AI fault diagnosis and fault-tolerant method and system for liquid cooling system

Abstract

The present application relates to the technical field of liquid cooling system fault diagnosis, and particularly relates to an AI fault diagnosis and fault-tolerant method and system for a liquid cooling system. Multi-scale spatiotemporal topological characteristics are obtained by modeling the operation data of the liquid cooling system, fault attractor structures and saddle point distributions are identified through time delay embedding mapping, Lyapunov index fields are calculated to identify dynamic bifurcation points, and fault evolution trajectory prediction results including bifurcation point time, bifurcation type and reachable state set are obtained. A causal inference graph that integrates thermodynamic conservation and fluid dynamics constraints is established, a minimum intervention action set for the bifurcation point is calculated, the causal path evolving towards the fault attractor is cut off, and a multi-stage fault-tolerant control sequence is output. The method realizes accurate fault evolution prediction and active fault-tolerant control, and improves the reliability and safety of the liquid cooling system.

Description

Technical Field

[0001] This invention relates to the field of liquid cooling system fault diagnosis technology, and in particular to an AI fault diagnosis and fault-tolerant method and system for liquid cooling systems. Background Technology

[0002] Liquid cooling systems are widely used in thermal management scenarios such as data centers, power electronics, and high-power lasers. Their operational reliability directly determines equipment lifespan and energy efficiency. Current conventional practices typically employ fault detection methods based on single-point threshold monitoring. This involves collecting physical quantities such as temperature, flow rate, and pressure, and combining this data with statistical process control or simple time-series anomaly detection models (such as moving averages and exponential smoothing) to identify out-of-limit events. In the fault diagnosis stage, mainstream industry solutions rely on predefined expert rule bases or shallow machine learning classifiers (such as support vector machines and random forests) to map sensor data to preset fault type labels (such as pump blockage, cold plate scaling, and pipe leaks). Fault-tolerant control often employs redundancy switching strategies (such as hot standby pump startup and bypass valve opening) or fixed parameter correction based on PID control, lacking the ability to dynamically respond to the evolution of faults.

[0003] The primary drawback of existing conventional methods lies in neglecting the spatiotemporal coupling characteristics of liquid cooling systems. The components of a liquid cooling system, such as cooling plates, pipes, pumps, and heat exchangers, constitute a complex spatial topology. Heat accumulation and fluid disturbances caused by faults propagate along spatially dependent paths, exhibiting temporal evolution patterns of transient temperature and pressure changes. Traditional methods process each sensor independently, failing to integrate spatial topological dependence and temporal dynamic characteristics. This results in insufficient multi-scale sensitivity to early fault symptoms and missed detection of early performance degradation trends. Furthermore, fault evolution exhibits nonlinear and multi-steady-state characteristics (such as local thermal runaway caused by airlocks and fouling), while existing diagnostic models rely on single static thresholds or fixed-frequency sampling criteria, making it difficult to capture the bifurcation behavior of the system state in phase space. Fault prediction can only provide the trigger alarm time, lacking quantitative characterization of bifurcation types, reachable states, and evolution trajectories.

[0004] Another drawback is the lack of causal reasoning and the principle of minimal intervention in fault-tolerance strategies. Conventional redundant switching or pre-defined rules often come at the cost of excessive system disturbance (such as flow shock caused by directly switching the main pump), failing to identify the key control nodes that block dynamic bifurcation by starting from the causal path of fault propagation. This fault-tolerance method based on empirical formulas is prone to triggering chain reactions, such as the premature opening of bypass valves disrupting the original thermal equilibrium and exacerbating the transfer of local hot spots. Because thermodynamic conservation (such as energy balance equations) and fluid dynamic constraints (such as Bernoulli's equations) are not structurally embedded into the decision-making logic, existing fault-tolerance methods are unable to bring the system back to the rated operating domain with the minimum set of actions while satisfying physical feasibility. Summary of the Invention

[0005] This invention provides an AI fault diagnosis and fault tolerance method and system for liquid cooling systems, which can solve the problems in the prior art.

[0006] A first aspect of the present invention provides an AI fault diagnosis and fault tolerance method for a liquid cooling system, comprising: The operational data of the liquid cooling system are modeled to obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics; The multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. In this space, the fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory are identified. Based on the saddle point distribution, the Lyapunov exponential field of the state trajectory in phase space is calculated. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. This yields a fault evolution trajectory prediction result containing bifurcation point time markers, bifurcation type labels, and the set of reachable states after the bifurcation. Based on the predicted fault evolution trajectory, a causal inference graph integrating domain physics knowledge is established. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. On the causal graph structure, the set of minimum intervention actions for the dynamic bifurcation point is calculated. The set of minimum intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

[0007] Modeling the operational data of the liquid cooling system yields a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics, including: The system collects operational data of the liquid cooling system at multiple points in time using a distributed sensor network. The sensor nodes, actuator nodes, and heat exchange unit nodes in the liquid cooling system are constructed as a set of vertices of a hypergraph. Each group of nodes with a heat flow transfer path or control feedback loop is identified and connected by hyperedges. The mutual information or correlation coefficient of the measured values ​​between the nodes is calculated based on the operating data as the weight of the hyperedge. Multiple hyperedge convolutional layers are set up. Each hyperedge convolutional layer uses a hyperedge aggregation operator to perform weighted aggregation of the features of all nodes connected to the same hyperedge, and then feeds the aggregation result back to each node connected by the hyperedge to update the hidden layer representation of the node. Through the layer-by-layer propagation of the multi-layer hyperedge convolutional layers, the node features are fused with dependency information from across physical subsystems. The final hidden layer representation of each node is then concatenated with the corresponding time label to form a snapshot feature vector sequence containing spatial topological dependencies. The snapshot feature vector sequence is input into the temporal coding module, which extracts the evolution pattern between adjacent snapshots by applying a cyclic connection structure in the time dimension, and outputs a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics.

[0008] The multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. The fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory are identified within this topological embedding space, including: Based on the multi-scale spatiotemporal topological representation, a time series vector is constructed. For each moment in the time series vector, the feature vectors of the current moment and a preset number of previous historical moments are extracted. The extracted feature vectors of multiple historical moments are concatenated in chronological order to form the delayed coordinate vector corresponding to the current moment. The delay coordinate vectors corresponding to all times are used to form a set of state trajectory points in the topological embedding space. The set of state trajectory points forms a trajectory curve of the liquid cooling system state evolving over time in the topological embedding space. Density clustering analysis is performed on the set of state trajectory points to identify clustered regions of state points in the topological embedding space, and clustered regions where state trajectories repeatedly converge are identified as attractor candidate regions. Calculate the liquid cooling system performance index in the operating data corresponding to the state point within the attractor candidate region, and determine the attractor candidate region where the liquid cooling system performance index exceeds the preset normal operating range as a fault attractor structure. The manifold topology of the state trajectory in the topological embedding space is identified. By calculating the expansion rate and contraction rate in different directions within the neighborhood of the state point, the position of the state point that has both expansion and contraction directions is identified. The position is marked as a saddle point, and the spatial distribution of the saddle points constitutes the saddle point distribution.

[0009] Based on the saddle point distribution, the Lyapunov exponential field of the state trajectory in phase space is calculated. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. The resulting fault evolution trajectory prediction results, including bifurcation point time markers, bifurcation type labels, and the set of reachable states after bifurcation, are as follows: Based on the saddle point and the state points within a preset range around the saddle point, the delay coordinate vector corresponding to the state point at the time is extracted, the Jacobian matrix of the delay coordinate vector in the phase space is calculated and the eigenvalues ​​are solved to obtain the local Lyapunov exponents of the state point in different directions. The local Lyapunov exponents are spatially mapped according to the position of the state point in the phase space to form the Lyapunov exponent field. Traverse the state points corresponding to each moment in chronological order, identify the moment when the Lyapunov exponent changes from negative to positive or from positive to negative, and mark the moment when the sign changes as the bifurcation point moment marker. Analyze the spatial distribution pattern of the Lyapunov exponential field in the neighborhood of the state point corresponding to each bifurcation point time marker, and determine the bifurcation type label based on the number and configuration relationship of expansion and contraction directions; Starting from the state point corresponding to each bifurcation point, the trajectory is extended along the expansion direction where the Lyapunov exponent is positive, and the attractor candidate regions that the state trajectory can reach are tracked. All tracked attractor candidate regions constitute the set of states that can be reached after bifurcation. The bifurcation point time identifier, the bifurcation type label, and the set of reachable states after the bifurcation are associated and integrated to form the fault evolution trajectory prediction result.

[0010] Based on the predicted fault evolution trajectory, a causal inference graph integrating domain physics knowledge is established. This causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. Each attractor candidate region in the set of reachable states after bifurcation is used as a state node in the causal graph structure. Establish an initial directed connection relationship between the state nodes. For each bifurcation point time marker, establish a directed edge between the state node corresponding to the bifurcation point and each state node in the set of reachable states after the bifurcation. The directed edge represents the reachable path of state evolution. Obtain the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system, and convert the energy balance relationship characterized by the thermodynamic conservation constraints and the mass conservation relationship and momentum conservation relationship characterized by the fluid dynamic constraints into physical constraints that must be satisfied between state nodes. Traverse each directed edge in the initial directed connection relationship, determine whether the state transition between the two state nodes connected by the directed edge satisfies the physical constraint conditions, delete the directed edges that do not satisfy the physical constraint conditions, retain the directed edges that satisfy the physical constraint conditions, and form a set of causal edges that conform to physical laws by retaining the retained directed edges. The state nodes are combined with the set of causal edges to construct a causal graph structure.

[0011] On the causal graph structure, a set of minimum intervention actions for the dynamic bifurcation point is calculated. This set of minimum intervention actions cuts off the causal path that causes the state trajectory to evolve towards the fault attractor structure, causing the liquid cooling system state to reconverge to the rated operating state domain. The resulting multi-stage fault-tolerant control sequence includes: In the cause-effect graph structure, identify the target state node corresponding to the rated working state. The target state node is the state node in the cause-effect graph structure that is not identified as a fault attracting substructure. For each dynamic bifurcation point in the causal graph structure, extract all causal paths from the state node corresponding to the dynamic bifurcation point through the causal edge set to the fault attractor structure, and identify all causal paths as the fault evolution path set. Traverse each causal path in the set of fault evolution paths, identify the blockable causal edges on the causal paths, the blockable causal edges are causal edges that can block the evolution of the state trajectory to the fault attractor structure after being cut off, calculate the control actions required to cut off each blockable causal edge, and establish a mapping relationship between the control actions and the corresponding blockable causal edges. With the goal of cutting off all causal paths in the set of fault evolution paths, a combination of control actions that can cover all fault evolution paths and has the lowest control cost is selected from the mapping relationship to form a set of minimal intervention actions. According to the order of occurrence of each dynamic bifurcation point in the time series, the set of minimum intervention actions corresponding to each dynamic bifurcation point is arranged in chronological order to form a multi-stage fault-tolerant control sequence.

[0012] A second aspect of the present invention provides an AI fault diagnosis and fault tolerance system for a liquid cooling system, comprising: The modeling and representation unit is used to model the operating data of the liquid cooling system and obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics. The fault prediction unit is used to map the multi-scale spatiotemporal topological representation to the topological embedding space through the time-delay embedding method, identify the fault attractor structure and saddle point distribution of the liquid cooling system state trajectory in the topological embedding space, calculate the Lyapunov exponential field of the state trajectory in the phase space based on the saddle point distribution, identify the dynamic bifurcation point in the fault evolution process according to the sign change of the Lyapunov exponential field, and obtain the fault evolution trajectory prediction result including the bifurcation point time identifier, bifurcation type label and the set of reachable states after bifurcation. The causal graph unit is used to establish a causal inference graph that integrates domain physics knowledge based on the fault evolution trajectory prediction results. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. A fault-tolerant control unit is used to calculate the minimum set of intervention actions for the dynamic bifurcation point on the causal graph structure. The minimum set of intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

[0013] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0014] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0015] The beneficial effects of this application are as follows: By integrating multi-scale spatiotemporal topological representations that combine spatial topological dependence and temporal evolution characteristics, the operating state of the liquid cooling system is accurately modeled as a dynamic network structure encompassing fluid connectivity between devices and temperature gradient changes. Time-delay embedding mapping further projects high-dimensional topological features into a low-dimensional embedding space, capturing the evolution of state trajectories in phase space, thus enabling the identification of fault attractor structures and saddle point distributions at an early stage. Based on the sign change analysis of the Lyapunov exponential field to determine dynamic bifurcation points, the evolution path of progressive faults such as coolant leakage, pump blockage, or heat exchange efficiency degradation is predicted, significantly improving the foresight of fault diagnosis and shifting traditional fault detection from reactive alarm to the critical period before the bifurcation point occurs.

[0016] Based on the predicted fault evolution trajectory, a causal inference graph integrating thermodynamic conservation and fluid dynamics constraints is constructed to generate structured prior knowledge, enabling explicit modeling of the physical dependencies between various state variables of the system. This graph clarifies the fault propagation path through directional causal edges, and the minimum set of intervention actions calculated on the causal graph precisely severs the key causal links that lead to the evolution of the state trajectory towards the fault attractor. The fault-tolerant control sequence is decomposed into multi-stage actions, such as adjusting coolant flow, switching redundant pump sets, or changing heat dissipation power, so that the system state dynamically converges to the rated operating domain, avoiding cascading failures caused by single-point faults, while controlling energy consumption fluctuations within a safe threshold.

[0017] By deeply integrating dynamic bifurcation point identification with causal intervention strategies, the online fault tolerance capability of liquid cooling systems is fundamentally improved. This method effectively reduces false alarm and false negative rates and improves the distinction between transient disturbances and real faults. In complex operating environments with multiphysics coupling, the energy consumption cost of fault-tolerant actions is reduced, extending the service life of critical equipment. Fault response time is shortened from minutes to seconds, while ensuring operational continuity in high-reliability scenarios such as data centers and power conversion, significantly reducing unplanned downtime and maintenance costs. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating an AI-based fault diagnosis and fault tolerance method for liquid cooling systems. Figure 2 A schematic diagram of the Lyapunov exponential field calculation and dynamic bifurcation point identification process. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0021] Figure 1 This is a flowchart illustrating the AI ​​fault diagnosis and fault tolerance method for liquid cooling systems according to an embodiment of the present invention. Figure 1 As shown, the method includes: The operational data of the liquid cooling system are modeled to obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics; The multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. In this space, the fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory are identified. Based on the saddle point distribution, the Lyapunov exponential field of the state trajectory in phase space is calculated. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. This yields a fault evolution trajectory prediction result containing bifurcation point time markers, bifurcation type labels, and the set of reachable states after the bifurcation. Based on the predicted fault evolution trajectory, a causal inference graph integrating domain physics knowledge is established. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. On the causal graph structure, the set of minimum intervention actions for the dynamic bifurcation point is calculated. The set of minimum intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

[0022] In one optional implementation, the operating data of the liquid cooling system is modeled to obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics, including: The system collects operational data of the liquid cooling system at multiple points in time using a distributed sensor network. The sensor nodes, actuator nodes, and heat exchange unit nodes in the liquid cooling system are constructed as a set of vertices of a hypergraph. Each group of nodes with a heat flow transfer path or control feedback loop is identified and connected by hyperedges. The mutual information or correlation coefficient of the measured values ​​between the nodes is calculated based on the operating data as the weight of the hyperedge. Multiple hyperedge convolutional layers are set up. Each hyperedge convolutional layer uses a hyperedge aggregation operator to perform weighted aggregation of the features of all nodes connected to the same hyperedge, and then feeds the aggregation result back to each node connected by the hyperedge to update the hidden layer representation of the node. Through the layer-by-layer propagation of the multi-layer hyperedge convolutional layers, the node features are fused with dependency information from across physical subsystems. The final hidden layer representation of each node is then concatenated with the corresponding time label to form a snapshot feature vector sequence containing spatial topological dependencies. The snapshot feature vector sequence is input into the temporal coding module, which extracts the evolution pattern between adjacent snapshots by applying a cyclic connection structure in the time dimension, and outputs a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics.

[0023] Liquid cooling systems typically deploy various sensing devices, including temperature sensors, flow sensors, pressure sensors, and conductivity sensors. These sensors are distributed at key locations such as cold plate inlets and outlets, pipe joints, pump units, and heat exchangers. The collected operational data covers the measurement sequence of each node within a continuous sampling period. The sampling frequency is configured according to the system's dynamic response characteristics to ensure the capture of short-term dynamic events such as temperature transients, flow fluctuations, and pressure pulses. During the acquisition process, outlier removal and missing value imputation of the raw data are necessary to ensure the integrity and consistency of the data used for subsequent modeling.

[0024] Sensor nodes, actuator nodes, and heat exchange unit nodes in a liquid cooling system are abstracted as a set of vertices in a hypergraph. Sensor nodes correspond to measurement points of various physical quantities, actuator nodes correspond to control components such as pumps, valves, and fans, and heat exchange unit nodes correspond to heat exchange components such as cold plates, radiators, and liquid cooling radiators. Each group of nodes with a heat flow transfer path or control feedback loop is identified and connected by hyperedges. Unlike ordinary graphs where each edge can only connect two nodes, hyperedges can simultaneously connect any number of nodes, thus naturally depicting the high-order interaction relationships of multiple nodes participating in the same heat exchange process or the same control loop in a liquid cooling system. For example, the inlet temperature sensor, outlet temperature sensor, corresponding flow sensor, and the heat exchange unit node of the cold plate can be connected by the same hyperedge, reflecting the physical fact that these four nodes jointly describe the same heat exchange process.

[0025] Based on the collected operational data, the mutual information or correlation coefficient of the measured values ​​between each node is calculated and used as the weight of the hyperedge. Mutual information can capture the nonlinear statistical dependencies between nodes and has a stronger expressive power for scenarios where there is a nonlinear coupling between temperature and flow rate; the correlation coefficient is suitable for node pairs with obvious linear dependencies and has lower computational cost. In practical implementation, mutual information or correlation coefficient can be selected as the basis for weight calculation for different types of hyperedges to balance expressive power and computational efficiency. Hyperedge Weights It reflects the overall dependency strength among the group of nodes associated with the hyperedge. The higher the weight, the more significant the physical interaction relationship described by the hyperedge.

[0026] Multiple hyperedge convolutional layers are configured. Each hyperedge convolutional layer performs weighted aggregation of features from all nodes connected to the same hyperedge using a hyperedge aggregation operator. Let the first layer be... Layer nodes The hidden layer is represented as Super-edge The aggregation is represented as Then the hyperedge aggregation process can be expressed as: ,in For nodes In the super-edge Normalized weights in For the first The learnable parameter matrix of the hyperedge convolution layer. This is a non-linear activation function. After completing hyperedge aggregation, the aggregation result will be... Return to superside For each connected node, update the hidden representation of the node: ,in For nodes From the hyper-edge Attention weights when receiving information For the first The learnable parameter matrix updated at each layer node. Attention weights. The hyperedge weights can be normalized. The results, obtained by combining the node degree information with the hyperedge information, show that hyperedges with stronger physical dependencies contribute more to node feature updates.

[0027] Through layer-by-layer propagation via multiple hyperedge convolutional layers, node features can be fused with information from nodes covered by adjacent hyperedges in each iteration. As the number of layers increases, the information propagation range gradually expands to long-range dependencies spanning multiple physical subsystems. After the hyperedge convolution, the final hidden layer representation of each node The spatial dependency information between this node and the global topology of the liquid cooling system has been implicitly encoded. The final hidden layer representation of each node is concatenated with its corresponding time label. The time label can be in the form of sine and cosine positional encoding of an absolute timestamp, thus embedding time information into the node features in a differentiable manner. For time... The captured snapshot is constructed by arranging the concatenated feature vectors of all nodes in node order, forming the snapshot feature vector at that moment. The snapshot feature vectors from multiple consecutive time points are arranged in chronological order to form a snapshot feature vector sequence. This sequence contains the spatial topological dependencies of the liquid cooling system at each sampling time.

[0028] The snapshot feature vector sequence is input into the temporal coding module, which extracts the evolution pattern between adjacent snapshots by applying a cyclic connection structure in the time dimension. The cyclic connection structure processes the input at the current time step. At the same time, it receives the hidden state from the previous moment. Output the hidden state at the current time. This allows the evolutionary information from historical moments to be transmitted to the current moment in a compressed manner. To alleviate the gradient vanishing problem in long sequences, the cyclic connection structure can employ a gating mechanism. The forget gate controls the retention ratio of historical information, while the input gate controls the writing ratio of new information at the current moment. This enables the timing coding module to selectively memorize dynamic events with long-term impact during the operation of the liquid cooling system, such as the continuous decreasing trend of coolant flow or the slow drift of temperature at specific nodes.

[0029] After processing the entire snapshot feature vector sequence, the temporal coding module outputs the hidden state sequence corresponding to each time step. The hidden states at each time step are then fused at multiple scales. Specifically, pooling operations are performed on the hidden states within different time windows to capture dynamic features at two different time scales: short-term rapid changes and long-term slow evolution. Short-term features correspond to rapid transient events such as pump start-up and shutdown, and valve switching in the liquid cooling system, while long-term features correspond to slow degradation processes such as heat accumulation and pipe scaling. The pooling results from multiple time scales are concatenated or weighted to obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependencies and temporal evolution characteristics. This representation simultaneously carries high-order node interaction information in the physical topology of the liquid cooling system as well as dynamic evolution patterns across time scales, providing a sufficiently informative state description foundation for subsequent identification of fault attractor structures and saddle point distributions in the topological embedding space.

[0030] In one optional implementation, the multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. Identifying the fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory within the topological embedding space includes: Based on the multi-scale spatiotemporal topological representation, a time series vector is constructed. For each moment in the time series vector, the feature vectors of the current moment and a preset number of previous historical moments are extracted. The extracted feature vectors of multiple historical moments are concatenated in chronological order to form the delayed coordinate vector corresponding to the current moment. The delay coordinate vectors corresponding to all times are used to form a set of state trajectory points in the topological embedding space. The set of state trajectory points forms a trajectory curve of the liquid cooling system state evolving over time in the topological embedding space. Density clustering analysis is performed on the set of state trajectory points to identify clustered regions of state points in the topological embedding space, and clustered regions where state trajectories repeatedly converge are identified as attractor candidate regions. Calculate the liquid cooling system performance index in the operating data corresponding to the state point within the attractor candidate region, and determine the attractor candidate region where the liquid cooling system performance index exceeds the preset normal operating range as a fault attractor structure. The manifold topology of the state trajectory in the topological embedding space is identified. By calculating the expansion rate and contraction rate in different directions within the neighborhood of the state point, the position of the state point that has both expansion and contraction directions is identified. The position is marked as a saddle point, and the spatial distribution of the saddle points constitutes the saddle point distribution.

[0031] Based on the spatial dependence and temporal evolution information carried by the multi-scale spatiotemporal topological representation, the time-delay embedding method projects the high-dimensional operating state of the liquid cooling system into the topological embedding space, thereby enabling the visualization and quantitative analysis of the dynamic structure originally hidden in the time-series data. Specifically, a continuous time-series vector is extracted from the multi-scale spatiotemporal topological representation, and each time-time component of this vector corresponds to the comprehensive state characteristics of the liquid cooling system at that time. For each time-time component in the time-series vector... Extract the current time and times before. A total of 10 historical moments (in total) The feature vectors at each time step are concatenated sequentially in chronological order to form the delay coordinate vector corresponding to the current time step. ,Right now ,in Indicates time State feature vector, For time delay step size, For embedding dimension. Time delay step size. The selection of embedding dimensions is usually determined based on the mutual information minimization criterion to ensure sufficient information independence between adjacent delay components; The selection is based on the pseudo-nearest neighbor method to ensure that the reconstructed phase space can fully unfold the attractor structure of the original dynamic system, and avoid the real topological features being obscured by trajectory self-intersection due to insufficient dimension.

[0032] Delay coordinate vectors corresponding to all times They converge to form a set of state trajectory points in the topological embedding space. ,in This represents the total number of time points in the time series. This set of points depicts the trajectory curve of the liquid cooling system's state evolution over time in the topological embedding space. When the liquid cooling system is in a stable, normal operating state, the state trajectory in the embedding space appears as a convergent bounded region or a regular periodic loop; when the liquid cooling system enters the fault evolution process, the trajectory curve deviates from the normal attractor region and migrates towards an abnormal aggregation region. This change in trajectory shape provides the geometric basis for subsequent attractor identification.

[0033] For the set of state trajectory points Perform density-based clustering analysis by neighborhood radius. and minimum number of points threshold Two parameters define the high-density region. In the embedding space, regions repeatedly traversed by the state trajectory form high-density point clusters. These high-density point clusters correspond to the long-term residence regions of the system state, i.e., attractor candidate regions. ( , (This represents the total number of candidate regions identified). During density clustering, noise points (i.e., low-density isolated points) are excluded, and only statistically significant clustered regions are retained as candidates. To improve the robustness of identification, the local density gradient of the trajectory points is also calculated, and connected high-density regions around local density maxima are merged into a single candidate region, avoiding fragmentation of the same attractor due to data noise.

[0034] For each attractor candidate region The system extracts the liquid cooling system performance indicators corresponding to the state trajectory points at each moment, including coolant outlet temperature, flow rate differential pressure, heat exchange efficiency, and thermal resistance values ​​of each key node. These performance indicators are then compared item by item with the preset normal operating range. If one or more performance indicators corresponding to state points within a candidate region consistently exceed the upper and lower bounds of the normal operating range, the candidate region is determined to be a fault attractor structure, denoted as […]. Conversely, if all performance indicators are within the normal operating range, then the candidate region corresponds to a normal operating attractor, denoted as... The physical meaning of the fault attractor structure is that once the liquid cooling system enters this state region, it will continue to operate in fault mode and will be difficult to spontaneously recover to normal operating state. Therefore, accurately identifying the boundary of the fault attractor is of decisive significance for subsequent fault-tolerant control.

[0035] After attractor identification, the manifold topology of the state trajectories in the topological embedding space is further analyzed to locate the saddle point distribution. For the point set... Each state point in In its neighborhood A local tangent space is constructed within a neighborhood radius of . Principal component analysis is performed on the displacement vectors of state points within the neighborhood to extract the expansion rates along each principal direction. With shrinkage rate (Direction index). Expansion rate Indicates along the first The rate at which the distance between adjacent trajectory points in each principal direction increases with time, the rate of contraction. This represents the rate at which distance decreases with time. If a certain state point... There exists at least one expansion direction in the neighborhood of ( ). ) and at least one direction of contraction ( If the state point has saddle point characteristics, it is identified as a saddle point candidate.

[0036] To improve the accuracy of saddle point identification, a secondary screening is performed on all saddle point candidates: the anisotropy index of the expansion and contraction directions at each candidate point is calculated. , defined as the ratio of the absolute value of the maximum expansion rate to the absolute value of the maximum contraction rate, i.e. .when Within a preset range (typically between 0.5 and 2.0), a point is considered to have a comparable degree of expansion and contraction, exhibiting the dynamic characteristics of a true saddle point. Candidate points deviating from this range are considered trajectory turning points or noise interference and are therefore discarded. The spatial distribution of the selected and retained saddle points in the topological embedding space constitutes a complete saddle point distribution. ,in This represents the total number of saddle points identified. In dynamical system theory, saddle points are located near the boundaries of different attractor basins. Their distribution reveals the critical positions where the state trajectory of the liquid cooling system migrates between normally functioning and faulty attractors, providing a precise spatial reference for subsequent calculations of the Lyapunov exponential field and identification of dynamic bifurcation points.

[0037] Through the complete process of time-delay embedding, density clustering, performance index mapping and saddle point geometric analysis, the topological embedding space simultaneously contains the spatial boundary information of the fault attractor structure and the critical position information of the saddle point. Together, they constitute the geometric skeleton of the fault evolution dynamics of the liquid cooling system, supporting the subsequent bifurcation point identification and fault-tolerant control sequence generation.

[0038] In one optional implementation, the Lyapunov exponential field of the state trajectory in phase space is calculated based on the saddle point distribution. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. The resulting fault evolution trajectory prediction result includes bifurcation point time markers, bifurcation type labels, and a set of reachable states after the bifurcation. Based on the saddle point and the state points within a preset range around the saddle point, the delay coordinate vector corresponding to the state point at the time is extracted, the Jacobian matrix of the delay coordinate vector in the phase space is calculated and the eigenvalues ​​are solved to obtain the local Lyapunov exponents of the state point in different directions. The local Lyapunov exponents are spatially mapped according to the position of the state point in the phase space to form the Lyapunov exponent field. Traverse the state points corresponding to each moment in chronological order, identify the moment when the Lyapunov exponent changes from negative to positive or from positive to negative, and mark the moment when the sign changes as the bifurcation point moment marker. Analyze the spatial distribution pattern of the Lyapunov exponential field in the neighborhood of the state point corresponding to each bifurcation point time marker, and determine the bifurcation type label based on the number and configuration relationship of expansion and contraction directions; Starting from the state point corresponding to each bifurcation point, the trajectory is extended along the expansion direction where the Lyapunov exponent is positive, and the attractor candidate regions that the state trajectory can reach are tracked. All tracked attractor candidate regions constitute the set of states that can be reached after bifurcation. The bifurcation point time identifier, the bifurcation type label, and the set of reachable states after the bifurcation are associated and integrated to form the fault evolution trajectory prediction result.

[0039] like Figure 2 As shown, the method includes: After obtaining the saddle point distribution, it is necessary to use the saddle point as the core anchor point and expand outward to state points within a predetermined range around the saddle point, incorporating these state points into the calculation range of the local Lyapunov exponent. The predetermined range can be adaptively determined based on the local density in the topological embedding space, for example, taking a spherical neighborhood centered on the saddle point with a radius several times the local average neighborhood spacing, ensuring coverage of a representative phase space region around the saddle point. For each state point included in the calculation, its corresponding time delay coordinate vector is extracted. This delay coordinate vector is composed of the state feature vectors of the previous time step arranged sequentially according to the time delay step, carrying complete phase space information of the local dynamics.

[0040] For each state point's delayed coordinate vector, its Jacobian matrix is ​​calculated in phase space. The Jacobian matrix reflects the local linearization dynamics of the state trajectory near that point in phase space, and its elements describe how small perturbations in each embedded dimension evolve over time. Specifically, a finite-difference approximation is performed on the difference between delayed coordinate vectors at adjacent time points to construct a linear mapping matrix of the local tangent space, i.e., a numerical estimate of the Jacobian matrix. Eigenvalue decomposition is then performed on this Jacobian matrix; the real parts of the resulting eigenvalues ​​correspond to the local Lyapunov exponents in each principal direction. A positive real part indicates that adjacent trajectories diverge in that direction, corresponding to an expansion direction; a negative real part indicates that adjacent trajectories converge in that direction, corresponding to a contraction direction. By repeating the above process for all state points included in the calculation, the set of local Lyapunov exponents for each state point in different directions is obtained.

[0041] The local Lyapunov exponents of each state point are spatially mapped according to their coordinate positions in phase space, that is, the position coordinates of each state point are associated with its corresponding local Lyapunov exponent value, forming a scalar field or vector field defined in phase space, constituting the Lyapunov exponent field. The distribution of this field in phase space reveals the dynamic stability characteristics of different regions: in the convergent region, the exponent field takes a negative value, indicating that the system tends to be stable; in the divergent region, the exponent field takes a positive value, indicating that the system is in an unstable expansion state; near the saddle point, the exponent field exhibits a mixed positive and negative distribution in different directions, reflecting the hyperbolic geometry of the saddle point. The spatial continuity of the Lyapunov exponent field is guaranteed by interpolation processing of discrete state points. Methods such as radial basis function interpolation or local weighted regression can be used to extend the exponent values ​​at discrete points into a continuous distribution in phase space.

[0042] After constructing the Lyapunov exponent field, the state points at each time point are traversed sequentially, and the trend of the maximum Lyapunov exponent along the state trajectory over time is continuously monitored. When the maximum Lyapunov exponent changes from negative to positive after crossing zero, it means that the system has entered a chaotic or divergent evolution mode from a stable evolution mode, corresponding to the triggering of fault aggravation or instability events. When the maximum Lyapunov exponent falls back from positive to negative, it means that the system has re-entered a convergent state, which may correspond to fault self-healing or the system entering a new stable attractor. The moments of these sign changes are recorded as bifurcation point time markers. Each bifurcation point time marker accurately locates the critical moment when the dynamic structure undergoes a qualitative change during the fault evolution process, providing a time window basis for subsequent intervention and control. To avoid spurious sign changes caused by noise, a persistence judgment threshold can be set, requiring the sign change to remain stable for a certain number of consecutive time points before it can be confirmed as a valid bifurcation point.

[0043] For each bifurcation point, the spatial distribution pattern of the Lyapunov exponential field in the neighborhood of its corresponding state point is analyzed, focusing on the number and spatial configuration of expansion and contraction directions to determine the bifurcation type label. If only a single expansion direction exists in the neighborhood while the rest are contraction directions, it corresponds to a saddle-node bifurcation, where the stable fixed point is lost near that point. If the real part of a pair of conjugate complex eigenvalues ​​changes from negative to positive, it corresponds to a Hopf bifurcation, transforming from a stable focus to a limiting cycle oscillation. If multiple directions simultaneously change from contraction to expansion, it corresponds to a higher-dimensional bifurcation type, such as a torus bifurcation or a chaotic bifurcation. Accurate identification of the bifurcation type label relies on a detailed analysis of the eigenvalue structure of the Jacobian matrix, including whether the eigenvalues ​​are real numbers, whether they appear in conjugate pairs, and the rate of change of the real part of the eigenvalues.

[0044] Starting from the state point corresponding to each bifurcation point, the trajectory is extended along the expansion direction with a positive Lyapunov exponent to trace the reachable region of the state trajectory in phase space. The trajectory extension employs a numerical integration method, using the state vector at the bifurcation point as the initial condition, applying a small perturbation along the expansion direction, and then integrating to gradually trace the long-term trend of the trajectory. When the trajectory enters a density clustering region and stably cycles or converges within it, this region is identified as a reachable attractor candidate region. Extending the trajectory in different expansion directions reveals multiple different attractor candidate regions, reflecting the reality that the system has multiple competing evolution paths after bifurcation. All attractor candidate regions traced from the same bifurcation point are collected to form the reachable state set corresponding to that bifurcation point. Different attractor candidate regions in the reachable state set correspond to different fault modes or operating states, providing a clear target state space for subsequent fault-tolerant control strategy selection.

[0045] By associating and integrating three types of information—bifurcation point time identifier, bifurcation type label, and the set of reachable states after bifurcation—with the bifurcation point time identifier as the primary key and the corresponding bifurcation type label and the set of reachable states as attribute fields, a structured fault evolution trajectory prediction result is formed. This prediction result fully describes when, in what bifurcation mode, and to which possible fault states the liquid cooling system will evolve from its current operating state under fault evolution drive, providing a precise dynamic basis for the subsequent construction of causal inference maps and the generation of multi-stage fault-tolerant control sequences.

[0046] In one optional implementation, based on the fault evolution trajectory prediction results, a causal inference graph integrating domain physics knowledge is established. This causal inference graph constructs its structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. Each attractor candidate region in the set of reachable states after bifurcation is used as a state node in the causal graph structure. Establish an initial directed connection relationship between the state nodes. For each bifurcation point time marker, establish a directed edge between the state node corresponding to the bifurcation point and each state node in the set of reachable states after the bifurcation. The directed edge represents the reachable path of state evolution. Obtain the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system, and convert the energy balance relationship characterized by the thermodynamic conservation constraints and the mass conservation relationship and momentum conservation relationship characterized by the fluid dynamic constraints into physical constraints that must be satisfied between state nodes. Traverse each directed edge in the initial directed connection relationship, determine whether the state transition between the two state nodes connected by the directed edge satisfies the physical constraint conditions, delete the directed edges that do not satisfy the physical constraint conditions, retain the directed edges that satisfy the physical constraint conditions, and form a set of causal edges that conform to physical laws by retaining the retained directed edges. The state nodes are combined with the set of causal edges to construct a causal graph structure.

[0047] After obtaining the predicted fault evolution trajectory, the candidate regions of each attractor in the set of reachable states after bifurcation are extracted and used as the basic building blocks of the causal graph structure, i.e., state nodes. Each candidate region of attractor corresponds to a stable or metastable operating mode of the liquid cooling system in phase space, such as the normal operating state domain, the local overheating state domain, and the flow imbalance state domain. Each state node carries the central feature vector, coverage area, and member point set information obtained by density clustering of the candidate region of attractor. The physical differences between different candidate regions of attractor constitute the semantic basis for subsequent causal inference.

[0048] Based on the state evolution information recorded by the bifurcation point time markers, initial directed connections are established between state nodes. For each bifurcation point time marker, directed edges are established between the source state node corresponding to that bifurcation point and all target state nodes in the set of reachable states after the bifurcation. The direction of the directed edges represents the temporal order of state evolution and the reachable path. If the bifurcation type label corresponding to a bifurcation point is a saddle-node bifurcation, then its number of successor state nodes is usually two, corresponding to two different stable attractors; if it is a transcritical bifurcation, then there is a stability exchange relationship between the successor state nodes. The initial directed connections constitute the topological skeleton of the causal graph, but at this time, the directed edges have not yet been physically validated, thus containing false connections that violate the physical laws of the liquid cooling system.

[0049] The thermodynamic and hydrodynamic constraints of the liquid cooling system are obtained and converted into physical constraints that must be satisfied between state nodes. The thermodynamic conservation constraints, centered on the energy balance relationship, require that the changes in heat input, output, and storage satisfy the energy conservation equation during state transitions between any two state nodes. Specifically, for the transition from state node... To the state node If the directed edge, This indicates the amount of heat absorbed by the system from the heat source during the transfer process. This represents the heat dissipated to the cooling medium. The energy balance constraint represents the change in the internal energy of the system. If the state transition corresponding to a directed edge violates the equation (outside the allowable numerical error range), then the directed edge is determined to not satisfy the thermodynamic conservation constraint.

[0050] Fluid dynamics constraints encompass two levels: mass conservation and momentum conservation. The mass conservation principle requires that at any pipe node in the liquid cooling system, the mass of coolant flowing in per unit time equals the mass of coolant flowing out, meaning there should be no unwarranted increase or decrease in mass. For two state nodes connected by a directed edge, if the corresponding flow characteristic components exhibit mass imbalance at each pipe node, then the directed edge violates the mass conservation constraint. The momentum conservation principle requires that the pressure drop and velocity distribution of the coolant in the pipe satisfy the simplified form of the Navier-Stokes equations, i.e., a reasonable proportional relationship exists between the pressure drop and the square of the velocity. For two state nodes connected by a directed edge, if the ratio between their pressure drop characteristic component and velocity characteristic component exceeds a reasonable range, then the directed edge violates the momentum conservation constraint. These three types of physical constraints are unified into computable discrimination rules, which serve as the basis for subsequent edge selection.

[0051] For each directed edge in the initial directed connection, the physical validity of the state transition between the two connected state nodes is judged sequentially. The judgment process proceeds in the order of energy balance constraint, mass conservation constraint, and momentum conservation constraint. If any one of these constraints is not satisfied, the directed edge is marked as pending deletion. After traversing all directed edges, all directed edges marked as pending deletion are removed from the initial directed connection, retaining only those directed edges that simultaneously satisfy all three types of physical constraints. The retained directed edges constitute a set of causal edges that conform to physical laws. Each causal edge in this set not only reflects the temporal reachability of state evolution but also guarantees the physical self-consistency of the state transition process at the thermodynamic and fluid dynamic levels.

[0052] After the causal edge selection is completed, the set of causal edges is further semantically annotated. For each retained causal edge, a semantic attribute is assigned according to its corresponding bifurcation type label. For example, it indicates whether the fault propagation mechanism represented by the causal edge is a heat accumulation path caused by insufficient coolant flow or a flow imbalance path caused by abnormal pump pressure. These semantic attributes provide physical support for the subsequent calculation of the minimum intervention action set on the causal graph structure, enabling intervention actions to accurately locate specific fault propagation links.

[0053] By combining the set of state nodes with the set of causal edges, a complete causal graph structure is constructed. The causal graph structure is presented as a directed acyclic graph, where each node corresponds to the operating state of the liquid cooling system described by an attractor candidate region, and each directed edge corresponds to a causal path of state evolution verified by physical constraints. Because spurious connections that do not satisfy physical constraints are removed, the topological relationships in the causal graph structure faithfully reflect the real causal dependencies that exist in the liquid cooling system during fault evolution, rather than pseudo-causal associations obtained merely based on statistical correlation. In actual liquid cooling systems, various physical quantities such as coolant temperature, flow rate, pump speed, and valve opening are coupled together. By embedding thermodynamic conservation constraints and fluid dynamic constraints as structured priors, the causal graph structure effectively filters out spurious causal connections introduced by sensor noise, measurement errors, or random disturbances, resulting in a causal inference graph with high physical reliability. This provides a reliable causal reasoning foundation for the generation of subsequent multi-stage fault-tolerant control sequences.

[0054] In one optional implementation, a set of minimum intervention actions for the dynamic bifurcation point is calculated on the causal graph structure. This set of minimum intervention actions, by cutting off the causal path leading to the evolution of the state trajectory towards the fault attractor structure, causes the liquid cooling system state to reconverge to the rated operating state domain, resulting in a multi-stage fault-tolerant control sequence including: In the cause-effect graph structure, identify the target state node corresponding to the rated working state. The target state node is the state node in the cause-effect graph structure that is not identified as a fault attracting substructure. For each dynamic bifurcation point in the causal graph structure, extract all causal paths from the state node corresponding to the dynamic bifurcation point through the causal edge set to the fault attractor structure, and identify all causal paths as the fault evolution path set. Traverse each causal path in the set of fault evolution paths, identify the blockable causal edges on the causal paths, the blockable causal edges are causal edges that can block the evolution of the state trajectory to the fault attractor structure after being cut off, calculate the control actions required to cut off each blockable causal edge, and establish a mapping relationship between the control actions and the corresponding blockable causal edges. With the goal of cutting off all causal paths in the set of fault evolution paths, a combination of control actions that can cover all fault evolution paths and has the lowest control cost is selected from the mapping relationship to form a set of minimal intervention actions. According to the order of occurrence of each dynamic bifurcation point in the time series, the set of minimum intervention actions corresponding to each dynamic bifurcation point is arranged in chronological order to form a multi-stage fault-tolerant control sequence.

[0055] After establishing the cause-effect graph structure, it is necessary to identify the target state nodes corresponding to the rated operating state of the liquid cooling system. The rated operating state domain refers to the set of states corresponding to the stable operation of the liquid cooling system within its design specifications, including states where core parameters such as coolant flow rate, temperature, and pressure are all within normal threshold ranges. The identification criteria for target state nodes are: in the cause-effect graph structure, any state node not identified as a fault attractor structure is considered a potential candidate for target state node. Furthermore, based on the analysis results of the Lyapunov exponent field, state nodes whose local Lyapunov exponents are all negative are selected as the final target state nodes. This means that the state trajectory in the neighborhood of this node has convergence and can represent the stable rated operating state of the system. Accurate identification of target state nodes is a prerequisite for subsequent calculation of the minimum intervention action set. Only by clearly defining the target state that the system needs to recover to can the fault evolution path be directionally cut off.

[0056] For each dynamic bifurcation point in the causal graph structure, all causal paths from the state node corresponding to that bifurcation point, through the set of causal edges, to the fault attractor structure are extracted. Specifically, the causal graph structure is treated as a directed graph, with the state node corresponding to the bifurcation point as the starting node and the state nodes corresponding to each fault attractor structure as the ending nodes. A depth-first search algorithm is used to traverse all directed paths in the directed graph, enumerating all directed paths from the starting node to each ending node. Each directed path consists of a series of sequentially connected causal edges, representing a possible causal propagation link in which the system state gradually evolves from the bifurcation point to the fault attractor structure. All enumerated directed paths are summarized to form the fault evolution path set corresponding to that bifurcation point. In actual liquid cooling systems, the fault evolution path set often contains multiple parallel or intersecting causal paths. For example, a decrease in coolant pump speed leads to insufficient flow, which in turn causes poor heat dissipation and ultimately triggers a thermal runaway fault attractor; or a partial blockage in the pipeline causes abnormal pressure difference, which triggers control instability through abnormal feedback from the temperature sensor, and so on.

[0057] Traverse each causal path in the fault evolution path set, identifying blockable causal edges on each path. The criterion for a blockable causal edge is: cutting off the causal edge will topologically break the corresponding causal path, meaning that the fault attractor structure cannot be reached again from the bifurcation point state node along the path. It is important to note that some causal edges physically correspond to internal physical processes in the liquid cooling system that cannot be directly intervened in (such as natural convection heat transfer). These causal edges are not blockable and should be excluded during the identification phase. For each identified blockable causal edge, calculate the control action required to cut it off. The calculation process for the control action is based on the thermodynamic conservation constraints and fluid dynamic constraints embedded in the causal graph structure, combined with the physical model of the liquid cooling system, to determine the control variables that need to be adjusted and their adjustment range. For example, if a blockable causal edge corresponds to the causal relationship of "insufficient coolant flow → increased thermal resistance," then the control action required to cut off this causal edge is to increase the coolant pump speed to the target speed value that restores the flow rate to the rated range. Each control action is mapped to its corresponding blockable causal edge to form a control action mapping table, which is used for subsequent optimization selection of the minimum set of intervention actions.

[0058] Suppose that the causal graph structure identifies the common features. There are 3 fault evolution paths, and the set of blockable causal edges on each path is denoted as . ( The control action mapping table contains a total of The candidate control action, the first The control cost of each candidate control action is denoted as . ( The objective of constructing the minimum set of intervention actions is to minimize the total control cost of the selected combination of control actions while satisfying the constraint of covering all fault evolution paths. Minimum, of which Let this be the set of indices for the selected control actions. This problem is formally equivalent to the weighted set covering problem, and can be solved using a greedy approximation algorithm: in each iteration, select the control action that covers the most fault evolution paths per unit cost and add it to the set. Then, remove already covered paths from the set of paths to be covered, repeating the above process until all fault evolution paths are covered. The final combination of control actions constitutes the minimum set of intervention actions for the current dynamic bifurcation point. Control cost The quantitative basis includes multi-dimensional evaluation indicators such as the energy consumption of the control action, the degree of disturbance to other subsystems of the liquid cooling system, and the response delay, which are calculated by weighted summation.

[0059] After obtaining the minimum intervention action set corresponding to each dynamic bifurcation point, these bifurcation points are arranged according to their temporal order. The temporal order of the bifurcation points is directly given by the bifurcation point time markers in the fault evolution trajectory prediction results; intervention actions corresponding to bifurcation points with earlier time markers should be executed first. The minimum intervention action sets for each bifurcation point are arranged sequentially according to their chronological order to form a multi-stage fault-tolerant control sequence. In the multi-stage fault-tolerant control sequence, each stage corresponds to a dynamic bifurcation point time, and the control actions to be executed within that stage are given by the corresponding minimum intervention action set. The time interval between adjacent stages is determined by the time difference between adjacent bifurcation points. After the control execution layer completes the control actions of the current stage, it waits until the next bifurcation point time arrives before executing the control actions of the next stage.

[0060] During the execution of the multi-stage fault-tolerant control sequence, the real-time status of the liquid cooling system needs to be continuously monitored to determine whether the current state trajectory has deviated from the attraction domain of the fault attractor structure and converged towards the target state node. If the system state has successfully converged to the rated operating state domain after executing the corresponding minimum intervention action set in a certain stage, the execution of control actions in subsequent stages is terminated to avoid unnecessary over-intervention. If the system state fails to converge as expected, a recalculation mechanism is triggered to re-extract the fault evolution path set and update the minimum intervention action set based on the latest system state, ensuring the adaptability and robustness of the fault-tolerant control sequence. Through the execution of the above multi-stage fault-tolerant control sequence, the liquid cooling system can receive precise intervention at key bifurcation points in the fault evolution process, guiding the system state back to the rated operating state domain from the potential fault trajectory with minimal control cost, thus achieving efficient fault-tolerant operation of the liquid cooling system.

[0061] A second aspect of the present invention provides an AI fault diagnosis and fault tolerance system for a liquid cooling system, comprising: The modeling and representation unit is used to model the operating data of the liquid cooling system and obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics. The fault prediction unit is used to map the multi-scale spatiotemporal topological representation to the topological embedding space through the time-delay embedding method, identify the fault attractor structure and saddle point distribution of the liquid cooling system state trajectory in the topological embedding space, calculate the Lyapunov exponential field of the state trajectory in the phase space based on the saddle point distribution, identify the dynamic bifurcation point in the fault evolution process according to the sign change of the Lyapunov exponential field, and obtain the fault evolution trajectory prediction result including the bifurcation point time identifier, bifurcation type label and the set of reachable states after bifurcation. The causal graph unit is used to establish a causal inference graph that integrates domain physics knowledge based on the fault evolution trajectory prediction results. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. A fault-tolerant control unit is used to calculate the minimum set of intervention actions for the dynamic bifurcation point on the causal graph structure. The minimum set of intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

[0062] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0063] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0064] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An AI-based fault diagnosis and fault tolerance method for liquid cooling systems, characterized in that, include: The operational data of the liquid cooling system are modeled to obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics; The multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. In this space, the fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory are identified. Based on the saddle point distribution, the Lyapunov exponential field of the state trajectory in phase space is calculated. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. This yields a fault evolution trajectory prediction result containing bifurcation point time markers, bifurcation type labels, and the set of reachable states after the bifurcation. Based on the predicted fault evolution trajectory, a causal inference graph integrating domain physics knowledge is established. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. On the causal graph structure, the set of minimum intervention actions for the dynamic bifurcation point is calculated. The set of minimum intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

2. The method according to claim 1, characterized in that, Modeling the operational data of the liquid cooling system yields a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics, including: The system collects operational data of the liquid cooling system at multiple points in time using a distributed sensor network. The sensor nodes, actuator nodes, and heat exchange unit nodes in the liquid cooling system are constructed as a set of vertices of a hypergraph. Each group of nodes with a heat flow transfer path or control feedback loop is identified and connected by hyperedges. The mutual information or correlation coefficient of the measured values ​​between the nodes is calculated based on the operating data as the weight of the hyperedge. Multiple hyperedge convolutional layers are set up. Each hyperedge convolutional layer uses a hyperedge aggregation operator to perform weighted aggregation of the features of all nodes connected to the same hyperedge, and then feeds the aggregation result back to each node connected by the hyperedge to update the hidden layer representation of the node. Through the layer-by-layer propagation of the multi-layer hyperedge convolutional layers, the node features are fused with dependency information from across physical subsystems. The final hidden layer representation of each node is then concatenated with the corresponding time label to form a snapshot feature vector sequence containing spatial topological dependencies. The snapshot feature vector sequence is input into the temporal coding module, which extracts the evolution pattern between adjacent snapshots by applying a cyclic connection structure in the time dimension, and outputs a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics.

3. The method according to claim 1, characterized in that, The multi-scale spatiotemporal topological representation is mapped to a topological embedding space using a time-delay embedding method. The fault attractor structure and saddle point distribution of the liquid cooling system's state trajectory are identified within this topological embedding space, including: Based on the multi-scale spatiotemporal topological representation, a time series vector is constructed. For each moment in the time series vector, the feature vectors of the current moment and a preset number of previous historical moments are extracted. The extracted feature vectors of multiple historical moments are concatenated in chronological order to form the delayed coordinate vector corresponding to the current moment. The delay coordinate vectors corresponding to all times are used to form a set of state trajectory points in the topological embedding space. The set of state trajectory points forms a trajectory curve of the liquid cooling system state evolving over time in the topological embedding space. Density clustering analysis is performed on the set of state trajectory points to identify clustered regions of state points in the topological embedding space, and clustered regions where state trajectories repeatedly converge are identified as attractor candidate regions. Calculate the liquid cooling system performance index in the operating data corresponding to the state point within the attractor candidate region, and determine the attractor candidate region where the liquid cooling system performance index exceeds the preset normal operating range as a fault attractor structure. The manifold topology of the state trajectory in the topological embedding space is identified. By calculating the expansion rate and contraction rate in different directions within the neighborhood of the state point, the position of the state point that has both expansion and contraction directions is identified. The position is marked as a saddle point, and the spatial distribution of the saddle points constitutes the saddle point distribution.

4. The method according to claim 3, characterized in that, Based on the saddle point distribution, the Lyapunov exponential field of the state trajectory in phase space is calculated. The dynamic bifurcation points in the fault evolution process are identified based on the sign changes of the Lyapunov exponential field. The resulting fault evolution trajectory prediction results, including bifurcation point time markers, bifurcation type labels, and the set of reachable states after bifurcation, are as follows: Based on the saddle point and the state points within a preset range around the saddle point, the delay coordinate vector corresponding to the state point at the time is extracted, the Jacobian matrix of the delay coordinate vector in the phase space is calculated and the eigenvalues ​​are solved to obtain the local Lyapunov exponents of the state point in different directions. The local Lyapunov exponents are spatially mapped according to the position of the state point in the phase space to form the Lyapunov exponent field. Traverse the state points corresponding to each moment in chronological order, identify the moment when the Lyapunov exponent changes from negative to positive or from positive to negative, and mark the moment when the sign changes as the bifurcation point moment marker. Analyze the spatial distribution pattern of the Lyapunov exponential field in the neighborhood of the state point corresponding to each bifurcation point time marker, and determine the bifurcation type label based on the number and configuration relationship of expansion and contraction directions; Starting from the state point corresponding to each bifurcation point, the trajectory is extended along the expansion direction where the Lyapunov exponent is positive, and the attractor candidate regions that the state trajectory can reach are tracked. All tracked attractor candidate regions constitute the set of states that can be reached after bifurcation. The bifurcation point time identifier, the bifurcation type label, and the set of reachable states after the bifurcation are associated and integrated to form the fault evolution trajectory prediction result.

5. The method according to claim 1, characterized in that, Based on the predicted fault evolution trajectory, a causal inference graph integrating domain physics knowledge is established. This causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. Each attractor candidate region in the set of reachable states after bifurcation is used as a state node in the causal graph structure. Establish an initial directed connection relationship between the state nodes. For each bifurcation point time marker, establish a directed edge between the state node corresponding to the bifurcation point and each state node in the set of reachable states after the bifurcation. The directed edge represents the reachable path of state evolution. Obtain the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system, and convert the energy balance relationship characterized by the thermodynamic conservation constraints and the mass conservation relationship and momentum conservation relationship characterized by the fluid dynamic constraints into physical constraints that must be satisfied between state nodes. Traverse each directed edge in the initial directed connection relationship, determine whether the state transition between the two state nodes connected by the directed edge satisfies the physical constraint conditions, delete the directed edges that do not satisfy the physical constraint conditions, retain the directed edges that satisfy the physical constraint conditions, and form a set of causal edges that conform to physical laws by retaining the retained directed edges. The state nodes are combined with the set of causal edges to construct a causal graph structure.

6. The method according to claim 5, characterized in that, On the causal graph structure, a set of minimum intervention actions for the dynamic bifurcation point is calculated. This set of minimum intervention actions cuts off the causal path that causes the state trajectory to evolve towards the fault attractor structure, causing the liquid cooling system state to reconverge to the rated operating state domain. The resulting multi-stage fault-tolerant control sequence includes: In the cause-effect graph structure, identify the target state node corresponding to the rated working state. The target state node is the state node in the cause-effect graph structure that is not identified as a fault attracting substructure. For each dynamic bifurcation point in the causal graph structure, extract all causal paths from the state node corresponding to the dynamic bifurcation point through the causal edge set to the fault attractor structure, and identify all causal paths as the fault evolution path set. Traverse each causal path in the set of fault evolution paths, identify the blockable causal edges on the causal paths, the blockable causal edges are causal edges that can block the evolution of the state trajectory to the fault attractor structure after being cut off, calculate the control actions required to cut off each blockable causal edge, and establish a mapping relationship between the control actions and the corresponding blockable causal edges. With the goal of cutting off all causal paths in the set of fault evolution paths, a combination of control actions that can cover all fault evolution paths and has the lowest control cost is selected from the mapping relationship to form a set of minimal intervention actions. According to the order of occurrence of each dynamic bifurcation point in the time series, the set of minimum intervention actions corresponding to each dynamic bifurcation point is arranged in chronological order to form a multi-stage fault-tolerant control sequence.

7. An AI fault diagnosis and fault-tolerance system for liquid cooling systems, used to implement the method as described in any one of claims 1-6, characterized in that, include: The modeling and representation unit is used to model the operating data of the liquid cooling system and obtain a multi-scale spatiotemporal topological representation that integrates spatial topological dependence and temporal evolution characteristics. The fault prediction unit is used to map the multi-scale spatiotemporal topological representation to the topological embedding space through the time-delay embedding method, identify the fault attractor structure and saddle point distribution of the liquid cooling system state trajectory in the topological embedding space, calculate the Lyapunov exponential field of the state trajectory in the phase space based on the saddle point distribution, identify the dynamic bifurcation point in the fault evolution process according to the sign change of the Lyapunov exponential field, and obtain the fault evolution trajectory prediction result including the bifurcation point time identifier, bifurcation type label and the set of reachable states after bifurcation. The causal graph unit is used to establish a causal inference graph that integrates domain physics knowledge based on the fault evolution trajectory prediction results. The causal inference graph constructs a causal graph structure by embedding the thermodynamic conservation constraints and fluid dynamic constraints of the liquid cooling system as structured priors. A fault-tolerant control unit is used to calculate the minimum set of intervention actions for the dynamic bifurcation point on the causal graph structure. The minimum set of intervention actions cuts off the causal path that causes the state trajectory to evolve into the fault attractor structure, so that the state of the liquid cooling system reconverges to the rated operating state domain, thus obtaining a multi-stage fault-tolerant control sequence.

8. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 6.

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