An artificial intelligence driven urban pipe network flood resilience assessment method and system

Abstract

The present application relates to the technical field of smart water affairs and urban public safety, and particularly relates to a kind of artificial intelligence driven urban pipe network flood resilience evaluation method and system, comprising: constructing Riemann metric tensor by using metric matrix containing potential barrier function, and establishing the Riemann manifold embedding space of pipe network physical state;Then, based on fluid energy, a Hamilton function is constructed, and a dynamics prediction model with physical conservation is obtained by using symplectic neural network and symplectic discrete integral format training;Subsequently, a second-order Hamilton-Jacobi-Aleksandrov partial differential equation describing stochastic differential game is constructed, and a physical perception neural network is used to solve and extract the resilience safety boundary;Finally, real-time data is mapped to the manifold space, the Riemann gradient is calculated, and a quadratic programming problem is solved to generate control instructions. The problem of lack of physical constraints and safety bottom line in pipe network control under extreme random working conditions is solved, and real-time closed-loop control with physical consistency is realized.

Description

Technical Field

[0001] This invention relates to the fields of smart water management and urban public safety technology, and in particular to an artificial intelligence-driven method and system for assessing the flood resilience of urban pipe networks. Background Technology

[0002] With the increasing frequency of extreme rainfall events due to global climate change, the resilience of urban drainage networks, as a lifeline infrastructure ensuring urban safety, is of paramount importance. Traditional urban water management technologies are gradually shifting from time-consuming hydrodynamic numerical simulations to data-driven artificial intelligence-based prediction and control, aiming to solve the challenges of real-time regulation.

[0003] However, traditional resilience assessments mostly employ probability optimization based on expectations. Due to the lack of boundary constraints for extreme long-tail events, scheduling strategies fail under sudden rainstorms. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides an artificial intelligence-driven method and system for assessing the flood resilience of urban pipe networks. It aims to improve the problem that traditional resilience assessments mostly adopt probability optimization based on expectations, which leads to the failure of scheduling strategies under sudden rainstorms due to the lack of boundary constraints for extreme long-tail events.

[0005] In a first aspect, the present invention provides the following technical solution: an artificial intelligence-driven method for assessing the flood resilience of urban pipe networks, comprising the following steps:

[0006] S1. Obtain pipeline network data, define node water level as generalized coordinates, and pipeline flow rate as generalized momentum; use a metric matrix containing a barrier function that reflects the potential barrier function that tends to infinity when the water level approaches the overflow threshold to construct a Riemann metric tensor and establish the Riemann manifold embedding space of the pipeline network physical state.

[0007] S2. Construct a Hamiltonian function based on fluid kinetic energy and potential energy including gravity and pressure potential energy; construct a symplectic neural network to fit the Hamiltonian vector field of the pipeline network, use the symplectic discrete integral scheme as the forward propagation rule, and obtain the pipeline network dynamic prediction model by minimizing the prediction error and energy conservation residual.

[0008] S3. The pipeline dynamics prediction model is modeled as a stochastic differential equation that includes control input, rainfall disturbance and random noise. Combined with the value function that characterizes the avoidance of entering the overflow failure set, a second-order stochastic Hamilton-Jacobi-Isaac partial differential equation is constructed.

[0009] S4. Construct a physical perception neural network to solve the partial differential equation, train the network with the equation residual as the loss function, output the risk value function field and extract the zero level set as the resilient safety boundary.

[0010] S5. Map the real-time collected data to the space, calculate the current risk value and the Riemann gradient on the tangent space of the manifold through the physical sensing neural network, solve the quadratic programming problem constrained by evolution along the gradient direction, and generate control instructions.

[0011] By adopting the above technical solution, a stochastic HJI equation based on Riemannian manifolds and symplectic dynamics is constructed to solve the absolute safety boundary, thereby theoretically determining the resilience baseline under the worst-case stochastic disturbance. This improves the problem that traditional resilience assessments mostly adopt probability optimization based on expectations, which lacks boundary constraints for extreme long-tail events, resulting in the failure of scheduling strategies under sudden rainstorms.

[0012] Preferably, in S1, the construction of the Riemann metric tensor includes:

[0013] Obtain the physical attribute data of the inspection well node, including the bottom elevation and the cover elevation;

[0014] Construct a node metric matrix in the form of a diagonal matrix, and define the diagonal elements of the node metric matrix as barrier functions with respect to the node water level;

[0015] Configure the structure of the barrier function to include a lower bound penalty term for the bottom elevation of the well and an upper bound penalty term for the top elevation of the well cover;

[0016] The node metric matrix is ​​combined with the identity matrix used to measure pipeline flow to generate a positive definite symmetric matrix in block diagonal form, and this positive definite symmetric matrix is ​​determined as the Riemann metric tensor.

[0017] Preferably, in S2, the construction of the Hamiltonian function based on fluid kinetic energy and potential energy including gravitational and pressure potential energy includes:

[0018] The pipe inertia coefficient is calculated based on the ratio of pipe length to pipe cross-sectional area, and the fluid kinetic energy function is constructed using the pipe inertia coefficient and the square of the pipe flow rate.

[0019] The gravitational potential energy is calculated based on the integral relationship between the node water level and the node water storage area, and the pressure potential energy is calculated in combination with the pipeline pressure distribution. The sum of the gravitational potential energy and the pressure potential energy is then used to construct a fluid potential energy function.

[0020] Adding the fluid kinetic energy function to the fluid potential energy function yields the Hamiltonian energy function, which describes the total energy of the pipeline system.

[0021] Preferably, in S2, the construction of the symplectic neural network fitting the Hamiltonian vector field of the pipeline network includes:

[0022] Construct a deep neural network containing multiple linear symplectic modules and activation functions, and use the generalized coordinate vector and generalized momentum vector at the current time step as network input;

[0023] The linear symplectic module is used to perform a symplectic-preserving transformation on the input vector. The symplectic-preserving transformation is achieved by parameterizing the transformation matrix as a product of upper triangular symplectic matrices or lower triangular symplectic matrices.

[0024] The Hamiltonian vector field is calculated using the partial derivative relationship of the Hamiltonian energy function with respect to the generalized momentum vector and the generalized coordinate vector, and the output of the symplectic neural network is configured as an approximation of the Hamiltonian vector field.

[0025] Preferably, in S2, the step of training the pipeline dynamics prediction model by minimizing the prediction error and the energy conservation residual includes:

[0026] Historical hydraulic monitoring time series data of the pipeline network were collected and divided into training sets;

[0027] Define a loss function for network training, which includes a data fitting term between the predicted state and the true state, and a physical constraint term constructed based on the Hamiltonian canonical equation.

[0028] During the network forward propagation process, the Leapfrog discrete integral scheme is used to alternately update the generalized coordinate vector and the generalized momentum vector;

[0029] The network weights are updated using the backpropagation algorithm until the loss function converges, resulting in a nonlinear dynamic prediction model that can characterize the evolution of the pipeline network state over time.

[0030] Preferably, in S3, the construction of the second-order stochastic Hamilton-Jacobi-Isax partial differential equation includes:

[0031] A stochastic differential equation is constructed to describe the evolution of the pipeline network state. The stochastic differential equation includes a control input term consisting of the pump station frequency and the gate opening, a disturbance input term consisting of the rainfall intensity, and a Brownian motion diffusion term.

[0032] Define a system failure set in the state space, which is the set of all state points where the water level at a node exceeds the elevation of the manhole cover.

[0033] Define a value function that represents the minimum cost for the system to remain outside the system failure set within a preset time window;

[0034] Based on the principle of dynamic programming, using the stochastic differential equation and the value function, a stochastic Hamilton-Jacobi-Isax partial differential equation containing time partial derivative terms, Hamiltonian operator terms, and second-order diffusion terms is derived.

[0035] Preferably, in S4, the construction of the physical sensing neural network to solve the partial differential equation includes:

[0036] Sampling is performed in the full state space and time domain of the pipeline network to generate a training dataset containing points within the domain, initial time points, and boundary points;

[0037] A deep neural network is constructed to fit the value function, and the weighted sum of the residuals of the stochastic Hamilton-Jacobi-Isaac partial differential equation at the in-domain points, the terminal condition residuals at the initial time point, and the boundary condition residuals at the boundary points is used as the total loss function.

[0038] The deep neural network is trained until the total loss function meets the convergence condition, and the risk value function field in the full state space is output.

[0039] Preferably, in S5, the calculation of the current risk value and the Riemann gradient on the tangent space of the manifold using a physical sensing neural network includes:

[0040] Receive real-time water level and flow data uploaded by pipeline network sensors and map them as state points in Riemannian manifold space;

[0041] The state points are input into the trained physical sensing neural network, and the corresponding risk value function value is output.

[0042] The risk value function value is compared with a preset safety buffer threshold and a zero value within a range.

[0043] When the risk value function value is less than the safety buffer threshold, it is determined to be in an absolutely safe state; when the risk value function value is between the safety buffer threshold and zero, it is determined to be in a critical warning state; when the risk value function value is greater than zero, it is determined to be in a failure state.

[0044] Preferably, in S5, the generation of control instructions includes:

[0045] In response to the determination of a critical warning state, the Euclidean gradient of the risk value function with respect to the state variable is calculated;

[0046] By multiplying the inverse matrix of the Riemann metric tensor with the Euclidean gradient, the Riemann gradient vector on the tangent space of the Riemann manifold is obtained.

[0047] Establish a quadratic programming optimization model and set minimizing the control cost as the objective function;

[0048] Set a linear inequality constraint, requiring that the rate of change of the system state along the direction of the Riemann gradient vector be less than a preset negative decay rate;

[0049] The optimal control vector is obtained by solving the quadratic programming optimization model, and the optimal control vector is then analyzed into specific action parameters of the pump station and the gate.

[0050] Secondly, this invention provides the following technical solution: an artificial intelligence-driven urban pipeline network flood resilience assessment system, comprising the following modules:

[0051] The spatial reconstruction module is used to acquire pipeline network data, define node water level as generalized coordinates and pipeline flow rate as generalized momentum; and construct a Riemann metric tensor using a metric matrix that includes a barrier function that reflects the water level approaching the overflow threshold and tending to infinity, thereby establishing the Riemann manifold embedding space of the pipeline network physical state.

[0052] The dynamic modeling module is used to construct a Hamiltonian function based on fluid kinetic energy and potential energy including gravity and pressure potential energy; construct a symplectic neural network to fit the Hamiltonian vector field of the pipeline network, use the symplectic discrete integral scheme as the forward propagation rule, and obtain the pipeline network dynamic prediction model by minimizing the prediction error and energy conservation residual.

[0053] The game equation construction module is used to model the model as a stochastic differential equation containing control input, rainfall disturbance and random noise, and combine it with the value function that represents avoiding entering the overflow failure set to construct a second-order stochastic Hamilton-Jacobi-Isaac partial differential equation.

[0054] The boundary solution module is used to construct a physical perception neural network to solve the partial differential equations, train the network with the equation residuals as the loss function, output the risk value function field and extract the zero level set as the resilient safety boundary.

[0055] The adaptive control module is used to map real-time collected data to the space, calculate the current risk value and the Riemann gradient on the tangent space of the manifold through a physical sensing neural network, solve a quadratic programming problem constrained by evolution along the gradient direction, and generate control instructions.

[0056] The present invention has the following beneficial effects:

[0057] 1. In this invention, the absolute safety boundary is calculated by constructing a stochastic HJI equation based on Riemannian manifolds and symplectic dynamics, thereby theoretically determining the resilience baseline under the worst-case stochastic disturbance. This improves the problem that traditional resilience assessments mostly adopt probability optimization based on expectations, which lacks boundary constraints for extreme long-tail events, resulting in the failure of scheduling strategies under sudden rainstorms.

[0058] 2. In this invention, by constructing a Riemannian manifold embedding space based on a potential barrier function, the geometric distance of high-risk regions is nonlinearly stretched using the Riemann metric tensor, thereby achieving natural avoidance of critical risks. This improves the problem that traditional pipeline control, which mostly uses Euclidean space metrics, cannot detect the nonlinear risks when the water level approaches the physical limit, resulting in sluggish response under extreme conditions.

[0059] 3. In this invention, a dynamic model is constructed by using a symplectic neural network and Hamiltonian function, and the energy conservation of the system is maintained by adopting a symplectic discrete integral scheme, thereby eliminating numerical drift in long-term time series prediction. This improves the problem that traditional data-driven models mostly use black-box fitting without physical constraints, which violates the law of fluid conservation and causes long-term prediction trajectory divergence and distortion.

[0060] 4. In this invention, by calculating the gradient of risk value on the tangent space of the Riemannian manifold, the system is guided to evolve along the geodesic direction where the risk decreases the fastest, thereby achieving optimal fast recovery that satisfies geometric constraints. This improves upon the problem that traditional optimization control mostly adopts the search direction along the Euclidean gradient, which ignores the nonlinear bending characteristics of the state space, resulting in low convergence efficiency in high-dimensional complex states. Attached Figure Description

[0061] Figure 1 This is a flowchart of an artificial intelligence-driven method for assessing the flood resilience of urban pipe networks proposed in this invention;

[0062] Figure 2 This invention presents a syntactic neural network dynamics modeling process for an AI-driven urban pipeline network flood resilience assessment method.

[0063] Figure 3 This invention presents a physical sensing neural network solution process for an AI-driven urban pipeline network flood resilience assessment method.

[0064] Figure 4 This is a real-time adaptive control logic diagram of an artificial intelligence-driven urban pipe network flood resilience assessment method proposed in this invention.

[0065] Figure 5 This is an architecture diagram of an artificial intelligence-driven urban pipeline network flood resilience assessment system proposed in this invention. Detailed Implementation

[0066] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Example 1:

[0068] In a first embodiment of the present invention, the present invention provides an artificial intelligence-driven method for assessing the flood resilience of urban pipe networks, such as... Figures 1-4 As shown, it includes the following steps:

[0069] S1. Obtain pipeline network data, define node water level as generalized coordinates, and pipeline flow rate as generalized momentum; use a metric matrix containing a barrier function that reflects the potential barrier function that tends to infinity when the water level approaches the overflow threshold to construct a Riemann metric tensor and establish the Riemann manifold embedding space of the pipeline network physical state.

[0070] Furthermore, in S1, constructing the Riemann metric tensor includes:

[0071] Obtain the physical attribute data of the inspection well node, including the bottom elevation and the cover elevation;

[0072] Construct a node metric matrix in the form of a diagonal matrix, and define the diagonal elements of the node metric matrix as barrier functions with respect to the node water level;

[0073] Configure the structure of the barrier function to include a lower bound penalty term for the bottom elevation of the well and an upper bound penalty term for the top elevation of the well cover;

[0074] The node metric matrix is ​​combined with the identity matrix used to measure pipeline flow to generate a positive definite symmetric matrix in block diagonal form, and this positive definite symmetric matrix is ​​determined as the Riemann metric tensor.

[0075] Specifically, it involves acquiring topological data of the urban drainage network and real-time sensor monitoring data. It also involves defining the physical state vector of the entire system. The vector consists of two parts: the first part is the generalized coordinate vector. This represents the real-time water level at each inspection well node in the pipeline network, with the dimension being... ,in The first part represents the total number of nodes; the second part represents the generalized momentum vector. This represents the real-time flow rate of each drainage pipe, with the following dimensions: ,in Total number of pipes. Physical state vector. Represented as and A combined vector.

[0076] Construction of Riemann metric tensor based on pipeline network physical properties Used to reconstruct the geometry of the state space. Riemann metric tensor. Constructed as a A dimensional block diagonal positive definite symmetric matrix. The structure of this matrix is ​​as follows:

[0077] ;

[0078] in Represents the Riemann metric tensor; This represents the node metric matrix used to measure the water level status of nodes, with dimensions of . ; This indicates the state used to measure pipeline flow. 3D identity matrix; This represents the zero matrix of the corresponding dimension.

[0079] Barrier function configuration and node metric matrix This is a diagonal matrix, with its diagonal elements composed of potential barrier functions. Physical attribute data for each inspection well node is obtained, including the bottom elevation. Elevation of manhole cover For any number of... Each node, its metric component The calculation formula is configured as follows:

[0080] ;

[0081] in Indicates the first Each node is at the current water level. The metric value under this dimension is the local scaling factor of the Riemannian manifold space in that dimension; Indicates the first Real-time water level monitoring values ​​of each node; Indicates the first The bottom elevation of each node, i.e., the physical lower limit of dryness; Indicates the first The elevation of the manhole cover at each node, i.e., the physical upper limit of the overflow; This represents the weighting coefficient for the lower bound penalty term, used to adjust the sensitivity to low water level conditions; This represents the weighting coefficient for the upper bound penalty term, used to adjust the sensitivity to overflow risk; This represents a tiny positive number that prevents the denominator from being zero, and is used to ensure the stability of numerical calculations.

[0082] By constructing the Riemannian manifold embedding space in the above manner, the transformation from physical constraints to geometric structures is realized. When the node water level... When the system is in its normal operating range, the barrier function value is relatively small, and the Riemann metric is relatively accurate. Approaching Euclidean metrics, the system control strategy prioritizes conventional energy consumption indicators. When the node water level... Approaching the elevation of the manhole cover or well bottom elevation When the denominator approaches zero, the metric component... The value increases dramatically. This numerical change manifests as a nonlinear stretching of local geometric distances in the Riemannian manifold space. That is, in high-risk areas, small water level changes are mapped as huge geometric displacements in the Riemannian space. Subsequent optimization control algorithms, when searching for the optimal path, tend to avoid these areas with extremely large metric values, thereby mathematically forcing the system state away from the physical boundaries of overflow or drying up. This achieves automatic avoidance and protection of the pipeline network's operational safety boundaries without the need for manually setting rigid logical judgment rules.

[0083] S2. Construct a Hamiltonian function based on fluid kinetic energy and potential energy including gravity and pressure potential energy; construct a symplectic neural network to fit the Hamiltonian vector field of the pipeline network, use the symplectic discrete integral scheme as the forward propagation rule, and obtain the pipeline network dynamic prediction model by minimizing the prediction error and energy conservation residual.

[0084] Furthermore, in S2, the Hamiltonian function is constructed based on fluid kinetic energy and potential energy including gravitational and pressure potential energy, including:

[0085] The pipe inertia coefficient is calculated based on the ratio of pipe length to pipe cross-sectional area, and the fluid kinetic energy function is constructed using the pipe inertia coefficient and the square of the pipe flow rate.

[0086] The gravitational potential energy is calculated based on the integral relationship between the node water level and the node water storage area, and the pressure potential energy is calculated in combination with the pressure distribution of the pipeline network. The sum of the gravitational potential energy and the pressure potential energy is constructed as the fluid potential energy function.

[0087] Adding the fluid kinetic energy function to the fluid potential energy function yields the Hamiltonian energy function, which describes the total energy of the pipeline system.

[0088] In S2, constructing the symplectic neural network to fit the Hamiltonian vector field of the pipeline network includes:

[0089] Construct a deep neural network containing multiple linear symplectic modules and activation functions, and use the generalized coordinate vector and generalized momentum vector at the current time step as network input;

[0090] The input vector is subjected to symplectic transformation using a linear symplectic module. The symplectic transformation is achieved by parameterizing the transformation matrix as a product of upper triangular symplectic matrices or lower triangular symplectic matrices.

[0091] The Hamiltonian vector field is calculated by using the partial derivatives of the Hamiltonian energy function with respect to the generalized momentum vector and the generalized coordinate vector, and the output of the symplectic neural network is configured as an approximation of the Hamiltonian vector field.

[0092] In S2, the pipeline dynamics prediction model is obtained by training by minimizing the prediction error and the energy conservation residual, including:

[0093] Historical hydraulic monitoring time series data of the pipeline network were collected and divided into training sets;

[0094] Define the loss function for network training. The loss function includes a data fitting term between the predicted state and the real state, as well as a physical constraint term constructed based on the Hamiltonian canonical equation.

[0095] During the network forward propagation process, the Leapfrog discrete integral scheme is used to alternately update the generalized coordinate vector and the generalized momentum vector;

[0096] The network weights are updated using the backpropagation algorithm until the loss function converges, resulting in a nonlinear dynamic prediction model that can characterize the evolution of the pipeline network state over time.

[0097] Specifically, the Hamiltonian energy function is constructed based on fluid mechanics principles. The total energy of a pipe network system consists of fluid kinetic energy and fluid potential energy. For the kinetic energy term, the pipe inertia matrix is ​​calculated based on the physical parameters of each pipe segment. The pipe inertia matrix is ​​a diagonal matrix, with its diagonal elements corresponding to the inertia coefficients of each pipe segment. The formula for calculating the inertia coefficient of a pipe section is as follows:

[0098] ;

[0099] in Indicates the first The fluid inertia coefficient of the pipe section, Indicates the first The length of the pipe section Indicates the first The cross-sectional area of ​​the pipe section Represents gravitational acceleration. A fluid kinetic energy function is constructed based on the pipe flow vector and the pipe inertia matrix. :

[0100] ;

[0101] in This represents the generalized momentum vector of the total network pipeline flow. This represents the inertia coefficient of each pipe section. The diagonal inertia matrix formed, Indicates matrix transpose. This represents finding the inverse of a matrix.

[0102] For the potential energy term, gravitational potential energy and pressure potential energy are calculated based on the water storage characteristics of each node. Fluid potential energy function of the node The calculation formula is as follows:

[0103] ;

[0104] in Indicates the first Water level at the node Indicates fluid density, Indicates the first Node at water level The water storage cross-sectional area at the location. The total potential energy function of the entire network. This is the sum of the potential energies of all nodes. Adding the fluid kinetic energy function to the fluid potential energy function yields the Hamiltonian energy function, which describes the total energy of the pipe network system. : .

[0105] Symmetric Neural Network Construction and Forward Propagation: A deep symmetric neural network is constructed to approximate the Hamiltonian dynamics evolution mechanism of a pipeline network system. The network input is the current time step. generalized coordinate vector and generalized momentum vector The network contains stacked linear symplectic modules. Each linear symplectic module performs a symplectic-preserving transformation on the input vector. This transformation matrix is ​​decomposed into a product of an upper triangular symplectic matrix and a lower triangular symplectic matrix to ensure that the transformation process strictly satisfies the symplectic geometric constraints, i.e., the Jacobian matrix of the transformation matrix satisfies the symplectic condition. The Leapfrog discrete integral scheme is used as the network's time evolution rule to update the state from the current time step to the next time step. The data flow and update process are as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] in Indicates the time step. This represents the momentum variable at the intermediate time point. This represents the partial derivative of the Hamiltonian function with respect to the generalized coordinates. This represents the partial derivative of the Hamiltonian function with respect to the generalized momentum. This represents the generalized coordinate vector at the next moment. Let represent the generalized momentum vector at the next moment. The above partial derivatives are obtained by using automatic differentiation techniques to calculate the Hamiltonian function fitted to the symplectic neural network.

[0110] Model training and parameter optimization involve constructing a training set using historical hydraulic monitoring data from the pipeline network. The data includes continuous time series data on nodal water levels and pipeline flow rates. A loss function is defined that incorporates data fitting terms and physical constraint terms. :

[0111] ;

[0112] in This represents the state vector predicted by the model for the next time step. This represents the state vector at the next moment in the actual monitoring. This represents the calculated Hamiltonian energy value. This represents the weighting coefficient of the physical constraint term. This represents the square of the Euclidean norm. The gradient of the loss function with respect to the network weights is calculated using the backpropagation algorithm. The network parameters are then iteratively updated through an optimizer until the loss function converges. The trained model is then the pipeline network nonlinear dynamics prediction model.

[0113] By introducing the Hamiltonian mechanics framework and symplectic neural networks, the model adheres to energy conservation and symplectic geometric preservation characteristics at the mechanistic level. Compared to purely data-driven neural networks, this approach eliminates numerical dissipation and non-physical drift in long-term predictions, ensuring the physical consistency and numerical stability of prediction results over long periods, and providing a high-fidelity dynamic kernel for subsequent robust control.

[0114] S3. The pipeline dynamics prediction model is modeled as a stochastic differential equation that includes control input, rainfall disturbance and random noise. Combined with the value function that characterizes the avoidance of entering the overflow failure set, a second-order stochastic Hamilton-Jacobi-Isaac partial differential equation is constructed.

[0115] Furthermore, in S3, the construction of second-order stochastic Hamilton-Jacobi-Isax partial differential equations includes:

[0116] A stochastic differential equation describing the evolution of the pipeline network state is constructed. The stochastic differential equation includes a control input term consisting of pump station frequency and gate opening, a disturbance input term consisting of rainfall intensity, and a Brownian motion diffusion term.

[0117] Define the system failure set in the state space as the set of all state points where the water level at a node exceeds the elevation of the manhole cover.

[0118] Define a value function, which represents the minimum cost for the system to remain outside the system failure set within a preset time window;

[0119] Based on the principle of dynamic programming, a stochastic Hamilton-Jacobi-Isax partial differential equation containing time partial derivatives, Hamiltonian operator terms, and second-order diffusion terms is derived using stochastic differential equations and value functions.

[0120] Specifically, the stochastic differential equations are constructed using the pipeline network nonlinear dynamics prediction model trained in step S2. Control input terms, adversarial disturbance terms, and random noise terms are introduced to establish stochastic differential equations describing the pipeline network state evolution. The mathematical expression of the stochastic differential equations is as follows:

[0121] ;

[0122] in express The physical state vector of the entire system at time t, which includes the generalized coordinate vector and the generalized momentum vector; express The control input vector at any given time is composed of the pump station operating frequency and the opening degree of the intercepting well gate; express The adversarial disturbance input vector at any given time, composed of rainfall intensity, is used to simulate the most severe weather conditions; The drift term function represents a defined drift term and describes the average evolution trend of the pipeline network under control and disturbance. This represents the diffusion coefficient matrix, used to characterize the uncertainty of the model and the intensity of environmental noise; This represents the standard Wiener process, i.e., the Brownian motion term, used to simulate the continuous disturbance of the system state by random noise; This represents a differential operator.

[0123] System failure set and value function definition: Define the system failure set in state space. Failure set This covers all pipeline network conditions where overflow violations occur, meaning the real-time water level at any node exceeds the elevation of the manhole cover at that node. The mathematical expression for the failure set is as follows:

[0124] ;

[0125] in Indicates the first Water levels at each node Indicates the first The elevation of manhole covers at each node. A value function is defined based on the failure set. The value function characterizes the system in its current state. and time Departure, within the preset time window Internally maintained in the failure set The minimum cost or maximum safety probability beyond that. Terminal time. The boundary conditions of the value function are set as follows ,in State point The symbolic distance function to the boundary of the failure set.

[0126] The derivation of the stochastic Hamilton-Jacobi-Isaks partial differential equation is based on the principle of dynamic programming. Combining the aforementioned stochastic differential equations and the value function, a second-order stochastic Hamilton-Jacobi-Isaks partial differential equation describing the spatiotemporal evolution of the value function is derived. The specific form of this equation is as follows:

[0127] ;

[0128] in It represents the partial derivative of the value function with respect to time, describing the rate of change of the system's security level over time; Represents a game operator that describes the adversarial process between the optimal control strategy and the worst disturbance conditions; This represents the first-order gradient vector of the value function with respect to the state vector; This represents the drift term in a stochastic differential equation, i.e., the system dynamics equation; Represents the trace operation of a matrix; Represents the diffusion coefficient matrix; The second-order Hessian matrix represents the value function with respect to the state vector. The product of this term and the diffusion coefficient matrix characterizes the second-order effect of random noise on the evolution of system security.

[0129] This step transforms the pipeline resilience assessment problem into a differential game problem. By constructing the HJI equation containing a second-order diffusion term, not only are deterministic hydraulic laws considered, but the uncertainty of rainfall and random disturbances caused by model errors are also explicitly introduced. The min-max operator in the equation simulates the game process of seeking the optimal scheduling strategy under the worst rainfall conditions. The value function field obtained by solving this partial differential equation is... Its zero-level set The resilience safety boundary of the pipeline network system was precisely defined. State points located within the boundary. This constitutes an absolute safety domain, meaning that regardless of changes in external rainfall, as long as the system state remains within this region, theoretically, there are feasible control strategies to prevent overflow. This process represents a leap from probabilistic risk assessment to deterministic safety boundary calculation, providing rigorous mathematical criteria for subsequent robust control.

[0130] S4. Construct a physical perception neural network to solve partial differential equations, train the network with the equation residuals as the loss function, output the risk value function field and extract the zero level set as the resilient safety boundary.

[0131] Furthermore, in S4, constructing a physical sensing neural network to solve partial differential equations includes:

[0132] Sampling is performed in the full state space and time domain of the pipeline network to generate a training dataset containing points within the domain, initial time points, and boundary points;

[0133] A deep neural network fitting value function is constructed, and the weighted sum of the residuals of the stochastic Hamilton-Jacobi-Isaac partial differential equation at the in-domain points, the terminal condition residuals at the initial time point, and the boundary condition residuals at the boundary points is used as the total loss function.

[0134] Train the deep neural network until the total loss function meets the convergence condition, and output the risk value function field in the full state space.

[0135] Specifically, the training dataset construction and sampling strategy defines the state space range and time evolution interval of the pipeline system. The state space range is determined by the physical upper and lower limits of node water levels and the extreme range of pipeline flow. A quasi-random sampling method is used to discretize the data points throughout the entire state space and time domain. The generated training dataset consists of three parts: a set of collocation points within the domain, a set of terminal time points, and a set of spatial boundary points. The set of collocation points within the domain is distributed within the state space and time interval, used to constrain the physical evolution of the partial differential equations; the set of terminal time points is distributed at the end of the time interval, used to constrain the terminal value conditions of the system; and the set of spatial boundary points is distributed at the physical boundaries of the state space, used to constrain the boundary behavior of the system.

[0136] Deep Neural Network Construction and Loss Function Definition: Constructing a multi-layer feedforward deep neural network to approximate a high-dimensional value function. The network's input layer receives the state vector. and time variables The output layer outputs the corresponding scalar value. Define the total loss function. This function is a weighted sum of the residual loss term, the terminal condition loss term, and the boundary condition loss term from the equation. Total Loss Function The calculation formula is as follows:

[0137] ;

[0138] in This represents the total loss function value used to train the neural network; , , These represent the weight coefficients of the residual term, terminal condition term, and boundary condition term of the equation, respectively, which are used to adjust the optimization priority under different constraints. , , These represent the number of samples at coordinate points within the domain, terminal time points, and spatial boundary points, respectively. This indicates that the neural network is in a certain state. and time The predicted output value; Indicates the end time of the preset time window; The known value of the value function at the terminal moment is determined by the symbolic distance function of the system failure set; The known value of the value function on the spatial boundary is determined by the Dirichlet boundary condition or the Neumann boundary condition. The residual operator representing the stochastic Hamiltonian-Jacobi-Isax partial differential equation is expressed as follows:

[0139] ;

[0140] in The partial derivative of the value function with respect to time is represented by automatic differentiation; This represents the first-order gradient vector of the value function with respect to the state vector; The second-order Hessian matrix represents the value function with respect to the state vector; This represents the deterministic drift term in a stochastic differential equation; This represents the diffusion coefficient matrix in a stochastic differential equation. This represents the matrix trace operation.

[0141] Network training and safety boundary extraction utilize a stochastic gradient descent optimization algorithm to iteratively update the weight parameters of the deep neural network. In each iteration, the total loss function described above is calculated. The gradients of the network parameters are calculated, and backpropagation is used to update the parameters until the total loss function converges to below a preset threshold. After training, the network parameters are fixed, and this network becomes the risk-value function field in the full state space. The risk-value function field is subjected to level set extraction, and the equation is solved. The resulting set of states constitutes the resilient safety boundary of the pipeline network system. This boundary divides the high-dimensional state space into two regions: satisfying... The region is defined as the absolute safety region, within which control strategies exist to prevent system overflow under arbitrary disturbances; satisfying... The region was identified as a potential failure domain.

[0142] This step employs a physical perceptron neural network to solve the high-dimensional stochastic HJI equations, overcoming the curse of dimensionality problem in traditional grid methods when dealing with high-dimensional state spaces. By directly encoding the physical constraints of the HJI equations into the loss function of the neural network, the trained value function field strictly follows the dynamics of differential games. The extracted zero-level set accurately quantifies the safety limits of the pipeline system, providing definite state constraint boundaries for subsequent control strategies. Compared to traditional probabilistic assessments, this reachability analysis-based method provides theoretical safety guarantees under worst-case random perturbations, achieving a mathematical definition of the pipeline network's resilience boundaries.

[0143] S5. Map the real-time collected data to space, calculate the current risk value and Riemann gradient on the tangent space of the manifold through the physical sensing neural network, solve the quadratic programming problem constrained by evolution along the gradient direction, and generate control instructions.

[0144] Furthermore, in S5, the calculation of the current risk value and the Riemann gradient on the tangent space of the manifold using a physical perception neural network includes:

[0145] Receive real-time water level and flow data uploaded by pipeline network sensors and map them as state points in Riemannian manifold space;

[0146] The state points are input into the trained physical sensing neural network, and the corresponding risk value function value is output.

[0147] The risk value function value is compared with the preset safety buffer threshold and zero value within a range.

[0148] When the value-at-risk (VAT) function value is less than the safety buffer threshold, it is determined to be in an absolutely safe state; when the VAT function value is between the safety buffer threshold and zero, it is determined to be in a critical warning state; when the VAT function value is greater than zero, it is determined to be in a failure state.

[0149] In S5, the generation of control commands includes:

[0150] In response to the determination of a critical warning state, the Euclidean gradient of the risk value function with respect to the state variables is calculated;

[0151] By multiplying the inverse matrix of the Riemann metric tensor with the Euclidean gradient, we obtain the Riemann gradient vector on the tangent space of the Riemann manifold.

[0152] Establish a quadratic programming optimization model and set minimizing the control cost as the objective function;

[0153] Set a linear inequality constraint that requires the rate of change of the system state along the Riemann gradient vector direction to be less than a preset negative decay rate;

[0154] The optimal control vector is obtained by solving the quadratic programming optimization model, and then the optimal control vector is analyzed into specific action parameters of the pump station and gate.

[0155] Specifically, online condition assessment and risk value calculation involve real-time acquisition of water level data from various monitoring points in the pipeline network, as well as flow data from key pipe sections. These physical quantities are then combined to form the current real-time condition vector. Based on the Riemann metric tensor determined in step S1 ,Will Map the state points to the Riemannian manifold space. Input the mapped state points into the physical sensing neural network trained in step S4. The neural network performs forward propagation calculations and outputs the value-at-risk function value corresponding to the current state. Set a safety buffer threshold. The calculated and and Numerical comparisons are performed to determine the current operating status of the system.

[0156] like The system is determined to be in an absolutely safe state, indicating that the current pipeline network is operating smoothly and is far from the overflow boundary;

[0157] like The system is determined to be in a critical warning state, indicating that the system is approaching the safety boundary and intervention control needs to be initiated.

[0158] like The system is determined to be in a failure state, indicating that an overflow has occurred or an irreversible overflow event is about to occur.

[0159] Riemann gradient calculation and optimal control solution: When the system is determined to be in a critical warning state, a control strategy based on the Riemann gradient is initiated. First, the risk-value function is calculated. Euclidean gradient of the state variable Subsequently, the inverse matrix of the Riemann metric tensor was used. Transforming the Euclidean gradient yields the Riemann gradient vector on the tangent space of the Riemann manifold. :

[0160] ;

[0161] Construct an optimization control model based on quadratic programming. The objective function is set to minimize the control cost, i.e., minimize the control input. With preset baseline control quantity Squared Euclidean distance between them:

[0162] ;

[0163] A linear inequality constraint is set to force the system state to evolve along the Riemann gradient direction, and the evolution rate must ensure that the risk-value function decays at a rate not less than a preset rate. The price is decreasing. The constraints are expressed as follows:

[0164] ;

[0165] in This represents the inner product induced by the Riemann metric. This represents the system dynamics equations under worst-case disturbance conditions. The optimal control vector is obtained by solving the quadratic programming problem using the interior-point method or the effective set method. .Will The commands are interpreted as specific instructions for the pump station's operating frequency and the opening degree of the intercepting well gate, and then sent to the SCADA system for execution.

[0166] This step achieves a closed loop from theoretical evaluation to engineering control. By introducing the Riemann gradient, the control strategy can be adjusted along the direction of the steepest manifold curvature, rather than the traditional Euclidean straight line direction. This enables the controller to achieve the fastest risk avoidance with minimal energy cost when facing high-risk nonlinear regions of the pipeline network. The optimization solution based on quadratic programming ensures the real-time performance of the control commands, while the inequality constraints mathematically mandate that the system must converge to the absolutely safe region, thus physically eliminating the possibility of control divergence or oscillation and ensuring the resilience of the pipeline network under extreme conditions.

[0167] Example 2:

[0168] This study presents an extreme defense scenario for deep-tunnel drainage systems in coastal megacities, simulating the combined impact of super typhoons and storm surges. In this scenario, a massive underground pipe network, tens of meters deep, constitutes a high-dimensional nonlinear fluid system with high inertia and long time delays. The system input faces short-duration, intense rainfall loads with strong spatiotemporal randomness, while the output faces backflow resistance from storm surges at the terminal pumping stations. The system's operational objective is to achieve optimal energy consumption scheduling of the pumping station group while ensuring that no overflow from manhole covers occurs at any node across the entire watershed.

[0169] In the aforementioned stochastic nonlinear control scenario of coastal deep tunnel systems responding to extreme typhoons and rainstorms, existing technologies struggle to balance physical consistency and absolute safety. On one hand, traditional Euclidean space-based control algorithms cannot accurately measure the exponentially increasing nonlinear risk when node water levels approach physical limits, leading to a lack of control sensitivity in critical states. On the other hand, conventional data-driven models lack constraints from physical conservation laws such as Hamiltonian mechanics, making long-term predictions prone to numerical drift that violates energy conservation. Furthermore, probability-based optimization methods cannot calculate the absolute safety boundary for handling worst-case stochastic disturbances, thus failing to theoretically eliminate the risk of system collapse and overflow under extreme long-tail conditions. To address these issues, this invention provides an AI-driven urban pipeline flood resilience assessment system, the structure of which is as follows: Figure 5 As shown. The specific implementation process of this system is as follows:

[0170] The spatial reconstruction module constructs a Riemann metric tensor using a metric matrix containing a barrier function, mapping the physical state of the pipeline network to the embedded space of the Riemann manifold. It achieves natural risk avoidance by nonlinearly stretching the geometric distance of high-risk states. The dynamic modeling module constructs a prediction model with physical conservation properties based on Hamiltonian functions and symplectic neural networks, eliminating non-physical drift in long-term predictions. The game equation construction module establishes a stochastic Hamiltonian-Jacobi-Isax partial differential equation containing a second-order diffusion term, quantifying the antagonistic relationship between optimal control and worst-case random disturbances. The boundary solution module solves the equation using a physical sensing neural network, extracting the zero-level set as a resilient safety boundary that precisely defines the absolute safety domain. The adaptive control module maps real-time data to the manifold space, uses the Riemann gradient to capture the geodesic direction of the fastest risk decrease, and generates control commands that force the system to converge to the safety domain by solving a quadratic programming problem, thereby achieving real-time closed-loop control with physical consistency and theoretical safety guarantees under extreme conditions.

[0171] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An AI-driven method for assessing the flood resilience of urban pipe networks, characterized in that, Includes the following steps: S1. Obtain pipeline network data, define node water level as generalized coordinates, and pipeline flow rate as generalized momentum; use a metric matrix containing a barrier function that reflects the potential barrier function that tends to infinity when the water level approaches the overflow threshold to construct a Riemann metric tensor and establish the Riemann manifold embedding space of the pipeline network physical state. S2. Construct a Hamiltonian function based on fluid kinetic energy and potential energy including gravity and pressure potential energy; construct a symplectic neural network to fit the Hamiltonian vector field of the pipeline network, use the symplectic discrete integral scheme as the forward propagation rule, and obtain the pipeline network dynamic prediction model by minimizing the prediction error and energy conservation residual. S3. The pipeline dynamics prediction model is modeled as a stochastic differential equation that includes control input, rainfall disturbance and random noise. Combined with the value function that characterizes the avoidance of entering the overflow failure set, a second-order stochastic Hamilton-Jacobi-Isaac partial differential equation is constructed. S4. Construct a physical perception neural network to solve the partial differential equation, train the network with the equation residual as the loss function, output the risk value function field and extract the zero level set as the resilient safety boundary. S5. Map the real-time collected data to the space, calculate the current risk value and the Riemann gradient on the tangent space of the manifold through the physical sensing neural network, solve the quadratic programming problem constrained by evolution along the gradient direction, and generate control instructions.

2. The AI-driven urban pipeline network flood resilience assessment method according to claim 1, characterized in that, In S1, the construction of the Riemann metric tensor includes: Obtain the physical attribute data of the inspection well node, including the bottom elevation and the cover elevation; Construct a node metric matrix in the form of a diagonal matrix, and define the diagonal elements of the node metric matrix as barrier functions with respect to the node water level; Configure the structure of the barrier function to include a lower bound penalty term for the bottom elevation of the well and an upper bound penalty term for the top elevation of the well cover; The node metric matrix is ​​combined with the identity matrix used to measure pipeline flow to generate a positive definite symmetric matrix in block diagonal form, and this positive definite symmetric matrix is ​​determined as the Riemann metric tensor.

3. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S2, the construction of the Hamiltonian function based on fluid kinetic energy and potential energy including gravitational and pressure potential energy includes: The pipe inertia coefficient is calculated based on the ratio of pipe length to pipe cross-sectional area, and the fluid kinetic energy function is constructed using the pipe inertia coefficient and the square of the pipe flow rate. The gravitational potential energy is calculated based on the integral relationship between the node water level and the node water storage area, and the pressure potential energy is calculated in combination with the pipeline pressure distribution. The sum of the gravitational potential energy and the pressure potential energy is then used to construct a fluid potential energy function. Adding the fluid kinetic energy function to the fluid potential energy function yields the Hamiltonian energy function, which describes the total energy of the pipeline system.

4. The AI-driven urban pipeline network flood resilience assessment method according to claim 1, characterized in that, In S2, the construction of the symplectic neural network fitting the Hamiltonian vector field of the pipeline network includes: Construct a deep neural network containing multiple linear symplectic modules and activation functions, and use the generalized coordinate vector and generalized momentum vector at the current time step as network input; The linear symplectic module is used to perform a symplectic-preserving transformation on the input vector. The symplectic-preserving transformation is achieved by parameterizing the transformation matrix as a product of upper triangular symplectic matrices or lower triangular symplectic matrices. The Hamiltonian vector field is calculated using the partial derivative relationship of the Hamiltonian energy function with respect to the generalized momentum vector and the generalized coordinate vector, and the output of the symplectic neural network is configured as an approximation of the Hamiltonian vector field.

5. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S2, the process of training the pipeline dynamics prediction model by minimizing the prediction error and the energy conservation residual includes: Historical hydraulic monitoring time series data of the pipeline network were collected and divided into training sets; Define a loss function for network training, which includes a data fitting term between the predicted state and the true state, and a physical constraint term constructed based on the Hamiltonian canonical equation. During the network forward propagation process, the Leapfrog discrete integral scheme is used to alternately update the generalized coordinate vector and the generalized momentum vector; The network weights are updated using the backpropagation algorithm until the loss function converges, resulting in a nonlinear dynamic prediction model that can characterize the evolution of the pipeline network state over time.

6. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S3, the construction of the second-order stochastic Hamilton-Jacobi-Isaacs partial differential equation includes: A stochastic differential equation is constructed to describe the evolution of the pipeline network state. The stochastic differential equation includes a control input term consisting of the pump station frequency and the gate opening, a disturbance input term consisting of the rainfall intensity, and a Brownian motion diffusion term. Define a system failure set in the state space, which is the set of all state points where the water level at a node exceeds the elevation of the manhole cover. Define a value function that represents the minimum cost for the system to remain outside the system failure set within a preset time window; Based on the principle of dynamic programming, using the stochastic differential equation and the value function, a stochastic Hamilton-Jacobi-Isax partial differential equation containing time partial derivative terms, Hamiltonian operator terms, and second-order diffusion terms is derived.

7. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S4, the construction of the physical sensing neural network to solve the partial differential equation includes: Sampling is performed in the full state space and time domain of the pipeline network to generate a training dataset containing points within the domain, initial time points, and boundary points; A deep neural network is constructed to fit the value function, and the weighted sum of the residuals of the stochastic Hamilton-Jacobi-Isaac partial differential equation at the in-domain points, the terminal condition residuals at the initial time point, and the boundary condition residuals at the boundary points is used as the total loss function. The deep neural network is trained until the total loss function meets the convergence condition, and the risk value function field in the full state space is output.

8. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S5, the calculation of the current risk value and the Riemann gradient on the tangent space of the manifold using a physical sensing neural network includes: Receive real-time water level and flow data uploaded by pipeline network sensors and map them as state points in Riemannian manifold space; The state points are input into the trained physical sensing neural network, and the corresponding risk value function value is output. The risk value function value is compared with a preset safety buffer threshold and a zero value within a range. When the risk value function value is less than the safety buffer threshold, it is determined to be in an absolutely safe state; when the risk value function value is between the safety buffer threshold and zero, it is determined to be in a critical warning state; when the risk value function value is greater than zero, it is determined to be in a failure state.

9. The artificial intelligence-driven method for assessing the flood resilience of urban pipe networks according to claim 1, characterized in that, In S5, the generation of control instructions includes: In response to the determination of a critical warning state, the Euclidean gradient of the risk value function with respect to the state variable is calculated; By multiplying the inverse matrix of the Riemann metric tensor with the Euclidean gradient, the Riemann gradient vector on the tangent space of the Riemann manifold is obtained. Establish a quadratic programming optimization model and set minimizing the control cost as the objective function; Set a linear inequality constraint, requiring that the rate of change of the system state along the direction of the Riemann gradient vector be less than a preset negative decay rate; The optimal control vector is obtained by solving the quadratic programming optimization model, and the optimal control vector is then analyzed into specific action parameters of the pump station and the gate.

10. An AI-driven urban pipeline network flood resilience assessment system, characterized in that, The AI-driven urban pipeline network flood resilience assessment method according to any one of claims 1-9 includes the following modules: The spatial reconstruction module is used to acquire pipeline network data, define node water level as generalized coordinates and pipeline flow rate as generalized momentum; and construct a Riemann metric tensor using a metric matrix that includes a barrier function that reflects the water level approaching the overflow threshold and tending to infinity, thereby establishing the Riemann manifold embedding space of the pipeline network physical state. The dynamic modeling module is used to construct a Hamiltonian function based on fluid kinetic energy and potential energy including gravity and pressure potential energy; construct a symplectic neural network to fit the Hamiltonian vector field of the pipeline network, use the symplectic discrete integral scheme as the forward propagation rule, and obtain the pipeline network dynamic prediction model by minimizing the prediction error and energy conservation residual. The game equation construction module is used to model the model as a stochastic differential equation containing control input, rainfall disturbance and random noise, and combine it with the value function that represents avoiding entering the overflow failure set to construct a second-order stochastic Hamilton-Jacobi-Isaac partial differential equation. The boundary solution module is used to construct a physical perception neural network to solve the partial differential equations, train the network with the equation residuals as the loss function, output the risk value function field and extract the zero level set as the resilient safety boundary. The adaptive control module is used to map real-time collected data to the space, calculate the current risk value and the Riemann gradient on the tangent space of the manifold through a physical sensing neural network, solve a quadratic programming problem constrained by evolution along the gradient direction, and generate control instructions.

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