A method for predicting bridge scour depth based on Markov processes

Abstract

This invention discloses a bridge scour depth prediction method based on Markov processes, belonging to bridge structural health monitoring technology. The method first calculates the scour velocity based on the sediment initiation velocity, then uses a hydraulic model to assess the relationship between velocity and flow rate to determine the scour threshold. Next, it uses a POT model to screen historical hydrological events exceeding the scour threshold and quantifies their characteristic parameters. Then, for the determined hydrological event variables, it selects the best-fitting univariate marginal distribution and conducts multivariate joint analysis based on Copula theory. Following this, it calibrates the scour depth model parameters based on measured hydrological and scour data, and uses discrete-time and discrete-state Markov processes to predict the scour depth throughout the bridge's lifespan. Finally, based on the prediction results, it derives the probability distribution of the bridge's lifespan scour depth, thereby determining whether the scour depth exceeds the foundation depth and implementing multi-level scour early warning based on this distance.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring technology and also relates to the field of artificial intelligence analysis, specifically to a method for predicting bridge scour depth based on Markov processes. Background Technology

[0002] Bridges are susceptible to various harsh environmental conditions and human factors throughout their service life, with foundation scour being widely recognized as the leading cause of bridge collapse and damage. In fact, most bridges spanning rivers (rivers, seas, etc.) are subject to flooding year-round, inevitably impacting their piers and foundations with scour. Furthermore, most major bridge accidents globally are related to reduced foundation depth caused by localized scour at the piers.

[0003] For a long time, researchers both at home and abroad have explored many practical assessment methods for bridge scour evaluation, which have played a significant role in the actual assessment of bridge scour depth. At the same time, various countries have also formulated their own bridge scour evaluation standards or technical methods based on their own hydrological conditions, geological characteristics, and other practical circumstances, providing specific guidance for bridge scour depth assessment.

[0004] Currently, the commonly used methods for assessing bridge scour depth both domestically and internationally mainly include:

[0005] Although the on-site measurement method is intuitive and simple to operate and the data is real and reliable, it is labor-intensive and resource-intensive, limited by hydrological conditions and environmental factors, and is difficult to measure, inefficient, and difficult to achieve long-term continuous monitoring.

[0006] Empirical formula methods require a good theoretical foundation and have low operating costs, but most formulas are developed based on specific riverbed types, have limited applicability, and cannot simulate the dynamic process of scour over time.

[0007] Physical model testing is highly intuitive and accurate, making it suitable for complex conditions. However, it is costly, time-consuming, and the scaling effect may affect the accuracy of the results, making it difficult to fully simulate the sediment transport characteristics of actual riverbeds.

[0008] Numerical simulation methods offer advantages such as quick parameter adjustment, high flexibility, and wide applicability. However, they are highly dependent on the accuracy of sediment transport models, and calculation errors may be significant. They require high-performance computing resources, and verification still relies on experimental or measured data.

[0009] Automated monitoring methods are accurate, efficient, and can achieve continuous monitoring and early warning. However, they require a large number of sensors, and underwater installation and long-term maintenance are costly and difficult. They are also prone to damage in complex hydrological environments, and extreme weather may affect monitoring accuracy.

[0010] It is evident that traditional bridge scour assessment methods suffer from drawbacks such as inconsistent standards, strong subjectivity, large-scale testing, high costs, and long time consumption. Meanwhile, new monitoring methods are still in the research stage and have many limitations in practical applications, making them difficult to promote and popularize. Summary of the Invention

[0011] Purpose of the invention: To address the shortcomings of the existing technology, this invention provides a method for predicting bridge scour depth based on Markov processes.

[0012] Technical solution: A method for predicting and early warning of bridge scour depth based on Markov processes, comprising the following steps:

[0013] (1) Calculate the scour occurrence velocity, river hydraulic characteristics and bridge geometric characteristics based on the sediment initiation velocity. Use a hydraulic model to evaluate the relationship between velocity and flow rate, determine the scour threshold q0, and then screen historical hydrological events that exceed the scour threshold q0 based on the POT model and quantify their characteristic parameters. The characteristic parameters include the scour occurrence velocity, river hydraulic characteristics and bridge geometric characteristics parameters.

[0014] (2) For the selected historical hydrological events, select the best-fitting univariate marginal distribution, and then conduct multivariate joint analysis based on Copula theory;

[0015] The univariate marginal distributions mentioned include the log-normal distribution, Gumbel distribution, Pearson type III distribution, generalized extreme value distribution, and generalized Pareto distribution;

[0016] (3) Based on the measured hydrological data and scour data, the parameters of the scour depth model are calibrated, and the scour depth during the entire life of the bridge is predicted by using a Markov process with discrete time and discrete state.

[0017] (4) The probability distribution of the scour depth of the bridge throughout its entire life is calculated based on the discrete Markov process, and then it is determined whether the scour depth exceeds the foundation depth. If it does, an early warning is issued in time; if it does not exceed, the distance from the scour pit to the bottom of the foundation is calculated, and a multi-level scour warning is formulated based on this distance.

[0018] Furthermore, the POT model includes the use of peak splitting method and lag autocorrelation coefficient to test the independence of hydrological series.

[0019] Step (2) specifically includes:

[0020] (21) Based on the fitting of the univariate marginal distribution, the theoretical cumulative distribution function is obtained through parameter estimation;

[0021] (22) Compare the theoretical cumulative distribution function with the empirical cumulative distribution function, and conduct fitting tests and screening of the marginal distribution using statistical indicators including KS test, root mean square error, AIC criterion and BIC criterion;

[0022] (2.3) Construct the joint distribution of hydrological variables based on Archimedes Copula functions including Gumbel, Clayton and Fran, and conduct fitting tests and screening of Copula functions through root mean square error, AIC criterion and BIC criterion.

[0023] The construction of the Markov process described in step (3) specifically includes:

[0024] Flood events in hydrological events are modeled using a homogeneous Poisson process. Let λ represent the flood event occurrence rate. Then, the probability of n events occurring within time t is... Expressed as:

[0025]

[0026] The scour depth is divided into N s There are finite discrete states, where the first state corresponds to the scour depth developing from zero initial scour depth under the weakest flood condition, and the last state corresponds to the equilibrium scour depth under the strongest flood condition. The calculation and analysis process is as follows:

[0027] Let k denote a flood event with flow rate Q > q0, and let... This indicates that after the known occurrence of the k-th flood event, the object is in a state of scouring, with depth j corresponding to the scouring depth. The probability of this can be obtained by:

[0028]

[0029] In the formula, This indicates that the bridge was at its scour depth when the flood began. The probability, The transition probability, i.e., the probability of reaching state j when the initial scour depth is i, is expressed in matrix form as follows:

[0030]

[0031] In the formula, and For the start and end of flood event k, the dimension is 1×N. s The scour depth probability vector For dimension N s ×N sThe transition probability matrix TPM is obtained, and thus the transition probability matrix TPM at the time of the kth flood can be determined by combining flood hazard, hydrological information and river hydraulic conditions.

[0032] Assuming that the change in scour depth during the k-th flood is entirely controlled by the hydraulic parameters of that event and is independent of the flood event k, the stochastic scour accumulation process is a homogeneous Markov chain, completely governed by the state transition matrix. Characterization, the probability mass function at the nth flood occurrence Expressed as:

[0033]

[0034] Given N = n floods, at time t, the scour depth s j The conditional probability is:

[0035]

[0036] Furthermore, the unconditional probability of being in depth j at time t is:

[0037]

[0038] Therefore, the expected value of the scour depth at time t is expressed as:

[0039]

[0040] Additionally, given The probability of time Expressed as:

[0041]

[0042] Finally, the transcendence probability of state j is expressed as:

[0043]

[0044] Solving the transition probability matrix of flood samples based on Monte Carlo simulation We obtain the probability mass distribution and complementary cumulative distribution of the lifetime scour depth.

[0045] Furthermore, the calibration preprocessing of the time-varying scour depth model parameters in step (3) is as follows:

[0046] Input basic parameter data, including measured river channel width, bridge pier geometry, and grain size distribution of riverbed sediments;

[0047] Input time series data of water depth, flow velocity, flow rate, and scour depth, and calculate the scour depth;

[0048] The root mean square error of the scour depth is calculated using a genetic algorithm, thereby estimating the optimal parameters of the dimensionless effective flow work model. The mathematical expression of the dimensionless effective flow work model is as follows:

[0049]

[0050] In the formula Z * To standardize the scour depth, c1, c2, and c3 are fitting parameters, W * It is the dimensionless effective work of the water flow.

[0051] Furthermore, step (3) allows for the fitting of a time-varying model of the bridge's scour depth based on the average scour depth at different times. The mathematical expression for this model is as follows:

[0052]

[0053] Where, d s (t) represents the time-varying scour depth; t represents the time parameter; a, b, c, and d are fitting coefficients. The four fitting coefficients are solved using the least squares method to obtain the time-varying scour depth of the bridge throughout its entire lifespan.

[0054] The implementation process of step (4) includes dimensionless processing using the ratio of bridge scour depth to foundation burial depth before scour, and then dynamically dividing multi-level early warning zones according to the scour depth throughout the entire life.

[0055] Beneficial effects: Compared with existing methods, this invention considers the influence of multi-parameter correlation of hydrological events and nonlinear dynamic evolution of scour during bridge scour depth prediction and early warning. It constructs multivariate dependencies through a Copula joint distribution and combines Markov processes to simulate the full-lifetime scour evolution. This solves the problems of traditional methods such as insufficient characterization of complex hydrological coupling effects, limited accuracy of dynamic scour depth prediction, and static early warning grading. Its substantial features and significant effects also include:

[0056] 1. A hydrological multivariate dependency model is constructed based on the Copula joint distribution. By optimizing the marginal distribution and Copula function type, the nonlinear correlation between hydrological parameters is accurately captured, overcoming the shortcomings of traditional univariate analysis in characterizing the coupling effect of hydrological events and improving the prediction reliability of extreme scour scenarios.

[0057] 2. Based on Markov process simulation, the dynamic evolution of scour throughout the entire life cycle is simulated. By using discrete state transition probability matrix and Monte Carlo simulation, the time-series cumulative effect of scour depth under different flood events is quantified. Combined with DFW model parameter optimization, continuous prediction from short-term scour increment to scour depth throughout the entire life cycle is realized, which solves the problem that traditional methods are difficult to reflect the time dependence of the scour process.

[0058] 3. Based on this invention, a dynamic multi-level early warning mechanism combining scour depth can be established; by dedimensionalizing the ratio of scour depth to foundation burial depth and combining the full life scour probability distribution, the early warning area is divided into several risk intervals, overcoming the limitation that static thresholds are difficult to adapt to the safety requirements of the entire life cycle of bridges. Attached Figure Description

[0059] Figure 1 This is a flowchart of a multi-level early warning method for bridge scour depth based on Copula joint distribution and Markov process according to an embodiment of the present invention.

[0060] Figure 2 A simplified flowchart of a bridge full-life scour depth prediction and early warning method according to an embodiment of the present invention;

[0061] Figure 3 This is a diagram showing the layout of bridge scour monitoring points according to an embodiment of the present invention (unit: cm).

[0062] Figure 4 This is a diagram showing the on-site measurement results of scouring and water flow synchronization according to an embodiment of the present invention;

[0063] Figure 5 This is a schematic diagram of a bridge structure according to an embodiment of the present invention (unit: cm).

[0064] Figure 6 This is a river daily average flow sequence diagram according to an embodiment of the present invention;

[0065] Figure 7 is a result diagram of the peak flood exceeding the threshold according to an embodiment of the present invention, wherein Figure 7(a) is a peak flood discharge diagram exceeding the threshold, and Figure 7(b) is the result of the hysteresis autocorrelation test;

[0066] Figure 8 shows the best marginal distribution fitting results of flood variables according to an embodiment of the present invention, wherein Figure 8(a) is the peak flow result and Figure 8(b) is the duration result;

[0067] Figure 9 shows the joint distribution results of flood variables in one embodiment of the present invention, wherein Figure 9(a) is the empirical cumulative distribution function and Figure 9(b) is the BB7 Copula cumulative distribution function.

[0068] Figure 10 is a time evolution diagram of local scour of a bridge according to an embodiment of the present invention, wherein Figure 10(a) is a DFW model fitting diagram and Figure 10(b) is a scour depth evolution diagram under flood wave.

[0069] Figure 11 This is a Monte Carlo simulation result of a flood sample according to an embodiment of the present invention;

[0070] Figure 12 is a diagram of the state transition matrix calculation results according to an embodiment of the present invention, wherein Figure 12(a) is a diagram of the state transition matrix of flood event q1, and Figure 12(b) is a diagram of the transition probability matrix of the flood sample;

[0071] Figure 13 shows the calculation results of a Markov process according to an embodiment of the present invention, wherein Figure 13(a) is the probability mass function of scour depth and Figure 13(b) is the complementary cumulative distribution function of scour depth.

[0072] Figure 14 This is a graph showing the calculation results of the mean and standard deviation of the time-varying scour depth according to an embodiment of the present invention;

[0073] Figure 15 This is a diagram showing the calculation results of the equilibrium scour depth using different standard formulas according to an embodiment of the present invention;

[0074] Figure 16 This is a diagram showing the early warning results of bridge scour depth throughout its entire lifespan, according to an embodiment of the present invention. Detailed Implementation

[0075] The technical solution of the present invention will be explained and described in detail below with reference to the accompanying drawings and specific embodiments.

[0076] The present invention provides a bridge scour depth prediction system and method based on Markov process. The method is based on the Copula joint distribution and Markov process for predicting and warning of bridge scour depth throughout its life cycle, including scour depth calculation and prediction and warning process. The following is a flowchart of one implementation of the method.

[0077] To achieve accurate prediction and dynamic early warning of bridge scour depth throughout its entire lifespan, it is necessary to comprehensively consider the correlation of hydrological variables and the temporal evolution characteristics of the scour process. Traditional assessment methods often employ univariate analysis or static models, which are insufficient to characterize the dynamic changes in scour depth under complex hydrological conditions. Furthermore, the cumulative process of scour depth over time exhibits both randomness and dependency, making it difficult for static models to reflect the evolutionary patterns throughout the entire lifespan. Therefore, as shown, this invention proposes a prediction method combining Copula joint distribution and Markov processes. First, a multivariate hydrological dependency model is constructed; then, the temporal evolution of scour depth is simulated; finally, risk levels are classified based on relative scour depth to achieve dynamic early warning throughout the entire lifespan. Specifically, this can be achieved through remote monitoring and / or on-site maintenance alerts.

[0078] I. Bridge Scour Data Collection and Analysis

[0079] Combination Figure 3Taking a bridge as an example, this paper illustrates the data acquisition process and method. The main bridge is 220m long, a seven-span variable cross-section continuous beam bridge (6×30+40)m, with the beam height varying according to a quadratic parabola. The bridge uses elliptical foundations, with piers 1.5m wide and pile foundations 2.5m wide. Flood flow was measured using an Acoustic Doppler Current Profiler (ADCP) (SonTek, RiverSurveyor M9), deployed at the water flow locations of the piers. Scour depth was measured at the piers using ultrasonic scour sensors (Airmar, Echorange SS510) at a frequency of 10 minutes. The parameters of the deployed scour sensors were processed. A six-day field measurement of scour and water flow was conducted on the bridge. The local scour and sediment deposition on the bridge piers during the flood wave were analyzed, and the effects of different water flow and sediment supply conditions were studied. Figure 4 Graphs of flood discharge and scour depth data obtained through measurements are presented. During field measurements, when the flood discharge exceeded the scour threshold, the scour depth increased rapidly during the rising portion of the flood discharge, but remained almost unchanged during the receding phase, with slight filling of the scour pit. In some time intervals, the scour depth did not increase because the flood discharge was lower than the flow rate required to induce scour. Therefore, multiple floods can cause bridges to reach the critical scour depth, and the probability increases with the number, intensity, and duration of floods. Most existing studies indicate that the cumulative effect of scour triggered by multiple flood events is considered a significant cause of bridge damage, demonstrating the rationality and necessity of the proposed method in scour analysis.

[0080] II. Extraction of Key Hydrological Events Based on the POT Model

[0081] The POT model, by appropriately selecting thresholds to control the number of flood events included in the analysis and reducing uncertainty in flood frequency analysis, is used in hydrological analyses such as flood frequency and trend analysis. It includes the following:

[0082] (2.1) First, the peak separation method proposed by the U.S. Water Resources Commission (USWRC) is used to test the independence of the peak sequence. This method requires that the time interval between consecutive flood peaks be at least five days plus the natural logarithm of the catchment area to ensure that the two events are not hydrologically correlated. In addition, it requires that the trough flow between two consecutive peaks (i.e., the minimum flow between events) must be less than 75% of the lower of the two flood events to avoid misclassifying the secondary peak of the same flood process as an independent event. Furthermore, the independence of the flood peak sequence is tested by calculating the lag autocorrelation coefficient.

[0083] (2.2) Then, the scour velocity is calculated by determining the sediment initiation velocity. Based on the hydraulic characteristics of the river channel and the geometric characteristics of the bridge, if the riverbed cross-section is regular and the cross-sectional area is easy to quantify, the Manning formula can be directly used to evaluate the relationship between velocity and flow rate, thereby calculating the threshold flow rate q0.

[0084] To verify the practicality of the proposed method, a typical scour scenario of a cross-river bridge with extended pile axle support is selected as a case study. The prototype of this case study is a Class I highway cross-river bridge with a span arrangement of 2×28m. The overall structure and geometric parameters are shown in the figure. The main beam is a T-beam structure with a total width of 13.2m and a beam height of 2.0m. The piers adopt the circular double-column frame piers commonly used in highway bridges, with a pier diameter of 1.5m and a height of 6m; the piles under the piers are 20m long, and 1.5m diameter bored piles are selected, with a foundation depth of 3m. The river channel has a rectangular cross-section and a width of 50m. The surface layer of the riverbed consists of fine sand and gravel with a relative density of 1.65 and a median particle size of 5mm; due to the clean and straight river channel, the Manning roughness coefficient is taken as 0.035. In addition, a hydrological observation station is located near the bridge, which records the daily average flow sequence of the river from January 1, 1950 to January 1, 2020. The data comes from the Hydrological Bureau's public database and provides basic hydrological information for scour analysis, as shown in the figure.

[0085] The sediment initiation velocity was calculated based on the recommended formula in the "Specifications for Hydrological Survey and Design of Highway Engineering" (JTG C30-2015). For cases with a wide channel and regular cross-section, the Manning formula was directly applied for back-calculation, yielding a threshold flow rate of 10.07 m³ / h. 3 / s. As shown in (a), the flood variables exceeding the threshold (considering peak flow and duration) are delineated using the peak-splitting method, and the relevant statistics are described in [reference needed]. Simultaneously, the independent and identically distributed hypothesis is verified using the lagged autocorrelation test of the flood variables. The test results (e.g.) As shown in (b), the autocorrelation of the two flood variables is not significant, indicating that the selected threshold does not violate the independent and identically distributed hypothesis. The flood occurrence process can be described by a homogeneous Poisson process with an annual occurrence rate of 5.48.

[0086] Table 1. Statistical description of flood variables

[0087]

[0088] III. Constructing a Multivariate Dependency Model Based on Copula Joint Distribution

[0089] As shown, six parameter distributions—LN, GUM, GAM, P-III, GEV, and GP—were used to fit the flood variable, and the parameters of each distribution were estimated using the maximum likelihood method. The KS test (D) was employed. nFour statistical methods—RMSE, AIC criterion, and BIC criterion—were used to measure the goodness of fit of the marginal distributions of flood variables. The results are shown in [Figure number missing]. At a 5% significance level, for peak flow P, only the GP and GEV distributions among the candidate distributions passed the hypothesis test. For duration D, the LN, GAM, and GEV distributions passed the hypothesis test. It is clear that for peak flow, the GP distribution provides the smallest RMSE, BIC, and AIC values; therefore, the GP distribution is selected as the optimal marginal distribution. For duration, the GAM distribution is selected as the optimal marginal distribution.

[0090] Table 2. Parameter distribution fit test

[0091]

[0092] The Archimedes Copula function, commonly used in hydrology, was used to construct the joint distribution of flood peak discharge and duration. The parameters of the Copula function were calculated using the maximum likelihood method, and the results are shown below. Finally, all Copula functions were compared in terms of RMSE, AIC, and BIC. It is clear that the BB7 and BB1 Copula functions are more suitable for constructing the joint distribution, followed by the Clayton Copula function. The empirical cumulative distribution function and the cumulative distribution function of the BB7 Copula are shown. As can be seen from the figure, the two joint cumulative distribution functions have almost the same shape, providing a good fit to the joint distribution of flood variables.

[0093] Table 3. Copula function fit test

[0094]

[0095] IV. Predicting Lifetime Scour Depth Based on Markov Processes

[0096] To assess the time-varying scour depth of a bridge under a given flood discharge line, a dimensionless effective flow work (DFW) model is employed. The DFW model utilizes the dimensionless effective flow work (W)... ∗ This method can accurately estimate the time-varying scour depth under complex hydraulic conditions. As shown in (a), the DFW model fits the field-measured scour depth, with a root mean square error of 0.023 m and a Nash efficiency coefficient of 0.96, indicating a very good model fit. (b) presents the results with zero scour depth as the initial condition and a peak flow rate of 300 m³ / h. 3 A flood event lasting 10 days was used, with an exponential function to describe the shape of the single-peak flood wave. The time evolution of the scour depth was calculated using the DFW model under fitted parameters.

[0097] After obtaining the joint distribution of flood variables, a set of N can be used. sample Monte Carlo simulations of 10,000 flood samples yielded flood events of varying durations (as shown). This was used to calculate TPM. Consider a set of N s The scour condition is 25, with a discrete scour depth of 0.15m. For 10,000 flood samples Q, the conditional TPM needs to be calculated first. , representing TPM conditioned on flood variables. This requires, under the actual flood line, for N s The maximum scour depth was calculated using different initial values ​​for scour depth. Notably, given the channel and riverbed properties and the determined hydraulic model parameters, there is a one-to-one relationship between flood events and scour depth.

[0098] For peak flow rate of 300m 3 / s, a flood event lasting 10 days It introduced The calculation process is as follows. From the results in (b), we know that when the initial scour depth is 0m (state 1), the obtained scour depth is 2.04m. This value corresponds to scour state 14, therefore, when j ≠ 14... When j = 14, the value is 1. Assuming an initial scour depth of 1.8m (state 13), under the same flood conditions, the final scour depth is 2.10m (state 15). Therefore, when j = 15, When j ≠ 15, it is 0. Finally, assuming the initial scour depth is 2.7m (state 19), due to the peak flow rate of 300m³ / h... 3 A flood of / s is too weak to cause an increase in scour depth. Therefore, when j = 19, When j ≠ 19, the value is 0. This process can be used to estimate N. sample q i Sample .

[0099] Evaluation matrix for each simulated flood event Then, the matrix can be estimated. for:

[0100]

[0101] The matrix of flood event q1 and transition probability matrix The chessboard diagram. As expected, if the flood occurs at a low scour depth, the likelihood of increasing the scour depth is high, while if the scour pit is already deep, the likelihood of increasing the scour depth is low.

[0102] Furthermore, the probability mass function p for scour depth at different times can be obtained. j (t). (a) shows the initial scour depth state when there is no scour (i.e., when j = 1). p obtained j (t) value. In addition, complementary cumulative distribution functions of scour depth under different bridge lifespans can be obtained (e.g., (b)).

[0103] It can be observed that the probability distribution of scour depth is relatively dispersed in the early stages, but as time increases, the probability distribution shifts towards higher values ​​of scour depth and gradually stabilizes. The average scour depth at different times can be obtained, and a time-varying model of the scour depth of the example bridge can be fitted based on the average value. The changes of the mean and standard deviation of the scour depth over time are shown below. As shown, the average scour depth increases over time, but the rate of increase decreases, reaching an average of 3.08 m after 100 years. Meanwhile, the standard deviation gradually decreases, indicating that the scour depth gradually stabilizes.

[0104] The equilibrium scour depth can be calculated using the Froehlich equation, Melville equation, Sheppard equation, HEC-18 equation, S / M equation, and several different formulas proposed in Chinese standards. For the example bridge, Chinese standards specify using a 100-year flood event to verify the scour depth. For example... Figure 15 As shown, the estimated values ​​of scour depth at different times (e.g.) Figure 14 The equilibrium scour depth values ​​calculated for floods with corresponding return periods were compared. In general, the scour depth estimates from different formulas are more dispersed compared to time-varying scour depth values. Taking a 100-year return period as an example, their average value is 3.46 m, and the standard deviation is 1.14. The scour depth obtained in this invention is relatively close to the estimate from the HEC-18 equation.

[0105] The HEC-18 equations are as follows:

[0106]

[0107] In the formula, The local scour depth (m) is the local scour depth. The width of the bridge pier (m) The pier shape coefficient, This is the correction factor for the angle of attack of the water flow. This is a correction factor for riverbed conditions. This is the sediment size distribution coefficient. This represents the maximum water depth (m) after typical flushing. It is a Froude number.

[0108] V. Dynamic Multi-Level Early Warning Judgment and Output for Scouring

[0109] To achieve dynamic multi-level early warning of foundation scour, this invention performs dimensionless processing on the ratio of scour depth to foundation burial depth, and then dynamically divides multi-level early warning zones based on the scour depth throughout the foundation's lifespan. Foundation burial depth is a key parameter determining a bridge's scour resistance and the risk of scour failure.

[0110] (5.1) Scouring risk indicators and classification

[0111]

[0112] In the formula, the relative scour depth D R As an indicator for classifying bridge scour risk, D T D represents the time-varying scour depth. F This refers to the depth of the bridge foundation.

[0113] (5.2) Multi-level early warning assessment of bridge scour

[0114] Based on relevant standards, engineering experience, and the characteristics of bridges, bridge scour risks are classified into three levels, as detailed in Table 4.

[0115] Table 4. Criteria for Assessing the Risk Level of Scour

[0116]

[0117] like Figure 16 As shown in the figure, the warning zones are dynamically divided into Level 1, Level 2, and Level 3 based on the relationship between relative scour depth and bridge service life. The figure indicates that when the bridge service life is 0-4.0 years, it is at Level 3 scour risk; when the bridge service life is 4.0-67.2 years, it is at Level 2 scour risk; and when the bridge service life is over 67.2 years, it is at Level 1 scour risk. Different alarm response measures are implemented according to different warning levels.

[0118] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting and warning the depth of bridge scour based on Markov processes, characterized in that, Includes the following steps: (1) Calculate the scour occurrence velocity, river hydraulic characteristics and bridge geometric characteristics based on the sediment initiation velocity. Use a hydraulic model to evaluate the relationship between velocity and flow rate, determine the scour threshold q0, and then screen historical hydrological events that exceed the scour threshold q0 based on the POT model and quantify their characteristic parameters. The characteristic parameters include the scour occurrence velocity, river hydraulic characteristics and bridge geometric characteristics parameters. (2) For the selected historical hydrological events, select the best-fitting univariate marginal distribution, and then conduct multivariate joint analysis based on Copula theory; The univariate marginal distributions mentioned include the log-normal distribution, Gumbel distribution, Pearson type III distribution, generalized extreme value distribution, and generalized Pareto distribution; (3) Based on the measured hydrological data and scour data, the parameters of the scour depth model are calibrated, and the scour depth during the entire life of the bridge is predicted by using a Markov process with discrete time and discrete state. (4) The probability distribution of the scour depth of the bridge throughout its entire life is calculated based on the discrete Markov process, and then it is determined whether the scour depth exceeds the foundation depth. If it does, an early warning is issued in time; if it does not exceed, the distance from the scour pit to the bottom of the foundation is calculated, and a multi-level scour warning is formulated based on this distance.

2. The bridge scour depth prediction and early warning method according to claim 1, characterized in that, The POT model includes the use of peak splitting method and lag autocorrelation coefficient to test the independence of hydrological series.

3. The bridge scour depth prediction and early warning method according to claim 1, characterized in that, Step (2) specifically includes: (21) Based on the fitting of the univariate marginal distribution, the theoretical cumulative distribution function is obtained through parameter estimation; (22) Compare the theoretical cumulative distribution function with the empirical cumulative distribution function, and conduct fitting tests and screening of the marginal distribution using statistical indicators including KS test, root mean square error, AIC criterion and BIC criterion; (2.3) Construct the joint distribution of hydrological variables based on Archimedes Copula functions including Gumbel, Clayton and Fran, and conduct fitting tests and screening of Copula functions through root mean square error, AIC criterion and BIC criterion.

4. The bridge scour depth prediction and early warning method according to claim 1, characterized in that, The construction of the Markov process described in step (3) specifically includes: Flood events in hydrological events are modeled using a homogeneous Poisson process. Let λ represent the flood event occurrence rate. Then, the probability of n events occurring within time t is... Represented as: ， The scour depth is divided into N s There are finite discrete states, where the first state corresponds to the scour depth developing from zero initial scour depth under the weakest flood condition, and the last state corresponds to the equilibrium scour depth under the strongest flood condition. The calculation and analysis process is as follows: Let k denote a flood event with flow rate Q > q0, and let... This indicates that after the known occurrence of the k-th flood event, the object is in a state of scouring, with depth j corresponding to the scouring depth. The probability of this can be obtained by: ， In the formula, This indicates that the bridge was at its scour depth when the flood began. The probability, The transition probability, i.e., the probability of reaching state j when the initial scour depth is i, is expressed in matrix form as follows: ， In the formula, and For the start and end of flood event k, the dimension is 1×N. s The scour depth probability vector For dimension N s ×N s The transition probability matrix TPM is obtained, and thus the transition probability matrix TPM at the time of the kth flood can be determined by combining flood hazard, hydrological information and river hydraulic conditions. Assuming that the change in scour depth during the k-th flood is entirely controlled by the hydraulic parameters of that event and is independent of the flood event k, the stochastic scour accumulation process is a homogeneous Markov chain, completely governed by the state transition matrix. Characterization, the probability mass function at the nth flood occurrence Represented as: ， Given N = n floods, at time t, the scour depth s j The conditional probability is: ， Furthermore, the unconditional probability of being in depth j at time t is: ， Therefore, the expected value of the scour depth at time t is expressed as: ， Additionally, given The probability of time Represented as: ， Finally, the transcendence probability of state j is expressed as: ， Solving the state transition matrix of flood samples based on Monte Carlo simulation. We obtain the probability mass distribution and complementary cumulative distribution of the lifetime scour depth.

5. The bridge scour depth prediction and early warning method according to claim 1 or 4, characterized in that, Step (3) involves the following preprocessing steps for calibrating the time-varying scour depth model parameters: Input basic parameter data, including measured river channel width, bridge pier geometry, and grain size distribution of riverbed sediments; Input time series data of water depth, flow velocity, flow rate, and scour depth, and calculate the scour depth; The root mean square error of the scour depth is calculated using a genetic algorithm, thereby estimating the optimal parameters of the dimensionless effective flow work model. The mathematical expression of the dimensionless effective flow work model is as follows: ， In the formula Z * To standardize the scour depth, c1, c2, and c3 are fitting parameters, and W * It is the dimensionless effective work of the water flow.

6. The bridge scour depth prediction and early warning method according to claim 1 or 4, characterized in that, Step (3) Based on the average scour depth at different times, a time-varying model of the bridge scour depth can be fitted, and its mathematical expression is as follows: ， In the formula, d s (t) represents the time-varying scour depth, where t represents the time parameter, and a, b, c, and d are fitting coefficients. The four fitting coefficients are solved using the least squares method to obtain the time-varying scour depth of the bridge throughout its entire lifespan.

7. The bridge scour depth prediction and early warning method according to claim 1, characterized in that, The implementation process of step (4) includes dimensionless processing using the ratio of bridge scour depth to foundation burial depth before scour, and then dynamically dividing multi-level early warning zones according to the scour depth throughout the life.

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