A method for simulating spatial chloride erosion field of bridge pier based on three-dimensional gaussian process

Abstract

This invention relates to a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, comprising: constructing a three-dimensional spatial coordinate system for the bridge pier; constructing a sample dataset containing input features and output labels; constructing a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space; training to obtain the optimal Gaussian process regression model; interpolating and reconstructing the spatial erosion field of chloride ions in the entire bridge pier; and assessing the corrosion risk of the bridge pier based on the reconstructed chloride ion erosion field. The beneficial effects of this invention are: it comprehensively covers the spatiotemporal characteristics of chloride ion erosion in bridge piers, solving the problem that traditional one-dimensional and two-dimensional models cannot characterize the three-dimensional spatial erosion differences of the entire bridge pier.

Description

Technical Field

[0001] This invention belongs to the field of structural durability monitoring technology, and in particular relates to a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process. Background Technology

[0002] As the core load-bearing component of a bridge, the durability of bridge piers directly determines the bridge's service safety and lifespan. In coastal, marine, or winter salt-de-icing areas, chloride ions can penetrate the piers through the pores and cracks in the concrete surface. When the chloride ion concentration reaches a critical value, it can cause steel corrosion, leading to concrete spalling, reduced structural stiffness, and in severe cases, pier failure and bridge safety accidents. Therefore, accurately simulating the chloride ion corrosion process of bridge piers and understanding the spatial distribution and temporal evolution of chloride ions within the piers is of great significance for bridge durability assessment and maintenance decision-making.

[0003] Currently, the simulation of chloride ion erosion in bridge piers mainly adopts the traditional Fick diffusion law. This method has the following obvious drawbacks: First, it is limited in dimension. Existing studies mostly use one-dimensional diffusion models, which can only calculate chloride ion concentration along a single dimension, either radial or vertical, of the bridge pier. A few two-dimensional models can only achieve the coupling of the transverse and radial directions of the cross section, and cannot take into account the non-uniformity of the bridge pier in the radial, circumferential, and vertical three-dimensional space. However, the actual chloride ion erosion of bridge piers is affected by environmental, construction, and material factors, and exhibits significant three-dimensional spatial distribution characteristics. For example, the degree of erosion differs greatly between the coastal side and the leeward side, and between the splash zone and the atmospheric zone. Second, it has a deterministic deficiency. Traditional methods can only output a single fixed value of chloride ion concentration, and cannot quantify the random variability and uncertainty of chloride ion erosion. First, it ignores the influence of factors such as the discreteness of concrete materials, construction deviations, and fluctuations in environmental loads, resulting in a large deviation between the simulation results and the actual situation. Second, it has a high dependence on sampling. Traditional methods require a large amount of dense core sampling data to ensure simulation accuracy. However, core sampling of bridge piers is a destructive test, which cannot achieve dense sampling of the entire bridge. Only a small amount of discrete point data can be obtained, making it difficult to reconstruct the continuous chloride ion erosion field of the entire bridge pier from these discrete points. Third, it does not consider spatial correlation. Chloride ion erosion inside bridge piers has obvious spatial correlation. The chloride ion concentration at adjacent locations does not change abruptly. However, traditional methods use linear interpolation and other methods to supplement the concentration data between discrete points, which cannot characterize this spatial correlation, resulting in low simulation accuracy.

[0004] Gaussian processes (GPs), as a powerful probabilistic modeling tool, are inherently adept at handling random field modeling, small sample interpolation, and uncertainty quantification. They can accurately characterize the spatial correlation and random variability of variables using a small number of discrete samples and output the probability distribution (mean + variance) of the variables. Currently, they have been applied in fields such as aerospace structural damage assessment and geotechnical engineering parameter prediction. However, in the field of bridge pier chloride ion erosion simulation, there is no relevant technology to apply Gaussian processes to three-dimensional spatial + temporal joint modeling, which cannot solve the aforementioned technical problems of traditional methods.

[0005] Therefore, developing a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process to fill the technological gap in this field has become an urgent need in current bridge durability research. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process.

[0007] Firstly, a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process is provided, including:

[0008] S1. Construct a three-dimensional spatial coordinate system for the bridge piers, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space;

[0009] S2. Obtain discrete chloride ion concentration sampling data on the bridge piers and construct a sample dataset containing input features and output labels;

[0010] S3. Select the Gaussian process kernel function to construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space;

[0011] S4. Input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and optimize the model hyperparameters to obtain the optimal Gaussian process regression model.

[0012] S5. Virtual grid points are set up in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model. The statistical characteristic of chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the spatial erosion field of chloride ions in the entire bridge pier.

[0013] S6. Based on the reconstructed chloride ion erosion field and combined with the preset critical chloride ion concentration, assess the corrosion risk of the bridge piers and output an assessment report.

[0014] Preferably, the spatial dimension in S1 includes the radial, circumferential, and vertical dimensions of the pier, or the equivalent horizontal, longitudinal, and vertical dimensions based on the geometric shape of the pier; the time dimension is the service life of the pier.

[0015] Preferably, the sampling data in S2 includes measured values ​​of chloride ion concentration at different spatial locations and for different service years; the input features are spatial coordinates and time coordinates, and the output label is the chloride ion concentration value at the corresponding location.

[0016] Preferably, in step S3, before constructing the Gaussian process kernel function, a step of dimensionless or standardized processing of the input features is also included.

[0017] Preferably, the Gaussian process kernel function in S3 is a Matern kernel or a squared exponent SE kernel; the kernel function is used to characterize the correlation of chloride ion concentration in the spatial dimension and the evolutionary correlation in the time dimension.

[0018] Preferably, the hyperparameters in S4 include spatial correlation length and noise variance; the optimization of the hyperparameters is achieved using the maximum likelihood estimation method.

[0019] Preferably, the assessment of corrosion risk in S6 includes: identifying high-risk corrosion areas based on a comparison between the mean and critical chloride ion concentrations; and assessing the reliability of the high-risk corrosion areas based on the variance and / or confidence intervals; the assessment report includes erosion field visualization results, a three-dimensional envelope of corrosion risk, erosion field evolution projection results under different service years, and maintenance recommendations.

[0020] Secondly, a simulation system for the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process is provided for performing any of the methods described in the first aspect, including:

[0021] The building module is used to construct the three-dimensional spatial coordinate system of the bridge pier, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space;

[0022] The acquisition module is used to acquire discrete chloride ion concentration sampling data on bridge piers and construct a sample dataset containing input features and output labels.

[0023] The selection module is used to select the Gaussian process kernel function and construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space.

[0024] The input module is used to input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and to optimize the model hyperparameters to obtain the optimal Gaussian process regression model.

[0025] The deployment module is used to deploy virtual grid points in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model, and the statistical characteristic of the chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the chloride ion spatial erosion field of the entire bridge pier.

[0026] The assessment module is used to assess the corrosion risk of bridge piers based on the reconstructed chloride ion erosion field and a preset critical chloride ion concentration, and output an assessment report.

[0027] Thirdly, a computer storage medium is provided, wherein a computer program is stored therein; when the computer program is run on a computer, the computer causes the computer to perform any of the methods described in the first aspect.

[0028] Fourthly, an electronic device is provided, comprising:

[0029] Memory, used to store computer programs;

[0030] A processor for executing the computer program to implement the method as described in any of the first aspects.

[0031] The beneficial effects of this invention are:

[0032] 1. This invention breaks through the dimensional limitations of traditional methods and establishes for the first time a four-dimensional Gaussian process erosion random field model of bridge piers in three-dimensional space (radial r, circumferential θ, vertical z) plus time t. It fully covers the spatiotemporal characteristics of chloride ion erosion of bridge piers and solves the problem that traditional one-dimensional and two-dimensional models cannot characterize the three-dimensional spatial erosion differences of the entire bridge pier. The simulation results are more in line with the actual engineering scenario.

[0033] 2. This invention utilizes the probabilistic modeling advantages of Gaussian processes to quantify the uncertainty of chloride ion concentration, outputting the mean, variance, and confidence interval for each location. This overcomes the shortcomings of traditional deterministic methods in quantifying random variability, providing a scientific basis for the probabilistic assessment of bridge pier durability and improving the reliability of the assessment results.

[0034] 3. This invention requires only a small amount of discrete core sampling data to reconstruct the continuous erosion field of the entire bridge pier, eliminating the need for intensive destructive sampling, reducing detection costs and minimizing damage to the bridge pier structure. It also solves the problems of high sampling dependence and low interpolation accuracy in traditional methods, thus addressing the pain point of sparse sampling data in actual engineering projects.

[0035] 4. This invention uses kernel functions to characterize the spatial and temporal correlation of chloride ion erosion, which can accurately reflect the erosion differences at different locations and with different service years, such as the erosion differences between the coastal side and the leeward side, the splash zone and the atmospheric zone, as well as the evolution of erosion over time, providing more accurate support for maintenance decisions.

[0036] 5. This invention is highly practical and easy to operate. It can be modeled using on-site measured data or simulation data, and is suitable for bridge piers of different types (cylindrical, rectangular) and different environments (coastal, coastal, winter salting). It also provides a complete visual evaluation report. It has high engineering application value and can be widely used in the field of bridge structure durability monitoring, evaluation and maintenance. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the three-dimensional spatial coordinate system of the bridge piers provided in the embodiments of this application;

[0038] Figure 2 A flowchart of a method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, provided in an embodiment of this application;

[0039] Figure 3 The full-pier chloride ion concentration field reconstruction cloud map provided in the embodiments of this application;

[0040] Figure 4 This is a system structure block diagram provided for an embodiment of this application. Detailed Implementation

[0041] The present invention will be further described below with reference to embodiments. The following content is primarily used to clarify the method logic, technical composition, and verification framework of the present invention, and does not constitute a limitation on the scope of protection of the present invention. For those skilled in the art, equivalent substitutions, parameter adjustments, or process optimizations made without departing from the principles of the present invention should all be considered within the scope of protection of the present invention.

[0042] Example 1:

[0043] To address the limitations of existing bridge pier chloride ion erosion simulation methods, such as dimensionality constraints, deterministic deficiencies, high sampling dependence, and inability to characterize spatial correlations, Embodiment 1 of this application provides a bridge pier chloride ion spatial erosion field simulation method based on a three-dimensional Gaussian process. This method achieves three-dimensional spatial and temporal joint simulation of bridge pier chloride ion erosion, accurately characterizes the spatial correlation and random variability of erosion, reconstructs the continuous erosion field of the entire bridge pier through a small amount of discrete sampling data, and quantifies the uncertainty of erosion, providing a scientific basis for bridge pier durability assessment and maintenance decisions.

[0044] Specifically, such as Figure 2 As shown, the method provided in this application includes:

[0045] S1. Construct a three-dimensional spatial coordinate system for the bridge piers, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space.

[0046] The spatial dimensions mentioned in S1 include the three dimensions of the bridge pier: radial (r), circumferential (θ), and vertical (z), or the equivalent lateral dimension based on the bridge pier's geometry. Vertical Vertical Three dimensions; the time dimension is the service life t of the bridge pier, ranging from 0 to the design service life, used to characterize the time evolution process of chloride ion erosion.

[0047] Specifically, the three-dimensional spatial coordinate system is determined based on the cross-sectional shape of the bridge pier:

[0048] For cylindrical bridge piers, a cylindrical coordinate system is used, defining the radial direction. Circumferential Vertical Among them: radial The direction from the center of the pier to the concrete surface, ranging from 0 to the radius of the pier cross-section, corresponds to the thickness of the concrete cover and the internal structure; circumferential direction. The circumferential direction of the bridge pier cross-section, ranging from 0 to 2π, is used to distinguish the differences in erosion between different orientations (such as the seaward side and the leeward side); vertical direction... This refers to the height of the bridge pier, ranging from 0 to the total height of the pier, and is used to distinguish between the underwater zone, the splash zone, and the atmospheric zone.

[0049] For rectangular bridge piers, a Cartesian coordinate system is used to define the lateral direction. Vertical Vertical ,in and These correspond to the two side length directions of the rectangular cross section, The vertical dimension is defined as the height, encompassing the geometric dimensions of the pier. Alternatively, to better describe the physical process of chloride ion erosion from the surface inwards, a surface normal depth coordinate system can be used: defining the depth along the surface normal inwards, with the outer surface of the pier as the reference. (0 represents the outer surface, and the maximum value corresponds to the internal depth of the concrete), and the coordinates of the surface tangent plane. Used to distinguish different surface locations, forming a three-dimensional space. This method can uniformly handle bridge piers of any shape; it only requires mapping the spatial location of the sampling points to... space.

[0050] Through the above four-dimensional modeling space or (Rectangle) or (Cylinder), which can fully cover the spatiotemporal characteristics of chloride ion erosion on bridge piers.

[0051] S2. Obtain discrete chloride ion concentration sampling data on the bridge piers and construct a sample dataset containing input features and output labels.

[0052] The sampling data in S2 includes measured values ​​of chloride ion concentration at different spatial locations and at different service years; the input features are spatial coordinates and time coordinates, and the output label is the chloride ion concentration value at the corresponding location.

[0053] Specifically, the sampling data includes measured values ​​of chloride ion concentration at different radial (r), circumferential (θ), and vertical (z) positions, as well as at different service years (t). The sample dataset format is input feature X=[r,θ,z,t] and output label Y=chloride ion concentration at the corresponding position.

[0054] There are two methods for acquiring sampling data, which can be selected according to actual needs:

[0055] Method 1: On-site core sampling. Destructive sampling is performed on the target bridge pier. Cores are drilled at different vertical z-heights (focusing on typical areas such as underwater, splash, and atmospheric zones), at the same height but with different circumferential θ-directions (such as east, south, west, and north), and at the same location with different radial r-depths (such as 10mm, 20mm, and 30mm within the protective layer, with sampling layer by layer). Mature chloride ion content detection methods such as silver nitrate titration and ion chromatography are used to obtain the measured chloride ion concentration values ​​at each sampling point, ensuring that the sampling points cover different erosion environments and locations of the bridge pier, thereby improving the representativeness of the samples.

[0056] Method 2: Simulation generation. For scenarios where on-site core sampling is not possible (such as newly built bridges or important cultural relic bridges), simulated sample points of chloride ion concentration are generated in batches based on Fick's second law. At the same time, random perturbations are added (simulating the discreteness of concrete materials, construction deviations, and other factors) as virtual measured data to construct a sample dataset, which can meet the needs of thesis research, engineering pre-evaluation, etc.

[0057] S3. Select the Gaussian process kernel function to construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space.

[0058] In S3, before constructing the Gaussian process kernel function, a step of dimensionless or standardized processing of the input features is also included.

[0059] Specifically, firstly, the input four-dimensional parameters... Dimensionless / standardized processing is performed, specifically using Z-score standardization:

[0060]

[0061] in and Let be the mean and standard deviation of this dimension in the training sample set, respectively; the standardized parameter is denoted as . .

[0062] Then, a Gaussian process kernel function is constructed based on the standardized parameters:

[0063] When using the squared exponent SE kernel, the covariance function is:

[0064]

[0065] in The distance is the standard Euclidean distance; this kernel function has the characteristics of good smoothness and high computational efficiency, and is suitable for characterizing the continuous evolution of chloride ion erosion.

[0066] When using the Matern kernel, the covariance function is:

[0067]

[0068] The , This is the hyperparameter of the kernel function. This kernel function has lower requirements for data smoothness, can better characterize the local fluctuations in the chloride ion erosion process, and is adapted to the erosion differences caused by the discreteness of concrete materials.

[0069] The expression for the three-dimensional spatiotemporal Gaussian process regression model is: ,in Given that the chloride ion concentration is a mean function, and considering the randomness of the chloride ion concentration, we take... Simplify model calculations; The covariance kernel function selected above is used to characterize the spatiotemporal correlation between sample points.

[0070] S4. Input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and optimize the model hyperparameters to obtain the optimal Gaussian process regression model.

[0071] S5. Virtual grid points are set up in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model, and the statistical characteristic of the chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the spatial erosion field of chloride ions of the entire bridge pier.

[0072] S6. Based on the reconstructed chloride ion erosion field and combined with the preset critical chloride ion concentration, assess the corrosion risk of the bridge piers and output an assessment report.

[0073] Example 2:

[0074] Based on Example 1, Example 2 of this application provides a more specific method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, including:

[0075] S1. Construct a three-dimensional spatial coordinate system for the bridge piers, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space.

[0076] S2. Obtain discrete chloride ion concentration sampling data on the bridge piers and construct a sample dataset containing input features and output labels.

[0077] S3. Select the Gaussian process kernel function to construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space.

[0078] The Gaussian process kernel function mentioned in S3 is the Matern kernel or the squared exponent SE kernel; the kernel function is used to characterize the correlation of chloride ion concentration in the spatial dimension and the evolutionary correlation in the time dimension.

[0079] S4. Input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and optimize the model hyperparameters to obtain the optimal Gaussian process regression model.

[0080] The hyperparameters mentioned in S4 include spatial correlation length and noise variance; the optimization of these hyperparameters is achieved using the maximum likelihood estimation method, which determines the optimal hyperparameters by minimizing the negative logarithmic marginal likelihood function, which is: ,in Output label vectors for the samples. The sample covariance matrix, For the sample size, For hyperparameter vectors (including kernel function hyperparameters) , and noise variance By using optimization algorithms such as gradient descent and genetic algorithm, the minimum value of the negative logarithmic marginal likelihood function is found, the optimal hyperparameters are obtained, and thus the optimal three-dimensional spatiotemporal Gaussian process regression model is determined.

[0081] S5. Virtual grid points are set up in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model, and the statistical characteristic of the chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the spatial erosion field of chloride ions of the entire bridge pier.

[0082] It should be noted that the virtual grid points described in S5 are limited to the concrete protective layer of the bridge pier and the area significantly affected by chloride ion erosion. The layout density is determined based on the size of the bridge pier and accuracy requirements, with a grid point spacing of 0.5cm-5cm. This ensures that the reconstructed erosion field is continuous and accurate, clearly reflecting the erosion differences at different locations. During the interpolation reconstruction process, the four-dimensional parameters of the virtual grid points are... Input the trained optimal model and use the posterior probability distribution of the Gaussian process to calculate the mean chloride ion concentration at each virtual grid point. and variance , where the mean ,variance , The covariance matrix between virtual grid points and sample points. The covariance matrix between sample points; based on the mean and variance The 95% confidence interval can be further calculated. This method quantifies the uncertainty of chloride ion concentration. By using the concentration data of all virtual grid points, a continuous spatial erosion field of chloride ions across the entire bridge pier can be reconstructed. When only sampling data for a single service year is available, the reconstruction only performs spatial interpolation for that year; when sampling data for multiple service years is obtained, the time dimension t can be included as input to achieve spatiotemporal joint reconstruction.

[0083] In addition, using k-fold cross-validation or independent test set method, 70% of the sampled data obtained in S2 is randomly selected as the training set and 30% as the validation set.

[0084] Under the same sparse sampling conditions, the following five methods are used to predict chloride ion concentration at the validation set locations:

[0085] (1) Traditional Fick one-dimensional diffusion model;

[0086] (2) Ordinary Kriging interpolation method;

[0087] (3) Ordinary SE kernel or Matern kernel Gaussian process regression models that are not optimized for spatiotemporal correlation;

[0088] (4) Linear interpolation method;

[0089] (5) The three-dimensional spatiotemporal Gaussian process regression model constructed in this invention.

[0090] The root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) were used as evaluation indicators for reconstruction accuracy; the identification accuracy, recall, and F1-score of high-risk rust areas (mean chloride ion concentration > critical concentration) were used as evaluation indicators for risk identification reliability.

[0091] The comparative results show that when the number of sampling points is reduced to 30% to 50% of the original sampling amount, the RMSE of the method of the present invention is reduced by an average of 35% to 55% compared with the other four methods, the R² is improved by 0.2 to 0.4, and the F1-score for identifying high-risk rust areas is improved by 0.3 to 0.6, which verifies the significant superiority of the present invention under sparse sampling conditions.

[0092] S6. Based on the reconstructed chloride ion erosion field and combined with the preset critical chloride ion concentration, assess the corrosion risk of the bridge piers and output an assessment report.

[0093] The assessment of corrosion risk described in S6 includes: identifying high-risk corrosion areas based on a comparison of the mean chloride ion concentration with the critical chloride ion concentration; and assessing the reliability of the high-risk corrosion areas based on the variance and / or confidence interval. The assessment report includes the results of the erosion field visualization, the three-dimensional envelope of corrosion risk, the results of the erosion field evolution projection under different service years, and maintenance recommendations.

[0094] For example, the critical chloride ion concentration is determined based on the type of steel reinforcement in the bridge pier (e.g., the critical chloride ion concentration of ordinary carbon steel reinforcement is generally...). When the average chloride ion concentration at a certain location exceeds the critical chloride ion concentration, that location is identified as a high-risk area for corrosion. Combining variance and confidence intervals further quantifies the uncertainty of corrosion risk. This can be achieved by inputting different service years... By obtaining the chloride ion concentration field of the entire bridge pier for the corresponding years, the temporal evolution of chloride ion corrosion can be deduced, and the changes in corrosion risk of the bridge pier within its design service life can be predicted. Finally, based on the above analysis, a complete report is output, including a visualized cloud map of the corrosion field, the location of high-risk corrosion areas, durability assessments for different service years, and recommendations for optimal maintenance timing and location, providing direct support for bridge maintenance decisions.

[0095] It should be noted that the parts in this embodiment that are the same as or similar to those in Embodiment 1 can be referred to each other, and will not be repeated in this application.

[0096] Example 3:

[0097] Based on Example 2, Example 3 of this application provides a more specific method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process. Taking a cylindrical bridge pier of a coastal expressway as an example, the specific implementation process of the present invention is described in detail. The bridge pier is 15m high, has a cross-sectional radius of 1.2m, a design service life of 100 years, a service life of 5 years, and is located in a coastal environment with a high risk of chloride ion erosion.

[0098] The methods provided in this application include:

[0099] Step 1: Construct a three-dimensional spatial coordinate system for the bridge piers, using a cylindrical coordinate system. Define the radial direction r (0-1.2m, from the center of the bridge pier to the surface), the circumferential direction θ (0-2π, four directions: east, south, west, and north), the vertical direction z (0-15m, 0-3m is the underwater zone, 3-6m is the splash zone, and 6-15m is the atmospheric zone), and the time dimension t (0-100 years, this time focusing on simulating t=5 years, 10 years, 20 years, 50 years, and 100 years), forming a four-dimensional modeling space (r, θ, z, t).

[0100] Step 2: Obtain discrete chloride ion concentration sampling data. On-site core drilling was used to collect samples at four vertical heights: z = 2m (underwater zone), 4.5m (splash zone), 9m (atmospheric zone), and 12m (atmospheric zone). At each height, four circumferential directions were established: θ = 0° (east, seaside), 90° (south), 180° (west, leeward side), and 270° (north, roadside). At each direction, six radial depths were established: r = 10mm, 20mm, 30mm, 50mm, 80mm, and 100mm. A total of 4 × 4 × 6 = 96 sampling points were collected. Ion chromatography was used to detect the chloride ion concentration at each sampling point. A sample dataset was constructed, with input features X = [r, θ, z, t = 5] and output label Y = chloride ion concentration at the corresponding location.

[0101] Step 3: Select the Matern kernel as the kernel function for the Gaussian process, with the covariance function being k(ξi,ξj)= (1+√3||ξi -ξj || / )exp(-√3||ξi -ξj || / A three-dimensional spatiotemporal Gaussian process regression model is constructed, with the mean function m(ξ)=0. In this embodiment, the mean and standard deviation of each dimension are calculated based on 96 training samples (with a fixed service life of t=5 years, so the t dimension is not included in the standardization for the time being):

[0102] radial Mean Standard deviation ;

[0103] Circumferential Mean Standard deviation ;

[0104] Vertical Mean Standard deviation .

[0105] For each sample point Subtract the corresponding mean from each and divide by the standard deviation to obtain the standardized value. If different service life t is considered later, then it is necessary to calculate them simultaneously. and Then, t is standardized. After standardization, the mean of each dimension is 0 and the standard deviation is 1, eliminating the dimensions. It can be directly used for Euclidean distance calculation in the kernel function, ensuring that the correlation weights of the radial, circumferential, vertical, and time dimensions are determined by the hyperparameters. Adaptive learning.

[0106] Step 4: Input 96 sample data into the model, use the maximum likelihood estimation method, and optimize the hyperparameters using the gradient descent method. , and noise variance Minimize the negative logarithmic marginal likelihood function to obtain the optimal combination of hyperparameters: , , The optimal three-dimensional spatiotemporal Gaussian process regression model was determined.

[0107] Step 5: In the concrete protective layer of the bridge pier and the area affected by erosion (radial range in this embodiment) That is, extending inward from the surface beyond the location of the reinforcing steel; circumferential. and vertical Virtual grid points were laid out across the entire pier area. The grid point spacing was 1cm, with 10 points radially (from 0.05m to 0.15m from the surface), 360 points circumferentially, and 1500 points vertically, for a total of... A virtual point. Since the actual measured sampling data in this embodiment are all service life... The year cannot be extrapolated from a single time segment to other years, therefore it only applies to the current service life. In 2018, interpolation reconstruction of the spatial erosion field of chloride ions across the entire bridge pier was performed. The virtual grid points were then used to reconstruct this field. The parameters are input into the optimal model, and the mean, variance, and 95% confidence interval of the chloride ion concentration at each virtual grid point are calculated to generate an erosion field contour map (e.g., ...). Figure 3 (As shown). If multiple sampling data with different service years are obtained in the project, this method can directly convert the time dimension. By incorporating four-dimensional input, the combined erosion field of three-dimensional space and time is reconstructed, and the evolution of chloride ion concentration over time is deduced.

[0108] Step 6: Determine the critical chloride ion concentration of the ordinary carbon steel reinforcing bars in the bridge pier. Based on the reconstructed erosion field, a three-dimensional envelope of corrosion risk for bridge piers at various service years is generated, including the average chloride ion concentration. The area is a high-risk zone for corrosion. Evolutionary analysis revealed that... In that year, the splashing area seaside radial The area is at high risk of corrosion. In 2010, the high-risk area for corrosion expanded to the entire circumference of the splash zone and the surface of the underwater zone; In that year, the high-risk area for corrosion penetrated radially. Based on the above analysis, a durability assessment report is generated, and recommendations are made at [location]. Corrosion protection treatment was carried out on the seaside of the splash zone every year. Every year, anti-corrosion maintenance is carried out on the entire circumference of the splash zone and the underwater zone to ensure the safe service of the bridge piers.

[0109] Furthermore, this method is also applicable to rectangular cross-section bridge piers. Taking a rectangular bridge pier of a coastal highway as an example, the cross-sectional dimensions of the pier are... ( Directional width , Directional Depth ),high It is designed for a 100-year service life and has a service life of 10 years.

[0110] Step 1: Coordinate System Selection: Use the Cartesian coordinate system and define... , , To simplify the description of surface erosion, it can also be converted into surface normal depth coordinates: the outer surface of the pier is discretized into multiple planar regions (four sides and the top surface), and the normal depth of each region is defined independently. (From the outside in), and using tangent plane coordinates. Mark the surface location.

[0111] Step Two: Data Acquisition: At different vertical heights of the bridge piers (underwater area) Splash Zone Atmospheric region and ), select different surface locations at each height (such as the center of the seaside side, the center of the leeward side, the frontal side, and the rearal side), along the normal depth Core sampling was performed, and a total of One sampling point.

[0112] Step 3: Standardization Processing: [This section appears to be incomplete and requires further context.] Z-score standardization was performed by calculating the mean and standard deviation for each dimension. Because and The ranges are different (1.5m vs 2.0m), and after standardization, the weights of the two are balanced.

[0113] Step 4: Model Construction and Reconstruction: Using the same three-dimensional spatiotemporal Gaussian process regression model as the cylindrical bridge pier (with the Matern kernel as the kernel function), input the standardized model... Output the mean and variance of chloride ion concentration. Virtual grid points are selected by... directional spacing 2cm directional spacing 2cm The chloride ion concentration field of the entire bridge pier is reconstructed by deploying the directional spacing of 5cm.

[0114] Through evolutionary deduction, it was found that the reconstruction results successfully captured the accumulation of chloride ion concentration at the corners of rectangular bridge piers (areas of abrupt changes in surface curvature), and identified the vicinity of the corners as a high-risk area for corrosion, thus verifying the adaptability of this method to rectangular bridge piers.

[0115] Furthermore, to verify the reconstruction accuracy and corrosion risk identification reliability of the present invention under sparse sampling conditions, a comparative verification experiment was conducted based on the data from 96 measured sampling points in the above embodiments. Verification setup: 30 sampling points were randomly selected as the training set (sparse sampling, approximately 31% of the total sampling points), and the remaining 66 points were used as the verification set; the following five methods were used to predict chloride ion concentration at the locations in the verification set: ① Fick one-dimensional diffusion model (radial fitting); ② Ordinary Kriging (spatial dimension only, time not considered); ③ Ordinary SE kernel Gaussian process regression (no three-dimensional spatial + temporal modeling); ④ Linear interpolation method (trilinear interpolation); ⑤ The method of the present invention (three-dimensional spatiotemporal Gaussian process, Matern kernel).

[0116] The evaluation index results (mean ± standard deviation, repeated 10 times of random sampling) are shown in Table 1.

[0117] Table 1

[0118]

[0119] Results Analysis: The method of this invention reduces RMSE by 35.7% compared to ordinary SE-GPR, 41.9% compared to ordinary Kriging, 57.1% compared to the Fick model, and 53.8% compared to linear interpolation; R² reaches 0.91, significantly higher than other methods; the F1-score for identifying high-risk corrosion areas reaches 0.89, which is 0.21 higher than the best comparison method (ordinary SE-GPR), proving that the present invention can more accurately locate the bridge pier areas that need maintenance under sparse sampling.

[0120] The above comparison and verification fully demonstrate that the present invention has significant technical advantages under sparse sampling conditions by constructing a three-dimensional spatiotemporal Gaussian process regression model and selecting an appropriate kernel function for the chloride ion erosion characteristics of bridge piers. This advantage cannot be simply derived by those skilled in the art based on conventional Gaussian process interpolation.

[0121] Example 4:

[0122] Based on Example 3, Example 4 of this application provides a simulation system for the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, including:

[0123] The building module is used to construct the three-dimensional spatial coordinate system of the bridge pier, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space;

[0124] The acquisition module is used to acquire discrete chloride ion concentration sampling data on bridge piers and construct a sample dataset containing input features and output labels.

[0125] The selection module is used to select the Gaussian process kernel function and construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space.

[0126] The input module is used to input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and to optimize the model hyperparameters to obtain the optimal Gaussian process regression model.

[0127] The deployment module is used to deploy virtual grid points in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model, and the statistical characteristic of the chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the chloride ion spatial erosion field of the entire bridge pier.

[0128] The assessment module is used to assess the corrosion risk of bridge piers based on the reconstructed chloride ion erosion field and a preset critical chloride ion concentration, and output an assessment report.

[0129] It should be noted that the system provided in this embodiment is the corresponding system of the method provided in embodiment 3. Therefore, the parts that are the same as or similar to those in embodiment 3 in this embodiment can be referred to each other, and will not be described again in this application.

Claims

1. A method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, characterized in that, include: S1. Construct a three-dimensional spatial coordinate system for the bridge piers, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space; S2. Obtain discrete chloride ion concentration sampling data on the bridge piers and construct a sample dataset containing input features and output labels; S3. Select the Gaussian process kernel function to construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space; S4. Input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and optimize the model hyperparameters to obtain the optimal Gaussian process regression model. S5. Virtual grid points are set up in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model. The statistical characteristic of chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the spatial erosion field of chloride ions in the entire bridge pier. S6. Based on the reconstructed chloride ion erosion field and combined with the preset critical chloride ion concentration, assess the corrosion risk of the bridge piers and output an assessment report.

2. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 1, characterized in that, The spatial dimension mentioned in S1 includes the radial, circumferential, and vertical dimensions of the bridge pier, or the equivalent horizontal, longitudinal, and vertical dimensions based on the geometric shape of the bridge pier; the time dimension is the service life of the bridge pier.

3. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 2, characterized in that, The sampling data in S2 includes measured values ​​of chloride ion concentration at different spatial locations and at different service years; the input features are spatial coordinates and time coordinates, and the output label is the chloride ion concentration value at the corresponding location.

4. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 3, characterized in that, In S3, before constructing the Gaussian process kernel function, a step of dimensionless or standardized processing of the input features is also included.

5. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 4, characterized in that, The Gaussian process kernel function mentioned in S3 is the Matern kernel or the squared exponent SE kernel; the kernel function is used to characterize the correlation of chloride ion concentration in the spatial dimension and the evolutionary correlation in the time dimension.

6. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 5, characterized in that, The hyperparameters mentioned in S4 include spatial correlation length and noise variance; the optimization of the hyperparameters is achieved using the maximum likelihood estimation method.

7. The method for simulating the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process according to claim 6, characterized in that, The assessment of corrosion risk described in S6 includes: identifying high-risk corrosion areas based on a comparison of the mean chloride ion concentration with the critical chloride ion concentration; and assessing the reliability of the high-risk corrosion areas based on the variance and / or confidence interval. The assessment report includes the results of the erosion field visualization, the three-dimensional envelope of corrosion risk, the results of the erosion field evolution projection under different service years, and maintenance recommendations.

8. A simulation system for the spatial erosion field of chloride ions in bridge piers based on a three-dimensional Gaussian process, characterized in that, For performing the method as described in any one of claims 1 to 7, comprising: The building module is used to construct the three-dimensional spatial coordinate system of the bridge pier, define the spatial and temporal dimensions of chloride ion erosion, and form a multi-dimensional modeling space; The acquisition module is used to acquire discrete chloride ion concentration sampling data on bridge piers and construct a sample dataset containing input features and output labels. The selection module is used to select the Gaussian process kernel function and construct a three-dimensional spatiotemporal Gaussian process regression model to describe the distribution of chloride ion concentration in the multidimensional modeling space. The input module is used to input the sample dataset into the three-dimensional spatiotemporal Gaussian process regression model for training, and to optimize the model hyperparameters to obtain the optimal Gaussian process regression model. The deployment module is used to deploy virtual grid points in the entire physical domain or target area of ​​the bridge pier. The spatial and temporal coordinates of the virtual grid points are input into the optimal Gaussian process regression model, and the statistical characteristic of the chloride ion concentration at each virtual grid point is output to complete the interpolation reconstruction of the chloride ion spatial erosion field of the entire bridge pier. The assessment module is used to assess the corrosion risk of bridge piers based on the reconstructed chloride ion erosion field and a preset critical chloride ion concentration, and output an assessment report.

9. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program is run on the computer, it causes the computer to perform the method described in any one of claims 1 to 7.

10. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the method as described in any one of claims 1 to 7.

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