Axial flow pump gas-containing stable operation method based on ensemble learning

Abstract

This invention discloses a method for stable operation of axial flow pumps in gas-filled conditions based on ensemble learning. To address the problem of difficulty in timely and effective adjustments before instability occurs in axial flow pumps under gas-filled conditions, and the lack of closed-loop control strategies driven by risk and stability margin outputs, thus hindering stable operation, this invention acquires time-series signals from multiple sensors and axial flow pump operating parameters. A sensor topology graph is established based on the physical connections of the pump body and pipelines, and the edge weights or adjacency relationships of the graph are dynamically updated according to the operating parameters. A pipeline propagation delay parameter is introduced to read historical node features from online sample sequences to generate delayed node features. A heterogeneous graph neural network ensemble model is employed and online domain adaptation is performed to output predicted values ​​for instability risk and stability margin. An upper bound for instability risk and a lower bound for stability margin are constructed based on operating condition grouping and time-weighted conformal prediction. Based on these upper and lower bounds, hierarchical hysteresis constraint control is implemented, and actuator commands are issued. This achieves reliable risk constraints and stability margin guarantees under gas-filled disturbance propagation and operating condition drift conditions, thereby improving the operational stability and safety of axial flow pumps in gas-filled conditions.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery operation monitoring, and in particular to a method for stable operation of an axial flow pump with gas based on ensemble learning. Background Technology

[0002] Axial flow pumps are widely used in water conservancy irrigation and drainage, circulating cooling, seawater desalination, and industrial transportation. In actual operation, axial flow pumps are prone to entering a gas-bearing operating state due to factors such as gas-bearing incoming liquid, localized air intake in pipelines, and rapid changes in operating conditions. The compressibility and slip effect of the gas-liquid two phases alter the flow structure and pressure wave propagation characteristics inside and outside the pump, causing phenomena such as head fluctuations, flow pulsations, increased vibration and noise. In severe cases, instability processes such as surge and rotational stall may occur, leading to decreased efficiency, component fatigue damage, and even shutdown accidents. Therefore, various technical approaches have been developed in engineering to address condition monitoring, instability early warning, and operational regulation under gas-bearing conditions.

[0003] Existing technologies typically include sensor-based online monitoring and threshold discrimination methods, stability evaluation methods based on mechanistic or empirical models, and data-driven intelligent diagnosis and prediction methods. Online monitoring often employs multi-source signals such as pressure, vibration, electrical parameters, and flow rate, using feature extraction and rule-based thresholding to identify anomalies. Mechanistic model methods often combine pump characteristic curves, phase content estimation, and stability criteria to determine operating condition boundaries. Data-driven methods use traditional machine learning or deep learning models to identify instability and predict trends, and in some scenarios, attempt to use the prediction results for operational adjustments.

[0004] The existing technology still has the following shortcomings:

[0005] 1. The ability to characterize the propagation of gas disturbances along pipelines and the coupling relationship of multiple measurement points is insufficient. Multiple source signals are often simply spliced ​​together or modeled independently, which makes it difficult to reflect the changes in topological coupling strength and propagation delay characteristics when operating conditions change, thus limiting the reliability of early warning and prediction.

[0006] 2. Faced with gas content fluctuations and operating condition drift, the model's generalization and online adaptability are insufficient. The prediction bias of the offline-trained model increases after the operating condition distribution changes, making it difficult to continuously and stably output state variables that can be used for control.

[0007] 3. The prediction results lack calibrable uncertainty boundaries, usually only providing point predictions or empirical thresholds, and cannot form quantitative indicators that can be directly used for safety constraints, such as risk upper bounds or stability margin lower bounds. As a result, it is difficult to establish closed-loop hierarchical adjustment strategies before instability and avoid controlling jitter.

[0008] Therefore, a method for stable operation of axial flow pumps with gas content that can overcome the shortcomings of the prior art is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0009] One objective of this invention is to propose a method for stable operation of axial flow pumps in gas-bearing conditions based on ensemble learning. Addressing the problems of existing technologies struggling to characterize the multi-point coupling changes and propagation delays caused by gas disturbances propagating along pipelines under gas-bearing conditions, insufficient generalization ability of models under operating condition drift, and the lack of reliable boundaries for closed-loop control in prediction results, thus hindering timely and effective adjustments and stable operation, the following technical solution is proposed: Acquire time-series signals from multiple sensors and operating parameters of the axial flow pump; establish a sensor topology based on the physical connections of the pump body and pipelines, and dynamically update edge weights or adjacency relationships according to operating parameters; determine the edge delay parameters of connecting edges based on pipeline length and mixed-phase propagation velocity; generate delayed node features by reading historical node features from online sample sequences; construct a heterogeneous graph from the dynamic topology and input it into an ensemble graph neural network model that is adaptively updated in the online domain, outputting instability risk prediction values ​​and stability margin prediction values; construct an upper bound for instability risk and a lower bound for stability margin based on operating condition grouping and time-weighted conformal prediction; and perform hierarchical hysteresis constraint control based on the upper and lower bounds and issue actuator adjustment commands. This invention has the technical effects of quantifying instability risks in advance and providing a reliable safety boundary, improving the robustness of prediction and control under gas-containing conditions, and realizing stable operation of axial flow pumps in gas-containing conditions.

[0010] This invention provides a method for stable operation of an axial flow pump with gas based on ensemble learning, comprising:

[0011] S1. Acquire historical operating data of the axial flow pump, establish sensor nodes and connecting edges based on the physical connection relationship of the axial flow pump and its pipeline, determine the sensor type, train a graph neural network ensemble model based on historical operating data, establish online sample sequences and calibration sample sequences, and initialize the control level; S2. In each control cycle, collect time-series signals from multiple sensors and axial flow pump operating condition parameters, synchronously preprocess the time-series signals and extract the current node features, calculate stability indices based on operating condition parameters and time-series signals, obtain stability margin observations, and generate instability state markers based on preset instability criteria; S3. Load the current node features into the sensor nodes and connecting edges to construct an initial sensor topology graph; S4. Update the edge weights or adjacency relationships of the initial sensor topology graph based on operating condition parameters to obtain a dynamic sensor topology graph, determine the edge delay parameters of each connecting edge based on preset pipeline length parameters and operating condition parameters, and generate delayed node features by reading historical node features from the online sample sequence according to the edge delay parameters; S5. Write the current node features and operating condition parameters into and update the online sample sequence, and use the updated online sample sequence to train the graph neural network ensemble model. The online domain adaptive update constructs a heterogeneous graph of the dynamic sensor topology according to sensor type, and inputs the heterogeneous graph and the features of the delayed nodes into the adaptive graph neural network ensemble model, outputting the adaptive instability risk prediction value and the adaptive stability margin prediction value; S6, the operating condition group is determined according to the operating condition parameters, the calibration samples belonging to the operating condition group are selected from the calibration sample sequence and time weights are applied to calculate the inconsistency score, and the risk quantile threshold and margin quantile threshold corresponding to the preset confidence level are determined respectively, thereby constructing the upper bound of instability risk and the lower bound of stability margin; S7. Determine the control level for this control cycle based on the upper bound of instability risk and the preset risk threshold, and the lower bound of stability margin and the preset margin threshold. Correct the control level based on the preset hysteresis threshold and the control level of the previous control cycle. Generate control commands based on the corrected control level and issue them to adjust the operating parameters. S8. Combine the predicted instability risk value and the instability state marker to form a risk calibration sample. Combine the predicted stability margin value and the observed stability margin value to form a margin calibration sample. Write the risk calibration sample and the margin calibration sample into the storage area corresponding to the operating condition group in the calibration sample sequence and update it.

[0012] Optionally, S1 includes:

[0013] The historical operating data includes time-series signals from multiple sensors and axial flow pump operating parameters corresponding to the time-series signals.

[0014] The historical running data is acquired and the time-series signal is synchronized and preprocessed to form historical node features for training.

[0015] Based on the physical connection relationship between the axial flow pump and its pipeline, fixed sensor nodes and connection edges are established, and the sensor type is determined for each sensor node.

[0016] The graph neural network ensemble model is trained based on the historical node features and the axial flow pump operating parameters, so that the at least two heterogeneous graph neural network sub-models output instability risk prediction values ​​and stability margin prediction values ​​respectively for different sensor type nodes using different message update rules, and the fusion module fuses the outputs of the at least two heterogeneous graph neural network sub-models.

[0017] The online sample sequence is established, and the sequence length and update rules of the online sample sequence are set so that the online sample sequence can be used to store node features and axial flow pump operating condition parameters according to the control cycle.

[0018] Establish the calibration sample sequence and preset the division rules of the operating condition group, so that the calibration sample sequence is stored according to the operating condition group for calibration samples used for conformal prediction;

[0019] Set the initial control level.

[0020] Optionally, S2 includes:

[0021] The operating parameters of the axial flow pump include speed, flow rate, pressure difference, and gas content characterization parameters.

[0022] In each control cycle, the timing signals of multiple sensors and the operating parameters of the axial flow pump in the current control cycle are collected according to the preset sampling frequency.

[0023] The time-series signal is synchronized and aligned according to the timestamp, and preprocessed by noise filtering, outlier removal and amplitude normalization.

[0024] Based on the preprocessed timing signal, the current node features corresponding to each sensor are extracted within the control cycle;

[0025] Stability indices are calculated based on the operating parameters of the axial flow pump and the timing signal.

[0026] The stability margin observation value is calculated based on the stability index and the preset stability threshold;

[0027] An instability state marker is generated based on the stability index and the preset instability criterion.

[0028] Optionally, S3 includes:

[0029] According to the sensor node and the sensor identifier corresponding to the sensor node, the current node features are matched one by one to the corresponding sensor node;

[0030] While keeping the connecting edges unchanged, the sensor nodes containing the characteristics of the current node are combined with the connecting edges to construct the initial sensor topology graph;

[0031] The initial sensor topology graph includes the sensor nodes, the connecting edges, the current node features corresponding to each sensor node, and the sensor type corresponding to each sensor node.

[0032] Optionally, S4 includes:

[0033] The operating parameters of the axial flow pump are input into the edge weight update function to update the edge weight of at least one connecting edge in the initial sensor topology graph or to update the adjacency relationship of the initial sensor topology graph, thereby obtaining the dynamic sensor topology graph.

[0034] Based on the preset pipeline length parameters and the axial flow pump operating condition parameters, the edge delay parameters of each connecting edge in the dynamic sensor topology diagram are calculated.

[0035] Based on the edge delay parameter, historical node features corresponding to the edge delay parameter are read from the online sample sequence, and the historical node features are used as input features of the connecting edge to generate delayed node features;

[0036] When there are no historical node features that satisfy the edge delay parameter in the online sample sequence, the current node features are used as the historical node features to generate the delayed node features.

[0037] Optionally, S5 includes:

[0038] The current node features are combined with the axial flow pump operating condition parameters to form an online sample. The online sample is written into the online sample sequence. When the online sample sequence reaches a preset length, the earliest written online sample is deleted to complete the update.

[0039] The feature alignment loss is calculated based on the updated online sample sequence, and the normalized parameters and feature alignment parameters of the graph neural network ensemble model are updated online according to the feature alignment loss to obtain the adaptive graph neural network ensemble model.

[0040] The dynamic sensor topology is divided into heterogeneous graphs according to sensor type, and the input features associated with each sensor node in the heterogeneous graph are set as delay node features;

[0041] The heterogeneous graph and the delayed node features are input into the adaptive graph neural network ensemble model, so that the at least two heterogeneous graph neural network sub-models output instability risk prediction values ​​and stability margin prediction values ​​respectively. The fusion module then fuses the outputs of the at least two heterogeneous graph neural network sub-models to obtain the adaptive instability risk prediction values ​​and adaptive stability margin prediction values.

[0042] Optionally, S6 includes:

[0043] The operating condition group is determined according to the preset operating condition group division rules and the operating condition parameters of the axial flow pump.

[0044] Read the risk calibration sample and margin calibration sample corresponding to the operating condition group from the calibration sample sequence;

[0045] The time weights for the risk calibration sample and the margin calibration sample are determined according to the time interval between the sample time and the current control cycle, and the inconsistency scores are calculated under the action of the time weights. The inconsistency score of the risk calibration sample is determined by the difference between the instability risk prediction value and the instability state label, and the inconsistency score of the margin calibration sample is determined by the difference between the stability margin prediction value and the stability margin observation value.

[0046] Based on a preset confidence level, risk quantile thresholds are determined for the inconsistency scores of the risk calibration samples, and margin quantile thresholds are determined for the inconsistency scores of the margin calibration samples. The risk quantile thresholds are added to the adaptive instability risk prediction value to construct an upper bound for instability risk, and the margin quantile thresholds are subtracted from the adaptive stability margin prediction value to construct a lower bound for stability margin. The upper bound for instability risk is used to satisfy risk constraints, and the lower bound for stability margin is used to satisfy margin constraints.

[0047] Optionally, the S7 includes:

[0048] A risk assessment result is generated based on the comparison between the upper bound of the instability risk and the preset risk threshold; a margin assessment result is generated based on the comparison between the lower bound of the stability margin and the preset margin threshold; and the control level of the current control cycle is determined based on the risk assessment result and the margin assessment result.

[0049] When the control level of the current control cycle changes relative to the control level of the previous control cycle, the control level of the current control cycle is corrected according to the preset hysteresis threshold, so that the control level of the previous control cycle remains unchanged when the upper bound of the instability risk does not reach the upgrade condition corresponding to the hysteresis threshold, and the control level of the previous control cycle remains unchanged when the lower bound of the stability margin does not reach the downgrade condition corresponding to the hysteresis threshold.

[0050] Control commands are generated based on the revised control level. The control commands include at least one adjustment to the axial flow pump actuator, including speed adjustment of the variable frequency speed control device, opening adjustment of the valve control device, angle adjustment of the guide vane control device, and start / stop control of the exhaust device. The control commands are then sent to the corresponding axial flow pump actuator to adjust the axial flow pump operating parameters.

[0051] Optionally, S8 includes:

[0052] The adaptive instability risk prediction value is combined with the instability state label to form a risk calibration sample, and the adaptive stability margin prediction value is combined with the stability margin observation value to form a margin calibration sample.

[0053] Determine the operating condition group based on the operating parameters of the axial flow pump;

[0054] The risk calibration sample and the margin calibration sample are respectively written into the storage area corresponding to the operating condition group in the calibration sample sequence;

[0055] When the number of samples in the storage area reaches the preset window length, the earliest written sample is deleted to satisfy the sliding window rule, thereby completing the calibration sample sequence update.

[0056] Optionally, the edge delay parameter is determined by the pipeline length parameter and the mixed phase propagation velocity. The mixed phase propagation velocity is obtained by calculating the average flow velocity from the flow rate and the pipeline cross-sectional area and correcting it with the gas characterization parameter. The edge delay parameter is quantized as the number of control cycles to read historical node features from the online sample sequence.

[0057] The beneficial effects of this invention are:

[0058] 1. By establishing a sensor topology based on the physical connection of the pump body and pipeline, and dynamically updating the edge weights or adjacency relationships in combination with operating parameters, and introducing edge delay parameters to read historical node characteristics to participate in message transmission, the propagation process of gas disturbance along the pipeline and the characteristics of multi-measuring point coupling with changing operating conditions can be characterized, thereby improving the accuracy and advance of instability risk and stability margin assessment.

[0059] 2. By utilizing online sample sequences to perform online domain adaptive updates on the graph neural network ensemble model, and constructing heterogeneous graphs according to sensor type to adopt differentiated message update rules, the model can achieve continuous and effective output under gas fluctuation and operating condition drift conditions, thereby improving the robustness and generalization ability of the prediction results.

[0060] 3. By grouping operating conditions and using time-weighted conformal prediction, an upper bound for instability risk and a lower bound for stability margin are constructed. Based on this, graded hysteresis constraint control is implemented to form a quantifiable, calibrable, and less prone to fluctuation closed-loop regulation strategy. This enables the axial flow pump to take timely adjustment measures before instability occurs, thereby improving the operational stability and safety under gas-containing conditions. Attached Figure Description

[0061] 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:

[0062] Figure 1This is a flowchart of a gas-filled stable operation method for an axial flow pump based on ensemble learning proposed in this invention. Detailed Implementation

[0063] 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.

[0064] refer to Figure 1 A method for stable operation of an axial flow pump with gas content based on ensemble learning includes:

[0065] S1. Acquire historical operating data of the axial flow pump, establish sensor nodes and connecting edges based on the physical connection relationship of the axial flow pump and its pipeline, determine the sensor type, train a graph neural network ensemble model based on historical operating data, establish online sample sequences and calibration sample sequences, and initialize the control level; S2. In each control cycle, collect time-series signals from multiple sensors and axial flow pump operating condition parameters, synchronously preprocess the time-series signals and extract the current node features, calculate stability indices based on operating condition parameters and time-series signals, obtain stability margin observations, and generate instability state markers based on preset instability criteria; S3. Load the current node features into the sensor nodes and connecting edges to construct an initial sensor topology graph; S4. Update the edge weights or adjacency relationships of the initial sensor topology graph based on operating condition parameters to obtain a dynamic sensor topology graph, determine the edge delay parameters of each connecting edge based on preset pipeline length parameters and operating condition parameters, and generate delayed node features by reading historical node features from the online sample sequence according to the edge delay parameters; S5. Write the current node features and operating condition parameters into and update the online sample sequence, and use the updated online sample sequence to train the graph neural network ensemble model. The online domain adaptive update constructs a heterogeneous graph of the dynamic sensor topology according to sensor type, and inputs the heterogeneous graph and the features of the delayed nodes into the adaptive graph neural network ensemble model, outputting the adaptive instability risk prediction value and the adaptive stability margin prediction value; S6, the operating condition group is determined according to the operating condition parameters, the calibration samples belonging to the operating condition group are selected from the calibration sample sequence and time weights are applied to calculate the inconsistency score, and the risk quantile threshold and margin quantile threshold corresponding to the preset confidence level are determined respectively, thereby constructing the upper bound of instability risk and the lower bound of stability margin; S7. Determine the control level for this control cycle based on the upper bound of instability risk and the preset risk threshold, and the lower bound of stability margin and the preset margin threshold. Correct the control level based on the preset hysteresis threshold and the control level of the previous control cycle. Generate control commands based on the corrected control level and issue them to adjust the operating parameters. S8. Combine the predicted instability risk value and the instability state marker to form a risk calibration sample. Combine the predicted stability margin value and the observed stability margin value to form a margin calibration sample. Write the risk calibration sample and the margin calibration sample into the storage area corresponding to the operating condition group in the calibration sample sequence and update it.

[0066] In this specific embodiment, S1 includes:

[0067] Historical operating data is read from the historical database of the axial flow pump monitoring system. The historical operating data is divided into control cycles on the time axis and includes time-series signals from multiple sensors and axial flow pump operating condition parameters corresponding to the time-series signals. The axial flow pump operating condition parameters include speed, flow rate, pressure difference, and gas content characterization parameters.

[0068] The timing signal is uniformly timestamped to eliminate the clock deviation between channels caused by the acquisition link. After alignment, noise filtering, outlier removal and amplitude normalization are performed in sequence to obtain the historical node features for training corresponding to each control cycle. The historical node features are constructed as feature vectors with the sensor as the granularity and together with the axial flow pump operating condition parameters of the control cycle to form training samples.

[0069] Subsequently, a fixed sensor topology is established based on the physical connection relationship between the axial flow pump and its pipeline. The fixed sensor topology includes sensor nodes and connecting edges. Each sensor node corresponds to a unique sensor identifier and is bound to its installation position. The connecting edges are determined by the internal flow channel connection relationship of the pump body and the external pipeline connection relationship and the direction is determined according to the main flow direction of the fluid. At the same time, the corresponding pipeline length parameter is fixed and stored for each connecting edge for use in subsequent steps to calculate the propagation delay.

[0070] On the fixed sensor topology, a sensor type is determined for each sensor node. The sensor type is consistent with the sensor physical quantity and is written into the node attribute. The sensor type set includes pressure type, vibration type, electrical parameter type, flow rate type and gas characterization type, so that different sensor types can be explicitly distinguished in the model.

[0071] Based on the historical node features and the axial flow pump operating parameters, a graph neural network ensemble model is trained. The graph neural network ensemble model consists of two heterogeneous graph neural network sub-models and a fusion module. The first heterogeneous graph neural network sub-model adopts a two-layer heterogeneous relational convolutional structure and configures independent linear transformation parameters for nodes of different sensor types to achieve type-related message update rules. The second heterogeneous graph neural network sub-model adopts a two-layer heterogeneous attention aggregation structure and configures independent attention parameters for nodes of different sensor types to achieve type-related message update rules. The hidden feature dimension of both heterogeneous graph neural network sub-models is set to 64, and the inter-layer activation function is ReLU with a random deactivation rate of 0.2 to suppress overfitting. The fusion module performs weighted fusion of the instability risk prediction value and stability margin prediction value output by the two heterogeneous graph neural network sub-models respectively. The fusion weight is a trainable parameter and is updated together with the sub-model parameters during training.

[0072] In terms of constructing training supervision signals, unstable state labels are generated based on the instability criteria consistent with step S2 in historical data as instability risk training labels, and stability margin observations are calculated based on stability indices and stability thresholds as stability margin training labels.

[0073] The training objective function uses a dual-task joint loss and is written as:

[0074] ;

[0075] in, This represents the total training loss of the graph neural network ensemble model. This represents the loss weight of the instability risk task and its value is... Represents the binary cross-entropy loss. This represents the predicted instability risk output by the graph neural network ensemble model, and its value range is... Indicates an unstable state flag with a value of 0 or This represents the loss weight for the stability margin task and takes a value of [value]. This indicates Huber's losses. This represents the stability margin prediction value output by the graph neural network ensemble model. This represents the observed stability margin value calculated from historical data;

[0076] The training process uses the Adam optimizer and sets the learning rate to [missing information]. The batch size is 128, the number of training rounds is 200, and training is stopped when the validation set loss does not decrease for 10 consecutive rounds to fix the final model parameters;

[0077] After offline training is completed, an online sample sequence is established. This online sample sequence is a first-in-first-out circular buffer that is recursively updated according to a control cycle, and the sequence length is set to [value missing]. Each control cycle consists of a set of online samples, each composed of node features and axial flow pump operating parameters for that control cycle, written sequentially over time. The writing process causes the cache to exceed [a certain limit]. The earliest written online sample is deleted to complete the update;

[0078] Simultaneously, a calibration sample sequence is established and a pre-defined operating condition group division rule is set. This rule takes an operating condition parameter vector composed of speed, flow rate, pressure difference, and gas-containing characterization parameters as input and maps it to a discrete operating condition group identifier. The calibration sample sequence is stored in an independent storage area for each operating condition group, and each storage area uses a length of [missing information]. A sliding window is used to store calibration samples for conformal prediction and the oldest sample is deleted when the window is full to keep the window length constant;

[0079] Finally, the initial control level is set to level 0 and written to the controller status register as the initial reference for hysteresis correction in step S7.

[0080] In this specific embodiment, S2 includes:

[0081] The controller operates according to a fixed control cycle. Run, and sample at a fixed frequency in each control cycle. The timing signals of multiple sensors and the operating parameters of the axial flow pump corresponding to the control cycle are collected simultaneously. The operating parameters of the axial flow pump consist of speed, flow rate, pressure difference and gas content characterization parameters, and are written into the same period data frame in a one-to-one correspondence with the timing signals according to the timestamp.

[0082] The synchronization of the timing signals is achieved by sampling triggering and recording with unified timestamps generated by the controller's unified clock. Before feature extraction, alignment verification is performed on all channels. When a channel loses a sample or the timestamp jumps, the control cycle of that channel is marked as invalid and the missing points are filled in by maintaining the unvalued value of the previous control cycle of that channel to ensure dimensional consistency.

[0083] Preprocessing is performed on the aligned timing signal. The preprocessing is carried out in the following order: noise filtering, outlier removal, and amplitude normalization. Noise filtering uses a fourth-order Butterworth low-pass filter with a cutoff frequency of 800 Hz. Outlier removal uses sliding median detection and replaces sampling points that deviate from the median of the control period by three times the absolute deviation of the median with the linear interpolation result of two adjacent points. Amplitude normalization uses the mean and standard deviation of each channel fixed in step S1 to standardize the channel signal to eliminate dimensional differences and ensure the comparability of characteristics of different sensor channels.

[0084] Within the control cycle, current node features corresponding to each sensor are extracted based on the preprocessed time-series signal. These current node features are fixed-length feature vectors with a dimension of 12, and their components include the mean, standard deviation, root mean square, peak-to-peak value, kurtosis, skewness, dominant frequency, dominant frequency amplitude, spectral centroid, low-frequency energy proportion, mid-frequency energy proportion, and high-frequency energy proportion of the signal during the control cycle. The dominant frequency and frequency band energy are determined by the length of the signal during the control cycle. The amplitude spectrum obtained from the fast Fourier transform was calculated, and the low-frequency, mid-frequency, and high-frequency bands were set as follows: and To cover the main frequency bands of head fluctuation and vibration enhancement under gas-bearing conditions;

[0085] Based on the operating parameters of the axial flow pump and the time-series signal, a stability index is calculated. This stability index consists of four components, each representing a normalized value of the outlet pressure pulsation coefficient, the root mean square of bearing vibration, the differential pressure fluctuation coefficient, and the gas content characterization parameter. All four components are mapped to the component statistics solidified in step S1. Normalized components are obtained from the interval. subscript This indicates the current control cycle number and is consistent with the online control cycle counter;

[0086] The stability margin observation value is calculated based on the stability index and the preset stability threshold. The stability margin observation value is defined as follows:

[0087] ;

[0088] in, Indicates the first Stability margin observations for each control period. This indicates a preset stability threshold and its value is [value missing]. This represents the number of components of the stability index and its value. Indicates the first The weights of each component and satisfying and take , Indicates the first Within the first control cycle, the first Normalized component values ​​of each component;

[0089] An instability state marker is generated based on the stability index and a preset instability criterion. The instability criterion is defined as the value of the stability margin observation when the stability margin observation value is... Mark the unstable state at that time Set to 1 and when Mark the unstable state at that time Set to 0, where Used to indicate the first Whether each control cycle enters an unstable state and whether the risk calibration sample construction in subsequent steps is consistent.

[0090] In this specific embodiment, S3 includes:

[0091] When the controller enters the graph construction phase, it reads the set of sensor nodes and the set of connecting edges from the sensor topology configuration table solidified in step S1, and reads the current node features of the current control cycle from the feature cache.

[0092] The sensor topology configuration table stores the sensor identifier and sensor type of each sensor node using the node index as the primary key. The node index is fixedly numbered according to the installation location and data channel order and remains unchanged during system operation. The sensor identifier is a unique code that corresponds one-to-one with the acquisition channel and serves as a feature matching key. The sensor type is one of the following: pressure type, vibration type, electrical parameter type, flow type, or gas characterization type, and is written into the node attributes.

[0093] During feature matching, the controller reads the sensor identifier of each sensor node and retrieves the current node feature vector corresponding to the same sensor identifier in the feature cache of the current control cycle. The retrieved current node feature vector is written into the node feature field of the sensor node to complete the one-to-one matching. When a sensor identifier does not have a valid feature in the feature cache of the current control cycle, the node feature field written by the sensor node in the previous control cycle is used as the current node feature vector to ensure that the node feature dimension and order remain unchanged.

[0094] While keeping the connecting edges unchanged, the controller combines the sensor nodes with the connecting edges that have been written with the current node characteristics to generate an initial sensor topology graph, and serializes the initial sensor topology graph into a graph data structure for subsequent steps. The graph data structure is stored in the form of a node table and an edge table. The node table contains at least a node index, sensor identifier, sensor type and current node characteristic fields, and the edge table contains at least a start node index, an end node index and an edge identifier field, and the direction of the edge is consistent with the fluid current direction established in step S1.

[0095] The initial sensor topology map is in the... Each control cycle is represented as:

[0096] ;

[0097] in, Indicates the first Initial sensor topology for each control cycle This represents a set of sensor nodes, where each element is a sensor node numbered by its node index. This represents a set of connecting edges whose elements are determined by the physical connection relationship between the pump body and the pipeline and remain unchanged in this step. Indicates the first The node feature matrix for each control cycle, with each row corresponding to the current node feature vector written by a sensor node, and maintaining the same arrangement order as the node index. This represents a node type vector, with each element corresponding to the sensor type of a sensor node, and is used to subsequently construct heterogeneous graphs by type.

[0098] In this specific embodiment, S4 includes:

[0099] The controller in Each control cycle reads the initial sensor topology map and reads the axial flow pump operating condition parameters of the control cycle to dynamically update the initial sensor topology map. The dynamic graph update includes edge weight update and adjacency relationship update, and both are performed under the same set of connection edge index system.

[0100] During edge weight update, the controller writes the edge weight for each connection edge in the initial sensor topology graph for that control cycle. The edge weight is calculated by an edge weight update function, which takes rotational speed, flow rate, pressure difference, and gas content characterization parameters as inputs and outputs a value located at... The coupling strength coefficient is implemented by linear weighting and saturation clipping, and the weights corresponding to flow rate are set to 0.5, pressure difference to 0.3, rotation speed to 0.1, and gas characterization parameters to 0.1. The above four inputs are standardized using the mean and standard deviation solidified in step S1 before entering the edge weight update function to ensure comparability under different dimensions.

[0101] When the adjacency relationship is updated, the controller uses the updated edge weight as the criterion and removes the connecting edges with edge weights lower than 0.15 from the adjacency relationship of this control cycle to obtain the dynamic sensor topology map. The direction and endpoint node index of the connecting edges that are not removed are kept unchanged to maintain the physical connection relationship with the pump body and pipeline.

[0102] Subsequently, based on the preset pipeline length parameters and axial flow pump operating condition parameters, the edge delay parameters of each connecting edge in the dynamic sensor topology diagram are calculated. The pipeline length parameters are fixed and stored with the connecting edges and are calibrated by the actual installation dimensions of the pump body and pipeline during system deployment. The edge delay parameters are represented by the number of control cycles and are used to read historical node features from the online sample sequence. The edge delay parameters are calculated using the following formula:

[0103] ;

[0104] in, Indicates the first Within each control cycle, the connection edge The edge delay parameter is expressed in control cycles. Indicates connecting edges Pipeline length parameters corresponding to the pipe section, in units of Indicates the first Within each control cycle, the connection edge The corresponding mixed phase propagation speed and the unit is Indicates the duration of the control cycle and its value is This indicates the floor operator, and 0.5 indicates the bias term used to implement rounding. This indicates the control cycle number and is generated by incrementing the controller cycle counter. This indicates the identifier of the connecting edge and is consistent with the edge table index;

[0105] The propagation speed of the mixed phase The flow and connection edges of this control cycle The average flow velocity is determined by calculating the cross-sectional area of ​​the corresponding pipe section, and the average flow velocity is reduced and corrected using gas-containing characterization parameters to reflect the propagation lag caused by gas content. At the same time, a lower limit constraint is applied to the corrected mixed-phase propagation velocity. To avoid non-physical infinite latency under low-volume operating conditions;

[0106] In obtaining Then, the controller presses... Historical node features are read from the online sample sequence to generate delayed node features. The online sample sequence stores node features according to the control cycle, and each record contains the current node features of all sensor nodes in the corresponding control cycle while maintaining the node index order. The controller processes each connection edge... Indexed by its starting node Use the query key and time offset To query the offset, read the first sample from the online sample sequence. The starting point of each control cycle Corresponding to the historical node features, and using these historical node features as the input features of the connection edge to participate in subsequent message passing;

[0107] To ensure that each sensor node has input features with fixed dimensions when inputting heterogeneous graphs in subsequent cycles, the controller performs a weighted summation of the historical node features corresponding to all incoming edges of each sensor node according to the edge weight of the control cycle to obtain an incoming edge aggregation vector. This incoming edge aggregation vector is then concatenated with the current node features of the node in a fixed order to form the delayed node features of the node. This results in the delayed node features containing both "local observations in the current cycle" and "upstream historical observations aligned with propagation delay".

[0108] When there is no such condition in the online sample sequence When the index's history or corresponding history is marked as invalid, the controller will select the starting node. In the The current node features of each control cycle replace the historical node features, and the incoming edge aggregation and splicing are continued to generate delayed node features.

[0109] In this specific embodiment, S5 includes:

[0110] The controller in Each control cycle receives a dynamic sensor topology diagram and the delay node characteristics of each sensor node, as well as the operating parameters of the axial flow pump.

[0111] The controller stacks the current node features of all sensor nodes in the current control cycle according to their node index order to form a node feature matrix, and writes it into the online sample sequence along with the axial flow pump operating parameters. The online sample sequence is a first-in-first-out circular buffer with a fixed length. A control cycle, when a write causes the cache length to exceed [a certain value]. The earliest written online sample is deleted in time to complete the update, thereby ensuring that the historical node features can be retrieved within the cache window for any subsequent edge delay parameters;

[0112] After completing the online sample sequence update, an online domain adaptive update is performed. This online domain adaptive update only updates the normalization parameters and feature alignment parameters in the graph neural network ensemble model, while keeping the weights of the remaining networks unchanged. The normalization parameters are the running mean and running variance of each normalization layer, adjusted according to the momentum coefficient. In each control cycle, the feature alignment parameter is updated recursively. It is an affine alignment layer parameter set at the input of the graph neural network ensemble model and includes a scaling vector and a translation vector. A dimension-wise linear transformation is performed on each input feature to eliminate the feature distribution shift caused by the operating condition drift.

[0113] The feature alignment loss is calculated based on the updated online sample sequence, and the controller truncates the most recent features from the online sample sequence. The node feature matrix of each control cycle is used as the online feature batch, and the source domain feature statistics solidified in the offline training stage of step S1 are used as the alignment reference. The source domain feature statistics include the source domain feature mean vector and the source domain feature covariance matrix, and are calculated from all historical node features when offline training is completed and stored in the model parameter area of ​​the controller.

[0114] Feature alignment loss is calculated using the following formula:

[0115] ;

[0116] in, Indicates the first Feature alignment loss per control cycle This represents the online feature mean vector calculated from the online feature batch and then averaged along the feature dimension. Represents the source domain feature mean vector. This represents the online feature covariance matrix obtained by the online feature batch calculation, calculated pairwise by feature dimension. Represents the source domain characteristic covariance matrix. Represents the L2 norm, Denotes the Frobenius norm;

[0117] The controller uses gradient descent with a fixed number of steps to perform online updates to the feature alignment parameters, where the number of online update steps is set to... And the learning rate is set to Furthermore, after each update step, the feature alignment parameters are cropped to a preset range to avoid numerical divergence caused by overcompensation. The preset range is defined as the range where each dimension of the scaling vector is located within a certain range. And each dimension of the translation vector is located at ;

[0118] After completing the online domain adaptive update, the controller constructs a heterogeneous graph of the dynamic sensor topology according to sensor type. The set of node types in the heterogeneous graph is consistent with that in step S1, and the sensor type is used as the node type identifier. The edge type of the heterogeneous graph is determined by the start node type and end node type of the connecting edge, and the edge direction is kept consistent with the dynamic sensor topology. Figure 1 Simultaneously, the input features associated with each sensor node in the heterogeneous graph are set as delayed node features so that message passing uses historical observations aligned by propagation delay;

[0119] The controller feeds the heterogeneous graph and its node input features into the adaptive graph neural network ensemble model to perform forward inference. At least two heterogeneous graph neural network sub-models of the graph neural network ensemble model perform differentiated message updates according to node type and edge type, and output instability risk prediction value and stability margin prediction value respectively. The fusion module performs weighted fusion on the outputs of the two sub-models with the same name to obtain the adaptive instability risk prediction value and the adaptive stability margin prediction value, and writes them into the prediction cache of the current control cycle.

[0120] In this specific embodiment, S6 includes:

[0121] The controller in Each control cycle reads the adaptive instability risk prediction value and the adaptive stability margin prediction value, and reads the axial flow pump operating condition parameters for that control cycle to determine the operating condition group.

[0122] The operating condition set is jointly indexed by four operating condition components: speed, flow rate, pressure difference, and gas content characterization parameters. The controller first standardizes the four operating condition components using the mean and standard deviation solidified in step S1, and then truncates them to limit them to a certain range. Intervals, then by intervals respectively The discrete gears of the four working condition components are obtained by quantization and spliced ​​together according to a fixed coding rule to form a working condition group identifier, so that each control cycle corresponds to a unique working condition group and the same working condition group corresponds to a similar working condition distribution.

[0123] The controller reads the risk calibration sample and margin calibration sample corresponding to the operating condition group from the calibration sample sequence according to the operating condition group identifier. The risk calibration sample consists of the instability risk prediction value and instability state mark of the historical control cycle. The margin calibration sample consists of the stability margin prediction value and stability margin observation value of the historical control cycle. Both types of calibration samples are stored in their respective operating condition group storage areas in chronological order and satisfy the sliding window rule.

[0124] When the number of samples in the storage area of ​​the working condition group is less than 200, the controller will expand the reading range to include the union of the working condition group and its neighboring working condition groups with a Manhattan distance of 1 in the four-dimensional gear space to ensure that the number of calibration samples meets the quantile estimation requirements.

[0125] The controller then calculates the inconsistency score and applies time weights to the read risk calibration sample and margin calibration sample respectively. The inconsistency score of the risk calibration sample is determined by the absolute difference between the predicted instability risk value and the instability state label in the sample. The inconsistency score of the margin calibration sample is determined by the absolute difference between the predicted stability margin value and the observed stability margin value in the sample. The time weight is determined by the interval between the sample time and the current control cycle time and adopts an exponential decay form. The controller converts the time interval by the difference between the control cycle number to which the sample belongs and the current control cycle number and calculates the time weight accordingly, so that the calibration sample closer to the current control cycle has a greater weight.

[0126] After obtaining the time-weighted set of inconsistent scores, the controller calculates the weighted quantile thresholds corresponding to the preset confidence level for both the risk inconsistency score set and the margin inconsistency score set. The confidence level is set as follows: and The weighted quantile threshold is determined by sorting the inconsistency scores from smallest to largest and calculating the corresponding cumulative proportion of time weight. When the cumulative proportion is not less than 0.95 for the first time, the inconsistency score at that position is taken as the quantile threshold, thus obtaining the risk quantile threshold and the margin quantile threshold respectively.

[0127] Finally, the controller applies the quantile threshold to the point prediction of this control cycle to construct an upper bound for instability risk and a lower bound for stability margin, and writes it to the boundary cache of this control cycle for use in step S7. The constructed relationship is as follows:

[0128] ;

[0129] in, Indicates the first The upper bound of the instability risk for each control cycle. Indicates the first The predicted value of instability risk after adaptation for each control cycle. This represents the risk quantile threshold calculated from the set of risk inconsistencies at the stated confidence level. Indicates the first The lower bound of the stability margin for each control cycle. Indicates the first The adaptive stability margin prediction value for each control cycle. This represents the margin quantile threshold calculated from the margin inconsistency score set at the stated confidence level. It indicates the control cycle number and is consistent with the controller cycle counter.

[0130] In this specific embodiment, S7 includes:

[0131] The controller in Each control cycle reads the upper bound of instability risk from the boundary buffer. With the lower bound of stability margin And read the control level of the previous control cycle from the controller status register. Used as a reference for hysteresis correction, where Indicates the first The upper bound of the instability risk for each control cycle and its range is [value missing]. Indicates the first The lower bound of the stability margin for each control period, and with the same dimensions as the observed stability margin. Indicates the first The control level is effective for each control cycle and has a value of 0, 1, or 2.

[0132] Controller pre-cured risk threshold With margin threshold Based on the comparison results, risk assessment results and margin assessment results are generated, and then the candidate control level for this control cycle is calculated. The calculation method is as follows:

[0133] ;

[0134] in, Indicates the first The candidate control level for each control cycle before hysteresis correction and its value is... or This indicates an indicator function that takes the value 1 when the condition within the parentheses is true, and otherwise takes the value _____. Indicates the first The upper bound of the instability risk for each control cycle. This indicates a preset risk threshold. Indicates the first The lower bound of the stability margin for each control cycle. Indicates the preset margin threshold;

[0135] When candidate control level Control level relative to the previous control cycle When changes occur, the controller adjusts the candidate control level according to the preset hysteresis threshold. The control level effective for this control cycle is obtained by making corrections. The risk hysteresis threshold used for upgrade determination is denoted as And the margin hysteresis threshold used for downgrade determination is denoted as ;

[0136] In terms of upgrade direction, when And simultaneously satisfy and At that time, the controller remains To avoid frequent upgrades caused by boundary estimation jitter, otherwise... ;

[0137] In the direction of demotion, when And simultaneously satisfy At that time, the controller remains To avoid premature downgrading before the lower bound of the margin has stabilized and recovered, otherwise... ;

[0138] After obtaining the effective control level Subsequently, the controller generates and issues control commands based on the control level, the control commands including the speed command of the variable frequency speed regulator. Valve regulating device opening command Angle commands for guide vane adjustment device and start / stop commands for the exhaust system ,in The unit is The unit is The unit is A value of 0 or 1 represents stopping and starting, respectively;

[0139] Controller fixed rated speed The actuator safety limit and slope limit are set, with the speed command limit range being [specified range]. And the upper limit of the rate of change of rotational speed is The valve opening command limit range is And the upper limit of the opening change rate is The guide vane angle command limit range is And the upper limit of the rate of change of angle is ;

[0140] when At that time, the controller remains and Parallel to the previous control cycle instruction To maintain the current operating conditions;

[0141] when At that time, the controller will reduce the speed command while meeting the slope limit and amplitude limit constraints. Increase the valve opening command. Adjust the guide vane angle command in the direction of load reduction. , and place To enhance exhaust capacity;

[0142] when At that time, the controller will reduce the speed command while meeting the slope limit and amplitude limit constraints. Increase the valve opening command. Adjust the guide vane angle command in the direction of load reduction. and keep To rapidly reduce the risk of gas-bearing instability and improve stability margin;

[0143] The controller will write the aforementioned control commands into the target registers of the frequency converter, valve actuator, guide vane actuator, and exhaust device via the fieldbus during this control cycle and perform consistency verification on the readback values. If the deviation between the readback value and the issued value exceeds the preset tolerance, it will... Lock to 2 and trigger the fault flag to enter conservative control mode.

[0144] In this specific embodiment, S8 includes:

[0145] The controller in At the end of each control cycle, the adaptive instability risk prediction value is read. With the adapted stability margin prediction and read the instability state flag. With stability margin observations Simultaneously read the control cycle timestamp given by the controller cycle counter. To ensure that calibration samples can be updated in chronological order;

[0146] The controller will and Combine to form risk calibration samples and and The two types of calibration samples are combined to form a margin calibration sample, and both types of calibration samples carry timestamps to support time-weighted conformal prediction. The two types of calibration samples are defined as follows: and ,in, Indicates the first Risk calibration samples for each control cycle Indicates the first The predicted instability risk after adaptation for each control cycle, with a value range of [value missing]. Indicates the first The instability state flag for each control cycle, with a value of 0 or... Indicates the first Each control cycle has a timestamp generated by the controller cycle counter and corresponds one-to-one with the control cycle. Indicates the first Margin calibration samples for each control cycle, Indicates the first The adaptive stability margin prediction value for each control cycle. Indicates the first Stability margin observations for each control cycle;

[0147] Subsequently, the controller follows the... Determine the operating condition parameters and operating condition group identifier for each control cycle of the axial flow pump. The operating condition group identifier The determination rules are consistent with those in step S6, and the same working condition group corresponds to the same storage area index, so that the conformal prediction calibration is performed on a sample set with approximately consistent condition distribution.

[0148] The controller locates the operating condition group identifier within the calibration sample sequence. The corresponding storage area, and the risk calibration samples Write the risk queue to this storage area and perform margin calibration samples. Write to the margin queue of this storage area. Both the risk queue and the margin queue are implemented using a first-in-first-out circular cache and maintain write pointers and sample counts respectively to ensure the determinism of writing and deletion.

[0149] When the number of samples in any queue within the storage area reaches the preset window length At that time, the controller executes the sliding window rules and deletes the earliest written sample in the queue, while updating the read / write pointers and sample count to maintain a constant window length, thereby completing the operation with the working condition group. The corresponding calibration sample sequence is updated, and the latest set of calibration samples that can be directly read is provided for step S6 of the next control cycle.

[0150] In this specific embodiment, when the controller calculates the edge delay parameters of each connected edge in step S4, it will connect the edges... Corresponding pipe length parameters Together with the mixed phase propagation velocity, the pipe length parameter is used to determine the side delay parameter. During the system deployment phase, the actual installation dimensions of the pump body and pipeline are calibrated and stored in the connection edge parameter table, and correspond one-to-one with the connection edge identifier;

[0151] The propagation velocity of the mixed phase is at the th The average flow velocity calculated from the flow rate and pipeline cross-sectional area within each control cycle is then corrected using gas-containing characterization parameters. The flow rate is the operating parameter acquired in step S2 and synchronized, denoted as […]. The cross-sectional area of ​​the pipeline is the cross-sectional area corresponding to the inner diameter of the pipe section as specified in the connection side parameter table. The gas-containing characterization parameters are those collected in step S2 and synchronized, and are denoted as follows: and Constrained The interval represents the change in gas content from zero gas content to high gas content;

[0152] The controller will average the flow rate Multiply by the gas content correction factor The corrected propagation velocity is obtained, and a lower limit constraint is applied to the corrected propagation velocity to avoid large non-physical time delays caused by low flow rates or high gas content. The proportional coefficient of the gas content correction factor is set to [value missing]. The lower limit of the propagation speed is set as ;

[0153] After obtaining the propagation speed, the controller quantizes the side delay parameter into the number of control cycles for reading historical node features from the online sample sequence. The quantization is performed by rounding to the nearest integer control cycle and calculated using the following formula:

[0154] ;

[0155] in, Indicates connecting edges In the The side delay parameter for each control cycle, with the unit being the number of control cycles. Indicates connecting edges The corresponding pipe length parameters and the unit is Indicates the duration of the control cycle and its value is Indicates the lower limit of propagation speed and the unit is Indicates the first The flow rate of each control cycle, and the unit is... Indicates connecting edges The cross-sectional area of ​​the corresponding pipe section, in units of This represents the gas content correction ratio and its value is... Indicates the first The gas-bearing characterization parameters for each control cycle, with a value range of [value range missing]. , The operator indicating that taking the larger value is used to implement the lower bound constraint on the propagation speed, This indicates the floor operator, and 0.5 indicates the bias term used to implement rounding. Indicates the connection edge identifier. Indicates the control cycle number;

[0156] The controller will calculate The edge attributes are written as unsigned integers to the dynamic sensor topology graph and subsequently offset from the online sample sequence over time. Read the corresponding historical node features to generate delayed node features so that message passing uses upstream historical observations aligned with pipeline propagation lag.

[0157] 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.

[0158] This invention integrates sensor topology modeling, online adaptive prediction, and confidence boundary constraint control into a closed-loop link: First, a sensor topology graph is constructed based on the physical connection relationship of the axial flow pump and pipeline, and multi-source time-series signals are fused in the graph structure; then, in each control cycle, the edge weights or adjacency relationships of the graph are dynamically updated based on operating conditions such as rotational speed, valve opening, flow rate, differential pressure, and gas characterization parameters, and pipeline propagation delay parameters are introduced to enable historical node features to participate in message transmission along the edges, so as to more closely approximate the real mechanism of gas disturbance propagation along the pipeline and multi-measuring point coupling changing with operating conditions; Furthermore, by combining online domain adaptation, the model can still stably output instability risk prediction and stability margin prediction values ​​under operating condition drift and gas-containing fluctuations. In addition, by constructing upper bounds for instability risk and lower bounds for stability margin through operating condition grouping and time-weighted conformal prediction, the prediction results have calibrable and credible boundaries. Finally, the upper bounds and lower bounds are used as constraints to trigger graded hysteresis control and output adjustment commands to actuators such as variable frequency speed, valves, guide vanes and exhaust, thereby achieving quantifiable, verifiable and non-vibrating adjustment decisions before instability occurs, and achieving the technical effect of stable operation under gas-containing conditions.

[0159] This invention incorporates improvements for engineering feasibility: First, it proposes an integrated structure of a heterogeneous graph neural network with a dynamic graph driven by operating conditions and time-delayed edges. This structure reflects the coupling strength as the operating conditions change through dynamic edge weights or adjacency relationships, expresses the disturbance propagation lag through edge time delay parameters, and employs differentiated message update rules for different sensor types such as pressure, vibration, and electrical parameters. Simultaneously, it jointly outputs two types of task results: instability risk and stability margin, thereby enhancing the characterization and lead time of instability evolution. Second, it proposes a conditional and time-weighted conformal prediction calibration method. Based on operating condition grouping, it uses a sliding window and time weights to recursively update inconsistency scores, enabling the output to directly form an upper bound for instability risk or a lower bound for stability margin, facilitating its use as a safety constraint in control. Third, it proposes a hierarchical hysteresis constraint control strategy based on upper and lower bounds to avoid frequent jitter caused by single-threshold control, and establishes a clear mapping between the prediction boundary and actuator adjustment, thereby more reliably achieving stable and safe operation under gas-containing conditions.

Claims

1. A method for stable operation of an axial flow pump with gas content based on ensemble learning, comprising: S1. Obtain historical operating data of the axial flow pump, establish sensor nodes and connection edges based on the physical connection relationship of the axial flow pump and its pipeline, determine the sensor type, train a graph neural network ensemble model based on historical operating data, establish online sample sequences and calibration sample sequences, and initialize the control level; S2. In each control cycle, collect time-series signals from multiple sensors and operating parameters of the axial flow pump. Synchronously preprocess the time-series signals and extract the current node features. Calculate the stability index based on the operating parameters and time-series signals to obtain the stability margin observation value. Generate an instability state marker according to the preset instability criterion. S3. Load the current node features into the sensor nodes and connection edges to construct the initial sensor topology. S4. Update the edge weights or adjacency relationships of the initial sensor topology map according to the operating conditions to obtain the dynamic sensor topology map, and determine the edge delay parameters of each connecting edge according to the preset pipeline length parameters and operating conditions. Read the historical node features from the online sample sequence according to the edge delay parameters to generate delayed node features. S5. Write the current node features and operating parameters into and update the online sample sequence. Use the updated online sample sequence to perform online domain adaptive update of the graph neural network ensemble model. Construct the dynamic sensor topology map into a heterogeneous map according to sensor type. Input the heterogeneous map and the delayed node features into the adaptive graph neural network ensemble model. Output the adaptive instability risk prediction value and the adaptive stability margin prediction value. S6. Determine the operating condition group based on the operating condition parameters, select calibration samples belonging to the operating condition group from the calibration sample sequence and apply time weights to calculate the inconsistency score, and determine the risk quantile threshold and margin quantile threshold corresponding to the preset confidence level respectively, thereby constructing the upper bound of instability risk and the lower bound of stability margin. S7. Determine the control level for this control cycle based on the upper bound of instability risk and the preset risk threshold, and the lower bound of stability margin and the preset margin threshold. Then, make corrections based on the preset hysteresis threshold and the control level of the previous control cycle. Generate control commands based on the corrected control level and issue them to adjust the operating parameters. S8. Combine the predicted instability risk value and the instability state label to form a risk calibration sample, combine the predicted stability margin value and the observed stability margin value to form a margin calibration sample, and write the risk calibration sample and the margin calibration sample into the storage area corresponding to the operating condition group in the calibration sample sequence and update it.

2. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S1 includes: The historical operating data includes time-series signals from multiple sensors and axial flow pump operating parameters corresponding to the time-series signals. The historical running data is acquired and the time-series signal is synchronized and preprocessed to form historical node features for training. Based on the physical connection relationship between the axial flow pump and its pipeline, fixed sensor nodes and connection edges are established, and the sensor type is determined for each sensor node. The graph neural network ensemble model is trained based on the historical node features and the axial flow pump operating parameters, so that the at least two heterogeneous graph neural network sub-models output instability risk prediction values ​​and stability margin prediction values ​​respectively for different sensor type nodes using different message update rules, and the fusion module fuses the outputs of the at least two heterogeneous graph neural network sub-models. The online sample sequence is established, and the sequence length and update rules of the online sample sequence are set so that the online sample sequence can be used to store node features and axial flow pump operating condition parameters according to the control cycle. Establish the calibration sample sequence and preset the division rules of the operating condition group, so that the calibration sample sequence is stored according to the operating condition group for calibration samples used for conformal prediction; Set the initial control level.

3. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S2 includes: The operating parameters of the axial flow pump include speed, flow rate, pressure difference, and gas content characterization parameters. In each control cycle, the timing signals of multiple sensors and the operating parameters of the axial flow pump in the current control cycle are collected according to the preset sampling frequency. The time-series signal is synchronized and aligned according to the timestamp, and preprocessed by noise filtering, outlier removal and amplitude normalization. Based on the preprocessed timing signal, the current node features corresponding to each sensor are extracted within the control cycle; Stability indices are calculated based on the operating parameters of the axial flow pump and the timing signal. The stability margin observation value is calculated based on the stability index and the preset stability threshold; An instability state marker is generated based on the stability index and the preset instability criterion.

4. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S3 includes: According to the sensor node and the sensor identifier corresponding to the sensor node, the current node features are matched one by one to the corresponding sensor node; While keeping the connecting edges unchanged, the sensor nodes containing the characteristics of the current node are combined with the connecting edges to construct the initial sensor topology graph; The initial sensor topology graph includes the sensor nodes, the connecting edges, the current node features corresponding to each sensor node, and the sensor type corresponding to each sensor node.

5. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S4 includes: The operating parameters of the axial flow pump are input into the edge weight update function to update the edge weight of at least one connecting edge in the initial sensor topology graph or to update the adjacency relationship of the initial sensor topology graph, thereby obtaining the dynamic sensor topology graph. Based on the preset pipeline length parameters and the axial flow pump operating condition parameters, the edge delay parameters of each connecting edge in the dynamic sensor topology diagram are calculated. Based on the edge delay parameter, historical node features corresponding to the edge delay parameter are read from the online sample sequence, and the historical node features are used as input features of the connecting edge to generate delayed node features; When there are no historical node features that satisfy the edge delay parameter in the online sample sequence, the current node features are used as the historical node features to generate the delayed node features.

6. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S5 includes: The current node features are combined with the axial flow pump operating condition parameters to form an online sample. The online sample is written into the online sample sequence. When the online sample sequence reaches a preset length, the earliest written online sample is deleted to complete the update. The feature alignment loss is calculated based on the updated online sample sequence, and the normalized parameters and feature alignment parameters of the graph neural network ensemble model are updated online according to the feature alignment loss to obtain the adaptive graph neural network ensemble model. The dynamic sensor topology is divided into heterogeneous graphs according to sensor type, and the input features associated with each sensor node in the heterogeneous graph are set as delay node features; The heterogeneous graph and the delayed node features are input into the adaptive graph neural network ensemble model, so that the at least two heterogeneous graph neural network sub-models output instability risk prediction values ​​and stability margin prediction values ​​respectively. The fusion module then fuses the outputs of the at least two heterogeneous graph neural network sub-models to obtain the adaptive instability risk prediction values ​​and adaptive stability margin prediction values.

7. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S6 includes: The operating condition group is determined according to the preset operating condition group division rules and the operating condition parameters of the axial flow pump. Read the risk calibration sample and margin calibration sample corresponding to the operating condition group from the calibration sample sequence; The time weights for the risk calibration sample and the margin calibration sample are determined according to the time interval between the sample time and the current control cycle, and the inconsistency scores are calculated under the action of the time weights. The inconsistency score of the risk calibration sample is determined by the difference between the instability risk prediction value and the instability state label, and the inconsistency score of the margin calibration sample is determined by the difference between the stability margin prediction value and the stability margin observation value. Based on a preset confidence level, risk quantile thresholds are determined for the inconsistency scores of the risk calibration samples, and margin quantile thresholds are determined for the inconsistency scores of the margin calibration samples. The risk quantile thresholds are added to the adaptive instability risk prediction value to construct an upper bound for instability risk, and the margin quantile thresholds are subtracted from the adaptive stability margin prediction value to construct a lower bound for stability margin. The upper bound for instability risk is used to satisfy risk constraints, and the lower bound for stability margin is used to satisfy margin constraints.

8. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S7 includes: A risk assessment result is generated based on the comparison between the upper bound of the instability risk and the preset risk threshold; a margin assessment result is generated based on the comparison between the lower bound of the stability margin and the preset margin threshold; and the control level of the current control cycle is determined based on the risk assessment result and the margin assessment result. When the control level of the current control cycle changes relative to the control level of the previous control cycle, the control level of the current control cycle is corrected according to the preset hysteresis threshold, so that the control level of the previous control cycle remains unchanged when the upper bound of the instability risk does not reach the upgrade condition corresponding to the hysteresis threshold, and the control level of the previous control cycle remains unchanged when the lower bound of the stability margin does not reach the downgrade condition corresponding to the hysteresis threshold. Control commands are generated based on the revised control level. The control commands include at least one adjustment to the axial flow pump actuator, including speed adjustment of the variable frequency speed control device, opening adjustment of the valve control device, angle adjustment of the guide vane control device, and start / stop control of the exhaust device. The control commands are then sent to the corresponding axial flow pump actuator to adjust the axial flow pump operating parameters.

9. The method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 1, S8 includes: The adaptive instability risk prediction value is combined with the instability state label to form a risk calibration sample, and the adaptive stability margin prediction value is combined with the stability margin observation value to form a margin calibration sample. Determine the operating condition group based on the operating parameters of the axial flow pump; The risk calibration sample and the margin calibration sample are respectively written into the storage area corresponding to the operating condition group in the calibration sample sequence; When the number of samples in the storage area reaches the preset window length, the earliest written sample is deleted to satisfy the sliding window rule, thereby completing the calibration sample sequence update.

10. A method for stable operation of an axial flow pump with gas based on ensemble learning according to claim 5, characterized in that, The edge delay parameter is determined by the pipeline length parameter and the mixed phase propagation velocity. The mixed phase propagation velocity is obtained by calculating the average flow velocity from the flow rate and the pipeline cross-sectional area and correcting it with the gas characterization parameter. The edge delay parameter is quantized as the number of control cycles to read historical node features from the online sample sequence.

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