A physical-guided pump-turbine variable operating condition unsupervised fault early warning method

Abstract

The application discloses a kind of physical guiding water pump water turbine variable working condition unsupervised fault early warning method.The application is aimed at the problem that monitoring signal is strong non-stationary under transition condition, normal condition migration and fault degradation is highly aliasing, a kind of physical knowledge guided early warning framework is designed.Firstly, a physical constraint trend decomposition module is proposed, the theoretical dynamic response is generated as the trend component by identifying time-varying equivalent physical parameters and combining mechanism model, the deviation between monitoring signal and theoretical response is used as disturbance component, signal decoupling with physical consistency is realized;Then, a multi-scale adaptive fusion mechanism is designed, the non-stationary intensity index is generated by defining the guide vane opening rate of change, and the multi-scale information is fused through learnable weight network and consistency loss, to construct trend perception Transformer to learn the joint evolution law of balance state and disturbance state under healthy working condition;Finally, balance state migration index and disturbance cumulative index are defined, the prediction error is decomposed into physical dimensions that can be independently explained, combined with dynamic working condition memory mechanism to realize the adaptive expansion of health benchmark space, effectively distinguish normal condition switching and fault degradation.The method significantly improves the accuracy and generalization ability of unsupervised fault early warning under variable working condition.

Description

Technical Field

[0001] This invention relates to the field of condition monitoring and fault diagnosis technology for pumped storage units, specifically to a physically guided, unsupervised fault early warning method and system for pump-turbines operating under varying conditions. This invention is particularly suitable for early fault warning of hydraulic machinery such as turbines and pump-turbines under highly unstable transient conditions such as start-up, shutdown, and load regulation. Background Technology

[0002] As the global energy structure shifts towards cleaner energy, hydropower, as a stable and renewable clean energy source, is becoming increasingly important. To improve the grid's capacity to absorb intermittent renewable energy sources such as wind and solar power, the peak-shaving, valley-filling, and frequency regulation functions of pumped storage power stations and their core equipment, pump-turbines, have become crucial. As the core equipment of pumped storage power stations, pump-turbines operate under transitional conditions such as start-up, shutdown, and load regulation for extended periods. Their hydraulic stability directly affects unit safety and the flexibility of power station dispatch. Hydraulic imbalance is a common early abnormal state during unit operation; if not detected in time, it can develop into serious runner damage or structural vibration failure. However, monitoring signals under transitional conditions exhibit strong non-stationary characteristics, with normal operating conditions and early fault symptoms highly overlapping in the time and frequency domains, posing a significant challenge to early warning systems.

[0003] Currently, fault early warning methods can be mainly categorized into three types: those based on signal decomposition, those based on reconstruction error, and those based on prediction error. Methods based on signal decomposition (such as moving average, wavelet transform, EMD, and VMD) use statistical methods to separate the signal into trend and fluctuation terms, achieving early warning by monitoring trend changes or fluctuation energy. However, their decomposition is based on the signal's frequency or statistical characteristics. Under transitional operating conditions, normal state transitions caused by changes in operating conditions and abnormal deviations induced by faults may have similar frequency band distributions, leading to a lack of physical interpretability in the decomposition results and difficulty in distinguishing between "normal operating condition changes" and "fault degradation." Methods based on reconstruction error (such as autoencoders and their variants) learn the data distribution of healthy states and use reconstruction error as an anomaly indicator. They perform well when operating conditions are relatively stable, but when faced with transitional processes not seen during the training phase, the reconstruction error is prone to increase significantly due to distribution shift, resulting in a high false alarm rate. Methods based on prediction error (such as LSTM and Transformer) use time-series models to predict monitored variables and judge anomalies through prediction residuals. However, existing methods typically model the original non-stationary signal directly, failing to decouple the deterministic dynamics caused by changes in operating conditions from the random disturbances caused by faults. The two components are confused in the prediction error, making it difficult to reflect fault evolution information separately.

[0004] The core challenge of the aforementioned methods lies in the fact that the monitoring signals of pump-turbine systems under transient operating conditions are a coupling of dynamic response to the operating condition and abnormal disturbances caused by faults. The lack of physically guided signal decomposition and modeling methods makes it difficult to effectively separate these two aspects. Specifically, at the decomposition level, traditional statistical decomposition methods rely solely on frequency characteristics, failing to assign physical meaning to the decomposition results, leading to a mixture of trends and disturbances. At the discrimination level, even if effective decomposition is achieved, normal operating condition transitions and fault degradation exhibit highly similar temporal patterns—the former manifests as equilibrium state migration accompanied by a transient increase in disturbance followed by recovery, while the latter manifests as abnormal shifts in equilibrium state accompanied by continuous accumulation of disturbance—traditional methods based on a single deviation index struggle to distinguish between the two. Furthermore, a fixed health baseline space cannot cover new operating conditions not encountered during the training phase under open operating conditions, leading to normal operating condition transitions being misjudged as faults.

[0005] To overcome the limitations of the aforementioned methods, hybrid modeling methods that integrate physical mechanisms and data-driven approaches have gradually gained attention from scholars. Among them, Physical Information Neural Networks (PINNs), as a hybrid modeling method that integrates physical laws and deep learning frameworks, have shown unique advantages in the field of complex system modeling. However, existing PINN methods still suffer from problems such as insufficient capture of time-series trends and limited ability to identify dynamic operating conditions and fault disturbances when facing non-stationary scenarios such as the transient operating conditions of water pumps and turbines, which involve complex features such as operating condition changes, random shocks, and time-varying parameters.

[0006] In summary, there is an urgent need for an unsupervised early warning method that can deeply integrate physical mechanisms with data-driven approaches, effectively decouple dynamic operating conditions from fault disturbances, and possess open operating condition adaptive capabilities. Summary of the Invention

[0007] This invention addresses the shortcomings of existing technologies and the difficulties in early warning of variable operating conditions in pump-turbine systems. Based on a hybrid modeling approach combining physical-guided state decoupling and evolutionary analysis, it designs an unsupervised fault early warning method. Compared to commonly used early warning methods, this invention not only achieves interpretable decomposition of trends and disturbances through physical constraints, but also effectively distinguishes between normal operating condition transitions and fault degradation through a joint discrimination mechanism, and achieves adaptive expansion of the health baseline space through a dynamic memory mechanism.

[0008] This invention first proposes a Physically Constrained Trend Decomposition Module (PCTD), which embeds a mechanistic model into the parameter identification process using differentiable physical equations. Through the identification of time-varying equivalent physical parameters within a sliding window, it generates a theoretical equilibrium response that satisfies physical laws as a trend component, thereby decoupling the original signal into a physical equilibrium trend and a disturbance deviation. Then, a multi-scale adaptive fusion mechanism is designed. A non-stationary intensity index is defined using the guide vane opening change rate to generate physical prior weights. A learnable weight network and consistency loss are used to organically combine data-driven approaches with physical priors, thus adaptively integrating decomposition results from different time scales. Based on this, a trend-aware Transformer is constructed to learn the joint evolution law of equilibrium and disturbance dynamics under healthy operating conditions and predict future trajectories. Finally, the Equilibrium Migration Index (EMI) and Disturbance Accumulation Index (DAI) are defined to decompose the prediction error into two independently interpretable physical dimensions. A Dynamic Operating Condition Memory (DOM) mechanism is introduced, and adaptive early warning under open operating conditions is achieved through operating condition prototype matching and incremental updates.

[0009] The technical solution of the present invention is as follows:

[0010] First, based on the physical characteristics of the pump-turbine under varying operating conditions, this invention defines monitoring signals and early warning targets. Monitoring signals include flow rate Q, guide vane opening α, head H, rotational speed ω, volute inlet pressure p_sp, bladeless zone pressure p_vl, draft tube inlet pressure p_dt1, and draft tube cone pressure p_dt2. Early warning targets are early faults such as unsupervised detection of hydraulic imbalance, requiring no fault labels.

[0011] Under complex and variable operating conditions, the monitoring signal of the pump-turbine is simultaneously modulated by both operating condition adjustments and fault evolution. For a healthy unit, although operating parameters change with load adjustments, the system always satisfies the internal energy conservation relationship and flow mechanism constraints, and its dynamic response should evolve around the physical equilibrium state corresponding to the current operating condition. When faults such as hydraulic imbalance gradually form, the system will gradually deviate from this theoretical equilibrium state, and the degree of deviation will continue to accumulate as the fault evolves. Based on this, this invention defines the theoretical dynamic response that satisfies the physical constraints as the trend component, and the deviation between the actual signal and the trend as the disturbance component. The specific steps are as follows:

[0012] First, time-varying physical parameters are identified, and time is set as... The operating condition input vector is This includes monitored variables such as flow rate, head, guide vane opening, rotational speed, and pressure. At any given time... The construction length is Forward sliding window This window covers the current moment and its preceding time. Each sampling point provides local temporal information for parameter identification. Within the window, it is assumed that the system can be represented by a set of time-varying equivalent physical parameters. The simplified mechanistic model described is used to obtain the optimal parameter estimates by solving an optimization problem:

[0013]

[0014] in The objective function is composed of the data fitting error and the physical constraint residuals:

[0015]

[0016] In the formula, To utilize parameters The theoretical response obtained through mechanistic model calculation. The equations representing the physical constraints that the system must satisfy. These are the weighting coefficients for the physical constraint terms.

[0017] Because the parameter identification process comprehensively utilizes the runtime information from multiple consecutive moments within the window, the parameters It reflects the local physical equilibrium state corresponding to the overall operating characteristics of the system within the window, rather than the transient characteristics of a single sampling point. This window-based aggregation effect naturally endows the identification parameter sequence with a certain smoothing characteristic. Therefore, this paper does not introduce additional post-processing operations such as exponential smoothing to avoid weakening the real rapid state change information during the switching of operating conditions.

[0018] Subsequently, the optimal physical parameters were obtained. Then, based on the current operating condition input, the physical equilibrium response is calculated using a mechanistic model.

[0019]

[0020] Define it as a trend component This trend component reflects the theoretical operating state of the system under current operating conditions when it meets physical constraints; it is the normal dynamic response caused by changes in operating conditions. Furthermore, the deviation between the monitoring signal and the trend component is defined as the disturbance component:

[0021]

[0022] Therefore, the original signal can be represented as:

[0023]

[0024] After decomposing the raw data into trends and fluctuations through physical constraints, multi-scale adaptive fusion and trend-aware prediction are performed. Decomposition at a single time scale is insufficient to simultaneously consider rapid transient response and long-term trend stability, and cannot effectively distinguish between operating condition changes and fault warnings. Therefore, this invention designs a physically prior-guided multi-scale adaptive fusion mechanism.

[0025] Within the PCTD framework, K sliding windows of different lengths are defined. Obtain the trend-perturbation decomposition results at K time scales. Subsequently, time-varying fusion weights guided by physical priors are applied. Under transient operating conditions, the rate of change of the guide vane opening directly reflects the drastic degree of operating condition adjustment. Based on this physical understanding, this paper defines the non-stationary strength index of the system using the rate of change of the guide vane opening.

[0026]

[0027] in This refers to the guide vane opening. To enhance robustness, [the following is added]: Short-time smoothing is obtained The greater the non-stationarity intensity, the more the system is undergoing rapid load adjustment, and the more it should rely on the transient response capability of the short window; the smaller the non-stationarity intensity, the more the system is approaching steady state or a slow-changing process, and the more it should rely on the stability of the long window.

[0028] Based on the above physical understanding, at each scale Presuppose a non-stationary intensity center for the "optimal response". The response intensity at this scale is then generated using a Gaussian kernel function.

[0029]

[0030] in Control the tolerance of this scale to non-stationary intensity deviations. Softmax normalization is performed on each scale to obtain the physical prior weight vector:

[0031]

[0032] This weight is entirely determined by the physical characteristics of the operating conditions and has clear interpretability.

[0033] While purely physical prior weights can be explained, their presupposed scale preference parameters ( , This may not be the optimal configuration. To enable the model to adaptively adjust scale preferences from the data, a lightweight learnable weight network is designed. This network takes the trend and perturbation components at each scale as input and outputs data-driven scale weights:

[0034]

[0035]

[0036] The MLP is a two-layer fully connected network with ReLU activation function in the hidden layers. The parameters of the learnable weight network are trained end-to-end along with the overall prediction model.

[0037] The final fusion weights are composed of physical prior weights and learnable weights through a learnable balancing coefficient. Combination:

[0038]

[0039] in These are trainable parameters, initialized to 0.5. During training, the relative importance of physical priors and data-driven factors is automatically adjusted. The multi-scale decomposition results are weighted and summed using fusion weights.

[0040]

[0041] To ensure that the learnable weights do not deviate too far from the physical prior, a weight consistency constraint is introduced into the training loss:

[0042]

[0043] This constraint allows learnable weights to be finely tuned near the physical prior, rather than being explored freely, thus balancing physical interpretability and data adaptability.

[0044] The trend component of the multi-scale adaptive fusion output obtained from the above operations and disturbance components To predict using a trend-aware Transformer, the fused trend component and perturbation component are first concatenated along the feature dimension to form a joint state representation.

[0045]

[0046] Using a length of Sliding window constructs historical state sequence And projected to via linear mapping Hidden Space:

[0047]

[0048] in This is a learnable mapping matrix. To preserve temporal information during state evolution, positional encoding is introduced. :

[0049]

[0050] A multi-layer Transformer encoder is used for deep modeling of the embedded features. Within each layer, a multi-head self-attention mechanism establishes global relationships between states at different time steps.

[0051]

[0052] Through a self-attention mechanism, the model can capture the long-term dependency between the equilibrium transition process and the disturbance evolution process, thereby learning the normal operating condition change law and the disturbance propagation law. Subsequently, through a feedforward network, residual connections, and layer normalization, deep temporal features of the system state are extracted layer by layer.

[0053] Based on the global temporal representation output by the encoder, the predicted trend components for the next K time steps are output through a linear prediction head. and predicted values ​​of disturbance components .

[0054] Prediction loss: The mean squared error between the predicted value and the true decomposition value (obtained by PCTD multi-scale fusion) is calculated separately for the trend and the disturbance.

[0055]

[0056] in This is the balance coefficient for predicting losses based on trends and disturbances.

[0057] Total loss: The joint prediction loss and weight consistency loss are trained end-to-end.

[0058]

[0059] in To ensure consistency loss weights, larger values ​​are set in the early stages of training to strengthen physical prior guidance, and then gradually decayed in the later stages to allow the model to learn more refined patterns from the data.

[0060] Through the above design, the multi-scale adaptive fusion mechanism integrates state information of different time scales according to the non-stationary intensity of the system. Based on this, the trend-aware Transformer learns the joint evolution law of equilibrium state and disturbance state under healthy operating conditions, realizes the prediction of the future state trajectory of the system, and provides a predictive basis for subsequent state evolution judgment and fault early warning.

[0061] The future equilibrium trajectory output by the trend-aware Transformer With future disturbance trajectory It contains key information about the system's state evolution. However, it is difficult to distinguish the source of error based solely on the magnitude of the prediction error: equilibrium changes caused by switching between normal operating conditions and the accumulation of disturbances caused by fault degradation can both increase the prediction error. Therefore, this section constructs a state evolution index from two dimensions: "whether the system is changing" and "whether there are any abnormalities during the change process," and combines it with a dynamic operating condition memory mechanism to achieve adaptive fault early warning under open operating conditions.

[0062] The essence of normal operating condition switching is the transformation of the system from one physical equilibrium state to another. During this process, the trend component undergoes a continuous directional change. Therefore, an equilibrium state transformation index is defined to quantify the degree of change in the future equilibrium state relative to the current state:

[0063]

[0064] in, This represents the predicted future equilibrium state. This represents the equilibrium state at the current moment. Indicates the future number The Euclidean distance between the equilibrium point of the previous step and the current equilibrium point. This index reflects the average degree to which the future running state deviates from the current equilibrium point. When the value is small, it indicates that the future equilibrium state will remain basically stable; when A larger value indicates that the system is migrating to a new equilibrium region.

[0065] The essence of fault development is the continuous accumulation of disturbance energy, leading to a gradual loss of the system's ability to return to equilibrium. Therefore, a disturbance accumulation index is defined to characterize the future evolution trend of disturbances.

[0066]

[0067] The first term is the mean of the disturbance energy within the prediction window, and the second term is the baseline mean of the disturbance energy within the historical window. This indicates that the future disturbance energy is higher than the recent baseline, and the disturbance shows a cumulative trend; This indicates that the disturbance remains at the baseline level or shows a decreasing trend.

[0068] Determined based on historical data of healthy working conditions migration threshold as well as Cumulative threshold Construct the following table of discrimination rules:

[0069] condition State determination meaning and Stable operation The equilibrium state is stable, and disturbances do not accumulate. and First back Normal operating condition switching Equilibrium state transition, perturbation is controllable and gradually decays. and Fault Development Trend Operating conditions are stable, but disturbances continue to accumulate.

[0070] The core value of this discrimination rule lies in decomposing the ambiguous abnormal signal of "increased prediction error" into two independently interpretable dimensions: "equilibrium state transition" and "disturbance accumulation," thereby effectively distinguishing between normal operating condition switching and real fault degradation.

[0071] The above joint discrimination rule depends on a threshold. However, under open operating conditions, the health baseline space established during the training phase cannot cover all possible operating conditions. When the unit enters a new operating condition that did not appear during the training phase, even if it is in a healthy state, its EMI and DAI may exceed the preset threshold, causing normal operating condition transitions to be misjudged as faults. To address this, this section introduces a Dynamic Operating-condition Memory (DOM) mechanism, which achieves adaptive expansion of the health baseline space through online matching and incremental updates of operating condition prototypes.

[0072] The encoder of the trend-aware Transformer learns a high-level representation of state evolution under healthy operating conditions during training. For healthy samples in the training set, the encoder output is extracted as a state evolution feature vector:

[0073] This method utilizes the state evolution features output by the trend-aware Transformer to construct a healthy operating condition prototype library, and achieves adaptive fault early warning under open operating conditions through online matching and incremental updates.

[0074]

[0075] in This represents the feature mapping function of the Transformer encoder. Based on the operating condition parameters and corresponding state evolution characteristics, healthy samples are clustered to obtain M typical healthy operating condition prototypes:

[0076]

[0077] Each working condition prototype This represents the central characteristic of the healthy operating state within the corresponding operating condition region. All operating condition prototypes together constitute a dynamic operating condition memory library, used to describe the distribution of healthy operating conditions observed during the training phase.

[0078] During the testing phase, for the current state characteristics Calculate the distance between it and the prototype of each working condition in the memory bank.

[0079]

[0080] Set matching threshold .when When the current state is determined to fall within the known operating condition distribution range, the corresponding threshold for EMI / DAI is used for discrimination. If the current state exceeds the coverage of existing working conditions, the unknown working condition judgment process will be initiated.

[0081] when When the current state falls within the known operating condition distribution range, the system performs a state assessment according to the corresponding health condition baseline; when When the current state exceeds the coverage of existing operating conditions, it is identified as a candidate state for an unknown operating condition. However, an unknown operating condition does not necessarily mean a fault. Since both normal operating condition switching and fault development can cause the current state to deviate from the existing operating condition prototype, it is difficult to make an accurate judgment based solely on the operating condition matching distance. Therefore, a joint analysis is performed by combining the future equilibrium trajectory predicted by the trend-aware Transformer with the future disturbance trajectory.

[0082] Unknown operating conditions may arise from two situations: entering a new healthy operating zone, or abnormal deviations caused by a fault. Relying solely on matching distance... Unable to distinguish between the two, a secondary determination is needed based on the physical meaning of the combined EMI / DAI assessment: New health condition determination: When , and First back When the system enters an unknown region, the equilibrium state is migrating towards a new stable region and the disturbance has not accumulated, indicating that the unknown state is the result of a normal operating condition switch and is judged as a new healthy operating condition.

[0083] Fault diagnosis: When , and When the system's operating conditions change significantly and disturbances accumulate, exhibiting typical fault degradation characteristics, it is determined to be a fault state and an early warning is triggered.

[0084] For samples that are consistently identified as having a new healthy working condition, their feature vectors are extracted. After confirming through a sliding window that its state evolution has a stable convergence trend, the features of this sample are added to the memory as a new prototype:

[0085]

[0086] Simultaneously, the corresponding EMI / DAI threshold parameters are initialized for this new operating condition region. As runtime accumulates, the memory gradually covers a wider range of healthy operating conditions, and the model's adaptability to open operating environments continues to improve.

[0087] Through the above steps, this invention realizes a complete early warning process from decoupling the original signal to the physical state, multi-scale fusion, evolution prediction, joint discrimination and memory update.

[0088] The beneficial effects of this invention are mainly reflected in:

[0089] Compared with the prior art, the present invention has the following significant advantages and beneficial effects:

[0090] This invention employs physical model constraints for trend decomposition, ensuring that the extracted trend components naturally satisfy the system's physical equations and possess clear physical meaning (equilibrium state migration caused by changes in operating conditions). The disturbance component reflects deviations caused by faults or noise, thus overcoming the inability to interpret the decomposition results of traditional statistical methods. Building upon this foundation, the invention further constructs the Equilibrium State Migration Index (EMI) and the Disturbance Accumulation Index (DAI), decomposing the prediction error into two independently interpretable physical dimensions. This effectively distinguishes between normal operating condition switching (equilibrium state migration with controllable disturbances) and genuine fault degradation (equilibrium state shift with continuous disturbance accumulation), fundamentally solving the problem of high false alarm rates under varying operating conditions. Simultaneously, this invention utilizes a Dynamic Operating Condition Memory (DOM) mechanism to identify newly emerging healthy operating conditions online and incrementally update the memory, achieving adaptive expansion of the health baseline space and significantly improving the model's generalization ability and early warning accuracy under open and unknown operating conditions. Furthermore, the Equilibrium State Migration Index (EMI) in this invention can capture early equilibrium point shifts in the early stages of faults, often issuing early warning signals earlier than traditional methods based on vibration energy, providing a possibility for early fault warning. Attached Figure Description

[0091] Figure 1 This is a schematic diagram of the overall process of the fault early warning method based on physical guidance state decoupling and evolution analysis of the present invention;

[0092] Figure 2 This is a schematic diagram of the Physical Constraint Trend Decomposition Module (PCTD) of the present invention;

[0093] Figure 3 This is a schematic diagram illustrating the principle of the multi-scale adaptive fusion and trend-aware prediction module of the present invention.

[0094] Figure 4 This is a flowchart illustrating the adaptive early warning and dynamic operating condition memory mechanism of the present invention. Detailed Implementation

[0095] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. This embodiment takes the pump turbine of a pumped storage power station as an example, and applies the method proposed in this invention for fault early warning. The process flow is as follows: Figure 1 As shown.

[0096] The first step is data acquisition and preprocessing. The following monitoring signals are acquired in real time using sensors: flow rate Q, guide vane opening α, head H, rotational speed ω, volute inlet pressure p_sp, bladeless zone pressure p_vl, tailrace inlet pressure p_dt1, and tailrace cone pressure p_dt2. The sampling frequency is 1000Hz. Data is segmented into time windows, and spatiotemporal difference processing is performed on the windowed data. Based on the time and spatial difference terms appearing in the mechanistic equations upon which the subsequent physical embedding module relies, the sensor data undergoes corresponding differential processing. Specifically, the central difference method is used to calculate the rate of change of parameters such as flow rate, head, and rotational speed over time. Simultaneously, based on the sensor placement and flow channel geometry, the spatial gradient of the physical quantities along the flow channel direction is calculated. This step transforms the original physical quantity signals into differential signals that directly reflect system dynamics and conform to the form of the physical equations. The training set uses data from the unit's healthy operation, covering various variable operating conditions (such as load adjustment, start-up, and shutdown). The test set includes healthy operating conditions and simulated hydraulic imbalance fault conditions.

[0097] The preprocessed data is then used for Physical Constraint Trend Decomposition (PCTD) implementation, such as... Figure 2 As shown. The sliding window length is set to L = 100. At each time t, the window is constructed. Parameter identification is performed using the mechanistic model equations provided by this invention. The mechanistic model used in this embodiment includes simplified turbine flow channel equations and rotor motion equations, as detailed below:

[0098] The equations of continuity and motion are combined as follows:

[0099]

[0100] Relationship between head, rotation speed, and opening degree:

[0101]

[0102] Volute pressure equation:

[0103]

[0104]

[0105] Pressure equation for the bladeless region:

[0106]

[0107] Tailwater pipe pressure relationship:

[0108]

[0109] in, yes , yes , yes , It is the friction term. yes , It is a fixed angle , yes , yes , yes , It is friction loss. It is the dynamic correction offset of head-flow-opening. It is the hydraulic loss of the spiral shell. This refers to hydraulic loss in the leafless zone. It is a loss of water head. It is the hydraulic loss in the tailrace pipe.

[0110] PINN minimizes the objective function within a window. The optimal parameter set is obtained by using the gradient descent method. In this embodiment, the physical constraint residual term consists of the residuals from the above equations. Substituting the identified parameters into the mechanistic model, the theoretical equilibrium response under the current operating condition is calculated, yielding the trend component. The original signal With trend components Subtracting them yields the disturbance component. .

[0111] Subsequently, multi-scale adaptive fusion and trend-aware prediction are implemented, such as... Figure 3 As shown. The specific measures are as follows: First, set K=3 scales. The three scales are the optimal parameters determined by the grid parameter optimization method, and the window lengths are respectively... =50、 =100、 =200. Perform PCTD decomposition for each scale separately.

[0112] Calculate the absolute value of the rate of change of guide vane opening. And perform moving average smoothing to obtain Preset the optimal response center for each scale. The response intensity at this scale is generated using a Gaussian kernel function:

[0113]

[0114] in Control the tolerance of this scale to non-stationary intensity deviations. Softmax normalization is performed on each scale to obtain the physical prior weight vector:

[0115]

[0116] This weight is entirely determined by the physical characteristics of the operating conditions and has clear interpretability.

[0117] Simultaneously, a two-layer fully connected network (64 neurons per layer, ReLU activation) is constructed as a learnable weight network. The input is a concatenated vector of trend and perturbation components at various scales (6K dimensions), and the output is K-dimensional weights, which are then normalized using softmax.

[0118]

[0119]

[0120] The MLP is a two-layer fully connected network, with the hidden layers using the ReLU activation function. The final fused weights are obtained by balancing the physical prior weights and the learnable weights using a learnable balancing coefficient. Combination:

[0121]

[0122] in These are trainable parameters, initialized to 0.5. During training, the relative importance of physical priors and data-driven factors is automatically adjusted. The multi-scale decomposition results are weighted and summed using fusion weights.

[0123]

[0124] To ensure that the learnable weights do not deviate too far from the physical prior, a weight consistency constraint is introduced into the training loss:

[0125]

[0126] This constraint allows learnable weights to be finely tuned near the physical prior, rather than being explored freely, thus balancing physical interpretability and data adaptability.

[0127] The fused trend and disturbance are concatenated into a state vector. (Dimensionality is 2 × number of features). A sequence is constructed using a historical window length L=100, projected onto a 128-dimensional latent space via a linear mapping, and learnable positional encoding is added. This is then fed into a 4-layer Transformer encoder, each layer containing 8 self-attention heads. The feedforward network has a dimension of 256, employing residual connections and layer normalization. The encoder output is used by a linear prediction head (single-layer fully connected) to predict the trend and perturbation sequences for the next K=50 time steps. The prediction loss is expressed as:

[0128]

[0129] Training was performed using the Adam optimizer with a learning rate of 0.001, a batch size of 32, and an early stopping patience value of 15. In the prediction loss, γ was set to 0.5 (giving slightly lower weight to perturbation predictions due to their higher noise levels). The total loss was... .

[0130] Finally, adaptive early warning and dynamic memory are implemented, specifically as follows: Figure 4 As shown. Based on the health data in the training set, EMI and DAI at each time point are calculated, and the migration threshold is set using the quantile method. and cumulative threshold Specifically, in this embodiment Set it to 0.05. Set it to 0.02.

[0131] During the testing phase, real-time calculations were performed. and Extract the output of the Transformer encoder at the current time step (after mean pooling in the last layer) as the state feature. (128 dimensions). Construction of dynamic working condition memory: K-means clustering is performed on the state features of healthy samples in the training set, with M clusters, resulting in M ​​working condition prototypes. Matching threshold Set it to 0.5 (based on 1.2 times the maximum distance between samples in the training set). Calculate the shortest distance between the current feature and the memory. .like If the value is less than 0.5, it is considered a known operating condition, according to the judgment rules in the table below:

[0132] condition State determination meaning and Stable operation The equilibrium state is stable, and disturbances do not accumulate. and First back Normal operating condition switching Equilibrium state transition, perturbation is controllable and gradually decays. and Fault Development Trend Operating conditions are stable, but disturbances continue to accumulate.

[0133] like If ≥ 0.5, proceed to unknown working condition judgment: if and If an alert is triggered; and If it is determined to be a new healthy working condition, then the sample will be... It is added to the memory bank as a new prototype, and its corresponding EMI / DAI threshold is initialized at the same time.

[0134] To verify the effectiveness of this invention, we conducted experiments using the publicly available dataset from the 2nd Francis-99 workshop initiated by the Waterpower Laboratory, Norwegian University of Science and Technology. The training and test sets were divided as follows: healthy operating periods (including stable operation under design conditions and normal load regulation processes) were selected from the dataset as the training set to train the physical constraint trend decomposition module, the multi-scale adaptive fusion network, and the trend-aware Transformer; operating periods containing fault injection or abnormal states, as well as some healthy periods, were used as the test set to verify the effectiveness of the early warning method. The training and test sets were divided in a 7:3 ratio, with the training set containing only healthy operating condition data, consistent with the unsupervised early warning scenario—the model does not encounter any fault labels during the training phase, and only performs anomaly detection for unknown states during the testing phase.

[0135] Evaluation metrics: False Alarm Rate (FAR), False Alarm Rate (MAR), and Early Warning Time are used. Comparison methods include: signal decomposition methods based on EMD / VMD, reconstruction methods based on autoencoders (AE), prediction methods based on LSTM and Transformers, and the method of this invention (Proposed).

[0136] The experimental results are shown in the table below.

[0137] category method False alarm rate underreporting rate false alarm rate during operating condition switching Warning time (sample) signal decomposition EMD 100.00% 0% 100% The second one VMD 1.98% 33.23% 56.1% The 60th SMA 5.51% 44.38% 73,17% The 60th Refactoring AE-PCTD 24.38% 22.98% 70.73% The 100th AE 0.412% 10.84% 10.84% The 87th LSTM-AE 2.63% 45.89% 75.61% The 60th predict LSTM 0.78% 49.35% 31.71% The 89th Transformer 0.48% 56.42% 19.51% The 60th PatchTST 0.84% 93.16% 34.15% The 60th Proposed PCTD+Transformer 2.515% 2.76% 7.32% The 83rd

[0138] Experimental results show that the PCTD+Transformer method proposed in this invention achieves the best overall performance in all evaluation indicators. In signal decomposition methods, EMD achieves zero false alarms but has a false alarm rate as high as 100%, completely unable to distinguish between operating condition transitions and actual faults. VMD and SMA, while reducing false alarm rates, still have false alarm rates of 33.23% and 44.38%, respectively, with false alarm rates for operating condition transitions exceeding 56%. In reconstruction methods, AE-PCTD performs better than standard AE and LSTM-AE, with a false alarm rate reduced to 22.98%, but its false alarm rate for operating condition transitions is still as high as 70.73%. Standard AE has a false alarm rate of only 0.412% but a false alarm rate of 10.84%, while LSTM-AE has a false alarm rate as high as 45.89% and a false alarm rate for operating condition transitions of 75.61%. In prediction methods, Transformer and PatchTST perform well in terms of false alarm rates for operating condition transitions (19.51% and 34.15%, respectively), but their false alarm rates are as high as 56.42% and 93.16%, respectively, while LSTM has a false alarm rate of 49.35%. It is worth noting that methods such as VMD, SMA, LSTM-AE, and PatchTST all issued alarms at the 60th sample, but at that moment only a normal operating condition switch had occurred, and no fault symptoms had yet appeared. Therefore, these alarms were all false alarms caused by the operating condition switch. In contrast, the method of this invention did not issue a false alarm at the 60th sample, with a false alarm rate of only 7.32% for operating condition switching. This indicates that its physical constraint trend decomposition and EMI / DAI joint discrimination mechanism can effectively distinguish between normal operating condition switching and real faults, avoiding false alarms when operating conditions change. More importantly, the method of this invention triggered an early warning at the 83rd sample, which corresponds precisely to the early stage when the fault is just beginning to appear slightly—at this time, the fault characteristics are not yet significant, and there are no obvious abnormal fluctuations in the original signal. However, this method has already captured the slight shift of the system equilibrium point through the equilibrium state migration index, achieving effective early warning. In contrast, other comparative methods triggered alarms in the 87th sample, LSTM in the 89th sample, and AE-PCTD in the 100th sample. While AE, with its lower false alarm rate, provided an earlier warning, it sacrificed its ability to distinguish between operating conditions, resulting in a false alarm rate of only 10.84% ​​for operating condition switching. This indicates that it reduces false alarms during operating condition switching by lowering overall sensitivity, at the cost of missing a large number of real faults. Overall, the present invention achieved a false alarm rate of 2.515%, a false alarm rate of only 2.76%, and a false alarm rate of 7.32% for operating condition switching. All three indicators are significantly better than the comparative methods. Furthermore, the warning time (the 83rd sample) corresponds to the true early stage of the fault's initial occurrence, fully verifying the superiority of the physical constraint trend decomposition and EMI / DAI joint discrimination mechanism in effectively distinguishing between operating condition switching and fault degradation, and capturing weak early fault signals.In summary, the unsupervised fault early warning method based on physical guidance state decoupling and evolution analysis proposed in this invention can effectively address the early warning challenges under varying operating conditions. It outperforms existing methods in terms of accuracy, generalization, and timeliness of early warning, and has significant engineering application value.

Claims

1. A physically guided, unsupervised fault early warning method for pump-turbines operating under varying conditions, characterized in that, Includes the following steps: Step 1: Acquire real-time monitoring signals of the pump-turbine, including flow rate Q, guide vane opening α, head H, rotational speed ω, volute inlet pressure p_sp, bladeless zone pressure p_vl, tailrace inlet pressure p_dt1, and tailrace cone pressure p_dt2; Based on the pump-turbine hydraulic-mechanical coupling model, identify time-varying equivalent parameters, and decompose the monitoring signals into physical equilibrium trend components reflecting changes in operating conditions and disturbance dynamic components reflecting fault evolution characteristics; Step 2: Adaptively fuse the trend components and disturbance components obtained from decomposition at multiple time scales based on the non-stationary strength of the system to obtain the fused trend components and disturbance components. Step 3: Construct a state representation based on the fused trend and disturbance components, use the Transformer model to learn the evolution law of the system state under healthy operating conditions, and predict the trend and disturbance components at future moments. Step 4: Calculate the equilibrium migration index (EMI) based on the predicted future trend components, calculate the disturbance accumulation index (DAI) based on the predicted future disturbance components, and combine the dynamic operating condition memory mechanism to use the joint discrimination rule of EMI and DAI for fault early warning.

2. The method according to claim 1, characterized in that, In step 1, decomposing the monitoring signal into trend components and disturbance components based on physical model constraints specifically includes: Step 1: Construct a forward sliding window of length L Within the window, the objective function, composed of the data fitting error and the physical constraint residuals, is solved. Identify time-varying equivalent physical parameters ; Step 2: Utilize the identified time-varying equivalent physical parameters Combined with the current operating conditions input The theoretical equilibrium response under the current operating condition is calculated using a mechanistic model. Treat it as a trend component ; Step 3: Transfer the monitoring signal With the trend component The difference is defined as the disturbance component. Therefore, the original monitoring signal is represented as a superposition of trend and disturbance components. The trend component The disturbance component reflects the process of changing operating conditions and the transition of the system's equilibrium state. It reflects the degree to which the actual operating state of the system deviates from the theoretical equilibrium state.

3. The method according to claim 2, characterized in that, The mechanistic model includes hydraulic-mechanical coupling equations describing the transient process of the pump-turbine, specifically including the following physical equations: The equations of continuity and motion are combined as follows: Relationship between head, rotation speed, and opening degree: Volute pressure equation: Pressure equation for the bladeless region: Tailwater pipe pressure relationship: in, yes , yes , yes , It is the friction term. yes , It is a fixed angle , yes , yes , yes , It is friction loss. It is the dynamic correction offset of head-flow-opening. It is the hydraulic loss of the spiral shell. This refers to hydraulic loss in the leafless zone. It is a loss of water head. It is the hydraulic loss in the tailrace pipe.

4. The method according to claim 1, characterized in that, Step 2, specifically, includes: Step 1: Set up K sliding windows of different lengths. Perform step 1 separately to obtain the trend components at K time scales. and disturbance components Short windows are more sensitive to rapid changes in operating conditions, while long windows extract stable long-term trends. Step 2: Define the non-stationary strength index based on the guide vane opening change rate. And perform short-time smoothing on I_t to obtain ; Step 3: Preset the non-stationary intensity center for the optimal response for each scale k. The response intensity at this scale is generated using a Gaussian kernel function: in Control the tolerance of this scale to non-stationary intensity deviations. Softmax normalization is performed on each scale to obtain the physical prior weight vector. ; Step 4: Construct a lightweight learnable weight network, which is a two-layer fully connected network, using the trend components and perturbation components at each scale at the current time as input. Output data-driven scale weights ; Step 5: The final fusion weights are composed of the physical prior weights and the learnable weights through a learnable balancing coefficient. Combination: in These are trainable parameters, initialized to 0.

5. During training, the relative importance of physical priors and data-driven factors is automatically adjusted. The multi-scale decomposition results are weighted and summed using fusion weights. To ensure that the learnable weights do not deviate too far from the physical prior, a weight consistency constraint is introduced into the training loss: This constraint allows for fine-tuning of learnable weights near the physical prior, balancing physical interpretability with data adaptability.

5. The method according to claim 1, characterized in that, In step 3, the construction and prediction of the trend-aware Transformer specifically includes: Step 1: Concatenate the fused trend component and perturbation component along the feature dimension to form a joint state. express; Step 2: Construct a historical state sequence using a sliding window of length L. And by projecting it onto a d-dimensional latent space through a linear mapping, positional encoding is introduced. Perform timing encoding; Step 3: A multi-layer Transformer encoder is used to perform deep modeling of the embedded features. In each layer, a multi-head self-attention mechanism establishes global associations between states at different time steps. The system captures the long-term dependency between the equilibrium state transition process and the disturbance evolution process, and then extracts the deep temporal features of the system state layer by layer through feedforward network, residual connection and layer normalization. Step 4: Based on the global time series representation output by the encoder, output the predicted trend components for the next K time steps using a linear prediction head. and predicted values ​​of disturbance components ; Step 5: Construct the prediction loss. Calculate the mean squared error between the predicted value and the true decomposition value (obtained after PCTD multi-scale fusion) for both the trend and disturbance, expressed as: in This is the balance coefficient for predicting losses based on trends and disturbances; Step 6: Construct the total loss, and perform end-to-end training by jointly analyzing the prediction loss and the weight consistency loss. in To ensure consistency loss weights, larger values ​​are set in the early stages of training to strengthen physical prior guidance, and then gradually decayed in the later stages to allow the model to learn more refined patterns from the data.

6. The method according to claim 1, characterized in that, In step 4, the steps for calculating the equilibrium migration index (EMI) based on the predicted future trend components and the disturbance accumulation index (DAI) based on the predicted future disturbance components are as follows: Step 1: Construct the equilibrium mobility index (EMI). The calculation formula is as follows: in, This represents the predicted future equilibrium state. This represents the equilibrium state at the current moment. Indicates the future number The Euclidean distance between the equilibrium point of the previous step and the current equilibrium point. This index reflects the average degree to which the future running state deviates from the current equilibrium point. When the value is small, it indicates that the future equilibrium state will remain basically stable; when A larger value indicates that the system is migrating to a new equilibrium region. Step 2: Construct the disturbance accumulation index DAI, calculated using the following formula: The first term represents the mean disturbance energy within the prediction window, and the second term represents the baseline mean disturbance energy within the historical window. This indicates that the future disturbance energy is higher than the recent baseline, and the disturbance shows a cumulative trend; This indicates that the disturbance remains at the baseline level or shows a decreasing trend.

7. The method according to claim 1, characterized in that, In step 4, the joint discrimination rule is specifically as follows: in and Based on the statistical distribution of healthy samples, this discrimination rule decomposes the increase in prediction error into two independently interpretable physical dimensions: equilibrium migration and disturbance accumulation, effectively distinguishing between normal operating condition switching and real fault degradation.

8. The method according to claim 1, characterized in that, In step 4, the dynamic operating condition memory mechanism specifically includes: Step 1: Extract the state evolution features of healthy operating condition samples using the trained Transformer encoder. Based on the operating condition parameters and corresponding state evolution characteristics, the healthy samples are clustered to obtain M typical healthy operating condition prototypes: Each working condition prototype This represents the central feature of the healthy operating status within the corresponding operating condition region. All operating condition prototypes together constitute a dynamic operating condition memory, used to describe the distribution of healthy operating conditions observed during the training phase; Step 2: During the testing phase, for the current state characteristics... Calculate the distance between it and the prototype of each working condition in the memory bank. Set matching threshold .when When the current state is determined to fall within the known operating condition distribution range, the corresponding threshold for EMI / DAI is used for discrimination. If the current state exceeds the coverage of existing working conditions, the unknown working condition judgment process will be initiated. Step 3 When When the current state falls within the known operating condition distribution range, the system performs a state assessment according to the corresponding health condition baseline; when When this occurs, it indicates that the current state exceeds the coverage of existing working conditions and is judged as an unknown working condition candidate state. Step 4: Determine the new health condition: When , and First back At this point, although the system enters an unknown region, the equilibrium state is migrating towards a new stable region and disturbances have not accumulated, indicating that this unknown state is the result of a normal operating condition switch. When #imgpt104#, #imgpt105#, and #imgpt106# are displayed, it is determined to be a new healthy operating condition; Step 5: Fault determination: When #imgpt107#, #imgpt108# and #imgpt109# are present, the system operating conditions change significantly and disturbances continue to accumulate, showing typical fault degradation characteristics. The system is determined to be in a fault state and an early warning is triggered. Step 6: For samples that are consistently identified as new healthy operating conditions, extract their feature vector #imgpt110#. After confirming that their state evolution has a stable convergence trend through a sliding window, add the sample features as a new prototype to the memory bank. #imgpt111# Simultaneously, the corresponding EMI / DAI threshold parameters are initialized for this new operating condition region. As runtime accumulates, the memory gradually covers a wider range of healthy operating conditions, and the model's adaptability to open operating environments continues to improve.

9. A physically guided pump-turbine variable operating condition unsupervised fault early warning system, used to execute the method described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to collect real-time monitoring signals of the water pump and turbine operation; A physical constraint trend decomposition module is used to execute the steps of the method described in claim 2 or 3; A multi-scale adaptive fusion module is used to perform the steps of the method described in claim 4; The trend-aware prediction module is used to execute the steps of the method described in claim 5; An adaptive warning module is used to perform the steps of the method described in any one of claims 6-8 and output a warning signal.

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