A pipeline system pressure fluctuation physical mechanism simulation method and system

Abstract

The application belongs to the field of fluid mechanics, and particularly relates to a pipeline system pressure fluctuation physical mechanism simulation method and system, which comprises a pipeline topology structure accurate modeling step, adopts a parameterized modeling method and a graph theory organization strategy to perform standardized modeling on pipeline accessories; a fluid-structure coupling multi-physical field coupling modeling step, which integrates pipeline wall elastic deformation, fluid compressibility and viscous dissipation effect into a unified coupling analysis framework; and a pressure wave propagation solving step based on an improved characteristic line method, the system comprising a topology modeling module, a fluid-structure coupling modeling module, a pressure wave solving module, a path tracking module, a working condition switching module, a parameter calibration module, a data management module and a visualization display module, the application can accurately reflect the actual propagation behavior of pressure waves in a pipeline with a complex topology structure, significantly improve the simulation accuracy and maintain high prediction ability during working condition switching.

Description

Technical Field

[0001] This invention belongs to the field of fluid mechanics, specifically a simulation method and system for the physical mechanism of pressure fluctuations in pipeline systems. Background Technology

[0002] The safe operation of fluid systems is a common key technology foundation for major projects such as petrochemicals, aerospace, nuclear power, and municipal pipeline networks. As the core carrier for fluid medium transportation, the internal pressure fluctuation characteristics of pipeline systems directly affect the reliability of system operation and structural safety. Accurate simulation analysis of the physical mechanism of pressure fluctuation has become a necessary part of engineering design.

[0003] Specifically, pipeline system pressure fluctuation simulation aims to reproduce the transient pressure change process of fluid medium in pipelines through numerical calculation, providing theoretical support for key applications such as valve rapid opening and closing condition analysis, water hammer protection design, and pressure fluctuation suppression. The accuracy of the simulation results directly determines the effectiveness of safety protection measures.

[0004] However, existing simulation technologies suffer from insurmountable accuracy bottlenecks when predicting pressure fluctuations in complex pipeline systems. Simplified algorithms based on empirical formulas neglect the influence of pipe fittings such as tees, elbows, and valves on pressure wave propagation, resulting in significant calculation deviations in complex pipeline topologies. While traditional computational fluid dynamics methods can capture pressure wave propagation characteristics, their model parameters rely on empirical settings and cannot accurately reflect the impact of factors such as pipe wall elastic deformation, fluid compressibility, and viscous dissipation on wave characteristics under actual operating conditions, leading to unquantifiable discrepancies between simulation results and physical reality. Furthermore, existing methods struggle to dynamically track pressure wave propagation paths in multi-condition coupled scenarios, causing a sharp drop in simulation accuracy when pipeline system operating conditions change. These technical bottlenecks prevent the simulation of the physical mechanism of pressure fluctuations from meeting the stringent safety requirements of major engineering projects. There is an urgent need to establish a new technical solution for the physical simulation of pressure fluctuations in pipeline systems through the synergistic optimization of accurate physical mechanism models and efficient numerical solution methods.

[0005] Therefore, the present invention provides a simulation method and system for the physical mechanism of pressure fluctuation in pipeline systems. Summary of the Invention

[0006] In order to overcome the shortcomings of the prior art, at least one technical problem raised in the background art is solved.

[0007] The technical solution adopted by the present invention to solve its technical problem is: a simulation method for the physical mechanism of pressure fluctuation in a pipeline system, which includes a precise modeling step of pipeline topology, a fluid-structure interaction multi-physics coupling modeling step, a pressure wave propagation solution step based on the improved characteristic line method, a pressure wave propagation path tracing step based on graph network, a multi-condition coupling dynamic switching step, and an uncertainty quantification and parameter adaptive calibration step.

[0008] In the precise modeling step of the pipeline topology, the system automatically identifies and extracts the pipe diameter, wall thickness, and material parameters of each pipe segment in the pipeline system, as well as the type, location, and local resistance coefficient of pipeline accessories such as tees, elbows, valves, and expansion joints, by acquiring the engineering design drawings and topological connections of the pipeline system. This constructs a topological model that accurately reflects the spatial geometric characteristics of the pipeline system. Specifically, this step first reads computer-aided design files or scalable vector graphics files through a drawing parsing module, extracting geometric parameters such as pipeline numbers, start and end node coordinates, pipe diameter series, and wall thickness specifications. Simultaneously, it extracts engineering parameters such as valve opening status, flange connection information, and support / hanger placement. The attribute information step further establishes a corresponding local head loss calculation model based on the fluid dynamic characteristics of the pipeline accessories. For tee accessories, the energy loss coefficient is calculated based on the incoming flow direction and the split ratio. For elbow accessories, the friction loss coefficient is calculated based on the bending angle and radius of curvature. For valve accessories, the corresponding flow characteristic curve is found based on the valve type and current opening. This step organizes all pipe segments and accessories in the pipeline system into a weighted directed graph structure using graph theory. The nodes of the graph correspond to the node equipment of the pipeline system, the edges of the graph correspond to the pipe segments and accessories, and the weight of the edge corresponds to the flow resistance of the fluid in that pipe segment or accessory. The establishment of this graph structure provides a mathematical basis for subsequent pressure wave propagation path tracing.

[0009] In the fluid-structure interaction (FSI) multiphysics coupling modeling step, this invention incorporates the pipe wall elastic deformation effect, fluid compressibility effect, and viscous dissipation effect into a unified coupling analysis framework, establishing a set of FSI governing equations that accurately describes the physical nature of pressure waves. This step first establishes the fluid continuity equation and momentum equation as the fundamental governing equations for pressure wave propagation. The continuity equation describes the fluid's compressibility by introducing the fluid's bulk modulus and density change rate, while the momentum equation describes the influence of viscous dissipation on pressure wave attenuation by introducing frictional resistance and local loss terms. This step further establishes the pipe wall radial expansion equation as the governing equation for pipe wall elastic deformation. The pipe wall radial expansion equation... The elastic modulus, Poisson's ratio, and wall thickness parameters of the pipe are introduced to describe the radial displacement of the pipe wall under internal pressure. This equation is bidirectionally coupled with the fluid control equation through a pressure-displacement coupling term. That is, changes in fluid pressure cause expansion and deformation of the pipe wall, and the deformation of the pipe wall, in turn, affects the fluid pressure distribution. In the discretization process of the coupled equations, a hybrid discretization strategy of the method of characteristics and the finite element method is adopted. The method of characteristics is used to discretize the axial direction of the pipe to ensure the numerical stability of pressure wave propagation, while the finite element method is used to discretize the radial direction of the pipe wall to accurately capture the non-uniform distribution characteristics of the pipe wall deformation. The time progression of the coupled equations adopts an implicit integration scheme to ensure that the stability conditions of the numerical calculation are not strictly limited by the mesh size.

[0010] In the pressure wave propagation solution step based on the improved method of characteristics, this invention addresses the limitations of the traditional method of characteristics in handling pipeline accessories by proposing an improved solution strategy. This strategy retains the advantage of the method of characteristics in efficiently tracing the pressure wave propagation path while improving computational accuracy by introducing local additional pressure correction terms and transient friction correction terms. Specifically, this step first transforms the partial differential equations into ordinary differential equations along the characteristic lines for solution. Within each computation time step, the motion trajectory of the fluid particle is traced along the positive and negative characteristic lines respectively. The tracing step size of the characteristic lines is dynamically adjusted according to the Courant stability condition to ensure the stability of the numerical calculation. The first step involves setting up virtual computing nodes at the locations of pipeline accessories and applying different boundary condition processing strategies based on the accessory type. For valve accessories, the pressure wave reflection coefficient and transmission coefficient at the valve are calculated based on the instantaneous change rate of valve opening. For tee accessories, the distribution ratio of pressure waves in different branch pipelines is calculated based on the fluid flow direction and tee geometry. This step also introduces a transient friction model to replace the traditional steady-state friction coefficient. The transient friction model describes the selective attenuation effect of viscous dissipation on pressure wave components of different frequencies by superimposing attenuation exponential functions at multiple frequencies. This improved method of characteristics solution strategy significantly improves the accuracy of pressure wave propagation calculation while ensuring computational efficiency.

[0011] In the pressure wave propagation path tracing step based on graph networks, this invention utilizes graph theory to explicitly model and dynamically track the propagation path of pressure waves in the pipeline system. This step first abstracts the topology of the pipeline system into a pressure wave propagation network graph. Each node in the graph represents a physical location within the pipeline system, and each edge represents a potential channel for pressure wave propagation between adjacent locations. The attributes of the edges include propagation delay, attenuation coefficient, and directional weight. This step further defines a dynamic evolution equation for pressure wave signal propagation on the pressure wave propagation network graph. This dynamic evolution equation considers the dispersion and nonlinear effects experienced by the pressure wave during propagation. The dispersion effect is corrected by introducing a frequency-related propagation speed. The nonlinear effect is described by introducing a propagation velocity correction term related to the pressure amplitude. This step calculates the pressure value of each node at different times through the message passing mechanism of the graph neural network. The message passing process includes receiving pressure signals from neighboring nodes, weighting and fusing the received signals according to the propagation delay and attenuation coefficient, and updating the pressure estimate at the current time according to the node's own historical pressure value. The parameters of the graph neural network are trained by a supervised learning method, and the training data comes from a hybrid annotation of high-precision computational fluid dynamics simulation and experimental measurement data. This graph network-based path tracing method can effectively capture the multi-path propagation and superposition effect of pressure waves in pipelines with complex topology.

[0012] In the multi-condition coupled dynamic switching step, this invention addresses the simulation accuracy degradation problem caused by condition switching during pipeline system operation. It proposes a dynamic switching strategy based on state prediction. This strategy can predict the switching direction and adjust the numerical solver parameters in advance before the condition switch occurs. This step first establishes a state machine model of the pipeline system. The state machine model abstracts typical operating conditions of the pipeline system into discrete state nodes, including rated operating condition, valve regulation operating condition, pump start / stop operating condition, and emergency discharge operating condition. Directed edges between state nodes represent possible condition switching paths. Each switching path is labeled with the switching trigger condition, switching duration, and switching process parameters. The boundary condition variation pattern is analyzed. This step further uses a machine learning classifier to predict the current operating state of the pipeline system and its possible switching direction. The input features of the classifier include the time series features of recent pressure monitoring data, valve opening change rate, and flow fluctuation features. The output of the classifier is the probability distribution of each possible switching direction. When the probability of the operating condition switching exceeds a preset threshold, this step triggers the pre-adjustment process of simulation parameters. The pre-adjustment process modifies the settings of the boundary condition processing module, updates the parameters of the transient friction model, and adjusts the step size control strategy of the time advancement scheme according to the predicted switching direction, so as to quickly enter the steady-state tracking state when the actual switching of the operating condition occurs.

[0013] In the uncertainty quantification and parameter adaptive calibration steps, this invention employs a polynomial chaotic expansion method to quantify the parameter uncertainties in the physical mechanism model of the pipeline system, and uses a Bayesian inference framework to achieve adaptive calibration of the model parameters. This step first identifies key parameters with significant uncertainties in the model, including the pipe material's elastic modulus, fluid viscosity coefficient, pipe wall roughness, and local resistance coefficient. The nominal values ​​of these parameters may deviate from the actual pipeline system. This step further uses a polynomial chaotic expansion method to expand the output containing uncertain parameters into an orthogonal polynomial series. Through a small number of deterministic calculation samples, the complete probability distribution characteristics of the output are reconstructed, thereby quantifying the impact of parameter uncertainty on pressure wave propagation characteristics. Simultaneously, this step establishes a Bayesian calibration framework. The framework uses the probability distribution obtained from the polynomial chaotic expansion as prior knowledge and experimental measurements or field monitoring data as likelihood information. The posterior distribution is estimated using a Markov chain Monte Carlo sampling method to obtain the optimal estimated values ​​and confidence intervals of the calibrated parameters. This step updates the calibrated parameter values ​​into the physical mechanism model, achieving continuous improvement in model accuracy.

[0014] Preferably, in the precise modeling step of the pipeline topology, the system uses a parametric modeling method to model the pipeline accessories. The parametric modeling method establishes standardized geometric templates and physical models for each type of pipeline accessory. The geometric templates are defined parametrically through key dimensional parameters. For example, the parameters of an elbow include bending angle, radius of curvature, and port diameter, while the parameters of a tee include main pipe diameter, branch pipe diameter, and branch angle. The physical model is defined through the corresponding head loss coefficient calculation formula. The empirical coefficients in the coefficient calculation formula are calibrated using fluid dynamics simulation data. The parametric modeling method enables the system to quickly construct the topology model of complex pipeline systems.

[0015] Preferably, in the fluid-structure interaction multiphysics coupling modeling step, the numerical solution of the coupled equations adopts a split-solution strategy. The split-solution strategy decomposes the coupled equations into two sub-modules according to the physical process: a fluid solver and a structural solver. The fluid solver is responsible for solving the fluid continuity equation and the momentum equation, while the structural solver is responsible for solving the pipe wall radial expansion equation. The two sub-modules are executed alternately in sequence to advance the time process. In each time step, the pipe wall displacement is fixed first to solve the fluid equation, and then the fluid pressure is fixed to solve the pipe wall equation. The process is iterated until the solutions of the two sub-modules converge. The split-solution strategy reduces the coupling complexity of the equations while ensuring computational accuracy.

[0016] Preferably, in the pressure wave propagation solution step based on the improved method of characteristics, the characteristic line tracking adopts an adaptive step size control scheme. The adaptive step size control scheme dynamically adjusts the characteristic line tracking step size according to the pressure gradient of the current calculation region. When the pressure gradient is large, the step size is automatically reduced to capture the steep leading edge of the pressure wave. When the pressure gradient is small, the step size is automatically increased to improve the calculation efficiency. The step size control scheme also considers the requirements of the Courant stability condition to ensure that the numerical calculation always meets the stability constraint.

[0017] Preferably, in the graph network-based pressure wave propagation path tracking step, the graph neural network is implemented using a graph attention network architecture. During message passing, the graph attention network assigns different attention weights to different neighbor nodes. The calculation of attention weights takes into account factors such as the type of neighbor node, historical pressure value, and propagation distance. Through the attention mechanism, the graph neural network can adaptively learn the importance of pressure waves on different propagation paths.

[0018] The present invention also provides a simulation system for the physical mechanism of pressure fluctuation in pipeline systems. The system includes a topology modeling module, a fluid-structure interaction modeling module, a pressure wave solving module, a path tracing module, a working condition switching module, a parameter calibration module, a data management module, and a visualization module.

[0019] The topology modeling module is connected to the data management module and is configured to read the design data of the pipeline system and automatically build the topology model. The module has a built-in drawing parsing engine and a parametric attachment library. The drawing parsing engine supports the import and parsing of various engineering drawing formats. The parametric attachment library stores geometric templates and physical models of common pipeline accessories such as tees, elbows, and valves. The topology model output by this module is stored in the data management module in the form of graph data, providing geometric and topological information input for subsequent calculation modules.

[0020] The fluid-structure interaction modeling module is connected to the topology modeling module and the data management module. It is configured to construct a set of fluid-structure interaction control equations based on the topology model. The module integrates a fluid control equation template library and a pipe wall deformation equation template library. It can automatically select the appropriate equation form and assemble a complete set of coupled equations according to the specific configuration of the pipeline system. The module also provides a framework for implementing a split solver, which supports parallel computation of the fluid solver and the structure solver.

[0021] The pressure wave solving module is connected to the fluid-structure interaction modeling module and the topology modeling module. It is configured to perform pressure wave propagation calculations based on the improved method of characteristics. The module contains a characteristic line tracing engine, a boundary condition processing unit, and a transient friction correction module. The characteristic line tracing engine is responsible for dynamically tracing the characteristic lines of the pressure wave according to the Courant stability condition. The boundary condition processing unit applies the corresponding boundary condition processing strategy according to the type of pipeline accessories. The transient friction correction module calculates the effect of viscous dissipation on pressure wave attenuation. The pressure field data calculated by this module at different times is stored in the data management module.

[0022] The path tracing module is connected to the pressure wave solving module and the data management module. It is configured to trace the propagation path of pressure waves in the pipeline system based on a graph attention network. The module contains a graph network construction unit and a message passing calculation unit. The graph network construction unit converts the pipeline topology into a pressure wave propagation network graph and initializes the node attributes. The message passing calculation unit performs multiple rounds of message passing iterations to update the pressure estimates of each node. The pressure wave propagation path tracing results output by the module are stored in the data management module in the form of dynamic trajectory data.

[0023] The operating condition switching module is connected to the pressure wave solving module, path tracing module, and data management module. It is configured to detect the switching events of the pipeline system's operating conditions and trigger the pre-adjustment process of simulation parameters. The module contains a state recognition unit and a parameter pre-adjustment unit. The state recognition unit analyzes the time-series data of the input features through a machine learning classifier to predict the current operating state and its possible switching direction. The parameter pre-adjustment unit modifies the solver's parameter settings in advance based on the prediction results. The module establishes a bidirectional data connection with the pressure wave solving module and the path tracing module to achieve dynamic parameter updates.

[0024] The parameter calibration module is connected to the data management module and is configured to perform uncertainty quantification and adaptive parameter calibration calculation. The module integrates a multinomial chaotic expansion calculation engine and a Bayesian calibration framework. The multinomial chaotic expansion calculation engine reconstructs the probability distribution characteristics of the output quantity based on the input uncertainty parameter samples. The Bayesian calibration framework updates the posterior distribution of the model parameters based on monitoring data and prior knowledge. The parameter values ​​calibrated by this module are written to the data management module to update the parameter configuration of the physical mechanism model.

[0025] The data management module establishes data connections with all computing modules and is configured to uniformly manage the input data, intermediate calculation results, and output data of the simulation system. This module adopts a distributed database architecture to store large-scale simulation data, supports high-speed concurrent read and write operations and data version management functions, and also provides data interface services for other modules to access data.

[0026] The visualization module is connected to the data management module and is configured to display the simulation calculation results to the user in a graphical manner. This module supports functions such as pressure field cloud map drawing, pressure wave propagation animation generation, path tracing result visualization, and multi-condition comparative analysis. Through the visualization module, users can intuitively understand the spatiotemporal evolution law of pressure fluctuations inside the pipeline system.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. The present invention provides a simulation method and system for the physical mechanism of pressure fluctuation in pipeline systems. By introducing a precise modeling step for pipeline topology, and employing parametric modeling methods and graph theory organization strategies, it achieves standardized modeling of pipeline accessories such as tees, elbows, and valves. This solves the technical problem that traditional empirical formula simplification algorithms neglect the influence of pipeline accessories on pressure wave propagation. This feature ensures that the simulation model can accurately reflect the actual propagation behavior of pressure waves in pipelines with complex topologies, significantly improving the applicability of simulation results in engineering practice.

[0029] 2. The simulation method and system for the physical mechanism of pressure fluctuation in a pipeline system described in this invention introduces a fluid-structure interaction multiphysics coupling modeling step, incorporating the pipe wall elastic deformation effect, fluid compressibility effect, and viscous dissipation effect into a unified coupling analysis framework and employing a split-solution strategy for numerical solution. This solves the technical problem that traditional computational fluid dynamics methods cannot accurately reflect the influence of multiphysics coupling on fluctuation characteristics under actual working conditions. This feature enables the simulation results to be closer to physical reality and eliminates the difficult-to-quantify deviation between simulation results and actual measurement data.

[0030] 3. The simulation method and system for the physical mechanism of pressure fluctuation in pipeline systems described in this invention introduces a pressure wave propagation path tracking step based on graph networks and uses the message passing mechanism of graph attention networks to dynamically track the propagation path of pressure waves in pipeline systems. This solves the technical problem that existing methods are difficult to achieve dynamic tracking of pressure wave propagation paths in multi-condition coupled scenarios. This feature enables the system to accurately capture the multi-path propagation and superposition effects of pressure waves in complex topologies, providing reliable simulation support for water hammer protection design and pressure fluctuation suppression.

[0031] 4. The simulation method and system for the physical mechanism of pressure fluctuation in pipeline systems described in this invention introduces a multi-condition coupled dynamic switching step and an uncertainty quantification parameter adaptive calibration step to establish a condition state machine model and a machine learning-based state prediction mechanism. The numerical solver parameters are pre-adjusted before condition switching, and polynomial chaotic expansion and Bayesian inference framework are used to continuously optimize the model parameters. This solves the technical problem of a sharp drop in simulation accuracy when pipeline system operating conditions switch, a problem inherent in existing methods. This feature ensures that the simulation system maintains high-precision prediction capabilities throughout the entire operating cycle and reduces safety hazards caused by model parameter deviations. Attached Figure Description

[0032] The invention will now be further described with reference to the accompanying drawings.

[0033] Figure 1 This is a structural block diagram of the simulation system for the physical mechanism of pressure fluctuation in a pipeline system in this invention;

[0034] Figure 2 This is a flowchart of the method for simulating the physical mechanism of pressure fluctuation in a pipeline system in this invention. Detailed Implementation

[0035] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0036] This embodiment is applied to the simulation analysis scenario of pressure fluctuation in a petrochemical pipeline transportation system. This scenario is characterized by a complex pipeline topology, a large number of pipeline accessories such as tees, elbows, and valves, and the coordinated operation of multiple delivery pumps, which places extremely high demands on the accuracy and efficiency of the simulation of the physical mechanism of pressure fluctuation.

[0037] like Figure 1As shown in the embodiment of this application, a simulation system for the physical mechanism of pressure fluctuation in a pipeline system includes a topology modeling module, a fluid-structure interaction modeling module, a pressure wave solution module, a path tracing module, a working condition switching module, a parameter calibration module, a data management module, and a visualization module. The topology modeling module executes step S1, reading pipeline system design data and constructing a weighted directed graph structure; the fluid-structure interaction modeling module executes step S2, establishing the fluid control equation and the pipe wall deformation equation and achieving bidirectional coupling; the pressure wave solution module executes step S3, using the improved characteristic line method to perform pressure wave propagation calculation; the path tracing module executes step S4, dynamically tracking the pressure wave propagation path based on a graph attention network; the working condition switching module executes step S5, predicting working condition switching and triggering parameter pre-adjustment through a machine learning classifier; the parameter calibration module executes step S6, performing uncertainty quantization and Bayesian parameter calibration; the data management module is responsible for uniformly managing the input and output data of each module; and the visualization module is responsible for displaying the simulation results to the user in a graphical manner.

[0038] The pipeline system pressure fluctuation physical mechanism simulation system constructed in this embodiment is divided into eight core modules according to function. The modules achieve data flow and functional collaboration through standardized data interfaces.

[0039] The topology modeling module is located at the data input end of the simulation system. This module includes three sub-components: a drawing parsing engine, a parametric attachment library, and a graph structure building unit. The drawing parsing engine supports the import and parsing of computer-aided design file formats and scalable vector graphics file formats. This engine has a built-in professional drawing recognition algorithm that can automatically identify pipeline numbering labels, start and end node coordinate labels, pipe diameter series labels, and wall thickness specification labels in engineering drawings, with a recognition accuracy rate of over 98%. The parameterized accessory library stores a geometric template library and a physical model library for pipe accessories. The geometric template library establishes standardized geometric parameter definitions for each type of pipe accessory. The geometric template for elbow accessories includes bending angle parameters, radius of curvature parameters, and port diameter parameters. The geometric template for tee accessories includes main pipe diameter parameters, branch pipe diameter parameters, and flow splitting angle parameters. The geometric template for valve accessories includes valve type parameters and current opening parameters. The physical model library establishes corresponding head loss coefficient calculation formulas for each type of pipe accessory. Elbow accessories calculate the friction loss coefficient based on the bending angle and radius of curvature. Tee accessories calculate the energy loss coefficient based on the incoming flow direction and flow splitting ratio. Valve accessories look up the corresponding flow characteristic curve based on the valve type and current opening. The graph structure construction unit constructs a weighted directed graph structure based on the drawing analysis results and the parameterized attachment library. The nodes of the graph correspond to the node equipment of the pipeline system, including tee joints, elbow ends, valve installation positions, and pipeline start and end points. The edges of the graph correspond to pipe segments and pipeline accessories, and the edge weight corresponds to the flow resistance value of the fluid in that pipe segment or accessory. The topological relationship of the directed graph is stored through the adjacency list data structure. Each entry in the adjacency list contains the target node number and the edge weight value. The graph structure data output by the topology modeling module is stored in the data management module for subsequent modules to call.

[0040] The fluid-structure interaction modeling module establishes a data connection with the topology modeling module. This module includes three sub-components: a fluid control equation template library, a pipe wall deformation equation template library, and a split solver. The fluid control equation template library stores fluid continuity equation templates and fluid momentum equation templates. The continuity equation template describes the compressibility of the fluid by introducing the bulk modulus and density change rate. The bulk modulus parameter in the equation template is automatically obtained from the material database based on the fluid type. The momentum equation template describes the effect of viscous dissipation on pressure wave attenuation by introducing frictional resistance and local loss terms. The frictional resistance term uses the Darcy-Weisbach formula to calculate the head loss along the pipe, and the local loss term obtains the local resistance coefficient from the topology modeling module based on the pipe fitting type. The pipe wall deformation equation template library stores a pipe wall radial expansion equation template. This template describes the radial displacement of the pipe wall under internal pressure by introducing the pipe's elastic modulus, Poisson's ratio, and wall thickness parameters. The material parameters in the equation template are automatically matched from the material database based on the pipe type. The split solver enables numerical solutions to the coupled equations. It decomposes the coupled equations into a fluid solver submodule and a structural solver submodule according to the physical process. The fluid solver submodule is responsible for solving the fluid continuity equation and momentum equation, while the structural solver submodule is responsible for solving the pipe wall radial expansion equation. The two submodules are executed alternately to advance the time process. In each time step, the pipe wall displacement is fixed first to solve the fluid equation, and then the fluid pressure is fixed to solve the pipe wall equation. The process is iterated until the solutions of the two submodules converge. The time advancement of the coupled equations adopts an implicit integration scheme to relax the stability constraints on the time step.

[0041] The pressure wave solution module establishes data connections with the fluid-structure interaction modeling module and the topology modeling module. This module includes three sub-components: a feature line tracing engine, a boundary condition processing unit, and a transient friction correction module. The feature line tracing engine implements the core solution logic of the improved feature line method. The engine first transforms the partial differential equations into ordinary differential equations along the feature lines. Within each computation time step, it traces the motion trajectory of the fluid particle along the positive and negative feature lines, respectively. The tracing step size is dynamically adjusted according to the Courant stability condition. The Courant number is calculated by multiplying the wave velocity by the time step and then dividing by the spatial step size. The calculated Courant number is compared with a preset stability threshold. When the Courant number exceeds the threshold, the time step is automatically reduced to ensure numerical stability. The boundary condition processing unit applies corresponding boundary condition processing strategies based on the type of pipeline accessory. For valve accessories, it calculates the reflection coefficient and transmission coefficient of the pressure wave based on the instantaneous rate of change of valve opening. The reflection coefficient is calculated by dividing the difference in characteristic line impedance by the sum of characteristic line impedances, and the transmission coefficient is calculated by dividing twice the characteristic line impedance by the sum of characteristic line impedances. For tee accessories, it calculates the distribution ratio of the pressure wave in different branch pipelines based on the fluid flow direction and tee geometry. The distribution ratio is calculated by weighting the cross-sectional area ratio of the branch pipelines and the flow direction angle. The transient friction correction module introduces a transient friction model to replace the traditional steady-state friction coefficient. The mathematical expression of the transient friction model adopts the form of a decay exponential function superimposed at multiple frequencies. The weights of each frequency component in the model are calibrated according to the frequency spectrum characteristics of the pressure wave. The transient friction model can describe the selective attenuation effect of viscous dissipation on pressure wave components of different frequencies.

[0042] The path tracing module establishes a data connection with the pressure wave solving module. This module includes two sub-components: a graph network construction unit and a message passing calculation unit. The graph network construction unit converts the pipeline topology into a pressure wave propagation network graph. The number of nodes in the graph is consistent with the number of critical physical locations in the pipeline system. Node attributes include the current pressure estimate and the historical pressure value sequence. Edge attributes include propagation delay parameters, attenuation coefficient parameters, and directional weight parameters. The propagation delay is calculated based on the pipeline length and wave velocity, the attenuation coefficient is determined based on the pipe wall roughness and fluid viscosity, and the directional weight is determined based on the fluid flow direction. The message passing computation unit implements the computation logic of the graph attention network. During the message passing process, this unit assigns different attention weights to different neighbor nodes. The calculation of attention weights adopts a multilayer perceptron structure to fuse node feature differences, edge attribute weights, and position encoding information. The calculated attention weights are normalized and used as message weighting coefficients. The message passing process includes receiving pressure signals from neighbor nodes, performing time alignment processing on the received signals according to propagation delay and attenuation coefficient, performing weighted fusion of the time-aligned signals according to the attention weights, and obtaining the current pressure estimate value through a cyclic update mechanism based on the node's own historical pressure value. The message passing unit performs multiple rounds of iterative calculations until the pressure estimates of each node converge.

[0043] The operating condition switching module establishes a bidirectional data connection with the pressure wave solution module and the path tracing module. This module includes two sub-components: a state recognition unit and a parameter pre-adjustment unit. The state recognition unit integrates a machine learning classifier, which employs a cascaded structure of a long short-term memory network and fully connected layers. Input features include the time-series characteristics of recent pressure monitoring data, the valve opening change rate sequence, and the flow fluctuation characteristic sequence. The output is the probability distribution of each possible switching direction. The state recognition unit first constructs fixed-length input samples from the raw time-series data using a sliding window mechanism. The sliding window duration is set to thirty seconds, and the window sliding step size is set to one second. The classifier performs inference operations on each input sample to obtain an estimate of the current operating state and a prediction of the operating condition switching. When the parameter pre-adjustment unit detects that the probability of switching operating conditions exceeds a preset threshold, it triggers the pre-adjustment process of simulation parameters. The pre-adjustment process performs three operations according to the predicted switching direction. First, it modifies the settings of the boundary condition processing module in advance, including updating the valve opening change rate and flow boundary conditions. Second, it updates the parameters of the transient friction model, including adjusting the attenuation coefficient and frequency weight. Finally, it adjusts the step size control strategy of the time advancement scheme, including increasing or decreasing the base time step and adjusting the step size adaptive parameters.

[0044] The parameter calibration module establishes a data connection with the data management module. This module includes two sub-components: a polynomial chaotic expansion calculation engine and a Bayesian calibration framework. The polynomial chaotic expansion calculation engine realizes the quantitative analysis function of uncertain parameters. The engine first identifies key parameters with significant uncertainties in the model, including the pipe elastic modulus, fluid viscosity coefficient, pipe wall roughness, and local resistance coefficient. Then, it constructs an orthogonal polynomial expansion expression containing the uncertain parameters. The number of terms in the expansion is determined according to the dimension of the uncertain parameters and the preset expansion order. In this embodiment, the expansion order is set to third order, and the maximum number of terms does not exceed twenty. The calculation engine generates a small number of deterministic calculation sample points through the Latin hypercube sampling method. A complete pressure wave propagation simulation calculation is performed on each sample point. After substituting the simulation results into the expansion, the estimated values ​​of each expansion coefficient are obtained by fitting using the least squares method. The fitted expansion can quickly reconstruct the complete probability distribution characteristics of the output, including the mean, variance, and quantiles. The Bayesian calibration framework enables adaptive calibration of model parameters. It uses the probability distribution obtained from multinomial chaotic expansion as prior knowledge and monitoring data as likelihood information. The posterior distribution is estimated using a Markov chain Monte Carlo sampling method. The proposed distribution of the Markov chain is generated using an adaptive metropolis-hastings algorithm. During sampling, the posterior estimates of each parameter are alternately updated using a Gibbs sampling strategy. After sampling convergence, the optimal estimates and confidence intervals of the calibrated parameters are obtained by calculating the mean and variance of the posterior samples. The calibrated parameter values ​​are then written to the data management module to update the parameter configuration of the physical mechanism model.

[0045] The data management module establishes data connections with all computing modules. This module employs a distributed database architecture to store large-scale simulation data. The database system is built on a hybrid deployment scheme of time-series and relational databases. The time-series database stores pressure field time-series data and sensor monitoring data, while the relational database stores pipeline topology data and model parameter configuration data. The database system supports high-speed concurrent write operations of 100,000 records per second and data version management functions. The version management function records the parameter configuration and calculation result snapshots for each simulation task, supporting historical data traceability and comparative analysis. The data management module also provides standardized data interface services for other modules to access data. Each module accesses the data management module's storage service through a remote procedure call interface. The interface calls use a request-response model and support both synchronous and asynchronous data access methods.

[0046] The visualization module establishes a data connection with the data management module. This module includes three sub-components: a pressure field rendering unit, an animation generation unit, and an interactive analysis unit. The pressure field rendering unit supports pressure field contour plotting. This unit maps the pressure field data output by the pressure wave solution module into a color gradient contour plot. The color mapping uses a blue-green-red gradient scheme: blue represents low-pressure areas, green represents medium-pressure areas, and red represents high-pressure areas. The rendering resolution supports multi-scale switching from the pipe cross-section level to the full field level. The animation generation unit supports pressure wave propagation animation generation. This unit reads pressure field snapshot data according to the time series and drives the 3D pipeline model for dynamic rendering. The animation frame rate is set to 30 frames per second, and the total animation duration is consistent with the simulation duration. The interactive analysis unit supports path tracing result visualization and multi-condition comparative analysis. Path tracing result visualization is achieved by highlighting key propagation paths in the pipeline and annotating propagation times. Multi-condition comparative analysis is achieved by overlaying simulation result curves under different conditions in the same coordinate system.

[0047] like Figure 2 As shown, the simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to the present invention includes the following steps:

[0048] Step 1: Pipeline topology modeling

[0049] The topology modeling module's drawing parsing engine first receives the computer-aided design file of the piping system imported by the user. After parsing the file, the engine automatically identifies and extracts geometric parameters such as pipeline numbers, start and end node coordinates, pipe diameter series, and wall thickness specifications. The identified geometric parameters include the start and end node coordinates of twenty-three pipe segments, pipe diameters ranging from fifty to five hundred millimeters, and wall thickness specifications ranging from four to twelve millimeters. The drawing parsing engine also extracts engineering attribute information such as valve opening status, flange connection information, and support / hanger placement. The identified engineering attributes include the current position and opening status of eight gate valves, the installation direction information of four check valves, and the support position information of fifteen sets of supports / hangers.

[0050] The parametric attachment library automatically matches and loads the corresponding pipeline attachment models based on the drawing analysis results. The tee attachment model loads the geometric templates and physical models of three equal-diameter tees and two reducing tees. The elbow attachment model loads twelve 90-degree elbows and six 45-degree elbows. The valve attachment model loads the parametric templates of four gate valves, two butterfly valves, and one regulating valve. The parametric attachment library establishes a local head loss calculation model based on the fluid dynamics characteristics of each attachment. For tee attachments, the incoming flow direction is determined based on the topological connection relationship to determine whether it is direct or lateral flow, and the energy loss coefficient is calculated based on the flow split ratio. For elbow attachments, the friction loss coefficient is calculated based on the bending angle of 30 degrees and the radius of curvature of 150 mm. For valve attachments, the local resistance coefficient is obtained by finding the flow characteristic curve based on the valve type (regulating valve) and the current opening degree of 60%.

[0051] The graph structure construction unit constructs a weighted directed graph structure based on the above analysis results. The graph has 35 nodes, corresponding to all node devices in the pipeline system, including pipe segment endpoints, tee joints, elbow endpoints, valve installation positions, and system start and end points. The graph has 46 edges, corresponding to all pipe segments and pipeline accessories. The weight of each edge is the flow resistance value of the fluid in that pipe segment or accessory. The flow resistance value is calculated according to the Darcy-Weisbach formula. The friction resistance of the pipe segment is calculated according to the local resistance coefficient. The topological relationship of the directed graph is stored through an adjacency list data structure. Each entry in the adjacency list contains the target node number and edge weight value. The topology modeling module stores the constructed graph structure data in the database through the interface service of the data management module.

[0052] Step 2: Fluid-structure Interaction Multiphysics Modeling

[0053] After reading the graph structure data output by the topology modeling module from the data management module, the fluid-structure interaction (FSI) modeling module begins constructing the FSI control equations. The fluid control equation template library first assembles the fluid continuity equation and momentum equation as the fundamental control equations for pressure wave propagation. The discrete form of the continuity equation is obtained by applying the principle of mass conservation to the control volume. The fluid's bulk modulus parameter (1800 MPa) and density change rate parameter are introduced to describe the fluid's compressibility. The discrete form of the momentum equation is obtained by applying the principle of momentum conservation to the control volume. A frictional resistance term is introduced, and the local loss term is calculated using the Darcy-Weisbach formula. The local resistance coefficient of the pipe fittings obtained from the topology modeling module is used for calculation.

[0054] The template library of pipe wall deformation equations assembles the radial expansion equation of the pipe wall as the governing equation for the elastic deformation of the pipe wall. The radial expansion equation of the pipe wall describes the radial displacement of the pipe wall under internal pressure by introducing the elastic modulus parameter of the pipe material of 206 GPa, the Poisson's ratio parameter of 0.3 and the wall thickness parameter of 8 mm. The equation achieves bidirectional coupling between the fluid control equation and the pipe wall deformation equation through the pressure-displacement coupling term. That is, the change of fluid pressure causes the expansion and deformation of the pipe wall, and the deformation of the pipe wall, in turn, affects the fluid pressure distribution.

[0055] The split solver decomposes the coupled equations into a fluid solver submodule and a structural solver submodule according to the physical process before starting the numerical solution. The fluid solver submodule first fixes the pipe wall displacement at zero and solves the fluid continuity equation and momentum equation to obtain the fluid pressure and velocity distribution in the first intermediate step. The structural solver submodule fixes the fluid pressure at the pressure value of the first intermediate step and solves the pipe wall radial expansion equation to obtain the radial displacement increment of the pipe wall. The two submodules are executed alternately until the pressure difference between two consecutive iterations is less than the convergence threshold of 0.01 Pa. The time advancement of the split solver adopts an implicit integration scheme. The implicit scheme has no stability limit on the time step and can use a larger step size to improve computational efficiency.

[0056] Step 3: Solving for pressure wave propagation

[0057] The characteristic line tracing engine of the pressure wave solution module begins executing the pressure wave propagation solution calculation based on the improved characteristic line method. The engine first determines the wave velocity parameters of the pipeline system; the wave velocity is calculated to be 1200 m / s based on the fluid bulk modulus and pipe elastic parameters. Then, it transforms the partial differential equations into ordinary differential equations along the positive and negative characteristic lines. Within each calculation time step, the engine traces the motion trajectory of the fluid particle from the upstream node to the downstream node along the positive characteristic line and simultaneously traces the motion trajectory of the fluid particle from the downstream node to the upstream node along the negative characteristic line. The characteristic line tracing step size is dynamically adjusted according to the Courant stability condition. When the pressure gradient in the computational domain is large, the step size is automatically reduced to capture the steep leading edge of the pressure wave; when the pressure gradient is small, the step size is automatically increased to improve computational efficiency.

[0058] The boundary condition processing unit sets up virtual calculation nodes at the locations of pipe fittings and applies different boundary condition processing strategies according to the fitting type. For the four gate valve fitting units, the pressure wave reflection coefficient and transmission coefficient at the valve are calculated based on the instantaneous rate of change of valve opening. The calculation process of the reflection coefficient is described as follows: First, the characteristic line impedance parameter is calculated. The characteristic line impedance is equal to the fluid density multiplied by the wave velocity divided by the pipe cross-sectional area. Then, the difference in characteristic line impedance and the sum of characteristic line impedances are calculated. Finally, the difference is divided by the sum to obtain the reflection coefficient. For the three tee fitting units, the distribution ratio of the pressure wave in different branch pipes is calculated based on the fluid flow direction and the tee geometry. The distribution ratio is calculated by weighting the cross-sectional area ratio of each branch pipe.

[0059] The transient friction correction module introduces a transient friction model to calculate the impact of viscous dissipation on pressure wave attenuation. The transient friction model is mathematically expressed as a superposition of attenuation exponential functions at three frequencies: the attenuation coefficient of the first frequency component is 0.5 with a weight of 0.4; the attenuation coefficient of the second frequency component is 0.8 with a weight of 0.3; and the attenuation coefficient of the third frequency component is 0.2 with a weight of 0.3. The model parameters are calibrated using experimental data. The attenuation contribution of each frequency component calculated by the transient friction model is superimposed on the pressure wave propagation process, resulting in faster attenuation of high-frequency pressure wave components and slower attenuation of low-frequency pressure wave components.

[0060] Step 4: Tracing the Propagation Path of Pressure Waves

[0061] The graph network construction unit of the path tracing module first converts the pipeline topology into a pressure wave propagation network graph. The number of nodes in the graph is the same as the number of nodes output by the topology modeling module, which is thirty-five nodes. Each node is initialized with the current pressure estimate set to zero and the historical pressure value sequence set to empty. The graph network construction unit sets attribute parameters for each edge of the graph: propagation delay is calculated by dividing the pipeline length by the wave velocity, the attenuation coefficient is determined by the pipe wall roughness of 0.2 mm and the fluid viscosity of 0.001 Pa·s, and the directional weight is determined by the fluid flow direction.

[0062] The message passing computation unit begins executing the message passing computation process of the graph attention network. In the first round of message passing, each node receives a pressure signal message from its neighboring nodes. The message content includes the historical pressure value of the neighboring nodes and the edge attribute weights. The calculation of attention weights adopts a multilayer perceptron structure. The input layer of the multilayer perceptron has four neurons, which respectively receive the historical pressure value of the current node, the historical pressure values ​​of the neighboring nodes, the propagation delay, and the attenuation coefficient. The hidden layer has eight neurons, and the activation function is a modified linear unit. The output layer has one neuron, which outputs the attention weight of the neighboring nodes. The attention weights are normalized by softmax and then used as message weighting coefficients.

[0063] The message-passing computation unit performs weighted fusion of the received pressure signals based on attention weights. Specifically, it multiplies the pressure signals of each neighboring node by their corresponding attention weights and sums them to obtain the aggregated pressure signal. Then, based on the node's own historical pressure values, it uses a Long Short-Term Memory (LSTM) update mechanism to obtain the current pressure estimate. The LSM update mechanism includes three gating units: a forget gate, an input gate, and an output gate. The forget gate determines how much historical information to retain, the input gate determines how much new information to add, and the output gate determines how much updated state information to output. After ten rounds of iterative computation, the pressure estimates of each node tend to converge.

[0064] Step 5: Operating Condition Switching Detection and Parameter Pre-adjustment

[0065] The status recognition unit of the operating condition switching module receives pressure monitoring data, timing data, valve opening data, and flow data from the data management module and then begins to perform operating condition switching detection. The status recognition unit first constructs an input sample using a sliding window mechanism. The sliding window duration is set to thirty seconds, and the window sliding step size is set to one second. Within each sliding window, three types of features are extracted: the first type is the statistical characteristics of the pressure monitoring data, including the mean, standard deviation, maximum value, minimum value, and first-order difference mean; the second type is the valve opening change rate feature, including the difference between the current opening and the opening at the previous moment, and the trend of change; the third type is the flow rate fluctuation feature, including the fluctuation amplitude and frequency of the flow curve.

[0066] The machine learning classifier performs inference operations on each input sample. The classifier employs a cascaded structure of a Long Short-Term Memory (LSTM) network and fully connected layers. The LSM network has 64 hidden nodes, and the fully connected layers contain two hidden layers with 32 and 16 nodes respectively. The classifier outputs probability distributions for four operating conditions: rated operating condition, valve regulation operating condition, pump start / stop operating condition, and emergency discharge operating condition. The state recognition unit determines the current operating state and its possible switching direction based on the probability distributions output by the classifier. When the probability of switching from rated operating condition to valve regulation operating condition exceeds 0.6, it determines that a valve regulation operating condition switch is about to occur.

[0067] The parameter pre-adjustment unit triggers the simulation parameter pre-adjustment process when it detects that the probability of a working condition switching exceeds a preset threshold of 0.5. The pre-adjustment process first modifies the settings of the boundary condition processing module in advance, updating the valve opening change rate from 5% per second to 20% per second and updating the corresponding pressure wave reflection coefficient calculation parameters. Then, it updates the parameters of the transient friction model, adjusting the attenuation coefficient to 1.2 times the original value to adapt to the high-frequency pressure fluctuations caused by rapid valve adjustment. Finally, it adjusts the step size control strategy of the time advancement scheme, reducing the basic time step from 0.001 seconds to 0.0001 seconds to improve the calculation accuracy during the working condition switching process.

[0068] Step Six: Uncertainty Quantification and Parameter Calibration

[0069] The polynomial chaotic expansion calculation engine of the parameter calibration module first identifies key parameters with significant uncertainties in the model. In this embodiment, four key uncertainty parameters are identified: the pipe elastic modulus uncertainty range is 190 GPa to 220 GPa, the fluid viscosity coefficient uncertainty range is 0.0008 Pascals to 0.001 Pascals, the pipe wall roughness uncertainty range is 0.15 mm to 0.25 mm, and the local resistance coefficient uncertainty range is 0.8 times to 1.2 times the nominal value.

[0070] The computational engine constructs an orthogonal polynomial expansion expression containing four uncertain parameters, with the expansion order set to third. Based on the number of uncertain parameters and the expansion order, the maximum number of terms in the expansion is calculated to be fifteen. The computational engine generates forty deterministic computational sample points using the Latin hypercube sampling method. The sampling process ensures that each parameter is uniformly distributed within its uncertainty range. A complete pressure wave propagation simulation is performed on each sample point to obtain the pressure field output corresponding to the sample point. After substituting the forty sets of input and output data into the expansion, the least squares method is used to fit and obtain the estimated values ​​of each expansion coefficient. The fitted expansion can quickly reconstruct the mean, variance, and 5% to 95% quantiles of the output pressure field at thirty-five nodes.

[0071] The Bayesian calibration framework uses the probability distribution obtained from polynomial chaotic expansion as prior knowledge. In this embodiment, the prior distribution of the pipe's elastic modulus is assumed to be a normal distribution with a mean of 206 GPa and a standard deviation of 8 GPa; the prior distribution of the fluid viscosity coefficient is assumed to be a log-normal distribution; and the prior distribution of the local drag coefficient is assumed to be a uniform distribution. The Bayesian calibration framework uses field monitoring data as likelihood information. The monitoring data includes measured time-series data from twenty pressure sensors. The likelihood function uses a Gaussian error model, assuming that the difference between the monitored values ​​and the model predicted values ​​follows a normal distribution with a mean of zero and a standard deviation of 1.5 kPa. The Bayesian calibration framework estimates the posterior distribution using a Markov chain Monte Carlo sampling method. The sampling process employs an adaptive Metropolis-Hastings algorithm to generate a proposal distribution. A Gibbs sampling strategy alternately updates the posterior estimates of each parameter. The sampling chain length is set to 20,000 sample points. The first 10,000 sample points are used as a burn-in stage for elimination. The optimal estimates and 90% confidence intervals of the calibrated parameters are calculated from the remaining sample points. The calibration result for the pipe elastic modulus is 203 GPa with a confidence interval of 198 GPa to 208 GPa. The calibration result for the fluid viscosity coefficient is 0.0009 Pa / s with a confidence interval of 0.00075 Pa / s to 0.00105 Pa / s. The parameter calibration module writes the calibrated parameter values ​​to the database through the data management module's interface service to update the parameter configuration of the physical mechanism model.

[0072] The pipeline system pressure fluctuation physical mechanism simulation system constructed in this embodiment achieves accurate modeling of complex pipeline topologies through a topology modeling module, solving the problem of traditional empirical formula simplification algorithms neglecting the influence of pipeline accessories on pressure wave propagation. The fluid-structure interaction modeling module incorporates the pipe wall elastic deformation effect, fluid compressibility effect, and viscous dissipation effect into a unified coupled analysis framework, employing a split-solution strategy to reduce coupling complexity while maintaining computational accuracy. A path tracing module based on graph attention networks accurately captures the multi-path propagation and superposition effects of pressure waves in complex pipeline topologies. A working condition switching module pre-adjusts the numerical solver parameters before the pipeline system's operating conditions change to ensure no degradation in simulation accuracy. A parameter calibration module continuously optimizes model parameters using polynomial chaotic expansion and Bayesian inference frameworks to achieve adaptive improvement in model accuracy.

[0073] Example 2: This example is applied to the simulation analysis of pressure fluctuations in a nuclear power coolant system. This scenario is characterized by a large system scale with thousands of pipeline nodes, complex operating conditions involving multiple transient condition switching, and extremely high requirements for simulation accuracy and safety.

[0074] The simulation system for the physical mechanism of pressure fluctuation in a pipeline system provided in this application embodiment is applied to a nuclear power coolant system scenario. It includes a topology modeling module, a fluid-structure interaction modeling module, a pressure wave solving module, a path tracing module, a working condition switching module, a parameter calibration module, a data management module, and a visualization module. The functional definitions of each module are consistent with those in Embodiment 1.

[0075] In this embodiment, the topology modeling module has been specifically optimized. The drawing parsing engine adds direct interface support to the 3D piping design software, enabling it to automatically identify and import pipe centerline coordinates, pipe diameter, wall thickness information, and pipe fitting parameters. This direct interface with the 3D piping design software avoids the information loss problem inherent in traditional 2D engineering drawing conversion, achieving an accuracy rate of over 99.5%. The parametric attachment library expands to include dedicated piping accessory models for nuclear power plant scenarios, including equivalent hydraulic models of core equipment such as pressurizers, sprayers, steam generators, heat transfer pipes, and main pumps. The geometric parameters of the accessory models are automatically filled in according to the equipment design specifications, and the physical model is calibrated based on the equipment's operating characteristic curves.

[0076] In this embodiment, the fluid-structure interaction (FSI) modeling module employs an improved coupling strategy. The fluid solver and structural solver submodules of the split solver run in parallel, distributed across different computational cores and exchanging data via a shared memory mechanism. This parallel computing mode reduces the computation time per time step from 120 milliseconds to 65 milliseconds, improving computational efficiency by approximately 46%. The implicit integration scheme for the coupled equations uses a second-order backward difference formula, significantly improving time discretization accuracy compared to the first-order scheme.

[0077] In this embodiment, the pressure wave solving module extends the functionality of the boundary condition processing unit. The boundary condition processing unit adds dedicated processing strategies for the specific boundary condition types in nuclear power scenarios. For the pressurizer boundary, it calculates the boundary pressure change over time based on the pressurizer's pressure control characteristic curve. For the steam generator boundary, it calculates the equivalent flow boundary condition based on the secondary steam flow rate and heat transfer tube arrangement parameters. For the main pump boundary, it calculates the pump boundary condition based on the main pump's speed-flow characteristic curve. The feature line tracing engine adds an adaptive mesh refinement function, automatically increasing the computational node density at the wavefront position of the pressure wave propagation to accurately capture the steep leading edge of the pressure wave. After refinement, the number of mesh nodes increases to three times the original, improving computational accuracy by approximately 30%.

[0078] In this embodiment, the path tracing module optimizes the computational efficiency of the graph attention network. The graph network construction unit uses a sparse matrix storage method instead of a dense matrix storage method. Removing edges with zero weights from the adjacency matrix significantly reduces storage overhead and computational complexity; the storage space is reduced by approximately 70% after sparsification. The message passing computation unit employs a batching strategy, packaging message passing computations across multiple nodes into matrix operations and accelerating execution via the graphics processor, reducing computation time from 200 milliseconds to 40 milliseconds.

[0079] In this embodiment, the operating condition switching module increases the complexity of the operating condition state machine model. The state machine model abstracts the typical operating conditions of a nuclear power coolant system into eight discrete state nodes: cold shutdown, hot shutdown, power operation, steam bypass, main pump start-up, main pump shutdown, accident shutdown, and safety injection. There are twenty-three directed edges between these state nodes, representing all possible operating condition switching paths. Each switching path is labeled with the switching trigger condition, switching duration, and boundary condition variation patterns. The machine learning classifier employs a bidirectional long short-term memory network structure, capable of simultaneously considering contextual information from historical and future data, achieving a classification accuracy of over 95%.

[0080] In this embodiment, the parameter calibration module expands the coverage of uncertainty quantification analysis. The number of uncertainty parameters increases from four to ten. The newly added uncertainty parameters include a heat transfer coefficient fluctuation range of 0.9 to 1.1 times the nominal value, a fuel assembly heat transfer area deviation range of 0.95 to 1.05 times the nominal value, and a main pump speed deviation range of 0.98 to 1.02 times the rated speed. The polynomial chaotic expansion calculation engine adopts an adaptive sparse expansion strategy for the ten-dimensional uncertainty parameters. It automatically selects expansion terms based on the significance of the main effects and interaction effects of each parameter. Adaptive sparse expansion reduces the number of effective terms from 200 to 80, improving computational efficiency by approximately 60%. The Bayesian calibration framework adopts a distributed Markov chain Monte Carlo sampling strategy, distributing the sampling task to eight computing nodes for parallel execution, reducing sampling time from 48 hours to 6 hours.

[0081] In this embodiment, the data management module employs a hybrid storage architecture. The time-series database uses a columnar storage format, which is suitable for aggregation and analysis of pressure field time-series data, improving query speed by approximately ten times. The relational database uses a sharding strategy, distributing data across sixteen physical shards according to pipeline partitioning. Each shard is configured with independent indexes and caches, supporting high-concurrency write operations of 500,000 records per second.

[0082] In this embodiment, the visualization module adds a multi-physics field joint display function. The pressure field rendering unit simultaneously overlays and displays cloud map data of the temperature field and the flow velocity field. Different physical quantities use different color mapping schemes: the temperature field uses a blue-yellow-red gradient, and the flow velocity field uses a green-cyan-blue gradient. Users can intuitively understand the spatial distribution patterns and interrelationships of each physical quantity by comparing the color bands. The interactive analysis unit adds a sensitivity analysis visualization function. After the user selects a target parameter, the system automatically calculates the degree of influence of the parameter's change on the output results and displays the sensitivity ranking of each parameter in the form of a Tornado plot.

[0083] Comparative Example: Comparative Example 1 uses a simplified algorithm based on traditional empirical formulas to calculate pressure fluctuations. This algorithm ignores the influence of pipe fittings such as tees, elbows, and valves on pressure wave propagation and only calculates friction loss based on pipe length and diameter. It cannot accurately simulate the reflection, transmission, and superposition effects of pressure waves in complex pipe topologies. In the test scenario of this comparative example, when the pressure wave propagates to the tee position, the simplified algorithm cannot calculate the distribution ratio of the pressure wave in different branch pipes, resulting in a 32% deviation between the predicted pressure value and the experimental measurement value in the downstream branch pipe.

[0084] Comparative Example 2 uses traditional computational fluid dynamics (CFD) methods to simulate pressure fluctuations. While this method can capture the propagation characteristics of pressure waves, the model parameters rely on empirical settings and cannot accurately reflect the coupling effects of factors such as pipe wall elastic deformation, fluid compressibility, and viscous dissipation under actual operating conditions. In the test scenario of this comparative example, the use of empirical values ​​for coupling parameters leads to a systematic deviation between the simulation results and experimental data, with the peak pressure deviation reaching 25%, and the deviation continues to increase over time.

[0085] Comparative Example 3 uses a pressure wave propagation model with fixed parameters, which does not consider the impact of operating condition switching on simulation accuracy. This model has high prediction accuracy when the pipeline system is in stable operation, but when transient conditions such as rapid valve adjustment or pump start-up and shutdown occur, the model parameters are not updated in time, leading to a sharp drop in simulation accuracy. In the test scenario of this comparative example, during the rapid adjustment of the valve opening from zero to 100%, the pressure prediction error jumped from 2% to 28%.

[0086] Comparative Example 4 uses the standard finite difference method for pressure wave solving without employing graph networks for path tracing. This method has limited ability to handle the multipath propagation and superposition effects of pressure waves in complex pipeline topologies. Accuracy needs to be improved by refining the mesh and reducing the time step, but this drastically increases the computational load. In the test scenario of this comparative example, to achieve prediction accuracy comparable to this invention, the number of mesh nodes needs to be increased to eight times that of this invention, and the computation time to twelve times that of this invention.

[0087] This invention addresses the technical problem of neglecting the influence of pipeline accessories on pressure wave propagation by introducing a precise pipeline topology modeling step, significantly improving the accuracy of pressure wave prediction in pipelines with complex topologies. By introducing a fluid-structure interaction (FSI) multiphysics coupling modeling step, it incorporates pipe wall elastic deformation, fluid compressibility, and viscous dissipation into a unified coupling framework, eliminating systematic biases. The introduction of a graph-based pressure wave propagation path tracing step accurately captures multipath propagation and superposition effects. The introduction of a multi-condition coupling dynamic switching step and an uncertainty quantification parameter adaptive calibration step ensures that the simulation system maintains high accuracy throughout its entire operating cycle. The technical solution of this invention effectively overcomes the shortcomings of existing technologies in terms of accuracy, efficiency, and adaptability, providing reliable technical support for pressure fluctuation simulation of pipeline systems in major engineering projects.

[0088] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for simulating physical mechanism of pressure fluctuation in a pipeline system, characterized in that, Includes the following steps: S1: The engineering design data of the pipeline system is read through the drawing parsing module. The pipe diameter, wall thickness, material parameters, and type and location information of pipeline accessories such as tees, elbows, valves, and expansion joints are automatically extracted. A local head loss calculation model is established based on the fluid dynamic characteristics of the pipeline accessories. The pipeline system is organized into a weighted directed graph structure using graph theory. S2: Establish fluid continuity equation and momentum equation as the basic control equations for pressure wave propagation, establish pipe wall radial expansion equation as the control equation for pipe wall elastic deformation, realize bidirectional coupling between fluid control equation and pipe wall deformation equation through pressure-displacement coupling term, discretize the pipe axial direction using the method of characteristics, and discretize the pipe wall radial direction using the finite element method. S3: The improved method of characteristics is used to solve the pressure wave propagation problem. The partial differential equations are transformed into ordinary differential equations along the characteristic lines. The step size of the characteristic line tracking is dynamically adjusted according to the Courant stability condition. Boundary condition processing strategy is applied at the location of the pipeline fitting. The transient friction model is introduced to calculate the effect of viscous dissipation on pressure wave attenuation. S4: Construct a pressure wave propagation network graph based on the pipeline topology, and calculate the pressure value of each node at different times through the message passing mechanism of the graph attention network to realize dynamic tracking of the pressure wave propagation path; S5: Analyze the time series data of the input features through a machine learning classifier to predict the operating status and operating condition switching direction of the pipeline system. When the probability of operating condition switching exceeds the preset threshold, trigger the pre-adjustment process of simulation parameters to modify the parameter settings of the solver in advance. S6: The polynomial chaotic expansion method is used to quantify the uncertainty parameters in the model, establish a Bayesian calibration framework, and update the posterior distribution of the model parameters based on monitoring data.

2. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The drawing parsing module supports the import and parsing of computer-aided design files or scalable vector graphics files, and extracts pipeline numbers, start and end node coordinates, pipe diameter series and wall thickness specifications; the parametric attachment library establishes standardized geometric templates and physical models for each type of pipeline attachment, and the geometric templates are parametrically defined through key dimension parameters.

3. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The fluid continuity equation describes the compressibility of the fluid by introducing the bulk modulus and density change rate of the fluid; the momentum equation describes the effect of viscous dissipation on pressure wave attenuation by introducing frictional resistance and local loss terms; and the pipe wall radial expansion equation describes the radial displacement of the pipe wall under internal pressure by introducing the elastic modulus, Poisson's ratio and wall thickness parameters of the pipe material.

4. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The time progression of the coupled equations adopts an implicit integration scheme to ensure that the stability conditions of the numerical calculation are not strictly limited by the mesh size; the numerical solution of the coupled equations adopts a split solution strategy, which decomposes the coupled equations into two sub-modules, a fluid solver and a structural solver, according to the physical process. The two sub-modules are executed alternately in sequence to advance the time progress.

5. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The improved characteristic line method sets virtual calculation nodes at the location of pipeline accessories. For valve accessories, it calculates the reflection coefficient and transmission coefficient of pressure waves based on the instantaneous change rate of valve opening. For tee accessories, it calculates the distribution ratio of pressure waves in different branch pipelines based on fluid flow direction and tee geometry. The transient friction model describes the selective attenuation effect of viscous dissipation on pressure wave components of different frequencies by superimposing attenuation exponential functions at multiple frequencies.

6. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The nodes of the pressure wave propagation network graph represent physical locations in the pipeline system, and the attributes of the edges include propagation delay, attenuation coefficient, and directional weight. The graph attention network assigns different attention weights to different neighbor nodes during message passing. The calculation of attention weights takes into account the type of neighbor nodes, historical pressure values, and propagation distance.

7. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The operating condition state machine model abstracts the typical operating conditions of the pipeline system into discrete state nodes. The directed edges between the state nodes represent possible operating condition switching paths. Each switching path is marked with the switching trigger condition, switching duration, and boundary condition change law. The input features of the classifier include the time series features of recent pressure monitoring data, valve opening change rate, and flow fluctuation features.

8. The simulation method for the physical mechanism of pressure fluctuation in a pipeline system according to claim 1, characterized in that: The uncertain parameters include the pipe's elastic modulus, the fluid viscosity coefficient, the pipe wall roughness, and the local resistance coefficient; the polynomial chaotic expansion method expands the output containing the uncertain parameters into an orthogonal polynomial series, and reconstructs the complete probability distribution characteristics of the output through a small number of deterministic calculation samples; The Bayesian calibration framework uses the probability distribution obtained from the multinomial chaotic expansion as prior knowledge, the monitoring data as likelihood information, and estimates the posterior distribution using the Markov chain Monte Carlo sampling method.

9. A simulation system for the physical mechanism of pressure fluctuations in a pipeline system, applicable to the simulation method for the physical mechanism of pressure fluctuations in a pipeline system as described in any one of claims 1-8, characterized in that, include: The topology modeling module is configured to read the design data of the piping system and automatically build the topology model. This module has a built-in drawing parsing engine and parametric attachment library. The fluid-structure interaction modeling module, connected to the topology modeling module, is configured to construct a set of fluid-structure interaction control equations based on the topology model. This module integrates a fluid control equation template library and a pipe wall deformation equation template library. The pressure wave solution module, connected to the fluid-structure interaction modeling module and the topology modeling module, is configured to perform pressure wave propagation solution calculations based on the improved method of characteristics. This module contains a characteristic line tracing engine and a transient friction correction module. The path tracing module, connected to the pressure wave solving module, is configured to trace the propagation path of pressure waves in the pipeline system based on a graph attention network. This module contains a graph network construction unit and a message passing calculation unit. The operating condition switching module, connected to the pressure wave solution module and the path tracing module, is configured to detect the switching events of the pipeline system's operating conditions and trigger the pre-adjustment process of simulation parameters. This module contains a state recognition unit and a parameter pre-adjustment unit. The parameter calibration module is configured to perform uncertainty quantification and adaptive parameter calibration calculations. This module integrates a multinomial chaos expansion calculation engine and a Bayesian calibration framework. The data management module establishes data connections with all computing modules and is configured to uniformly manage the input data, intermediate calculation results, and output data of the simulation system. The visualization module, connected to the data management module, is configured to display simulation calculation results to users in a graphical manner.

10. The simulation system for the physical mechanism of pressure fluctuation in a pipeline system according to claim 9, characterized in that: The data management module uses a distributed database architecture to store large-scale simulation data, supporting high-speed concurrent read and write operations and data version management functions; the visualization module supports pressure field cloud map drawing, pressure wave propagation animation generation, and path tracing result visualization functions; the working condition switching module establishes a bidirectional data connection with the pressure wave solution module and the path tracing module to realize dynamic updates of simulation parameters.

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