Train a deep operator network for physical information based on the constructed dataset;

[0089] like Figure 2 The diagram shows the architecture of the physical information deep operator network of the present invention. The physical information deep operator network adopts a dual-tower structure and includes:

[0090] Branch network: used to encode the features of the input working condition parameter vector u and output the working condition feature vector;

[0091] Backbone network: used for processing input spatial coordinates (in, These are the polar radius and polar angle in polar coordinates, respectively. M The position is encoded for the total number of structured grid cell nodes on a thrust bearing, and the spatial basis function vector is output.

[0092] Finally, the predicted field value is obtained by the dot product of the branch network output and the backbone network output, specifically expressed as:

[0093]

[0094] in, The dimension of the feature vector; , The output vectors of the branch network and the backbone network are respectively the first and second generations of the output vectors. 1 vector element; This is a bias term.

[0095] The branch network and backbone network of the physical information deep operator network both adopt fully connected neural networks, containing 3 hidden layers with 100 neurons in each layer, and the Tanh function is preferred as the activation function.

[0096] To ensure the physical consistency of the model under sparse samples, a composite loss function is constructed, which specifically includes a data-driven error term and a physical equation residual term. The physical equation residual term includes at least the Reynolds equation residual and the energy equation residual. The physical equation residual term is obtained by calculating the partial derivative of the network output with respect to spatial coordinates using automatic differentiation techniques and substituting it into the generalized Reynolds equation and the energy equation.

[0097] The loss function of the physical information deep operator network is in the form of:

[0098]

[0099] in, Data-driven error; The residuals of the Reynolds equation; The residuals of the energy equation; λ1, λ2, and λ3 are the boundary condition residuals; λ1, λ2, and λ3 are the weighting coefficients.

[0100] S2. Real-time ultrasonic reflected echo signals are collected by an ultrasonic sensor array arranged on the back of the tilting bearing, the oil film thickness at multiple points is calculated, and a geometric inversion optimizer is constructed based on the parameterized oil film thickness model to identify the geometric attitude parameters and thermal deformation parameters of the tilting bearing at the current moment.

[0101] S201, Ultrasonic signal acquisition and film thickness calculation;

[0102] Please see Figure 3 This document describes the basic structure of a tilting pad thrust bearing and the layout of the ultrasonic sensors in this embodiment. The tilting pad thrust bearing includes a thrust plate 1, a liner 2, tilting pads 3, and a rotating base 4. Multiple tilting pads 3 are used to form an oil film with the thrust plate 1 and bear the load. The tilting pads 3 are hinged to the stationary rotating base 4 via a back support, and the rotating base 4 is fixed to the unit housing. The liner 2 is disposed on the working surface of each tilting pad 3 and is separated from the thrust plate 1 by a dynamic oil film. Three ultrasonic sensors are arranged on the back of each tilting pad 3 near the oil inlet and outlet edges to collect real-time pulse reflection echoes. The local oil film thickness at each measuring point is calculated using a resonance model or a spring model. ,in N s represents the number of ultrasonic sensors.

[0103] S202. Record the measured film thickness at different ultrasonic sensor measurement points and the model-calculated film thickness at the corresponding points, and perform geometric inversion optimization.

[0104] First, a parametric oil film thickness model is constructed, specifically represented as follows:

[0105]

[0106] in, The oil film thickness at any location; This is the reference value for the film thickness at the tilting bearing support point; For the radial tilt angle and circumferential dip angle The resulting change in film thickness; This represents the amount of thermal arching deformation.

[0107] Please see Figure 4 This embodiment illustrates the definition of thermal arching deformation and its geometric parameters in tilting bearing pads. Given that tilting bearing pads typically generate significant heat during operation due to factors such as fluid shear, and that different areas of the tilting bearing pad exhibit varying heat dissipation conditions, a significant temperature gradient forms within the pad, inducing non-uniform thermal expansion deformation. This thermal expansion deformation macroscopically manifests as a bulge on the surface of the tilting bearing pad, i.e., thermal arching. Therefore, this embodiment uses a parabolic function to approximate the thermal arching morphology, establishing a geometrical mathematical model of the thermal deformation of the tilting bearing pad. Thus, the amount of thermal arching deformation... The following function can be used to approximate the description:

[0108]

[0109] in, C q θ is the thermal arching deformation coefficient; r and θ are the polar radius and polar angle, respectively.

[0110] Finally, using the objective function of minimizing the sum of squared errors between the measured film thickness at the ultrasonic measurement point and the film thickness calculated by the parameterized oil film thickness model, the Levenberg-Marquardt optimization algorithm is employed to solve for the geometric parameter vector containing the fulcrum film thickness, radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient. The objective function is expressed as:

[0111]

[0112] in, The vector of geometric parameters to be identified; The oil film thickness was measured using an ultrasonic sensor. N s represents the number of ultrasonic sensors; The calculated film thickness at the corresponding ultrasonic sensor measurement point is calculated by the physical information depth operator network. is the coefficient of the regularization term.

[0113] S3. Construct a data assimilation framework based on ensemble Kalman filtering. Use the geometric attitude parameters and thermal deformation parameters identified in step S2 as observation values, and use the predicted state of the physical information deep operator network in step S1 as the background field. Calculate the Kalman gain and update the input state vector of the surrogate model in real time.

[0114] S301. Construct the augmented state vector;

[0115] To simultaneously estimate the full-field state and unknown model parameters of the tilting pad thrust bearing, this embodiment defines the system in... t Augmented state vector X at time step t The augmented state vector consists of two parts: one part is the physical field state vector (model output) X. state The other part is the unknown model parameter vector (model input) X to be identified. param Let the pressure and temperature fields output by PI-DeepONet be discretized as follows: N p and N T If there are nodes, then the augmented state vector X can be represented as:

[0116]

[0117] in, This is a discrete pressure vector across the entire field. The discrete temperature vector across the entire field; This is the lubricating oil viscosity correction factor (dimensionless, nominal value 1.0). This is the load correction factor (dimensionless, nominal value 1.0).

[0118] S302, Set initialization;

[0119] The Monta Carlo sampling method is used to generate a sample containing... M c The initial state set of the sample, for the th sample in the initial state set i Sample Its parameter part introduces Gaussian random perturbations within a preset error range:

[0120]

[0121] in, N Represents a normal distribution; To initialize the variance. This generates... M c The samples together constitute the initial probability distribution that can characterize the uncertainty of the system.

[0122] S303, Forward prediction step;

[0123] The PI-DeepONet model trained in step S1 is used as a nonlinear evolution operator. Update each sample in the initial state set at each time step. Input the parameter components of each sample into... Calculate the corresponding physical field to obtain the current time. t Prior prediction set Specifically, it is expressed as:

[0124]

[0125] in, Indicates the current time. i The predicted state vector of each sample. Indicates the previous moment. i The analysis state vector of each sample.

[0126] Specifically, the predicted state vector represents the theoretical physical state and prior parameter estimates obtained by relying solely on the PI-DeepONet model based on the state at the previous moment without fusing the observation data at the current moment; while the analytical state vector represents the result after optimally weighting and correcting the predicted state by combining the measured data from the ultrasonic sensor. For the specific calculation process, please refer to step S305.

[0127] Based on the calculated set of predicted state vectors, the prediction error covariance matrix P can be calculated. f Approximate value:

[0128]

[0129] in, The prediction error covariance matrix P is the mean vector of the predicted state vector set. f Implicitly, it includes the nonlinear correlation between physical field variables and model input parameters.

[0130] S304. Construct the observation operator;

[0131] Obtain the geometric inversion result of the tiltable bearing output in step S2 as the measured observation vector Z at the current moment. t In this embodiment, These correspond to the radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient of the tilting bearing, respectively. Since the augmented state vector X contains the discretized full-field pressure distribution... With temperature distribution Instead of direct geometric feature observations, an observation operator is defined. It is responsible for extracting the corresponding geometric feature prediction values ​​(including the tilt angle of the tilting bearing and the thermal arching deformation coefficient) from the augmented state vector, which can be specifically expressed as: The calculation process for each part is as follows:

[0132] Firstly, the operator for observing thermal arching deformation... The thermal arching deformation observation operator is responsible for extracting the full-field temperature node data from the augmented state vector, and using the least squares method to fit the extracted temperature field into a parabolic surface, i.e.: The coefficient of its quadratic term is taken as the coefficient of thermal arching deformation.

[0133] For tilt angle observation operator and The tilt angle observation operator calculates the pressure center of the oil film pressure using the full-field pressure distribution in the augmented state vector, and solves the theoretical tilt angle required to maintain this pressure distribution based on the pivot equilibrium equation of the thrust bearing.

[0134] The pressure center of the oil film pressure is calculated using the following formula:

[0135]

[0136] The observation operator is obtained by solving. Then, the predicted observation vector at the current moment can be directly calculated from the current predicted state vector. .

[0137] S305. Calculate the Kalman gain matrix and perform state update.

[0138] Kalman gain matrix K t The correction weights of the observed data on the state prediction values ​​are quantified, and the specific calculation formula is as follows:

[0139]

[0140] in, R represents the observation prediction error covariance matrix; R is the observation noise covariance matrix, which is determined by the measurement uncertainty of the ultrasonic sensor.

[0141] Using Kalman gain and observation residuals, a posterior correction is performed on each sample in the predicted state vector set to obtain the analytical state vector at the current time. The specific update formula is as follows:

[0142]

[0143] in, This term is introduced to observe disturbance noise in order to prevent the filter from diverging due to excessively rapid contraction of the ensemble variance.

[0144] S306, Parameter adaptive update and status output;

[0145] Through the above update steps, the parameter part X in the augmented state vector is... param The value is automatically corrected to be closest to the actual physical state, and the mean of the updated set of analytical state vectors is taken. The final state output of the system in the previous time step is used as the initial condition for the prediction step in the next time step, so as to realize the adaptive state update of the closed loop.

[0146] S4. Input the updated input state vector into the physical information depth operator network to reconstruct the pressure and temperature distribution of the entire field of the tilting pad thrust bearing, and identify the minimum film thickness position and the highest temperature point based on the reconstruction results for state monitoring and fault early warning.

[0147] Step S4 introduces a life prediction mechanism based on the Pammgren-Miner linear cumulative damage theory. Specifically, the system uses the full-field dynamic pressure distribution reconstructed by PI-DeepONet as an alternating stress source to calculate the fatigue damage increment of the Babbitt alloy liner on the tilting bearing surface under the current working condition in real time, while updating the total historical cumulative damage.

[0148] For the fault warning described in step S4, the method of the present invention constructs a multi-dimensional hierarchical warning strategy:

[0149] On the one hand, monitor the instantaneous physical extremes (including minimum film thickness and maximum temperature) in the reconstructed flow field, and trigger an early warning of sudden failure when they exceed the safety threshold;

[0150] On the other hand, it monitors the cumulative amount of fatigue damage and triggers a durability failure warning when it exceeds a preset lifespan threshold.

[0151] The aforementioned graded early warning strategy further achieves dual protection against sudden failures and progressive failures of tilting pad thrust bearings.

[0152] In another embodiment of the present invention, an ultrasonic digital-analog fusion-based tilting pad thrust bearing condition monitoring system is provided. This system can be used to implement the above-mentioned ultrasonic digital-analog fusion-based tilting pad thrust bearing condition monitoring method. Specifically, the ultrasonic digital-analog fusion-based tilting pad thrust bearing condition monitoring system includes a construction module, an inversion module, an update module, and an early warning module.

[0153] Among them, the construction module is used to build a physical information deep operator network and establish a mapping proxy model from working parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing;

[0154] The inversion module is used to acquire real-time ultrasonic reflection echo signals from the back of the tilting bearing in the tilting pad thrust bearing, and calculate multi-point oil film thickness measurements. Based on the preset parameterized oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tilting bearing at the current moment are obtained through geometric inversion optimization identification.

[0155] The update module is used to use the geometric attitude parameters and thermal deformation parameters as observation vectors, use the mapping proxy model to predict the physical field state based on the input state vector of the previous moment as the background field, calculate the Kalman gain by assimilating the Kalman filter data, and update the input state vector at the current moment.

[0156] The early warning module is used to input the updated input state vector into the mapping proxy model to reconstruct the pressure and temperature distribution of the tilting pad thrust bearing in the entire field; and to perform state monitoring and fault early warning based on the reconstructed pressure and temperature distribution.

[0157] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used in the operation of an ultrasonic analog-to-digital fusion method for monitoring the condition of tilting tile thrust bearings, including:

[0158] A physical information deep operator network is constructed to establish a mapping proxy model from operating parameters to the overall pressure and temperature distribution of the tilting pad thrust bearing. Real-time ultrasonic reflection echo signals from the back of the tilting pad in the tilting pad thrust bearing are collected, and multi-point oil film thickness measurements are calculated. Based on a preset parameterized oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tilting pad at the current moment are identified through geometric inversion optimization. Using the identified geometric attitude parameters and thermal deformation parameters as observation vectors, and utilizing the established mapping proxy model, the physical field state is predicted based on the input state vector of the previous moment as the background field. Kalman gain is calculated through ensemble Kalman filter data assimilation, and the current input state vector is updated. The updated current input state vector is input into the established mapping proxy model to reconstruct the overall pressure and temperature distribution of the tilting pad thrust bearing. Condition monitoring and fault early warning are performed based on the reconstructed pressure and temperature distribution.

[0159] Please see Figure 7 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the ultrasonic digital-analog fusion method for monitoring the condition of tilting tile thrust bearings in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the ultrasonic digital-analog fusion system for monitoring the condition of tilting tile thrust bearings in this embodiment. To avoid repetition, these details are not elaborated here.

[0160] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 7 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0161] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0162] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0163] Furthermore, the memory 62 may include both internal storage units and external storage devices of the computer device 60. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0164] Please see Figure 8 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0165] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 1 The steps are shown in the figure.

[0166] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0167] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0168] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0169] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0170] Example 4

[0171] This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0172] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0173] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0174] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0175] A physical information deep operator network is constructed to establish a mapping proxy model from operating parameters to the overall pressure and temperature distribution of the tilting pad thrust bearing. Real-time ultrasonic reflection echo signals from the back of the tilting pad in the tilting pad thrust bearing are collected, and multi-point oil film thickness measurements are calculated. Based on a preset parameterized oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tilting pad at the current moment are identified through geometric inversion optimization. Using the identified geometric attitude parameters and thermal deformation parameters as observation vectors, and utilizing the established mapping proxy model, the physical field state is predicted based on the input state vector of the previous moment as the background field. Kalman gain is calculated through ensemble Kalman filter data assimilation, and the current input state vector is updated. The updated current input state vector is input into the established mapping proxy model to reconstruct the overall pressure and temperature distribution of the tilting pad thrust bearing. Condition monitoring and fault early warning are performed based on the reconstructed pressure and temperature distribution.

[0176] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchain. The processors involved in the embodiments provided in this application may be, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc.

[0177] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0178] To more intuitively and clearly demonstrate the data interaction logic and closed-loop correction principle between the physical entity and the digital twin in this invention, the following is combined with... Figure 5 To provide further explanation.

[0179] Please see Figure 5 This invention demonstrates the interactive principle of the closed-loop flow of virtual and real data between physical entities and digital twins during online monitoring. As shown in the figure, the system's data flow is logically divided into a physical observation link, a digital inference link, and a central assimilation and correction stage. Figure 5 The left side represents the physical observation link, the right side represents the digital inference link, and the middle represents the assimilation and correction link. These three links are connected by a black line representing a closed-loop feedback link. In the physical observation link, the ultrasonic sensor array of the tilting pad thrust bearing collects echo signals, which are then processed and used by a geometric inversion optimizer to extract measured observation vectors (including radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient). In the digital inference link, a pre-trained physical information deep operator network analyzes the state vector and prior operating parameters based on the previous time step, generates a predicted state vector, and transforms it into a predicted observation vector through an observation operator. The assimilation and correction link receives two types of vectors, calculates the observation residual and Kalman gain, and feeds the correction amount back to the surrogate model, forming a closed-loop mechanism of prediction-comparison-correction-re-prediction, effectively overcoming the accuracy divergence problem caused by parameter drift in open-loop models.

[0180] In the physical observation link, the tilting pad thrust bearing in actual operation is the monitored object. An ultrasonic sensor array attached to the back of the tilting pad continuously collects ultrasonic echo signals that reflect oil film thickness information. The collected signals are input to the sensing layer module, and after signal processing and geometric inversion optimizer solving, the measured observation vector Z that can characterize the current true state of the tilting pad is extracted. Specifically, it includes the radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient of the tilting pad. This link aims to provide an objective physical fact benchmark for subsequent closed-loop correction.

[0181] In the digital inference pipeline, the pre-trained PI-DeepONet model acts as the evolution engine for the digital twin. Based on the previous time-stamped state estimate (i.e., the analyzed state vector) and the current prior operating parameters, it rapidly performs forward inference to generate a predicted state vector containing the overall pressure and temperature distribution. This predicted state vector is then processed by the observation operator. After mapping, it is transformed into a virtual predicted observation vector. This link aims to provide theoretical predictions of the operating conditions of tilting pad thrust bearings based on relevant physical mechanisms.

[0182] The EnKF data assimilation layer forms the logical hub connecting the virtual and real worlds. This layer receives in real time the measured observation vector Z from the physical link and the predicted observation vector from the digital link. The algorithm calculates the observation residuals between the two. Using the Kalman gain matrix derived from ensemble statistics, it maps this residual into a correction factor for the model input parameters.

[0183] like Figure 5 As shown in the data flow diagram, the model input parameters, after correction by ensemble Kalman filtering, are fed back to the PI-DeepONet model as input conditions for prediction at the next time step. This forms a closed-loop feedback mechanism of "prediction-comparison-correction-re-prediction," effectively overcoming the accuracy divergence problem caused by uncertainties such as lubricant aging and thermal deformation drift in open-loop models, thus ensuring that the digital twin can always maintain a high degree of synchronization with the trajectory of the physical entity.

[0184] Please see Figure 6 The hardware-software collaborative architecture of the ultrasonic digital-analog fusion tilting tile thrust bearing condition monitoring system of this invention is divided into two parts: a sensing module (physical data acquisition link) and a digital twin workstation (virtual data processing link). The functions, data flow and collaborative logic of each module are as follows:

[0185] The sensing module provides the system with measured data input and consists of 5 functional units, with data flowing in one direction:

[0186] Ultrasonic sensor array: Arranged on the back of the tilting bearing, it receives electrical pulse drive from the ultrasonic pulse transmitter and receiver, transmits ultrasonic signals to the working surface of the tilting bearing, and simultaneously receives the reflected echo signals from the oil film interface, and transmits the ultrasonic signals back to the transmitter and receiver.

[0187] Ultrasonic pulse transmitter and receiver: It outputs high-frequency electrical pulses to the sensor array to excite ultrasonic signals, and at the same time receives the reflected echo signals transmitted back by the sensors, and transmits the analog echo signals to the signal acquisition card.

[0188] Signal acquisition card: Converts analog echo signals into digital signals, eliminates signal noise interference, and then transmits them to the signal processing unit.

[0189] Signal processing unit: Filters and extracts features from digital echo signals to obtain effective signal features that can be used for film thickness calculation, and transmits them to the film thickness calculation unit.

[0190] Film thickness calculation unit: Using a resonance model / spring model, it calculates the local oil film thickness at each sensor measurement point based on signal characteristics, and finally outputs discrete film thickness values, which are then transmitted to the calculation module of the digital twin workstation.

[0191] The digital twin workstation provides the system with digital-analog fusion processing and result output, and is divided into a calculation module, a correction module, and a display and interaction module, forming a closed-loop data flow.

[0192] Calculation module

[0193] Geometric Inversion Optimizer: Receives discrete film thickness values ​​from the sensing module, calls the parameterized oil film thickness model, aims to minimize the sum of squared errors between the measured film thickness and the model-calculated film thickness, obtains the observation value Z through the Levenberg-Marquardt algorithm, and transmits the observation value Z to the correction module.

[0194] PI-DeepONet Inference Engine: It calls a deep operator network of physical information pre-trained in the historical database, predicts the background field of the physical field of the tilting tile thrust bearing based on the input state vector of the previous time step, and transmits the background field data to the correction module.

[0195] Historical database: Stores thermal-elastic-fluid coupling simulation datasets, historical operating status data of tilting tile thrust bearings, historical film thickness measurement data, etc., providing data support for geometric inversion optimization and PI-DeepONet inference.

[0196] Correction module

[0197] EnKF State Estimator: also known as the ensemble Kalman filter state estimator, receives the observation value Z and the physical field background field from the calculation module, calculates the prediction error covariance matrix and Kalman gain, and completes the update of the input state vector.

[0198] Parameter Adaptive Update Unit: Based on the update results of EnKF, the model parameters of PI-DeepONet are adaptively adjusted, and the corrected input state vector is fed back to the PI-DeepONet inference engine.

[0199] The display interaction module receives the final reconstructed data output by the calculation module:

[0200] Full-field cloud map rendering unit: Visualizes and renders the pressure and temperature distribution of the entire field as a cloud map, intuitively displaying the spatial distribution characteristics of the physical field inside the tilting pad thrust bearing.

[0201] Warning threshold setting unit: Supports user-defined safety thresholds such as minimum film thickness and maximum temperature. When the reconstructed data exceeds the threshold, a sudden fault warning is triggered.

[0202] Life assessment unit: Based on the reconstructed full-field pressure distribution and combined with the Pammgren-Miner linear cumulative damage theory, the cumulative fatigue damage of the Babbitt alloy liner is calculated in real time, the remaining life of the tilting pad thrust bearing is displayed, and a durability failure warning is triggered.

[0203] By combining precise physical sensing, virtual digital-analog fusion, and closed-loop dynamic correction, a breakthrough has been achieved in reconstructing the entire field state from local measured data. This not only ensures the authenticity of data acquisition but also compensates for the limitations of pure hardware monitoring through physical information models and data assimilation technology. It is a concrete implementation of the ultrasonic digital-analog fusion technology solution of this invention.

[0204] In summary, this invention presents an ultrasonic numerical-model fusion method and system for monitoring the condition of tilting pad thrust bearings. By employing a Physical Information Deep Operator Network (PI-DeepONet), it accelerates the time-consuming thermo-elastohydrodynamic coupling simulation to millisecond-level online computation. Simultaneously, embedded physical equation constraints ensure the rationality of the prediction mechanism and its generalization ability. Secondly, utilizing sparse ultrasonic thickness measurement data, combined with a parametric model and geometric inversion, it accurately identifies the tilting pad bearing's attitude and thermal deformation. Furthermore, through an EnKF data assimilation framework, it deeply fuses these local geometric observations with the full-field predictions of the surrogate model, achieving high-precision real-time reconstruction of the full-field distribution of oil film pressure and temperature, making the invisible internal state of the tilting pad thrust bearing clearly visible. An adaptively evolving digital twin is constructed: EnKF continuously calibrates model parameters online, enabling the virtual model to track the performance drift of the physical entity caused by lubricating oil aging and wear, maintaining long-term prediction accuracy. Based on the reconstructed full-field state, the system can monitor the minimum film thickness and maximum temperature in real time, and use the cumulative damage theory to predict fatigue life, realizing a leap from passive alarm to predictive maintenance, and significantly improving the operational safety and maintenance economy of major equipment.

[0205] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0206] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0207] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0208] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0209] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0210] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0211] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0212] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0213] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0214] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0215] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for monitoring the condition of tilting pad thrust bearings using ultrasonic digital-analog fusion, characterized in that, Includes the following steps: S1. Construct a physical information deep operator network to establish a mapping proxy model from operating parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing. The physical information deep operator network adopts a dual-tower structure, including a branch network and a backbone network. The branch network is used to encode the features of the input operating parameter vector and output the operating feature vector. The backbone network is used to encode the position of the input spatial coordinates in the polar coordinate system and output the spatial basis function vector. The predicted field value is obtained by the dot product operation between the output of the branch network and the output of the backbone network. S2. Acquire real-time ultrasonic reflection echo signals from the back of the tilting bearing pad in the tilting pad thrust bearing, and calculate the oil film thickness measurements at multiple points. Based on the preset parameterized oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tilting bearing pad at the current moment are obtained through geometric inversion optimization. The objective function is to minimize the sum of squared errors between the measured film thickness at the ultrasonic measurement points and the film thickness calculated by the parameterized oil film thickness model. The Levenberg-Marquardt optimization algorithm is used to solve the geometric parameter vector containing the fulcrum film thickness, radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient. The objective function is expressed as: in, The vector of geometric parameters to be identified; The oil film thickness was measured using an ultrasonic sensor. N s represents the number of ultrasonic sensors; The calculated film thickness at the corresponding ultrasonic sensor measurement point is calculated by the physical information depth operator network. The coefficient of the regularization term; S3. Using the geometric attitude parameters and thermal deformation parameters identified in S2 as observation vectors, and using the mapping proxy model established in S1, the physical field state is predicted based on the input state vector of the previous moment as the background field. The Kalman gain is calculated by assimilating the Kalman filter data, and the input state vector of the current moment is updated. S4. Input the current input state vector obtained by updating S3 into the mapping proxy model established in S1 to reconstruct the pressure distribution and temperature distribution of the tilting pad thrust bearing in the entire field; perform state monitoring and fault early warning based on the reconstructed pressure distribution and temperature distribution.

2. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S1, the construction process of the mapping proxy model includes: Based on the thermo-elastic-fluid coupling dynamic characteristics of tilting pad thrust bearings, a thermo-elastic-fluid coupling dynamic simulation dataset is generated using Latin hypercube sampling within a preset working condition space. The working condition parameters include the spindle speed, specific pressure load, inlet oil temperature, and basic viscosity of the lubricating oil of the tilting pad thrust bearing. The simulation dataset includes the full-field oil film pressure distribution and temperature distribution of the tilting pad thrust bearing. The physical information deep operator network is trained using the simulation dataset. The loss function of the physical information deep operator network includes a data-driven error term and a physical equation residual term.

3. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 2, characterized in that, Both the branch network and the backbone network adopt a fully connected neural network, which contains 3 hidden layers, each with 100 neurons, and the activation function is the Tanh function.

4. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 2, characterized in that, The physical equation residuals include at least the Reynolds equation residuals, the energy equation residuals, and the boundary condition residuals; the physical equation residuals are obtained by calculating the partial derivatives of the network output with respect to spatial coordinates using automatic differentiation techniques, and then substituting them into the generalized Reynolds equation and the energy equation. The expression for the loss function is: in, Data-driven error; The residuals of the Reynolds equation; The residuals of the energy equation; λ1, λ2, and λ3 are the boundary condition residuals; λ1, λ2, and λ3 are the weighting coefficients.

5. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S2, the ultrasonic reflected echo signal is acquired by an ultrasonic sensor array arranged on the back of the tilting bearing; the ultrasonic sensor array is arranged as follows: Three ultrasonic sensors are arranged on the back of the tilting bearing near the oil inlet and oil outlet edges; The calculation method for the multi-point oil film thickness measurement value is as follows: The local oil film thickness at each ultrasonic sensor measuring point is obtained by calculating the ultrasonic reflected echo signal using a resonance model or a spring model.

6. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S2, the expression for the parameterized oil film thickness model is: in, For the oil film thickness at any location, The polar radius in polar coordinates. The polar angle in polar coordinates; This is the reference value for the film thickness at the tilting bearing support point; For the radial tilt angle and circumferential dip angle The resulting change in film thickness; This represents the amount of thermal arching deformation.

7. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S3, the input state vector is the augmented state vector X. t The augmented state vector X t From the physical field state vector X state and the unknown model parameter vector X to be identified param Composition; the physical field state vector X state This includes the discretized full-field pressure vector and full-field temperature vector; the unknown model parameter vector X param This includes lubricating oil viscosity correction factor and load correction factor; The initialization process for the Kalman filter data assimilation of the set is as follows: The Monta Carlo sampling method is used to generate a sample containing... M c The initial state set of samples is used to introduce Gaussian random perturbations into the parameter part of each sample in the initial state set within a preset error range, forming an initial probability distribution that characterizes the uncertainty of the system.

8. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S3, the ensemble Kalman filter data assimilation further includes constructing an observation operator, which is used to extract geometric feature prediction values ​​from the physical field state of the background field. The geometric feature prediction values ​​include the radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient of the tilting bearing. The Kalman gain is calculated as follows: in, for The Kalman gain matrix at time t. For the prediction error covariance matrix, To observe the transpose of the operator matrix, R is the observation prediction error covariance matrix; R is the observation noise covariance matrix; The update formula for the input state vector is: in, for Time of the first The analysis state vector of each sample, for Time of the first The predicted state vector of each sample. for The observation vector at time t, For the first The observational perturbation noise corresponding to each sample The observation operator matrix.

9. The ultrasonic digital-analog fusion method for monitoring the condition of tilting pad thrust bearings according to claim 1, characterized in that, In S4, the condition monitoring includes lifetime prediction based on the Pamgren-Miner linear cumulative damage theory, specifically: Using the reconstructed full-field pressure distribution as an alternating stress source, the fatigue damage increment of the Babbitt alloy liner on the surface of the tilting bearing is calculated in real time, and the total historical accumulated damage is updated, with the total historical accumulated damage being used as the cumulative fatigue damage. The fault early warning system adopts a multi-dimensional hierarchical strategy: When the instantaneous physical extreme values ​​in the reconstructed pressure and temperature distributions exceed the safety threshold, an emergency fault warning is triggered. When the accumulated fatigue damage exceeds a preset lifespan threshold, a durability failure warning is triggered.

10. An ultrasonic digital-analog fusion system for monitoring the condition of tilting pad thrust bearings, characterized in that, include: A construction module is used to build a physical information deep operator network to establish a mapping proxy model from operating parameters to the full-field pressure and temperature distribution of the tilting pad thrust bearing. The physical information deep operator network adopts a dual-tower structure, including a branch network and a backbone network. The branch network is used to encode the features of the input operating parameter vector and output the operating feature vector. The backbone network is used to encode the position of the input spatial coordinates in polar coordinates and output the spatial basis function vector. The predicted field value is obtained by the dot product operation between the output of the branch network and the output of the backbone network. The inversion module is used to acquire real-time ultrasonic reflection echo signals from the back of the tilting bearing pad in the tilting pad thrust bearing and calculate the oil film thickness measurement values ​​at multiple points. Based on the preset parametric oil film thickness model and the multi-point oil film thickness measurements, the geometric attitude parameters and thermal deformation parameters of the tiltable bearing at the current moment are obtained through geometric inversion optimization. The objective function is to minimize the sum of squared errors between the measured film thickness at the ultrasonic measurement points and the film thickness calculated by the parametric oil film thickness model. The Levenberg-Marquardt optimization algorithm is used to solve for the geometric parameter vector containing the fulcrum film thickness, radial tilt angle, circumferential tilt angle, and thermal arching deformation coefficient. The objective function is expressed as: in, The vector of geometric parameters to be identified; The oil film thickness was measured using an ultrasonic sensor. N s represents the number of ultrasonic sensors; The calculated film thickness at the corresponding ultrasonic sensor measurement point is calculated by the physical information depth operator network. The coefficient of the regularization term; The update module is used to use the geometric attitude parameters and thermal deformation parameters as observation vectors, use the mapping proxy model to predict the physical field state based on the input state vector of the previous moment as the background field, calculate the Kalman gain by assimilating the Kalman filter data, and update the input state vector at the current moment. The early warning module is used to input the updated input state vector into the mapping proxy model to reconstruct the pressure and temperature distribution of the entire field of the tilting pad thrust bearing; and to perform state monitoring and fault early warning based on the reconstructed pressure and temperature distribution.

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