Pier scouring prediction method and system based on single-beam sonar and water tank experiment

Abstract

The invention discloses a pier scour prediction method and system based on a single-beam sonar and water tank experiment, and the method comprises the steps: carrying out the quantitative evaluation of a pier position in a navigable river channel, and selecting a pier with the highest comprehensive scour risk as a monitoring object; acquiring field flow field parameters; setting a pier model and a riverbed scene in the water tank, and carrying out a water tank scouring experiment; detecting the section of a scouring pit on the upstream side of the pier after the water tank scouring experiment, and obtaining a curve shape from the pit bottom to an edge transition area; extracting water tank scouring experiment data, and constructing a training data set; training a pre-established pier scouring curve prediction model by adopting the training data set; and acquiring field real-time data and inputting the field real-time data into the trained pier scour curve prediction model to obtain a pier scour prediction curve. According to the method, a small number of sonar sensors are installed on actual piers to monitor the depth of the scouring pit, and calculation and prediction of the section curve of the scouring pit of the multiple piers of the actual bridge are achieved in combination with a prediction model trained through a water tank model experiment and a data driving method.

Description

Technical Field

[0001] This invention belongs to the field of bridge safety early warning technology, specifically relating to a method and system for predicting bridge pier scour based on single-beam sonar and flume experiments. Background Technology

[0002] Scouring of bridge pier foundations creates scour pits of varying depths around the piers, a key factor contributing to bridge structural damage. Under the long-term scouring action of riverbed sediment, fine particles are carried long distances by turbulent currents. As flow velocity increases, coupled with the effects of horseshoe vortices and wakes generated before and after the piers, larger particles are also locally swept up and moved, gradually scouring out pits around the piers. As the scouring process continues, the structural strength of the riverbed material decreases, leading to a reduction in the actual embedment depth of the pier foundations. This weakens the lateral and vertical bearing capacity of the piers, significantly increasing the risk of uneven settlement or even overturning and collapse of the entire bridge.

[0003] Existing research mainly focuses on predicting the scour depth of a single pier, or relies on empirical formulas and scaled-down tests, or uses machine learning and neural network methods to directly fit the relationship between hydrodynamic parameters and scour depth. Although it can provide local results under specific conditions, it generally suffers from problems such as high monitoring costs, prediction results limited to single values, insufficient continuity across piers, and poor environmental adaptability, making it difficult to meet the actual engineering needs for monitoring and predicting the evolution of scour at the whole bridge scale. Summary of the Invention

[0004] The purpose of this invention is to address the problems in the prior art by providing a method and system for predicting bridge pier scour based on single-beam sonar and flume experiments. By installing a small number of sonar sensors on actual bridge piers to monitor the depth of scour pits, and combining flume model experiments with a prediction model trained by a data-driven method, the invention enables the calculation and prediction of the profile curves of scour pits on multiple bridge piers of actual bridges, thereby providing technical support for bridge safety monitoring and scour early warning.

[0005] To achieve the above objectives, the present invention provides the following technical solution: Firstly, a method for predicting bridge pier scour based on single-beam sonar and flume experiments is provided, including: A quantitative assessment of the piers in navigable waterways was conducted, and the piers with the highest overall scour risk were selected as monitoring targets. For the bridge piers that are the monitoring targets, obtain the on-site flow field parameters; Based on the on-site flow field parameters, a bridge pier model and a riverbed scene were set up in the water tank to conduct a water tank scouring experiment. After the water tank scouring test, the cross-section of the scouring pit on the water-facing side of the bridge pier was examined to obtain the curved shape of the transition zone from the bottom of the pit to the edge. Based on the curve shape of the transition zone from the bottom of the pit to the edge, water tank flushing experimental data were extracted to construct a training dataset. The pre-established pier scour curve prediction model was trained using a training dataset; Real-time on-site data is acquired and input into a trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve.

[0006] As a preferred approach, the step of quantitatively assessing the piers within navigable waterways and selecting the piers with the highest overall scour risk as monitoring targets involves a quantitative assessment of the piers within the navigable waterways based on four dimensions: hydraulic factors, pier structural geometry, bed characteristics, and riverbed morphology. Specifically, regarding hydraulic factors, in normally navigable waterways, piers corresponding to sections with a water depth H > 3m and satisfying a relative depth of 1.0 ≤ H / D ≤ 2.5 are selected, where D is the pier diameter. A dual-threshold method based on velocity difference is employed. The hydraulic similarity screening rule involves sampling 5% to 10% of the piers under the premise of isomorphic piers and similar bed conditions. The dual-threshold hydraulic similarity screening rule based on velocity difference selects the larger of ±10% or ±0.15m / s velocity difference. Piers in the shallow section are considered representative boundary points and are mandatory selections to ensure the constraint of the curves at both ends of the span. For pier structural geometry, circular piers with a diameter D > 2m, as well as square, blunt-headed, and angled piers are selected. For bed characteristics, d... 50 Bridge piers in areas with fine sand-silt beds of <0.5mm and in areas with non-uniform riverbed material and covered by fine sand and underlying hard layer; for riverbed morphology, select bridge piers located at the outer bend radius R <5B, where B is the river width; or bridge span piers with a contraction rate >20%.

[0007] As a preferred approach, a single-beam echo sounder is installed on the upstream side of the selected bridge pier to measure the depth changes of the riverbed scour pits within the coverage area of ​​the detection beam in real time, and the real-time scour pit depth is calculated according to the following expression:

[0008] In the formula, H 1 represents the sonar installation elevation; y 0 represents the elevation of the surrounding riverbed; H 2 represents the depth measured by sonar.

[0009] As a preferred embodiment, the step of obtaining on-site flow field parameters for the bridge piers, which are the monitoring objects, includes measuring the vertically stratified flow velocities in the upstream area of ​​the bridge piers using a flow meter, with the flow velocity vertical lines arranged from the water surface to the riverbed. n Each measurement point, obtained for vertical layering n The vertical average velocity is calculated by weighted averaging of the given velocity values, as shown in the following expression:

[0010] In the formula, the weights The closer to the bottom of the bridge pier, the greater the weight. h i For the first i The depth corresponding to each measuring point v i For the first i The flow velocity measured at each measuring point; H The total water depth.

[0011] As a preferred embodiment, in the step of setting up a bridge pier model and riverbed scene in a flume according to the on-site flow field parameters and conducting a flume scouring experiment, the bridge pier model is installed in the pre-set flume at a scale of 1:α. The Froude similarity criterion is used for model and parameter design to ensure that the experiment is similar to the actual hydrodynamics. The riverbed is divided into the following three categories according to the material: fine sand-silt bed is group A, and the average particle size of the model is d. 50 The average particle size is 0.05–0.20 mm; for ordinary sandy beds, group B has an average particle size d. 50 The average particle size is 0.06–0.18 mm; the gravel-brick bed is group C, and the model average particle size d 50 The flow rate is 0.7–3.3 mm. Five flow conditions are set within each material group. The strategy of the same flow rate between groups and different flow rates within groups is adopted. Each flow rate is repeated multiple times to obtain multiple scouring curve coordinate data under the same flow rate. The flow rate is adjusted by the tailgate of the water tank and the circulation pump to achieve steady state. The bed is laid independently according to the group to avoid cross-contamination.

[0012] As a preferred embodiment, in the step of obtaining the curve shape of the transition zone from the bottom to the edge of the scour pit on the water-facing side of the bridge pier after the detection of the scour test, when the scour reaches quasi-equilibrium, a 3D scanner is used on a predefined upstream cross-section to obtain the riverbed scour curve and the coordinate information of key points on the curve; based on the fact that the deepest scour point on the upstream side of the bridge pier appears immediately adjacent to the pier foundation, a sonar probe is installed at a protruding position on the outer side of the upstream side of the bridge pier; the upstream cross-section is set at a distance of D / 2 + Δ from the center of the pier, where Δ is the equipment installation gap, calculated based on the size of the sonar probe and the beam opening angle, as shown in the following expression:

[0013] In the formula, r The radius of the probe housing; h The distance from the probe to the bed surface; θε represents the beam opening angle; ε is the margin reserved for manufacturing and installation errors; the scanning section extracts data points within a range of 3 times the scour depth on both sides of the pit bottom to fully capture the curve shape from the pit bottom to the edge transition zone; combining the typical morphological characteristics and formation mechanism of the scour curve, the following locations are selected as training points for the response surface model: left and right slope bottom points: located at the junction of the scour pit slope and the unscoured area, reflecting the pit width and boundary position; left and right transition points: located in the gentle transition area between the slope bottom and the far-field reference plane, reflecting the shape of the pit area connecting to the stable riverbed; left and right far-field reference points: located in the stable reference bed surface area unaffected by local scour, providing a reference for the original bed elevation; sonar monitoring points: located below the centerline on the upstream side of the bridge pier, reflecting the maximum scour depth of the pit bottom.

[0014] As a preferred embodiment, in the step of extracting flue scour experimental data based on the curve shape of the transition zone from the bottom of the pit to the edge and constructing a training dataset, for bridge piers without sonar, the scour depth is estimated using observation data of bridge piers with sonar installed within the same bridge span. This includes, under the condition of similar riverbed material type and water flow conditions, taking the scour pit depth of other monitored bridge piers in the corresponding span. The average value is used as the proxy scour depth for the corresponding bridge piers without sonar. : ,

[0015] Define indicator variable m sonar This indicates the sonar monitoring status; when sonar is installed on the bridge pier, m sonar =1, when the bridge pier is not equipped with sonar, m sonar =0, therefore, the actual or proxy flushing depth is uniformly expressed as:

[0016] The lateral length of the scour curve in front of each pier is determined based on three times the sonar-monitored scour depth. Therefore, the lateral coordinate range of the scour curve in front of the pier is [x]. a ,x b Defined as: ,

[0017] The local scour curves in front of different piers are mapped onto a unified coordinate system within the span, and a position indicator parameter is defined for each pier. η i This is used to mark the relative position of the corresponding pier within the span, and the expression is as follows: ,

[0018] In the formula, xL and x R These are the coordinates of the leftmost and rightmost piers, respectively. After the above processing, the scour profiles at different bridge piers are all transformed into a unified dimensionless coordinate system, providing a standardized data format for subsequent modeling. The input set for each bridge pier is as follows:

[0019] In the formula, Fr The Froude number reflects the ratio of fluid inertial force to gravity and is used to replace flow velocity as an input. H / D This refers to the relative water depth ratio; Input the dimensionless scour depth of the bridge pier; b The riverbed material type is a category variable. The training of the response surface model extracts the coordinates of key points and the corresponding coordinates of the centerline on the upstream side of the pier from each scour curve. These coordinates are then dimensionless and used as the output dependent variable of the RSM, with the corresponding Froude number as the input. Fr Relative water depth ratio H / D Relative scour depth The riverbed material type was used as the independent variable for fitting training. The following inputs were used during training:

[0020] in, The calculation formula is:

[0021] m sonar Take 1 if there is a sonar on the bridge pier, and 0 if there is no sonar; When sonar is available, the sonar monitoring value is used; when sonar is not available, the average relative pit depth ratio of bridge piers with sonar installed under the same cross section and bed conditions is used to estimate the proxy scour depth. The specific calculation method is the same as above. The supervision for training deep learning and response surface model is the dimensionless coordinate data (x, y) and the keypoint coordinate data, respectively. x ik , y ik After being organized, two datasets were formed for model training: one dataset was used to train a deep learning model to predict the complete scour curve, and the other dataset was used to train a response surface model to correct the key points of the curve.

[0022] As a preferred approach, in the step of training the pre-established pier scour curve prediction model using a training dataset, the pier scour curve is generated by constructing a combined prediction model; the model training uses local curve segments centered on the pier as basic samples, and inputs sonar or proxy information and masks containing the target pier and its left and right adjacent piers; in the inference stage, local dimensionless curve segments are output for each pier within the span, and then RSM key points are introduced for minimum curvature spline correction, and then kernel weight functions are used to overlap and splice on a unified abscissa to obtain the entire scour profile curve that passes through all anchor points and is smooth and consistent at the junction of each segment; To avoid training instability caused by directly regressing a large number of coordinate points, a parameterized curve decoder for a multilayer perceptron (MLP) is designed, employing a set of one-dimensional smooth basis functions. The preliminary dimensionless curve expression is defined as follows:

[0023] In the formula, , For the first i Sonar monitoring locations of each bridge pier; Anchor the vertical dimension of the curve to the sonar to prevent the entire curve from drifting up and down. Let a0 = -1, representing the position of the sonar. The value is always -1, so the network only needs to start from the input. u DL The remaining coefficients are predicted using the following expression:

[0024] In the i Discrete summation is performed over the segment domain, and the loss function is:

[0025] In the formula: The weights are determined by the number of samples; samples without sonar have lower weights, while samples with sonar have higher weights. For data items, make the curve closely resemble the real curve; Used to suppress oscillations and smooth the curve; For the angle of repose constraint, where The value is determined based on the bed material; The parameters for the endpoints to return to the far-field datum plane are used to bring the two ends far from the scour pit back to the vicinity of the original bed surface. Perform RSM key anchor point correction: For each key point on the scour curve in front of the pier, including the left and right slope bottom points, left and right transition points, left and right far-field base points, and the dimensionless coordinates corresponding to the sonar monitoring points. Establish with u RSM For the multivariate response surface of the independent variable, the least squares loss is used during training, and a regularization term is added to ensure regression stability; In the reasoning phase, in the segment domain Introducing the minimum curvature spline correction function To correct the dimensionless curve of the local area in front of the pier initially obtained by the decoder. The expression is as follows: st

[0026] The corrected dimensionless curve in front of the pier is obtained, and its expression is as follows: ,

[0027] During the model application phase, the local predicted curves of each pier within the span need to be merged into a scour profile of the entire span. Using the center position of the target pier as the kernel, a weight function with a finite support domain is assigned to each predicted curve segment. The weight function uses a Gaussian kernel with finite support, with the center position of the target pier as the kernel. η i For the core, β This is the expansion factor. k This is a segment width coefficient, with the width uniformly equal to the target bridge scour depth. k The weight is multiplied by a factor of 1, with the weight maximizing at the center and decreasing towards the boundary. The expression is as follows: ,

[0028] Among them, [a i ,b i [ ] represents the dimensionless physical coordinates of the computational domain:

[0029] When there are blank areas or the support domain cannot be covered between adjacent local segments, the segment width coefficient k is increased first to expand the support range of each segment and make it overlap sufficiently; when there is already overlap between segments but the transition at the splice is not smooth, the shape of the kernel function is changed by fine-tuning the widening coefficient β to make the weight distribution of the overlapping area smoother or more concentrated. By normalizing and weighting all local curve segments according to their weight functions, the final dimensionless curve obtained by splicing the entire span is obtained: .

[0030] As a preferred embodiment, in the step of acquiring real-time on-site data and inputting it into a trained bridge pier scour curve prediction model to obtain a predicted bridge pier scour curve, a complete scour curve prediction is generated based on the real-time on-site input. Simultaneously, the response surface model calculates correction values ​​for key anchor points based on the input parameters, and applies these anchor point constraints to the initial deep learning curve. If the values ​​of the initial curve at key points are inconsistent with the RSM prediction, the curve is adjusted and interpolated to make it pass through these anchor points. The adjustment method is to scale and translate the initial curve vertically and laterally, or to use local polynomial approximation near the key points to fit the target value given by the RSM. After the anchor point correction process, the obtained scour profile curve is consistent with the empirical or physical model at key positions, while the overall shape is still provided by the deep learning model, ensuring the smoothness and rationality of the curve. Since both the training data and the data processed from actual bridge monitoring are dimensionless, directly inputting the actual bridge data into the model will yield a dimensionless predicted scour curve. Scale transformation can then be performed to obtain the scour profile at the actual scale. The inverse transformation of the horizontal coordinate is expressed as follows:

[0031] The inverse transformation of the vertical coordinate is expressed as follows: .

[0032] Secondly, a bridge pier scour prediction system based on single-beam sonar and flume experiments is provided, including: The monitoring target pier selection module is used to quantitatively assess the piers in navigable waterways and select the piers with the highest comprehensive scour risk as monitoring targets. The on-site flow field parameter acquisition module is used to acquire on-site flow field parameters for the bridge piers that are the monitoring objects. The flume scouring experiment module is used to set up a bridge pier model and a riverbed scene in a flume according to the on-site flow field parameters, and to conduct flume scouring experiments. The scour pit detection module is used to detect the cross-section of the scour pit on the water-facing side of the bridge pier after the water tank scour test, and to obtain the curve shape from the bottom of the pit to the edge transition zone. The training dataset building module is used to extract water tank flushing experimental data based on the curve shape of the transition zone from the bottom of the pit to the edge, and to build the training dataset. The pier scour curve prediction model training module is used to train a pre-established pier scour curve prediction model using a training dataset. The model prediction module is used to acquire real-time on-site data and input it into a trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve.

[0033] Compared with the prior art, the first aspect of the present invention has at least the following beneficial effects: By quantitatively assessing the piers within navigable waterways, the piers with the highest overall scour risk are selected for monitoring. This avoids installing expensive monitoring equipment on every pier, and this sampling monitoring strategy balances comprehensiveness and economy. It enables focused monitoring of high-risk piers while extrapolating predictions for low-risk piers, far surpassing traditional methods in terms of low-cost real-time monitoring, providing a feasible path for large-scale bridge deployment. Compared to traditional scaled physical model tests and static empirical formulas, this invention offers advantages in applicability and accuracy. Scaled physical model tests are costly and time-consuming, and due to the scaling effect, they cannot realistically reproduce the complex water flow scour process on-site. Static empirical formulas typically only provide limited indicators such as scour depth and are often based on ideal assumptions, failing to dynamically reflect the changing scour patterns on-site. The method of this invention, relying on real-time monitoring data and a data-driven intelligent model, can directly output the scour shape of the entire bridge cross-section at a real scale. Therefore, it significantly outperforms traditional methods in terms of accuracy and real-time performance, providing a more efficient and reliable technical means for bridge safety monitoring and disaster prevention. Furthermore, traditional scour prediction methods are mostly limited to providing the maximum scour depth or the depth value at a certain point. However, this invention can output the scour morphology curve of the entire river span. For multiple monitored bridge piers, the scour curve segments measured on the water-facing side of each pier are spliced ​​together in space to form a continuous scour pit profile through response surface model interpolation. This yields the curve shape from the bottom of the pit to the edge transition zone, upgrading the bridge scour safety analysis from one-dimensional point value judgment to two-dimensional profile assessment. The method of this invention, combined with real-time monitoring data, can continuously update the profile curve when floods occur, achieving real-time dynamic prediction, which is unattainable by static empirical formulas, greatly improving the accuracy and reliability of the judgment.

[0034] Furthermore, this invention trains a pre-established pier scour curve prediction model using a training dataset, and utilizes a deep learning model to make detailed predictions of the local scour morphology of each pier, capturing complex nonlinear local scour characteristics. Simultaneously, by fusing an RSM global response surface model, the spliced ​​overall profile is smoothed and constrained, ensuring that the prediction results of each locality are logically connected and morphologically continuous within the global scope. This "two-step fusion" strategy significantly improves prediction accuracy and reliability: local details match actual scour patterns, while the overall bridge curve satisfies the requirements of overall water-sediment balance and physical consistency.

[0035] Furthermore, the bridge pier scour prediction method of the present invention is fault-tolerant. When some bridge piers lack sonar monitoring data, the missing parts can still be reasonably extrapolated based on the measured information of other bridge piers and the overall scour trend. Specifically, the anchor point depth and curve shape at the missing bridge pier are extrapolated using the scour characteristics of adjacent bridge piers through an RSM model, ensuring the integrity and continuity of the entire scour profile. This extrapolation capability allows for a reliable prediction of the scour status of the entire bridge even when monitoring sensors are not fully deployed or individual devices fail, preventing data gaps from affecting the judgment.

[0036] Furthermore, the bridge pier scour prediction method of this invention employs a prediction structure combining a deep learning model and a key-point response surface model. Addressing the complex nonlinearity and overall consistency requirements of scour prediction, this invention proposes a unique hierarchical modeling architecture. This fusion structure significantly improves prediction accuracy and reliability. Specifically, local details match the actual shape of the scour pit, while the overall trend of the entire bridge satisfies water-sediment balance and physical consistency. The output not only provides scour values ​​for each key pier but also a complete riverbed scour profile curve, offering higher information content and practical value than traditional methods that only predict single points. Attached Figure Description

[0037] The accompanying drawings, which form part of this application, are used to provide a further understanding of the technical solutions of this application. The illustrative embodiments and descriptions of this application are only used to explain this application and do not constitute an improper limitation on the scope of protection of this application.

[0038] Figure 1 Schematic diagram of riverbed scour pit depth calculation according to an embodiment of the present invention; Figure 2 Schematic diagram of sonar deployment pier distribution according to an embodiment of the present invention; Figure 3 A schematic diagram comparing the actual scour curve and the predicted scour curve in an embodiment of the present invention; Figure 4 Schematic diagram of key points in the scour profile of this invention; Figure 5 The flowchart of the bridge pier scour prediction method based on single-beam sonar and water tank experiment in this invention is shown in the embodiment of the invention. Detailed Implementation

[0039] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0040] It should be noted that, in the description of the embodiments of the present invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0041] Furthermore, in the description of this invention, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0042] To address the issues of incomplete information and difficulty in obtaining overall scour patterns in existing bridge pier scour monitoring methods, this invention proposes a bridge pier scour prediction method based on single-beam sonar and flume experiments. This method offers significant advantages in real-time acquisition of scour depth data on the upstream side of bridge piers and rapid prediction of scour patterns. By installing a small number of sonar sensors on actual bridge piers to monitor scour pit depths, and combining flume model experiments with a prediction model trained using data-driven methods, the method can calculate and predict the profile curves of scour pits on multiple bridge piers of actual bridges, thereby providing technical support for bridge safety monitoring and scour early warning.

[0043] Please see Figure 5 The present invention provides a method for predicting bridge pier scour based on single-beam sonar and flume experiments, comprising: S1. Conduct a quantitative assessment of the piers in the navigable waterway and select the piers with the highest comprehensive scour risk as the monitoring targets; S2. Obtain on-site flow field parameters for the bridge piers that are the monitoring targets; S3. Based on the on-site flow field parameters, set up a bridge pier model and a riverbed scene in the water tank and conduct a water tank scouring experiment. S4. After the water tank scouring test, inspect the cross-section of the scouring pit on the water-facing side of the bridge pier and obtain the curve shape from the bottom of the pit to the edge transition zone. S5. Based on the curve shape of the transition zone from the bottom of the pit to the edge, extract the water tank flushing experimental data and construct a training dataset; S6. The pre-established pier scour curve prediction model is trained using the training dataset. S7. Obtain real-time on-site data and input it into the trained pier scour curve prediction model to obtain the pier scour prediction curve.

[0044] In one possible implementation, before deploying the single-beam sonar in step S1, the piers in the navigable waterway are first quantitatively assessed according to four dimensions: hydraulic factors, pier structure geometry, bed characteristics, and riverbed morphology. The piers with the highest comprehensive scour risk are selected as monitoring targets. The assessment process and judgment thresholds are as follows.

[0045] (1) Hydraulic factors In normally navigable waterways, when the water depth H > 3m and the relative depth 1.0 ≤ H / D ≤ 2.5 (D is the pier diameter), horseshoe vortices and wake vortices can fully develop. For candidate piers used for sampling in this section, this embodiment of the invention proposes a dual-threshold hydraulic similarity screening rule based on velocity difference (±10% or ±0.15m / s, whichever is larger) in the monitoring point selection strategy. This rule is used to conduct 5%–10% sampling under the premise of isomorphic piers and the same bed mass. Piers in the shoal section, as representative boundary points, are listed as mandatory sampling objects to ensure the constraint of the curves at both ends of the span. In summary, piers in the main channel section are prioritized for inclusion in the monitoring list because the water depth and relative depth are more likely to trigger ultimate scour. At the same time, shoals on both sides are mandatory to provide boundary anchor points.

[0046] (2) Bridge pier structure geometry Circular piers with a diameter D > 2m, as well as square, blunt-headed, and angular piers, require priority monitoring. If the above-mentioned types of piers are located in deep trenches, sonar should be deployed.

[0047] (3) Bed material characteristics For d 50 Fine sand-silt beds with a thickness of <0.5mm are highly susceptible to erosion, and bridge piers in this area must be monitored. Gravel-brick beds and sandy riverbeds with an armored layer can be given a lower priority due to their limited erosion capacity. If the riverbed material is non-uniform and has a fine sand overlying a hard layer, monitoring is still required to prevent potential scour risks.

[0048] (4) Riverbed morphology Bridge piers located with an outer bend radius R < 5B (B is the river width) or bridge span piers with a shrinkage rate > 20% require priority monitoring; inner bends or sandbank side piers are mainly subject to siltation and are relatively safe.

[0049] A single-beam echo sounder is installed on the upstream side of the selected bridge pier to measure the depth changes of the riverbed scour pits within the coverage area of ​​the detection beam in real time. The sonar installation elevation (H1) is known; the surrounding riverbed elevation (y0) can be obtained from river hydrological data; the depth measured by the sonar (H2) is obtained through sonar monitoring. The real-time scour pit depth is calculated according to the following formula:

[0050] In a specific example, according to the method of an embodiment of the present invention, a highway bridge (hereinafter referred to as "the bridge") spans a navigable river. The river is a gentle bend with a total width of about 200m. The bridge crosses the central main channel and the shallows on both sides. The water depth is about 3.2-4.5m throughout the year, and the flow velocity is between 0.9-1.6m / s. The river has a cross-sectional shape of shallows on both sides and the central main channel in the bridge area. The bridge has 12 equally spaced circular piers, each with a diameter D of 2.2m. The riverbed is mainly composed of a mixture of medium and fine sand and silt, with fine sediment particles and weak erosion resistance.

[0051] 1. Key Pier Selection and Sonar Deployment Scheme: Based on the evaluation principles proposed in this invention, this embodiment ultimately selected four piers to install sonar sensors for real-time scour monitoring, such as... Figure 2 As shown: left bank shallow shoal pier (pier No. 1), right bank shallow shoal pier (pier No. 12), main channel center pier (assumed to be pier No. 7), main channel center pier (assumed to be pier No. 8).

[0052] Each sonar is installed at a slightly protruding position on the upstream side of the corresponding pier (the outer side of the pier facing the water, with the probe approximately D / 2 + installation gap Δ from the center of the pier) to ensure that the sonar detection wave is directed vertically towards the bottom of the scour pit and is not affected by the pier body.

[0053] In one possible implementation, step S2 involves the collection and processing of key parameters. During implementation, the real-time vertical average flow velocity V can be calculated based on data obtained from actual measurements by a current meter; the water depth H can be obtained by measuring along the bridge span using an echo sounder, or by subtracting the riverbed elevation from the river level; the initial riverbed elevation y0 is obtained through field measurements or design data and used as a reference surface for scour calculations; the riverbed material type b is determined by collecting riverbed sediment samples and performing particle analysis; and the diameter D of the bridge piers is provided by the bridge design drawings.

[0054] The vertical average velocity is calculated using the following formula: ,

[0055] In the formula, the first i The depth corresponding to each measuring point is h i The measured flow velocity was v i The total water depth is H , ω i As weight; The Froude number Fr reflects the ratio of fluid inertial force to gravity and is used as an input instead of flow velocity.

[0056] The riverbed material in this embodiment is fine sand-silt, therefore, the riverbed material type b is input as [1,0,0].

[0057] For bridge piers equipped with sonar sensors, the scour depth is calculated using the following expression, where y0 is the initial elevation of the riverbed, which can be obtained by consulting hydrological data for that area. The calculation principle is as follows: Figure 1 As shown:

[0058] For bridge piers without sonar sensors, the method of this invention estimates the scour depth using observation data from bridge piers with sonar installed within the same span: that is, under the conditions of the same riverbed material type and similar water flow conditions, the average value of the scour pit depth of other monitored bridge piers in the same span is used as the proxy scour depth for the corresponding bridge pier without sonar. .

[0059] ,

[0060] Define indicator variable m sonar This indicates the sonar monitoring status; when sonar is installed on the bridge pier, m sonar =1, conversely, m when there is no sonar sonar =0. The actual or proxy flushing depth can be uniformly expressed as:

[0061] The lateral length of the scour curve in front of each pier is determined based on three times the sonar-monitored scour depth, i.e., the lateral coordinate range of the scour curve in front of the pier [x]. a ,x b Defined as: ,

[0062] Since it is necessary to map the local scour curves in front of different piers onto a unified coordinate system within the span, a position indicator parameter is defined for each pier. η i This is used to mark the relative position of the pier within the span, and the calculation expression is as follows: ,

[0063] in, x L and x R The coordinates of the leftmost and rightmost bridge piers are respectively. After the above processing, the scour profiles at different bridge piers can be transformed into a unified dimensionless coordinate system, providing a standardized data format for subsequent modeling. The input set for each bridge pier is as follows: .

[0064] In one possible implementation, step S3 involves conducting a bridge pier model experiment in a water tank, installing the bridge pier model at a 1:α scale. The Froude similarity criterion is used for model and parameter design to ensure the gravity-inertia ratio of the model's water flow is consistent with reality. Using the aforementioned scale relationship, the actual water flow rate, velocity, relative density, median particle size, and settling velocity in the actual riverbed environment are converted into model scale.

[0065] Riverbeds are classified into three categories based on their material composition: fine sand-silt beds (Group A, model d) 50 Approximately 0.05–0.20 mm), ordinary sandy bed (Group B, model d) 50 Approximately 0.06–0.18 mm) and gravel-brick beds (Group C, model d) 50 These three types of riverbeds (approximately 0.7–3.3 mm) can cover the vast majority of natural riverbed scenarios.

[0066] Five flow conditions were set within each material group, employing a strategy of identical flow rates between groups but different flow rates within each group. Each flow rate was repeated multiple times to obtain multiple scouring curve coordinate data at the same flow rate, thereby increasing the amount of training data and generalization ability of the model. The flow rate was regulated to achieve steady-state operation via the water tank tailgate and circulation pump. Independent testing was conducted for each group during bed preparation to avoid cross-contamination.

[0067] Specifically, this embodiment of the invention focuses on the scour pit profile on the upstream side of the bridge pier. Therefore, after each scour stage reaches quasi-equilibrium, a 3D scanner is used to acquire the riverbed scour curve and the coordinate information of key points on the curve at a predefined upstream cross-section. The deepest point of scour on the upstream side of the bridge pier usually appears immediately adjacent to the pier foundation. The sonar probe is installed at a slightly protruding position on the outer side of the upstream side of the pier. The upstream cross-section is set at a position approximately D / 2 + Δ from the center of the pier, where Δ is the equipment installation gap. The installation gap Δ can be calculated and determined based on the size of the sonar probe and the beam angle, as shown in the following expression:

[0068] in, r The radius of the probe housing; h The distance from the probe to the bed surface; θ This is the beam opening angle; in this formula, it is a full angle. If it is a half angle, simply replace it. ε Allowance of approximately 5–10 mm is reserved for manufacturing and installation errors.

[0069] In one possible implementation, step S4 preferably involves scanning the cross-section and extracting data points within a range approximately three times the scour depth to the left and right of the pit bottom to fully capture the curve shape of the transition zone from the pit bottom to the edge. See also... Figure 4 Based on the typical morphological characteristics and formation mechanism of the scour curve, this invention selects the following locations as training points for the response surface model: (1) Left and right slope bottom points: located at the junction of the scour pit slope and the unscoured area, which can accurately reflect the pit width and boundary position.

[0070] (2) Left and right transition points: The gentle transition area between the bottom of the slope and the far field reference plane reflects the shape of the pit area connecting to the stable riverbed, ensuring that the slope length of the curve is reasonable and the transition is smooth.

[0071] (3) Left and right far field reference points: located in a stable reference bed area that is not affected by local scour. They are usually taken at 2 to 3 times the scour depth outside the pit area to provide a reference for the original bed elevation, which helps to eliminate the overall scour and siltation trend and measurement error.

[0072] (4) Sonar monitoring point: Located below the center line on the upstream side of the pier, it directly reflects the maximum scour depth of the pit bottom and is the core anchor point for controlling the vertical scale of the curve and the degree of scour.

[0073] In one possible implementation, when extracting the water tank flushing experiment data in step S5, in order to ensure that data from different sources can be processed uniformly during the training process, the main symbols and parameters involved are first explained, and the dimensionless methods of horizontal and vertical dimensions are defined. The meanings of the symbols are shown in Table 1.

[0074] Table 1

[0075] During the model training phase, data from multiple sources needs to be extracted and organized to construct a unified training dataset. Since not all bridge piers are equipped with sonar in practical applications, a marker indicating "whether sonar observations are present" is added to the data annotations. sonar This corresponds to a binary feature dimension, and when sonar data is missing, this feature mask instructs the model to ignore the corresponding sonar input.

[0076] The lateral length of the scour curve in front of each pier is determined based on three times the sonar-monitored scour depth, i.e., the lateral coordinate range of the scour curve in front of the pier [x]. a ,x b Defined as: ,

[0077] This allows us to obtain the discrete coordinate point set of the profile of the scoured curve sample, which includes the coordinates of the deepest point at the bottom of each pier pit, the bottom of the slope, the transition point, and the far-field reference point.

[0078] ( x , y ( ) represents the coordinates of the point on the scour curve in front of the pier. For any position, the lateral coordinates are... x This invention uses the horizontal length of the curve as the normalized reference length to transform the horizontal coordinate into a dimensionless form: ,

[0079] Vertical axis y The scouring depth is indicated by the reference zero point, which is the elevation y0 of the unscourized bed surface in the far field. This ensures that all curves are referenced to the original bed surface. The expression is as follows:

[0080]

[0081] m sonar Take 1 if there is a sonar on the bridge pier, and take 0 if there is no sonar.

[0082] When sonar monitoring is lacking for bridge piers, the average relative pit depth ratio γ of bridge piers with sonar installed in the same span and under the same bed conditions is used to estimate the current proxy scour depth of the bridge piers. The expression is as follows: ,

[0083] When there is sonar When there is no sonar .

[0084] Through the aforementioned dimensionless processing, the experimental data from the water tank and future actual engineering data can be compared and trained in the same parameter space to ensure that the laws learned by the model are scale-independent, making it easier to extend the experience gained in the training phase to the field application phase.

[0085] During data processing, it is also necessary to extract corresponding features according to the needs of different models. The target output required for training deep learning models is the complete shape of the scour curve, which requires function fitting of the coordinate points, that is, using a function to approximate the entire curve, and using the fitting parameters as the learning target.

[0086] Since it is necessary to map the local scour curves in front of different piers onto a unified coordinate system within the span, a position indicator parameter is defined for each pier. η i This is used to mark the relative position of the pier within the span. The calculation expression is as follows: ,

[0087] in, x L and x R These are the coordinates of the leftmost and rightmost piers, respectively. Simultaneously, record the average inflow velocity corresponding to the scouring curve. V Average water depth at the control section H Diameter of the bridge pier model in the water tank D And the types of riverbed materials.

[0088] The processed data is dimensionless to eliminate scale differences and facilitate the fusion of data from different sources. Dimensionless parameters with clear physical meaning are selected as model input features. This invention uses the following inputs during training:

[0089] in, Fr The Froude number reflects the ratio of fluid inertial force to gravity and is used to replace flow velocity as an input. H / D This refers to the relative water depth ratio; Input the dimensionless scour depth of the bridge pier; b The riverbed material types are categorical variables. To avoid introducing false size and order relationships, the three materials are input as [1,0,0], [0,1,0], and [0,0,1] respectively, ensuring that each material is spatially independent during the model learning process. The training of the response surface model focuses on the extraction and summarization of key anchor point coordinate data. The coordinates of key points and the corresponding coordinates of the pier's upstream centerline are extracted from each scour curve. These coordinates are then dimensionless and used as the output dependent variable of the RSM, with the corresponding Froude number as the input. Fr Relative water depth ratio H / D Relative scour depth The riverbed material type was used as an independent variable for fitting training. The following inputs were used during training:

[0090] in, The calculation formula is:

[0091] m sonar Take 1 if there is a sonar on the bridge pier, and 0 if there is no sonar; When sonar is available, the sonar monitoring value is used; when sonar is unavailable, the proxy scour depth is estimated by the average relative pit depth ratio of bridge piers with sonar installed under the same span and bed conditions. The specific calculation method is the same as above.

[0092] The supervision for training deep learning and response surface model are the dimensionless coordinate data ( x , y ) and key point coordinate data ( x ik , y ik After processing, two datasets were ultimately formed for model training: one for training a deep learning model to predict the complete scour curve, and the other for training a response surface model to correct key points of the curve.

[0093] In one possible implementation, after data preparation, this embodiment of the invention generates pier scour curves by constructing a combined prediction model. Model training uses local curve segments centered on the piers as basic samples, inputting sonar / proxy information and masks containing the target pier and its left and right adjacent piers. During the inference phase, local dimensionless curve segments are output for each pier within the span. Then, RSM keypoints are introduced for minimum curvature spline correction, and finally, a kernel weight function is used to overlap and stitch the segments on a unified abscissa, resulting in a smooth and consistent scour profile curve that traverses all anchor points and is consistent across the boundaries of each segment.

[0094] The experimental parameters were made dimensionless using the same processing method as the key parameters in the actual bridge construction, resulting in the input set for the training model:

[0095] The supervision during training of the deep learning model and the response surface model are the dimensionless scour curve coordinate data. x , y ) and key point coordinate data (x ik , y ik ).

[0096] (1) MLP parametric curve decoder To avoid training instability caused by directly regressing a large number of coordinate points, a set of one-dimensional smooth basis functions is used. Define a preliminary dimensionless curve, expressed as follows:

[0097] in, , Let be the sonar monitoring location of the i-th pier.

[0098] To achieve hard anchoring of the sonar, the vertical dimension of the curve is firmly anchored to the sonar to prevent the entire curve from drifting up and down. Let a0 = -1, that is, at the sonar position... The value is always -1, so the network only needs to start from the input u. DL Predict the remaining coefficients:

[0099] In the i Discrete summation is performed over the segment domain, and the loss function is:

[0100] in, The weights are determined by the number of samples; samples without sonar have lower weights, while samples with sonar have higher weights. For data items, make the curve closely resemble the real curve; Suppress oscillations and smooth the curve; For the angle of repose constraint, where The value is determined based on the bed material; The endpoints are returned to the far-field datum parameters so that the two ends far from the scour pit return to the vicinity of the original bed surface.

[0101] (2) RSM critical anchor point correction For the dimensionless coordinates of each key point on the scour curve in front of the pier Establish with u RSM For the multivariate response surface of the independent variable, the least squares loss is used during training, and a regularization term is added to ensure regression stability.

[0102] In the reasoning phase, in the segment domain Introducing the minimum curvature spline correction function To correct the dimensionless curve of the local area in front of the pier initially obtained by the decoder. The expression is as follows: st

[0103] The corrected dimensionless curve in front of the pier is obtained, and its expression is as follows: ,

[0104] (3) Overlapping splicing During the model application phase, the local predicted curves of each pier within the span need to be merged into a scour profile for the entire span. Using the center position of the target pier as the kernel, a weight function with a finite support domain is assigned to each predicted curve segment. The weight function uses a Gaussian kernel with finite support, as shown in the following equation, with the center position of the target pier as the kernel. η i For the core, βThis is the expansion factor, which generally ranges from 0.5 to 0.8; k This is the segment width coefficient. The width is uniformly set at the target bridge scour depth. k The weight is maximized at the center and decreases towards the boundary over a range of times. ,

[0105] in,[ a i , b i [ ] represents the dimensionless physical coordinates of the computational domain:

[0106] When gaps appear between adjacent local segments and the support domain cannot cover them, the segment width coefficient should be increased first. k Expand the support range of each segment to create sufficient overlap; and when segments already overlap but the transition at the joint is not smooth (such as abrupt changes in slope or smoothing out details), fine-tune the widening coefficient. β Changing the shape of the kernel function makes the weight distribution in the overlapping region smoother or more concentrated. Therefore, k Used to solve the problem of "whether there is overlap". β Used to optimize "overlapping transitions", adjust first during splicing. k Adjust again β .

[0107] By normalizing and weighting all local curve segments according to their weight functions, the final dimensionless curve obtained by splicing the entire span is obtained:

[0108] In the model application phase, since both the training data and the data processed from the actual bridge monitoring are dimensionless, directly inputting the actual bridge data into the model will yield a dimensionless predicted scour curve, such as... Figure 3 As shown. Simultaneously, the response surface model calculates corrected values ​​for key anchor points based on the input parameters. These anchor point constraints are then applied to the initial deep learning curve: if the values ​​of the initial curve at key points are inconsistent with the RSM prediction, the curve is appropriately adjusted and interpolated to pass through these anchor points. The adjustment methods include scaling and shifting the initial curve vertically and laterally, or using local polynomial approximation near the key points to fit the target values ​​given by the RSM. After this anchor point correction process, the final scour profile curve maintains consistency with the empirical / physical model at key locations, while the overall shape is still provided by the deep learning model, ensuring the smoothness and reasonableness of the curve. This embodiment of the invention also requires scale conversion to obtain the scour profile at the actual scale: Inverse transformation of the horizontal coordinate:

[0109] Inverse transformation of the vertical coordinate:

[0110] It should be noted that determining the anchor point (i.e., the center point of the pier) is particularly crucial during the scale conversion process. If sonar monitoring data is available for the corresponding pier, this invention prioritizes using the maximum scour depth value measured on the pier as the anchor point depth, thereby performing vertical inverse normalization of the dimensionless curve to ensure consistency between the predicted profile and the actual situation on site. If sonar measurement data is lacking for a pier, the proxy scour depth of the current pier can be estimated based on the average relative pit depth ratio of piers with sonar installed under the same span and bed conditions, and then restored according to the normalized scale of the proxy scour depth. Through this on-site application process design, using a small number of measured parameters combined with model prediction, efficient reconstruction of the scour profile of the entire bridge is achieved, and reasonable scale conversion ensures that the results have practical engineering significance.

[0111] To ensure the effective implementation of the method of this invention, model training and construction are crucial. Before performing the online predictions described above, the deep learning model needs to be trained offline using a large amount of historical data. For training data preparation, data from various sources can be utilized, including: measured scour profile data accumulated during bridge operation, scour pit shape data obtained from model experiments such as flumes, and simulation data generated by high-resolution numerical simulations. To improve the model's generalization ability, it is recommended that the training samples cover as wide a range of working conditions and bridge type parameters as possible, for example, different Froude numbers. Fr Relative water depth H / D Combinations of different diameters D Different riverbed materials, etc. All training samples underwent the aforementioned dimensionless normalization process, and the corresponding scour profile curve coordinate data were used as supervision signals to train the deep learning model.

[0112] In summary, the prediction method provided by this invention, by flexibly introducing various parameters and combining them with sufficient training data, can adapt to a variety of hydrological conditions and has wide applicability and robustness in practical applications.

[0113] In existing technologies, for example, the Institute of Acoustics, Chinese Academy of Sciences, proposed a real-time monitoring system for underwater pile scour based on broadband high-frequency sonar. This system acquires the scour morphology of the seabed around the piles through multi-angle sonar detection and uses a computer to analyze and fit the echo signals, providing a real-time scour curve showing the change in water depth around the piles over time. This method relies primarily on hardware monitoring, providing a real-time and intuitive reflection of the scour situation. However, equipment investment increases linearly with the number of piles, making it difficult to deploy at low cost across multiple piers of a bridge. Furthermore, the scour curve only provides a local view of a single pier rather than the entire span, lacking information fusion, extrapolation, and consistency constraints across the span. In contrast, this invention deploys single-beam sonar only on a few key piers, significantly reducing overall costs. It uses deep learning to output a local dimensionless curve for each pier, and then uses weighted splicing combined with global correction of key points using RSM to obtain a continuous scour profile of the entire span. For piers without sonar, reliable extrapolation can be performed from adjacent piers and test databases.

[0114] Zhang Yuhang et al. addressed the scour problem of a novel single-pillar-composite cylindrical offshore wind turbine foundation, comparing the predictive performance of various machine learning algorithms and selecting the optimal model for scour depth prediction. The paper integrates single-pile physical test data and MCCBF numerical simulation data, evaluating the accuracy of seven typical regression models under different feature parameter processing schemes to find a high-precision scour prediction method suitable for this novel foundation. The proposed method uses single-pile point value prediction for the regression models, failing to handle the spatial continuity of multiple piers and lacking sensor-free data fusion. In contrast, this invention provides curve-level output and multi-pier splicing, ensuring smooth and consistent cross-pier data. It uses sonar monitoring values ​​as anchor point constraints and robustly extrapolates to sensor-free piers, making it closer to engineering judgments than single-pile point value output.

[0115] Chen Li et al. proposed a method to establish a local scour depth prediction formula using measured field scour data to improve the accuracy of scour estimation for large-diameter monopile foundations. By selecting key influencing parameters and combining them with field data, the authors used multiple linear regression to fit an empirical formula for scour depth applicable to specific sea areas, and compared it with commonly used empirical formulas to verify the effectiveness of the new formula. However, this method relies on extensive field calibration, has limited portability, and does not generate cross-sectional curves. In contrast, this invention uses primarily flume experimental data for training, resulting in lower calibration costs. It improves cross-regional adaptability by dimensionless data during training and RSM anchor point correction during output, and the output result is a full-span profile.

[0116] To address the problem that current standards and empirical formulas for calculating bridge pier scour depth are conservative and inaccurate, Wang Qiusheng et al. introduced least squares support vector machine (LSM) from machine learning to establish a local scour depth prediction model for bridge piers. Compared to this method, this invention uses local curves as the smallest output unit and generates the entire cross-sectional scour curve through kernel-weighted splicing and RSM correction, resulting in a more intuitive output.

[0117] Based on the analysis of bridge pier scour mechanisms and energy balance theory, Wang Fei et al. established a local equilibrium scour depth prediction equation for bridge piers applicable to sandy riverbeds. By comparing with experimental data, they summarized the range of water depth to pier width ratios corresponding to various flow field types under clear water scour and moving bed scour conditions, and verified the applicability of the categorical equations. The research conclusions show that establishing scour prediction equations according to flow field types can effectively improve prediction accuracy. However, this method requires prior identification of the flow field type, and the output is still a single pier point value, making it difficult to handle mixed flow field types and local anomalies along the span. Compared to this method, the local curves generated in this invention undergo deep learning adaptive morphology, which can accommodate changes in conditions along the span, and the output form is a complete span shape, which is more comprehensive than point values.

[0118] Meng Qingfeng et al. constructed a local scour depth prediction model for bridge piers using a backpropagation (BP) neural network, and improved the prediction accuracy and stability by refining the training algorithm. They screened the main factors affecting the scour depth of bridge piers through hypothesis testing and statistical analysis, and used these factors as inputs to establish a three-layer BP neural network model, training the network to fit the nonlinear relationship of scour depth. This method is purely data-driven, lacks actual physical anchor points in the output, does not produce full-span curves, and has no constraints on the spatial consistency of the full-span output. Compared to this method, this invention uses actual sonar monitoring anchor points and RSM physical constraints to suppress black-box distortion, and weighted splicing ensures no steps between segments, resulting in better engineering interpretability.

[0119] Zhao Xin'ao et al. established a local equilibrium scour depth prediction model for single-pile foundations considering wave and water flow effects. They employed a multi-layer feedforward neural network and trained it with extensive data to improve prediction accuracy. The paper compared and analyzed the influence of dimensional and dimensionless input variables on the prediction results and conducted a systematic sensitivity analysis to identify key influencing parameters. The final model was established for both pure water flow and pure wave effects, and the prediction results were compared with empirical formulas to verify the advantages of the neural network method in scour depth prediction. However, this method does not generate curves or integrate prediction curves across multiple piers. In contrast, this invention uses flue test data to cover multiple flow regimes and employs sonar anchor points in the actual environment for calibration. It outputs local curves for each pier and splices them across piers to form an integrated full-span profile. This proposes a non-immersive, dynamic, full-process experimental testing method that allows real-time monitoring of the evolution of scour topography around the pier in the laboratory.

[0120] Wu Jiyi et al., focusing on cross-sea bridges, first compared single-factor calculations of standard formulas and reduced variables such as flow velocity, water depth, pier width, and particle size to three dimensionally consistent parameters (height-to-diameter ratio, flow intensity, and Froude number) for modeling. The method's objective output focused on the maximum scour depth of a pier and its temporal evolution, without providing the continuous shape of the entire scour curve along the cross-section, and lacking a unified splicing strategy for multiple piers. In contrast, this invention uses a limited amount of sonar and flume experimental data as its core, directly outputting local curve segments rather than single depths using deep learning, then using kernel weights to splice the entire span profile, and using RSM key points for small curvature spline correction, balancing smoothness and physical consistency.

[0121] Zhang Ruiqian et al. used Flow-3D analysis to examine the impact of flow velocity, water depth, and pier diameter on scour depth. Given insufficient data to support deep network training, they collected field measurement data to train a BP neural network, verifying the feasibility of using the neural network to predict local scour depth. Compared to this invention, this method still outputs a depth scalar, not a continuous curve across the cross-section. It lacks the curve splicing and anchor point correction process for multiple piers and the entire span, and it does not introduce explicit geometric regularization and key point constraints for physical consistency, making it difficult to directly output the curve geometry required for decision-making.

[0122] Zhang Liping et al. compiled pile group test data and constructed a deep neural network to predict the local scour depth of pile groups. They used ReLU activation and backpropagation to minimize the loss, achieving better performance in correlation coefficient and error index compared with the FDOT formula. They also conducted sensitivity analysis on nine input factors. Compared with this invention, this method studies pile groups and targets the scour depth scalar, but does not cover the modeling of continuous profile curves and whole-span fusion, nor does it consider the smooth splicing and boundary constraints of multiple piers on the same cross section.

[0123] In summary, existing research largely focuses on predicting scour depth at single piers, relying either on empirical formulas and scaled-down experiments, or using machine learning and neural network methods to directly fit the relationship between hydrodynamic parameters and scour depth. While these methods can provide local results under specific conditions, they generally suffer from high monitoring costs, predictions limited to single values, insufficient continuity across piers, and poor environmental adaptability, making it difficult to meet the monitoring and prediction needs of actual engineering projects for scour evolution at the entire bridge scale. This invention addresses these shortcomings by providing a low-cost, real-time monitoring and prediction technology with significant advantages in instantly acquiring scour depth data on the upstream side of bridge piers and rapidly predicting scour patterns.

[0124] Another embodiment of the present invention proposes a pier scour prediction system based on single-beam sonar and flume experiments, comprising: The monitoring target pier selection module is used to quantitatively assess the piers in navigable waterways and select the piers with the highest comprehensive scour risk as monitoring targets. The on-site flow field parameter acquisition module is used to acquire on-site flow field parameters for the bridge piers that are the monitoring objects. The flume scouring experiment module is used to set up a bridge pier model and a riverbed scene in a flume according to the on-site flow field parameters, and to conduct flume scouring experiments. The scour pit detection module is used to detect the cross-section of the scour pit on the water-facing side of the bridge pier after the water tank scour test, and to obtain the curve shape from the bottom of the pit to the edge transition zone. The training dataset building module is used to extract water tank flushing experimental data based on the curve shape of the transition zone from the bottom of the pit to the edge, and to build the training dataset. The pier scour curve prediction model training module is used to train a pre-established pier scour curve prediction model using a training dataset. The model prediction module is used to acquire real-time on-site data and input it into a trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve.

[0125] Another embodiment of the present invention provides an electronic device comprising: A memory that stores at least one instruction; and a processor that executes the instruction stored in the memory to implement the bridge pier scour prediction method based on single-beam sonar and flume experiments.

[0126] Another embodiment of the present invention provides a computer-readable storage medium storing at least one instruction, which is executed by a processor in an electronic device to implement the bridge pier scour prediction method based on single-beam sonar and flume experiment.

[0127] For example, the instructions stored in the memory can be divided into one or more modules / units. These modules / units are stored in a computer-readable storage medium and executed by the processor to complete the bridge pier scour prediction method based on single-beam sonar and flume experiments of the present invention. The one or more modules / units can be a series of computer-readable instruction segments capable of performing specific functions, which describe the execution process of the computer program on the server.

[0128] The electronic device may be a smartphone, laptop, PDA, or cloud server, among other computing devices. It may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the electronic device may also include more or fewer components, or combinations of certain components, or different components; for example, it may also include input / output devices, network access devices, buses, etc.

[0129] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0130] The memory can be an internal storage unit of the server, such as a hard drive or RAM. Alternatively, it can be an external storage device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or FlashCard. Furthermore, the memory may include both internal and external storage units. The memory is used to store computer-readable instructions and other programs and data required by the server. It can also be used to temporarily store data that has been output or will be output.

[0131] It should be noted that the information interaction and execution process between the above-mentioned module units are based on the same concept as the method embodiment. For details on their specific functions and technical effects, please refer to the method embodiment section. They will not be repeated here.

[0132] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0133] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying the computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0134] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0135] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

[0136] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting bridge pier scour based on single-beam sonar and flume experiments, characterized in that, include: A quantitative assessment of the piers in navigable waterways was conducted, and the piers with the highest overall scour risk were selected as monitoring targets. For the bridge piers that are the monitoring targets, obtain the on-site flow field parameters; Based on the on-site flow field parameters, a bridge pier model and a riverbed scene were set up in the water tank to conduct a water tank scouring experiment. After the water tank scouring test, the cross-section of the scouring pit on the water-facing side of the bridge pier was examined to obtain the curved shape of the transition zone from the bottom of the pit to the edge. Based on the curve shape of the transition zone from the bottom of the pit to the edge, water tank flushing experimental data were extracted to construct a training dataset. The pre-established pier scour curve prediction model was trained using a training dataset; Real-time on-site data is acquired and input into a trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve.

2. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of quantitatively assessing piers within navigable waterways and selecting the piers with the highest overall scour risk as monitoring targets, the piers within the navigable waterways are quantitatively assessed according to four dimensions: hydraulic factors, pier structural geometry, bed characteristics, and riverbed morphology. Specifically, regarding hydraulic factors, in normally navigable waterways, piers corresponding to sections with a water depth H > 3m and satisfying a relative depth of 1.0 ≤ H / D ≤ 2.5 are selected, where D is the pier diameter. A dual-threshold hydraulic similarity method based on velocity difference is used. The screening rules involve sampling 5% to 10% of the piers under the premise of homogeneous piers and similar bed conditions. The dual-threshold hydraulic similarity screening rule based on velocity difference selects the larger of ±10% or ±0.15m / s velocity difference. Piers in the shallow section are considered representative boundary points and are mandatory selections to ensure the constraint of the curves at both ends of the span. For pier structural geometry, circular piers with a diameter D > 2m, as well as square, blunt-headed, and angled piers are selected. For bed characteristics, d... 50 Bridge piers in areas with fine sand-silt beds of <0.5mm and in areas with non-uniform riverbed material and covered by fine sand and underlying hard layer; for riverbed morphology, select bridge piers located at the outer bend radius R <5B, where B is the river width; or bridge span piers with a contraction rate >20%.

3. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, A single-beam echo sounder is installed on the upstream side of the selected bridge pier as the monitoring target to measure the depth change of the riverbed scour pit within the coverage area of ​​the detection beam in real time, and the real-time scour pit depth is calculated according to the following expression: In the formula, H 1 represents the sonar installation elevation; y 0 represents the elevation of the surrounding riverbed; H 2 represents the depth measured by sonar.

4. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, The steps for obtaining on-site flow field parameters for the bridge piers, which are the monitoring objects, include measuring the vertically stratified flow velocity in the upstream area of ​​the bridge piers using a flow meter. The flow velocity vertical lines are arranged from the water surface to the riverbed. n Each measurement point, obtained for vertical layering n The vertical average velocity is calculated by weighted averaging of the given velocity values, as shown in the following expression: In the formula, the weights The closer to the bottom of the bridge pier, the greater the weight. h i For the first i The depth corresponding to each measuring point v i For the first i The flow velocity measured at each measuring point; H The total water depth.

5. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of setting up a bridge pier model and riverbed scene in a water tank according to the on-site flow field parameters and conducting a water tank scouring experiment, the bridge pier model is installed in the pre-set water tank at a scale of 1:α, and the Froude similarity criterion is used to design the model and parameters to ensure that the experiment is similar to the actual hydrodynamics. Riverbeds are classified into three categories based on their material composition: fine sand-silt beds are classified as Group A, with an average particle size d in the model. 50 The average particle size is 0.05–0.20 mm; for ordinary sandy beds, group B has an average particle size d. 50 The average particle size is 0.06–0.18 mm; the gravel-brick bed is group C, and the model average particle size d 50 The flow rate is 0.7–3.3 mm. Five flow conditions are set within each material group. The strategy of the same flow rate between groups and different flow rates within groups is adopted. Each flow rate is repeated multiple times to obtain multiple scouring curve coordinate data under the same flow rate. The flow rate is adjusted by the tailgate of the water tank and the circulation pump to achieve steady state. The bed is laid independently according to the group to avoid cross-contamination.

6. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of obtaining the curve shape from the bottom of the pit to the edge transition zone by measuring the scour pit profile on the water-facing side of the bridge pier after the water scour test, after the scour reaches quasi-equilibrium, a 3D scanner is used on a predefined upstream cross-section to obtain the riverbed scour curve and the coordinate information of key points on the curve. Since the deepest scour point on the upstream side of the bridge pier appears immediately adjacent to the pier foundation, a sonar probe is installed at a protruding position on the outer side of the upstream side of the pier. The upstream cross-section is set at a distance of D / 2 + Δ from the center of the pier, where Δ is the equipment installation gap, calculated based on the size of the sonar probe and the beam opening angle. The calculation expression is as follows: In the formula, r The radius of the probe housing; h The distance from the probe to the bed surface; θ ε represents the beam opening angle; ε is the margin reserved for manufacturing and installation errors; the scanning section extracts data points within a range of 3 times the scour depth on both sides of the pit bottom to fully capture the curve shape from the pit bottom to the edge transition zone; combining the typical morphological characteristics and formation mechanism of the scour curve, the following locations are selected as training points for the response surface model: left and right slope bottom points: located at the junction of the scour pit slope and the unscoured area, reflecting the pit width and boundary position; left and right transition points: located in the gentle transition area between the slope bottom and the far-field reference plane, reflecting the shape of the pit area connecting to the stable riverbed; left and right far-field reference points: located in the stable reference bed surface area unaffected by local scour, providing a reference for the original bed elevation; sonar monitoring points: located below the centerline on the upstream side of the bridge pier, reflecting the maximum scour depth of the pit bottom.

7. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of extracting flue scour experimental data and constructing a training dataset based on the curve shape of the transition zone from the bottom to the edge of the pit, for bridge piers without sonar, the scour depth is estimated using observation data of bridge piers with sonar installed within the same span. This includes taking the scour pit depth of other monitored bridge piers in the corresponding span when the riverbed material type is the same and the water flow conditions are similar. The average value is used as the proxy scour depth for the corresponding bridge piers without sonar. : ， Define indicator variable m sonar This indicates the sonar monitoring status; when sonar is installed on the bridge pier, m sonar =1, when the bridge pier is not equipped with sonar, m sonar =0, therefore, the actual or proxy flushing depth is uniformly expressed as: The lateral length of the scour curve in front of each pier is determined based on three times the sonar-monitored scour depth. Therefore, the lateral coordinate range of the scour curve in front of the pier is [x]. a ,x b Defined as: ， The local scour curves in front of different piers are mapped onto a unified coordinate system within the span, and a position indicator parameter is defined for each pier. η i This is used to mark the relative position of the corresponding pier within the span, and the expression is as follows: ， In the formula, x L and x R These are the coordinates of the leftmost and rightmost piers, respectively. After the above processing, the scour profiles at different bridge piers are all transformed into a unified dimensionless coordinate system, providing a standardized data format for subsequent modeling. The input set for each bridge pier is as follows: In the formula, Fr The Froude number reflects the ratio of fluid inertial force to gravity and is used to replace flow velocity as an input. H / D This refers to the relative water depth ratio; Input the dimensionless scour depth of the bridge pier; b The riverbed material type is a category variable. The training of the response surface model extracts the coordinates of key points and the corresponding coordinates of the centerline on the upstream side of the pier from each scour curve. These coordinates are then dimensionless and used as the output dependent variable of the RSM, with the corresponding Froude number as the input. Fr Relative water depth ratio H / D Relative scour depth The riverbed material type was used as the independent variable for fitting training. The following inputs were used during training: in, The calculation formula is: m sonar Take 1 if there is a sonar on the bridge pier, and 0 if there is no sonar; When sonar is available, the sonar monitoring value is used; when sonar is not available, the average relative pit depth ratio of bridge piers with sonar installed under the same cross section and bed conditions is used to estimate the proxy scour depth. The specific calculation method is the same as above. The supervision for training deep learning and response surface model is the dimensionless coordinate data (x, y) and the keypoint coordinate data, respectively. x ik , y ik After being organized, two datasets were formed for model training: one dataset was used to train a deep learning model to predict the complete scour curve, and the other dataset was used to train a response surface model to correct the key points of the curve.

8. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of training the pre-established pier scour curve prediction model using the training dataset, the pier scour curve is generated by constructing a combined prediction model; the model training uses the local curve segment centered on the pier as the basic sample, and inputs the sonar or proxy information and mask of the target pier and its left and right adjacent piers; in the inference stage, the local dimensionless curve segment is output for each pier in the span, and then RSM key points are introduced for minimum curvature spline correction, and then the kernel weight function is used to overlap and splice on a unified abscissa to obtain the whole scour profile curve that passes through all anchor points and is smooth and consistent at the junction of each segment; To avoid training instability caused by directly regressing a large number of coordinate points, a parameterized curve decoder for a multilayer perceptron (MLP) is designed, employing a set of one-dimensional smooth basis functions. The preliminary dimensionless curve expression is defined as follows: In the formula, , For the first i Sonar monitoring locations of each bridge pier; Anchor the vertical dimension of the curve to the sonar to prevent the entire curve from drifting up and down. Let a0 = -1, representing the position of the sonar. The value is always -1, so the network only needs to start from the input. u DL The remaining coefficients are predicted using the following expression: In the i Discrete summation is performed over the segment domain, and the loss function is: In the formula: The weights are determined by the number of samples; samples without sonar have lower weights, while samples with sonar have higher weights. For data items, make the curve closely resemble the real curve; Used to suppress oscillations and smooth the curve; For the angle of repose constraint, where The value is determined based on the bed material; The parameters for the endpoints to return to the far-field datum plane are used to bring the two ends far from the scour pit back to the vicinity of the original bed surface. Perform RSM key anchor point correction: For each key point on the scour curve in front of the pier, including the left and right slope bottom points, left and right transition points, left and right far-field base points, and the dimensionless coordinates corresponding to the sonar monitoring points. Establish with u RSM For the multivariate response surface of the independent variable, the least squares loss is used during training, and a regularization term is added to ensure regression stability; In the reasoning phase, in the segment domain Introducing the minimum curvature spline correction function To correct the dimensionless curve of the local area in front of the pier initially obtained by the decoder. The expression is as follows: s.t. The corrected dimensionless curve in front of the pier is obtained, and its expression is as follows: ， During the model application phase, the local predicted curves of each pier within the span need to be merged into a scour profile of the entire span. Using the center position of the target pier as the kernel, a weight function with a finite support domain is assigned to each predicted curve segment. The weight function uses a Gaussian kernel with finite support, with the center position of the target pier as the kernel. η i For the core, β This is the expansion factor. k This is a segment width coefficient, with the width uniformly equal to the target bridge scour depth. k The weight is multiplied by a factor of 1, with the weight maximizing at the center and decreasing towards the boundary. The expression is as follows: ， Among them, [a i ,b i [ ] represents the dimensionless physical coordinates of the computational domain: When there are blank areas or the support domain cannot be covered between adjacent local segments, the segment width coefficient k is increased first to expand the support range of each segment and make it overlap sufficiently; when there is already overlap between segments but the transition at the splice is not smooth, the shape of the kernel function is changed by fine-tuning the widening coefficient β to make the weight distribution of the overlapping area smoother or more concentrated. By normalizing and weighting all local curve segments according to their weight functions, the final dimensionless curve obtained by splicing the entire span is obtained: 。 9. The method for predicting bridge pier scour based on single-beam sonar and flume experiments according to claim 1, characterized in that, In the step of acquiring real-time on-site data and inputting it into the trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve, a complete scour curve prediction is generated based on the real-time on-site input. Meanwhile, the response surface model calculates correction values ​​for key anchor points based on the input parameters and applies these anchor point constraints to the initial deep learning curve: if the values ​​of the initial curve at key points are inconsistent with the RSM prediction, the curve is adjusted and interpolated to pass through these anchor points; the adjustment method is to scale and translate the initial curve vertically and laterally, or to use local polynomial approximation near the key points to fit the target value given by the RSM; after the anchor point correction process, the obtained scour profile curve is consistent with the empirical or physical model at key locations, while the overall shape is still provided by the deep learning model, ensuring the smoothness and rationality of the curve; Since both the training data and the data processed from actual bridge monitoring are dimensionless, directly inputting the actual bridge data into the model will yield a dimensionless predicted scour curve. Scale transformation can then be performed to obtain the scour profile at the actual scale. The inverse transformation of the horizontal coordinate is expressed as follows: The inverse transformation of the vertical coordinate is expressed as follows: 。 10. A bridge pier scour prediction system based on single-beam sonar and flume experiments, characterized in that, include: The monitoring target pier selection module is used to quantitatively assess the piers in navigable waterways and select the piers with the highest comprehensive scour risk as monitoring targets. The on-site flow field parameter acquisition module is used to acquire on-site flow field parameters for the bridge piers that are the monitoring objects. The flume scouring experiment module is used to set up a bridge pier model and a riverbed scene in a flume according to the on-site flow field parameters, and to conduct flume scouring experiments. The scour pit detection module is used to detect the cross-section of the scour pit on the water-facing side of the bridge pier after the water tank scour test, and to obtain the curve shape from the bottom of the pit to the edge transition zone. The training dataset building module is used to extract water tank flushing experimental data based on the curve shape of the transition zone from the bottom of the pit to the edge, and to build the training dataset. The pier scour curve prediction model training module is used to train a pre-established pier scour curve prediction model using a training dataset. The model prediction module is used to acquire real-time on-site data and input it into a trained bridge pier scour curve prediction model to obtain the bridge pier scour prediction curve.

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