Method for predicting deformation of face rockfill dam based on CBMA and DE-MCMC algorithm

Abstract

The application discloses a panel rock-fill dam deformation prediction method based on CBMA and DE-MCMC algorithms, constructs a panel rock-fill dam deformation monitoring model according to water pressure, temperature and aging components, replaces the original uniform distribution assumption of a Bayesian model mean with a Copula function joint distribution between a measuring point settlement and an influence factor, inputs the panel rock-fill dam monitoring model and the measuring point data into a mean calculation system of a Copula Bayesian model, combines a differential evolution Markov chain Monte Carlo algorithm to improve the model, and applies the method to panel rock-fill dam deformation monitoring. The prediction method based on CBMA and DE-MCMC algorithms can better quantitatively analyze the uncertainty of the model in the process of predicting the rock-fill dam deformation, can more effectively analyze the rock-fill dam deformation law and characteristics, and retains good interpretability and measured fitting of the statistical model.

Description

Technical Field

[0001] This invention belongs to the field of pumped storage unit control technology, specifically relating to a method for predicting the deformation of panel rockfill dams based on CBMA and DE-MCMC algorithms. Background Technology

[0002] Concrete-faced rockfill dams are one of the main types of earth-rockfill dams. Compared with traditional earth-rockfill dams, they have significant advantages in safety, economy, and adaptability, and have broad application prospects. Concrete-faced rockfill dams use rockfill for support and a concrete face on the upstream surface for seepage prevention. However, the difference in stiffness between the two can lead to deformation coordination problems. Therefore, dam deformation becomes an important aspect of safety monitoring for concrete-faced rockfill dams and a key indicator for measuring the structural safety state of the dam. The spatial distribution of the physical and mechanical parameters of the dam construction materials and the soil and rock mass of the dam foundation and abutments is uneven and dynamically changes over time. The complex natural environmental conditions at the dam site lead to the randomness of dynamic changes in dam loads and effects. Various factors interact with each other, and different projects have unique characteristics, resulting in significant uncertainties in the monitoring system of concrete-faced rockfill dams. Therefore, how to accurately and efficiently predict the deformation of concrete-faced rockfill dams has always been a problem requiring in-depth research. Currently, the most widely studied dam deformation prediction models based on monitoring data are mainly statistical models and machine learning models. For statistical models, as the number of input influencing factors increases, the model's fit also increases, but this also increases the model's complexity and can easily lead to a decrease in its generalization ability. Although some scholars have made progress in the research of statistical model optimization methods, how to reduce the complexity of the model while ensuring the accuracy of the prediction model remains the main research problem in statistical models of dam deformation.

[0003] Due to the uncertainties in the deformation monitoring system of panel rockfill dams, it is necessary to introduce uncertainty information analysis methods for more comprehensive monitoring and prediction of the dam. Bayesian theory has proven effective in this regard, as it can integrate information from multiple sources, update the probability distribution of target parameters, and has been widely applied in deformation prediction. Bayesian model averaging (BMA) has demonstrated powerful predictive and decision support capabilities in many fields. BMA not only integrates the advantages of multiple models, weighting and combining the fitting ability and predictive accuracy of each model, but can also be combined with other methods to obtain more reliable overall prediction results. Seifi et al. used BMA to implement multi-mode integrated prediction of evaporation in evaporating pans. BMA calculations often involve sampling high-dimensional parameter spaces and complex probability distributions. Previous studies have frequently used Markov chain Monte Carlo (MCMC) to address this challenge, but traditional MCMC suffers from autocorrelation among samples and slow exploration in high-dimensional spaces. To improve this problem, the algorithm combining adaptive differential evolution with Markov chain Monte Carlo (DE-MCMC) is a good choice. This method uses differential evolution to achieve full parameter space search and uses the Metropolis sampling algorithm to adaptively adjust the acceptance probability. Multi-chain parallel search and outlier chain removal operations improve the solution quality while also ensuring convergence speed.

[0004] To address the problem of numerous influencing factors and the difficulty in quantifying uncertainties in monitoring systems leading to complex and inaccurate deformation prediction models for rockfill dams with concrete panels, this paper proposes a deformation prediction model for such dams based on the CBMA and DE-MCMC algorithms. The feasibility of this method is then examined in a practical engineering project. This paper first introduces the relevant theoretical methods, then describes the process of constructing a deformation prediction model for rockfill dams based on the CBMA and DE-MCMC algorithms, and finally verifies the practicality of the proposed deformation prediction method through an engineering example. Summary of the Invention

[0005] The purpose of this invention is to provide a deformation prediction method for panel rockfill dams based on CBMA and DE-MCMC algorithms, which solves the problems in the existing technology where there are many factors affecting the deformation of panel rockfill dams and the uncertainty of the monitoring system is difficult to quantify, resulting in complex deformation prediction models and low accuracy.

[0006] The first technical solution adopted in this invention is: a deformation prediction method for panel rockfill dams based on CBMA and DE-MCMC algorithms. This method constructs a deformation monitoring model for panel rockfill dams, replaces the uniform distribution assumption of the Bayesian model with the joint distribution of Copula functions between the settlement at measuring points and influencing factors, substitutes the panel rockfill dam monitoring model and the measuring point data into the averaging calculation system of the Copula Bayesian model, and improves the model by combining the differential evolution Markov chain Monte Carlo algorithm. This method is then applied to the deformation monitoring of panel rockfill dams. The specific operations are as follows:

[0007] Step 1: Continuously monitor the monitoring points on the rockfill dam to obtain the settlement of the monitoring points and the corresponding water level and temperature environmental data. Preprocess the obtained environmental data and normalize the settlement of the monitoring points.

[0008] Step 2: Construct a deformation monitoring model for panel rockfill dams, taking water pressure, temperature, and time as influencing factors;

[0009] Step 3: Construct the optimal joint distribution Copula function between the settlement at the measuring point and each influencing factor;

[0010] Step 4: Replace the original uniform distribution assumption in the average system of the Bayesian model with the optimal joint distribution Copula function obtained in Step 3 to form the Copula Bayesian model. Substitute the panel rockfill dam monitoring model and the settlement of the measuring points into the average calculation system of the Copula Bayesian model. Calculate the posterior probability of each influencing factor and the monitoring model using the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

[0011] The invention is further characterized in that,

[0012] Step 1 preprocessing methods include interpolation and elimination of outliers.

[0013] The specific expression for the normalization process in step 1 is as follows:

[0014]

[0015] In equation (1), C i The normalized settlement data; x i For input variables; x max and x min The input variables x are respectively i The maximum and minimum values.

[0016] The deformation monitoring model of the panel rockfill dam in step 2 is shown in equation (2):

[0017]

[0018] In the formula: a0 is the regression constant coefficient; a i Here are the regression coefficients for the water pressure factor, i = 1 to 7; H i The depth of the upstream water is the power of i. c is the average water depth of the previous i days; 1j c 2j d1, d2, and d3 are the regression coefficients of the temperature factor, n is the number of cycles of the simple harmonic component in one year. If n = 1, it means that one year is taken as a cycle; if n = 2, it means that half a year is taken as a cycle; t is the number of days between the monitoring day and the initial monitoring day; d1, d2, and d3 are the regression coefficients of the time factor. D m This represents the cumulative deformation over the previous seven days.

[0019] Step 3 is as follows:

[0020] The marginal distribution of settlement and influencing factors is determined by the kernel density estimation method. Finally, the parameters in the Copula function are obtained by the semi-parametric estimation method and the fit is optimized. The optimal Copula function form is selected based on the squared Euclidean distance.

[0021] The DE-MCMC algorithm is a combination of the adaptive differential evolution algorithm and the Markov chain Monte Carlo algorithm, as detailed below:

[0022] Step 1: Generate initial samples and calculate posterior probability density

[0023] If the number of parameters to be optimized is n, then 2n Markov chains are randomly initialized, that is, 2n sets of samples of parameter vectors v to be optimized are generated. The posterior probability density f(v) is calculated using the sum of the squares of the differences between the measured and predicted values ​​of the displacement at the observation points of the panel rockfill dam. i ), i = 1, ..., 2n;

[0024] Step 2: Implement mutation operations using the differential evolution method.

[0025] For sample v of the i-th chain i Perform the mutation operation according to formula (3) to obtain the corresponding new mutated chain, i.e., the new candidate sample z. i ;

[0026]

[0027] In the formula: δ is the logarithm used to generate candidate samples; r(j), r(l)∈{1,…,2n}, r(j)≠r(l)≠i; ε is the model error;

[0028] Step 3: Implement cross-operations

[0029] Determine whether to use the old sample v according to formula (4). i Replace the new sample zi ;

[0030]

[0031] In the formula: CR is the crossover probability; U∈[0,1] is the random sampled value with uniform probability;

[0032] Step 4: Decide whether to accept the transfer

[0033] Calculate the posterior probability density f(z) of the new sample. i ) and Metropolis acceptance probability β(v i ,z i ), and then according to β(v i ,z i Decide whether to accept the transfer;

[0034]

[0035] If the new sample is accepted, take the next sample point v of the Markov chain. i =z i Otherwise, do not accept new samples and maintain the current position of the parallel sequence, return to the second step to evolve again;

[0036] Step 5: Remove useless chains

[0037] Calculate the average posterior probability density Ω for each chain, and then calculate the interquartile range of the posterior probability density of these samples, i.e., the difference between the 75th quantile Q3 and the 25th quantile Q1. Remove useless chains that satisfy the condition Ω < (Q1 - 2IQR).

[0038] Step 6: Determine convergence

[0039] The convergence criterion GR is calculated based on the variance within and between chains for each parameter. If If the GR convergence criterion is met, the calculation ends; otherwise, return to step two and continue until the maximum number of iterations is reached.

[0040] The specific method for calculating the posterior inclusion probability of the panel rockfill dam deformation monitoring model in step 4 is as follows:

[0041] The influencing factors of the deformation monitoring model for panel rockfill dams have two options during the modeling process: either include them or exclude them, thus forming the entire model space. The posterior probabilities of its model parameters are obtained from equation (6):

[0042]

[0043] In the formula: yis the vector of parameters to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor in the deformation monitoring model of the panel rockfill dam; D is the sample of observed dam settlement data. Let p(y|D) be the deformation monitoring model of the k-th panel rockfill dam in the model space; p(y|D) is the posterior probability of parameter y in the model space, that is, the posterior inclusion probability of each influencing factor of the prediction model. Let be the posterior probability of the deformation monitoring model of the k-th panel rockfill dam in the model space; To determine the parameters in the deformation monitoring model of the k-th panel rockfill dam y The posterior probability.

[0044] The beneficial effects of this invention are:

[0045] (1) Based on the original Bayesian model BMA, the joint distribution between the deformation of the measuring point and the alternative influencing factors is found by fitting the Copula function. The assumption of uniform distribution of the prior parameters of BMA is replaced. This means that the distribution of the posterior parameters is relaxed, making it have a more flexible data structure and the prediction results are more reliable and accurate.

[0046] (2) For complex nonlinear problems such as deformation prediction of rockfill dams, DE-MCMC can avoid the slow convergence or inability to converge of traditional optimization methods. By integrating the algorithm into CBMA to predict dam deformation, it can perform a global search in the entire model space, find a closer option to the best option in dealing with multiple local optima, and improve the computational efficiency of high-dimensional model space.

[0047] (3) The prediction method proposed in this invention, which integrates CBMA and DE-MCMC algorithms, performs better quantitative analysis of the uncertainty of the model in the process of predicting the deformation of rockfill dams. It can more effectively analyze the deformation law and characteristics of rockfill dams. It not only retains the good interpretability and experimental fit of the statistical model, but also has a significant improvement in accuracy and stability compared with other deformation prediction models. Attached Figure Description

[0048] Figure 1 This is a flowchart of the deformation prediction method for panel rockfill dams based on CBMA and DE-MCMC algorithms of this invention;

[0049] Figure 2 This is a diagram showing the layout of settlement measuring points at the 0+130.00m section on the left side of the dam in Embodiment 5 of the present invention;

[0050] Figure 3 This is a normalized settlement deformation curve of the training sequence of the selected measuring points in Embodiment 5 of the present invention;

[0051] Figure 4(a) is the empirical distribution function and kernel distribution estimation diagram of the displacement of measuring point 8 in Embodiment 5 of the present invention;

[0052] Figure 4(b) is the empirical distribution function and kernel distribution estimation diagram of X1 in the water pressure factor at measuring point 8 in Embodiment 5 of the present invention;

[0053] Figure 5(a) is a displacement frequency histogram of measuring point 8 in Embodiment 5 of the present invention;

[0054] Figure 5(b) is a histogram of the X1 frequency in the water pressure factor at measuring point 8 in Embodiment 5 of the present invention;

[0055] Figure 6 This is a binary frequency histogram of the marginal distribution of X1 in the water pressure factor at measuring point 8 in Embodiment 5 of the present invention.

[0056] Figure 7 The squared Euclidean distance diagram of the joint distribution of deformation of measuring point 8 and various influencing factors using the Copula function in Embodiment 5 of this invention;

[0057] Figure 8 This is the posterior probability distribution diagram of the coefficients of measurement point 8 and each factor in Embodiment 5 of the present invention;

[0058] Figure 9 This is a marginal posterior probability diagram of different factor coefficients in the deformation model of measuring point 8 in Embodiment 5 of the present invention;

[0059] Figure 10 This is a 95% confidence interval diagram of the CBMA deformation prediction at measuring point 8 in Embodiment 6 of the present invention;

[0060] Figure 11 This is the predicted monthly settlement deformation diagram of measuring point 8 in Embodiment 6 of the present invention; Detailed Implementation

[0061] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, so that the advantages and features of the present invention can be more readily understood by those skilled in the art.

[0062] Example 1

[0063] This invention presents a deformation prediction method for panel rockfill dams based on CBMA and DE-MCMC algorithms. It constructs a deformation monitoring model for panel rockfill dams, replaces the uniform distribution assumption of the Bayesian model with the joint distribution of Copula functions between the settlement at measuring points and influencing factors, substitutes the panel rockfill dam monitoring model and the measuring point data into the average calculation system of the Copula Bayesian model, and improves the model by combining the differential evolution Markov chain Monte Carlo algorithm. This method is then applied to the deformation monitoring of panel rockfill dams.

[0064] Example 2

[0065] The present invention provides a method for predicting the deformation of panel rockfill dams based on CBMA and DE-MCMC algorithms. The specific operation is as follows:

[0066] Step 1: Continuously monitor the monitoring points on the rockfill dam to obtain the settlement of the monitoring points and the corresponding water level and temperature environmental data. Preprocess the obtained environmental data and normalize the settlement of the monitoring points.

[0067] Step 2: Construct a deformation monitoring model for panel rockfill dams, taking water pressure, temperature, and time as influencing factors;

[0068] Step 3: Construct the optimal joint distribution Copula function between the settlement at the measuring point and each influencing factor;

[0069] Step 4: Replace the original uniform distribution assumption in the average system of the Bayesian model with the optimal joint distribution Copula function obtained in Step 3 to form the Copula Bayesian model. Substitute the panel rockfill dam monitoring model and the settlement of the measuring points into the average calculation system of the Copula Bayesian model. Calculate the posterior probability of each influencing factor and the monitoring model using the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

[0070] Example 3

[0071] The present invention provides a method for predicting the deformation of panel rockfill dams based on CBMA and DE-MCMC algorithms. The specific operation is as follows:

[0072] Step 1: Continuously monitor the monitoring points on the rockfill dam to obtain the settlement of the monitoring points and the corresponding water level and temperature environmental data. Preprocess the obtained environmental data and normalize the settlement of the monitoring points.

[0073] Preprocessing includes interpolation and elimination of outliers;

[0074] The specific expression for normalization is as follows:

[0075]

[0076] In equation (1), C i The normalized settlement data; x i For input variables; x max and x min The input variables x are respectively i The maximum and minimum values;

[0077] Step 2: Construct a deformation monitoring model for panel rockfill dams, taking water pressure, temperature, and time as influencing factors;

[0078] Step 2: The panel-based rockfill dam deformation monitoring model is shown in equation (2):

[0079]

[0080] In the formula: a0 is the regression constant coefficient; a i Here are the regression coefficients for the water pressure factor, i = 1 to 7; H i The depth of the upstream water is the power of i. c is the average water depth of the previous i days; 1j c 2j d1, d2, and d3 are the regression coefficients of the temperature factor, n is the number of cycles of the simple harmonic component in one year. If n = 1, it means that one year is taken as a cycle; if n = 2, it means that half a year is taken as a cycle; t is the number of days between the monitoring day and the initial monitoring day; d1, d2, and d3 are the regression coefficients of the time factor. D m This represents the cumulative deformation over the previous seven days.

[0081] Step 3: Construct the optimal joint distribution Copula function between the settlement at the measuring point and each influencing factor;

[0082] Step 4: Replace the original uniform distribution assumption in the average system of the Bayesian model with the optimal joint distribution Copula function obtained in Step 3 to form the Copula Bayesian model. Substitute the panel rockfill dam monitoring model and the settlement of the measuring points into the average calculation system of the Copula Bayesian model. Calculate the posterior probability of each influencing factor and the monitoring model using the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

[0083] Example 4

[0084] Based on Example 3,

[0085] Step 3 is as follows:

[0086] The marginal distribution of settlement and influencing factors is determined by the kernel density estimation method. Finally, the parameters in the Copula function are obtained by the semi-parametric estimation method and the fit is optimized. The optimal Copula function form is selected based on the squared Euclidean distance.

[0087] The DE-MCMC algorithm is a combination of the adaptive differential evolution algorithm and the Markov chain Monte Carlo algorithm; the specific details of the DE-MCMC algorithm are as follows:

[0088] Step 1: Generate initial samples and calculate posterior probability density

[0089] If the number of parameters to be optimized is n, then 2n Markov chains are randomly initialized, that is, 2n sets of samples of parameter vectors v to be optimized are generated. The posterior probability density f(v) is calculated using the sum of the squares of the differences between the measured and predicted values ​​of the displacement at the observation points of the panel rockfill dam. i), i = 1, ..., 2n;

[0090] Step 2: Implement mutation operations using the differential evolution method.

[0091] For sample v of the i-th chain i Perform the mutation operation according to formula (3) to obtain the corresponding new mutated chain, i.e., the new candidate sample z. i ;

[0092]

[0093] In the formula: δ is the logarithm used to generate candidate samples; r(j), r(l)∈{1,…,2n}, r(j)≠r(l)≠i; ε is the model error;

[0094] Step 3: Implement cross-operations

[0095] Determine whether to use the old sample v according to formula (4). i Replace the new sample z i ;

[0096]

[0097] In the formula: CR is the crossover probability; U∈[0,1] is the random sampled value with uniform probability;

[0098] Step 4: Decide whether to accept the transfer

[0099] Calculate the posterior probability density f(z) of the new sample. i ) and Metropolis acceptance probability β(v i ,z i ), and then according to β(v i ,z i Decide whether to accept the transfer;

[0100]

[0101] If the new sample is accepted, take the next sample point v of the Markov chain. i =z i Otherwise, do not accept new samples and maintain the current position of the parallel sequence, return to the second step to evolve again;

[0102] Step 5: Remove useless chains

[0103] Calculate the average posterior probability density Ω for each chain, and then calculate the interquartile range of the posterior probability density of these samples, i.e., the difference between the 75th quantile Q3 and the 25th quantile Q1. Remove useless chains that satisfy the condition Ω < (Q1 - 2IQR).

[0104] Step 6: Determine convergence

[0105] The convergence criterion GR is calculated based on the variance within and between chains for each parameter. If If the GR convergence criterion is met, the calculation ends; otherwise, return to step two and continue until the maximum number of iterations is reached.

[0106] The specific method for calculating the posterior inclusion probability of the panel rockfill dam deformation monitoring model in step 4 is as follows:

[0107] The influencing factors of the deformation monitoring model for panel rockfill dams have two options during the modeling process: either include them or exclude them, thus forming the entire model space. The posterior probabilities of its model parameters are obtained from equation (6):

[0108]

[0109] In the formula: y is the vector of parameters to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor in the deformation monitoring model of the panel rockfill dam; D is the sample of observed dam settlement data. Let p(y|D) be the deformation monitoring model of the k-th panel rockfill dam in the model space; p(y|D) is the posterior probability of parameter y in the model space, that is, the posterior inclusion probability of each influencing factor of the prediction model. Let be the posterior probability of the deformation monitoring model of the k-th panel rockfill dam in the model space; To determine the parameters in the deformation monitoring model of the k-th panel rockfill dam y The posterior probability.

[0110] The DE-MCMC algorithm effectively reduces the autocorrelation of samples through mutation, crossover, and acceptance probability evaluation operations during the sample generation process. Furthermore, it can effectively explore the parameter space of complex deformation monitoring models for panel rockfill dams, complete parameter estimation, quantify the uncertainty of the model, and further improve the accuracy of the simulation.

[0111] Example 5

[0112] Continuous monitoring is conducted at monitoring points on the rockfill dam to obtain data on settlement at the monitoring points, as well as corresponding environmental data such as water level and temperature. The obtained data is preprocessed by interpolation, outlier removal, and normalization of the deformation training set data at the monitoring points.

[0113] A deformation monitoring model for panel rockfill dams was constructed, taking water pressure, temperature, and time as influencing factors. Table 1 shows the influencing factors of each component of the deformation prediction model for panel rockfill dams.

[0114] Table 1. Impact Factors

[0115]

[0116]

[0117] In Table 1, The average water depth of the previous i days; The average water depth over the previous i days; t is the number of days between the monitoring day and the initial monitoring day; δ i D represents the deformation on day i. m This represents the cumulative deformation over the previous seven days.

[0118] The Gongboxia rockfill dam with a face panel was selected as the research object. The maximum dam height is 132.2m. Three vertical monitoring sections were arranged inside the dam body (0+075.00m on the left side of the dam, 0+130.00m on the left side of the dam, and 0+230.00m on the left side of the dam). Monitoring instruments were deployed at the three elevations within each monitoring section. This study takes the measuring point on the 0+130.00m section on the left side of the dam as an example. The settlement monitoring layout of this section is as follows: Figure 2 As shown. Data from measuring points 3, 4, and 7 are invalid and will not be used in the selection of measuring points.

[0119] This application study selected four representative measurement points (e.g., Figure 2 As shown in the figure, prediction models were established for measuring points 6, 8, 10, and 15. The normalized settlement sequence for each measuring point is as follows: Figure 3 As shown. Settlement data monitored from September 1, 2004 to June 1, 2008 were used as the training set, and settlement data monitored from June 1, 2008 to December 31, 2009 were used as the test set.

[0120] Taking the process of determining the optimal Copula function for the joint distribution between the deformation of measuring point 8 and X1 in the water pressure factor as an example, Figures 4(a) and 4(b) show the empirical distribution function of the two and the cumulative probability plot of the kernel distribution estimate. The marginal distribution of the variable is determined from the given data sample set by this non-parametric method.

[0121] After determining the edge distribution, a preliminary selection of the Copula function is performed based on the frequency distribution histogram, skewness, and kurtosis analysis between the measuring point deformation and the factor. Figures 5(a) and 5(b) show the frequency histograms of the measuring point deformation and the water pressure factor X1. Figure 6 Table 2 shows the binary frequency histograms of the marginal distributions of the two data points, and the table also presents the kurtosis analysis data. As can be seen from the charts, Figure 6The frequency distribution tails of the two marginal distributions are asymmetrical and the distribution pattern is not obvious. Moreover, after calculation, the pattern also conforms to the distribution patterns of the other factors and the deformation of the measuring points. Therefore, this application selects the Gumbel, Clayton and Frank functions in the Archimedes-Copula function to describe the correlation structure between the original data samples of the variables. The specific function forms are shown in Table 2.

[0122] Table 2 shows the types of Copula functions used.

[0123]

[0124] Table 3 shows the semi-parametric estimation of the bivariate joint distribution Copula function between each factor and the deformation at the measuring point, as well as the calculation results of the fit test. Figure 6 The goodness of fit of different Copula functions for each factor was compared. Based on this, it was finally determined that the joint distribution between X1, X2, X3, X4, X5, X6, and X7 and the deformation of the measuring point adopts the Clayton-Copula function form, X8, X9, X10, X11, and X14 adopt the Frank-Copula function form, and X12 and X13 adopt the Gumbel function form.

[0125] Table 3. Parameter estimates and squared Euclidean distances for the Copula function.

[0126]

[0127] After determining the bivariate joint distribution Copula function of each variable and the deformation of the panel rockfill dam measuring points, this distribution replaces the assumption of a uniform distribution of the prior parameters in the original Bayesian model, completing the computational preparation work for the Copula Bayesian model (CBMA). In the Bayesian model computation system, each influencing factor has two possibilities: selection or non-selection. This embodiment has 14 potential factors, meaning the total number of factors in the model is 2^3. 14 =16384. Taking measurement point 8 as an example, Table 4 lists the statistical data of the selected influencing factor set. Due to the large numerical differences between the influencing factor sets, data standardization is required before model selection to minimize these differences. To find the best model for predicting the deformation of the rockfill dam measurement point, DE-MCMC is used for global exploration in the model space. DE-MCMC sampling is performed until the number of unique models in the sample exceeds the total number of models or the number of iterations exceeds twice the number of models. The smaller of the two is chosen by default. Before analyzing the reasonableness of the results, a diagnostic function is used to observe whether a sufficiently long space exploration has been performed to ensure the convergence of the posterior probability.

[0128] Table 4. Statistical analysis of impact factor set data.

[0129]

[0130] To observe the distribution more clearly, the posterior distribution of these coefficients is plotted as shown in the figure. From Figure 8 The results show that the probability distributions of X4, X5, X6, X7, and X10 have a very high point density at 0, while the remaining X9, X12, X13, and X14 only have a small point peak at 0. Although this indicates that the posterior inclusion probability of these four variables is not exactly 1, it basically confirms that X9, X12, X13, and X14 should be assigned a larger weight in the Bayesian model's average. This result is consistent with... Figure 9 The marginal posterior probability results for different factors in the complete model are consistent. Figure 9 The variables in the red column have a marginal posterior inclusion probability greater than 0.5, meaning that X1, X2, X3, X8, X9, X12, X13, and X14 are relatively important for predicting the deformation of the rockfill dam. The remaining blue columns represent marginal posterior probabilities less than 0.5, meaning that X4, X5, X6, X7, X10, and X11 have a smaller impact on deformation prediction.

[0131] To verify the superiority of the proposed model, two machine learning models without temporal modeling capabilities—the traditional stepwise regression (SR) model, the extreme learning machine (ELM), and the extreme gradient boosting (XGBoost)—were selected as comparison models for this test, along with two deep learning models with temporal modeling capabilities at the input end: the gated recurrent unit (GRU) and the particle swarm optimization-long short-term memory (PSO-LSTM) neural network.

[0132] Table 5 shows the calculation results of settlement evaluation indices at each model measuring point. The results indicate that the RMSE and MAE indices of the prediction model (CBMA) proposed in this invention are both maintained at approximately 1–3 mm. 2 Maintaining a value above 0.85 can clearly reflect the changing trend of the deformation sequence, and it has strong adaptability to different deformation sequences and good stability.

[0133] Table 5 Evaluation Indicators for Each Measurement Point of Different Models

[0134]

[0135] Example 6

[0136] Based on Example 5,

[0137] To demonstrate the improvement in average modeling accuracy of the improved Copula Bayesian model compared to the original BMA, its ability to predict deformation uncertainties, and its application value in engineering, the Gongboxia panel rockfill dam was used as an example. The deformation of measuring point 8 on the left 0+130.00m section of the dam was predicted using both the improved and unimproved BMA models. The training set used monitoring data from December 31, 2004 to December 31, 2009. Long-term deformation prediction for the measuring point was carried out for one year, starting from December 31, 2009. Figure 10 The study demonstrates that CBMA has a 95% prediction uncertainty for deformation at measuring point 8. By characterizing the uncertainty of dam deformation, risks can be better addressed and the reliability of the prediction results can be improved.

[0138] Figure 11 To improve the monthly settlement deformation prediction results of measuring point 8 using BMA before and after the experiment, the prediction accuracies of BMA and CBMA were 82.89% and 92.48% respectively, compared with the measured values. Compared with the original BMA, CBMA improved accuracy by 11.56% and had higher computational efficiency. For engineering applications, this measuring point is located near the bottom of the dam, close to the panel, and its settlement deformation exhibits a trend of stepwise growth. The results show that under the influence of cyclic loading and unloading deformation caused by water level fluctuations, the settlement deformation at this measuring point continuously accumulates, reaching a cumulative amount of 15.63 mm. The cumulative amounts predicted by BMA and CBMA also reached 18.85 mm and 16.59 mm respectively, indicating that the growth rate of dam deformation has not converged, and close monitoring of the dam's deformation development is still necessary in the future.

Claims

1. A method for predicting the deformation of panel rockfill dams based on CBMA and DE-MCMC algorithms, characterized in that, A deformation monitoring model for a panel rockfill dam was constructed. The Copula function joint distribution between the settlement at monitoring points and influencing factors replaced the uniform distribution assumption of the Bayesian model. The monitoring model and monitoring point data were substituted into the averaging calculation system of the Copula Bayesian model, and the model was improved by combining the differential evolution Markov chain Monte Carlo algorithm. This method was then applied to the deformation monitoring of the panel rockfill dam. The specific operations are as follows: Step 1: Continuously monitor the monitoring points on the rockfill dam to obtain the settlement of the monitoring points and the corresponding water level and temperature environmental data. Preprocess the obtained environmental data and normalize the settlement of the monitoring points. The preprocessing includes interpolation and outlier removal; The specific expression for the normalization process is as follows: （1） In equation (1), The settlement data is normalized. For input variables; and Input variables The maximum and minimum values; Step 2: Construct a deformation monitoring model for the panel rockfill dam, taking water pressure, temperature, and time as influencing factors; the deformation monitoring model for the panel rockfill dam is shown in Equation (2): （2） In the formula: These are regression constant coefficients; The regression coefficients for the water pressure factor are... ; For the upstream water depth i Power; For the front i The average water depth of the day; The regression coefficients for the temperature factor are... n The number of cycles of the simple harmonic component within one year, if n= 1 indicates that a year is considered as a cycle; if n= 2 indicates that a six-month period is taken as a cycle; t This represents the number of days between the monitoring day and the initial monitoring day. , , The regression coefficients for the time-sensitive factor; ; This represents the cumulative deformation over the previous seven days. Step 3: Construct the optimal joint distribution Copula function between the settlement at the measuring point and each influencing factor; details are as follows: The marginal distribution of settlement and influencing factors is determined by the kernel density estimation method. Finally, the parameters in the Copula function are obtained by the semi-parametric estimation method and the fit is optimized. The optimal Copula function form is selected based on the squared Euclidean distance. Step 4: Replace the original uniform distribution assumption in the Bayesian model's average system with the optimal joint distribution Copula function obtained in Step 3 to form a Copula Bayesian model. Substitute the panel rockfill dam monitoring model and the settlement at the measuring points into the average calculation system of this Copula Bayesian model. Calculate each influencing factor and the posterior probability of the monitoring model using the DE-MCMC algorithm to complete the quantification of the model's uncertainty. The specific method for calculating the posterior probability of the panel rockfill dam deformation monitoring model is as follows: The influencing factors of the deformation monitoring model for panel rockfill dams have two options during the modeling process: either include them or exclude them, thus forming the entire model space. The posterior probabilities of its model parameters are obtained from equation (6): （6） In the formula: This is the vector of parameters to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor in the deformation monitoring model of the panel rockfill dam; D This is a sample of data for the observed dam settlement. For the first in the model space k Deformation monitoring model for panel rockfill dams; Parameters in model space The posterior probability, i.e., the posterior inclusion probability of each influencing factor in the prediction model; For the first in the model space k Posterior probability of a deformation monitoring model for a panel rockfill dam; In the first k Parameters in the deformation monitoring model of a panel rockfill dam The posterior probability.

2. The method for predicting the deformation of panel rockfill dams based on CBMA and DE-MCMC algorithms according to claim 1, characterized in that, The DE-MCMC algorithm is a combination of the adaptive differential evolution algorithm and the Markov chain Monte Carlo algorithm; the specific details of the DE-MCMC algorithm are as follows: Step 1: Generate initial samples and calculate posterior probability density If the number of parameters to be selected is n Then randomly initialize 2 n A Markov chain, that is, producing 2 n Group of parameter vectors to be selected v For the sample, the posterior probability density is calculated using the sum of squares of the differences between the measured and predicted displacements at observation points of the panel rockfill dam. ; Step 2: Implement mutation operations using the differential evolution method. For the i Chain samples v i Perform the mutation operation according to formula (3) to obtain the corresponding mutated new chain, i.e., the new candidate sample. z i ; （3） In the formula: This is the logarithm used to generate candidate samples; ; , , ; This refers to model error; Step 3: Implement cross-operations Determine whether to use the old sample based on formula (4). v i Replace new sample z i ; （4） In the formula: The crossover probability; These are randomly sampled values ​​with uniform probability. Step 4: Decide whether to accept the transfer Calculate the posterior probability density of the new sample With Metropolis acceptance probability And then according to Decide whether to accept the transfer; （5） If the new sample is accepted, take the next sample point of the Markov chain. Otherwise, do not accept new samples and maintain the current position of the parallel sequence, return to the second step to evolve again; Step 5: Remove useless chains Calculate the mean posterior probability density for each chain. Then calculate the posterior probability density interquartile range (IQR) of these samples, which is the 75th percentile. Q 3 and 25th percentile Q The difference of 1, remove the values ​​that satisfy the condition. Unnecessary chains of conditions; Step 6: Determine convergence Convergence criteria are calculated based on the variance within and between chains for each parameter. GR ,if This means that the condition is satisfied. GR Convergence criteria, calculation complete; Otherwise, return to step two and continue until the maximum number of iterations is reached.

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