Water turbine operation state monitoring method based on digital twinning

Abstract

The invention discloses a water turbine operation state monitoring method based on digital twinning, which comprises the following steps: collecting vibration and pressure signals of limited measuring points of a water turbine in real time to form observation data; establishing a physical constraint Fourier operator network based on the observation data, and obtaining an operation state prediction result; performing data assimilation processing on a prediction result by using the observation data as a constraint condition through an iteration set Kalman smoother; the Fourier operator network is corrected through feedback of an optimization estimation result; and reconstructing vibration and pressure states of unmeasurable positions of the water turbine, realizing state field reconstruction, and judging abnormal positions and types. Accurate monitoring and real-time abnormity early warning of the running state of the water turbine can be achieved, and the monitoring accuracy and stability are improved.

Description

Technical Field

[0001] This invention relates to the field of hydropower technology, and in particular to a method for monitoring the operating status of hydro turbines based on digital twins. Background Technology

[0002] Hydropower turbine operation status monitoring technology is a crucial foundation for ensuring the long-term safe and efficient operation of hydropower units. Currently, turbine monitoring methods mainly include two technical approaches: direct sensor measurement and mathematical model simulation prediction. Direct sensor measurement involves deploying multiple sensors at key locations on the equipment to acquire real-time data on operating parameters such as vibration and pressure. The measured data is then analyzed to determine the unit's operating status and issue early warnings. However, limitations in installation space and economic costs make it difficult to deploy a large number of sensors in all critical areas of the turbine, resulting in insufficient monitoring coverage and constrained monitoring accuracy.

[0003] Mathematical model simulation prediction methods utilize fluid dynamics theory and finite element analysis to establish simulation models of turbine operation, and then solve these models to predict and analyze the operating conditions. While this method alleviates the problem of insufficient sensor quantity to some extent, such models are prone to significant prediction errors when the actual operating conditions of the turbine deviate from the design conditions. Furthermore, due to frequent changes in operating conditions, traditional monitoring methods with fixed threshold settings struggle to adaptively adjust to changes in operating conditions, often failing to identify early faults or abnormal signs in a timely and accurate manner.

[0004] In recent years, methods for monitoring the operational status of hydroelectric turbines using digital twin technology have emerged. Digital twin technology constructs a high-precision digital model corresponding to the actual hydroelectric turbine in virtual space, and synchronizes operational data in real time to achieve efficient monitoring of equipment operating status. However, existing digital twin technologies generally lack effective real-time data assimilation methods, making it difficult to accurately integrate physical laws and real-time monitoring data, resulting in significant discrepancies between the accuracy of the prediction model and the actual state.

[0005] Therefore, how to provide a method for monitoring the operating status of hydro turbines based on digital twins is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose a method for monitoring the operating status of a hydro turbine based on digital twins. Addressing the problem that existing technologies cannot adaptively adjust monitoring thresholds when the turbine deviates from its operating conditions, leading to unreliable early fault identification, this invention proposes a data assimilation processing method based on the deep fusion of a physically constrained Fourier operator network and an iterative ensemble Kalman smoother. This method achieves accurate reconstruction of the turbine's state field under all operating conditions and provides early warning of anomalies. This invention offers the advantages of high monitoring accuracy, strong adaptability, and timely and accurate anomaly warning.

[0007] The method for monitoring the operating status of a hydro turbine based on digital twins according to embodiments of the present invention includes: Real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data; The raw monitoring data is denoised and transformed to form observation data; A physical constraint Fourier operator network for the operating state of a water turbine is established based on observation data, and physical constraint training is performed to obtain the operating state prediction results that satisfy the physical laws of water turbine operation. Using the observed data as constraints, an iterative ensemble Kalman smoother is used to assimilate the predicted operating state results, thereby obtaining the optimized estimation results of the turbine's operating state. The optimized estimation results of the running state are fed back to the physical constraint Fourier operator network as new initial conditions to correct the running state prediction results and obtain the assimilated and corrected running state prediction results. Based on the assimilation-corrected operational state prediction results, virtual observation values ​​of vibration and pressure states at unmeasurable locations of the turbine are determined, and the reconstructed state field of the turbine under all operating conditions is obtained. Based on the reconstruction results of the turbine's full operating condition state field, determine whether the turbine's operating state is abnormal and output the location and type of the abnormal state.

[0008] Optionally, the real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data specifically involves: In the turbine runner and volute area, several candidate measuring points are arranged according to the equipment operating conditions, and vibration and pressure signals are collected under typical operating conditions and multiple deviated operating conditions to form a multi-condition characteristic data matrix of the candidate measuring points. Based on the multi-condition feature data matrix, the covariance eigenvalues ​​of each candidate measuring point are calculated and sorted to obtain the preliminary assessment results of the sensitivity of the candidate measuring points to changes in operating status. Measuring points that exceed the preset sensitivity screening threshold are selected to form a preliminary set of measuring points. The mutual information redundancy of vibration and pressure signals between each measuring point in the initial set of measuring points and the other measuring points is calculated in turn to form an information redundancy matrix between measuring points. Set an information redundancy limit, determine the measurement point pair with the largest information redundancy between measurement points based on the information redundancy matrix, and remove measurement points from the measurement point pair whose preliminary sensitivity assessment results are lower than the preset sensitivity screening threshold, and update the initial set of measurement points. Repeat the calculation of information redundancy, identification and elimination of redundant measurement points until the information redundancy of all measurement points in the initial set of measurement points is lower than the information redundancy limit, and obtain an optimized set of finite measurement points. Vibration sensors and pressure sensors are installed at the optimized set of limited measuring points to collect vibration and pressure signals from the limited measuring points during turbine operation, thereby obtaining raw monitoring data.

[0009] Optionally, the denoising and transformation processing of the original monitoring data to form observation data specifically includes: The vibration and pressure signals in the original monitoring data are extracted by sliding windows to obtain continuous time-series data segments for each measuring point. The wavelet threshold filtering method is used to denoise continuous time series data segments to obtain denoised time series data segments. Perform a Fourier transform on the denoised time-series data segment to obtain the corresponding spectral data; Frequency bands are divided based on the spectrum data, and the energy distribution characteristic parameters within each frequency band are calculated to obtain the frequency band energy distribution data for each measurement point. The spectral entropy value of each measuring point is calculated based on the frequency band energy distribution data, and the frequency band energy distribution data and spectral entropy value are combined into observation data.

[0010] Optionally, the step of establishing a physical constraint Fourier operator network for the turbine's operating state based on observation data and training it with physical constraints to obtain an operating state prediction result that satisfies the physical laws of turbine operation is specifically as follows: Based on the observation data, the initial network structure of the physically constrained Fourier operator network is established, and the frequency band energy distribution data and spectral entropy value in the observation data are used as the input variables of the network input layer, respectively. In the hidden layer of the network, the input variables are subjected to Fourier transform to map the input variables from the original observation space to the Fourier spectrum space, thereby obtaining intermediate features in the spectrum domain. The continuity equation and the law of conservation of momentum are introduced as physical constraints in the hidden layer of the network. Based on the basic laws of fluid dynamics in the operation of the water turbine, a loss function is constructed. The loss function is backpropagated to calculate and the network weight coefficients are updated so that the prediction results output by the network conform to the physical constraints of the turbine operation. Set a stopping criterion for network training iterations: stop the iterative training of the network when the change in the loss function is less than a preset threshold in a number of consecutive iterations. After completing iterative training, the spectral domain prediction results in the output layer of the physical constraint Fourier operator network are subjected to inverse Fourier transform to obtain the running state prediction results.

[0011] Optionally, the step of using observed data as constraints and employing an iterative ensemble Kalman smoother to assimilate the predicted operating state results to obtain optimized estimation results of the turbine's operating state specifically involves: The initial state set of the ensemble Kalman smoother is generated using the prediction results of the operating state. Each member of the initial state set is represented as a state vector of the turbine's operating state. The observation vector is determined based on the frequency band energy distribution data and spectral entropy value in the observation data, and a data assimilation observation operator based on the state vector and the observation vector is constructed using a Kalman smoother. The predicted values ​​of state set members in the observation space are calculated by using the data assimilation observation operator, and the difference between the predicted values ​​and the actual observation vectors is calculated to obtain the observation space deviation vector of the state set members. Calculate the covariance matrix and Kalman gain matrix of the state set members based on the observation space bias vector of the state set members; The state vectors of the members of the state set are updated using the Kalman gain matrix to obtain the updated state set; The updated set of states is used to perform data assimilation processing of the set of Kalman smoothers again, and the process is iterated until the change in the state vector within the set of states is lower than a preset threshold in a number of consecutive iterations. The arithmetic mean of the state vectors in the iteratively stabilized state set is used to obtain the optimized estimation result of the turbine's operating state.

[0012] Optionally, feeding back the operational state optimization estimation result to the physically constrained Fourier operator network as a new initial condition to correct the operational state prediction result and obtain the assimilated and corrected operational state prediction result specifically involves: The vibration and pressure signals in the operational state optimization estimation results are converted into input vectors of the corresponding physical constraint Fourier operator network input layer to form a corrected input data matrix; Using the corrected input data matrix as the initial input variable of the physically constrained Fourier operator network, the Fourier transform operation of the hidden layer of the network is re-executed to obtain the corrected intermediate features in the spectral domain. Based on the corrected intermediate features in the spectral domain, the loss function of the physically constrained Fourier operator network is recalculated in conjunction with the continuity equation of the turbine operation process and the law of conservation of momentum. Backpropagation is recalculated based on the updated loss function, and the connection weight coefficients of the physical constraint Fourier operator network are updated accordingly. Repeat the forward and backward propagation calculations of the network until the change in the network loss function is less than a preset threshold for several consecutive iterations. After the network iterative stabilization, the spectral domain correction prediction results in the output layer nodes of the physical constraint Fourier operator network are extracted, and an inverse Fourier transform is performed to obtain the assimilated and corrected running state prediction results.

[0013] Optionally, the virtual observations of vibration and pressure states at unmeasurable locations of the turbine, determined based on the assimilated and corrected operating state prediction results, to obtain the reconstructed state field results of the turbine under full operating conditions, specifically include: Based on the spatial locations of the limited measuring points already arranged in the turbine runner and spiral casing, a spatial grid covering the turbine's operating area is established. The vibration and pressure signal values ​​at the measured locations in the assimilated and corrected operational state prediction results are used as state reference values ​​for known locations in the spatial grid. Using the continuity equation and the law of conservation of momentum as physical constraints, the spatial interpolation weighting coefficients between grid nodes in the spatial grid are calculated. Based on the spatial interpolation weighting coefficients and the state reference values ​​of known locations in the spatial grid, the vibration and pressure signals of the grid nodes corresponding to the unmeasurable locations of the turbine are calculated. The vibration and pressure signals obtained from the grid nodes at the unmeasurable locations of the water turbine are subjected to inverse Fourier transform to form virtual observations of the vibration and pressure states at the corresponding unmeasurable locations. By combining the vibration and pressure signals from all measured locations with the calculated virtual observations from unmeasurable locations, a complete reconstruction of the turbine's state field under all operating conditions is formed.

[0014] Optionally, the step of determining whether the turbine's operating state is abnormal and outputting the location and type of the abnormality based on the turbine's full-condition state field reconstruction results specifically involves: Based on the reconstruction results of the turbine's full-condition state field, the time-domain amplitude and spectral energy values ​​of the vibration and pressure signals at all grid nodes were calculated. Determine the normal operating reference thresholds for the amplitude and spectral energy of vibration and pressure signals at each grid node under typical working conditions; Calculate the deviation of the amplitude and spectral energy of the vibration and pressure signals at each grid node from the normal operating reference threshold, and obtain the state deviation values ​​of all grid nodes; Set a state deviation threshold for determining abnormal states, compare the state deviation value of each grid node with the state deviation threshold, and determine the grid node whose state deviation value exceeds the state deviation threshold as an abnormal state node. The location distribution of all abnormal state nodes within the spatial grid is statistically analyzed, and the frequency range of deviations in the vibration and pressure signals of the abnormal state nodes is determined. Based on the location distribution of abnormal state nodes and the frequency range of deviations, determine the abnormal type and specific location of the abnormal state nodes, and output the data information of abnormal type and corresponding location; Based on the identified anomaly type and specific location, an early warning message for abnormal turbine operation status is generated and output in real time.

[0015] (1) This invention achieves accurate prediction and anomaly identification of turbine operating status through a data assimilation method based on the deep fusion of physical constraint Fourier operator network and iterative set Kalman smoother, effectively improving the monitoring accuracy and the accuracy of anomaly warning, and improving the adaptability and reliability of the monitoring system to deviation from the operating condition.

[0016] (2) This invention realizes the virtual observation of vibration and pressure signals at unmeasurable locations of the turbine through the arrangement of limited measuring points and the reconstruction technology of the full working condition field. It effectively expands the monitoring coverage, significantly improves the spatial accuracy of condition monitoring, and shows better adaptability and monitoring effect in the complex working conditions of the turbine.

[0017] (3) In the monitoring of turbine deviation from operating conditions, this invention effectively solves the problem of unreliable early anomaly identification caused by insufficient adaptive monitoring threshold in the prior art by adopting the optimization estimation result feedback correction network prediction mechanism, breaks through the bottleneck of limited model prediction accuracy in the prior art, and achieves a significant improvement in monitoring accuracy and reliability, effectively improving the technical level in the field of turbine operation monitoring. Attached Figure Description

[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is an overall flowchart of the water turbine operation status monitoring method based on digital twin proposed in this invention; Figure 2 This is a diagram of the physical constraint Fourier operator network structure of the water turbine operation status monitoring method based on digital twin proposed in this invention. Figure 3 This is a flowchart of the iterative set Kalman smoother data assimilation process for the water turbine operation status monitoring method based on digital twins proposed in this invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0020] refer to Figures 1-3 A method for monitoring the operating status of hydro turbines based on digital twins includes: Real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data; The raw monitoring data is denoised and transformed to form observation data; A physical constraint Fourier operator network for the operating state of a water turbine is established based on observation data, and physical constraint training is performed to obtain the operating state prediction results that satisfy the physical laws of water turbine operation. Using the observed data as constraints, an iterative ensemble Kalman smoother is used to assimilate the predicted operating state results, thereby obtaining the optimized estimation results of the turbine's operating state. The optimized estimation results of the running state are fed back to the physical constraint Fourier operator network as new initial conditions to correct the running state prediction results and obtain the assimilated and corrected running state prediction results. Based on the assimilation-corrected operational state prediction results, virtual observation values ​​of vibration and pressure states at unmeasurable locations of the turbine are determined, and the reconstructed state field of the turbine under all operating conditions is obtained. Based on the reconstruction results of the turbine's full operating condition state field, it is determined whether the turbine's operating state is abnormal and the location and type of the abnormal state are output, thereby achieving accurate monitoring and early warning of the turbine's operating state.

[0021] In this embodiment, the real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data specifically includes: In the turbine runner and volute area, several candidate measuring points are arranged according to the equipment operating conditions, and vibration and pressure signals are collected under typical operating conditions and multiple deviated operating conditions to form a multi-condition characteristic data matrix of the candidate measuring points. Based on the multi-condition feature data matrix, the covariance eigenvalues ​​of each candidate measuring point are calculated and sorted to obtain the preliminary assessment results of the sensitivity of the candidate measuring points to changes in operating status. Measuring points that exceed the preset sensitivity screening threshold are selected to form a preliminary set of measuring points. The calculation process for the preliminary sensitivity assessment results is as follows: The vibration and pressure signal data of each candidate measuring point under various working conditions in the multi-working condition feature data matrix of the candidate measuring points are standardized to obtain the standardized data matrix of the corresponding candidate measuring points. Calculate the covariance matrix of each candidate measurement point based on the standardized data matrix, and obtain all the eigenvalues ​​of the covariance matrix; Calculate the arithmetic mean of the eigenvalues ​​of the covariance matrix for each candidate measurement point to obtain the covariance eigenvalues ​​of each candidate measurement point. The covariance eigenvalues ​​of each candidate measuring point are sorted from high to low to obtain a preliminary assessment of the sensitivity of the candidate measuring points to changes in operating status. The mutual information redundancy of vibration and pressure signals between each measuring point in the initial set of measuring points and the other measuring points is calculated in turn to form an information redundancy matrix between measuring points. The calculation process for the mutual information redundancy is as follows: Select any one measurement point from the initial set of measurement points as the current calculation measurement point, extract the standardized data of vibration and pressure signals of the current calculation measurement point under all working conditions, and extract the standardized data of vibration and pressure signals of each measurement point in the initial set of measurement points other than the current calculation measurement point under all working conditions. Calculate the mutual information values ​​of the vibration signals and the mutual information values ​​of the pressure signals between the current calculation measurement point and each measurement point in the initial selection set other than the current calculation measurement point. The arithmetic mean of the mutual information values ​​corresponding to the vibration signal and the pressure signal is used to obtain the information redundancy value between the current measurement point and each other measurement point. The above process is repeated until all measuring points in the initial set of measuring points have completed the calculation of information redundancy values. All the calculated information redundancy values ​​are then arranged in the order of the measuring points to form an information redundancy matrix between the measuring points. Set an information redundancy limit, determine the measurement point pair with the largest information redundancy between measurement points based on the information redundancy matrix, and remove measurement points from the measurement point pair whose preliminary sensitivity assessment results are lower than the preset sensitivity screening threshold, and update the initial set of measurement points. Repeat the calculation of information redundancy, identification and elimination of redundant measurement points until the information redundancy of all measurement points in the initial set of measurement points is lower than the information redundancy limit, and obtain an optimized set of finite measurement points. Vibration sensors and pressure sensors are installed at the optimized set of limited measuring points to collect vibration and pressure signals from the limited measuring points during turbine operation and obtain raw monitoring data. The data format of the original monitoring data is as follows: The two-dimensional data sequence consists of vibration and pressure signals collected in real time by vibration and pressure sensors at each measuring point in the optimized finite measuring point set during turbine operation. Each row represents the vibration and pressure signal data collected by all measuring points in the optimized finite measuring point set at the same sampling time, and each column represents the vibration and pressure signal data of the same measuring point within a continuous sampling time period. The vibration and pressure signals are stored separately to form two sets of synchronized two-dimensional numerical matrices.

[0022] In this embodiment, the denoising and transformation processing of the original monitoring data to form observation data specifically involves: The vibration and pressure signals in the original monitoring data are extracted by sliding windows to obtain continuous time-series data segments for each measuring point. The wavelet threshold filtering method is used to denoise continuous time-series data segments to remove high-frequency noise interference introduced by sensors or environmental factors, and to obtain denoised time-series data segments. The denoising process for continuous time-series data segments specifically includes: Discrete wavelet transform is performed on the continuous time-series data segments at each measurement point to obtain a wavelet coefficient matrix composed of wavelet coefficients at multiple decomposition scales. Based on the statistical properties of the high-frequency scaling coefficients in the wavelet coefficient matrix, the threshold for the corresponding scale is calculated. Soft thresholding is applied to the high-frequency wavelet coefficients at each scale. Wavelet coefficients with absolute values ​​below the selected threshold are set to zero, while wavelet coefficients exceeding the threshold are corrected according to the difference between the value and the threshold. Perform inverse wavelet transform on all high-frequency wavelet coefficients after thresholding and the unprocessed low-frequency wavelet coefficients to reconstruct a denoised time-series data segment. Fourier transform is performed on the denoised time-series data segments to convert the vibration and pressure signals from the time domain to the frequency domain, thereby obtaining the corresponding spectral data. Frequency bands are divided based on the spectrum data, and the energy distribution characteristic parameters within each frequency band are calculated to obtain the frequency band energy distribution data for each measurement point. The calculation process for the energy distribution characteristic parameters within each frequency band is as follows: The spectral data of each measurement point is divided into several frequency bands according to a preset frequency range; For all spectral data within each frequency band, calculate the square of the amplitude of each frequency component, and sum the squared values ​​to obtain the total energy value within the corresponding frequency band. Calculate the proportion of the total energy value in each frequency band to the total energy value of all frequency bands to obtain the normalized energy distribution characteristic parameters in each frequency band; The normalized energy distribution characteristic parameters of each frequency band of all measurement points are combined to form the frequency band energy distribution data of each measurement point; The spectral entropy value of each measuring point is calculated based on the frequency band energy distribution data, and the frequency band energy distribution data and spectral entropy value are combined into observation data that can reflect the characteristics of the turbine's operating state. The calculation process of the spectral entropy value is as follows: Based on the frequency band energy distribution data of each measurement point, determine the normalized energy distribution characteristic parameters within each frequency band; Take the base-2 logarithm of the normalized energy distribution characteristic parameters in each frequency band to obtain the energy information value in the corresponding frequency band; The frequency band entropy value of each frequency band is calculated by multiplying the energy distribution characteristic parameter in each frequency band with the energy information value in the corresponding frequency band. The spectral entropy value of each measurement point is obtained by summing the frequency band entropy values ​​of each frequency band and taking the negative value.

[0023] In this embodiment, the step of establishing a physical constraint Fourier operator network for the turbine's operating state based on observation data, and training it with physical constraints to obtain an operating state prediction result that satisfies the physical laws of turbine operation, specifically involves: Based on the observation data, the initial network structure of the physically constrained Fourier operator network is established, and the frequency band energy distribution data and spectral entropy value in the observation data are used as the input variables of the network input layer, respectively. The frequency band energy distribution data and spectral entropy value of each measurement point in the observation data are used to form independent input vectors. The input vectors of each measurement point are arranged sequentially to form the initial input matrix of the network input layer. The number of nodes in the input layer of the physical constraint Fourier operator network is set according to the dimension of the vectors in the input matrix, and the number of nodes in the hidden layer and the number of network layers are determined. The initial network structure of the physically constrained Fourier operator network is constructed by connecting the nodes of the input layer with the nodes of the hidden layer, the nodes of each hidden layer, and the nodes of the hidden layer with the nodes of the output layer in a fully connected manner. All connection weight coefficients of the network are initially assigned values ​​using a random initialization method to complete the initial setting of the network structure and parameters; In the hidden layer of the network, the input variables are subjected to Fourier transform to map the input variables from the original observation space to the Fourier spectrum space, thereby obtaining intermediate features in the spectrum domain. The input variables of the input layer of the physical constraint Fourier operator network are passed to each node of the hidden layer through a fully connected method to obtain the initial input values ​​of the hidden layer nodes. Perform Discrete Fourier Transform (DFT) operations on the initial input values ​​of the hidden layer nodes to transform the original input values ​​from the time domain to the frequency domain, and obtain the corresponding Fourier spectrum coefficients. The real and imaginary parts of the Fourier spectrum coefficients of the hidden layer nodes are extracted respectively to form the intermediate feature vector in the spectrum domain of the hidden layer nodes; The intermediate feature vectors of each node in the hidden layer are combined to form an intermediate feature matrix in the spectral domain, which is used as the intermediate feature data output by the hidden layer. The continuity equation and the law of conservation of momentum are introduced as physical constraints in the hidden layer of the network. Based on the basic laws of fluid dynamics in the operation of the water turbine, a loss function is constructed. Based on the continuity equation and momentum conservation law satisfied during the operation of the water turbine, the flow continuity relationship and mechanical equilibrium relationship that should be satisfied between the intermediate features in the spectral domain corresponding to the hidden layer nodes are determined respectively. Based on the continuity relationship of traffic flow, a continuity constraint term is constructed in the form of the sum of squared traffic prediction deviations of the intermediate features of each hidden layer node; Based on the mechanical equilibrium relationship, a momentum conservation constraint term is constructed in the form of the sum of squares of mechanical prediction deviations of the intermediate features of each hidden layer node; The physical constraint term is formed by linearly superimposing the values ​​of the continuity constraint term and the momentum conservation constraint term; The loss function is composed of the sum of squared differences between the physical constraint terms, the predicted output values ​​of the physical constraint Fourier operator network, and the actual observed data. The loss function is backpropagated to calculate and the network weight coefficients are updated so that the prediction results output by the network conform to the physical constraints of the turbine operation. After obtaining the predicted output value through forward computation using a physically constrained Fourier operator network, the partial derivative of the loss function with respect to the predicted output value of the output layer nodes is calculated; based on the connection weight coefficients between the network output layer and the hidden layer, the partial derivative of the loss function with respect to the intermediate features in the spectral domain of the hidden layer nodes is calculated. Based on the Fourier transform operation of the hidden layer nodes, calculate the partial derivatives of the intermediate features in the spectral domain with respect to the initial input values ​​of the hidden layer nodes. According to the chain rule, the above partial derivatives are passed sequentially towards the input layer to calculate the partial derivatives of the loss function with respect to the connection weight coefficients of the physical constraint Fourier operator network. Based on the above partial derivatives, the values ​​of each connection weight coefficient are updated using the gradient descent algorithm; After updating the weight coefficients, the predicted output values ​​of the network output layer are obtained again, and the corresponding loss function values ​​are calculated. Continue performing the backpropagation calculations described above until the loss function value satisfies the network training iteration stopping criterion. Set a stopping criterion for network training iterations: stop the iterative training of the network when the change in the loss function is less than a preset threshold in a number of consecutive iterations. During the training of the physically constrained Fourier operator network, the corresponding loss function value is recorded after each iteration of training. Calculate the difference between the loss function value of the current iteration step and the previous iteration step, and take the absolute value to obtain the change in the loss function; Record and compare the changes in the loss function calculated in multiple consecutive iterations; Set preset thresholds for the number of consecutive iterations and the change in the loss function; When the change in all loss functions is less than a preset threshold in multiple consecutive iterations, the network training iteration stopping criterion is met, and the iterative training of the physical constraint Fourier operator network is stopped. After completing iterative training, the spectral domain prediction results in the output layer of the physical constraint Fourier operator network are subjected to inverse Fourier transform to obtain the running state prediction results. Extract the spectral domain prediction results of each node in the output layer of the physical constraint Fourier operator network, and extract the real and imaginary part values ​​corresponding to the spectral domain prediction results respectively. Construct the complex form of the spectral coefficients for the corresponding nodes based on the real and imaginary part values; Perform an inverse Fourier transform operation on the spectral coefficients constructed for each output node to map the prediction results in the spectral domain from the frequency domain space back to the original observation space; The time-domain prediction sequences of vibration and pressure signals corresponding to each output node are obtained, and the time-domain prediction sequences of all output nodes are merged to form a complete operating state prediction result.

[0024] In this embodiment, the step of using observed data as constraints and employing an iterative ensemble Kalman smoother to assimilate the predicted operating state results to obtain optimized estimation results of the turbine's operating state specifically involves: The initial state set of the ensemble Kalman smoother is generated using the prediction results of the operating state. Each member of the initial state set is represented as a state vector of the turbine's operating state. The predicted operating state output by the physical constraint Fourier operator network is transformed into an initial state vector composed of the predicted values ​​of vibration and pressure signals corresponding to each measuring point. Based on the numerical distribution characteristics of the initial state vector and the preset state perturbation amplitude, multiple random perturbation vectors following a Gaussian distribution are generated. The random perturbation vectors are superimposed on the initial state vectors to form multiple state vectors with different initial perturbation states. All state vectors are combined to form the initial state set of the ensemble Kalman smoother; The observation vector is determined based on the frequency band energy distribution data and spectral entropy value in the observation data, and a data assimilation observation operator based on the state vector and the observation vector is constructed using a Kalman smoother. Extract the energy distribution data and spectral entropy value of all frequency bands corresponding to each measuring point from the observation data; The frequency band energy distribution data and spectral entropy values ​​are combined into a one-dimensional numerical vector, respectively. The one-dimensional numerical vectors of all measurement points are arranged sequentially according to the measurement point order to form the observation vector used for ensemble Kalman smoother data assimilation processing; Each numerical unit in the observation vector corresponds to a specific frequency band energy distribution value or spectral entropy value at a unique measurement point; Based on the correspondence between each numerical unit in the state vector and each numerical unit in the observation vector, the mapping relationship from the state space to the observation space is determined. A data assimilation observation operator matrix is ​​constructed based on the mapping relationship from the state space to the observation space. Each matrix element in the observation operator matrix represents the linear mapping coefficient from the corresponding state vector numerical element to the observation vector numerical element. The state vector is multiplied by the data assimilation observation operator matrix to achieve the transformation of the state vector into the observation space; The mapping accuracy of the data assimilation observation operator matrix is ​​evaluated based on the difference between the predicted observation space value obtained from the state vector transformation and the actual observation vector. The data assimilation observation operator matrix is ​​dynamically adjusted based on the evaluation results until the mapping error of the data assimilation observation operator matrix is ​​lower than the preset error limit. The adjusted data assimilation observation operator matrix is ​​determined to be the data assimilation observation operator of the ensemble Kalman smoother; The predicted values ​​of state set members in the observation space are calculated by using the data assimilation observation operator, and the difference between the predicted values ​​and the actual observation vectors is calculated to obtain the observation space deviation vector of the state set members. The calculation process for the predicted value is as follows: Extract the state vector corresponding to each member of the state set, and perform matrix multiplication operation between the state vector and the data assimilation observation operator; The result of matrix multiplication is transformed into the predicted value of the corresponding state set member in the observation space, forming the predicted observation vector of each state set member. Arrange the predicted observation vectors of all state set members in the order of the state set members to form the predicted values ​​of the state set members in the observation space. Calculate the covariance matrix and Kalman gain matrix of the state set members based on the observation space bias vector of the state set members; The state vectors of the members of the state set are updated using the Kalman gain matrix to obtain the updated state set; The updated set of states is used to perform data assimilation processing of the set of Kalman smoothers again, and the process is iterated until the change in the state vector within the set of states is lower than a preset threshold in a number of consecutive iterations. The arithmetic mean of the state vectors in the iteratively stabilized state set is used to obtain the optimized estimation result of the turbine's operating state. The specific parameters, such as the number of hidden layer nodes and the number of iterations, of the physically constrained Fourier operator network are set based on the following: The number of measuring points obtained after the sensor arrangement and the frequency band energy distribution dimension of each measuring point Based on this, the number of input layer nodes is set to This ensures that the network can fully receive the energy characteristics and spectral entropy information of the observation space; In setting the number of hidden layer nodes, the cumulative energy contribution rate is calculated by performing principal component analysis and singular value decomposition on the sample data. When the cumulative contribution rate reaches 95% or more, the corresponding number of principal components is used as the minimum configuration base number of single-layer hidden layer nodes. The number of hidden layer nodes is determined by an empirical proportional coefficient. The expansion of the principal component count results in the number of hidden layer nodes typically ranging from 64 to 256. According to the sampling theorem of Fourier transform in the frequency domain, the number of nodes must be at least twice the input dimension to avoid aliasing of frequency domain information. Therefore, the final number of nodes is... Rounding down to the nearest integer determines the result. In terms of network layer setting, considering the degree of coupling between physical constraint terms in different layers, in order to ensure gradient propagation stability and physical constraint propagation depth, a 4-6 layer structure is adopted, in which the first two layers are spectral feature extraction layers, the middle two layers are physical constraint coupling layers, and the last two layers are state inversion layers. Plot the loss function's decline curve during the initial training phase to observe the convergence trend; When the rate of decrease of the loss function slows down and the rate of change of loss after 5 consecutive iterations When the model reaches a steady state, it is considered to have entered a steady state. Therefore, the maximum number of iterations is set to 5000, and an early stopping mechanism is set to terminate training when the rate of change condition is met for 5 consecutive iterations. Sensitivity analysis was performed on different combinations of the number of nodes and the number of iterations. When the number of hidden layer nodes is less than 64, the network cannot fully represent the high-spectral energy distribution characteristics, and the prediction error increases by about 8%. When the number of nodes exceeds 256, the loss function decreases further, but the generalization error increases. The model did not converge when the number of iterations was less than 1000, and the loss convergence rate approached zero when the number of iterations exceeded 5000, indicating that the set range was the optimal interval.

[0025] In this embodiment, feeding back the operational state optimization estimation result to the physical constraint Fourier operator network as a new initial condition to correct the operational state prediction result and obtain the assimilated and corrected operational state prediction result specifically involves: The vibration and pressure signals in the operational state optimization estimation results are converted into input vectors of the corresponding physical constraint Fourier operator network input layer to form a corrected input data matrix; Using the corrected input data matrix as the initial input variable of the physically constrained Fourier operator network, the Fourier transform operation of the hidden layer of the network is re-executed to obtain the corrected intermediate features in the spectral domain. Based on the corrected intermediate features in the spectral domain, the loss function of the physically constrained Fourier operator network is recalculated in conjunction with the continuity equation of the turbine operation process and the law of conservation of momentum. Backpropagation is recalculated based on the updated loss function, and the connection weight coefficients of the physical constraint Fourier operator network are updated accordingly. Repeat the forward and backward propagation calculations of the network until the change in the network loss function is less than a preset threshold for several consecutive iterations. After the network iterative stabilization, the spectral domain correction prediction results in the output layer nodes of the physical constraint Fourier operator network are extracted, and an inverse Fourier transform is performed to obtain the assimilated and corrected running state prediction results.

[0026] In this embodiment, the virtual observation values ​​of vibration and pressure states at unmeasurable locations of the turbine are determined based on the assimilated and corrected operating state prediction results, and the reconstructed state field results of the turbine under all operating conditions are obtained as follows: Based on the spatial locations of the limited measuring points already arranged in the turbine runner and spiral casing, a spatial grid covering the turbine's operating area is established. The vibration and pressure signal values ​​at the measured locations in the assimilated and corrected operational state prediction results are used as state reference values ​​for known locations in the spatial grid. Using the continuity equation and the law of conservation of momentum as physical constraints, the spatial interpolation weighting coefficients between grid nodes in the spatial grid are calculated. The calculation logic for the spatial interpolation weight coefficients is as follows: A spatial grid covering the turbine's operating area is established based on the spatial locations of the limited measuring points already arranged in the turbine runner and spiral casing. The vibration and pressure signal values ​​at the measured locations in the assimilated and corrected operational state prediction results are used as state reference values ​​for known locations in the spatial grid. Using the continuity equation and the law of conservation of momentum as physical constraints, the spatial interpolation weighting coefficients between grid nodes in the spatial grid are calculated. Based on the spatial interpolation weight coefficient, determine the interpolation weight value between each grid node corresponding to an unmeasurable location and all grid nodes of measured locations; The vibration and pressure signals corresponding to each measured location node in the spatial grid are extracted respectively. The vibration signal corresponding to each measured location node is multiplied by the interpolation weight value between the corresponding unmeasurable location node and the measured location node, and the product values ​​are summed to obtain the vibration signal of the unmeasurable location node. Then, the pressure signals corresponding to each measured location node are multiplied by the interpolation weight value between the corresponding unmeasurable location node and the measured location node, and the product values ​​are summed to obtain the pressure signals of the unmeasurable location nodes. Repeat the above calculation process until the vibration and pressure signals of all unmeasurable nodes have been calculated. Based on the spatial interpolation weighting coefficients and the state reference values ​​of known locations in the spatial grid, the vibration and pressure signals of the grid nodes corresponding to the unmeasurable locations of the turbine are calculated. Based on the spatial interpolation weight coefficient, determine the interpolation weight value between each grid node corresponding to an unmeasurable location and all grid nodes of measured locations; Extract the vibration and pressure signals corresponding to each measured location node in the spatial grid; The vibration signal corresponding to each measured position node is multiplied by the interpolation weight value between the corresponding unmeasurable position node and the measured position node, and the product values ​​are summed to obtain the vibration signal of the unmeasurable position node. The pressure signal corresponding to each measured location node is multiplied by the interpolation weight value between the corresponding unmeasurable location node and the measured location node, and the product values ​​are summed to obtain the pressure signal of the unmeasurable location node. Repeat the above calculations until the vibration and pressure signals of all unmeasurable nodes have been calculated. The vibration and pressure signals obtained from the grid nodes at the unmeasurable locations of the water turbine are subjected to inverse Fourier transform to form virtual observations of the vibration and pressure states at the corresponding unmeasurable locations. By combining the vibration and pressure signals from all measured locations with the calculated virtual observations from unmeasurable locations, a complete reconstruction of the turbine's state field under all operating conditions is formed.

[0027] In this embodiment, determining whether the turbine's operating state is abnormal and outputting the location and type of the abnormality based on the turbine's full-condition state field reconstruction results specifically involves: Based on the reconstruction results of the turbine's full-condition state field, the time-domain amplitude and spectral energy values ​​of the vibration and pressure signals at all grid nodes were calculated. Determine the normal operating reference thresholds for the amplitude and spectral energy of vibration and pressure signals at each grid node under typical working conditions; Calculate the deviation of the amplitude and spectral energy of the vibration and pressure signals at each grid node from the normal operating reference threshold, and obtain the state deviation values ​​of all grid nodes; Set a state deviation threshold for determining abnormal states, compare the state deviation value of each grid node with the state deviation threshold, and determine the grid node whose state deviation value exceeds the state deviation threshold as an abnormal state node. The method for setting the state deviation threshold is as follows: After obtaining the reconstruction results of the turbine's full operating condition state field, the time-domain amplitude and spectral energy values ​​of the vibration signal and pressure signal at each spatial grid node were calculated respectively. Under typical stable operating conditions, multiple sample time periods were selected, and long-term statistics were performed on the vibration amplitude and pressure energy of each grid node. The average value, standard deviation, and range of variation under normal operating conditions were calculated to obtain the normal operating reference threshold for each node. The difference between the current amplitude and spectral energy of each node under the monitoring condition and the corresponding normal reference value is calculated to obtain the state deviation value. Based on the structural characteristics of the turbine and the hydrodynamic response characteristics under different operating conditions, a deviation limit that can distinguish between normal fluctuations and potential anomalies is selected. Taking into account the signal noise level, the sensitivity of the measuring point and the tolerance for false alarms, the state deviation threshold range is set. The range of deviation from the threshold is determined by comparing historical operating data and iterating through multiple experiences, so that under normal operating conditions, the proportion of nodes with a deviation rate lower than the threshold is greater than 95%, while the deviation value of the corresponding node is significantly higher than the threshold when there are abnormal conditions such as structural vibration, cavitation or hydraulic imbalance. The location distribution of all abnormal state nodes within the spatial grid is statistically analyzed, and the frequency range of deviations in the vibration and pressure signals of the abnormal state nodes is determined. Based on the location distribution of abnormal state nodes and the frequency range of deviations, determine the abnormal type and specific location of the abnormal state nodes, and output the data information of abnormal type and corresponding location; Based on the identified anomaly type and specific location, an early warning message for abnormal turbine operation status is generated and output in real time. Example

[0028] To verify the feasibility of this invention in practice, it was applied to the real-time monitoring and fault early warning of the turbine unit's operating status at a hydropower station, focusing on the identification and early warning of abnormal states deviating from operating conditions during long-term operation. In this application scenario, existing monitoring solutions typically use a small number of sensors at fixed locations to measure vibration and pressure data, and manually set fixed thresholds to determine whether an anomaly has occurred. Because the load changes significantly during the long-term operation of the turbine, the fixed thresholds cannot adaptively adjust with the operating conditions, resulting in low accuracy in early anomaly identification. This often leads to delayed response or even missed alarms when actual faults occur, resulting in significant monitoring blind spots and a high false alarm rate.

[0029] In this embodiment, technicians select several candidate measuring points within the turbine runner chamber and volute region. Vibration and pressure sensors are used to collect vibration and pressure signals from the unit under typical operating conditions and multiple deviating operating conditions, forming a multi-condition feature data matrix for the candidate measuring points. Subsequently, the covariance eigenvalues ​​of each candidate measuring point are calculated based on the multi-condition feature data matrix and sorted. A comprehensive selection is then performed according to a set sensitivity screening threshold and information redundancy limit to obtain an optimized set of finite measuring points. In practical applications, technicians install sensors at the optimized set of measuring points to collect raw vibration and pressure signal data during turbine operation in real time. Data denoising and Fourier transform processing are then performed to generate observation data.

[0030] Technicians further trained the observed data using a physically constrained Fourier operator network. Frequency band energy distribution data and spectral entropy values ​​were used as input variables. The hidden layers of the network performed Fourier transform operations, and the continuity equation and the law of conservation of momentum were introduced as physical constraints to construct the loss function. The backpropagation algorithm was used to optimize the network weight coefficients. After repeated training, training stopped when the change in the loss function was below a preset threshold of 0.0001 for 10 consecutive iterations, completing the network construction and prediction, and obtaining a predicted operating state that satisfies the physical laws of turbine operation.

[0031] Subsequently, the system imports the prediction results into an iterative ensemble Kalman smoother for data assimilation. The initial number of state ensemble members is set to 50, and the state vector dimension is set to 128. Using the frequency band energy distribution data and spectral entropy as observation vectors, a data assimilation observation operator is constructed. By calculating the deviation between the predicted values ​​of the ensemble members and the actual observed vectors, the state vector is updated until the iteration converges, ultimately obtaining the optimized estimation result of the running state. Statistically, in actual implementation, the number of iterations of this assimilation process is generally stable between 15 and 20, and the threshold for the change in the ensemble member deviation vector is set to 0.001.

[0032] The system then feeds back the optimized estimation results to the physical constraint Fourier operator network as new input conditions, and re-executes the network training iteration to correct the running state prediction results. It usually reaches stable convergence after 8-12 iterations, and obtains the corrected high-precision running state prediction results.

[0033] Finally, based on the corrected prediction results, the system establishes a spatial grid throughout the turbine runner chamber and volute. Using the continuity equation and the law of conservation of momentum, spatial interpolation weighting coefficients are constructed. Virtual observations of vibration and pressure states at unmeasurable locations within the grid nodes are calculated via interpolation, resulting in a complete reconstruction of the state field under all operating conditions. Furthermore, based on the normal operating baseline threshold set under typical conditions, the deviation of vibration and pressure states at each grid node is calculated. Grid nodes with deviations exceeding the state deviation threshold of 0.05 are identified as abnormal nodes. The spatial location and signal anomaly type of these abnormal nodes are automatically output, and real-time early warning information is generated.

[0034] To verify the monitoring accuracy, this embodiment randomly selected five real operating data samples under different working conditions and compared them with the state prediction and anomaly early warning results of the present invention. Specific data are shown in the table below: Table 1 Comparison of Measured and Predicted Values ​​of Hydropower Turbine Operating Status

[0035] As can be seen from the actual monitoring results shown in Table 1 above, the system of the present invention exhibits high consistency with the actual measured values ​​in predicting key state indicators such as vibration amplitude, pressure amplitude, and spectral entropy. Specifically, the vibration amplitude prediction error is controlled within 4.11%, the pressure amplitude prediction error does not exceed 2.76%, and the spectral entropy error is as low as 0.86%. In particular, in sample 5, the vibration amplitude and pressure amplitude prediction errors are 1.82% and 1.32%, respectively, and the spectral entropy error is only 0.62%, demonstrating the high-precision monitoring advantage of the method of the present invention under complex operating conditions.

[0036] Statistical analysis of abnormal state identification and location shows that the method of this invention achieves an accuracy rate of over 95% in identifying abnormal nodes, and reduces the false alarm rate to below 1.5%. Compared with existing monitoring schemes, the accuracy and response speed of abnormal early warning are significantly improved, fully meeting the engineering application requirements for the long-term safe and stable operation of hydro-turbine units. This embodiment fully demonstrates that the hydro-turbine operation status monitoring scheme based on digital twin and data assimilation methods proposed in this invention has good engineering applicability and significant technical advantages in practical application scenarios.

[0037] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for monitoring the operating status of a hydro turbine based on digital twins, characterized in that, include: Real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data; The raw monitoring data is denoised and transformed to form observation data; A physical constraint Fourier operator network for the operating state of a water turbine is established based on observation data, and physical constraint training is performed to obtain the operating state prediction results that satisfy the physical laws of water turbine operation. Using the observed data as constraints, an iterative ensemble Kalman smoother is used to assimilate the predicted operating state results, thereby obtaining the optimized estimation results of the turbine's operating state. The optimized estimation results of the running state are fed back to the physical constraint Fourier operator network as new initial conditions to correct the running state prediction results and obtain the assimilated and corrected running state prediction results. Based on the assimilation-corrected operational state prediction results, virtual observation values ​​of vibration and pressure states at unmeasurable locations of the turbine are determined, and the reconstructed state field of the turbine under all operating conditions is obtained. Based on the reconstruction results of the turbine's full operating condition state field, determine whether the turbine's operating state is abnormal and output the location and type of the abnormal state.

2. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The method involves real-time acquisition of vibration and pressure signals from a limited number of measuring points during turbine operation to obtain raw monitoring data, specifically: In the turbine runner and volute area, several candidate measuring points are arranged according to the equipment operating conditions, and vibration and pressure signals are collected under typical operating conditions and multiple deviated operating conditions to form a multi-condition characteristic data matrix of the candidate measuring points. Based on the multi-condition feature data matrix, the covariance eigenvalues ​​of each candidate measuring point are calculated and sorted to obtain the preliminary assessment results of the sensitivity of the candidate measuring points to changes in operating status. Measuring points that exceed the preset sensitivity screening threshold are selected to form a preliminary set of measuring points. The mutual information redundancy of vibration and pressure signals between each measuring point in the initial set of measuring points and the other measuring points is calculated in turn to form an information redundancy matrix between measuring points. Set an information redundancy limit, determine the measurement point pair with the largest information redundancy between measurement points based on the information redundancy matrix, and remove measurement points from the measurement point pair whose preliminary sensitivity assessment results are lower than the preset sensitivity screening threshold, and update the initial set of measurement points. Repeat the calculation of information redundancy, identification and elimination of redundant measurement points until the information redundancy of all measurement points in the initial set of measurement points is lower than the information redundancy limit, and obtain an optimized set of finite measurement points. Vibration sensors and pressure sensors are installed at the optimized set of limited measuring points to collect vibration and pressure signals from the limited measuring points during turbine operation, thereby obtaining raw monitoring data.

3. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The process of denoising and transforming the original monitoring data to form observation data specifically involves: The vibration and pressure signals in the original monitoring data are extracted by sliding windows to obtain continuous time-series data segments for each measuring point. The wavelet threshold filtering method is used to denoise continuous time series data segments to obtain denoised time series data segments. Perform a Fourier transform on the denoised time-series data segment to obtain the corresponding spectral data; Frequency bands are divided based on the spectrum data, and the energy distribution characteristic parameters within each frequency band are calculated to obtain the frequency band energy distribution data for each measurement point. The spectral entropy value of each measuring point is calculated based on the frequency band energy distribution data, and the frequency band energy distribution data and spectral entropy value are combined into observation data.

4. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The physical constraint Fourier operator network for the turbine's operating state is established based on observation data, and physical constraint training is performed to obtain operating state prediction results that satisfy the physical laws of turbine operation. Specifically: Based on the observation data, the initial network structure of the physically constrained Fourier operator network is established, and the frequency band energy distribution data and spectral entropy value in the observation data are used as the input variables of the network input layer, respectively. In the hidden layer of the network, the input variables are subjected to Fourier transform to map the input variables from the original observation space to the Fourier spectrum space, thereby obtaining intermediate features in the spectrum domain. The continuity equation and the law of conservation of momentum are introduced as physical constraints in the hidden layer of the network. Based on the basic laws of fluid dynamics in the operation of the water turbine, a loss function is constructed. The loss function is backpropagated to calculate and the network weight coefficients are updated so that the prediction results output by the network conform to the physical constraints of the turbine operation. Set a stopping criterion for network training iterations: stop the iterative training of the network when the change in the loss function is less than a preset threshold in a number of consecutive iterations. After completing iterative training, the spectral domain prediction results in the output layer of the physical constraint Fourier operator network are subjected to inverse Fourier transform to obtain the running state prediction results.

5. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The process of using observed data as constraints and employing an iterative ensemble Kalman smoother to assimilate the predicted operating state results to obtain optimized estimation results for the turbine's operating state is as follows: The initial state set of the ensemble Kalman smoother is generated using the prediction results of the operating state. Each member of the initial state set is represented as a state vector of the turbine's operating state. The observation vector is determined based on the frequency band energy distribution data and spectral entropy value in the observation data, and a data assimilation observation operator based on the state vector and the observation vector is constructed using a Kalman smoother. The predicted values ​​of state set members in the observation space are calculated by using the data assimilation observation operator, and the difference between the predicted values ​​and the actual observation vectors is calculated to obtain the observation space deviation vector of the state set members. Calculate the covariance matrix and Kalman gain matrix of the state set members based on the observation space bias vector of the state set members; The state vectors of the members of the state set are updated using the Kalman gain matrix to obtain the updated state set; The updated set of states is used to perform data assimilation processing of the set of Kalman smoothers again, and the process is iterated until the change in the state vector within the set of states is lower than a preset threshold in a number of consecutive iterations. The arithmetic mean of the state vectors in the iteratively stabilized state set is used to obtain the optimized estimation result of the turbine's operating state.

6. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The step of feeding back the optimized estimation result of the operating state to the physically constrained Fourier operator network as a new initial condition to correct the operating state prediction result and obtain the assimilated and corrected operating state prediction result is as follows: The vibration and pressure signals in the operational state optimization estimation results are converted into input vectors of the corresponding physical constraint Fourier operator network input layer to form a corrected input data matrix; Using the corrected input data matrix as the initial input variable of the physically constrained Fourier operator network, the Fourier transform operation of the hidden layer of the network is re-executed to obtain the corrected intermediate features in the spectral domain. Based on the corrected intermediate features in the spectral domain, the loss function of the physically constrained Fourier operator network is recalculated in conjunction with the continuity equation of the turbine operation process and the law of conservation of momentum. Backpropagation is recalculated based on the updated loss function, and the connection weight coefficients of the physical constraint Fourier operator network are updated accordingly. Repeat the forward and backward propagation calculations of the network until the change in the network loss function is less than a preset threshold for several consecutive iterations. After the network iterative stabilization, the spectral domain correction prediction results in the output layer nodes of the physical constraint Fourier operator network are extracted, and an inverse Fourier transform is performed to obtain the assimilated and corrected running state prediction results.

7. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, Based on the assimilated and corrected operating state prediction results, the virtual observation values ​​of vibration and pressure states at unmeasurable locations of the turbine are determined, and the reconstructed state field results of the turbine under all operating conditions are obtained, specifically as follows: Based on the spatial locations of the limited measuring points already arranged in the turbine runner and spiral casing, a spatial grid covering the turbine's operating area is established. The vibration and pressure signal values ​​at the measured locations in the assimilated and corrected operational state prediction results are used as state reference values ​​for known locations in the spatial grid. Using the continuity equation and the law of conservation of momentum as physical constraints, the spatial interpolation weighting coefficients between grid nodes in the spatial grid are calculated. Based on the spatial interpolation weighting coefficients and the state reference values ​​of known locations in the spatial grid, the vibration and pressure signals of the grid nodes corresponding to the unmeasurable locations of the turbine are calculated. The vibration and pressure signals obtained from the grid nodes at the unmeasurable locations of the water turbine are subjected to inverse Fourier transform to form virtual observations of the vibration and pressure states at the corresponding unmeasurable locations. By combining the vibration and pressure signals from all measured locations with the calculated virtual observations from unmeasurable locations, a complete reconstruction of the turbine's state field under all operating conditions is formed.

8. The method for monitoring the operating status of a hydro-turbine based on digital twins according to claim 1, characterized in that, The process of determining whether the turbine's operating state is abnormal based on the reconstructed state field results of the turbine's full operating conditions and outputting the location and type of the abnormality is as follows: Based on the reconstruction results of the turbine's full-condition state field, the time-domain amplitude and spectral energy values ​​of the vibration and pressure signals at all grid nodes were calculated. Determine the normal operating reference thresholds for the amplitude and spectral energy of vibration and pressure signals at each grid node under typical working conditions; Calculate the deviation of the amplitude and spectral energy of the vibration and pressure signals at each grid node from the normal operating reference threshold, and obtain the state deviation values ​​of all grid nodes; Set a state deviation threshold for determining abnormal states, compare the state deviation value of each grid node with the state deviation threshold, and determine the grid node whose state deviation value exceeds the state deviation threshold as an abnormal state node. The location distribution of all abnormal state nodes within the spatial grid is statistically analyzed, and the frequency range of deviations in the vibration and pressure signals of the abnormal state nodes is determined. Based on the location distribution of abnormal state nodes and the frequency range of deviations, determine the abnormal type and specific location of the abnormal state nodes, and output the data information of abnormal type and corresponding location; Based on the identified anomaly type and specific location, an early warning message for abnormal turbine operation status is generated and output in real time.

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