Bridge scour depth prediction method based on Markov process

Abstract

The invention discloses a Markov process-based bridge scouring depth prediction method, and belongs to a bridge structure health detection technology. The method comprises the following steps: firstly, calculating a scouring occurrence flow velocity according to a sediment starting flow velocity, evaluating a relationship between the flow velocity and a flow rate by adopting a hydraulic model, determining a scouring threshold value, then screening historical hydrological events exceeding the scouring threshold value based on a POT model, and quantifying characteristic parameters of the historical hydrological events; then, for the determined hydrological event variables, selecting optimally-fitted single-variable edge distribution, and carrying out multivariable conjoint analysis on the basis of a Copula theory; then, according to actually measured hydrological data and scouring data, scouring depth model parameters are calibrated, and the scouring depth of the bridge in the whole life period is predicted through the Markov process of discrete time and a discrete state; and finally, obtaining probability distribution of the full-life scouring depth of the bridge according to a prediction result, further judging whether the scouring depth exceeds the foundation burial depth or not, and implementing multi-stage early warning of scouring according to the distance.

Description

Technical Field

[0001] The present invention relates to bridge structure health monitoring technology and also to the field of artificial intelligence analysis, in particular to a bridge scour depth prediction method based on a Markov process. Background Art

[0002] Throughout their service life, bridges are susceptible to a variety of adverse environmental conditions and human factors. Foundation scour is widely recognized as the leading cause of bridge collapse and failure. In fact, most bridges spanning rivers (rivers, seas, etc.) are subject to frequent flooding, and scour inevitably impacts their piers and foundations. Furthermore, the majority of major bridge accidents worldwide are associated with reduced foundation depth due to localized scour at the piers.

[0003] For a long time, researchers at home and abroad have developed a number of practical assessment methods for bridge scour assessment. These methods have played a significant role in the actual evaluation of bridge scour depth. At the same time, each country has also developed its own bridge scour assessment standards or technical methods based on its own hydrological conditions, geological characteristics, and other actual conditions, providing specific guidance for bridge scour depth assessment.

[0004] At present, the commonly used methods for bridge scour depth assessment at home and abroad mainly include:

[0005] The on-site measurement method is intuitive and simple to operate, and the data is authentic and reliable. However, it consumes manpower and material resources, is limited by hydrological conditions and environmental factors, is difficult to measure, has low efficiency, and is difficult to achieve long-term continuous monitoring.

[0006] The empirical formula method requires a good theoretical basis and has low operating costs, but most formulas are developed based on specific riverbed types, have a limited scope of application, and cannot simulate the dynamic process of scour development over time.

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

[0008] Numerical simulation methods can quickly adjust parameters, have high flexibility, and a wide range of applications. However, they rely heavily on the accuracy of the sediment movement model, and the calculation error may be large. They require high-performance computing resources, and verification still needs to rely on experimental or measured data.

[0009] The automated monitoring method is accurate, efficient, and can achieve continuous monitoring and early warning. However, it requires a large number of sensors, and the underwater installation and long-term maintenance costs are high and difficult to maintain. It is easily damaged in complex hydrological environments, and extreme weather may affect monitoring accuracy.

[0010] It can be seen that the traditional bridge scour assessment method has defects such as inconsistent standards, strong subjectivity, large test scale, high cost, and long time consumption. The new monitoring method is still in the research stage and has many limitations in practical applications, making it difficult to promote and popularize. Summary of the Invention

[0011] Purpose of the invention: In view of the above-mentioned deficiencies in the prior art, the present invention provides a bridge scour depth prediction method based on Markov process.

[0012] Technical solution: A bridge scour depth prediction and early warning method based on Markov process, including the following steps:

[0013] (1) The scour velocity, river hydraulic characteristics, and bridge geometric characteristics are calculated based on the sediment initiation velocity. The relationship between velocity and flow is evaluated using a hydraulic model to determine the scour threshold q0. Then, based on the POT model, historical hydrological events exceeding the scour threshold q0 are screened and their characteristic parameters are quantified. The characteristic parameters include the scour velocity, river hydraulic characteristics, and bridge geometric characteristics.

[0014] (2) For the historical hydrological events screened, the best-fitting single-variable marginal distribution is selected, and then a multivariate joint analysis is conducted based on the Copula theory;

[0015] The univariate marginal distributions include lognormal distribution, Gumbel distribution, Pearson type III distribution, generalized extreme value distribution and generalized Pareto distribution;

[0016] (3) Calibrate the scour depth model parameters based on measured hydrological data and scour data, and use a discrete-time and discrete-state Markov process to predict the scour depth over the entire life of the bridge;

[0017] (4) The probability distribution of the scour depth over the entire life of the bridge is calculated based on the discrete Markov process, and then it is determined whether the scour depth exceeds the foundation burial depth. If it does, an early warning is issued in time; if it does not, 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 using a peak separation method and a lagged autocorrelation coefficient to test the independence of the 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 marginal distributions using statistical indicators including KS test, root mean square error, AIC criterion, and BIC criterion;

[0022] (2.3) The joint distribution of hydrological variables is constructed based on the Archimedean Copula functions including Gumbel, Clayton and Fran, and the fitting test and screening of the Copula functions are carried out using the root mean square error, AIC criterion and BIC criterion.

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

[0024] The flood events in the hydrological events are modeled by the homogeneous Poisson process, and the occurrence rate of flood events is represented by λ. Then the probability of n events occurring in 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 represent a flood event with flow Q > q0, let It means that after the occurrence of the kth flood event, the water level is in the scouring state j and the corresponding depth is The probability of , and then we get:

[0028]

[0029] Where, Indicates that the bridge was at scour depth when the flood began The probability of It represents the transition probability, that is, the probability of reaching state j when the initial scour depth state is i, which is expressed in matrix form as:

[0030]

[0031] Where, and The dimension is 1×N for the start and end of flood event k s The scour depth probability vector, is dimension N s ×N sThe transfer probability matrix TPM of the kth flood can be determined by combining flood hazard, hydrological information and river hydraulic conditions;

[0032] Assuming that the change of scour depth during the kth flood is completely controlled by the hydraulic parameters of the event and has nothing to do with the flood event k, the random scour accumulation process is a homogeneous Markov chain, which is completely determined by the state transition matrix Characterize the probability mass function when the nth flood occurs Expressed as:

[0033]

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

[0035]

[0036] The unconditional probability of being in depth state j at time t is further obtained as:

[0037]

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

[0039]

[0040] In addition, the given The probability of Expressed as:

[0041]

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

[0043]

[0044] Solving the flood sample transition probability matrix based on Monte Carlo simulation , the probability mass distribution and complementary cumulative distribution of the life-cycle scour depth are obtained.

[0045] Furthermore, the calibration preprocessing process of the scour depth model parameters that vary with time in step (3) is as follows:

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

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

[0048] The root mean square error of the scouring depth is calculated by genetic algorithm, thereby completing the estimation of the optimal parameters of the dimensionless effective water flow work model. The mathematical expression of the dimensionless effective water flow work model is:

[0049]

[0050] Where Z * is the standardized scour depth, c1, c2, c3 are fitting parameters, W * is the dimensionless effective water flow work.

[0051] Furthermore, in step (3), the time-varying model of bridge scour depth can be fitted based on the average scour depth at different times, and its mathematical expression is as follows:

[0052]

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

[0054] The implementation process of step (4) includes dedimensionalizing the ratio of the bridge scour depth to the foundation burial depth before scour, and then dynamically dividing the multi-level warning areas according to the full life scour depth.

[0055] Beneficial Effects: Compared with existing methods, this invention considers the influence of factors such as the multi-parameter correlation of hydrological events and the nonlinear dynamic evolution of scour during the bridge scour depth prediction and early warning process. It constructs multivariate dependency relationships through Copula joint distribution and combines Markov processes to simulate the time series evolution of scour throughout the life cycle. It solves the problems of traditional methods inadequate description of complex hydrological coupling effects, limited accuracy of scour depth dynamic prediction, and static early warning classification. Its substantial features and significant effects also include:

[0056] 1. Constructing a hydrological multivariate dependency model based on the Copula joint distribution. By optimizing the marginal distribution and Copula function type, it accurately captures the nonlinear correlation between hydrological parameters, overcomes the shortcomings of traditional univariate analysis in insufficiently characterizing the coupling effects of hydrological events, and improves the prediction reliability of extreme scour scenarios.

[0057] 2. The dynamic evolution of scour over the entire life cycle is simulated based on a Markov process. Using a discrete state transition probability matrix and Monte Carlo simulation, the temporal cumulative effect of scour depth under different flood events is quantified. Combined with DFW model parameter optimization, this method achieves continuous prediction of scour depth from short-term scour increments to the entire life cycle, resolving the problem that traditional methods have difficulty in reflecting the time dependence of the scour process.

[0058] 3. Based on the present invention, a dynamic multi-level early warning mechanism can be established in combination with the scour depth; by dedimensionalizing the ratio of the scour depth to the foundation burial depth and combining it with the full life scour probability distribution, the early warning area is divided into several levels of risk intervals, overcoming the limitation that static thresholds are difficult to adapt to the safety requirements of the entire life cycle of the bridge. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0060] Figure 2 This is a simplified flow chart of a method for predicting and warning the scour depth of a bridge throughout its life cycle according to an embodiment of the present invention;

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

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

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

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

[0065] FIG7 is a result diagram of flood peak values ​​exceeding a threshold value according to an embodiment of the present invention, wherein FIG7(a) is a diagram of flood peak flow exceeding a threshold value, and FIG7(b) is a result of a lagged autocorrelation test;

[0066] FIG8 is a diagram showing the best marginal distribution fitting results of flood variables according to an embodiment of the present invention, wherein FIG8(a) shows the peak flow result, and FIG8(b) shows the duration result;

[0067] FIG9 is a diagram showing the joint distribution results of flood variables according to an embodiment of the present invention, wherein FIG9(a) is an empirical cumulative distribution function diagram, and FIG9(b) is a BB7 Copula cumulative distribution function diagram;

[0068] FIG10 is a graph showing the temporal evolution of local scour on a bridge according to an embodiment of the present invention, wherein FIG10( a ) is a DFW model fitting graph, and FIG10( b ) is a graph showing the evolution of scour depth under flood waves;

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

[0070] FIG12 is a diagram showing the calculation results of the state transition matrix according to an embodiment of the present invention, wherein FIG12(a) is a diagram showing the state transition matrix of the flood event q1, and FIG12(b) is a diagram showing the transition probability matrix of the flood sample;

[0071] FIG13 is a diagram of the Markov process calculation results according to an embodiment of the present invention, wherein FIG13(a) is a diagram of the probability mass function of the scour depth, and FIG13(b) is a diagram of the complementary cumulative distribution function of the 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 Graph showing calculation results of equilibrium scour depth using different standard formulas according to an embodiment of the present invention;

[0074] Figure 16 This is a diagram showing the warning results of the scour depth over the entire life cycle of a bridge according to an embodiment of the present invention. DETAILED DESCRIPTION

[0075] The technical solution of the present invention is explained and illustrated 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 prediction and early warning of the scour depth of the bridge throughout its life cycle, which is based on the Copula joint distribution and the Markov process. It includes scour depth calculation and prediction and early warning processes. The figure shows an implementation flow chart of the method.

[0077] In order to achieve accurate prediction and dynamic early warning of the scour depth throughout the life cycle of a bridge, it is necessary to comprehensively consider the correlation of hydrological variables and the temporal evolution characteristics of the scour process. Traditional evaluation methods mostly use single-variable analysis or static models, which are difficult to characterize the dynamic changes of scour depth under complex hydrological conditions. At the same time, the accumulation process of scour depth over time is random and dependent, and static models are difficult to reflect the evolution law throughout the life cycle. Based on this, as shown, the present invention proposes a prediction method that combines Copula joint distribution and Markov process. First, a multivariate hydrological dependency model is constructed, and then the temporal evolution of scour depth is simulated. Finally, the risk level is divided based on the relative scour depth to achieve dynamic early warning throughout the life cycle. Specifically, remote monitoring and early warning and / or on-site maintenance prompts can be used.

[0078] 1. Bridge Scour Data Collection and Analysis

[0079] Combine Figure 3Taking a bridge as an example, the data collection process and methods are illustrated. The main bridge, with a total length of 220 meters, is a seven-span (6 × 30 + 40) m continuous beam with a variable cross-section. The beam height varies according to a quadratic parabola. The bridge utilizes an elliptical foundation with 1.5 m wide piers and 2.5 m wide pile foundations. Flood discharge was measured using an Acoustic Doppler Current Profiler (ADCP) (SonTek, RiverSurveyor M9) deployed at the flow site of the bridge piers. Ultrasonic scour sensors (Airmar, Echorange SS510) were used at the piers of the measured bridge at a 10-minute frequency to measure scour depth. The deployed scour sensor parameters were processed. Field measurements of scour and flow were conducted on the bridge over a six-day period. Local scour and sediment deposition on the bridge piers during the flood wave were analyzed, and the impact of varying flow and sediment supply conditions was studied. Figure 4 Flood flow and scour depth data obtained through measurements are presented. During the field measurements, when the flood flow exceeded the scour threshold flow, the scour depth increased rapidly during the rising flood flow phase, but remained almost unchanged during the receding flood flow phase, with the scour pit slightly filling. During some time intervals, the scour depth did not increase because the flood flow was below the flow required to induce scour. Therefore, the occurrence of multiple floods may cause bridges to reach the critical scour depth, and the probability of this occurring increases with the number, intensity, and duration of floods. Most existing studies have shown that the cumulative effect of scour induced by multiple flood events has been considered a significant cause of many bridge failures, which demonstrates the rationale and necessity of the proposed method for scour analysis.

[0080] 2. Extraction of key hydrological events based on the POT model

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

[0082] (2.1) First, the independence of the peak sequences was tested using the peak separation method proposed by the United States Water Resources Commission (USWRC). This method requires that the interval between consecutive flood peaks be at least five days, plus the natural logarithm of the basin area, to ensure that the two events are hydrologically uncorrelated. Furthermore, the valley 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 misidentifying secondary peaks of the same flood process as independent events. Furthermore, the independence of the flood peak sequences was tested by calculating the lagged autocorrelation coefficient.

[0083] (2.2) The scour rate is then calculated by determining the initial sediment velocity. Based on the hydraulic characteristics of the river channel and the geometric properties of the bridge, if the riverbed has a regular cross-sectional morphology and the cross-sectional area is easily quantified, the Manning equation can be used to directly evaluate the relationship between velocity and flow, thereby calculating the threshold flow rate q0.

[0084] To validate the practicality of the proposed method, a typical scour scenario for a river-crossing bridge supported by an extended pile shaft was selected as a case study. The prototype for this case study is a river-crossing bridge on a certain highway, with a span of 2 × 28 m. The overall structural and geometric parameters are shown in the figure. The main beam is a T-beam structure with an overall width of 13.2 m and a beam height of 2.0 m. The piers are circular double-column frame piers, commonly used in highway bridges, with a diameter of 1.5 m and a height of 6 m. The piles below the piers are 20 m long and are bored and cast-in-place piles with a diameter of 1.5 m. The foundation is buried at a depth of 3 m. The river channel has a rectangular cross-section and a width of 50 m. The riverbed surface is composed of fine sand and gravel, with a relative density of 1.65 and a median sediment particle size of 5 mm. Due to the clean and straight river channel, the Manning roughness coefficient was set at 0.035. In addition, there is a hydrological observation station near the bridge, which records the average daily flow series of the river from January 1, 1950 to January 1, 2020. The data comes from the public database of the Hydrological Bureau, providing a basic hydrological basis for scour analysis, as shown.

[0085] The sediment starting velocity was calculated based on the formula recommended in the "Highway Engineering Hydrological Survey and Design Code" (JTG C30-2015). For wide river channels with regular cross-sections, the Manning formula was directly used to calculate the threshold flow rate, which was 10.07m 3 / s. As shown in (a), the flood variables exceeding the threshold (considering peak flow and duration) are circled by using the peak separation method. The relevant statistics are described in detail. At the same time, the flood variable lagged autocorrelation test is used to verify the independent and identically distributed hypothesis. The test results (such as As shown in (b), the autocorrelations of the two flood variables are not significant, indicating that the selected threshold does not violate the independent and identically distributed assumption. The flood 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] 3. Building a multivariate dependency model based on Copula joint distribution

[0089] As shown, six distributions, LN, GUM, GAM, P-III, GEV, and GP, were used to fit flood variables, and the parameters of each distribution were estimated using the maximum likelihood method. The KS test (D n), RMSE, AIC criterion, and BIC criterion are used to measure the goodness of fit of the marginal distribution of flood variables. The results are shown in Figure 2. At a significance level of 5%, for peak flow rate P, only the GP and GEV distributions pass the hypothesis test among the alternative distributions. For duration D, the LN, GAM, and GEV distributions pass the hypothesis test. It can be clearly seen that for peak flow rate, the GP distribution gives the smallest RMSE, BIC, and AIC values, so 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 Archimedean Copula function, commonly used in hydrology, was used to construct the joint distribution of flood peak discharge and duration. The copula function parameters were calculated using the maximum likelihood method (see the results). 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. The empirical cumulative distribution function of the joint distribution of flood variables 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 identical shapes, providing a good fit for the joint distribution of flood variables.

[0093] Table 3. Copula function fitting test

[0094]

[0095] 4. Prediction of life-cycle scour depth based on Markov process

[0096] For the temporal evolution of local scour of a bridge under a given flood flow line, the dimensionless effective flow work (DFW) model is used to evaluate the time-varying scour depth. ∗ ), can accurately estimate the time-varying scour depth under complex hydraulic scenarios. (a) shows the results of fitting the DFW model to the field-measured scour depth. The root mean square error and Nash efficiency coefficient are 0.023m and 0.96, respectively, indicating that the model fit is very good. (b) shows the results of the model with zero scour depth as the initial condition and a peak flow of 300m 3 / s, and a flood event lasting 10 days. An exponential function is used to describe the shape of the single-peak flood wave. The time evolution diagram of the scour depth is calculated by the DFW model under the fitted parameters.

[0097] After obtaining the joint distribution of flood variables, we can use a set of N sample Flood events of different durations obtained from a Monte Carlo simulation of 10,000 flood samples (as shown). In order to calculate TPM , consider a set N s = 25 scour state, the discrete scour depth is 0.15m. For 10,000 flood samples Q, we first need to calculate the conditional TPM , represents the TPM conditioned on the flood variable. This requires that N s The maximum scour depth is calculated for different initial values ​​of scour depth. It is worth noting that, with given channel and riverbed properties and determined hydraulic model parameters, there is a one-to-one relationship between flood events and scour depth.

[0098] For peak flow 300m 3 / s, flood events lasting 10 days , introduced From the result of (b), we can see that when the initial scour depth is 0m (state 1), the scour depth is 2.04m. This value corresponds to scour state 14, so when j ≠ 14 , is 1 when j = 14. Assuming the initial scour depth is 1.8m (state 13), the final scour depth under the same flood conditions is 2.10m (state 15). Therefore, when j = 15, , is 0 when j ≠ 15. Finally, assuming the initial scour depth is 2.7m (state 19), due to the peak flow of 300m 3 / s flood is too weak to cause an increase in scour depth. Therefore, when j = 19, , is 0 when j ≠ 19. This process can be used to estimate N sample q i Sample .

[0099] For each simulated flood event, the matrix Then, we can estimate the matrix for:

[0100]

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

[0102] We can further obtain the probability mass function p of the scour depth at different times j (t). (a) shows the initial scour depth state is determined and there is no scour (i.e. when j = 1 ) The obtained p j In addition, the complementary cumulative distribution function of scour depth under different bridge life can be obtained (such as (b)).

[0103] It can be observed that the probability distribution of scour depth is relatively dispersed in the early stage, but as time goes by, the probability mass shifts to higher values ​​of scour depth and gradually stabilizes. The average scour depth at different times can be obtained, and the time-varying model of the scour depth of the example bridge can be fitted based on the average value. The change of the mean and standard deviation of the scour depth over time is shown in Figure 2. As shown in the figure, the average scour depth increases over time, but the increase is becoming smaller and smaller, reaching an average of 3.08m after 100 years. The standard deviation decreases gradually, indicating that the scour depth is gradually stabilizing.

[0104] For the calculation of the equilibrium scour depth, the equilibrium scour depth can be calculated based on the Froehlich equation, Melville equation, Sheppard equation, HEC-18 equation, S / M equation and several different formulas proposed in the Chinese Standards. For the case bridge, the Chinese Standards stipulate that the scour depth should be calculated using a flood with a return period of 100 years. Figure 15 As shown, the estimated scour depths at different times (e.g. Figure 14 ) were compared with equilibrium scour depths calculated for floods with corresponding return periods. Overall, the scour depth estimates from different formulas are more dispersed compared to the time-varying scour depth values. For a 100-year return period, their average value is 3.46 m, with a standard deviation of 1.14. The scour depths obtained by this method are relatively close to those estimated by the HEC-18 equation.

[0105] The HEC-18 equation is as follows:

[0106]

[0107] Where, is the local scour depth (m), is the pier width (m), is the pier shape coefficient, is the water attack angle correction coefficient, is the riverbed condition correction coefficient, is the sediment size distribution coefficient, is the maximum water depth after general scouring (m), is the Froude number.

[0108] 5. Scour dynamic multi-level warning judgment and output

[0109] To achieve dynamic, multi-level early warning for foundation scour, this invention dedimensionalizes the ratio of scour depth to foundation burial depth, then dynamically divides the warning zones into multiple levels based on the lifetime scour depth. Foundation burial depth is a key parameter that determines a bridge's scour resistance and the risk of scour failure.

[0110] (5.1) Scour risk indicators and classification

[0111]

[0112] In the formula, the relative scour depth D R As an indicator for bridge scour risk classification, D T is the time-varying scour depth, D F The buried depth of the bridge foundation.

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

[0114] Based on relevant specifications, engineering experience, and bridge characteristics, bridge scour risks are divided into three levels, as shown in Table 4.

[0115] Table 4. Scour risk assessment criteria

[0116]

[0117] like Figure 16 As shown in the figure, the relationship between relative scour depth and bridge service life is used to dynamically divide the warning areas into Level 1, Level 2, and Level 3. As can be seen from the figure, when the bridge life is 0-4.0 years, it is at Level 3 scour risk; when the bridge life is 4.0-67.2 years, it is at Level 2 scour risk; when the bridge life is over 67.2 years, it is at Level 1 scour risk. Different alarm response measures are taken according to different warning levels.

[0118] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A bridge scour depth prediction and early warning method based on Markov process, characterized in that: The steps include: (1) The scour velocity, river hydraulic characteristics, and bridge geometric characteristics are calculated based on the sediment initiation velocity. The relationship between velocity and flow is evaluated using a hydraulic model to determine the scour threshold q0. Then, based on the POT model, historical hydrological events exceeding the scour threshold q0 are screened and their characteristic parameters are quantified. The characteristic parameters include the scour velocity, river hydraulic characteristics, and bridge geometric characteristics. (2) For the historical hydrological events screened, the best-fitting single-variable marginal distribution is selected, and then a multivariate joint analysis is conducted based on the Copula theory; The univariate marginal distributions include lognormal distribution, Gumbel distribution, Pearson type III distribution, generalized extreme value distribution and generalized Pareto distribution; (3) Calibrate the scour depth model parameters based on measured hydrological data and scour data, and use a discrete-time and discrete-state Markov process to predict the scour depth over the entire life of the bridge; (4) The probability distribution of the scour depth over the entire life of the bridge is calculated based on the discrete Markov process, and then it is determined whether the scour depth exceeds the foundation burial depth. If it does, an early warning is issued in time; if it does not, 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 is characterized in that: The POT model includes the use of peak separation method and lagged autocorrelation coefficient to test the independence of hydrological series.

3. The bridge scour depth prediction and early warning method according to claim 1 is 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 marginal distributions using statistical indicators including KS test, root mean square error, AIC criterion, and BIC criterion; (2.3) The joint distribution of hydrological variables is constructed based on the Archimedean Copula functions including Gumbel, Clayton and Fran, and the fitting test and screening of the Copula functions are carried out using the root mean square error, AIC criterion and BIC criterion.

4. The bridge scour depth prediction and early warning method according to claim 1 is characterized in that: The Markov process construction described in step (3) specifically includes: The flood events in the hydrological events are modeled by the homogeneous Poisson process, and the occurrence rate of flood events is represented by λ. Then the probability of n events occurring in time t is Expressed 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 represent a flood event with flow Q > q0, let It means that after the occurrence of the kth flood event, the water level is in the scouring state j and the corresponding depth is The probability of , and then we get: ， Where, Indicates that the bridge was at scour depth when the flood began The probability of It represents the transition probability, that is, the probability of reaching state j when the initial scour depth state is i, which is expressed in matrix form as: ， Where, and The dimension is 1×N for the start and end of flood event k s The scour depth probability vector, is dimension N s ×N s The transfer probability matrix TPM of the kth flood can be determined by combining flood hazard, hydrological information and river hydraulic conditions; Assuming that the change of scour depth during the kth flood is completely controlled by the hydraulic parameters of the event and has nothing to do with the flood event k, the random scour accumulation process is a homogeneous Markov chain, which is completely determined by the state transition matrix Characterize the probability mass function when the nth flood occurs Expressed as: ， Given N = n floods, at time t the scour depth s j The conditional probability is: ， The unconditional probability of being in depth state j at time t is further obtained as: ， Therefore, the expected value of the scour depth at time t is expressed as: ， In addition, the given The probability of Expressed as: ， Finally, the exceedance probability of state j is expressed as: ， Solving the state transition matrix of flood samples based on Monte Carlo simulation , the probability mass distribution and complementary cumulative distribution of the life-cycle scour depth are obtained.

5. The bridge scour depth prediction and early warning method according to claim 1 or 4, characterized in that: Step (3) is to calibrate the model parameters of the scour depth over time as follows: 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, discharge and scour depth, and calculate scour depth; The root mean square error of the scouring depth is calculated by genetic algorithm, thereby completing the estimation of the optimal parameters of the dimensionless effective water flow work model. The mathematical expression of the dimensionless effective water flow work model is: ， Where Z * is the standardized scour depth, c1, c2, c3 are fitting parameters, W * is the dimensionless effective water flow work.

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

7. The bridge scour depth prediction and early warning method according to claim 1 is characterized in that: The implementation process of step (4) includes dedimensionalizing the ratio of the bridge scour depth to the foundation burial depth before scour, and then dynamically dividing the multi-level warning areas according to the full life scour depth.

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