A pick iterative random characteristic flow field deduction and reconstruction method and system for bridge wind engineering

Abstract

The application discloses a Pick iterative random characteristic flow field deduction and reconstruction method and system for bridge wind engineering and belongs to the technical field of bridge wind engineering and structural health monitoring. The application divides a global space-time calculation domain, constructs local affine mapping and a space-time random characteristic base function, adopts Pick iterative linearization incompressible Navier-Stokes equations, avoids Jacobian matrix calculation, assembles a global over-determined linear equation group containing momentum, mass conservation, boundary and interface constraints, forms a double-enhanced linear system through algebraic row balance and physical enhancement layered weighting, realizes high-fidelity reconstruction of a flow field through least square solution, supports unknown fluid parameter alternating inversion under sparse data, and can automatically generate bridge wind-induced vibration early warning. The application eliminates edge device memory bottleneck, improves solution robustness and precision, strictly guarantees physical conservation, and is suitable for real-time deduction of bridge complex flow fields, sparse observation reconstruction and safety monitoring.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of bridge wind engineering and structural health monitoring, specifically relating to a method and system for predicting and reconstructing the stochastic characteristic flow field of a bridge wind engineering system. Background Technology

[0002] In the field of bridge wind engineering and structural health monitoring, accurately obtaining the evolution law of the three-dimensional complex flow field around the bridge structure (such as main beam, cable, and pier) is crucial for the wind-resistant design and aerodynamic performance evaluation of bridges.

[0003] In forward simulation and prediction of flow fields, traditional grid-based numerical methods are computationally expensive and cannot meet the real-time simulation requirements of digital twin systems for complex flow fields. Furthermore, in practical bridge health monitoring or reverse reconstruction tasks from large wind tunnel tests, the high cost of sensor deployment and physical space constraints often limit the deployment of only a very limited number of fluid sensors (such as anemometers or pressure probes) on the structural surface or in localized areas of the flow field. The resulting measured flow field data is extremely sparse. How to achieve efficient forward flow field prediction while simultaneously utilizing extremely sparse sensor signals to accurately reconstruct a globally complex, strongly nonlinear flow field and inversely derive unknown hydrodynamic parameters (such as the incoming Reynolds number) is a pressing technical challenge in the field of wind engineering testing.

[0004] In recent years, deep learning methods such as Physical Information Neural Networks (PINN) have been introduced into flow field computation. However, their training suffers from ill-conditioned loss surfaces and extremely slow convergence, failing to meet the monitoring requirements for real-time flow field evolution. To overcome this bottleneck, the Random Feature Method (RFM) has been proposed. However, existing RFM methods, when dealing with strongly nonlinear fluid equations containing convection terms, must be embedded in a robust Newton-Raphson iterative framework equipped with line search techniques. This traditional algorithm exposes the following significant technical bottlenecks in the deployment of monitoring hardware in actual engineering fields:

[0005] (1) Memory overflow bottleneck of field edge computing devices: Flow field monitoring nodes usually use edge computing devices with limited computing power. The traditional Newton method requires the calculation and storage of an extremely dense Jacobian matrix for each iteration, which consumes a lot of memory. As a result, the field edge devices are prone to crashing due to memory overflow, and cannot realize the local real-time simulation and reconstruction of the flow field.

[0006] (2) Algorithm divergence failure under sparse sensor data: In actual working conditions where wind tunnel test or field monitoring data is extremely sparse, due to the lack of sufficient constraint information, the traditional Newton method is extremely sensitive to the initial value, and the condition number of the Jacobian matrix is ​​easily deteriorated, resulting in divergence of the iterative update step size and direct system collapse failure.

[0007] (3) Soft constraints lead to distortion of physical mechanisms: Traditional least squares algorithms process sensor boundary data and mass conservation equations in the form of "soft constraints". In complex wake shedding phenomena, the residuals of the momentum equation can easily mask small mass conservation errors, making it difficult for the calculated flow field to strictly satisfy the basic physical laws of nature such as fluid incompressibility, thus producing non-physical pseudo-solutions. Summary of the Invention

[0008] Based on the above shortcomings, this invention provides a method and system for iterative stochastic characteristic flow field extrapolation and reconstruction for bridge wind engineering. It solves the problems faced by existing technologies in the forward evolution extrapolation and sparse data assimilation and reconstruction of complex flow fields in bridge wind engineering, such as edge computing device memory overflow, easy algorithm divergence, and distortion of physical conservation mechanisms. This method abandons the gradient update of traditional deep learning and fundamentally avoids the dependence on Jacobian matrix calculation and line search backtracking in the nonlinear decoupling process, realizing high-fidelity extrapolation of flow fields and parameter inversion under computing power-constrained architecture.

[0009] The technical solution adopted in this invention is as follows: A method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering, comprising the following steps:

[0010] Step 1: Acquisition of Input Data for Complex Structure Flow Field and Construction of Spatiotemporal Region Decomposition Basis Functions: Input data of the flow field environment in physical space is acquired. Based on the geometric boundaries of the bridge structure and the scale characteristics of the flow field computational domain, the global spatiotemporal computational domain of the flow field is divided into multiple sub-regions. For each sub-region, a local affine mapping from physical coordinates to standard reference coordinates is established. A single-layer neural network with randomly fixed hidden layer weights and biases during initialization and not involved in training is used to generate spatiotemporal random feature basis functions. Combined with a spatiotemporal unit decomposition function with compact support characteristics, an approximate expression of the global spatiotemporal flow field parameters is constructed.

[0011] Step 2: Decoupling of nonlinear fluid dynamics partial differential equations based on Picard iteration: For the nonlinear convection term in the nonlinear control equation of fluid dynamics, the velocity field approximation result of the previous iteration step is used as the known fluid background field and substituted into the nonlinear convection term of the equation in the current step to avoid the Jacobian matrix evaluation process, thereby achieving linear decoupling of the nonlinear control equation.

[0012] Step 3: Fine assembly of the global overdetermined linear equation system: The global overdetermined linear equation system is assembled by globally assembling the momentum control equation residual matrix calculated from internal configuration points, the mass conservation matrix calculated based on divergence, the boundary constraint matrix calculated based on boundary points or sparse observation points, the initial condition matrix calculated based on the initial time point, and the interface matrix constructed to enforce the continuous condition. The unknowns to be solved in the global overdetermined linear equation system are a global unified random feature expansion coefficient column vector composed of the local expansion coefficients of each sub-region.

[0013] Step 4: Algebraic Row Balancing and Physical Enhancement Layered Weighting: Construct a diagonal scaling matrix to perform algebraic row balancing on the global overdetermined linear equation system. The diagonal elements of the diagonal scaling matrix are determined by the inverse of the infinite norm of the corresponding row vectors of the global overdetermined linear equation system. Based on this, construct a physical space weight diagonal matrix to apply dominant physical penalty weights, which are at least 10 to 1000 times higher than the weights of the momentum control equations, to the mass conservation residuals, boundary conditions or sparse observation point constraints, and the continuity conditions of the interfaces between adjacent sub-regions, thereby generating a weighted linear system with dual enhancements.

[0014] Step 5: Weighted system solution and flow field parameter derivation and inversion for forward and inverse problems: The weighted linear system is solved by the linear least squares direct solution algorithm to obtain all the random feature expansion coefficients and reconstruct the global spatiotemporal flow field parameters, which are used for the derivation of the fluid dynamic performance of structures such as bridges or for safety early warning.

[0015] Furthermore, in step one, the single-layer neural network combines a nonlinear activation function to generate the spatiotemporal random feature basis function, wherein the nonlinear activation function is preferably a hyperbolic tangent activation function.

[0016] Furthermore, in step one, the spatiotemporal unit decomposition function is a local support function constructed based on the indicator function; the approximate expression of the global spatiotemporal flow field parameters is: multiplying the spatiotemporal random characteristic basis functions in each sub-region with the corresponding spatiotemporal unit decomposition function, and then linearly superimposing the summation over all sub-regions to obtain the global spatiotemporal flow field parameters.

[0017] Furthermore, in step two, the fluid dynamics nonlinear control equation is preferably the incompressible Navier-Stokes equation.

[0018] Furthermore, when the fluid dynamics nonlinear control equations contain unknown physical parameters, step five employs the following alternating optimization strategy for parameter inversion and flow field reconstruction: In each alternating iteration, firstly, the estimated value of the current unknown physical parameter is fixed, and the weighted linear system is solved to obtain the stochastic characteristic expansion coefficients, reconstructing the approximate solution of the global spatiotemporal flow field parameters for the current step; subsequently, the approximate solution of the global spatiotemporal flow field parameters is fixed, and based on the residuals of the actual measurement data at the internal sparse observation points and the residuals of the partial differential equation control equations, the unknown physical parameters are directly solved and updated individually using a direct algebraic solution based on residual minimization or a least squares projection algorithm; this process is repeated alternatingly until the iteration converges.

[0019] Furthermore, after the flow field reconstruction is completed, when the reconstructed wake characteristics meet the structural resonance induction conditions, that is, when the difference between the vortex shedding frequency of the wake and the natural frequency of the bridge structure is within the preset resonance danger threshold range, or when the aerodynamic amplitude induced by the flow field exceeds the preset safety threshold, a wind-induced vibration or fluid resonance safety warning signal or three-dimensional flow field visualization monitoring data for the bridge structure is automatically generated.

[0020] This invention also provides a system for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering using a pickup truck, realizing the method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering as described above. The system includes:

[0021] The spatiotemporal region decomposition and basis function construction module is used to acquire the flow field environment input data in physical space. Based on the geometric boundary of the bridge structure and the scale characteristics of the flow field computation domain, the global spatiotemporal computation domain is divided into multiple sub-regions. A local affine mapping from physical coordinates to standard reference coordinates is established for each sub-region. Spatiotemporal random feature basis functions are generated using a single-layer neural network that is randomly fixed during initialization and does not participate in training. Combined with the spatiotemporal unit decomposition function with compact support characteristics, an approximate expression of the global spatiotemporal flow field parameters is constructed.

[0022] The nonlinear equation Pica iteration decoupling module is used to address the nonlinear convection term in the incompressible Navier-Stokes equations. It employs Pica iteration to substitute the approximate velocity field result from the previous iteration step into the current step equation as a known fluid background field, thus avoiding the Jacobian matrix evaluation process and achieving linear decoupling of the nonlinear control equations.

[0023] The global overdetermined equation assembly module is used to assemble a global overdetermined linear equation system with the column vector of the expansion coefficients of the global unified stochastic features to be solved as unknowns, based on the residuals of the momentum control equation after linear decoupling, the residuals of mass conservation, the boundary conditions or sparse observation point constraints, and the continuity conditions of the interface between adjacent sub-regions.

[0024] The algebraic and physical dual-weighting module is used to construct a diagonal scaling matrix whose diagonal elements are determined by the inverse of the infinite norm of the row vectors corresponding to the global overdetermined linear equation system, complete the algebraic row balancing process, and construct the physical space weight diagonal matrix. It applies physical penalty weights that are 10 to 1000 times higher than the weights of the momentum control equations to the mass conservation residuals, boundary constraints, and interface continuity conditions, thereby generating a dual-enhanced weighted linear system.

[0025] The weighted system solution and flow field deduction and early warning module is used to solve the weighted linear system using the linear least squares algorithm, obtain the random feature expansion coefficients and reconstruct the global spatiotemporal flow field parameters, complete the deduction of the hydrodynamic performance of the bridge structure, and automatically generate wind-induced vibration or fluid resonance safety early warning signals or three-dimensional flow field visualization monitoring data when the wake feature triggers the resonance danger threshold or the aerodynamic amplitude exceeds the safety threshold.

[0026] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering.

[0027] The present invention also provides a computer program product, characterized in that it includes a computer program or instructions, which, when executed by a processor, implement the above-described method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering.

[0028] The present invention also provides a computer-readable storage medium storing a computer program or instructions thereon, which, when executed by a processor, implements the above-described method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering.

[0029] This invention is mainly used for forward digital twin extrapolation of complex wake fields around bridge structures (such as cables and piers) under edge computing architecture, high-fidelity reconstruction under extremely sparse data, inversion of unknown flow field physical parameters, and real-time monitoring of wind environment conditions. The core idea of ​​this invention is to transform the solution of complex aerodynamic control equations into a convex linear least squares problem by using the meshless stochastic feature method (RFM), and to completely avoid the Jacobian matrix calculation and line search backtracking in the nonlinear decoupling process by introducing Picard iteration. It has the following advantages and beneficial effects:

[0030] (1) Eliminating Jacobian overhead and completely overcoming the memory bottleneck of edge devices: This method completely avoids the calculation and line search of dense Jacobian matrices in the traditional Newton method when dealing with nonlinear flow fields. While ensuring extremely high accuracy, it significantly reduces the computational load and memory usage, making it perfectly deployable in edge devices in wind tunnels or bridges with limited computing power. The forward derivation speed is about 30% to 1 times faster than the robust Newton method and several orders of magnitude faster than PINN.

[0031] (2) Physically enhanced hierarchical weighting to achieve physical conservation of approximate numerical hard constraints: It breaks through the limitation that traditional deep learning dynamic weighting is prone to numerical oscillation. By using dominant penalty weights, the incompressibility (mass conservation) and boundary consistency of the fluid are strictly enforced, which fundamentally eliminates the obscuring of key physical mechanisms by momentum residuals and prevents the generation of non-physical pseudo-solutions in flow field reconstruction.

[0032] (3) Excellent robustness against inverse problems under extremely sparse sensing conditions: The alternating optimization framework fundamentally isolates the high-dimensional non-convex risk caused by mixing physical parameters with network expansion coefficients. In extremely unsteady scenarios with a severe lack of pressure field information and only a very small number of discrete flow velocity observation points, when the traditional robust Newton method completely collapses due to the deterioration of the Jacobian matrix condition number caused by initial value sensitivity, this invention can still converge robustly, achieving accurate identification of unknown fluid parameters (such as Reynolds number) and high-fidelity reconstruction of the flow field. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for iterative stochastic characteristic flow field deduction and reconstruction using a pickup truck for bridge wind engineering, as described in this invention.

[0034] Figure 2 This is a schematic diagram of the core algorithm architecture for stochastic characteristic flow field inference combined with Jacobi-Picard iteration in this invention;

[0035] Figure 3 The velocity and pressure field distributions and their absolute error contour plots are reconstructed from the forward extrapolation of the flow field of a two-dimensional Kovasznay flow.

[0036] Figure 4 The velocity and pressure field distributions and their absolute error contour maps are reconstructed from the forward extrapolation of the flow field around a two-dimensional unsteady cylinder.

[0037] Figure 5 This is a graph showing the relationship between divergence weights and their effect on global prediction accuracy and the control effect on divergence residuals.

[0038] Figure 6 The graph shows the relationship between the boundary condition weights and the accuracy and boundary residuals of the solution system.

[0039] Figure 7The diagram shows the comprehensive analysis of the interface weights and the distribution curve of the local absolute error, where (a) represents the interface weights. The relationship curve between global solution accuracy and the influence of continuous residuals at the interface is shown in (b), which is the local absolute error distribution curve near the interface under different interface weights.

[0040] Figure 8 The figure shows a comparison of the relative errors between the proposed method and the existing robust Newton method (RFM-Newton) in the inverse problem of reconstructing sparse observation data.

[0041] Figure 9 To compare the absolute error contour plots of the proposed method with existing methods for reconstructing the flow field under extremely sparse observation points;

[0042] Figure 10 This is an iterative convergence curve of the unknown Reynolds number under different numbers of observation points in the parameter identification task. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0044] Example 1

[0045] like Figure 1 As shown in the figure, this embodiment provides a method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering using a pickup truck. The specific steps are as follows:

[0046] Step 1: Acquisition of Input Data for Complex Structure Flow Field and Construction of Spatiotemporal Decomposition Basis Functions: Acquire known physical boundary conditions used for positive flow field prediction in the physical space of the bridge or wind tunnel test, or sparse observation data collected by sparsely distributed sensors (such as anemometers); divide the global spatiotemporal computation domain into multiple sub-regions and establish local affine mappings to unify the spatiotemporal scale; within each sub-region, use a single-layer neural network with randomly fixed hidden layer parameters during initialization and not participating in training to generate spatiotemporal random feature basis functions, and combine them with spatiotemporal unit decomposition functions with compact support characteristics to construct approximate expressions for global flow field parameters (such as velocity field and pressure field).

[0047] To handle complex geometries such as cables and piers, this embodiment adopts the basic premise of the meshless random feature method. The system establishes a local affine mapping to divide the global flow field into... Each sub-region is designed to maintain a unified spatiotemporal scale. Within each sub-region, a single-layer neural network with hidden layer parameters randomly fixed during initialization (not involved in training) is used to generate... Spatiotemporal random characteristic basis functions Combined with a spacetime unit decomposition function that has compact support properties Construct an approximate expression for the physical parameters of the global flow field (the expansion coefficient matrix is...). ).

[0048] Step 2: Decoupling of Nonlinear Fluid Dynamics Partial Differential Equations Based on Picard Iteration: Taking the incompressible Navier-Stokes (NS) equations describing the flow field evolution around a bridge structure as an example, consider the decoupling in the spatiotemporal domain... The incompressible Navier-Stokes equations on:

[0049]

[0050] in, The velocity is dimensionless; Dimensionless pressure; The Reynolds number is used to characterize the flow regime;

[0051] Represents boundary / sensor observation constraint operators; For set values ​​or sparse measured data; These are the initial conditions; = For spatial coordinates, Hamiltonian operator; Laplace operator.

[0052] For the strongly nonlinear convection terms in the Navier-Stokes equations, the approximate values ​​of the flow field physical quantities from the previous iteration are extracted and substituted into the convection terms of the momentum equation in the current step, transforming them into a known fluid background field. This completely avoids the differentiation evaluation and line search backtracking operations of the dense Jacobian matrix in the traditional Newton method, achieving complete linear decoupling of the strongly nonlinear fluid dynamics partial differential equations in the entire time and space domain.

[0053] Existing technologies for handling strongly nonlinear convection terms In practice, the robust Newton-Raphson method is commonly relied upon, requiring the evaluation of a dense Jacobian matrix at each step. This makes edge computing devices highly susceptible to memory overflow and prone to divergence due to condition number deterioration in sparse data inverse problems. To completely overcome the Jacobian memory computation bottleneck of edge devices, this invention introduces Picard iteration: extracting the previous iteration step (the... Step 1) Given approximate values ​​of the flow field and Substitute it as a known constant background field into the solution of the first... The linearized momentum equation is explicitly reconstructed as:

[0054]

[0055] This strategy completely avoids nonlinear differentiation and line search backtracking across the entire time and space domain.

[0056] Step 3: Fine assembly of the global overdetermined linear equation system: Based on the Picard linearization results in Step 2, select internal placement points, boundary placement points (or sparse sensor observation points), initial condition placement points, and cross-subdomain interface placement points to assemble a global overdetermined linear equation system containing the expansion coefficients of all stochastic features to be solved.

[0057]

[0058] in, This is the global column vector of coefficients to be solved.

[0059] To accurately correspond to the subsequent physical layering weighting strategy, the global weighting coefficient matrix... With the right end item Strictly based on the underlying physical mechanism, the block structure is as follows:

[0060]

[0061] Global weighted coefficient matrix The local sub-matrixes correspond to the momentum governing equation matrix, divergence equation matrix, boundary / observation condition matrix, initial condition matrix, and interface matrix that forces continuity to compensate for jumps in the unit decomposition function. The explicit construction logic of each local sub-matrix is ​​as follows:

[0062] (1) Momentum equation: Given the known fluid background field Directly embedded in the build process. (For the first...) Internal configuration points within each subdomain Its matrix row expression is explicitly linearized as:

[0063]

[0064] (2) Divergence equation (mass conservation): For incompressible conditions, divergence sub-blocks The line expression at the configuration point is:

[0065]

[0066] (3) Boundary and initial condition equations: for spatiotemporal boundary points (or sparse observation points) relative to the initial point Its matrix sub-blocks directly calculate the value of the spatiotemporal random characteristic basis function at that point:

[0067]

[0068]

[0069] (4) Interface continuity equation (cross-domain coupling): to realize adjacent sub-regions and Continuity constraints of the flow field between points, for any interface configuration Construct sparsely coupled constraint rows:

[0070]

[0071] in, and Representing sub-regions and Random characteristic basis functions at the interface.

[0072] After calculating the residuals and constraint matrices for the above terms, the corresponding submatrices are concatenated to assemble a global system matrix containing the expansion coefficients of all the stochastic features to be solved. Simultaneously, with the global system matrix The macroscopic row block structure strictly corresponds to the construction of the right-hand side column vector of the global overdetermined linear equation system. ;

[0073] (1) Among them For the right-hand side of the momentum equation: during the Jacobi-less Picard iteration linearization, all terms containing unknown coefficients, such as the nonlinear convection term and the viscous diffusion term, have been moved to the left-hand side of the equation to construct the system matrix. For a flow field without external volume forces (such as source-free terms), the right-hand side term is a zero vector, i.e. .

[0074] (2) The right-hand side of the mass conservation equation: based on the property that the divergence of an incompressible fluid is zero ( This term is the zero vector, i.e. .

[0075] (3) For the right-hand side of the boundary condition equation: for spatiotemporal boundary points (or sparse observation points). The right-hand side of this equation corresponds to the boundary conditions (or sparse observation data) in the system's governing equations. This term consists of a vector of known set values ​​at the boundary points, i.e. .

[0076] (4) For the right-hand side of the initial condition equation: with respect to the initial condition point Its right-hand side corresponds to the initial conditions in the system control equations. This term consists of the known initial value vectors at the placement points within the initial time domain, i.e. .

[0077] (5) For the right-hand side of the interface continuity term: To enforce the continuity requirement of the flow field parameters and their derivatives at the interface of adjacent sub-regions, the difference between the physical quantities on both sides of the interface must be zero, i.e. .

[0078] Thus, the globally overdetermined linear equations under fluid dynamic physical constraints have been completed. The complete build assembly.

[0079] Step 4: Algebraic Linear Balance and Physically Enhanced Hierarchical Weighting: To address the severe numerical stiffness and physical magnitude imbalance challenges encountered when transforming fluid partial differential equations into least squares problems (i.e., the failure of traditional "soft constraints"), a hierarchical weighting strategy with dual algebraic and physical enhancements is systematically proposed.

[0080] First, calculate the diagonal scaling matrix. Its diagonal elements are determined by the inverse of the infinity norm of the corresponding row vector of the system matrix:

[0081]

[0082] This allows for "algebraic row balancing" of the globally overdetermined system. This eliminates systematic numerical biases caused by discretization.

[0083] Subsequently, this invention overcomes the limitations of dynamic weighting in PINN, which aims to eliminate gradient pathology, and specifically constructs a "physically enhanced spatial weight matrix" for linear least squares systems. Its definition is:

[0084]

[0085] By assigning boundary conditions / sparse observations ( Subdomain interface continuity ( ) and the mass conservation equation ( The weighted linear system, significantly larger than the dominant penalty weight of the momentum equation, effectively utilizes the properties of linear algebra to enforce an approximate "numerical hard constraint" physical conservation effect within a soft constraint framework, ensuring that the reconstructed flow field strictly adheres to fundamental physical laws such as fluid incompressibility. The resulting dual-weighted linear system is characterized as follows:

[0086]

[0087] Step 5: Weighted system solution and flow field parameter derivation and inversion for forward and inverse problems: Direct solution of the convex linear system after the above double weighting. Obtain the global random feature expansion coefficient matrix This outputs high-fidelity flow field parameters (such as velocity and pressure fields) that satisfy strict physical conservation laws, used for forward digital twin prediction of the bridge fluid environment. Furthermore, when the fluid dynamics control equations involve unknown fluid physics parameters (such as the unknown incoming Reynolds number Re) and only extremely sparse sensor data is available, the system introduces an alternating optimization strategy for parameter inverse assimilation: in each alternating iteration, the estimated value of the current unknown physical parameters is first fixed, and the weighted linear system is solved once to obtain the stochastic feature expansion coefficient matrix. The approximate solution of the flow field parameters in the current step is reconstructed. Then, the flow field parameters are fixed, and the unknown physical parameters Re are independently updated by scalar optimization or projection method based on the residuals of the real flow velocity measurement data and the residuals of the partial differential control equations at the internal extremely sparse observation points. This process is repeated until the iteration converges, and safety warning signals (such as wind-induced vibration warnings) or three-dimensional flow field visualization monitoring data of the bridge structure are generated accordingly.

[0088] Example 2

[0089] This embodiment verifies the actual engineering effect of the above-mentioned flow field deduction and reconstruction technology solution by combining specific bridge wind engineering test examples and application scenarios:

[0090] Taking the forward simulation of a two-dimensional Kovasznay flow (equivalent to local flow around a bridge structure) controlled by the incompressible Navier-Stokes equations as an example, we illustrate the basic operating configuration and high-precision solution capability of the system.

[0091] Specifically, the computing system first performs spatiotemporal decomposition, dividing the global computing domain into... Each sub-region is defined. For each sub-region, a local affine mapping is defined to uniformly map the physical coordinates to the standard reference coordinate system. Within this sub-region, a single-layer neural network with hidden layer parameters randomly fixed during initialization and not used in training is constructed, using the hyperbolic tangent activation function tanh to generate the hidden layer. A random characteristic basis function.

[0092] For the nonlinear convection term in the momentum equation The system extracts the first Substituting the known physical field approximations of the previous step into the current step, a Jacobian-free Picard iterative scheme is constructed. Based on 3600 internal residual points ( ), 240 boundary configuration points and 120 interface configuration points, assemble a weighted overdetermined linear equation system containing the global unsolved expansion coefficient matrix and solve it.

[0093] To verify the superior performance of the proposed method in this embodiment, it is compared with the robust Newton-Raphson method (RFM-Newton) and PINN (using the Adam optimizer, configured with 10,000 interior points and 4,000 boundary points, with a neural network size of [missing information - likely a specific value]. The learning rate is ,train A quantitative comparison was conducted on the number of rounds. Specific error and computational cost comparison data are shown in Table 1.

[0094] like Figure 3 As shown in Table 1, the quantitative data and corresponding predicted contour maps, along with the velocity and pressure fields predicted by the RFM-Picard method proposed in this embodiment, represent the results. The relative error reached an extremely high level. to Its accuracy is comparable to that of RFM-Newton and is five orders of magnitude higher than that of the PINN method. Furthermore, because it completely avoids the calculation of the Jacobian matrix and line search backtracking, its flow field reconstruction time is reduced by about 30% compared to the robust Newton method and nearly two orders of magnitude higher than that of PINN.

[0095] Table 1. Comparison of accuracy and training cost in solving Kovasznay flow.

[0096]

[0097] Example 3

[0098] This embodiment selects the classic two-dimensional incompressible cylinder flow (simulating the wind conditions of bridge stay cables or circular piers) from bridge wind engineering as a typical example. This flow field exhibits significant unsteady, strongly nonlinear vortex shedding characteristics, and the Reynolds number is set to [value missing]. .

[0099] The center of the cylinder is located at The diameter of the cylinder is The solution space domain is... The time domain is To accurately capture the evolution of the high-gradient shear layer in the near field and the Karman vortex street in the far field of the cylinder, the system decomposes the computational domain into... Each sub-region is configured with [number] sub-domains. A random characteristic basis function. The nonlinear convection term is processed using the Jacobi-free Picard iteration described in this invention.

[0100] like Figure 4 As shown, the velocity field cloud map reconstructed by the method proposed in this invention is in high agreement with the true solution, and can accurately restore the alternating Kármán vortex street topology behind the cylinder.

[0101] Example 4

[0102] This embodiment verifies the effect of "algebraic row balancing" and "physical enhancement layered weighting" on the forced constraint of the physical mechanism of the flow field, which is common in bridge wind engineering.

[0103] In practical overdetermined linear systems In this context, momentum evolution, mass conservation (divergence), and the residuals of the equations corresponding to boundary conditions differ significantly in numerical magnitude. This embodiment takes the solution of the more complex unsteady three-dimensional Beltrami flow with strong three-dimensional coupling characteristics as an example to illustrate the implementation details of the proposed dual strategy of "algebraic row balancing" and "physically enhanced layered weighting" and its effect on the forced physical constraint of the three-dimensional flow field.

[0104] The system first calculates the diagonal scaling matrix. To eliminate numerical rigidity, all equations are normalized to the same algebraic order of magnitude. Then, a diagonal weight matrix for physical space is constructed. For a 3D Beltrami flow, the specific values ​​for each physical weight are: , , , .

[0105] like Figure 5 As shown, with from Order of magnitude increased to The divergence residuals exhibit a strictly monotonically decreasing trend across multiple orders of magnitude (from approximately...). dropped to about During this convergence process, the components of the three-dimensional velocity field ( , , and pressure field The L2 relative error in the initial stage ( from Increase to The error rate showed a significant decrease and subsequently stabilized at an extremely low level. This phenomenon indicates that in complex three-dimensional flow fields, applying a strong divergence penalty can extremely effectively drive the numerical solution to approximate the real physical manifold that satisfies the incompressibility condition. By strengthening the mass conservation constraint, the system effectively utilizes the pressure field as a Lagrange multiplier to maximally correct the non-physical divergence error of multiple degrees of freedom in three-dimensional space.

[0106] like Figure 6 As shown, in a three-dimensional complex flow field, the boundary residuals change with... The increase in exhibits excellent monotonic decreasing characteristics. However, the physical quantities of the three-dimensional flow field ( , , , The L2 relative error curve exhibits a very typical "U-shaped" distribution characteristic. When In to When the interval is within a certain range, the model's ability to capture boundary information is enhanced, and the errors of all variables decrease across the board, reaching optimal accuracy. However, as... With further increases, the errors in all physical quantities deteriorated and rebounded significantly, especially in the pressure field. The error increases sharply. This result profoundly reveals that in three-dimensional high-degree-of-freedom systems, excessively penalized boundary conditions easily lead to ill-conditioned system matrices and severe numerical stiffness. Excessively large boundary weights cause the residuals of the internal domain momentum evolution to be completely marginalized in the global least-squares objective function. Therefore, appropriately setting... It is the key to balancing the fit of the three-dimensional boundary with the accuracy of the internal flow field evolution.

[0107] like Figure 7 As shown in a, with The improvement in [the quality of the flow] leads to a significant and monotonically decreasing interface jump residual, which characterizes the coupling strength of the domain decomposition. It is worth noting that, due to the higher and more complex interface coupling dimensions in the three-dimensional flow field, when [the quality of the flow] increases... Exceed After that, global physical quantities (especially pressure) and speed The L2 relative error showed a slight increase, indicating that overly rigid interface constraints may have affected the coordination flexibility of the global basis functions to some extent. Despite the aforementioned minor trade-off in global accuracy, Figure 7 b shows the interface ( The local absolute error distribution near (y=z=0, t=0.5) conclusively proves the indispensability of increasing this weight. When At lower levels (e.g., equal to 1.0), the predicted solution exhibits extremely severe numerical abrupt changes and physical separations at the subdomain boundaries (manifested as steep error jumps); while as... As the values ​​are successively increased to 100.0, 500.0, and even 1000.0, the error cracks at the interface are strongly "stitched up," and the distribution curve gradually evolves into a smooth and continuous transition shape. This microscopic evidence fully demonstrates that assigning a sufficiently large penalty weight to the interface continuity condition can fundamentally eliminate the non-physical fragmentation effect inherent in the multidimensional domain decomposition method and strictly guarantee the flow field continuity constraint across subdomains in the spatiotemporal prediction solution.

[0108] Example 5

[0109] This embodiment demonstrates robustness when dealing with only a very small number of discrete anemometer observations. When assembling the global equations, the original boundary conditions are replaced with extremely sparse internal observation data, and the global flow field is reconstructed directly using velocity measurement residuals as constraints. To verify the robustness of this embodiment, the number of available random observation data points is progressively reduced in the data assimilation task for a two-dimensional Kovasznay flow.

[0110] like Figure 8 As the comparative data shows, the unsteadiness of the reconstruction problem is severely amplified as the number of observation data points decreases sharply. When the number of data points drops to 30, the existing RFM-Newton method, due to its extreme sensitivity to initial values, causes the condition number of the Jacobian matrix to deteriorate rapidly, ultimately resulting in complete computational failure. In contrast, the RFM-Picard method used in this invention fundamentally eliminates the dependence on Jacobian matrix differentiation and line search backtracking, and can still converge robustly even under the harsh condition of only 30 observation points. Its direct reconstruction computational efficiency is extremely high, and the computational cost is basically equivalent to the forward simulation in Example 1.

[0111] To visually verify the high spatial fidelity of the reconstructed flow field in this embodiment Figure 9 The paper presents a comparison of the spatial distribution of absolute errors in the reconstructed flow field using the proposed method (RFM-Picard) and the existing robust Newton method (RFM-Newton) with the same number of sparse observation points (200). As shown in the figure, although the existing RFM-Newton method can barely achieve convergence after increasing the number of observation points, its reconstructed flow field (especially the pressure field) exhibits extremely obvious error clusters in the internal region, showing severe local numerical fluctuations. In contrast, the absolute error cloud map of the RFM-Picard method used in this invention is extremely uniform and stable across the entire domain, and the transition at the subdomain boundaries is extremely smooth. The overall magnitude of its absolute error is significantly lower than that of the existing methods. This intuitive comparison of spatial errors conclusively proves that the Jacobian-less iterative mechanism of this invention is not only more robust in algebraic solution, but also perfectly approximates the original real physical manifold with extremely low local reconstruction errors, eliminating the local distortion and non-physical oscillation problems that are easily generated in sparse inverse problems.

[0112] Example 6

[0113] In bridge on-site monitoring, the incoming flow parameters are often unknown. This embodiment demonstrates how the system performs parameter identification and synchronous flow field reconstruction.

[0114] Because the unknown parameter Re is strongly coupled with the nonlinear convection term, mixing it with tens of thousands of network weights for overall high-dimensional gradient descent can easily lead to local optima or divergence. Therefore, this embodiment introduces an alternating optimization strategy for a peel-off solution. In each alternating iteration:

[0115] (1) Reconstructing the flow field: First, fix the current Re estimate, and then directly solve the weighted linear system. Obtain the random feature expansion coefficient matrix of the current step in one go. This allows us to reconstruct an approximate solution for the current global flow field.

[0116] (2) Update parameters: fix the coefficient matrix obtained in step 1. Based solely on the residuals of the actual velocity measurement data at extremely sparse internal observation points and the residuals of the partial differential equation governing equations, the value of the unknown parameter Re is independently updated through scalar projection or scalar optimization.

[0117] like Figure 10 As shown, the above two steps are performed alternately until iterative convergence. Comparative results show that in the parameter identification and flow field synchronous reconstruction task, as the number of observation data points increases, both the proposed RFM-Picard method and the existing RFM-Newton method can overcome unsteadiness and achieve convergence, successfully learning the true Reynolds value. However, a deep comparison of the error convergence curves clearly shows that, under the same data sparsity, the RFM-Picard framework in this embodiment consistently exhibits lower L2 relative errors for each physical quantity than the robust Newton method, demonstrating higher reconstruction fidelity and better convergence evolution characteristics. Especially in the low-frequency range where data points are extremely limited, the error reduction trend of RFM-Picard is smoother and more stable.

[0118] In summary, the alternating optimization framework of this invention, combined with the Jacobi-less iterative mechanism, not only fundamentally isolates the high-dimensional non-convex risk brought about by mixing parameters with a large number of network coefficients for optimization, but also provides a reverse modeling capability with greater accuracy and evolutionary robustness than the robust Newton method while ensuring accurate parameter identification.

Claims

1. A method for iterative stochastic characteristic flow field deduction and reconstruction in bridge wind engineering, characterized in that, The method includes the following steps: Step 1: Acquisition of Input Data for Complex Structure Flow Field and Construction of Spatiotemporal Region Decomposition Basis Functions: Input data of the flow field environment in physical space is acquired. Based on the geometric boundaries of the bridge structure and the scale characteristics of the flow field computational domain, the global spatiotemporal computational domain of the flow field is divided into multiple sub-regions. For each sub-region, a local affine mapping from physical coordinates to standard reference coordinates is established. A single-layer neural network with randomly fixed hidden layer weights and biases during initialization and not involved in training is used to generate spatiotemporal random feature basis functions. Combined with a spatiotemporal unit decomposition function with compact support characteristics, an approximate expression of the global spatiotemporal flow field parameters is constructed. Step 2: Decoupling of nonlinear fluid dynamics partial differential equations based on Picard iteration: For the nonlinear convection term in the nonlinear control equation of fluid dynamics, the velocity field approximation result of the previous iteration step is used as the known fluid background field and substituted into the nonlinear convection term of the equation in the current step to avoid the Jacobian matrix evaluation process, thereby achieving linear decoupling of the nonlinear control equation. Step 3: Fine assembly of the global overdetermined linear equation system: The global overdetermined linear equation system is assembled by globally assembling the momentum control equation residual matrix calculated from internal configuration points, the mass conservation matrix calculated based on divergence, the boundary constraint matrix calculated based on boundary points or sparse observation points, the initial condition matrix calculated based on the initial time point, and the interface matrix constructed to enforce the continuous condition. The unknowns to be solved in the global overdetermined linear equation system are a global unified random feature expansion coefficient column vector composed of the local expansion coefficients of each sub-region. Step 4: Algebraic Row Balancing and Physical Enhancement Layered Weighting: Construct a diagonal scaling matrix to perform algebraic row balancing on the global overdetermined linear equation system. The diagonal elements of the diagonal scaling matrix are determined by the inverse of the infinite norm of the corresponding row vectors of the global overdetermined linear equation system. Based on this, construct a physical space weight diagonal matrix to apply dominant physical penalty weights, which are at least 10 to 1000 times higher than the weights of the momentum control equations, to the mass conservation residuals, boundary conditions or sparse observation point constraints, and the continuity conditions of the interfaces between adjacent sub-regions, thereby generating a weighted linear system with dual enhancements. Step 5: Weighted system solution and flow field parameter derivation and inversion for forward and inverse problems: The weighted linear system is solved by the linear least squares direct solution algorithm to obtain all the random feature expansion coefficients and reconstruct the global spatiotemporal flow field parameters, which are used for the derivation of the fluid dynamic performance of structures such as bridges or for safety early warning.

2. The method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering according to claim 1, characterized in that, In step one, the single-layer neural network generates the spatiotemporal random feature basis function by combining a nonlinear activation function, wherein the nonlinear activation function is a hyperbolic tangent activation function.

3. The method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering according to claim 1, characterized in that, In step one, the spatiotemporal unit decomposition function is a local support function constructed based on the indicator function; the approximate expression of the global spatiotemporal flow field parameters is to multiply the spatiotemporal random characteristic basis functions in each sub-region with the corresponding spatiotemporal unit decomposition function, and then linearly superimpose the summation over all sub-regions to obtain the global spatiotemporal flow field parameters.

4. The method according to claim 1, characterized in that, In step two, the fluid dynamics nonlinear control equation is the incompressible Navier-Stokes equation.

5. The method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering according to claim 1, characterized in that, When the fluid dynamics nonlinear control equations contain unknown physical parameters, step five employs the following alternating optimization strategy for parameter inversion and flow field reconstruction: In each alternating iteration, firstly, the estimated value of the current unknown physical parameter is fixed, and the weighted linear system is solved to obtain the stochastic characteristic expansion coefficients, reconstructing the approximate solution of the global spatiotemporal flow field parameters for the current step; then, the approximate solution of the global spatiotemporal flow field parameters is fixed, and based on the residuals of the actual measurement data at the internal sparse observation points and the residuals of the partial differential equation control equations, the unknown physical parameters are directly solved and updated individually using a direct algebraic solution based on residual minimization or a least squares projection algorithm; this process is repeated alternatingly until the iteration converges.

6. The method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering according to claim 5, characterized in that, After the flow field reconstruction is completed, when the reconstructed wake characteristics meet the structural resonance induction conditions, that is, when the difference between the vortex shedding frequency of the wake and the natural frequency of the bridge structure is within the preset resonance danger threshold range, or when the aerodynamic amplitude induced by the flow field exceeds the preset safety threshold, a wind-induced vibration or fluid resonance safety warning signal or three-dimensional flow field visualization monitoring data for the bridge structure is automatically generated.

7. A system for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering, implementing the method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering as described in any one of claims 1-6, characterized in that, The system includes: The spatiotemporal region decomposition and basis function construction module is used to acquire the flow field environment input data in physical space. Based on the geometric boundary of the bridge structure and the scale characteristics of the flow field computation domain, the global spatiotemporal computation domain is divided into multiple sub-regions. A local affine mapping from physical coordinates to standard reference coordinates is established for each sub-region. Spatiotemporal random feature basis functions are generated using a single-layer neural network that is randomly fixed during initialization and does not participate in training. Combined with the spatiotemporal unit decomposition function with compact support characteristics, an approximate expression of the global spatiotemporal flow field parameters is constructed. The nonlinear equation Pica iteration decoupling module is used to address the nonlinear convection term in the incompressible Navier-Stokes equations. It employs Pica iteration to substitute the approximate velocity field result from the previous iteration step into the current step equation as a known fluid background field, thus avoiding the Jacobian matrix evaluation process and achieving linear decoupling of the nonlinear control equations. Global overdetermined equation assembly module: used to assemble a global overdetermined linear equation system with the column vector of coefficients of the global unified stochastic feature to be solved as unknowns, based on the residuals of the momentum control equation after linear decoupling, the residuals of mass conservation, the boundary conditions or sparse observation point constraints, and the continuity conditions of the interface between adjacent sub-regions. The algebraic and physical dual-weighting module is used to construct a diagonal scaling matrix whose diagonal elements are determined by the inverse of the infinite norm of the row vectors corresponding to the global overdetermined linear equation system, complete the algebraic row balancing process, and construct the physical space weight diagonal matrix. It applies physical penalty weights that are 10 to 1000 times higher than the weights of the momentum control equations to the mass conservation residuals, boundary constraints, and interface continuity conditions, thereby generating a dual-enhanced weighted linear system. The weighted system solution and flow field deduction and early warning module is used to solve the weighted linear system using the linear least squares algorithm, obtain the random feature expansion coefficients and reconstruct the global spatiotemporal flow field parameters, complete the deduction of the hydrodynamic performance of the bridge structure, and automatically generate wind-induced vibration or fluid resonance safety early warning signals or three-dimensional flow field visualization monitoring data when the wake feature triggers the resonance danger threshold or the aerodynamic amplitude exceeds the safety threshold.

8. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering as described in any one of claims 1-6.

9. A computer program product, characterized in that, It includes a computer program or instructions that, when executed by a processor, implement a method for iterative stochastic characteristic flow field deduction and reconstruction for bridge wind engineering as described in any one of claims 1-6.

10. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the program or instruction is executed by the processor, it implements the method for iterative stochastic characteristic flow field deduction and reconstruction of bridge wind engineering as described in any one of claims 1-6.

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