A method and apparatus for thermodynamic coupling field state inversion in compressor hot-loading process

Abstract

This application discloses a method and apparatus for thermo-coupling field state inversion in compressor hot-assembly processes, relating to the fields of intelligent manufacturing and digital twin technology. The method includes: offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller to obtain a reduced-order model and a physics-data hybrid evolution model that meet preset conditions; using the reduced-order model to reduce the order of the observed state at the previous moment, obtaining a reduced-order state and a reduced-order orthogonal basis matrix; calculating the estimated state at the current moment using the physics-data hybrid evolution model based on the reduced-order state; calculating the target estimated state using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data; and performing inversion using a preset projection function based on the target estimated state and the reduced-order orthogonal basis matrix to obtain the inversion result. This method improves the accuracy of the inversion results and can improve the assembly quality of high-end equipment.

Description

Technical Field

[0001] This invention relates to the fields of intelligent manufacturing and digital twin technology, and in particular to a method and apparatus for thermodynamic coupling field state inversion in compressor hot-loading process. Background Technology

[0002] The assembly of heavy rotating machinery such as large compressor rotors and gas turbine rotors typically employs a thermal assembly process. This process involves complex transient heat conduction, thermal expansion, and contact mechanical coupling.

[0003] Existing technologies for monitoring rotor thermal fitment present several challenges: Firstly, industrial sites are often limited by installation space, typically allowing only a limited number of thermocouples or infrared temperature measurement points to be placed on the outer surface of the impeller. The temperature field and deformation deep within the impeller and mating surfaces cannot be directly measured, making it difficult for operators to accurately assess the internal fit and potentially leading to jamming or destructive thermal stress. Secondly, while traditional high-fidelity finite element simulations can calculate full-field data, a single calculation can take tens of minutes to several hours, making them unsuitable for real-time on-site monitoring. Surrogate model technology, used to lightweight finite element simulation models, is currently a popular approach. Existing surrogate models are based on purely data-driven predictive models; while fast, they lack physical constraints and cannot provide mathematical proofs of upper bounds on error. In production involving high-value components, engineers are hesitant to trust the output of "black box" models.

[0004] In view of the above-mentioned shortcomings in the existing technology, there is an urgent need for a method that can guarantee real-time performance, provide mathematical credibility proof, and invert the internal state through surface data. Summary of the Invention

[0005] In view of this, the present invention provides a method and apparatus for thermo-coupling field state inversion in compressor hot fitting process. The main purpose is to solve the problem that in current industrial sites, due to limited installation space, only a limited number of thermocouples or infrared temperature measurement points can be arranged on the outer surface of the impeller. The temperature field and deformation inside the impeller and deep in the mating surface cannot be directly measured, which makes it impossible for operators to accurately judge the internal mating state and easily leads to jamming or destructive thermal stress.

[0006] To address the aforementioned problems, this application provides a method for thermo-coupling field state inversion in compressor hot-loading processes, comprising:

[0007] Offline modeling was performed based on historical temperature and displacement data of key nodes of the compressor impeller to obtain a reduced-order model and a hybrid physical and data evolution model that meet the preset conditions.

[0008] The order reduction model is used to reduce the order of the observed state at the previous time step, resulting in the reduced order state and the reduced order orthogonal basis matrix;

[0009] Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment;

[0010] The target estimated state is obtained by using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data.

[0011] Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result.

[0012] Optionally, the offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller yields a reduced-order model and a hybrid physical-data evolution model that meet preset conditions, specifically including:

[0013] A historical state snapshot matrix is ​​constructed based on historical temperature and displacement data of key nodes of the compressor impeller.

[0014] Offline modeling is performed using the historical state snapshot matrix to obtain a reduced-order model and a physical-data hybrid evolution model that meet preset conditions.

[0015] Optionally, the step of using the historical state snapshot matrix for offline modeling to obtain a reduced-order model that meets preset conditions specifically includes:

[0016] Step 1: Initialize the model parameters of the initial reduced-order model, including the truncation order;

[0017] Step 2: Perform singular value decomposition on the historical state snapshot matrix to obtain the left singular vector representing the spatial mode, the right singular vector representing the temporal mode, and the singular value diagonal matrix representing the energy contribution.

[0018] Step 3: Based on the truncation order, truncate the singular value diagonal matrix to obtain the first singular value diagonal submatrix and the second singular value diagonal submatrix;

[0019] Step 4: Calculate the upper bound of the truncation error based on the second singular value diagonal submatrix and the singular value diagonal matrix;

[0020] Step 5: When the upper bound of the truncation error is less than or equal to the preset upper bound threshold of the truncation error, the initial order reduction model is determined as an order reduction model that meets the preset conditions. When the upper bound of the truncation error is greater than the preset upper bound threshold of the truncation error, the truncation order is updated to obtain the current order reduction model.

[0021] Step 6: Repeat steps 2 to 5 based on the updated truncation order to repeatedly update the current reduced-order model until the upper bound of the truncation error of the updated current reduced-order model is less than or equal to the preset upper bound threshold of the truncation error. Then, determine the current reduced-order model of the current iteration as a reduced-order model that meets the preset conditions.

[0022] Optionally, the offline modeling using the historical state snapshot matrix to obtain a hybrid physical and data evolution model specifically includes:

[0023] The historical state snapshot matrix is ​​reduced in order using the aforementioned order reduction model to obtain the historical reduced-order states;

[0024] A first-state model is obtained by performing linear physical evolution on the historical reduced-order states;

[0025] The historical reduced-order state is corrected by nonlinear deviation to obtain the second-state model;

[0026] The physical and data hybrid evolution model is obtained by performing an addition operation based on the first state model and the second state model.

[0027] Optionally, the method further includes:

[0028] Based on the offline calibration dataset, a conformal prediction method is used to calculate the distribution of prediction errors of the physical and data hybrid evolution model, and a safety factor is obtained.

[0029] Based on the safety factor, a dynamic confidence interval is constructed and the confidence interval is mapped to the process noise covariance matrix of the extended Kalman filter method.

[0030] Optionally, the target estimated state is calculated using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data.

[0031] The prior error covariance is obtained by calculating the process noise covariance matrix and the Jacobian matrix of the physical and data hybrid evolution model.

[0032] The current observation data is reduced in order using the reduced-order model to obtain the observation matrix of the current reduced-order orthogonal basis;

[0033] The Kalman gain is obtained by calculating the prior error covariance, the observation matrix of the current reduced-order orthogonal basis, and the measurement noise covariance.

[0034] The estimated state is corrected based on the Kalman gain, sparse measurement data, and the current reduced-order orthogonal basis matrix to obtain the target estimated state.

[0035] Optionally, the step of inverting the thermo-mechanical coupling field state of the compressor hot-loading process using a preset projection function based on the target estimated state and the reduced-order orthogonal basis matrix to obtain the thermo-mechanical coupling field state inversion result specifically includes:

[0036] The historical state snapshot matrix is ​​subjected to mean calculation to obtain a mean vector;

[0037] Based on the mean vector, the estimated target state, and the reduced-order orthogonal basis matrix, a preset projection function is used to calculate and process the reconstructed state, thereby obtaining the state inversion result of the thermo-coupled field.

[0038] To address the aforementioned problems, this application provides a thermo-coupled field state inversion device for compressor hot-loading processes, comprising:

[0039] The model building module is used for offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller, to obtain a reduced-order model and a hybrid physical and data evolution model that meet preset conditions;

[0040] The order reduction processing module is used to reduce the order of the observed state at the previous time step using the order reduction model to obtain the reduced order state and the reduced order orthogonal basis matrix.

[0041] The first calculation module is used to perform calculations based on the reduced-order state using the physical and data hybrid evolution model to obtain the estimated state at the current moment;

[0042] The second calculation module is used to calculate the target estimated state based on the estimated state and the real-time acquired current observation data using the extended Kalman filter method.

[0043] The inversion module is used to invert the thermo-mechanical coupling field state of the compressor hot-loading process based on the target estimated state and the reduced-order orthogonal basis matrix using a preset projection function, and obtain the thermo-mechanical coupling field state inversion result.

[0044] To address the aforementioned problems, this application provides a storage medium storing a computer program that, when executed by a processor, implements the steps of the aforementioned method for thermo-coupled field state inversion in compressor hot-fitting processes.

[0045] To address the aforementioned problems, this application provides an electronic device, comprising at least a memory and a processor. The memory stores a computer program, and the processor, when executing the computer program in the memory, implements the steps of the aforementioned thermo-coupled field state inversion method for compressor hot-fitting process.

[0046] The beneficial effects of this application are as follows: This application can accurately and in real-time invert the full-field temperature distribution and thermal deformation field of the unmeasurable area inside the impeller by arranging only a small number of sparse temperature sensors on the outer surface of the impeller. Through mathematical proof of the upper bound of the error truncation by singular value decomposition, and combined with the dynamic confidence interval provided by conformal prediction technology, a clear and reliable quantifiable index is provided for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weight between model prediction and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of the impeller, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0047] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0048] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0049] Figure 1 A schematic flowchart of a thermo-coupled field state inversion method for compressor hot-loading process provided in an embodiment of this application is shown.

[0050] Figure 2 This illustration shows a flowchart of a thermo-coupled field state inversion method for compressor hot-loading process according to another embodiment of this application;

[0051] Figure 3 A structural block diagram of a thermo-coupled field state inversion device for compressor hot-loading process is shown in another embodiment of this application. Detailed Implementation

[0052] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0053] It should be understood that various modifications can be made to the embodiments described herein. Therefore, the above description should not be considered as limiting, but merely as an example of embodiments. Other modifications within the scope and spirit of this application will be apparent to those skilled in the art.

[0054] The accompanying drawings, which are included in and form part of this specification, illustrate embodiments of the present application and, together with the general description of the present application given above and the detailed description of the embodiments given below, serve to explain the principles of the present application.

[0055] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0056] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application.

[0057] The above and other aspects, features and advantages of this application will become more apparent when taken in conjunction with the accompanying drawings and in view of the following detailed description.

[0058] Specific embodiments of this application are described thereafter with reference to the accompanying drawings; however, it should be understood that the claimed embodiments are merely examples of this application, which can be implemented in various ways. Well-known and / or repeated functions and structures are not described in detail to avoid unnecessary or redundant details that could obscure the application. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely to teach those skilled in the art to use this application in a variety of substantially any suitable detailed structures.

[0059] This specification may use the phrases “in one embodiment,” “in another embodiment,” “in yet another embodiment,” or “in other embodiments,” all of which may refer to one or more of the same or different embodiments according to this application.

[0060] This application provides a method for thermo-coupling field state inversion in compressor hot-loading processes, such as... Figure 1 As shown, it includes:

[0061] Step S101: Based on the historical temperature data and historical displacement data of the key nodes of the compressor impeller, perform offline modeling to obtain a reduced-order model and a physical and data hybrid evolution model that meet the preset conditions;

[0062] In the specific implementation process of this step, a historical state snapshot matrix is ​​constructed based on the historical temperature data and historical displacement data of the key nodes of the compressor impeller; the historical state snapshot matrix is ​​used for offline modeling to obtain a reduced-order model and a physical and data hybrid evolution model that meet the preset conditions.

[0063] Step S102: Use the reduced-order model to reduce the order of the observed state at the previous time step to obtain the reduced-order state and the reduced-order orthogonal basis matrix;

[0064] In this step, a snapshot matrix corresponding to the previous moment is constructed using the observed state at the previous moment. The observed state includes a temperature vector and a key displacement vector. Specifically, the temperature vector and the key displacement vector are stacked to obtain the snapshot matrix. Each column of the snapshot matrix contains both thermal and force field information in physical space. The snapshot matrix is ​​processed to obtain the mean of the state snapshot. Singular value decomposition is performed on the state snapshot matrix to obtain the left singular vector representing the spatial mode, the right singular vector representing the temporal mode, and the diagonal matrix representing the energy contribution at the previous moment. The left singular vector representing the spatial mode at the previous moment is truncated using the truncation parameters of the physics and data hybrid evolution model to obtain the reduced-order orthogonal basis matrix at the previous moment. Based on the reduced-order orthogonal basis matrix, the snapshot matrix, and the mean of the state snapshot at the previous moment, the reduced-order state at the previous moment is obtained.

[0065] Step S103: Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment;

[0066] In this step, the first state model of the physical and data hybrid evolution model is used to perform linear physical evolution on the reduced-order state to obtain the first state; the second state model of the physical and data hybrid evolution model is used to perform nonlinear deviation correction on the reduced-order state to obtain the second state; the first state and the second state are added together to obtain the estimated state at the current time.

[0067] Step S104: Based on the estimated state and the real-time acquired current observation data, the extended Kalman filter method is used to calculate and obtain the target estimated state;

[0068] In this step, the prior error covariance is calculated based on the process noise covariance matrix and the Jacobian matrix of the physical and data hybrid evolution model. The order reduction model is used to reduce the order of the current observation data to obtain the current reduced-order orthogonal basis matrix. The Kalman gain is calculated based on the prior error covariance, the current reduced-order orthogonal basis matrix, and the measurement noise covariance. The estimated state is then corrected based on the Kalman gain, sparse measurement data, and the current reduced-order orthogonal basis matrix to obtain the target estimated state.

[0069] Step S105: Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result.

[0070] In this step, the historical state snapshot matrix is ​​processed by mean calculation to obtain a mean vector; based on the mean vector, the target estimated state, and the reduced-order orthogonal basis matrix, a preset projection function is used to calculate and process the reconstructed state to obtain the thermo-coupled field state inversion result.

[0071] This application achieves real-time and accurate inversion of the full-field temperature distribution and thermal deformation field in the unmeasurable region inside the impeller using only a small number of sparse temperature sensors deployed on the outer surface of the impeller. Mathematical proof of the upper bound of the error truncation through singular value decomposition, combined with the dynamic confidence interval provided by conformal prediction technology, provides a clear and reliable quantifiable index for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model's prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weights between model predictions and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of impellers, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0072] Another embodiment of this application provides a different method for thermo-coupled field state inversion in compressor hot-loading processes, such as... Figure 2 As shown, it includes:

[0073] Step S201: Construct a historical state snapshot matrix based on historical temperature data and historical displacement data of key nodes of the compressor impeller;

[0074] In this step, the key nodes of the compressor impeller include surface nodes, internal nodes, and deformation nodes. A high-fidelity finite element simulation method can be used to obtain the node temperature sequence and key node displacement sequence during the compressor rotor's thermal assembly process. Specifically, a finite element model of the compressor rotor is established to simulate the entire impeller cooling and heating process, with a time step of [time step value missing]. Extract the temperature vector composed of historical temperature data from all grid nodes at each time point. Displacement vector composed of historical displacement data of key nodes .in This represents the total number of temperature data points. This represents the total number of displacement data. represent k Sampling time points, number of time points: The two are then concatenated to form a state vector. A snapshot matrix is ​​constructed based on the state vectors at different time points. ,in, ; Snapshot matrix The number of elements; These are the state vectors corresponding to different times. This stacking method ensures that the reduced-order model can capture the strong physical coupling between the temperature field and the deformation field. Each column vector of the historical snapshot matrix contains both thermal and force field information in physical space.

[0075] Step S202: Use the historical state snapshot matrix to perform offline modeling to obtain a reduced-order model that meets preset conditions;

[0076] This step, in its specific implementation, includes the following steps:

[0077] Step 1: Initialize the model parameters of the initial order reduction model, including the truncation order. ;

[0078] Step 2: Perform singular value decomposition on the historical state snapshot matrix to obtain the left singular vector representing the spatial mode, the right singular vector representing the temporal mode, and the singular value diagonal matrix representing the energy contribution; the mathematical expression of singular value decomposition can be expressed by the following formula (1):

[0079]

[0080] in, It is a singular value diagonal matrix. It is a singular value, and An energy retention threshold is set, which can be 99.9%. The value of the energy retention threshold can be set according to actual needs. It is a left singular vector; It is a right singular vector; This is a transpose matrix operation.

[0081] Step 3: Based on the truncation order, truncate the singular value diagonal matrix to obtain the first singular value diagonal submatrix and the second singular value diagonal submatrix;

[0082] Specifically, the singular value diagonal matrix is ​​truncated based on the truncation order of the initial reduced-order model to obtain the first singular value diagonal submatrix and the second singular value diagonal submatrix.

[0083] Step 4: Calculate the upper bound of the truncation error based on the second singular value diagonal submatrix and the singular value diagonal matrix;

[0084] In practice, the upper bound of the truncation error The mathematical expression for can be represented by the following formula (2):

[0085]

[0086] in, This represents the cumulative sum of the elements of the second singular value diagonal submatrix; This represents the cumulative sum of all elements in the singular valued diagonal matrix. This metric explicitly quantifies the degree to which the reduced-order model loses physical information.

[0087] Step 5: When the upper bound of the truncation error is less than or equal to the preset upper bound threshold of the truncation error, the initial order reduction model is determined as an order reduction model that meets the preset conditions. When the upper bound of the truncation error is greater than the preset upper bound threshold of the truncation error, the truncation order is updated to obtain the current order reduction model.

[0088] In practice, the preset upper limit threshold for truncation error can be: In specific applications, the preset upper bound threshold for truncation error can be set according to actual needs. When the upper bound for truncation error is less than or equal to the preset upper bound threshold, the model is considered mathematically reliable. The initial reduced-order model is determined as a reduced-order model that satisfies the preset conditions. When the upper bound for truncation error is greater than the preset upper bound threshold, the truncation order is updated to obtain the current reduced-order model.

[0089] Step 6: Repeat steps 2 to 5 based on the updated truncation order to repeatedly update the current reduced-order model until the upper bound of the truncation error of the updated current reduced-order model is less than or equal to the preset upper bound threshold of the truncation error. Then, determine the current reduced-order model of the current iteration as a reduced-order model that meets the preset conditions.

[0090] In specific implementation, steps two to five are repeatedly executed based on the updated truncation order to repeatedly update the current reduced-order model until the upper bound of the truncation error of the updated current reduced-order model is less than or equal to the preset upper bound threshold of the truncation error. Then, the current reduced-order model of the current iteration is determined as a reduced-order model that meets the preset conditions.

[0091] Step S203: Use the historical state snapshot matrix to perform offline modeling to obtain a physical and data hybrid evolution model;

[0092] In the specific implementation process of this step, the order reduction model is used to reduce the order of the historical state snapshot matrix to obtain the historical reduced-order state. The historical reduced-order states are subjected to linear physical evolution to obtain the first-state model. The historical reduced-order states are corrected for nonlinear deviations to obtain the second-state model. Based on the first state model and the second state model, an addition operation is performed to obtain the physical and data hybrid evolution model. The mathematical expression of the physical and data hybrid evolution model can be expressed by the following formula (3):

[0093]

[0094] in, This represents a historical downgraded state. It is the transpose of the historical reduced-order orthogonal basis matrix; The linear evolution matrix is ​​learned from the projected data using the least squares method through operator inference and represents the dominant physical law of heat conduction. This is a residual neural network used to fit nonlinear physical terms such as changes in contact thermal resistance and radiative heat transfer. The residual neural network is a fully connected network with a single hidden layer. The hidden layer uses the ReLU activation function, the input is a reduced-order state vector, and the output is used to compensate for nonlinear biases.

[0095] Step S204: Based on the offline calibration dataset, the conformal prediction method is used to calculate the distribution of the prediction error of the physical and data hybrid evolution model to obtain the safety factor;

[0096] In this step, conformal prediction technology is used to calculate a safety factor for the model's prediction error on an offline calibration dataset. Safety factor The mathematical formula for calculating it can be shown in the following formula (4):

[0097]

[0098] in, Let be the infimum operator, representing the minimum value that satisfies the condition; This represents the total number of samples in the offline calibration dataset. For the first i The absolute prediction error of each calibration sample; For the historical state snapshot matrix, the first... i Each element value; The prediction obtained using a hybrid physical and data evolution model is compared with the historical state snapshot matrix. i The predicted value corresponding to each element; For the model to the first i Sample The given standard deviation of the forecast; For indicator functions; The significance level; This is a candidate threshold, which can be set according to actual needs. Given a reliability requirement of 1- Given the condition that the scores of all distribution quantiles that meet the reliability requirements are obtained, the minimum score of the scores that meet the reliability requirements is determined as the safety factor.

[0099] Step S205: Construct a dynamic confidence interval based on the safety factor and map the confidence interval to the process noise covariance matrix of the extended Kalman filter method;

[0100] In the specific implementation process of this step, a dynamic confidence interval is constructed, and the confidence interval is mapped to the process noise covariance matrix in the extended Kalman filter. The mathematical expression can be represented by the following formula (5):

[0101] (5)

[0102] Where, diag is the operator for constructing a diagonal matrix; the process noise covariance matrix It is used to adjust the confidence weight of the physical model predictions online, and automatically increases the correction weight of the measurement data when the prediction uncertainty increases.

[0103] Step S206: Use the reduced-order model to reduce the order of the observed state at the previous time step to obtain the reduced-order state and the reduced-order orthogonal basis matrix;

[0104] In this step, a snapshot matrix corresponding to the previous moment is constructed using the observed state at the previous moment. The observed state includes a temperature vector and a key displacement vector. Specifically, the temperature vector and the key displacement vector are stacked to obtain the snapshot matrix. Each column of the snapshot matrix contains both thermal and force field information in physical space. The snapshot matrix is ​​processed to obtain the mean of the state snapshot. Singular value decomposition is performed on the state snapshot matrix to obtain the left singular vector representing the spatial mode, the right singular vector representing the temporal mode, and the diagonal matrix representing the energy contribution at the previous moment. The left singular vector representing the spatial mode at the previous moment is truncated using the truncation parameters of the physics and data hybrid evolution model to obtain the reduced-order orthogonal basis matrix at the previous moment. Based on the reduced-order orthogonal basis matrix, the snapshot matrix, and the mean of the state snapshot at the previous moment, the reduced-order state at the previous moment is obtained.

[0105] Step S207: Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment;

[0106] In the specific implementation process of this step, the first state model of the physical and data hybrid evolution model is used to perform linear physical evolution on the reduced-order state to obtain the first state; the mathematical expression of the linear physical evolution can be shown by the following formula (6):

[0107]

[0108] in, A This is the first state; The evolution matrix of the linear system is obtained by inferring the linear dynamic operators using the least squares method. The mathematical expression can be shown in the following formula (7):

[0109]

[0110] in, , for Time and t The reduced-order state snapshot matrix at time +1; T This is a transpose matrix operation.

[0111] The reduced-order state is corrected for nonlinear deviation using a second-state model based on a hybrid physical and data evolution model to obtain the second state; the mathematical expression can be expressed as follows (8):

[0112]

[0113] in, B This is the second state; For a residual neural network, the mathematical expression can be represented by the following formula (9):

[0114]

[0115] in, This is the input layer weight matrix; The input layer bias vector; RELU For activation functions; This is the output layer weight matrix; This is the output layer bias vector; This is the model parameter set. The training objective of this method is to minimize the error between the differential derivative of the snapshot data and the predicted value of the linear model in fitting the nonlinear change deviation of the contact thermal resistance in the physical process. The first state and the second state are added together to obtain the estimated state at the current moment. The mathematical expression of the estimated state can be expressed as follows: (10)

[0116]

[0117] in, This represents the estimated state at the current moment.

[0118] Step S208: Based on the estimated state and the real-time acquired current observation data, the extended Kalman filter method is used to calculate and obtain the target estimated state;

[0119] In the specific implementation process, this step is based on the process noise covariance matrix. The Jacobian matrix of the physical and data hybrid evolution model The prior error covariance is obtained through calculation. Jacobian matrix The mathematical expression for can be represented by the following formula (11):

[0120] in, for k The estimated state at time -1; To construct the Jacobian matrix operation; The evolution matrix of the linear system. Prior error covariance. The mathematical expression for can be represented by the following formula (12):

[0121]

[0122] The order reduction model is used to reduce the order of the current observation data, resulting in the observation matrix of the current reduced-order orthogonal basis. H ; Observation matrix H From reduced orthogonal basis The row vectors corresponding to the sensor positions are composed of the vectors. Let be the posterior error covariance, representing the corrected covariance of the previous moment; the Kalman gain is obtained by calculating based on the prior error covariance, the observation matrix of the current reduced-order orthogonal basis, and the measurement noise covariance; the mathematical expression can be represented by the following formula (13):

[0123]

[0124] in, Kalman gain; H This is the observation matrix of the current reduced-order orthogonal basis; To measure the noise covariance; The prior error covariance; T This is a transpose matrix operation.

[0125] The estimated state is corrected based on the Kalman gain, sparse measurement data, and the current reduced-order orthogonal basis matrix to obtain the target estimated state. The mathematical expression of the target estimated state can be shown in the following formula (14):

[0126]

[0127] in, Estimate the state for the target; To estimate the state; Kalman gain; H This is the observation matrix of the current reduced-order orthogonal basis; This is sparse measurement data.

[0128] Step S209: Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result.

[0129] In this step, the historical state snapshot matrix is ​​averaged to obtain a mean vector. Based on the mean vector, the estimated target state, and the reduced-order orthogonal basis matrix, a preset projection function is used to calculate and process the reconstructed state, thereby obtaining the state inversion result of the thermo-coupled field. The mathematical expression of the preset projection function can be expressed as follows (15):

[0130]

[0131] in, In a reconstructed state; Estimate the state for the target; It is the mean vector; It is a reduced-order orthogonal basis matrix.

[0132] This application achieves real-time and accurate inversion of the full-field temperature distribution and thermal deformation field in the unmeasurable region inside the impeller using only a small number of sparse temperature sensors deployed on the outer surface of the impeller. Mathematical proof of the upper bound of the error truncation through singular value decomposition, combined with the dynamic confidence interval provided by conformal prediction technology, provides a clear and reliable quantifiable index for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model's prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weights between model predictions and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of impellers, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0133] Another embodiment of this application provides a thermo-coupled field state inversion device 300 for compressor hot-loading process, such as Figure 3 As shown, it includes:

[0134] The model building module 301 is used for offline modeling based on historical temperature data and historical displacement data of key nodes of the compressor impeller, to obtain a reduced-order model and a physical and data hybrid evolution model that meet preset conditions.

[0135] The order reduction processing module 302 is used to perform order reduction processing on the observation state at the previous time step using the order reduction model to obtain the order reduction state and the order reduction orthogonal basis matrix.

[0136] The first calculation module 303 is used to perform calculations based on the reduced-order state using the physical and data hybrid evolution model to obtain the estimated state at the current moment;

[0137] The second calculation module 304 is used to calculate the target estimated state based on the estimated state and the real-time acquired current observation data using the extended Kalman filter method.

[0138] The inversion module 305 is used to invert the thermo-mechanical coupling field state of the compressor hot-loading process based on the target estimated state and the reduced-order orthogonal basis matrix using a preset projection function, and obtain the thermo-mechanical coupling field state inversion result.

[0139] In the specific implementation process, the model building module 301 is specifically used to construct a historical state snapshot matrix based on the historical temperature data and historical displacement data of the key nodes of the compressor impeller; and to perform offline modeling using the historical state snapshot matrix to obtain a reduced-order model and a physical and data hybrid evolution model that meet the preset conditions.

[0140] In the specific implementation process, the model construction module 301 is further used for: Step 1, initializing the model parameters of the initial reduced-order model, the model parameters including the truncation order; Step 2, performing singular value decomposition on the historical state snapshot matrix to obtain a left singular vector representing the spatial mode, a right singular vector representing the temporal mode, and a singular value diagonal matrix representing the energy contribution; Step 3, truncating the singular value diagonal matrix based on the truncation order to obtain a first singular value diagonal submatrix and a second singular value diagonal submatrix; Step 4, calculating the truncation error based on the second singular value diagonal submatrix and the singular value diagonal matrix. Step 5: When the upper bound of the truncation error is less than or equal to the preset upper bound threshold of the truncation error, the initial reduced-order model is determined as a reduced-order model that meets the preset conditions. When the upper bound of the truncation error is greater than the preset upper bound threshold of the truncation error, the truncation order is updated to obtain the current reduced-order model. Step 6: Based on the updated truncation order, steps 2 to 5 are repeated to update the current reduced-order model repeatedly until the upper bound of the truncation error of the updated current reduced-order model is less than or equal to the preset upper bound threshold of the truncation error. Then, the current reduced-order model in the current iteration is determined as a reduced-order model that meets the preset conditions.

[0141] In the specific implementation process, the model construction module 301 is further used to: reduce the order of the historical state snapshot matrix using the reduced-order model to obtain the historical reduced-order state; perform linear physical evolution on the historical reduced-order state to obtain the first state model; perform nonlinear deviation correction on the historical reduced-order state to obtain the second state model; and perform addition operation on the first state model and the second state model to obtain the physical and data hybrid evolution model.

[0142] In specific implementation, the device also includes an offline verification module, which is specifically used to calculate the distribution of prediction error of the physical and data hybrid evolution model based on the offline calibration dataset using a conformal prediction method to obtain a safety factor; construct a dynamic confidence interval based on the safety factor and map the confidence interval to the process noise covariance matrix of the extended Kalman filter method.

[0143] In the specific implementation process, the second calculation module 304 is specifically used to: perform calculations based on the process noise covariance matrix and the Jacobian matrix of the physical and data hybrid evolution model to obtain the prior error covariance; use the reduced-order model to reduce the order of the current observation data to obtain the observation matrix of the current reduced-order orthogonal basis; perform calculations based on the prior error covariance, the observation matrix of the current reduced-order orthogonal basis, and the measurement noise covariance to obtain the Kalman gain; and correct the estimated state based on the Kalman gain, sparse measurement data, and the current reduced-order orthogonal basis matrix to obtain the target estimated state.

[0144] In the specific implementation process, the inversion module 305 is specifically used to perform mean calculation on the historical state snapshot matrix to obtain a mean vector; based on the mean vector, the target estimated state, and the reduced-order orthogonal basis matrix, a preset projection function is used to perform calculation to obtain the reconstructed state, so as to obtain the thermo-coupled field state inversion result.

[0145] This application achieves real-time and accurate inversion of the full-field temperature distribution and thermal deformation field in the unmeasurable region inside the impeller using only a small number of sparse temperature sensors deployed on the outer surface of the impeller. Mathematical proof of the upper bound of the error truncation through singular value decomposition, combined with the dynamic confidence interval provided by conformal prediction technology, provides a clear and reliable quantifiable index for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model's prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weights between model predictions and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of impellers, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0146] Another embodiment of this application provides a storage medium storing a computer program, which, when executed by a processor, implements the following method steps:

[0147] Step 1: Perform offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller to obtain a reduced-order model and a physical-data hybrid evolution model that meet the preset conditions.

[0148] Step 2: Use the reduced-order model to reduce the order of the observed state at the previous time step to obtain the reduced-order state and the reduced-order orthogonal basis matrix;

[0149] Step 3: Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment;

[0150] Step 4: Based on the estimated state and the real-time acquired current observation data, the extended Kalman filter method is used to calculate and obtain the target estimated state;

[0151] Step 5: Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result.

[0152] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0153] 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 used as 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.

[0154] The specific implementation process of the above method steps can be found in any of the above embodiments of the thermo-coupling field state inversion method for compressor hot-loading process, and will not be repeated here.

[0155] This application achieves real-time and accurate inversion of the full-field temperature distribution and thermal deformation field in the unmeasurable region inside the impeller using only a small number of sparse temperature sensors deployed on the outer surface of the impeller. Mathematical proof of the upper bound of the error truncation through singular value decomposition, combined with the dynamic confidence interval provided by conformal prediction technology, provides a clear and reliable quantifiable index for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model's prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weights between model predictions and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of impellers, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0156] Another embodiment of this application provides an electronic device, which can be a server. The electronic device includes a processor, a memory, a network interface, and a database connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile and / or volatile storage media and internal memory. The non-volatile storage media stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external clients via a network connection. When the program is executed by the processor, it implements the functions or steps of a server-side method for thermo-coupled field state inversion in a compressor hot-fitting process.

[0157] In one embodiment, an electronic device is provided, which can be a client. The electronic device includes a processor, memory, a network interface, a display screen, and an input device connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface is used to communicate with an external server via a network connection. When the program of the electronic device is executed by the processor, it implements the functions or steps of a client-side method for thermo-coupled field state inversion in a compressor hot-fitting process.

[0158] Another embodiment of this application provides an electronic device, including at least a memory and a processor. The memory stores a computer program, and the processor, when executing the computer program in the memory, performs the following method steps:

[0159] Step 1: Perform offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller to obtain a reduced-order model and a physical-data hybrid evolution model that meet the preset conditions.

[0160] Step 2: Use the reduced-order model to reduce the order of the observed state at the previous time step to obtain the reduced-order state and the reduced-order orthogonal basis matrix;

[0161] Step 3: Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment;

[0162] Step 4: Based on the estimated state and the real-time acquired current observation data, the extended Kalman filter method is used to calculate and obtain the target estimated state;

[0163] Step 5: Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result.

[0164] The specific implementation process of the above method steps can be found in any of the above embodiments of the thermo-coupling field state inversion method for compressor hot-loading process, and will not be repeated here.

[0165] This application achieves real-time and accurate inversion of the full-field temperature distribution and thermal deformation field in the unmeasurable region inside the impeller using only a small number of sparse temperature sensors deployed on the outer surface of the impeller. Mathematical proof of the upper bound of the error truncation through singular value decomposition, combined with the dynamic confidence interval provided by conformal prediction technology, provides a clear and reliable quantifiable index for the model output. The extended Kalman filter method is used to fuse field sensor data in real time, dynamically correcting the model's prediction state; and the uncertainty quantification results are used to adaptively adjust the process noise covariance, balancing the trust weights between model predictions and measured data. This overcomes the bottlenecks of traditional methods in terms of invisibility, slow computation, and unreliability, ultimately forming an efficient, reliable, and practical real-time inversion method for the thermo-coupling field of impellers, improving the assembly quality, reliability, and intelligence level of high-end rotating machinery.

[0166] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. Those skilled in the art can make various modifications or equivalent substitutions to this application within the scope and nature of this application, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for thermo-coupling field state inversion in compressor hot-loading process, characterized in that, include: A historical state snapshot matrix is ​​constructed based on historical temperature and displacement data of key nodes of the compressor impeller. Offline modeling is performed using the historical state snapshot matrix to obtain a reduced-order model and a hybrid physical and data evolution model that meet preset conditions; The order reduction model is used to reduce the order of the observed state at the previous time step, resulting in the reduced order state and the reduced order orthogonal basis matrix; Based on the reduced-order state, the physical and data hybrid evolution model is used to calculate and obtain the estimated state at the current moment; The target estimated state is obtained by using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data. Based on the target estimated state and the reduced-order orthogonal basis matrix, the thermo-mechanical coupling field state of the compressor hot-loading process is inverted using a preset projection function to obtain the thermo-mechanical coupling field state inversion result; The offline modeling using the historical state snapshot matrix to obtain a reduced-order model that meets preset conditions specifically includes: Step 1: Initialize the model parameters of the initial reduced-order model, including the truncation order; Step 2: Perform singular value decomposition on the historical state snapshot matrix to obtain the left singular vector representing the spatial mode, the right singular vector representing the temporal mode, and the singular value diagonal matrix representing the energy contribution. Step 3: Based on the truncation order, truncate the singular value diagonal matrix to obtain the first singular value diagonal submatrix and the second singular value diagonal submatrix; Step 4: Calculate the upper bound of the truncation error based on the second singular value diagonal submatrix and the singular value diagonal matrix; Step 5: When the upper bound of the truncation error is less than or equal to the preset upper bound threshold of the truncation error, the initial order reduction model is determined as an order reduction model that meets the preset conditions. When the upper bound of the truncation error is greater than the preset upper bound threshold of the truncation error, the truncation order is updated to obtain the current order reduction model. Step 6: Repeat steps 2 to 5 based on the updated truncation order to repeatedly update the current reduced-order model until the upper bound of the truncation error of the updated current reduced-order model is less than or equal to the preset upper bound threshold of the truncation error. Then, determine the current reduced-order model of the current iteration as a reduced-order model that meets the preset conditions. The offline modeling using the historical state snapshot matrix to obtain a hybrid physical and data evolution model specifically includes: The historical state snapshot matrix is ​​reduced in order using the aforementioned order reduction model to obtain the historical reduced-order states; A first-state model is obtained by performing linear physical evolution on the historical reduced-order states; The historical reduced-order state is corrected by nonlinear deviation to obtain the second-state model; The physical and data hybrid evolution model is obtained by performing an addition operation based on the first state model and the second state model.

2. The method as described in claim 1, characterized in that, The method further includes: Based on the offline calibration dataset, a conformal prediction method is used to calculate the distribution of prediction errors of the physical and data hybrid evolution model, and a safety factor is obtained. Based on the safety factor, a dynamic confidence interval is constructed and the confidence interval is mapped to the process noise covariance matrix of the extended Kalman filter method.

3. The method as described in claim 2, characterized in that, The target estimated state is calculated using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data, specifically including: The prior error covariance is obtained by calculating the process noise covariance matrix and the Jacobian matrix of the physical and data hybrid evolution model. The current observation data is reduced in order using the reduced-order model to obtain the observation matrix of the current reduced-order orthogonal basis; The Kalman gain is obtained by calculating the prior error covariance, the observation matrix of the current reduced-order orthogonal basis, and the measurement noise covariance. The estimated state is corrected based on the Kalman gain, sparse measurement data, and the current reduced-order orthogonal basis matrix to obtain the target estimated state.

4. The method as described in claim 1, characterized in that, The process of inverting the thermo-mechanical coupled field state of the compressor hot-loading process using a preset projection function based on the target estimated state and the reduced-order orthogonal basis matrix to obtain the thermo-mechanical coupled field state inversion result specifically includes: The historical state snapshot matrix is ​​subjected to mean calculation to obtain a mean vector; Based on the mean vector, the estimated target state, and the reduced-order orthogonal basis matrix, a preset projection function is used to calculate and process the reconstructed state, thereby obtaining the state inversion result of the thermo-coupled field.

5. A thermo-coupled field state inversion device for compressor hot-loading process, used to implement any one of the thermo-coupled field state inversion methods for compressor hot-loading process as described in claims 1 to 4, characterized in that, include: The model building module is used to construct a historical state snapshot matrix based on historical temperature and displacement data of key nodes of the compressor impeller. Offline modeling is performed using the historical state snapshot matrix to obtain a reduced-order model and a hybrid physical and data evolution model that meet preset conditions; The order reduction processing module is used to reduce the order of the observed state at the previous time step using the order reduction model to obtain the reduced order state and the reduced order orthogonal basis matrix. The first calculation module is used to perform calculations based on the reduced-order state using the physical and data hybrid evolution model to obtain the estimated state at the current moment; The second calculation module is used to calculate the target estimated state based on the estimated state and the real-time acquired current observation data using the extended Kalman filter method. The inversion module is used to invert the thermo-mechanical coupling field state of the compressor hot-loading process based on the target estimated state and the reduced-order orthogonal basis matrix using a preset projection function, and obtain the thermo-mechanical coupling field state inversion result.

6. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the thermo-coupled field state inversion method for compressor hot-loading process as described in any one of claims 1-4.

7. An electronic device, characterized in that, It includes at least a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program in the memory, implements the steps of the thermo-coupled field state inversion method for compressor hot-loading process as described in any one of claims 1-4.

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