Bridge support dynamic digital twinborn model construction method based on 4D Gaussian sputtering

Abstract

The invention discloses a method for constructing a dynamic digital twinborn model of a bridge support based on 4D Gaussian sputtering. The method comprises the following steps: acquiring dynamic evolution original data of the bridge support; performing three-dimensional sparse point cloud reconstruction and Gaussian primitive parameterization through an SfM algorithm to obtain an initial static Gaussian model; introducing a deformation field function based on a multi-layer perceptron (MLP) to perform time sequence correction on the center, direction and shape of a Gaussian element in the initial static Gaussian model; pixel-level correction is carried out through a differentiable sputtering renderer, a multi-objective loss function is constructed, primitive parameters and MLP deformation field parameters are updated through back propagation of an Adam optimizer, and an optimized 4D Gaussian model is output; dynamically adjusting the density of the Gaussian primitives according to the motion significance of the Gaussian primitives and a regional density strategy, and outputting a space-time adaptive lightweight 4D Gaussian model; the model is embedded into a bridge intelligent operation and maintenance platform, a bridge support 4D dynamic digital twinning body is output, and seamless conversion from an algorithm model to industrial-grade digital twinning is achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge structure health monitoring, and more particularly relates to a bridge support dynamic digital twin model construction method based on 4D Gaussian sputtering. BACKGROUND

[0002] As the core force transmission component connecting the upper structure and the lower structure of the bridge, the operation state of the bridge support directly determines the overall structural safety and long-term service performance of the super-large bridge. Under the existing technical conditions, the support state monitoring mainly relies on a network of physical sensors such as displacement meters and accelerometers for discrete point monitoring. This kind of method has the following deficiencies in providing high-precision, continuous spatial and temporal resolution dynamic sensing capability:

[0003] (1) Insufficient spatial coverage: only limited data of preset measuring points can be obtained, and it is difficult to capture the global three-dimensional deformation field of the support, and the spatial resolution is ≤10 cm;

[0004] (2) Weak dynamic perception: lack of continuous spatio-temporal analysis capability for transient impact response and micro-displacement evolution and other key dynamic behaviors;

[0005] (3) Lack of state correlation: the mapping relationship between physical monitoring data and structural damage relies on empirical models, and it is difficult to establish a visual expression of the mechanical state.

[0006] Although the implicit three-dimensional reconstruction technology such as neural radiation field (NeRF) has made progress in static scenes in recent years, its implicit expression method has the problems of high computational cost and low rendering efficiency in dynamic engineering monitoring scenes, which makes it difficult to meet the requirements of real-time and editability of bridge engineering, and the specific manifestations are as follows:

[0007] (1) Computational efficiency bottleneck: the rendering process highly dependent on neural network parameter optimization is extremely time-consuming, making it difficult to meet the real-time requirement;

[0008] (2) Poor engineering adaptability: the implicit expression method is difficult to integrate mechanical prior knowledge, and has poor editability for support kinematic parameters (such as rotation angle and slip amount);

[0009] (3) Dynamic expansion limitations: the 4D-NRF method for time-varying scenes has problems such as poor temporal consistency and motion artifacts. SUMMARY

[0010] In view of the above defects or improvement needs of the prior art, the present application provides a bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering, which realizes four fundamental breakthroughs through the three-order innovation of "4D Gaussian primitive explicit expression + MLP physical driven deformation field + dynamic density self-adaptation": for the first time, millimeter-level spatiotemporal resolution support dynamic holographic modeling is realized in an engineering scenario; the real-time barrier of dynamic reconstruction is broken (from minute-level to millisecond-level response); the first quantifiable strain / displacement bridge digital twin standard model is established; the lightweight model supports seamless embedding of industrial platforms, directly serving intelligent operation and decision-making; through the innovative 4D Gaussian sputtering technology, the deficiencies of the prior art in spatial coverage, dynamic perception, mechanical state visualization, computational efficiency, engineering adaptability, dynamic expandability, model lightweight, and interactive display are comprehensively solved, providing an efficient, accurate, and real-time solution for dynamic monitoring and health diagnosis of bridge supports.

[0011] In order to achieve the above-mentioned purpose, one aspect of the present application provides a bridge support dynamic digital twin model construction method based on 4D Gaussian sputtering, comprising the following steps:

[0012] S1: obtaining original visual data of dynamic evolution of a bridge support; the original visual data is a structured triple data set containing a time label, a multi-view image set, and a corresponding camera pose;

[0013] S2: based on the multi-view image set at the initial time and the corresponding camera pose in the original visual data, performing three-dimensional sparse point cloud reconstruction through an SfM algorithm, and parameterizing each three-dimensional point in the reconstructed point cloud with a Gaussian primitive, to obtain an initial static Gaussian model;

[0014] S3: introducing a deformation field function based on a multi-layer perceptron MLP to sequentially correct the Gaussian ellipsoid center, direction, and shape in the initial static Gaussian model, and expanding it to a spatiotemporal continuous expression, to output a parameterized dynamic 4D Gaussian model;

[0015] S4: performing pixel-level correction on the dynamic 4D Gaussian model through a differentiable sputtering renderer, constructing a multi-objective loss function, and jointly updating the primitive parameters and MLP deformation field parameters through an Adam optimizer through backpropagation, to output an optimized 4D Gaussian model;

[0016] S5: dynamically adjusting the Gaussian primitive density according to the motion saliency of the Gaussian primitive and the regional density strategy, to output a spatiotemporal self-adaptive lightweight 4D Gaussian model;

[0017] S6: Derive the complete trajectory dataset of all Gaussian primitives in the time domain to encapsulate the time-varying primitive parameters, embed the spatiotemporal adaptive lightweight 4D Gaussian model into the bridge intelligent operation and maintenance platform through WebGL technology or Unity engine, and perform dynamic interactive display to output the standardized 4D dynamic digital twin of the bridge support.

[0018] Further, step S2 comprises:

[0019] SIFT / SURF feature point cross-view matching and bundle adjustment are used to optimize the multi-view image set and the corresponding camera pose at the initial time, and three-dimensional sparse point cloud reconstruction is completed;

[0020] Each three-dimensional point in the reconstructed point cloud directly inherits the point coordinates as the center position of the Gaussian primitive; the covariance matrix is calculated through neighborhood point cloud principal component analysis (PCA) to determine the ellipsoid direction and scale, the color attribute is generated by fitting multi-view color observations using spherical harmonic functions (SH), and the transparency is uniformly initialized, and finally the initial static Gaussian model composed of N parameterized ellipsoids is output, realizing the conversion of the support structure from discrete point cloud to explicit renderable primitive;

[0021] The initial static Gaussian model in step S2 is represented by formula (1):

[0022] G i ={μ i ,∑ i ,C i ,α i ,Y i}(1)

[0023] Wherein, μ i is the center position of the Gaussian primitive i, μ i ∈R 3 , R represents a real number set, R 3 indicates that the center position of the Gaussian primitive is a three-dimensional real vector; ∑ i is a covariance matrix, ∑ i ∈R 3x3 , which represents the ellipsoid direction and scale, and the covariance matrix is a 3×3 real matrix; C i is the RGB color vector of the Gaussian primitive i; α i is the transparency of the Gaussian primitive i, α i ∈[0,1]; Y i is the spherical harmonic function coefficient.

[0024] Further, step S3 comprises:

[0025] The initial static Gaussian model inputs initial Gaussian cell parameters and time variables, outputs center position offset by position deformation field, and outputs covariance matrix correction by morphology deformation field, to dynamically generate real-time Gaussian cell position and morphology;

[0026] The real-time Gaussian cell position is represented by equation (2):

[0027]

[0028] Wherein, μ i (t) is the center position of the i-th Gaussian cell at time t; is the center position of the i-th Gaussian cell at the initial time; is the position deformation field function, a vector-valued function learned by multi-layer perception MLP, which outputs the displacement correction of the cell center at time t;

[0029] The real-time Gaussian cell morphology is represented by equation (3):

[0030]

[0031] Wherein, ∑ i (t) is the covariance matrix of the i-th Gaussian cell at time t, which controls the direction and scale of the ellipsoid cell i at time t; is the covariance matrix of the i-th Gaussian cell at the initial time, which is a 3x3 matrix, describing the size and direction of the ellipsoid cell at the initial time; is the morphology deformation field function, a matrix-valued function learned by multi-layer perception MLP, which outputs the deformation correction of the covariance matrix of the cell center at time t;

[0032] The dynamic 4D Gaussian model expression is as follows:

[0033] G i (t) = { μ i (t), ∑ i (t), C i , α i , Y i}

[0034] Wherein, G i (t) is the dynamic expression of the i-th Gaussian cell at time t; ∑ i (t) is the covariance matrix of the i-th Gaussian cell at time t.

[0035] Further, step S4 comprises:

[0036] The dynamic 4D Gaussian model and the real image dataset generated in the input step S3 are input into the differentiable sputter rendering device, and a differentiable rendering is performed on each pixel p at each timestamp to obtain a color prediction value I(p, t) of the rendered image at the pixel p and the timestamp t;

[0037] According to the color prediction value I(p, t) of the rendered image at the pixel p and the timestamp t and the color value I gt (p, t) of the real image at the pixel p and the timestamp t, a multi-objective loss function is constructed;

[0038] Further, the color prediction value I(p, t) of the rendered image at the pixel p and the timestamp t is expressed as:

[0039]

[0040] wherein N is a Gaussian primitive set affecting the current pixel p; α i is the transparency, α i ∈ [0, 1], which determines the contribution weight of the primitive i to the final color; C i is an RGB color vector, which represents the color attribute of the primitive i; represents that the larger the ellipsoid size trace is, the smaller the primitive space influence range is; x p ∈ R 3 represents the coordinates of the pixel p in the three-dimensional space; exp(·) is a Gaussian kernel function, which calculates the spatial influence weight of the primitive on the pixel.

[0041] Further, the multi-objective loss function is expressed as:

[0042]

[0043] wherein ‖I(p, t)-I gt (p, t)‖1 represents a reconstruction loss, which is used to calculate the absolute error of I(p, t) of the rendered image and I gt (p, t) of the real image at the pixel level; λ1 is a reconstruction loss weight coefficient; SSIM(I, I gt ) is a structural similarity index of the rendered image and the real image, which is used to evaluate the perceptual similarity of the rendered image and the real image in three dimensions of brightness, contrast, and structure, and the value range is [0, 1], and 1 represents complete consistency; λ2 is a structural similarity loss weight coefficient; R(θ) is a regularization function, which punishes abnormal deformation of the primitive; λ3 is a regularization loss weight coefficient; the hyperparameters λ1≥0, λ2≥0, and λ3≥0.

[0044] Further, the step S5 comprises:

[0045] calculating a significance index of the Gaussian primitive:

[0046]

[0047] wherein S i (t) is the saliency index value of the Gaussian cell i at time t, expressing the intensity of the change of the cell in the image projection space and time domain; is the spatial gradient of the rendered image at the projection position p i of the Gaussian cell i; Var Δt is the variance operator within the time window At; μ i (t) is the center position of the Gaussian cell i at time t;

[0048] The sub-region density strategy is executed:

[0049]

[0050] wherein δ is the upper threshold of the cell motion saliency, S i (t) > δ indicates a high motion area cell, which needs to be split or cloned; S i (t) < ε indicates a low saliency area cell, which needs to be deleted or merged with adjacent cells; ε represents the lower limit of the cell motion saliency.

[0051] Further, the expression of the spatio-temporal adaptive lightweight 4D Gaussian model is:

[0052]

[0053] wherein, represents the spatio-temporal adaptive lightweight 4D Gaussian model at time t;

[0054] G i (t) is the dynamic expression form of the i-th Gaussian cell at time t;

[0055] S i (t) is the saliency index value of the Gaussian cell i at time t, expressing the intensity of the change of the cell in the image projection space and time domain; ε is the lower limit of the cell motion saliency, used to eliminate low-impact cells; I(t) is the set of Gaussian cell indexes selected adaptively according to the current motion characteristics under the resource constraint; |S i (t) ≥ ε indicates that only the cells with sufficient dynamic importance at the current moment are retained.

[0056] Further, the expression of the standardized bridge support 4D dynamic digital twin in step S6 is:

[0057]

[0058] The second aspect of the application provides a bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering, for realizing the bridge support dynamic digital twin model construction method based on 4D Gaussian sputtering, comprising:

[0059] A space-time synchronous acquisition module is configured to acquire original visual data of dynamic evolution of a bridge support; the original visual data is a structured triple data set comprising a time label, a multi-view image set and a corresponding camera pose;

[0060] A static primitive modeling module is configured to construct an initial renderable Gaussian expression of the support; specifically, based on the multi-view image set and the corresponding camera pose at the initial time (t=0) in the original visual data, a three-dimensional sparse point cloud is reconstructed through an SfM (Structure from Motion) algorithm, and each three-dimensional point in the reconstructed point cloud is parameterized into a Gaussian primitive to obtain an initial static Gaussian model;

[0061] A dynamic field expansion module is configured to upgrade the static model to a 4D dynamic expression; specifically, the center, direction and shape of the Gaussian ellipsoid in the initial static Gaussian model are sequentially corrected by introducing a deformation field function based on a multi-layer perception (MLP) to expand into a space-time continuous expression, and a parameterized dynamic 4D Gaussian model is output;

[0062] A physics-driven optimization module is configured to correct model parameters to achieve visual-physical consistency; a pixel-level correction is performed on the dynamic 4D Gaussian model by a differentiable sputtering renderer, a multi-objective loss function is constructed, and the primitive parameters and MLP deformation field parameters are jointly updated through an Adam optimizer by back propagation, and an optimized 4D Gaussian model is output;

[0063] A density adaptive module is configured to dynamically adjust the primitive distribution to adapt to the motion complexity; specifically, the motion saliency of the Gaussian primitive is calculated, the Gaussian primitive density is dynamically adjusted according to the motion saliency and a regional density strategy, and a space-time adaptive lightweight 4D Gaussian model is output;

[0064] A twin generation module is configured to output a 4D digital twin available under a standardized working condition; time-varying parameters are encapsulated, time-varying trajectories are derived, the space-time adaptive lightweight 4D Gaussian model is embedded into a bridge intelligent operation and maintenance platform through WebGL technology or a Unity engine, dynamic interactive display is performed, and a standardized bridge support 4D dynamic digital twin is output.

[0065] Overall, the above technical solutions conceived by the application can achieve the following beneficial effects compared with the prior art:

[0066] (1) The bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering of the application can collect dynamic evolution image sequences through a multi-view synchronous trigger high-definition camera array, record the camera pose in combination with an inertial measurement unit (IMU) or a laser tracker, and generate a structured triple data set containing a time tag, a multi-view image set, and a corresponding camera pose. The SfM algorithm is used for three-dimensional sparse point cloud reconstruction, and a Gaussian model is further generated, which can comprehensively cover the global three-dimensional deformation field of the support and realize accurate perception of the overall structure of the support.

[0067] (2) The bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering of the application can introduce a deformation field function based on a multi-layer perception machine (MLP) to perform time sequence correction on the initial static Gaussian model, construct a parameterized dynamic 4D Gaussian model, and can capture the transient impact response and micro-displacement evolution of the support in real time, provide continuous spatiotemporal analysis capability, and meet the high requirements of bridge engineering for dynamic monitoring.

[0068] (3) The bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering of the application can directly map the mechanical state (such as the rotation angle and the slip amount) of the support to the geometric and color attributes of the model through the parameterized representation of the Gaussian model. Through a differentiable sputtering renderer, the dynamic 4D Gaussian model can be corrected at the pixel level, and in combination with an optimization algorithm, the visualization of the mechanical state can be realized, which provides an intuitive basis for the health monitoring and damage diagnosis of the bridge structure. The Gaussian sputtering rendering technology is adopted, the dynamic 4D Gaussian model is corrected at the pixel level through a differentiable renderer, and the parameters are updated in combination with an Adam optimizer. This method can ensure the rendering accuracy while significantly improving the calculation efficiency, and can meet the real-time requirements of bridge engineering.

[0069] (4) The bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering of the application can dynamically adjust the position and shape of the Gaussian element based on the deformation field function of the MLP, has good editability, and can adapt to the kinematic parameter changes of different bridge supports. Through the construction of the dynamic 4D Gaussian model, in combination with the differentiable rendering and optimization algorithm, the continuous motion and deformation modeling of the three-dimensional structure of the support on the time axis can be realized, the time sequence inconsistency and motion artifact problems are avoided, and the dynamic expandability is improved. The motion saliency of the Gaussian element is calculated, and the Gaussian element density is dynamically adjusted according to the regional density strategy, and a spatiotemporal adaptive lightweight 4D Gaussian model is output. This method can ensure the model accuracy while significantly reducing the calculation burden, and breaks through the limitations of traditional methods.

[0070] (5) The bridge support dynamic digital twin model construction method and system based on 4D Gaussian sputtering of the application realize dynamic interactive display by embedding the time-space adaptive lightweight 4D Gaussian model into the bridge intelligent operation and maintenance platform through WebGL technology or Unity engine. Users can control the historical state playback through a time slider, and map the eigenvalue changes of the covariance matrix to the local strain values of the support and color-encode them for visual superposition, thereby providing intuitive and real-time monitoring tools for bridge operation and maintenance personnel. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 FIG. 1 is a flowchart of a bridge support dynamic digital twin model construction method based on 4D Gaussian sputtering according to an embodiment of the application;

[0072] Figure 2 FIG. 2 is a structural diagram of a bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering according to an embodiment of the application;

[0073] Figure 3 FIG. 3 is a structural diagram of an electronic device according to an embodiment of the application. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical scheme and advantages of the application clearer, further detailed description will be made to the application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0075] As shown in FIG. 1, one aspect of the application provides a bridge support dynamic digital twin model construction method based on 4D Gaussian sputtering, which comprises the following steps: Figure 1

[0076] S1: Obtain original visual data of dynamic evolution of the bridge support; the original visual data is a structured triple data set containing a time label, a multi-view image set and a corresponding camera pose;

[0077] S2: Based on the multi-view image set at the initial time (t=0) and the corresponding camera pose in the original visual data, perform three-dimensional sparse point cloud reconstruction through an SfM (Structure from Motion) algorithm, and parameterize each three-dimensional point in the reconstructed point cloud with a Gaussian primitive, to obtain an initial static Gaussian model;

[0078] S3: Introduce a deformation field function based on a multi-layer perception (MLP) to sequentially correct the Gaussian ellipsoid center, direction and shape in the initial static Gaussian model, extend it to a time-space continuous expression, and output a parameterized dynamic 4D Gaussian model;​

[0079] S4: pixel-level correction of the dynamic 4D Gaussian model is performed by a differentiable sputtering renderer, a multi-target loss function is constructed, and the primitive parameters and MLP deformation field parameters are jointly updated by the Adam optimizer through back propagation, and an optimized 4D Gaussian model is output;

[0080] S5: motion saliency of the Gaussian primitive is calculated, the Gaussian primitive density is dynamically adjusted according to the motion saliency and the regional density strategy, and a spatio-temporal adaptive lightweight 4D Gaussian model is output;

[0081] S6: the complete trajectory dataset of all Gaussian primitives in the time domain is derived for time-varying primitive parameter packaging, the spatio-temporal adaptive lightweight 4D Gaussian model is embedded into the bridge intelligent operation and maintenance platform through WebGL technology or the Unity engine, dynamic interactive display is performed, and a standardized bridge support 4D dynamic digital twin is output.

[0082] Further, step S1 comprises:

[0083] A multi-view synchronous trigger high-definition camera array is arranged around the bridge support, a two-dimensional image sequence of the dynamic evolution of the support is continuously collected at a fixed time interval Δt, and camera space pose parameters (camera three-dimensional coordinates + orientation angle) of each frame of image are synchronously recorded in combination with an inertial measurement unit (IMU) or a laser tracker and bound to a millisecond-level precision timestamp, and finally a structured triple data set containing time labels, multi-view image sets and corresponding camera poses is generated Wherein, represents the image taken by the jth camera at time t; represents the camera pose (position + orientation) corresponding to the image taken by the jth camera at time t;

[0084] The present application can comprehensively cover the global three-dimensional deformation field of the support, and realize accurate perception of the overall structure of the support.

[0085] Further, step S2 comprises:

[0086] SIFT / SURF feature point cross-view matching and bundle adjustment are adopted to optimize the parameters of the multi-view image set and the corresponding camera pose at the initial time (t=0), and three-dimensional sparse point cloud reconstruction is completed;

[0087] The center position of each three-dimensional point in the reconstructed point cloud is directly inherited as the center position of the Gaussian primitive; the covariance matrix is calculated by principal component analysis (PCA) of the neighborhood point cloud to determine the ellipsoid direction and scale, the color attribute is generated by fitting the multi-view color observation value using spherical harmonic function (SH), and the transparency is uniformly initialized, and finally an initial static Gaussian model composed of N parameterized ellipsoids is output, realizing the conversion of the support structure from discrete point cloud to explicit renderable primitive;

[0088] The initial static Gaussian model in step S2 is represented by formula (1):

[0089] G i ={μ i ,∑ i ,C i ,α i ,Y i}(1)

[0090] Wherein, μ i is the center position of the Gaussian primitive i, μ i ∈R 3 , R represents the real number set, R 3 indicates that the center position of the Gaussian primitive is a three-dimensional real vector; ∑ i is the covariance matrix, ∑ i ∈R 3x3 , which represents the ellipsoid direction and scale, and the covariance matrix is a 3*3 real matrix; C i is the RGB color vector of the Gaussian primitive i, which describes the appearance attribute of the Gaussian primitive i; α i is the transparency of the Gaussian primitive i, α i ∈[0,1]; Y i is the spherical harmonic function coefficient, that is, the color distribution coefficient based on the spherical harmonic function, which is used to encode the color change under multi-view;

[0091] Further, step S3 includes:

[0092] The initial static Gaussian model inputs the initial Gaussian primitive parameters and the time variable, outputs the center position offset by the position deformation field, and outputs the covariance matrix correction by the shape deformation field, dynamically generates the real-time Gaussian primitive position and shape; finally, a parameterized dynamic 4D Gaussian model is output, realizing the continuous motion and deformation modeling of the support three-dimensional structure on the time axis;

[0093] The real-time Gaussian primitive position is represented by formula (2):

[0094]

[0095] (3) Wherein, μ i (t) is the center position of the i-th Gaussian primitive at time t; is the center position (three-dimensional spatial coordinates) of the i-th Gaussian cell at the initial time; is a position deformation field function, a vector-valued function learned by a multi-layer perceptron (MLP) to output the displacement correction of the cell center at time t;

[0096] The real-time Gaussian cell shape is represented by formula (3):

[0097]

[0098] wherein, i is the covariance matrix of the i-th Gaussian cell at time t (the real-time shape and orientation of the ellipsoid), that is, the dynamic covariance matrix, which controls the direction and scale of the ellipsoid cell i at time t; is the covariance matrix of the i-th Gaussian cell at the initial time, which is a 3x3 matrix, describing the size and direction of the ellipsoid cell at the initial time; is a shape deformation field function, a matrix-valued function learned by a multi-layer perceptron (MLP) to output the deformation correction of the covariance matrix of the cell center at time t;

[0099] The dynamic 4D Gaussian model expression is as follows:

[0100] G i (t)={μ i (t),∑ i (t),C i ,α i ,Y i}

[0101] wherein, i G i (t) is the dynamic expression of the i-th Gaussian cell at time t; and i (t) is the covariance matrix of the i-th Gaussian cell at time t;

[0102] The present application introduces a deformation field function based on a multi-layer perceptron (MLP) to perform time sequence correction on an initial static Gaussian model, dynamically generates real-time Gaussian cell position and shape, and constructs a parameterized dynamic 4D Gaussian model. The model can capture the transient impact response and micro-displacement evolution of the support in real time, provide continuous spatiotemporal analytical capability, and meet the high requirements of bridge engineering for dynamic monitoring.

[0103] Further, step S4 comprises:

[0104] The dynamic 4D Gaussian model generated in step S3 and the real image data set are input into a differentiable splatting renderer, and differentiable rendering (Differentiable Splatting) is performed on each pixel p at each timestamp to obtain the color prediction value I(p, t) of the rendered image at pixel p and time t:

[0105]

[0106] where N is the set of Gaussian basis elements that affect the current pixel p (the set of basis elements that contribute to the color of pixel p), the set of spatial indices; a i is the transparency, a i ∈ [0, 1] determines the contribution weight of basis element i to the final color (0 = completely transparent, 1 = completely opaque); C i is the RGB color vector, representing the color property of basis element i (usually encoded by spherical harmonics for view-dependent reflectance); represents the larger the size trace of the ellipsoid, the smaller the range of influence of the basis element in space; x p ∈ R 3 represents the coordinates of pixel p in three-dimensional space (calculated by the camera model); exp(·) is the Gaussian kernel function, which calculates the spatial influence weight of the basis element on the pixel (the closer to the center, the greater the contribution);

[0107] According to the color prediction value I(p, t) of the rendering image at pixel p and time t and the color value I gt (p, t) of the real image at pixel p and time t, a multi-objective loss function is constructed:

[0108]

[0109] where ‖I(p, t)-I gt (p, t)‖1 represents the reconstruction loss, which is used to calculate the absolute error of I(p, t) of the rendering image and I gt (p, t) of the real image at the pixel level; λ1 is the reconstruction loss weight coefficient; SSIM(I, I gt ) is the structural similarity index of the rendering image and the real image, which is used to evaluate the perceptual similarity of the rendering image and the real image in three dimensions of brightness, contrast and structure, and the value range is [0, 1], and 1 represents complete consistency; λ2 is the structural similarity loss weight coefficient; R(θ) is a regularization function that penalizes abnormal deformation of the basis element; λ3 is the regularization loss weight coefficient; the hyperparameters λ1≥0, λ2≥0, λ3≥0; the present application corrects the 4D Gaussian model parameters through the differentiable rendering, so that the dynamic rendering result approximates the real observation data;

[0110] The present application directly maps the mechanical state (such as the rotation angle, the slip amount, etc.) of the support into the geometry and color properties of the model through the parameterized representation of the Gaussian model. Through the pixel-level correction of the dynamic 4D Gaussian model by the differentiable sputtering renderer, and combined with the optimization algorithm, the visual expression of the mechanical state can be realized, which provides an intuitive basis for the health monitoring and damage diagnosis of the bridge structure.

[0111] Further, step S5 comprises:

[0112] Computing the saliency indicator of a Gaussian cell:

[0113]

[0114] where S i (t) is the saliency indicator value of the Gaussian cell i at time t, expressing the intensity of the variation of the cell in the image projection space and time domain; is the spatial gradient of the rendered image at the projection position p i of the Gaussian cell i; Var Δt is the variance operator over the time window At; μ i (t) is the center position of the Gaussian cell i at time t;

[0115] Performing the sub-region density strategy:

[0116]

[0117] where δ is the upper threshold of the cell motion saliency, usually set by statistical saliency analysis, generally the 90% quantile of the saliency indicator distribution in the training set, S i (t) > δ indicates a high motion area cell, which needs to be split (1 cell into 2) or cloned (copied and translated); S i (t) < ε indicates a low saliency area cell, which needs to be deleted or merged with adjacent cells; ε represents the lower limit of cell motion saliency, generally taking the 10% quantile of the saliency distribution in the training set, or setting a fixed small threshold (such as 0.01) to control the degree of model lightweight; at the same time, by constraining the total number of cells N≤5×10 6 to meet the real-time rendering requirements of GPU;

[0118] Further, the expression of the spatio-temporal adaptive lightweight 4D Gaussian model is:

[0119]

[0120] wherein, represents the spatio-temporal adaptive lightweight 4D Gaussian model at time t;

[0121] G i (t) is the dynamic expression form of the i-th Gaussian cell at time t;

[0122] S i (t) is the saliency indicator value of the Gaussian cell i at time t, expressing the intensity of the variation of the cell in the image projection space and time domain; ε is the lower limit of cell motion saliency (empirical value) for removing low-impact cells; I(t) is the set of Gaussian cell indexes selected adaptively according to the current motion characteristics under resource constraints; |Si (t) >= epsilon means: only keep primitives with sufficient dynamic importance at current time instant;

[0123] The present application carries out dynamic adjustment of Gaussian primitive density by quantifying motion saliency, and outputs a spatio-temporal adaptive lightweight model; the unsupervised motion analysis based on image gradient and the density and motion intensity coupling adjustment mechanism break through the contradiction between motion complexity and computational efficiency of traditional dynamic reconstruction methods.

[0124] Further, the step S6 comprises:

[0125] Deriving a complete trajectory dataset Q of all primitives in the time domain [0, T] to carry out time-varying primitive parameter packaging;

[0126]

[0127] The Gaussian parameters are converted into the PointCloud material of Three.js for the Web environment, and the GPU parallel sputtering rendering is realized by using the Compute Shader for the Unity platform;

[0128] The time slider is embedded in the bridge intelligent operation and maintenance platform to control the historical state playback, and the eigenvalue change of the covariance matrix Sigma i (t) is mapped to the local strain value of the support and is color-coded for visualization superposition, and a standardized 4D dynamic digital twin of the bridge support is output, thereby providing an intuitive and real-time monitoring tool for bridge operation and maintenance personnel;

[0129] The expression of the 4D dynamic digital twin of the bridge support is:

[0130]

[0131] The present application guarantees engineering reusability through parameter standardization packaging, breaks the landing bottleneck of a lightweight engine, and realizes physical-visual fusion interaction to directly hit the core demand of operation and maintenance, thereby realizing seamless conversion from an algorithm model to an industrial digital twin; the 4D Gaussian model is directly embedded into an industrial operation and maintenance platform for the first time, thereby breaking the bottleneck of traditional models in dynamic precision and real-time performance, and providing a digital twin service with millimeter-level spatio-temporal resolution for the bridge support.

[0132] As shown in Figure 2 The second aspect of the present application provides a bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering, which is used to realize the above-mentioned design method, and comprises:

[0133] The space-time synchronous acquisition module is used to acquire original visual data of dynamic evolution of the bridge support; the original visual data is a structured triple data set comprising a time label, a multi-view image set and a corresponding camera pose;

[0134] a static primitive modeling module, configured to construct an initial renderable Gaussian expression of the support; specifically, based on a multi-view image set at an initial time (t=0) in the original visual data and corresponding camera poses thereof, a three-dimensional sparse point cloud is reconstructed through an SfM (Structure from Motion) algorithm, and each three-dimensional point in the reconstructed point cloud is parameterized as a Gaussian primitive to obtain an initial static Gaussian model;

[0135] a dynamic field expansion module, configured to upgrade the static model to a 4D dynamic expression; specifically, the center, direction, and shape of the Gaussian ellipsoid in the initial static Gaussian model are sequentially corrected by introducing a deformation field function based on a multi-layer perception (MLP) to expand to a spatiotemporal continuous expression, and a parameterized dynamic 4D Gaussian model is output;

[0136] a physics-driven optimization module, configured to correct model parameters to achieve visual-physical consistency; a dynamic 4D Gaussian model is corrected at a pixel level by a differentiable sputtering renderer, and a multi-objective loss function is constructed, and the parameters of the primitive and the MLP deformation field are jointly updated by an Adam optimizer through back propagation, and an optimized 4D Gaussian model is output;

[0137] a density adaptive module, configured to dynamically adjust the distribution of primitives to adapt to the complexity of motion; specifically, the motion saliency of the Gaussian primitive is calculated, and the density of the Gaussian primitive is dynamically adjusted according to the motion saliency and a regional density strategy, and a spatiotemporally adaptive lightweight 4D Gaussian model is output;

[0138] a twin generation module, configured to output a 4D digital twin available for a standardized working condition; complete trajectory data sets of all primitives in the time domain are derived for time-varying primitive parameter packaging, the spatiotemporally adaptive lightweight 4D Gaussian model is embedded into a bridge intelligent operation and maintenance platform through WebGL technology or a Unity engine for dynamic interactive display, and a standardized 4D dynamic digital twin of the bridge support is output.

[0139] It should be noted that the bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering provided in the embodiment can be a computer program (including program code) running in a computer device, for example, the bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering is an application software; the bridge support dynamic digital twin model construction system based on 4D Gaussian sputtering can be used to execute the corresponding steps in the above method provided in the embodiments of the present application.

[0140] In some feasible implementations, the bridge bearing dynamic digital twin model construction system based on 4D Gaussian sputtering provided in this embodiment can be implemented in a combination of hardware and software. As an example, the bridge bearing dynamic digital twin model construction system based on 4D Gaussian sputtering provided in this application embodiment can be a processor in the form of a hardware decoding processor, which is programmed to execute the bridge bearing dynamic digital twin model construction method based on 4D Gaussian sputtering provided in this application embodiment. For example, the processor in the form of a hardware decoding processor can be one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0141] In some feasible implementations, the bridge bearing dynamic digital twin model construction system based on 4D Gaussian sputtering provided in this embodiment can be implemented in software. It can be software in the form of programs and plug-ins, and includes a series of modules to implement the bridge bearing dynamic digital twin model construction method based on 4D Gaussian sputtering provided in this embodiment of the invention.

[0142] A third aspect of the present invention also provides an electronic device, Figure 3 This is a schematic diagram of the electronic device in this embodiment, as shown below. Figure 3 As shown, the electronic device 1000 in this embodiment may include: a processor 1001, a network interface 1004, and a memory 1005. Furthermore, the electronic device 1000 may also include: a user interface 1003, and at least one communication bus 1002. The communication bus 1002 is used to implement communication between these components. The user interface 1003 may include a display screen and a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed RAM memory or a non-volatile memory, such as at least one disk storage device. Optionally, the memory 1005 may also be at least one storage device located remotely from the aforementioned processor 1001. Figure 3As shown, the memory 1005, which is a computer-readable storage medium, may include an operating system, a network communication module, a user interface module, and a device control application.

[0143] like Figure 1 In the electronic device 1000 shown, the network interface 1004 provides network communication functions; the user interface 1003 is mainly used to provide an input interface for users; and the processor 1001 can be used to call the device control application stored in the memory 1005 to implement the various steps of the method for constructing a dynamic digital twin model of a bridge support based on 4D Gaussian sputtering.

[0144] It should be understood that in some feasible implementations, the processor 1001 described above may be a central processing unit (CPU), which may also be other general-purpose processors, DSPs, ASICs, FPGAs, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

[0145] In specific implementation, the aforementioned electronic device 1000 can perform the above-described actions through its built-in functional modules. Figure 1 The implementation methods provided for each step are detailed in the above-mentioned implementation methods, and will not be repeated here.

[0146] This application also provides a computer-readable storage medium storing a computer program that is executed by a processor to implement... ​ The methods provided in each step are detailed in the implementation methods provided in the above steps, and will not be repeated here.

[0147] Any references to memory, storage, database, or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0148] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering, characterized in that, Includes the following steps: S1: Obtain the raw visual data of the dynamic evolution of bridge bearings; the raw visual data is a structured triplet dataset containing time labels, multi-view image sets and corresponding camera poses. S2: Based on the multi-view image set at the initial moment and its corresponding camera pose in the original visual data, three-dimensional sparse point cloud is reconstructed using the SfM algorithm, and Gaussian meta-parameterization is performed on each three-dimensional point in the reconstructed point cloud to obtain an initial static Gaussian model. S3: By introducing a deformation field function based on a multilayer perceptron (MLP), the center, orientation, and shape of the Gaussian ellipsoid in the initial static Gaussian model are temporally corrected, extended into a spatiotemporally continuous expression, and a parameterized dynamic 4D Gaussian model is output. S4: The dynamic 4D Gaussian model is pixel-level corrected by a differentiable sputtering renderer, and a multi-objective loss function is constructed. The primitive parameters and MLP deformation field parameters are jointly updated by backpropagation through the Adam optimizer, and the optimized 4D Gaussian model is output. S5: Dynamically adjust the Gaussian density based on the motion saliency of Gaussian elements and the regional density strategy to output a spatiotemporally adaptive lightweight 4D Gaussian model. S6: Export the complete trajectory dataset of all Gaussian primitives in the time domain, encapsulate the time-varying primitive parameters, and embed the spatiotemporally adaptive lightweight 4D Gaussian model into the bridge intelligent operation and maintenance platform through WebGL technology or Unity engine for dynamic interactive display, and output a standardized 4D dynamic digital twin of bridge support.

2. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 1, characterized in that: Step S2 includes: SIFT / SURF feature point cross-view matching and bundle adjustment are used to optimize the parameters of the initial multi-view image set and its corresponding camera pose to complete the 3D sparse point cloud reconstruction. The coordinates of each 3D point in the reconstructed point cloud are directly inherited as the center position of the Gaussian primitive. The covariance matrix is ​​calculated by principal component analysis (PCA) of the neighborhood point cloud to determine the ellipsoid orientation and scale. The color attributes are generated by fitting multi-view color observations using the spherical harmonic function SH and the transparency is uniformly initialized. Finally, the initial static Gaussian model composed of N parameterized ellipsoids is output, realizing the transformation of the support structure from discrete point cloud to explicit renderable primitive. The initial static Gaussian model in step S2 is expressed by equation (1): G i ={μ i ,∑ i ,C i ,a i ,Y i }(1) Where, μ i μ is the center position of Gaussian element i. i ∈R 3 R represents the set of real numbers. 3 The center of the Gaussian element is a three-dimensional real vector; ∑ i Let ∑ be the covariance matrix. i ∈R 3x3 The covariance matrix represents the ellipsoidal orientation and scale; it is a 3×3 real matrix. i Let α be the RGB color vector of Gaussian element i; i For the transparency of Gaussian element i, α i ∈[0,1];Y i These are the coefficients of the spherical harmonic function.

3. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 2, characterized in that: Step S3 includes: The initial Gaussian element parameters and time variables are input into the initial static Gaussian model. The center position offset is output by the position deformation field and the covariance matrix correction is output by the shape deformation field, and the real-time Gaussian element position and shape are dynamically generated. The real-time position of the Gaussian element is expressed by equation (2): Where, μ i (t) represents the center position of the i-th Gaussian element at time t; Let be the center position of the i-th Gaussian element at the initial time; The position deformation field function is the vector-valued function learned by the multilayer perceptron (MLP) that outputs the displacement correction of the primitive center at time t. The real-time Gaussian metamorphism is represented by equation (3): Where, ∑ i (t) is the covariance matrix of the i-th Gaussian element at time t, which controls the direction and scale of the ellipsoidal element i at time t; Let be the covariance matrix of the i-th Gaussian element at the initial time, which is a 3×3 matrix describing the size and orientation of the ellipsoidal element at the initial time; The shape deformation field function is the deformation correction of the primitive center with respect to the covariance matrix at time t, which is output by the matrix-valued function learned by the multilayer perceptron (MLP). The expression for the dynamic 4D Gaussian model is as follows: G i (t)={μ i (t),∑ i (t),C i ,α i ,Y i } Among them, G i (t) represents the dynamic representation of the i-th Gaussian element at time t; ∑ i (t) is the covariance matrix of the i-th Gaussian element at time t.

4. A method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to any one of claims 1-3, characterized in that: Step S4 includes: Input the dynamic 4D Gaussian model and real image dataset generated in step S3 into the differentiable sputtering renderer, perform differentiable rendering on pixel p at each time stamp, and obtain the color prediction value I(p,t) of the rendered image at pixel p and time t. The color prediction value I(p,t) of the rendered image at pixel p and time t is compared with the color value I of the real image at pixel p and time t. gt (p,t) constructs a multi-objective loss function.

5. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 4, characterized in that: The expression for the color prediction value I(p,t) of the rendered image at pixel p and time t is: Where N is the set of Gaussian elements that affect the current pixel p; α i For transparency, α i ∈[0,1], determines the contribution weight of primitive i to the final color; C i This is an RGB color vector representing the color attribute of primitive i; This indicates that the larger the ellipsoidal trace, the smaller the influence range of the primitive space; x p ∈R 3 This represents the coordinates of pixel p in three-dimensional space; exp(·) is the Gaussian kernel function, which calculates the spatial influence weight of the primitive on the pixel.

6. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 5, characterized in that: The expression for the multi-objective loss function is as follows: Among them, ‖I(p,t)-I gt (p,t)‖1 represents the reconstruction loss, used to calculate the difference between I(p,t) of the rendered image and I of the ground image. gt (p,t) represents the absolute error at the pixel level; λ1 is the reconstruction loss weight coefficient; SSIM(I,I) gt ) is the structural similarity index between the rendered image and the real image, used to evaluate the perceptual similarity between the rendered image and the real image in three dimensions: brightness, contrast, and structure. The value range is [0,1], where 1 indicates complete similarity; λ2 is the structural similarity loss weight coefficient; R(θ) is the regularization function, which penalizes abnormal deformation of primitives; λ3 is the regularization loss weight coefficient; the hyperparameters λ1≥0, λ2≥0, λ3≥0.

7. A method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to any one of claims 1-3, 5, and 6, characterized in that: Step S5 includes: Calculate the significance index of Gaussian elements: Among them, S i (t) is the significance index value of Gaussian element i at time t, which expresses the intensity of the change of this element in the image projection space and time domain; To render the image at the Gaussian element i-projection position p i Spatial gradient; Var Δt μ is the variance operator within the time window Δt; i (t) represents the center position of Gaussian element i at time t; Implement a region-specific density strategy: Where δ is the upper threshold for the significance of the elementary motion, S i (t)>δ represents a primitive in the high-motion region, which needs to be split or cloned; S i (t)<ε indicates a low-significance primitive, which needs to be deleted or its adjacent primitives merged; ε represents the lower limit of the significance of primitive movement.

8. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 7, characterized in that: The expression for the spatiotemporal adaptive lightweight 4D Gaussian model is as follows: in, This represents a spatiotemporally adaptive lightweight 4D Gaussian model at time t; G i (t) is the dynamic representation of the i-th Gaussian element at time t; S i (t) represents the significance index of Gaussian primitive i at time t, expressing the intensity of change of this primitive in the image projection space and time domain; ε is the lower limit of primitive motion significance, used to eliminate low-impact primitives; I(t) is the set of Gaussian primitive indices adaptively selected based on the current motion characteristics under resource constraints; |S i (t)≥ε means that only primitives that have sufficient dynamic importance at the current moment are retained.

9. The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering according to claim 8, characterized in that: The standardized 4D dynamic digital twin expression for the bridge bearing mentioned in step S6 is as follows:

10. A system for constructing dynamic digital twin models of bridge supports based on 4D Gaussian sputtering, characterized in that, The method for constructing a dynamic digital twin model of bridge bearings based on 4D Gaussian sputtering as described in any one of claims 1-9 includes: The time-space synchronous acquisition module is used to acquire raw visual data of the dynamic evolution of bridge bearings; the raw visual data is a structured triplet dataset containing time labels, multi-view image sets and corresponding camera poses. The static primitive modeling module is used to construct the initial renderable Gaussian representation of the support. Specifically, based on the multi-view image set at the initial time (t=0) in the original visual data and its corresponding camera pose, the three-dimensional sparse point cloud is reconstructed by the SfM (Structure from Motion) algorithm, and Gaussian primitive parameterization is performed on each three-dimensional point in the reconstructed point cloud to obtain the initial static Gaussian model. The dynamic field extension module is used to upgrade the static model to a 4D dynamic expression. Specifically, by introducing a deformation field function based on a multilayer perceptron (MLP), the center, orientation, and shape of the Gaussian ellipsoid in the initial static Gaussian model are temporally corrected, and extended to a spatiotemporally continuous expression, outputting a parameterized dynamic 4D Gaussian model. The physics-driven optimization module is used to correct model parameters to achieve visual-physical consistency. It performs pixel-level correction on the dynamic 4D Gaussian model through a differentiable sputtering renderer, constructs a multi-objective loss function, and jointly updates the primitive parameters and MLP deformation field parameters through backpropagation of the Adam optimizer, outputting the optimized 4D Gaussian model. The density adaptive module is used to dynamically adjust the distribution of primitives to adapt to the motion complexity. Specifically, by calculating the motion saliency of Gaussian primitives, the density of Gaussian primitives is dynamically adjusted according to the motion saliency and the regional density strategy, and a spatiotemporally adaptive lightweight 4D Gaussian model is output. The twin generation module is used to output standardized 4D digital twins usable under working conditions; it encapsulates time-varying parameters, exports time-varying trajectories, and embeds the spatiotemporally adaptive lightweight 4D Gaussian model into the bridge intelligent operation and maintenance platform through WebGL technology or Unity engine for dynamic interactive display, outputting standardized 4D dynamic digital twins of bridge supports.

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