Method and system for predicting unsteady flow field of inlet and outlet port based on online calibration POD-galerkin model and storage medium

Abstract

The application discloses a kind of based on online calibration POD-Galerkin model's inlet and outlet port unsteady flow field prediction method, system and storage medium.Method is: obtaining the fluctuating flow field snapshot data under typical working condition of inlet and outlet port;Leading POD space mode and corresponding POD time coefficient are extracted by eigenvalue orthogonal decomposition;POD-Galerkin low-dimensional dynamic system containing constant term, linear term and quadratic nonlinear term is constructed based on leading POD space mode;Flow velocity sensor is arranged at the section of trash rack, and the mapping relationship between it and flow field grid is established;Predicted flow velocity is obtained by using low-dimensional dynamic system to reconstruct flow field;Constant term and linear term coefficient are corrected according to the flow velocity difference of measured and predicted flow velocity of flow velocity sensor;The future flow field is continued to reconstruct by using the low-dimensional dynamic system after correction.This application overcomes the defect that traditional POD-Galerkin model fixed coefficient is difficult to adapt to working condition change.

Description

Technical Field

[0001] This invention relates to the field of fluid dynamics reduced-order modeling and digital twin technology, specifically to a method, system, and storage medium for predicting unsteady flow fields at inlets and outlets based on an online calibration POD-Galerkin model. Background Technology

[0002] With the rapid development of pumped storage power stations, the hydraulic performance of the inlet and outlet has a significant impact on the station's operating efficiency, unit stability, and the safety of its hydraulic structures. The flow at the inlet and outlet, and in their trash rack areas, typically exhibits characteristics such as unsteady separation, localized high-speed jets, flow deviation, and complex vortex structures, which can lead to energy loss, increased velocity pulsations, trash rack vibration, and operational safety risks. Therefore, rapid prediction of the unsteady flow field at the inlet and outlet, and real-time mapping of the prediction results to a digital twin platform, is of great significance for operational monitoring, flow pattern analysis, and risk early warning.

[0003] Currently, methods for predicting and analyzing unsteady flow fields at inlets and outlets mainly include CFD numerical simulation (Computational Fluid Dynamics, a technique that uses numerical methods to solve fluid control equations to obtain flow field information), pure data-driven methods, conventional reduced-order model methods, and POD-Galerkin physical reduced-order model methods. CFD methods can obtain high-precision, high-dimensional flow field information, but they are computationally intensive and time-consuming, making it difficult to meet the needs of real-time prediction and online visualization in engineering projects. Pure data-driven methods can establish a mapping relationship between historical data and future flow fields through neural networks, but they typically rely on a large amount of high-quality training data and lack flow dynamic constraints, easily leading to problems such as insufficient physical consistency, weak generalization ability across operating conditions, and long-term accumulation of prediction errors. Conventional reduced-order models such as Intrinsic Orthogonal Decomposition (POD decomposition) and Dynamic Mode Decomposition (DMD decomposition) can extract the dominant flow structure and reduce computational complexity, but in online applications, it is still necessary to obtain or predict modal time coefficients. When only a small amount of sparse sensor data is available on-site, it is difficult to correct the deviation between the model and the actual operating state in a timely manner.

[0004] The POD-Galerkin method, based on POD modes, establishes ordinary differential equations with modal time coefficients through Galerkin projection. This transforms high-dimensional flow field prediction into solving low-dimensional dynamic systems, offering good physical interpretability and high computational efficiency. However, traditional POD-Galerkin models are typically built once based on offline CFD or experimental data, with their Galerkin ordinary differential equation coefficients remaining fixed during online operation. When actual operating conditions such as flow rate, water level, boundary conditions, inlet / outlet directions, or local flow patterns in the trash rack area differ from the offline modeling conditions, the fixed-coefficient POD-Galerkin model is prone to prediction drift, causing the reconstructed flow field to gradually deviate from the actual flow field. Especially at the trash rack cross-section, local velocity changes directly affect the stress and vibration risk of the trash rack, and existing POD-Galerkin methods lack a mechanism to utilize the velocity errors at sparse measurement points in this cross-section for online calibration of the Galerkin equivalent coefficients.

[0005] In summary, there is an urgent need for a method, system, and storage medium for predicting unsteady flow fields at inlets and outlets based on an online calibration POD-Galerkin model to address the problems existing in the current technology. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model, aiming to solve the problem that the fixed coefficients of the traditional POD-Galerkin model are difficult to adapt to changes in actual operating conditions. The specific technical solution is as follows: A method for predicting unsteady flow fields at inlet and outlet based on an online calibrated POD-Galerkin model includes: Obtain high-dimensional unsteady flow field snapshots of inlet and outlet under typical operating conditions, and obtain pulsating flow field snapshot data based on the high-dimensional unsteady flow field snapshots. Intrinsic orthogonal decomposition was performed on the snapshot data of the pulsating flow field to extract the dominant POD spatial mode and the corresponding POD time coefficient; Galerkin projection was performed using the dominant POD spatial mode as the test function to construct a low-dimensional POD-Galerkin dynamical system containing constant terms, linear terms, and quadratic nonlinear terms; Multiple flow velocity sensors are installed on the cross-section of the trash rack at the inlet and outlet, and a mapping relationship between each flow velocity sensor and the flow field grid is established. The POD-Galerkin low-dimensional dynamic system is used to advance the POD time coefficient and reconstruct the flow field. The predicted flow velocity at each velocity sensor location is obtained according to the mapping relationship. Calculate the residual at the measurement point based on the measured flow velocity collected by each flow velocity sensor and its corresponding predicted flow velocity; The constant term coefficients and linear term coefficients in the POD-Galerkin low-dimensional dynamical system are corrected based on the measurement point residuals. We continue to advance the POD time coefficient and reconstruct the future flow field using the modified POD-Galerkin low-dimensional dynamic system.

[0007] Preferably, a high-dimensional unsteady flow field snapshot of the inlet and outlet area of ​​the pumped storage power station under typical operating conditions is obtained through CFD numerical simulation, model test or historical operation data; the average flow field of the high-dimensional unsteady flow field snapshot is calculated, and the pulsed flow field snapshot data is obtained by subtracting the average flow field from the high-dimensional unsteady flow field snapshot.

[0008] Preferably, the snapshot data of the fluctuating flow field is subjected to intrinsic orthogonal decomposition, specifically: Singular value decomposition is performed on the snapshot data of the pulsating flow field to obtain the spatial mode matrix, the singular value diagonal matrix, and the time feature matrix. The cumulative energy proportion of each POD spatial mode is calculated based on the singular values ​​in the singular value diagonal matrix. The top few POD spatial modes whose cumulative energy proportion reaches a preset threshold are selected as the dominant POD spatial modes. The POD time coefficients corresponding to each dominant POD spatial mode are calculated using the singular value diagonal matrix and the time feature matrix.

[0009] Preferably, a POD-Galerkin low-dimensional dynamic system is constructed, specifically: A low-dimensional representation of the flow field is established based on the average flow field of the high-dimensional unsteady flow field snapshot, the dominant POD spatial mode, and the POD time coefficients corresponding to the dominant POD spatial mode. Substituting the low-dimensional representation of the flow field into the Navier-Stokes equations and using the dominant POD spatial mode as the test function for Galerkin projection, we obtain the POD-Galerkin low-dimensional dynamic system.

[0010] Preferably, the vector form of the POD-Galerkin low-dimensional dynamical system is: in, express The derivative of the POD time coefficient vector at time t; , Represents the vector of coefficients for the constant term; , Represents the coefficient matrix of the linear terms; , Represents a quadratic nonlinear term; express The POD time coefficient vector at time t; Represents the real number field; This indicates the order of the dominant POD spatial mode that is retained.

[0011] Preferably, a mapping relationship is established between each velocity sensor and the flow field grid, specifically: KD-tree nearest neighbor search is used to obtain the nearest neighbor grid node of the velocity sensor location in the flow field grid, and the velocity of the reconstructed flow field at the nearest neighbor grid node is used as the predicted velocity at the velocity sensor location.

[0012] Preferably, the coefficients of the constant term and the coefficients of the linear term in the POD-Galerkin low-dimensional dynamical system are corrected based on the residuals at the measurement points, specifically as follows: An optimization objective function is constructed within a time window. This objective function consists of a first part and a second part, where the first part is the sum of squared residuals between the predicted and measured flow velocities at each flow velocity sensor location, and the second part is the corrected coefficients. Compared with the coefficients before correction The L2 norm regularization term for the difference; With the objective function as the minimum, the coefficients of the corrected constant term are obtained by solving the problem. and the corrected linear term coefficients ;in, , , The coefficients of the constant term before correction. These are the coefficients of the linear term before correction.

[0013] Preferably, it also includes mapping the reconstructed future flow field onto a digital twin platform for dynamic visualization, specifically: In the digital twin platform, a set of sliced ​​mesh nodes is constructed based on the three-dimensional structural model of the inlet and outlet. The predicted flow field is mapped to the slice grid nodes to obtain the predicted velocity vector at each slice grid node; Select the physical quantity to be visualized and normalize the physical quantity values ​​of the sliced ​​mesh nodes; The normalized physical quantity values ​​are converted into RGB color values ​​using a color mapping function; The RGB color values ​​of each slice grid node are updated smoothly over time. The updated RGB color values ​​are assigned to the slice grid nodes in the digital twin platform.

[0014] The present invention also provides a system for predicting unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model, comprising a memory and a processor. The memory stores a computer program, and the processor executes the method for predicting unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model when running the computer program.

[0015] The present invention also provides a storage medium storing a computer program, which, when executed by a processor, performs the aforementioned method for predicting unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model.

[0016] The application of the technical solution of the present invention has the following beneficial effects: This invention extracts the dominant POD spatial modes through offline POD decomposition (i.e., intrinsic orthogonal decomposition) and establishes a low-dimensional ordinary differential dynamic system with POD time coefficients based on Galerkin projection. During online operation, only this low-dimensional system needs to be advanced to obtain the POD time coefficients for future moments. The global flow field is then rapidly reconstructed through the superposition of POD spatial modes, eliminating the need for repeatedly solving high-dimensional computational fluid dynamics control equations. Compared to traditional CFD methods, the online computational load is reduced from tens of thousands to millions of degrees of freedom to tens to hundreds of dimensions, meeting the time requirements for real-time monitoring and early warning in pumped storage power stations.

[0017] Traditional POD-Galerkin models, whose coefficients are determined once from offline data and remain unchanged during online operation, are prone to prediction drift when actual operating conditions (such as flow rate, water level, and inlet / outlet direction) differ from offline conditions. This invention utilizes a small number of velocity sensors deployed along the cross-section of the trash rack to collect data at measurement points in real time. The residual between the measured flow velocity and the predicted flow velocity reconstructed by the POD-Galerkin model is used as feedback to construct an optimization objective function within a time window. This function corrects the constant and linear terms in the low-dimensional dynamic system online while maintaining the quadratic nonlinear term unchanged. This mechanism allows the POD-Galerkin model to be progressively calibrated according to actual operating conditions, effectively suppressing prediction drift and significantly improving prediction accuracy and robustness across operating conditions.

[0018] This invention employs KD-tree nearest neighbor search to quickly establish the mapping relationship between the sensor and the grid nodes. The flow velocity at the nearest neighbor grid node is used as the predicted value to ensure that the measured and predicted flow velocities are compared at the same spatial location, providing a reliable basis for subsequent residual calculation and coefficient correction.

[0019] The objective function of this invention includes both the sum of squared residuals and a regularization term, which improves fitting accuracy while constraining the variation of coefficients, preventing the POD-Galerkin model from becoming unstable due to excessive correction caused by noisy data. An adaptive triggering mechanism (performing corrections every fixed number of steps or when the average error of the measurement points exceeds a threshold) balances the timeliness of corrections with the online computational burden, ensuring the system's real-time stable operation.

[0020] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0021] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the inlet and outlet unsteady flow field prediction method based on the online calibration POD-Galerkin model in Example 1; Figure 2 This is a simulation diagram of the flow velocity in the x direction at the inlet and outlet at a future time in the application case of Example 1; Figure 3 This is a simulation diagram of the flow velocity in the y-direction at the inlet and outlet in the future time in the application case of Example 1; Figure 4 This is a simulation diagram of the flow velocity in the z-direction at the inlet and outlet in the future time of the application case of Example 1. Detailed Implementation

[0022] To facilitate understanding of the present invention, a more complete description is provided below, along with preferred embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the present invention.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0024] Example 1: See Figure 1 This embodiment provides a method for predicting unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model, including the following steps: Offline phase: Obtain high-dimensional unsteady flow field snapshots of inlet and outlet under typical operating conditions, and obtain pulsating flow field snapshot data based on the high-dimensional unsteady flow field snapshots. Intrinsic orthogonal decomposition was performed on the snapshot data of the pulsating flow field to extract the dominant POD spatial mode and the corresponding POD time coefficient; Galerkin projection was performed using the dominant POD spatial mode as the test function to construct a low-dimensional POD-Galerkin dynamical system containing constant terms, linear terms, and quadratic nonlinear terms; Multiple flow velocity sensors are installed on the cross-section of the trash rack at the inlet and outlet, and a mapping relationship between each flow velocity sensor and the flow field grid is established. Online phase: The POD-Galerkin low-dimensional dynamic system is used to advance the POD time coefficient and reconstruct the flow field. The predicted flow velocity at each velocity sensor location is obtained according to the mapping relationship. Calculate the residual at the measurement point based on the measured flow velocity collected by each flow velocity sensor and its corresponding predicted flow velocity; The constant term coefficients and linear term coefficients in the POD-Galerkin low-dimensional dynamical system are corrected based on the measurement point residuals. We continue to advance the POD time coefficient and reconstruct the future flow field using the modified POD-Galerkin low-dimensional dynamic system.

[0025] The method for predicting unsteady flow fields at the inlet and outlet in this embodiment will be explained in detail below: In this embodiment, "inlet and outlet" refers to the channel structure used for water entry and exit in a pumped storage power station, including the inlet during pumping operation, the outlet during power generation operation, and a shared channel for both operation modes. A trash rack is installed at the front end of this inlet and outlet structure to intercept debris in the water.

[0026] In this embodiment, the POD spatial mode refers to the spatial feature structure extracted by Proper Orthogonal Decomposition (POD decomposition), reflecting the main structural information at different scales in the flow field; the POD time coefficient refers to the coefficient corresponding to each POD spatial mode changing over time, used to describe the dynamic evolution of the flow field; the Galerkin projection is a mathematical method that projects partial differential equations onto a finite-dimensional subspace (such as the space spanned by the POD spatial modes) to derive a low-dimensional ordinary differential equation system; the POD-Galerkin low-dimensional dynamic system is a low-dimensional ordinary differential equation system based on the POD spatial modes and the Galerkin projection, used to describe the evolution of the POD time coefficient over time, and is a reduced-order model for high-dimensional flow field prediction; the Galerkin coefficient correction refers to updating the coefficients or additional correction terms of the ordinary differential equations in the POD-Galerkin low-dimensional dynamic system based on the accumulated measurement point residuals over a period of time, so that the low-dimensional dynamic system gradually adapts to the actual operating conditions.

[0027] Preferably, the pulsating flow field snapshot data is obtained based on a high-dimensional unsteady flow field snapshot, specifically: For the inlet and outlet areas (including the trash rack area) of pumped storage power stations, high-dimensional unsteady flow field snapshots under typical operating conditions are obtained through CFD numerical simulation, model tests, or historical operating data. The average flow field of the high-dimensional unsteady flow field snapshots is calculated, and the pulsating flow field snapshot data is obtained by subtracting the average flow field from the high-dimensional unsteady flow field snapshots. The typical operating conditions include pumping conditions, power generation conditions, different flow rate conditions, different water level conditions, and conditions with switching inlet and outlet directions. CFD numerical simulation refers to computational fluid dynamics, a technique that uses numerical methods to solve fluid control equations to obtain flow field information.

[0028] Specifically, set the time In spatial location A snapshot of the high-dimensional unsteady flow field at the location is ,Will A snapshot matrix is ​​composed of snapshots of the high-dimensional unsteady flow field at each moment. , represented as: in, , , Represents the real number field. This represents the number of spatial degrees of freedom in a single snapshot of a high-dimensional unsteady flow field. This represents the number of snapshots of a high-dimensional unsteady flow field. Represents the spatial coordinates of the flow field. Indicates time In spatial location The flow field variables at that location.

[0029] If the velocity field is selected as the prediction target, then the flow field variables Represented as; in, express exist The velocity component in the direction, express exist The velocity component in the direction, express exist The velocity component in the direction, superscript This represents the transpose of a vector.

[0030] Therefore, spatial position is calculated. The average flow field at that location is: Subtract the average flow field from each snapshot to obtain the fluctuating flow field snapshot data: in, Indicates spatial location The average flow field at that location, Indicates spatial location The snapshot matrix of the fluctuating flow field after removing the mean flow field.

[0031] Preferably, the snapshot data of the fluctuating flow field is subjected to intrinsic orthogonal decomposition, specifically: snapshot data of fluctuating flow field (i.e., snapshot matrix of fluctuating flow field) Singular value decomposition is performed to obtain the spatial mode matrix, singular value diagonal matrix, and temporal feature matrix. The cumulative energy proportion of each POD spatial mode is calculated based on the singular values ​​in the singular value diagonal matrix. The top few POD spatial modes whose cumulative energy proportion reaches a preset threshold are selected as the dominant POD spatial modes. The POD time coefficients corresponding to each dominant POD spatial mode are calculated using the singular value diagonal matrix and the temporal feature matrix. Specifically, the snapshot matrix of the fluctuating flow field Singular value decomposition is represented as: in, Let be the spatial mode matrix, and let its column vectors be the POD spatial modes; It is a singular value diagonal matrix used to characterize the contribution of each POD spatial mode to the flow field energy; This is the time feature matrix; superscript This represents the transpose of a vector.

[0032] Furthermore, the top [energy percentage] is selected based on the cumulative energy percentage. The dominant mode order in the POD space, and the preserved mode order. satisfy: in, The preset cumulative energy threshold is (usually set to 0.99 or 0.999). Indicates the first A singular value, To preserve the modal order, .

[0033] Therefore, the truncated dominant POD spatial mode matrix Recorded as: in, Indicates the first POD spatial modes of order, This indicates the order of the dominant POD spatial mode that is retained.

[0034] Furthermore, using singular value diagonal matrices and time feature matrix This allows for the calculation of the POD time coefficients corresponding to each dominant POD spatial mode, and the POD time coefficient matrix... Represented as: in, A singular value diagonal matrix The former Before departure Submatrix ( (diagonal array) Time feature matrix The former Submatrix ( ), POD time coefficient matrix ( ), its first The row corresponds to the first The time coefficient sequence of the dominant POD spatial mode.

[0035] Preferably, a POD-Galerkin low-dimensional dynamic system is constructed, specifically: Based on the average flow field of the high-dimensional unsteady flow field snapshot, the dominant POD spatial mode, and the POD time coefficients corresponding to the dominant POD spatial mode, a low-dimensional representation of the flow field is established. The low-dimensional representation of the flow field is substituted into the Navier-Stokes equations, and the dominant POD spatial mode is used as the test function for Galerkin projection to obtain the ordinary differential equations of the POD time coefficients (i.e., the POD-Galerkin low-dimensional dynamic system).

[0036] Specifically, based on the previous For the first-order POD mode, the low-dimensional representation of the flow field at any time is: The matrix form is as follows: in, Indicates time In spatial location Reconstructing or predicting the flow field at the location; Indicates spatial location The average flow field at that location; Indicates the first The dominant POD spatial mode in spatial location The value at; Indicates the first The dominant POD spatial mode at time 1 Time coefficient; Indicates time Reconstructing or predicting the flow field vector; Indicates from the previous The modal matrix composed of the dominant POD spatial modes; This represents the POD time coefficient vector. ; This represents the column vector consisting of the average flow field at all spatially discrete points.

[0037] Furthermore, the POD-Galerkin low-dimensional dynamical system (i.e., the ordinary differential equation with POD time coefficients) is expressed as: in, , Indicates the first The coefficients of the constant term in the first-order modal equations; Indicates the first The dominant POD spatial mode of the first order The linear action coefficient of the dominant POD spatial mode; Indicates the first Rank and first The dominant POD spatial mode of the first order The second-order nonlinear coupling coefficient of the dominant POD spatial mode; Indicates the first The dominant POD spatial mode at time 1 POD time coefficient, Indicates the first The dominant POD spatial mode at time 1 The POD time coefficient.

[0038] Furthermore, the vector form of the POD-Galerkin low-dimensional dynamical system is as follows: in, express The derivative of the POD time coefficient vector at time t; , Represents the vector of coefficients for the constant term; , Represents the coefficient matrix of the linear terms; , Represents a quadratic nonlinear term; express The POD time coefficient vector at time t; Represents the real number field.

[0039] Furthermore, the second-order nonlinear term The Each component is represented as: in, Represents a quadratic nonlinear term The Each component.

[0040] Preferably, the mapping relationship between each velocity sensor and the flow field grid is established by: using KD-tree nearest neighbor search to obtain the nearest neighbor grid node of the velocity sensor location in the flow field grid, and using the velocity of the reconstructed flow field at the nearest neighbor grid node as the predicted velocity at the velocity sensor location.

[0041] KD-tree is a tree-shaped data structure used for nearest neighbor search in high-dimensional space. In this embodiment, it is used to quickly locate the nearest neighbor node of the flow velocity sensor in the flow field grid.

[0042] Specifically, multiple flow velocity sensors are installed on the cross-section of the trash racks at the inlet and outlet to collect data from sparse measuring points online. Let the number of flow velocity sensors be... , No. The spatial coordinates of the flow velocity sensors are , Simultaneously, the set of flow field mesh nodes containing the POD-Galerkin reconstructed flow field was determined. .

[0043] Since the location of the velocity sensor usually does not completely coincide with the flow field grid node, this embodiment uses a KD-tree data structure to search for the nearest flow field grid node in the flow field grid node set for each velocity sensor, and uses the POD-Galerkin reconstructed velocity at the nearest neighbor flow field grid node as the predicted velocity at the location of the velocity sensor.

[0044] Furthermore, the distance from the first The nearest flow field grid node to the flow velocity sensor is represented as follows: in, Indicates the relationship with the first The number of the nearest flow field grid node to the flow velocity sensor; Represents the 2-norm of a vector; Indicates the first The location of each flow field grid node; This represents the total number of nodes in the flow field grid.

[0045] Furthermore, if the first If a flow velocity sensor has two or more nearest neighbor flow field grid nodes, then the average reconstructed flow velocity of several nearest neighbor flow field grid nodes is taken as the flow velocity sensor value. Predicted flow velocity at the location.

[0046] Furthermore, if the flow rate sensor measures the velocity component of a target (e.g., If the direction velocity is given, the predicted flow velocity at the location of the flow velocity sensor is directly taken from the velocity component reconstructed from the nearest neighbor flow field grid node. in, express Time of the first Predicted flow velocity at each flow sensor location; express At time POD-Galerkin reconstructed flow field at nearest neighbor flow field grid node The target velocity component at that location, Represents the nearest neighbor flow field grid node Spatial location.

[0047] If the flow velocity sensor measures the velocity amplitude, then the predicted flow velocity is taken as the magnitude of the velocity vector at the nearest neighbor flow field grid node: in, express Time of the first Predicted flow velocity at each flow sensor location; express At time POD-Galerkin reconstructed flow field at nearest neighbor flow field grid node The predicted velocity vector at that location; Represents the nearest neighbor flow field grid node Spatial location; Represents the predicted velocity vector The length of the module.

[0048] Thus, a mapping relationship was established from the reconstructed flow field to the flow velocity predicted by the flow velocity sensor location, providing a basis for subsequent calculation of the error between the measured flow velocity and the predicted flow velocity.

[0049] Preferably, the POD-Galerkin low-dimensional dynamic system is used to advance the POD time coefficient and reconstruct the flow field. The predicted flow velocity at each velocity sensor location is obtained according to the mapping relationship. Specifically: Given the current POD time coefficient Furthermore, given the known POD-Galerkin coefficients, time progression is performed on the POD-Galerkin low-dimensional dynamical system to obtain the next time step. POD time coefficient, Indicates the time step.

[0050] If explicit time progression is used, then: in, This represents the POD time coefficient at the current moment. This represents the POD time coefficient for the predicted next moment.

[0051] Then, the global flow field at the next moment is reconstructed using the mean flow field and the dominant POD spatial mode: Or it can be written as: in, This represents the flow field at the next moment predicted and reconstructed by POD-Galerkin; Indicates the first The dominant POD spatial mode in the next moment Time coefficient; Indicates the first The dominant POD spatial mode in spatial location The value at; Indicates spatial location From the front The modal matrix composed of the dominant POD spatial modes; Indicates the next moment The POD time coefficient vector.

[0052] Based on the established mapping relationship, the predicted flow velocity at each velocity sensor location is extracted from the reconstructed flow field. For the first... A flow velocity sensor, whose predicted flow velocity is expressed as: .

[0053] Therefore, the vector composition of the predicted flow velocities from all flow velocity sensors can be represented as: in, express The predicted velocity vectors of the POD-Galerkin reconstructed flow field at all velocity sensor locations on the cross-section of the trash rack; Indicates the number of flow rate sensors; superscript This represents the transpose of a vector.

[0054] Preferably, the residual at the measurement point is calculated based on the measured flow velocity collected by each flow velocity sensor and its corresponding predicted flow velocity. Specifically: set up The measured flow velocity vectors of each flow velocity sensor at each time point are: in, for The measured flow velocity vector at all flow velocity sensor locations across the cross-section of the trash rack at all times. Indicates the first A flow rate sensor in The measured flow rate at any given time.

[0055] The measured flow velocity data were normalized to obtain preprocessed measurement point data: in, for The time-normalized measured flow velocity vectors of all flow velocity sensors express Time of the first The measured flow velocity is normalized by a flow velocity sensor.

[0056] The normalization process is represented as follows: in, express Time of the first The measured flow velocity of each flow sensor express Time of the first Normalized measured flow velocity from a flow velocity sensor , This embodiment prevents extremely small positive numbers with a denominator of zero. Take as , This represents the minimum flow velocity used for normalization. This represents the maximum flow rate used for normalization.

[0057] After normalizing the predicted flow velocities from all flow velocity sensors, the preprocessed predicted flow velocity component vector is obtained. , The residual between the measured flow velocity and the predicted flow velocity at any given time can be expressed as: in, express The residual vector of the measurement point at time t. Indicates the first The measuring point (i.e. the th measuring point) The difference between the measured flow velocity and the predicted flow velocity at each flow velocity sensor. Residual. The deviation between the current POD-Galerkin model prediction results and the actual monitored flow conditions was quantified, providing a target basis for subsequent optimization of the constant term coefficients and linear term coefficients in the POD-Galerkin low-dimensional dynamic system. Preferably, in this embodiment, the normalization method for the flow velocity predicted by the velocity sensor is the same as the normalization method for the measured flow velocity.

[0058] Furthermore, The average error index of the measuring points at time t is expressed as: in, express The average error of the measurement points at any given time.

[0059] Preferably, the coefficients of the constant term and the coefficients of the linear term in the POD-Galerkin low-dimensional dynamical system are corrected based on the residuals at the measurement points, specifically as follows: Within the time window, an optimization objective function is constructed. The optimization objective function consists of the sum of the first part and the second part. The first part is the sum of squared residuals between the predicted flow velocity and the measured flow velocity at each flow velocity sensor location. The second part is the L2 regularization term of the difference between the corrected coefficient and the original coefficient. With the goal of minimizing the objective function, the corrected coefficients of the constant term and the linear term are obtained by solving the problem; at the same time, the quadratic nonlinear term is kept unchanged.

[0060] Specifically, to avoid directly correcting all the quadratic nonlinear coefficients This leads to an excessive number of parameters, difficulty in identification, and online model instability. Therefore, this embodiment preferably corrects the coefficients of the constant term and the linear term. The following will explain in detail how to solve for the corrected constant term coefficients. and linear term coefficients .

[0061] The modified POD-Galerkin low-dimensional dynamical system is represented as follows: in, This represents the derivative of the POD time coefficient vector with respect to time.

[0062] In the time window Built-in optimization objective function: in, For parameters to be optimized, , The coefficients are the ones before correction (initially offline coefficients, and the subsequent coefficients are the ones after the last correction). , The coefficients of the constant term before correction. The coefficients of the linear term before correction. The regularization coefficient is . The length of the time window used for coefficient correction. Indicates the first A flow rate sensor in Normalized measured flow velocity at time point Indicates the use of parameters The POD-Galerkin model reconstruction yielded the first Normalized predicted flow velocity at each flow sensor location Represents the L2 norm, Indicates parameters used for online correction. The least squares optimization objective function.

[0063] Time window The error vector is composed of the residuals between the measured and predicted flow velocities of each internal flow velocity sensor at different times: in, , Indicates the first A flow sensor at time The residual between the measured flow velocity and the predicted flow velocity.

[0064] The optimization problem can then be expressed as: Solve using the iterative least squares method: As initial values, these are substituted into the POD-Galerkin model to calculate the predicted flow velocity at each time step, thus obtaining the residual vector. Then update the parameters and repeat until the residual decreases to less than the preset tolerance value or the maximum number of iterations is reached, to obtain the final result. In each iteration, the Jacobian matrix can be obtained through numerical differencing or automatic differentiation. This represents the initial value of the parameter iteration, taken as the coefficient vector before correction, i.e. ; Indicates the first The parameter vector obtained after the nth iteration. The parameter is The error vector at that time.

[0065] Furthermore, each iteration can employ standard least squares solution steps such as Gauss-Newton or gradient descent to ultimately obtain the corrected coefficients of the constant term. and linear term coefficients To ensure the real-time performance of online calculations, it is not necessary to make corrections at every time step; corrections can be made every fixed number of steps. Update once, or when the average error of the measuring points is... Exceeding the preset threshold Time-triggered correction; among which, Indicates the coefficient update interval. This indicates a preset error threshold. Of course, it is possible that in some embodiments, the parameters of the POD-Galerkin low-dimensional dynamical system are updated at each time step.

[0066] Of course, in some embodiments it is also possible to make , , Thus, the constant term coefficient correction can be solved using the iterative least squares method. Correction amount for linear term coefficients Thus, the updated and .

[0067] Preferably, the modified POD-Galerkin low-dimensional dynamic system is used to further advance the POD time coefficient and reconstruct the future flow field, specifically: The corrected constant term coefficient and linear term coefficients Substituting the POD-Galerkin low-dimensional power system into the above, we obtain a new low-dimensional power system adapted to actual working conditions: Based on this revised model, we will continue to advance the POD time coefficient for future moments: Then reconstruct the future flow field: in, Indicates the time step.

[0068] This cycle repeats continuously, allowing the system to predict unsteady flow fields at the inlet, outlet, and trash rack areas. In each prediction round, newly arrived measured sensor data is used for possible coefficient corrections, enabling the model to adapt to changes in actual operating conditions and effectively suppress prediction drift.

[0069] Preferably, this embodiment also includes mapping the reconstructed future flow field onto a digital twin platform for dynamic visualization: In the digital twin platform, a set of sliced ​​mesh nodes is constructed based on the three-dimensional structural model of the inlet and outlet. The predicted flow field is mapped to the slice grid nodes to obtain the predicted velocity vector at each slice grid node; Select the physical quantity to be visualized and normalize the physical quantity values ​​of the sliced ​​mesh nodes; The normalized physical quantity values ​​are converted into RGB color values ​​using a color mapping function; The RGB color values ​​of each slice grid node are updated smoothly over time. The updated RGB color values ​​are assigned to the slice grid nodes in the digital twin platform.

[0070] Specifically, in the digital twin platform, a set of sliced ​​mesh nodes is constructed based on the three-dimensional structural model of the inlet and outlet, represented as: in, This represents the set of sliced ​​grid nodes in a digital twin platform. Indicates the first The position of each slice grid node; This indicates the total number of nodes in the slice grid.

[0071] Mapping the predicted flow field to the target mesh slice nodes is represented as: in, Represents slice mesh nodes exist The predicted velocity vector at time t, express Time slice mesh node exist Predicted velocity components in direction, express Time slice mesh node exist Predicted velocity components in the direction, express Time slice mesh node exist Predicted velocity component in direction.

[0072] Select a target physical quantity for visualization, for example Directional velocity, Directional velocity, Directional velocity, velocity amplitude, or vorticity (which can be calculated from the predicted velocity field). Taking directional velocity as an example, for slice mesh nodes The normalized representation of directional velocity is as follows: in, Represents the normalized i-th Each slice grid node in velocity in the direction; Indicates the current set of sliced ​​mesh nodes Minimum value of directional prediction velocity; Indicates the current set of sliced ​​mesh nodes The maximum value of the directional prediction velocity; This embodiment prevents extremely small positive numbers with a denominator of zero. Take as .

[0073] Define a color mapping function: in, , Indicates the first Each slice grid node at time... RGB color values, Indicates the first Each slice grid node at time... The red channel value, Indicates the first Each slice grid node at time... The green channel value, Indicates the first Each slice grid node at time... The blue channel value, This represents the color mapping function.

[0074] To improve the stability of dynamic displays, a time-smooth update mechanism is introduced: in, , Represents the smoothing coefficient. Indicates the time step.

[0075] Finally, the color values ​​of all slice grid nodes are updated to the slice grid nodes in the digital twin platform: in, Indicates time The set of node colors for each slice grid node in the digital twin platform.

[0076] This embodiment constructs a low-dimensional POD-Galerkin dynamic system offline, transforming high-dimensional flow field prediction into solving low-dimensional ordinary differential equations, significantly reducing online computation and meeting the real-time monitoring requirements of pumped storage power stations. Using measured data from sparse velocity sensors on the trash rack cross-section, the coefficients of constant and linear terms are corrected online, enabling the low-dimensional model to adaptively track changes in actual operating conditions, effectively suppressing prediction drift and significantly improving prediction accuracy across operating conditions. Simultaneously, KD-tree spatial mapping ensures spatial consistency between measuring points and the flow field grid, regularized least squares optimization ensures the stability of the correction process, and an adaptive triggering strategy balances real-time performance and computational burden. Finally, the corrected predicted flow field is mapped in real-time to a digital twin platform, achieving dynamic visualization of complex unsteady flow fields. This provides an efficient, accurate, and intuitive technical means for monitoring the operation of inlets / outlets and trash racks, flow regime analysis, and risk warning.

[0077] Application examples: This embodiment takes a pumped storage power station in Nanning, Guangxi as an example, focusing on the typical two-dimensional slice flow field at the inlet and outlet. The input data includes the coordinates and connection relationships of the slice grid nodes, the snapshot matrix of the instantaneous velocity field of the two-dimensional slice at multiple times (i.e., the reconstructed flow field), and the snapshot sampling time step. The coordinates of each flow velocity sensor on the cross-section of the trash rack and their measured flow velocity data.

[0078] Selected in this case , , The flow velocity in three directions is visualized. For example... Figures 2-4 As shown in the figure, they are respectively displayed , , The simulation results show the prediction of complex separation flow in three directions in the next second. The results demonstrate that the corrected POD-Galerkin model can effectively predict and reconstruct the flow. , , Sliced ​​flow field in three directions. For example... Figure 2 As shown, influenced by the diffusion angle at the top of the diffuser section at the inlet and outlet and the adverse pressure gradient, the flow undergoes significant separation during diffusion. The mainstream gradually shifts towards the lower part of the channel, while a low-velocity recirculation zone forms at the top. This flow characteristic is consistent with the basic physical laws of separated flow in the diffuser section. Meanwhile, as... Figure 3 and Figure 4 As shown, direction and The alternating distribution of high and low velocity stripes in the directional velocity field reflects the transverse and vertical turbulent fluctuation structure within the flow field. These results demonstrate that the corrected POD-Galerkin model can reconstruct the main spatial distribution characteristics of the unsteady fluctuating flow field effectively.

[0079] The method in this embodiment enables dynamic cloud map display, slice display, multi-view interactive analysis, and key section flow pattern change display of unsteady flow fields near the inlet, outlet, and trash rack, thereby improving the system's real-time performance and engineering application value.

[0080] Example 2: This embodiment provides a prediction system for unsteady flow fields at inlets and outlets based on an online calibrated POD-Galerkin model, including a memory and a processor. The memory stores a computer program, and the processor executes the prediction method in Embodiment 1 when running the computer program.

[0081] Example 3: This embodiment provides a storage medium storing a computer program, which is executed by a processor to perform the prediction method in Embodiment 1.

[0082] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting unsteady flow fields at inlet and outlet based on an online calibrated POD-Galerkin model, characterized in that, include: Obtain high-dimensional unsteady flow field snapshots of inlet and outlet under typical operating conditions, and obtain pulsating flow field snapshot data based on the high-dimensional unsteady flow field snapshots. Intrinsic orthogonal decomposition was performed on the snapshot data of the pulsating flow field to extract the dominant POD spatial mode and the corresponding POD time coefficient; Galerkin projection was performed using the dominant POD spatial mode as the test function to construct a low-dimensional POD-Galerkin dynamical system containing constant terms, linear terms, and quadratic nonlinear terms; Multiple flow velocity sensors are installed on the cross-section of the trash rack at the inlet and outlet, and a mapping relationship between each flow velocity sensor and the flow field grid is established. The POD-Galerkin low-dimensional dynamic system is used to advance the POD time coefficient and reconstruct the flow field. The predicted flow velocity at each velocity sensor location is obtained according to the mapping relationship. Calculate the residual at the measurement point based on the measured flow velocity collected by each flow velocity sensor and its corresponding predicted flow velocity; The constant term coefficients and linear term coefficients in the POD-Galerkin low-dimensional dynamical system are corrected based on the measurement point residuals. We continue to advance the POD time coefficient and reconstruct the future flow field using the modified POD-Galerkin low-dimensional dynamic system.

2. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, High-dimensional unsteady flow field snapshots of the inlet and outlet areas of pumped storage power stations under typical operating conditions are obtained through CFD numerical simulation, model tests, or historical operating data. The average flow field of the high-dimensional unsteady flow field snapshots is calculated, and the pulsed flow field snapshot data is obtained by subtracting the average flow field from the high-dimensional unsteady flow field snapshots.

3. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, The intrinsic orthogonal decomposition of the snapshot data of the fluctuating flow field is performed as follows: Singular value decomposition is performed on the snapshot data of the pulsating flow field to obtain the spatial mode matrix, the singular value diagonal matrix, and the time feature matrix. The cumulative energy proportion of each POD spatial mode is calculated based on the singular values ​​in the singular value diagonal matrix. The top few POD spatial modes whose cumulative energy proportion reaches a preset threshold are selected as the dominant POD spatial modes. The POD time coefficients corresponding to each dominant POD spatial mode are calculated using the singular value diagonal matrix and the time feature matrix.

4. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, The construction of the POD-Galerkin low-dimensional dynamical system specifically involves: A low-dimensional representation of the flow field is established based on the average flow field of the high-dimensional unsteady flow field snapshot, the dominant POD spatial mode, and the POD time coefficients corresponding to the dominant POD spatial mode. Substituting the low-dimensional representation of the flow field into the Navier-Stokes equations and using the dominant POD spatial mode as the test function for Galerkin projection, we obtain the POD-Galerkin low-dimensional dynamic system.

5. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 4, characterized in that, The vector form of the POD-Galerkin low-dimensional dynamical system is as follows: in, express The derivative of the POD time coefficient vector at time t; , Represents the vector of coefficients for the constant term; , Represents the coefficient matrix of the linear terms; , Represents a quadratic nonlinear term; express The POD time coefficient vector at time step; Represents the real number field; This indicates the order of the dominant POD spatial mode that is retained.

6. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, Establish the mapping relationship between each velocity sensor and the flow field grid, specifically: KD-tree nearest neighbor search is used to obtain the nearest neighbor grid node of the velocity sensor location in the flow field grid, and the velocity of the reconstructed flow field at the nearest neighbor grid node is used as the predicted velocity at the velocity sensor location.

7. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, The constant term coefficients and linear term coefficients in the POD-Galerkin low-dimensional dynamical system are corrected based on the residuals at the measurement points, specifically as follows: An optimization objective function is constructed within a time window. This objective function consists of a first part and a second part, where the first part is the sum of squared residuals between the predicted and measured flow velocities at each flow velocity sensor location, and the second part is the corrected coefficients. Compared with the coefficients before correction The L2 norm regularization term for the difference; With the objective function as the minimum, the coefficients of the corrected constant term are obtained by solving the problem. and the corrected linear term coefficients ;in, , , The coefficients of the constant term before correction. These are the coefficients of the linear term before correction.

8. The method for predicting unsteady flow fields at inlets and outlets based on the online calibration POD-Galerkin model according to claim 1, characterized in that, This also includes mapping the reconstructed future flow field onto a digital twin platform for dynamic visualization, specifically: In the digital twin platform, a set of sliced ​​mesh nodes is constructed based on the three-dimensional structural model of the inlet and outlet. The predicted flow field is mapped to the slice grid nodes to obtain the predicted velocity vector at each slice grid node; Select the physical quantity to be visualized and normalize the physical quantity values ​​of the sliced ​​mesh nodes; The normalized physical quantity values ​​are converted into RGB color values ​​using a color mapping function; The RGB color values ​​of each slice grid node are updated smoothly over time. The updated RGB color values ​​are assigned to the slice grid nodes in the digital twin platform.

9. A system for predicting unsteady flow fields at inlet and outlet based on an online calibrated POD-Galerkin model, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the inlet and outlet unsteady flow field prediction method based on the online calibration POD-Galerkin model as described in any one of claims 1-8 when running the computer program.

10. A storage medium, characterized in that, The storage medium contains a computer program that, when executed by a processor, performs the inlet and outlet unsteady flow field prediction method based on the online calibration POD-Galerkin model as described in any one of claims 1-8.

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