Water engineering group risk toughness regulation and control method considering uncertainty

Abstract

The invention discloses a water engineering group risk toughness regulation and control method considering uncertainty, and the method comprises the steps: building a double-track dynamic hierarchical structure based on the obtained working condition and hydrological data of a water engineering group, and generating a toughness performance boundary representing the lower limit of system performance and a current toughness performance state considering the uncertainty; the method comprises the following steps: judging the regulation potential of a toughness failure project by identifying a performance gap and tracking a cross-level failure chain, and dividing the toughness failure project into a regulable failure project set and a non-regulable failure project set; and aiming at the two types of failure project sets, carrying out self regulation and control optimization by adopting a multi-target reinforcement learning guided mixed gradient search algorithm and carrying out collaborative regulation and control optimization by adopting a collaborative-competitive co-evolution algorithm so as to output an optimal scheduling scheme set. According to the method, the system structure can be dynamically cognized, the risk conduction can be accurately traced, and the risk active defense capability and the system toughness of the water engineering group under uncertainty disturbance can be remarkably improved.

Description

Technical Field

[0001] The present invention relates to water conservancy project scheduling technology, in particular to a water project group risk resilience control method considering uncertainty. Background Art

[0002] As complex systems composed of various hydraulic facilities, including reservoirs, levees, and sluice gates, water conservancy projects are the core physical carriers of flood control and disaster reduction, water resource optimization, and ecological and environmental protection in river basins. Therefore, improving the control capabilities of water conservancy projects in the face of strong disturbances such as super-standard floods and forecast uncertainty, and shifting from the traditional passive response and single-objective optimization model to an active defense and intelligent, refined control model centered on system resilience, has become a cutting-edge scientific issue that urgently needs to be addressed in the field of water conservancy engineering. It has significant theoretical and practical significance for ensuring river basin security and promoting sustainable development.

[0003] Research on the optimization of water conservancy project operations has made considerable progress. Existing technical solutions are mostly based on a deterministic flood forecasting process, employing conventional optimization algorithms such as linear programming, dynamic programming, or genetic algorithms to optimize the scheduling rules for a conservancy project. In terms of system description, hydraulic models are typically constructed based on fixed, physical connections between projects (such as upstream and downstream river connections) to simulate flood evolution. Regarding scheduling objectives, these methods often focus on a single, deterministic flood control metric, such as minimizing peak flow or maximum inundation level at a key downstream section. In actual operation, many conservancy projects still rely on relatively fixed scheduling procedures or flood control water level control rules based on historical experience, operating in a phased, rule-based manner during floods to ensure basic flood control safety. These methods are effective in addressing standard, routine flood events with high forecast accuracy and constitute a crucial technical foundation for the safe operation of conservancy projects.

[0004] However, as understanding of the complexity of water project systems and the uncertainties of their operating environments deepens, existing solutions are facing a series of profound technical problems in addressing future challenges. These problems primarily arise from insufficient understanding of the system's dynamic characteristics and a poor understanding of risk transmission mechanisms, which limits the accuracy and foresight of regulatory decisions.

[0005] Specifically, current methods overly rely on fixed physical topologies to describe the system, failing to reveal the ever-changing dynamic hydraulic connections between projects under extreme hydrological conditions, resulting in a disconnect between the basis for decision-making and the true state of the system. When risks occur, existing technologies can only identify isolated points of failure, but are unable to trace the root cause of the failure and its complete chain of transmission across multiple levels and dimensions within the system. The absence of these underlying mechanisms makes it difficult to precisely implement regulatory measures and effectively predict potential cascading collapse risks. Summary of the Invention

[0006] The purpose of the invention is to provide a method for regulating the risk resilience of water engineering groups taking uncertainty into account in order to solve the technical problems existing in the prior art.

[0007] The technical solution is a risk resilience control method for water project groups considering uncertainty, including:

[0008] Based on the acquired water project group operating conditions and hydrological data, a dual-track dynamic hierarchical structure is established, and the resilience performance boundary and current resilience performance status are generated;

[0009] Based on the dual-track dynamic hierarchical structure, toughness performance boundary and current toughness performance status, the control potential of toughness failure engineering is determined and divided into two types of failure engineering sets: controllable and uncontrollable.

[0010] For the two types of failure engineering sets, self-control optimization and collaborative control optimization are performed respectively to output the optimal scheduling solution set.

[0011] Optionally, establish a dual-track dynamic hierarchy, including:

[0012] Read the permanent engineering connection relationship from the water project group working condition data to build a steady-state physical skeleton hierarchy;

[0013] In response to the real-time hydraulic state presented by hydrological data, a hydraulic coupling tensor is established to quantify the strength of dynamic correlation between projects, and a time-varying dynamic response hierarchy is generated based on the hydraulic coupling tensor;

[0014] Based on the hydraulic coupling tensor, the physical skeleton level and the dynamic response level are weightedly fused to obtain a dual-track dynamic hierarchical structure.

[0015] Optionally, construct a hydraulic coupling tensor, including:

[0016] Based on the real-time hydraulic status, the water level propagation relationship representing the mutual influence of water levels between projects, the flow propagation relationship representing the mutual influence of flows, and the water level-flow coupling relationship representing the influence of water levels on downstream flows are calculated respectively.

[0017] The three relationships are quantified into water level propagation matrix, flow propagation matrix and water level-flow coupling matrix respectively;

[0018] The water level propagation matrix, the flow propagation matrix, and the water level-flow coupling matrix are weightedly combined to synthesize the hydraulic coupling tensor.

[0019] Optionally, based on the hydraulic coupling tensor, a weighted fusion of the physical skeleton level and the dynamic response level is performed, including:

[0020] Calculate the spatial variance of the hydraulic coupling tensor and determine the time-varying hierarchical fusion weight coefficient based on the spatial variance;

[0021] The hierarchical fusion weight coefficient is used to perform a weighted combination of the physical skeleton level and the dynamic response level to generate a dual-track dynamic hierarchical structure.

[0022] Optionally, before determining the control potential of the toughness failure engineering, the following is also included:

[0023] Compare the current toughness performance state with the toughness performance boundary and calculate the performance gap;

[0024] Calculate the probability of failure risk when the performance gap is lower than the preset value under uncertain disturbance;

[0025] When the absolute mean of the failure risk probability and the performance gap exceeds their respective probability thresholds and performance gap thresholds at the same time, the corresponding project is determined to be a resilient failure node, forming a resilient failure node set.

[0026] Optionally, determining the control potential of the resilience failure project, after obtaining the resilience failure node set, further includes:

[0027] Based on the current resilience performance status and resilience performance boundary, nodes with surplus performance are selected to form a set of control sources;

[0028] For any resilient failure node in the resilient failure node set, search for a closed-loop collaborative path connecting the failure node and at least one control source in the dual-track dynamic hierarchical structure;

[0029] At least one feasibility score of the closed-loop collaborative path is calculated to characterize the control potential of the resilient failure node.

[0030] Optionally, a feasibility score of the closed-loop collaborative path is calculated, including:

[0031] Comprehensively evaluate at least two of the following performance indicators of the closed-loop collaborative path: path length, total response time, control efficiency, and net performance improvement;

[0032] Based on the evaluation results of at least two performance indicators, a feasibility score is generated.

[0033] Optionally, it is divided into two types of failure engineering sets: controllable and uncontrollable, including:

[0034] comparing the feasibility score to a preset feasibility score threshold;

[0035] If the feasibility score is not less than the feasibility score threshold, the corresponding toughness failure node is divided into the controllable failure engineering set;

[0036] Otherwise, the resilient failure nodes are divided into the uncontrollable failure engineering set.

[0037] Optionally, for the two types of failure engineering sets, performing self-control optimization and collaborative control optimization respectively includes:

[0038] For the set of controllable failure engineering, a hybrid gradient search algorithm guided by multi-objective reinforcement learning is used for optimization;

[0039] The uncontrollable failure engineering set is combined with its matching auxiliary control engineering set and optimized using the collaborative-competitive co-evolution algorithm.

[0040] Optionally, the set of controllable failure engineering projects is optimized using a hybrid gradient search algorithm guided by multi-objective reinforcement learning, including:

[0041] Based on the physical constraints of the controllable failure engineering set, a safe exploration space is established to limit the range of control actions;

[0042] In the safe exploration space, a multi-objective reinforcement learning agent is used to generate initial control actions;

[0043] The gradient search algorithm is used to fine-tune the initial control action, while ensuring that the adjusted action does not exceed the boundary of the safe exploration space, thereby obtaining an optimized control action sequence.

[0044] Beneficial effects include dynamically understanding system structure, accurately tracing risk transmission, and significantly improving the proactive risk prevention capabilities and system resilience of water projects under uncertain perturbations. Related technical effects will be described later. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the present invention.

[0046] Figure 2 It is a flow chart of establishing a dual-track dynamic hierarchical structure according to the present invention.

[0047] Figure 3 It is a flow chart of constructing the hydraulic coupling tensor of the present invention.

[0048] Figure 4 It is a flow chart of the present invention based on the hydraulic coupling tensor, weighted fusion of the physical skeleton level and the dynamic response level. DETAILED DESCRIPTION

[0049] In order to solve the above problems existing in the prior art, the applicant conducted an in-depth analysis and found that:

[0050] Existing methods generally rely on static system topologies and are unable to accurately capture the dynamic hydraulic coupling relationships between projects that change in real time during floods. The system structure of a water project cluster is not static. Under extreme flood scenarios, factors such as river channel backflow, tributary support, or inter-regional flood surges can cause temporary, highly coupled relationships with significant impacts between projects that are weakly hydraulically connected under normal conditions, and the original key hydraulic transmission paths may also change. Existing methods build models and make decisions based on fixed physical connections. This static understanding ignores the dynamic response characteristics of the system structure, resulting in the inability to identify the truly dominant influencing paths and key nodes during floods. This can lead to suboptimal or even erroneous regulatory decisions based on outdated or inaccurate system states.

[0051] Existing risk assessments and regulatory responses lack the ability to deeply trace the root causes of resilience failures and track the structured transmission pathways. Traditional risk identification is typically point-based and one-dimensional, determining whether a single indicator (such as water level) of a single project exceeds a limit. This approach fails to answer a deeper question: when a system-level resilience failure occurs (such as a decline in the resilience of an entire river basin), exactly which performance type (such as resistance or absorption capacity) at which project node or nodes first fails, and how this failure is transmitted and amplified across different levels (from individual projects to subsystems to the larger system) through interactions between projects. Lacking the ability to track and diagnose this cross-level failure chain, existing approaches often produce delayed and untargeted regulatory responses to systemic risks, making it difficult to precisely address the root causes of risk and proactively intervene in potential cascading failures.

[0052] To this end, the following solutions are provided, combined with Figures 1 to 4 Various embodiments of the present invention are described.

[0053] Example 1: Describe the overall process of the risk resilience control method of a water project group considering uncertainty.

[0054] In this embodiment, a method for regulating risk resilience of a water project group considering uncertainty includes:

[0055] In the first step, based on the acquired water project group operating conditions and hydrological data, a dual-track dynamic hierarchical structure is established, and a resilience performance boundary and a current resilience performance state are generated.

[0056] This step corresponds to a system initialization and status assessment phase. Specifically, the system first reads the basic data of the water project group, such as the project's geographical location, physical connection relationship, storage capacity, discharge capacity and other working condition data, as well as real-time water level, flow and other hydrological data. Then, based on these data, a dual-track hierarchical structure is constructed that can simultaneously reflect the fixed physical topology and real-time hydraulic dynamic relationship between projects. At the same time, through the simulation of historical extreme flood scenarios, the resilience performance boundary that represents the performance bottom line of the system under the most unfavorable conditions is calculated and generated; and, under the composite disturbance considering the uncertainty of the current flood forecast, the system resilience performance state corresponding to the current control scheme is evaluated.

[0057] In the second step, the control potential of the resilience failure engineering is determined based on the hierarchical structure, performance boundaries and performance status, and it is divided into two types of failure engineering sets: controllable and uncontrollable.

[0058] This step corresponds to a risk identification and potential determination stage. The system first compares the current resilience performance state with the resilience performance boundary, quantifies the performance gap, and identifies the engineering nodes with resilience failure based on the probability of exceeding the safety threshold under uncertain disturbances. For these failure nodes, a dual-track hierarchical structure is used to locate and construct failure transmission chains across different levels through a top-down tracking mechanism. On this basis, the system further analyzes whether the failed project can restore its performance through internal or external coordinated regulation, that is, to determine its regulation potential, and finally divide all failed projects into two sets: controllable and uncontrollable. The latter will also match them with corresponding auxiliary regulation resources.

[0059] In the third step, for the two types of failure engineering sets, self-control optimization and collaborative control optimization are performed respectively to output an optimal scheduling solution set.

[0060] This step corresponds to a multi-objective scheduling optimization phase. For the set of controllable failure projects, the system employs an optimization algorithm that focuses on exploiting their inherent regulatory capabilities, such as the multi-objective reinforcement learning-guided hybrid gradient search algorithm (MORL-HG), for adaptive control. For the set of uncontrollable failure projects, the system combines it with a matching set of auxiliary control projects and employs an optimization algorithm that focuses on multi-agent collaboration and resource competition, such as the collaborative-competitive co-evolution algorithm (CCEA-LF), for synergistic efficiency-enhancing control. The solutions generated by the two optimization algorithms are integrated and screened, outputting a set of Pareto-optimal scheduling solutions for decision makers to use.

[0061] In this embodiment, by constructing a dynamic hydraulic coupling tensor based on real-time hydrological data and establishing a dual-track dynamic hierarchical structure based on it, the technical flaw of existing methods, which rely on static topology and fail to reflect true hydraulic connections, is overcome. This solution shifts the understanding of system structure from static to dynamic, real-time mapping, capable of capturing temporary strong coupling paths formed by backwaters and jacking during extreme floods. All subsequent regulatory decisions are based on the most realistic system state, improving their accuracy and relevance. By introducing a cross-level mechanism for tracking and diagnosing resilience failure chains, this approach overcomes the problem of existing risk assessments that can only identify isolated failure points and fail to deeply trace the risk. When systemic risks arise, this method can trace and construct the complete failure transmission path from top to bottom, accurately locating the root project and its specific failure dimension. This shifts the regulatory response from a blind response to a precise attack on the source of the risk, effectively preventing the occurrence of cascading failures. In summary, the present invention improves the proactive risk defense capability and overall resilience of water engineering groups under uncertain disturbances through dynamic cognitive system structure and precise traceability of risk transmission, making scheduling and control more forward-looking, scientific and effective.

[0062] Example 2: This example mainly describes the construction process of the dual-track dynamic hierarchical structure, especially the calculation method of the hydraulic coupling tensor.

[0063] In this embodiment, the process of establishing a dual-track dynamic hierarchical structure specifically includes the following steps:

[0064] Step 1: Analyze the permanent engineering connection relationship included in the water project group operating data and build a steady-state physical skeleton hierarchy.

[0065] The specific implementation method is to read the project number, geographical location, upstream and downstream relationship, and permanent connection information defined by hydraulic structures (such as dams, channels, and tunnels) in the basic data of the water project group. Based on this information, an engineering topology adjacency matrix A is constructed. physical , where if the matrix element A ij =1 indicates that there is a direct and fixed physical connection between project i and project j, otherwise it is 0. On this basis, according to the natural river network structure of the basin, single project nodes are clustered into subsystems (for example, a group of reservoirs on the same tributary), and then the subsystems are combined to form a large system covering the entire basin, thus forming a relatively stable physical skeleton hierarchy L with a three-layer structure of single project-subsystem-large system. physical .

[0066] Step 2: In response to the real-time hydraulic state presented by the hydrological data, a hydraulic coupling tensor is established to quantify the dynamic correlation strength between projects, and a time-varying dynamic response hierarchy is generated based on the hydraulic coupling tensor.

[0067] In this embodiment, the process of constructing a hydraulic coupling tensor is:

[0068] Based on the real-time hydraulic status, the water level propagation relationship that characterizes the mutual influence of water levels between projects, the flow propagation relationship that characterizes the mutual influence of flows, and the water level-flow coupling relationship that characterizes the influence of water levels on downstream flows are calculated respectively.

[0069] The three relationships are quantified into water level propagation matrix, flow propagation matrix and water level-flow coupling matrix respectively.

[0070] The specific implementation method is to read the real-time water level data H(t) and flow data Q(t) and calculate the hydraulic propagation time τ ij (t)=L ij / (g×h avg ) 0.5， Among them L ij is the river distance from project i to project j, g is the acceleration of gravity, h avg is the average water depth of the interval.

[0071] Calculate the water level propagation matrix H HH :H HH,ij =(dH j / dH i )×exp(-τ ij (t) / T0); where H HH,ij The attenuated intensity of the impact of the water level change of project i on the water level of project j; dH j / dH i is the partial derivative affected by water level, which can be approximated by hydraulic model or finite difference method; exp(-τ ij (t) / T0) is an exponential decay term, which indicates that the impact decreases with propagation time; T0 is a characteristic time constant, and its value can be determined according to the flood propagation characteristics of the basin. For example, it can be taken as 50% of the time required for a typical flood wave to propagate to the downstream control section, such as 6 hours.

[0072] Calculate the traffic propagation matrix H QQ :H QQ,ij =(dQ j / dQ i )×exp(-τ ij (t) / T0); where H QQ,ij The attenuated intensity of the impact of the flow change of project i on the flow of project j; dQ j / dQ i is the partial derivative affected by flow.

[0073] Calculate the water level-flow coupling matrix H HQ :H HQ,ij =(dQj / dH i )×exp(-τ ij (t) / T0); where H HQ,ij The attenuated intensity of the impact of the water level change of project i on the flow of project j; dQ j / dH i is the partial derivative of the water level-discharge effect.

[0074] The water level propagation matrix, the flow propagation matrix, and the water level-flow coupling matrix are weightedly combined to synthesize the hydraulic coupling tensor.

[0075] The comprehensive hydraulic coupling strength is calculated as: H ij (t)=w1×|H HH,ij ∣+w2×∣H QQ,ij ∣+w3×∣H HQ,ij ∣; where H ij (t) is the comprehensive hydraulic coupling strength between projects i and j at time t; w1, w2, w3 are weight coefficients, which can be determined based on expert experience or analysis of hydraulic propagation characteristics. For example, for a system mainly used for water level regulation, w1=0.4, w2=0.3, w3=0.3 can be set; |*| represents the absolute value to ensure that the coupling strength is non-negative. The N×N dimensional matrix H(t) calculated in this way is the hydraulic coupling tensor. On this basis, a coupling strength threshold H is set. threshold (For example, the 95% quantile of historical data statistics can be taken). ij (t)>H threshold When , it is considered that there is a temporary strong hydraulic coupling between projects i and j, so a temporary edge is established in the dynamic graph. Subsequently, the community discovery algorithm such as spectral clustering is used to cluster this dynamically generated graph to obtain the time-varying dynamic response level L dynamic (t).

[0076] In step three, based on the hydraulic coupling tensor, the physical skeleton level and the dynamic response level are weightedly integrated to jointly construct a dual-track dynamic hierarchical structure.

[0077] In this step, the spatial variance of the hydraulic coupling tensor is calculated, and a time-varying hierarchical fusion weight coefficient is determined based on the spatial variance. Specifically, the spatial variance V of all element values ​​in the hydraulic coupling tensor matrix H(t) is calculated. ariance (H ij This variance can reflect the uniformity or anomaly of the hydraulic connection across the entire system. When the variance is small, it indicates that the system hydraulic state is stable, and in this case, more emphasis should be placed on stable physical connections. Conversely, when the variance is large, it indicates that strong coupling caused by local flooding or abnormal scheduling may have occurred, and in this case, more attention should be paid to dynamic response relationships. The hierarchical fusion weight system is calculated as follows:

[0078] α(t)=1 / (1+K×V ariance (H ij )); where α(t) is the weight of the physical layer at time t, and its value range is (0,1]; K is the sensitivity coefficient, which is used to adjust the sensitivity of the variance to the weight. It can be calibrated according to historical data or take an empirical value, such as K=0.1.

[0079] Accordingly, the hierarchical fusion weight coefficient is used to perform a weighted combination of the physical skeleton level and the dynamic response level to generate a dual-track dynamic hierarchical structure. The final hierarchical structure L final Determined by weighted fusion decision, for example, for a specific decision (such as determining whether two projects belong to the same subsystem), the decision result can be expressed as Decision = α(t) × D physical +(1-α(t))×D dynamic , where D physical and D dynamic The decision results are based on the physical level and the dynamic level respectively. In this way, a dual-track hierarchical structure is generated that takes into account both static structure and dynamic response.

[0080] Example 3. This example describes an indicator system for quantifying the toughness performance boundary and the current toughness performance state, especially its multi-level aggregation method and weight determination method.

[0081] In this embodiment, the toughness performance boundary and the current toughness performance state are quantified based on a dimensionless performance indicator system including the following four dimensions: resistance performance; absorption performance; recovery performance; and adaptability performance.

[0082] First, it is necessary to calculate a series of normalized structural characteristic factors, such as storage capacity utilization rate Cu, safety elevation margin Hs, dispatch response time lag Td, historical failure frequency θ, etc. These factors are the basis for calculating the four types of performance indicators.

[0083] Specifically, at the single project level, the calculation method for performance indicators in each dimension is as follows:

[0084] Resistance performance Pr(single)=ω r1 ×C u,norm +ω r2 ×H s,norm +ω r3 ×exp(-λ×T d,norm ); This index characterizes the initial ability of the project to resist disturbance, where C u,norm 、H s,norm 、T d,norm are the normalized storage capacity utilization rate, safety height margin and dispatch response time lag respectively; ω r1 ,ωr2 ,ω r3 for their respective weights.

[0085] Absorption performance Pa (single) = (1-θ norm ) ωa1 ×(1-α norm ) ωa2 ×(1-η norm ) ωa3 ; This index characterizes the ability of a project to absorb and withstand damage when subjected to impact, where θ norm ,α norm ,η norm are the normalized historical failure frequency, disturbance sensitivity and functional coupling respectively; ωa1, ωa2, ωa3 are weights.

[0086] Restoration performance Ph(single) = κ norm ωh1 / (1+Δt norm / T ref ) ωh2 ; This indicator characterizes the speed and degree of recovery of the project from the damaged state, where κ norm ,Δt norm are the normalized recovery elastic coefficient and recovery time; T ref is the reference time constant; ωh1, ωh2 are weights.

[0087] Adaptability performance: Adaptability is more reflected at the system level. The single engineering layer may not be calculated separately, or it may be replaced by an indicator of comprehensive learning ability.

[0088] Furthermore, quantification is performed based on a performance indicator system, further including a step of aggregating indicators at a subsystem level.

[0089] In this embodiment, this step aims to reflect the weak link effect and synergistic effect of system engineering. Specific aggregation methods include but are not limited to:

[0090] Subsystem resilience performance Pr(sub) = ∑wi × P r,i (单) ; Where wi is the importance weight of the i-th project in the subsystem, calculated using the weighted average method.

[0091] Adopting the minimum value principle, the minimum value of the absorption performance index of each single project in the subsystem is determined as the absorption performance of the subsystem to reflect the short board effect. (子) =min{P a,i (单) This approach ensures that the absorptive capacity of a subsystem is determined by its weakest link.

[0092] The harmonic mean principle is adopted to calculate the harmonic mean of the resilience performance indicators of each single project in the subsystem, and it is determined as the resilience performance of the subsystem to reflect the collaborative recovery characteristics.

[0093] That is, Ph (子) =n / ∑(1 / P h,i (单) ), where n is the number of projects in the subsystem. The harmonic mean focuses more on individual projects with smaller values, reflecting that the overall recovery efficiency is significantly affected by the slowest-restoring project.

[0094] Subsystem adaptability performance Ps (子) =ωs1×ln(1+C c,norm ×D l,norm ); where C c,norm and D l,norm are the normalized factors that characterize the command and coordination capabilities and scheduling flexibility of the subsystem respectively.

[0095] Optionally, at the macro-system level, the subsystem performance indicators can be further aggregated. For example, the resilience of the macro-system can take into account the unevenness of spatial distribution and be expressed as Pr (大) =μ(Pr (子) )-σ(Pr (子) ), which is the mean of the subsystem resilience minus its standard deviation, so as to reduce the weight of the subsystem with large resilience dispersion.

[0096] The double short board effect is adopted, not only the weakest subsystem is considered, but also the aggregation degree of the vulnerable subsystem is reflected by the tail mean. The absorption capacity of the large system is expressed as Pa (大) =min{P a,j (子)}×∑P a,j (子,弱) / k, which is the absorption force of the shortest board of the subsystem multiplied by its tail mean, with the default k=0.3n.

[0097] The calculation of the large system recovery force is mainly based on the harmonic mean, and the coefficient of variation is used to penalize the discreteness of the recovery speed, that is, Ph (大) =n / ∑(1 / P h,j (大) )×(1-σ(Pr (子) ) / μ(Pr (子) )).

[0098] Large system adaptability performance Ps (大) =α / μ(Ps (子) )+(1-α)×min{P s,j (子)}, balance the overall level and bottleneck, and α is recommended to be 0.65.

[0099] In a preferred solution of this embodiment, the method for determining all the above-mentioned weight coefficients (such as ωr1, ωa1, wi, etc.) is: using a combination of objective weighting method and subjective weighting method.

[0100] Specifically, we collect the actual response data of various projects in multiple historical flood events, and use the entropy weight method to calculate a set of objective weights w based on these data. j e At the same time, experts in the organization field compare and score the importance of each indicator, build a judgment matrix through the analytic hierarchy process (AHP) and calculate another set of subjective weights w j a The final combination weight calculation formula is: ω j =β×w j e +(1-β)×w j a ; Where β is the preference coefficient. For example, taking β=0.6 means that more emphasis is placed on the rules reflected by objective data.

[0101] In this embodiment, through multi-level indicator aggregation and dynamic coupling, a resilience quantification system covering single projects, subsystems, and large systems is constructed, solving the problem of difficulty in uniformly quantifying the resilience characteristics of complex water engineering groups under multi-scale and multi-coupling relationships. Based on the four-dimensional indicators of resistance, absorption, recovery, and adaptability, each level is dynamically aggregated to achieve an accurate characterization of resilience performance from local to global levels. This solution can be dynamically adjusted as the project structure changes and the operating status evolves. It is more suitable for application scenarios that simulate system evolution and resilience strategy adjustments under extreme working conditions, providing a quantitative basis for risk prevention and control and resilience improvement of water engineering groups.

[0102] Example 4: This example is used to describe the generation process of the toughness performance boundary to illustrate how the performance lower limit serving as a risk assessment benchmark is established.

[0103] In this embodiment, the process of generating the toughness performance boundary specifically includes the following steps:

[0104] Step 1: Construct extreme flood scenario set S extreme. The specific implementation method is that the system reads the local historical flood database (for example, containing all recorded flood process data in the past 50 years) and the design standard flood data of the area (for example, the design flood process lines of once in a hundred years and once in a thousand years issued by the water conservancy department). By screening and combining these data, a set of extreme flood scenarios that can represent the most severe challenges that the water conservancy project group may encounter is constructed. For example, the set may include: flood events with the largest peak flow that have actually occurred in history, flood events with the largest total flood volume in history, and possible maximum flood (PMF) process lines derived from PMP (possible maximum rainfall), etc.

[0105] Step 2: Calculate the disturbance effect of extreme scenarios on the normalized characteristic factors. Specifically, the extreme flood scenario set S constructed in step 1 is extreme As external disturbance input. The system is controlled by a disturbance response function Φ(l)(S extreme ) to calculate the impact of these extreme scenarios on each normalized characteristic factor in the system (such as storage capacity utilization C u,norm , Safety height margin H s,norm For example, for the safety elevation margin, an extreme flood scenario will reduce the margin by raising the reservoir water level. The updated characteristic factor value is calculated as x m ′=x m +Δx m,extreme ; where x m is the initial value of the characteristic factor; Δx m,extreme is the change of the characteristic factor under extreme circumstances; x m ′ is the characteristic factor value after disturbance.

[0106] Step 3: Calculate the toughness performance value under extreme scenarios. All characteristic factor values ​​x obtained in step 2 after extreme scenario disturbance are m Substitute ' into the multi-dimensional resilience performance index system constructed in Example 3. Using the calculation method defined in this system, calculate the performance index values ​​for the system at the three levels of single project, subsystem, and macrosystem, and in the four dimensions of resistance, absorption, recovery, and adaptability, for each extreme scenario.

[0107] Step 4: Determine the final toughness performance boundary R boundary In this embodiment, in order to adopt a risk-averse conservative strategy, the resilience performance boundary is defined as the most unfavorable performance that the system can achieve under all possible extreme scenarios. The specific implementation method is to take the minimum value of each performance dimension for the performance values ​​under all extreme scenarios calculated in step 3. That is, R (l) boundary,k =mins∈S extreme {Pk,s(l)}; where R (l) boundary,k is the toughness performance boundary value of the kth performance dimension (such as absorption capacity) at the lth level (such as the subsystem level); S extreme is the set of extreme flood scenarios; P k,s(l) is the corresponding performance value calculated under the extreme scenario s. This approach generates a set of performance baselines covering all levels and dimensions, forming the resilience performance boundary. It provides a clear, physically meaningful reference benchmark for subsequent risk assessments.

[0108] Example 5: This example is used to describe how to construct a composite disturbance and evaluate the current toughness performance state while taking uncertainty into consideration.

[0109] In this embodiment, the current toughness performance state is evaluated under a composite disturbance, wherein the generation of the composite disturbance includes the following steps:

[0110] Step 1: Based on the statistical characteristics of flood forecast data and its historical forecast errors, a set of disturbance samples that represent forecast uncertainty is generated by random sampling. The specific implementation method is that the system first reads the latest flood forecast data, such as the inflow forecast process line Q for the next 72 hours. forecast At the same time, the system analyzes historical forecast data and measured data to extract the statistical characteristics of forecast errors. For example, it is found that the historical forecast errors approximately follow the mean μ err =-0.05, standard deviation is σ err =0.15, that is, ε Q ~N(-0.05,0.152), which indicates that the forecast has a systematic tendency to underestimate. In order to efficiently generate disturbance samples that can reflect this uncertainty, this embodiment preferably adopts an improved Latin hypercube sampling method. This method divides the probability distribution space of the error into N (for example, N=100) equal probability intervals, and then independently randomly extracts an error sample value ε in each interval. i By applying these error samples to the forecast value, N sets of perturbed traffic sequences can be generated: Q perturbed,i =Q forecast ×(1+εi), where i = 1...N. This set constitutes the perturbation sample that characterizes the forecast uncertainty.

[0111] Step 2: Use the dynamic time warping algorithm to match the maximum similarity historical flood scenario that is most similar to the current forecast flood process from the historical and design flood data.

[0112] Since a single forecast uncertainty often cannot fully capture the complex spatiotemporal evolution characteristics of floods (such as the steepness of the flood peak, multi-peak characteristics, etc.), introducing similar flood scenarios that have actually occurred can serve as an effective supplement. The specific implementation method is to first extract a three-dimensional feature vector V=(Q peak ,W total,γ ); where Q peak is the peak flow; W total is the total amount of flood; γ is the coefficient that characterizes the shape of the process line (such as the ratio of peak time to flood duration). Then, the dynamic time warping (DTW) algorithm is used to calculate the similarity D between the current forecast flood process line and each historical flood process line. DTW ,This algorithm is particularly suitable for comparing time series of different lengths or with time offsets. The comprehensive similarity is calculated using the weighted formula: S total =w p ×exp(-|Q p,h -Q p,c ∣ / Q p,c )+w w ×exp(-|W t,h -W t,c ∣ / W t,c )+w d ×exp(-D DTW / D0); where subscripts h and c represent history and current respectively; w p ,w w ,w d is the weight; D0 is the normalization constant. Select S total The historical flood with the largest value is taken as the maximum similar historical flood scenario.

[0113] Step three combines the disturbance samples with the most similar historical flood scenario to construct a composite disturbance. Specifically, the system combines the uncertainty disturbance samples generated in step one (representing the uncertainty in the forecast values) with the most similar historical flood scenario matched in step two (representing the uncertainty in the flood morphology). A preferred combination method is to superimpose N groups of disturbance samples onto the process line of the most similar historical flood scenario, thereby generating N groups of composite disturbance scenarios. Each group of composite disturbance scenarios incorporates both the randomness of forecast errors and the evolutionary morphology of real floods.

[0114] On this basis, these N sets of composite disturbance scenarios were used as input and applied to the water project cluster model one by one. For each set of scenarios, the system's resilience performance indicators at all levels and dimensions were calculated according to the method in Example 3, resulting in N sets of current resilience performance state values. These N sets of values ​​constitute the final evaluated current resilience performance state, fully accounting for uncertainty.

[0115] Example 6: This example describes how to identify resilient failure nodes, and how to trace and construct cross-level failure transmission chains.

[0116] In this embodiment, before determining the control potential of the toughness failure engineering, the following steps are also included:

[0117] Step 1: Compare the current toughness performance state with the toughness performance boundary and calculate a performance gap. Specifically, the system calculates the N groups of current toughness performance state values ​​P obtained by the evaluation in Example 5. current,i (where i = 1...N), and the toughness performance boundary R generated in Example 4 boundary The performance gap is defined as ΔP i =P current,i -R boundary When ΔP i When ≤0, it means that under the i-th disturbance sample, the performance of the project or system has fallen below the safety bottom line and there is a tendency to fail.

[0118] Step 2: Count the failure risk probability when the performance gap is lower than the preset value under uncertainty disturbance. Specifically, count the performance gap ΔP in N simulations. i The number of times ≤0 is recorded as N fail The failure risk probability is calculated as P fail =N fail / N. This probability intuitively reflects the possibility of ductile failure in an engineering project when uncertainty is taken into account.

[0119] In step three, when the absolute mean of the failure risk probability and the performance gap simultaneously exceed their respective probability thresholds and performance gap thresholds, the corresponding project is identified as a resilient failure node, thus forming a resilient failure node set. This dual-threshold criterion is designed to avoid false risk alerts due to occasional, minor performance fluctuations.

[0120] Specifically, a probability threshold θp and a performance gap threshold δp are set. The value of θp can be determined based on risk tolerance. For example, for critical projects, θp = 5%, indicating that as long as the failure probability exceeds 5%, vigilance is required. The value of δp can be determined based on the physical meaning of the performance indicator. For example, it can be set to 10% of the performance boundary value, that is, δp = 0.1 × R boundaryAt the same time, calculate the absolute mean ΔP of the performance gap among all failed samples avg =∑i|ΔPi≤0|ΔPi| / N fail , which reflects the average severity of failure. fail >θp and ΔP avg >δ p Only when all the above conditions are met, the system will determine the project or subsystem as a resilient failure node. All the determined nodes together constitute the resilient failure node set.

[0121] After forming the resilient failure node set, the method further includes: based on a dual-track dynamic hierarchical structure, using a top-down tracing mechanism, starting from the macro-system level, gradually locates the failed subsystems and failed single projects in the resilient failure node set to construct a cross-level failure chain that characterizes the failure transmission relationship. This step is implemented as follows:

[0122] Identify failure triggers at the macro-system level: First, check whether the comprehensive performance indicators at the macro-system level have been determined to be failures. If so, mark the failure dimension (e.g., failure of macro-system absorptive capacity) and record it as the starting point of the failure chain.

[0123] Drill down layer by layer to locate the failed subsystem: For each failure dimension at the large system level, traverse all its subordinate subsystems. Utilize the dual-track hierarchical structure constructed in Example 2 to check which subsystems have also been determined to have failed on the same dimension. Calculate the contribution of each subsystem to the failure of the large system, and select subsystems whose contribution exceeds the threshold as intermediate links in the failure chain.

[0124] Accurately locate the failure node of a single project: within each located failure subsystem, further traverse all the single projects contained therein. Find the single project node that fails in the corresponding dimension. At the same time, use the hydraulic coupling tensor H calculated in Example 2 ij (t) As a measure of the failure transmission intensity, identify the project that is the main failure source within the subsystem (i.e., its transmission intensity to other projects is the highest).

[0125] Constructing a structured failure chain mapping: By integrating the failure node information from the three aforementioned levels, a cross-level failure chain is constructed, such as failure of the large system's absorption capacity, failure of the tributary A subsystem's absorption capacity, and failure of the A-2 reservoir's absorption capacity. Furthermore, the failure chain type (e.g., series, parallel, cascade) can be annotated and its criticality calculated to prioritize subsequent regulatory decisions. In this way, abstract system failure issues are transformed into clear, traceable, and structured transmission paths.

[0126] Example 7: This example describes how to construct a hierarchical resilience control response map, which is a map prerequisite for path search.

[0127] In this example, to systematically search for and evaluate control paths, a hierarchical resilience control response graph must first be constructed. This graph is constructed for each failed project in the cross-level failure chain identified in Example 6, based on the characteristics of each level. Specifically, the following steps are involved:

[0128] Step 1: Construct a control-response graph at the single-project level. At this level, the nodes in the graph are defined as the states of the three core performance dimensions of a single project: resilience, absorptivity, and recovery. The edges in the graph represent the coupling paths for control and transformation between these performance dimensions. For example, an action to improve resilience through pre-discharge (a control action) can be modeled as an edge from the current resilience state node to a node with a higher resilience state. This edge is assigned attributes such as required time, resource consumption, and potential negative impacts on other performance dimensions (such as absorptivity).

[0129] Step 2, construct a control response graph at the subsystem level. At this level, the nodes in the graph are defined as the comprehensive performance status of each single project within the subsystem. The edges in the graph represent the collaborative control links between projects. The establishment of an edge requires two basic conditions: spatial connectivity and time responsiveness. Specifically, only when there is an effective hydraulic connection between the two projects in the dual-track hierarchical structure constructed in Example 2, and the control action of one project can have an effective impact on the other project within the required time limit (for example, within the critical time window of flood evolution), can a collaborative control edge be established between the two project nodes. For example, if the water release action of the upstream reservoir A can reach the downstream sluice B within 6 hours and can effectively raise its water level, then an edge can be established between A and B.

[0130] Step three is to construct a control response graph at the large system level. At this level, the nodes in the graph usually represent the performance status of all key projects within the entire river basin. The edges in the graph mainly represent remote control trigger links across regions and subsystems. Such links usually do not rely on direct hydraulic connections, but are implemented through global scheduling rules and instructions. For example, when it is monitored that a key section of the main stream is about to exceed the warning water level, the scheduling center can issue instructions requiring multiple reservoir groups located in different tributaries to reduce the discharge flow at the same time. This scheduling decision based on global information forms a cross-regional control trigger edge between the nodes of these scheduled reservoir groups.

[0131] Step 4, assign control cost attributes to all edges. In order to be able to perform quantitative evaluation in subsequent path searches, it is necessary to assign a set of control cost attributes to each edge in all the above-mentioned hierarchical response graphs. In this embodiment, these attributes include at least: response time (the time from the start of the action to the production of the expected effect), control efficiency (the amount of performance improvement that can be brought about by unit resource consumption), and path complexity (the complexity of control instruction transmission and execution). These attribute values ​​can be obtained through hydraulic model calculations, historical data statistics or expert evaluation. Through the above steps, a hierarchical resilience control response graph containing multiple levels that can fully reflect the various control possibilities and their corresponding costs in the system is finally output. This graph is the data basis for subsequent control potential determination.

[0132] Example 8: This example describes how to determine the control potential of toughness failure engineering and how to classify it.

[0133] In this embodiment, after obtaining the set of resilient failure nodes, the process of determining the control potential of the resilient failure project further includes:

[0134] Step 1: Based on the current resilience performance status and resilience performance boundary, select nodes with surplus performance to form a control source set.

[0135] Specifically, the system traverses all engineering nodes that have not been judged as failed and calculates their performance margin ΔP surplus =P current -R boundary . Filter out those performance margins that are greater than a preset margin threshold (e.g. θ surplus =0.2, indicating that the performance is at least 20% higher than the boundary) as potential control sources capable of supporting other failed nodes. These control sources together constitute the control source candidate set S source .

[0136] Step 2: For any resilient failure node in the resilient failure node set, search for a closed-loop collaborative path connecting the failure node and at least one control source in the dual-track dynamic hierarchical structure.

[0137] In this embodiment, a closed-loop collaborative path refers to a control sequence that starts from a failed node, passes through the support of one or more control sources, and can eventually make the performance state of the failed node return to the valid state range above the resilience performance boundary. The specific implementation method is that, on the hierarchical resilience control response graph constructed in Example 7, starting from each resilience failure node, an improved depth-first search algorithm (DFS) is used to traverse the path in the graph. The search process sets constraints, such as the path length cannot exceed 5 hops (that is, the number of projects involved does not exceed 5), the total path response time cannot exceed 6 hours, and the path must contain at least one from the control source candidate set S source All paths that meet these constraints are recorded to form a candidate path set.

[0138] Step 3: Calculate a feasibility score for the closed-loop collaborative path. This feasibility score is used to characterize the control potential of the resilient failure node. In this embodiment, the method for calculating a feasibility score for the closed-loop collaborative path is to comprehensively evaluate at least two of the following performance indicators of the closed-loop collaborative path: path length, total response time, control efficiency, and net performance improvement; and generate a feasibility score based on the evaluation results of at least two performance indicators.

[0139] A preferred feasibility score function is:

[0140] F(P i )=λ1×(1 / |P i ∣)+λ2×(1 / T total )+λ3×C efficiency (P i )+λ4×ΔΦ net (P i );

[0141] Among them, F(P i ) is the path P i Feasibility score of |P i ∣ is the path length (number of nodes), and its reciprocal represents the path length penalty term; T total is the sum of the response times of all edges on the path, and its reciprocal represents the timeliness score; C efficiency (Pi) is the control efficiency, which represents the ratio of the total performance transfer to the total capacity consumption paid by the control source; ΔΦ net (Pi) is the net performance improvement, which represents the performance improvement ultimately achieved by the failed node minus the transmission loss on the path; λ1, λ2, λ3, and λ4 are the weight coefficients of each indicator. For example, they can be set to λ1=0.2, λ2=0.3, λ3=0.3, and λ4=0.2 based on decision preferences, and their sum is 1.

[0142] Step 4: Classify the failure nodes into two types: controllable and uncontrollable. Specifically, the feasibility score is compared with a preset feasibility score threshold. If the feasibility score is not less than the feasibility score threshold, the corresponding resilient failure node is classified into the controllable failure engineering set; otherwise, the resilient failure node is classified into the uncontrollable failure engineering set.

[0143] First, all candidate paths of a failed node are ranked according to their feasibility scores F(P i ) in descending order, and select the path with the highest score as the optimal closed-loop path. Then, the score F of the optimal path is optimal With a preset feasibility score threshold θ loop The threshold can be determined based on historical experience or simulation analysis, for example, loop =0.6.

[0144] If F optimal ≥θ loop , then it is considered that there is a high-quality, feasible control path to restore the performance of the node, so the resilient failure node is divided into the controllable failure engineering set. If there is no feasible closed-loop path, or the highest score of all paths is less than θ loop , it is considered that under the current system state, its performance cannot be effectively restored through internal coordination, so it is divided into the uncontrollable failure engineering set. Optionally, multiple thresholds can be set, for example, when the score is in a certain middle range (such as 0.4≤F optimal <0.6), it can be classified as a weakly controllable failure engineering set, indicating that stronger external auxiliary support is needed.

[0145] In this embodiment, by analyzing the multidimensional resilience status of project nodes and identifying the presence of closed-loop self-rescue paths in the control response graph, the potential for self-organizing control is determined, and the failed projects are then classified as controllable or uncontrollable. Unlike traditional methods that rely on fixed thresholds and single-path judgments, this solution integrates multi-source control paths for closed-loop identification based on the dynamic response characteristics of the network structure. This approach better reflects the multidimensional coupling characteristics of actual resilience recovery and is suitable for cross-dimensional control potential identification at multiple levels and in multiple regions.

[0146] Embodiment 9: This embodiment provides a clear and explicit mathematical optimization model, which defines the objective function and constraints that the algorithm needs to solve.

[0147] In this embodiment, before executing the specific control optimization algorithm, a multi-objective resilient balanced scheduling model must be constructed. This model is constructed by reading the controllable failure project set, the uncontrollable failure project set, and their matching auxiliary control project sets identified in Example 8, and then constructing the optimization objective function hierarchically.

[0148] Single project level optimization objective function: The objectives at this level focus on the risk control and efficiency of a single project.

[0149] As the basic unit of resilience, a single project has a simple structure and direct functions, making it susceptible to delayed response and boundary-breaking events. The key is to control the response speed and prevent single-point failures. The key optimization targets are local control performance and critical state prevention and control capabilities. Therefore, the single-project level aims to minimize failure risk, minimize response lag, and maximize resilience surplus, giving priority to ensuring the dynamic stability and timely control of single-point projects. Its objective function can be constructed as:

[0150] F 单 =min{a1×P fail +a2×T d -a3×ΔP res};

[0151] Among them, F 单 is the comprehensive optimization objective of a single engineering layer, aiming to minimize this value; P fail is the expected failure risk probability of the project after regulation; T d is the response lag time of the control action; ΔP res The goal is to maximize the resilience surplus or redundancy of the project after regulation, so it is preceded by a negative sign; a1, a2, and a3 are the weight coefficients of each sub-goal.

[0152] Subsystem-level optimization objective function: The objectives at this level focus on the overall coordination and cost-effectiveness within the subsystem.

[0153] A subsystem is a collection of several individual projects, possessing a certain degree of autonomous control capability. However, its control effectiveness depends on the resilience coordination of its individual projects. It is important to optimize the internal control balance and synergy benefits at this level to prevent the spread of chain failures. Therefore, the subsystem level aims to minimize resilience imbalance, minimize redundant control costs, and maximize synergy effectiveness to improve overall response consistency and resource allocation efficiency. Its objective function can be constructed as follows:

[0154] F 子 =min{b1×σ(P 子 )+b2×C cost -b3×E coop};

[0155] Among them, F 子 is the comprehensive optimization target of the subsystem layer; σ(P 子 ) is the standard deviation of the engineering toughness performance within the subsystem, which is used to measure the toughness imbalance, and the goal is to minimize it; C costThe total cost required to implement coordinated regulation (such as water loss, power generation loss, etc.); E coop is the synergistic effect, that is, the additional performance gain brought about by collaborative regulation, and the goal is to maximize this item; b1, b2, and b3 are weight coefficients.

[0156] Large system level optimization objective function: The objectives at this level focus on global risk exposure and overall system resilience.

[0157] The large system is an overall network that is cross-regional and cross-level, and has network linkage and cross-regional coupling properties. However, its structure is complex, the risk chain is long, and regulatory conflicts are prone to occur. The focus should be on the regulatory coordination capabilities between subsystems and the overall comprehensive resilience level to avoid local failures causing global imbalances. Therefore, the large system level aims to minimize system risk exposure, minimize regulatory conflicts, and maximize system resilience, emphasizing overall situation improvement and global coordination capabilities. Its objective function can be constructed as: F 大 =min{c1×R exposure +c2×C conflict -c3×ΔP 大};

[0158] Among them, F 大 is the comprehensive optimization goal of the large system layer; R exposure is the comprehensive risk exposure of the entire system after regulation; C conflict is the control action conflict between different subsystems or projects, the goal is to minimize the conflict; ΔP 大 is the total improvement in the comprehensive resilience performance of the entire system, and the goal is to maximize this item; c1, c2, and c3 are weight coefficients.

[0159] In addition, the entire optimization model needs to be solved under a series of constraints. These constraints include at least:

[0160] Water balance constraints: The inflow and outflow of each project and river section, as well as the interval water supply, must satisfy the water balance equation.

[0161] Control boundary constraints: All control actions (such as discharge flow and reservoir water level) must be within the safe operating boundaries of the project design. For example, the reservoir water level cannot be higher than the flood control high water level or lower than the dead water level; the discharge flow cannot exceed the maximum discharge capacity of the flood discharge facility.

[0162] Resilience validity constraint: The control scheme must ensure that it can restore the resilience performance value of the failed node to at least the resilience performance boundary R boundary Above.

[0163] By constructing the above-mentioned complete mathematical model that includes hierarchical objective functions and various constraints, it provides clear and computable optimization objectives and feasible domains for the subsequent use of specific optimization algorithms such as multi-objective reinforcement learning and collaborative co-evolution.

[0164] Example 10: Multi-objective self-regulation optimization of controllable failure engineering.

[0165] This embodiment elaborates on the multi-objective reinforcement learning-guided hybrid gradient search algorithm (MORL-HG) used for the controllable failure engineering set.

[0166] In this embodiment, a hybrid gradient search algorithm guided by multi-objective reinforcement learning is used to optimize the set of controllable failure engineering. The process specifically includes:

[0167] Step 1: Based on the physical constraints of the controllable failure engineering set, a safe exploration space is established to limit the range of control actions.

[0168] Specifically, the system first reads the current operating status of the controllable failure project (such as water level Z, discharge flow Q, and reservoir capacity V) and its physical properties. Then, based on hydraulics and engineering safety criteria, it establishes a series of inequality constraints to define the safety boundaries of the control action.

[0169] For example, these constraints may include:

[0170] Discharge capacity constraint: Q out ≤C×L×H 1.5 Among them, Q out is the discharge flow action; C is the discharge coefficient; L is the spillway width; and H is the head above the weir. This constraint ensures that the dispatching instructions do not exceed the maximum discharge capacity of the project.

[0171] Water level change rate constraint: |dZ / dt|≤dZ max ; Among them, dZ / dt is the rate of change of water level caused by regulation; dZ max The maximum permissible water level change rate (e.g. 0.5 m / h) is used to prevent slope instability caused by rapid water level fluctuations.

[0172] Storage capacity constraint: V dead ≤V(t+1)≤V flood ; Where V(t+1) is the expected storage capacity after the control action is executed; V dead and V flood They are dead storage capacity and flood control limited storage capacity respectively.

[0173] The set of all continuous control actions that satisfy the above physical constraints (such as the specific value of the discharge flow) together constitutes the safe exploration space A safe(s), where s represents the current state. The principle of this step is that by pre-defining an absolutely safe action space, it is possible to fundamentally avoid the optimization algorithm from generating dangerous instructions that may damage the engineering entity during the exploration process.

[0174] Step 2: In the safe exploration space, a multi-objective reinforcement learning agent is used to generate an initial control action.

[0175] The specific implementation method is to first initialize a multi-objective reinforcement learning (MORL) agent. The agent's state space S can be a multidimensional feature vector containing the current water level, inflow, outflow, and four-dimensional resilience performance indicators. Its action space A is set to continuous control actions.

[0176] Then, a multi-objective reward function is designed for the agent to guide its learning direction. The reward function can be designed as: total =r risk +r performance +r robust ; Among them, r risk =-w1×max(0,P fail -P threshold ), is a penalty term that gives a negative reward when the expected failure risk exceeds a threshold;

[0177] r performance =w2×(P current -P previous ), is a performance reward item that encourages the agent to take actions that can improve resilience performance;

[0178] r robust =w3×(1-σ(P scenarios ) / μ(P scenarios )) is a robustness reward that encourages the agent to find actions that are relatively stable in different uncertainty scenarios; w1, w2, w3 are weights, for example, they can be set to 0.4, 0.4, 0.2.

[0179] During training and decision-making, the agent can be pre-trained using historical control data to obtain an initial strategy π0. At the decision-making moment, the agent outputs an initial control action a with good overall performance based on its learned strategy according to the current state s.

[0180] In step three, a gradient search algorithm is used to fine-tune the initial control action, while ensuring that the adjusted action does not exceed the boundary of the safe exploration space to obtain the optimized control action sequence.

[0181] While reinforcement learning excels at finding a good direction at the macro-strategy level, it can be less efficient at fine-tuning specific values. Therefore, gradient search is introduced for local fine-tuning. Specifically, after the agent generates an initial control action a, a gradient search is performed within a neighborhood of that action to find a more optimal action value. For example, this is done by calculating the gradient of the immediate performance function J with respect to action a and performing an iterative update:

[0182] a′=a+α×▽J(a); where a is the fine-tuned action; α is the learning step size, for example 0.01.

[0183] After each iterative update, it is necessary to check whether the adjusted action a′ is still in the safe exploration space A constructed in step 1. safe If a′ goes out of the boundary, it needs to be projected back to the nearest point on the safety boundary to ensure that the final output action is always absolutely safe.

[0184] By combining the global exploration capability of MORL with the local optimization capability of gradient search, we can efficiently find a series of optimized control actions while ensuring safety, and form the final self-control optimization solution.

[0185] Example 11: This example describes a collaborative control process for a set of uncontrollable failed projects, including a matching mechanism for auxiliary projects and a specific implementation of a collaborative-competitive co-evolution algorithm (CCEA-LF).

[0186] In this embodiment, the uncontrollable failure engineering set is combined with a matching auxiliary control engineering set and optimized using a cooperative-competitive co-evolution algorithm. The process specifically includes:

[0187] Step 1: Match an auxiliary control project set to the uncontrollable failure project set.

[0188] First, a resilience demand vector is established for the failure projects in the set of uncontrollable failure projects, and a resilience supply vector is established for the candidate projects in the system. Specifically, for an uncontrollable failure project, its resilience demand vector V need It can be composed of the gap values ​​in various failure performance dimensions, such as V need =[ΔPr,ΔPa,ΔPh]. For other projects with surplus capacity in the system (i.e. potential auxiliary projects), their resilience supply vector V supply It can be composed of the performance margin it can provide in various dimensions.

[0189] Secondly, the matching degree between the resilience demand vector and the resilience supply vector is calculated, where the matching degree is determined based on the cosine similarity between the vectors and the hydraulic propagation distance between the failed project and the candidate project. A preferred matching degree calculation formula is: M ij =cos(V need,i ,V supply,j )×exp(-d ij / d0); where M ij is the matching degree of candidate project j to failed project i; cos(*) calculates the directional similarity between the demand vector and the supply vector. The more consistent the direction, the more suitable the supply. The exp(*) term is a term based on the hydraulic propagation distance d. ij The attenuation term indicates that the longer the distance, the worse the support effect. d0 is a characteristic distance constant.

[0190] Finally, the system selects several candidate projects with the highest matching scores to form the auxiliary control project set. For each failed project, the system calculates the matching scores of all candidate projects with it and selects the top-K projects with the highest matching scores to form its exclusive auxiliary control project set.

[0191] Step 2: For the uncontrollable failure engineering set, a matching auxiliary control engineering set is combined and optimized using the cooperative-competitive co-evolution algorithm.

[0192] In this step, a separate evolving population is created for each auxiliary project in the auxiliary control project set. Each individual in this population encodes a support decision. For example, the population size can be set to 50, and each individual can be a string of codes that defines the support action for that project (such as the discharge increment and scheduling timing).

[0193] Then, in the iterative process, individuals are combined from each evolutionary population to form a collaborative control scheme, and the evolutionary population is evaluated and updated according to the comprehensive impact of the collaborative control scheme on the set of uncontrollable failure projects to obtain the final collaborative control optimization scheme.

[0194] The specific implementation method is as follows:

[0195] Combination and Evaluation: Select the optimal individuals (i.e., the optimal support decisions) from each auxiliary project population and combine them to form a complete collaborative control solution. Then, through model simulation, evaluate the overall performance improvement of this collaborative solution on the target failure project.

[0196] Fitness Update: Based on the evaluation results, the fitness of each participating individual is updated. The fitness function here takes into account multi-level feedback. For example, it considers both the individual's direct contribution to the failure engineering (local contribution) and the impact of the collaborative solution on the resilience of the entire subsystem or large system (system contribution), and dynamically adjusts the contribution weight.

[0197] Evolutionary operations: Each population independently performs genetic algorithm operations such as selection (such as tournament selection), crossover (such as arithmetic crossover), and mutation (such as Gaussian mutation) based on the updated individual fitness to produce a new generation of population.

[0198] Competition and Alliances: When resources are limited (e.g., the total available support water volume is limited), a competition mechanism is introduced, giving individuals or collaborative groups with higher fitness priority access to resources. Simultaneously, the system dynamically adjusts alliances based on synergy, removing projects with consistently low contributions from the support set.

[0199] This iterative process continues until the maximum number of iterations is reached or the solution converges. Ultimately, the algorithm outputs a collaborative control optimization solution that includes the specific support actions, execution timing, and collaborative paths for each auxiliary project.

[0200] Example 12: In this embodiment, after obtaining the self-regulation optimization solution set for the controllable project and the collaborative regulation optimization solution set for the uncontrollable project, the system needs to perform the following steps to output the final optimal scheduling solution set:

[0201] Step 1: Spatiotemporal coordination of the solution sets. Specifically, the system places all control actions in the two solution sets under a unified spatiotemporal coordinate system for inspection to identify and eliminate potential conflicts.

[0202] For example, a coordinated control scheme might require upstream reservoir A to release water at time T to support a failed downstream project C, while a self-regulation scheme might require reservoir B, located between A and C, to reduce its discharge at time T to improve its resilience. These two actions may conflict hydraulically. In this case, the system needs to adjust the execution time or action range of one scheme based on pre-set priority rules (for example, rules prioritizing key protection targets) or through re-simulation evaluation to ensure the global feasibility of the integrated scheme.

[0203] Step 2: Screening for non-inferior solutions based on the Pareto dominance relationship. All feasible solutions after coordination constitute a large pool of candidate solutions. Because the optimization objectives of the present invention are multi-dimensional (such as risk, cost, and efficiency in Example 9), these objectives often conflict with each other, and there is no perfect solution that optimizes all objectives. Therefore, this example uses the Pareto optimality theory to screen solutions.

[0204] Specifically, the system compares all solutions in the candidate pool pairwise. If solution X is superior to or equal to solution Y in all optimization objectives and strictly superior to solution Y in at least one objective, then solution X is said to dominate solution Y. After traversing all solutions and eliminating those dominated by other solutions, the remaining set of solutions is the set of non-inferior solutions, also known as the Pareto optimal frontier. Every solution on this frontier is an optimal solution, because improving any objective of any solution necessarily comes at the expense of at least one other objective.

[0205] Step 3: Select representative solutions and output the solution set. Finally, the system presents the Pareto optimal frontier obtained in Step 2 to the decision maker. Optionally, the system can automatically select several representative solutions from the frontier based on preset decision preferences or equilibrium principles.

[0206] For example, a risk-averse solution (i.e., the point on the frontier that minimizes risk), a cost-effective solution (i.e., the point on the frontier with the lowest cost), and a balanced solution (i.e., the inflection point on the frontier closest to the origin) can be provided. The final output, the optimal scheduling solution set, is a structured data set that clearly lists the specific control parameters (such as the downstream flow process curves of each project), the execution sequence (the start and end times of each action), the expected resilience improvement effect, and the corresponding costs for each representative solution.

[0207] Example 13: Assume a simplified water project system consisting of an upstream reservoir A, a midstream sluice gate B, and a downstream control section C, all located sequentially along a river. This example calculates the hydraulic coupling strength between the projects in this system at a specific time t and determines the weight coefficients used to integrate the physical and dynamic layers.

[0208] Real-time hydrological data (time t):

[0209] Water level H of each project A =150.0 m, H B =85.0 meters.

[0210] Flow rate of each project Q A =1200m 3 / s,Q B =1250m 3 / s (including interval flow).

[0211] Physical and model parameters, including:

[0212] The distance between the projects is LAB = 30,000 meters. The acceleration of gravity is g = 9.8 m / s. 2The average water depth of the interval is havg = 10.0 m. The characteristic time constant T0 = 10800 seconds (3 hours). The sensitivity coefficient K = 0.1. The tensor combination weights w1 = 0.4, w2 = 0.3, and w3 = 0.3.

[0213] Step 1: Calculate the hydraulic propagation time τ ij (t), according to the formula τ ij (t)=L ij / (g×h avg ) 0.5 :

[0214] The travel time τ from reservoir A to sluice gate B AB =30000 / (9.8×10.0) 0.5 =30000 / 9.899≈3030.5 seconds.

[0215] Step 2: Calculate the partial derivatives of each relationship matrix

[0216] In this case, the finite difference method is used to approximate the partial derivatives. This requires running a perturbation simulation on the hydraulic model. Suppose we apply a small perturbation to the operating conditions of upstream reservoir A and observe the response of downstream sluice gate B.

[0217] Assume that at the next moment, the discharge of reservoir A increases by a small amount ΔQ A =10m 3 / s, resulting in a small change in the water level ΔH A =0.02 meters.

[0218] Through simulation of hydraulic models (such as HEC-RAS or similar one-dimensional models), it is observed that the AB After a certain time, the disturbance propagates to sluice gate B, causing the flow at B to increase by ΔQ B =9.5m 3 / s, water level increases by ΔH B =0.15 meters.

[0219] Based on this, calculate the approximate partial derivative: dH B / dH A ≈ΔH B / ΔH A =0.15 / 0.02=7.5. dQ B / dQ A ≈ΔQ B / ΔQ A =9.5 / 10=0.95. dQ B / dH A ≈ΔQ B / ΔH A =9.5 / 0.02=475.

[0220] Step 3: Calculate the three types of coupling relationship matrices

[0221] According to the formula and the results of steps 1 and 2, calculate the influence element value of A on B in each relationship matrix:

[0222] Water level propagation matrix element H HH,AB :

[0223] H HH,AB =(dH B / dH A )×exp(-τ AB / T0)=7.5×exp(-3030.5 / 10800)=7.5×exp(-0.2806)=7.5×0.7553≈5.665.

[0224] Traffic propagation matrix element H QQ,AB :

[0225] H QQ,AB =(dQ B / dQ A )×exp(-τ AB / T0)=0.95×0.7553≈0.718.

[0226] Water level-flow coupling matrix element H HQ,AB :

[0227] H HQ,AB =(dQ B / dH A )×exp(-τ AB / T0)=475×0.7553≈358.768.

[0228] Step 4: Synthesize the comprehensive hydraulic coupling tensor H(t)

[0229] According to the formula H ij (t)=w1×|H HH,ij ∣+w2×∣H QQ,ij ∣+w3×∣H HQ,ij ∣:

[0230] Calculate the comprehensive hydraulic coupling strength H of A to B AB (t): H AB (t)=0.4×∣5.665∣+0.3×∣0.718∣+0.3×∣358.768∣=2.266+0.2154+107.6304≈110.11.

[0231] Assuming that other elements are calculated by similar methods (for example, the influence of B on A is small, the influence of itself on itself is negligible or 0, and the influence of A on C needs to be calculated piecewise, etc.), we can finally obtain a simplified 2×2 hydraulic coupling tensor matrix (considering only A and B): H(t)=(0, 110.11; HBA, 0);

[0232] Among them H BA This is the reverse effect of B on A, which is usually small and is set to 5.0 in this example.

[0233] Step 5: Calculate the hierarchical fusion weight coefficient α(t).

[0234] Calculate the spatial variance of the hydraulic coupling tensor (H ij ):

[0235] The elements in the matrix are {0,110.11,5.0,0}. The mean value H mean =(0+110.11+5.0+0) / 4=28.7775.

[0236] Among them, Variance (H ij )=Σ(H ij -H mean ) 2 / (N2-1)=[(0-28.78) 2 +(110.11-28.78) 2 +(5.0-28.78) 2 +(0-28.78) 2 ] / (4-1)≈2945.57.

[0237] Calculate the hierarchical fusion weight coefficient α(t):

[0238] α(t)=1 / (1+K×Variance(H ij ))=1 / (1+0.1×2945.57)=1 / (1+294.557)=1 / 295.557≈0.00338.

[0239] At the specific time t in this case: the calculated comprehensive hydraulic coupling strength H AB (t)≈110.11, which is a relatively high value, indicating that the operating status of the upstream reservoir A has a very strong hydraulic impact on the midstream sluice B.

[0240] The calculated hierarchical fusion weight coefficient α(t)≈0.00338, which is very close to 0. This means that the weight of the physical skeleton level is only about 0.34%, while the weight of the dynamic response level (1-α(t)) is as high as about 99.66%.

[0241] This calculation shows that at this point, due to the intense hydraulic dynamics between projects (as evidenced by the extreme variance in coupling strength), system decisions should rely almost entirely on the dynamic response hierarchy generated based on the real-time hydraulic state, essentially ignoring the fixed physical connections. This fully demonstrates the dynamic adaptability of the dual-track hierarchical structure of the present invention.

[0242] According to one aspect of the present application, a dual-track dynamic hierarchical structure is constructed by introducing a hydraulic coupling tensor dynamically calculated based on real-time hydrological data and utilizing the spatial variance of this tensor to weightedly fuse a static physical skeleton hierarchy with a time-varying dynamic response hierarchy. This technical solution has the beneficial effect of transforming the understanding of the system structure of a water conservancy complex from a static characterization to a dynamic, real-time mapping, greatly improving the accuracy and timeliness of system state recognition. Specifically, in extreme flood scenarios, by inputting real-time water level and flow data, this method can quantify and identify temporary strong coupling paths caused by factors such as river channel backflow and tributary support, which are not physically significant but play a dominant role under current hydraulic conditions. This directly overcomes the technical shortcomings of prior art methods that rely on fixed topological structures and fail to capture the dynamic response of the system, resulting in a disconnect between the decision-making basis and the actual system state. Ultimately, this precise understanding of the system state provides a high-fidelity operational map for subsequent risk identification, path tracing, and regulatory decision-making, ensuring that regulatory instructions are formulated based on the most realistic system hydraulic connections, significantly improving the relevance and effectiveness of the overall regulatory plan.

[0243] According to one aspect of the present application, by adopting a top-down tracking mechanism based on a dual-track dynamic hierarchical structure, a cross-level, structured conduction chain for resilience failures is constructed. The beneficial effect of this technical solution is that it deepens the granularity of risk diagnosis from traditional, isolated point failure judgments (such as the water level exceeding the limit of a single reservoir) to the complete tracing of the systemic risk conduction chain. Specifically, when a system-level resilience indicator (such as the absorption capacity of a large system) fails, the method can input the failure signal and use the hierarchical structure and hydraulic coupling relationship to reversely locate the specific performance dimensions at the subsystem or even single engineering level that caused the failure of the system (such as the lack of resilience of a certain project). This directly solves the technical difficulties in the background technology that it is impossible to deeply trace the risk and understand the failure conduction mechanism. By obtaining this structured failure chain of large system → subsystem → single project, decision makers can not only know where the problem occurred, but also have a deeper understanding of why and how the problem occurred. This allows them to formulate regulatory strategies with surgical precision that directly address the root causes of risks, effectively prevent the further transmission and amplification of risks, and avoid the occurrence of cascading collapses.

[0244] According to one aspect of the present application, by searching for closed-loop collaborative paths connecting failed nodes with nodes with surplus performance on a hierarchical control response graph and calculating a quantitative feasibility score that integrates path length, response time, control efficiency, and net performance improvement, the control potential of failed projects can be accurately determined. The beneficial effect of this technical solution is that it provides a scientific and quantitative decision-making basis for subsequent scheduling optimization and resource allocation, thereby improving the efficiency and rationality of overall control. Specifically, in the specific scenario of flood control scheduling of water project groups, this method can transform the abstract question of whether a project is rescueable into a computable score. By comparing this score with a preset threshold, the system can automatically classify failed projects into two categories: those that can be internally coordinated and regulated, and those that require strong external support. This avoids wasting valuable scheduling resources (such as valuable flood control storage capacity of upstream reservoirs) on failed projects with low internal coordination potential and low rescue success rates. This data-driven classification enables the subsequent targeted use of different optimization algorithms (such as self-optimization for controllable ones and collaborative optimization for uncontrollable ones), achieving tailored control strategies and significantly improving the resource utilization efficiency and overall control performance of water project groups under complex flood conditions.

[0245] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. A method for regulating the risk resilience of a water project group considering uncertainty, characterized in that: include: Based on the acquired water project group operating conditions and hydrological data, a dual-track dynamic hierarchical structure is established, and the resilience performance boundary and current resilience performance status are generated; Based on the dual-track dynamic hierarchical structure, toughness performance boundary and current toughness performance status, the control potential of toughness failure engineering is determined and divided into two types of failure engineering sets: controllable and uncontrollable. For the two types of failure engineering sets, self-control optimization and collaborative control optimization are performed respectively to output the optimal scheduling solution set.

2. The method according to claim 1, characterized in that Establish a dual-track dynamic hierarchical structure, including: Read the permanent engineering connection relationship from the water project group working condition data to build a steady-state physical skeleton hierarchy; In response to the real-time hydraulic state presented by hydrological data, a hydraulic coupling tensor is established to quantify the strength of dynamic correlation between projects, and a time-varying dynamic response hierarchy is generated based on the hydraulic coupling tensor; Based on the hydraulic coupling tensor, the physical skeleton level and the dynamic response level are weightedly fused to obtain a dual-track dynamic hierarchical structure.

3. The method according to claim 2, characterized in that Construct the hydraulic coupling tensor, including: Based on the real-time hydraulic status, the water level propagation relationship representing the mutual influence of water levels between projects, the flow propagation relationship representing the mutual influence of flows, and the water level-flow coupling relationship representing the influence of water levels on downstream flows are calculated respectively. The three relationships are quantified into water level propagation matrix, flow propagation matrix and water level-flow coupling matrix respectively; The water level propagation matrix, the flow propagation matrix, and the water level-flow coupling matrix are weightedly combined to synthesize the hydraulic coupling tensor.

4. The method according to claim 2, characterized in that Based on the hydraulic coupling tensor, the physical skeleton level and the dynamic response level are weightedly integrated, including: Calculate the spatial variance of the hydraulic coupling tensor and determine the time-varying hierarchical fusion weight coefficient based on the spatial variance; The hierarchical fusion weight coefficient is used to perform a weighted combination of the physical skeleton level and the dynamic response level to generate a dual-track dynamic hierarchical structure.

5. The method according to claim 1, characterized in that Before determining the control potential of resilient failure engineering, it also includes: Compare the current toughness performance state with the toughness performance boundary and calculate the performance gap; Calculate the probability of failure risk when the performance gap is lower than the preset value under uncertain disturbance; When the absolute mean of the failure risk probability and the performance gap exceeds their respective probability thresholds and performance gap thresholds at the same time, the corresponding project is determined to be a resilient failure node, forming a resilient failure node set.

6. The method according to claim 5, characterized in that Determining the control potential of the resilience failure project, after obtaining the resilience failure node set, further includes: Based on the current resilience performance status and resilience performance boundary, nodes with surplus performance are selected to form a set of control sources; For any resilient failure node in the resilient failure node set, search for a closed-loop collaborative path connecting the failure node and at least one control source in the dual-track dynamic hierarchical structure; At least one feasibility score of the closed-loop collaborative path is calculated to characterize the control potential of the resilient failure node.

7. The method according to claim 6, characterized in that Calculate the feasibility score of the closed-loop collaborative path, including: Comprehensively evaluate at least two of the following performance indicators of the closed-loop collaborative path: path length, total response time, control efficiency, and net performance improvement; Based on the evaluation results of at least two performance indicators, a feasibility score is generated.

8. The method according to claim 6, characterized in that It is divided into two types of failure engineering sets: controllable and uncontrollable, including: comparing the feasibility score to a preset feasibility score threshold; If the feasibility score is not less than the feasibility score threshold, the corresponding toughness failure node is divided into the controllable failure engineering set; Otherwise, the resilient failure nodes are divided into the uncontrollable failure engineering set.

9. The method according to claim 1, characterized in that For the two types of failure engineering sets, the self-control optimization and collaborative control optimization are performed respectively, including: For the set of controllable failure engineering, a hybrid gradient search algorithm guided by multi-objective reinforcement learning is used for optimization; The uncontrollable failure engineering set is combined with its matching auxiliary control engineering set and optimized using the collaborative-competitive co-evolution algorithm.

10. The method according to claim 9, characterized in that For the set of controllable failure engineering, a hybrid gradient search algorithm guided by multi-objective reinforcement learning is used for optimization, including: Based on the physical constraints of the controllable failure engineering set, a safe exploration space is established to limit the range of control actions; In the safe exploration space, a multi-objective reinforcement learning agent is used to generate initial control actions; The gradient search algorithm is used to fine-tune the initial control action, while ensuring that the adjusted action does not exceed the boundary of the safe exploration space, thereby obtaining an optimized control action sequence.

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