Method for predicting deformation of concrete faced rockfill dam based on CBMA and DE-MCMC algorithms

Abstract

The invention discloses a concrete faced rockfill dam deformation prediction method based on CBMA and DE-MCMC algorithms, and the method comprises the steps: constructing a concrete faced rockfill dam deformation monitoring model according to the water pressure, temperature and aging component, replacing the original uniform distribution assumption of averaging a Bayesian model with the Copula function joint distribution between the settlement amount of a measurement point and an influence factor, and predicting the deformation of the concrete faced rockfill dam. A concrete faced rockfill dam monitoring model and measuring point data are substituted into an average calculation system of a Copula Bayesian model, the model is improved in combination with a differential evolution Markov chain Monte Carlo algorithm, and the method is applied to deformation monitoring of the concrete faced rockfill dam. According to the prediction method based on the CBMA and DE-MCMC algorithms, the uncertainty of the model is subjected to better quantitative analysis in the process of predicting the deformation of the rockfill dam, the deformation rule and characteristics of the rockfill dam can be analyzed more effectively, and good interpretability and actual measurement fitting of a statistical model are reserved.

Description

Technical Field

[0001] The invention belongs to the technical field of pumped storage unit control, and in particular relates to a concrete face rockfill dam deformation prediction method based on CBMA and DE-MCMC algorithms. Background Art

[0002] Concrete face rockfill dam is one of the main types of earth-rock dams. Compared with traditional earth-rock dams, it has obvious advantages in safety, economy and adaptability, and has broad application prospects. The face rockfill dam is supported by rockfill body, and concrete face plate is arranged on the upstream surface for anti-seepage. However, due to the different stiffness of the two, deformation coordination problems will occur. Therefore, the deformation of the dam body becomes an important project for the safety monitoring of face rockfill dam, and it is also a key indicator for measuring the safety state of dam structure. The physical and mechanical parameters of the dam materials and the rock and soil of the dam foundation and abutment of the concrete face rockfill dam are unevenly distributed in space and change dynamically over time. The complex natural environmental conditions in the dam site area will lead to the randomness of the dynamic changes of the dam load and effect. The various factors affect each other, and different projects have unique characteristics, which makes the monitoring system of the face rockfill dam have strong uncertainty. Therefore, how to accurately and efficiently predict the deformation of the face rockfill dam has always been a problem that needs in-depth research. At present, the dam deformation prediction model based on monitoring data is mainly based on statistical models and machine learning models. For statistical models, as the number of input influencing factors increases, the degree of model fitting will increase, while increasing the complexity of the model, which can easily lead to a decrease in the generalization ability of the model. Although some scholars have made progress in the research direction of statistical model optimization methods, how to reduce the complexity of the model while ensuring the accuracy of the prediction model is still the main problem in the current research of dam deformation statistical models.

[0003] Due to the uncertainty of the deformation monitoring system of the concrete face rockfill dam, it is necessary to introduce the uncertainty information analysis method to conduct more comprehensive monitoring and prediction of the dam. In this regard, Bayesian theory has a good application effect. Its theory can integrate information from multiple sources and update the probability distribution of the target parameters. It has been widely used in deformation prediction. In Bayesian theory, Bayesian model averaging (BMA) has demonstrated strong prediction and decision support capabilities in many fields. BMA can not only integrate the advantages of multiple models, weightedly combine the fitting ability and prediction accuracy of each model, but also combine other methods to obtain more reliable overall prediction results. Seifi et al. used CBMA to implement multi-mode integrated prediction of evaporation of evaporation pans. The calculation of BMA often involves sampling of high-dimensional parameter space and complex probability distribution. In previous studies, Markov chain Monte Carlo (MCMC) was often used to solve the problem, but there is autocorrelation between samples of traditional MCMC and the exploration of high-dimensional space is relatively slow. To improve this problem, the algorithm combining adaptive differential evolution and Markov chain Monte Carlo (DE-MCMC) is a good choice. This method uses the differential evolution method to realize the search of the entire parameter space, and uses the Metropolis sampling algorithm to complete the adaptive adjustment of the acceptance probability, multi-chain parallel search and abnormal chain removal operations, which improves the solution quality while taking into account the convergence speed.

[0004] To this end, in view of the fact that there are many factors affecting the deformation of the concrete face rockfill dam and the uncertainty factors of the monitoring system are difficult to quantify, resulting in a complex deformation prediction model with low accuracy, this paper proposes a concrete face rockfill dam deformation prediction model based on CBMA and DE-MCMC algorithms, and examines the feasibility of the method in actual engineering. This paper first introduces the relevant theoretical methods, then introduces the process of constructing a concrete face rockfill dam deformation prediction model based on CBMA and DE-MCMC algorithms, and finally verifies the practicality of the proposed rockfill dam deformation prediction method through engineering examples. Summary of the invention

[0005] The purpose of the present invention is to provide a deformation prediction method for a concrete face rockfill dam based on CBMA and DE-MCMC algorithms, which solves the problem in the prior art that there are many factors affecting the deformation of concrete face rockfill dams and the uncertainty factors of the monitoring system are difficult to quantify, resulting in a complex deformation prediction model and low accuracy.

[0006] The first technical solution adopted by the present invention is: a deformation prediction method for a panel rockfill dam based on CBMA and DE-MCMC algorithms, a deformation monitoring model for a panel rockfill dam is constructed, the Copula function joint distribution between the settlement of the measuring point and the influencing factor replaces the uniform distribution assumption of the Bayesian model, the panel rockfill dam monitoring model and the measuring point data are substituted into the average calculation system of the Copula Bayesian model, and the model is improved in combination with the differential evolution Markov chain Monte Carlo algorithm, and the method is applied in the deformation monitoring of the panel rockfill dam; the specific operations are as follows:

[0007] Step 1: Continuously monitor the monitoring points on the concrete face rockfill dam to obtain the settlement of the measuring points and the corresponding water level and temperature environmental data, pre-process the obtained environmental data, and normalize the settlement of the measuring points;

[0008] Step 2: Construct a deformation monitoring model for the concrete face rockfill dam by taking water pressure, temperature and time as influencing factors;

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

[0010] Step 4: The optimal joint distribution Copula function obtained in step 3 replaces the original uniform distribution hypothesis in the Bayesian model average system to form a Copula Bayesian model. The panel rockfill dam monitoring model and the settlement of the measuring point are substituted into the average calculation system of the Copula Bayesian model. The posterior probability of each influencing factor and the monitoring model is calculated by the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

[0011] The present invention is also characterized in that:

[0012] Step 1: Preprocessing methods include interpolation and supplementation, and removal of outliers.

[0013] The specific expression of normalization processing in step 1 is as follows:

[0014]

[0015] In formula (1), C i is the normalized sedimentation data; x i is the input variable; x max and x min The input variables x are i The maximum and minimum values ​​of .

[0016] The deformation monitoring model of the concrete face rockfill dam in step 2 is shown in formula (2):

[0017]

[0018] Where: a0 is the regression constant coefficient; a i is the water pressure factor regression coefficient, i = 1 ~ 7; H i is the ith power of the upstream water depth; is the average water depth of the previous i days; c 1j 、c 2j is the regression coefficient 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 one cycle; if n = 2, it means that half a year is taken as one cycle; t is the number of days between the monitoring day and the initial monitoring day; d1, d2, d3 are the regression coefficients of the aging factor; D m It is the cumulative deformation in the previous seven days.

[0019] Step 3 is as follows:

[0020] The marginal distribution of sedimentation and influencing factors was determined by kernel density estimation method. Finally, the parameters in the Copula function were obtained by semi-parametric estimation method and fitted and optimized. The best Copula function form was selected according to 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 follows:

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

[0023] If the number of parameters to be optimized is n, 2n Markov chains are randomly initialized, that is, 2n sets of samples of parameter vectors v to be optimized are generated, and the square sum of the difference between the measured value and the predicted value of the displacement of the observation point of the panel rockfill dam is used to calculate the posterior probability density f(v i ), i=1,…,2n;

[0024] Step 2: Use differential evolution to implement mutation operations

[0025] For the sample v of the i-th chain i According to formula (3), the mutation operation is performed to obtain the corresponding mutation new chain, that is, the new candidate sample z i ;

[0026]

[0027] Where: 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 crossover operations

[0029] According to formula (4), determine whether to use the old sample v i Replace the new sample zi ;

[0030]

[0031] Where: CR is the crossover probability; U∈[0,1] is the random sampling value of uniform probability;

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

[0033] Calculate the posterior probability density f(z 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 keep the current point position of the parallel sequence, and return to the second step to evolve again;

[0036] Step 5: Remove useless chains

[0037] Calculate the average posterior probability density Ω of each chain, and then calculate the interquartile range IQR of the posterior probability density of these samples, that is, the difference between the 75% quantile Q3 and the 25% quantile Q1, and remove useless chains that meet 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, it returns to the second step and continues until the maximum number of iterations.

[0040] The calculation method of the posterior inclusion probability of the concrete face rockfill dam deformation monitoring model in step 4 is as follows:

[0041] There are two options for the influencing factors of the deformation monitoring model of the concrete face rockfill dam in the modeling process, namely, selection or non-selection, thus forming all the model spaces. The posterior probability of the model parameters is obtained by formula (6):

[0042]

[0043] Where: yis the parameter vector to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor of the concrete face rockfill dam deformation monitoring model; D is the observed dam settlement data sample; is the deformation monitoring model of the kth 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; is the posterior probability of the kth concrete face rockfill dam deformation monitoring model in the model space; is the parameter in the kth concrete face rockfill dam deformation monitoring model y The posterior probability of .

[0044] The beneficial effects of the present invention are:

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

[0046] (2) For nonlinear and complex problems such as rockfill dam deformation prediction, DE-MCMC can avoid the slow convergence or non-convergence problem of traditional optimization methods. By integrating this algorithm into CBMA to predict dam deformation, a global search can be performed in the entire model space. It can find options that are closer to the best when dealing with multiple local optimal problems, and it also improves the computational efficiency of high-dimensional model space.

[0047] (3) The prediction method integrating CBMA and DE-MCMC algorithms proposed in the present invention can better quantify the uncertainty of the model in the process of predicting the deformation of rockfill dams, and can more effectively analyze the deformation law and characteristics of rockfill dams. It not only retains the good interpretability and measured fitting of the statistical model, but also has significantly improved accuracy and stability compared with other deformation prediction models. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of the deformation prediction method of the concrete face rockfill dam based on CBMA and DE-MCMC algorithm of the present invention;

[0049] Figure 2 This is a diagram of the settlement measuring points arrangement of the dam left section 0+130.00m in Example 5 of the present invention;

[0050] Figure 3 is a normalized settlement deformation curve diagram of the selected measuring point training sequence in Example 5 of the present invention;

[0051] FIG4(a) is an empirical distribution function and kernel distribution estimation diagram of the displacement of measuring point No. 8 in Example 5 of the present invention;

[0052] FIG4( b ) is an empirical distribution function and kernel distribution estimation diagram of X1 in the water pressure factor of measuring point No. 8 in Example 5 of the present invention;

[0053] FIG5( a ) is a displacement frequency histogram of measuring point No. 8 in Example 5 of the present invention;

[0054] FIG5( b ) is a histogram of the X1 frequency in the water pressure factor of measuring point No. 8 in Example 5 of the present invention;

[0055] Figure 6 is a binary frequency histogram of the marginal distribution of X1 in the displacement of measuring point No. 8 and the water pressure factor in Example 5 of the present invention;

[0056] Figure 7 The squared Euclidean distance diagram of the joint distribution Copula function of the deformation of the measuring point No. 8 and each influencing factor in Example 5 of the present invention;

[0057] Figure 8 is a posterior probability distribution diagram of coefficients of measurement point No. 8 and various factors in Example 5 of the present invention;

[0058] Fig. 9 is a marginal posterior probability diagram of different factor coefficients in the deformation model of measuring point No. 8 in Example 5 of the present invention;

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

[0060] Fig.11 It is the monthly settlement deformation prediction diagram of measuring point No. 8 in Example 6 of the present invention; DETAILED DESCRIPTION

[0061] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments so that the advantages and features of the present invention can be more easily understood by those skilled in the art.

[0062] Example 1

[0063] The present invention is based on a concrete face rockfill dam deformation prediction method based on CBMA and DE-MCMC algorithms, constructs a concrete face rockfill dam deformation monitoring model, replaces the uniform distribution assumption of the Bayesian model with the Copula function joint distribution between the settlement of the measuring point and the influencing factor, substitutes the concrete face rockfill dam monitoring model and the measuring point data into the average calculation system of the Copula Bayesian model, improves the model in combination with the differential evolution Markov chain Monte Carlo algorithm, and applies the method to the deformation monitoring of the concrete face rockfill dam.

[0064] Example 2

[0065] The concrete operation of the concrete face rockfill dam deformation prediction method based on CBMA and DE-MCMC algorithm is as follows:

[0066] Step 1: Continuously monitor the monitoring points on the concrete face rockfill dam to obtain the settlement of the measuring points and the corresponding water level and temperature environmental data, pre-process the obtained environmental data, and normalize the settlement of the measuring points;

[0067] Step 2: Construct a deformation monitoring model for the concrete face rockfill dam by taking water pressure, temperature and time as influencing factors;

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

[0069] Step 4: The optimal joint distribution Copula function obtained in step 3 replaces the original uniform distribution hypothesis in the Bayesian model average system to form a Copula Bayesian model. The panel rockfill dam monitoring model and the settlement of the measuring point are substituted into the average calculation system of the Copula Bayesian model. The posterior probability of each influencing factor and the monitoring model is calculated by the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

[0070] Example 3

[0071] The concrete operation of the concrete face rockfill dam deformation prediction method based on CBMA and DE-MCMC algorithm is as follows:

[0072] Step 1: Continuously monitor the monitoring points on the concrete face rockfill dam to obtain the settlement of the measuring points and the corresponding water level and temperature environmental data, pre-process the obtained environmental data, and normalize the settlement of the measuring points;

[0073] Preprocessing includes interpolation and supplementation, and removal of outliers;

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

[0075]

[0076] In formula (1), C i is the normalized sedimentation data; x i is the input variable; x max and x min The input variables x are i The maximum and minimum values ​​of ;

[0077] Step 2: Construct a deformation monitoring model for the concrete face rockfill dam by taking water pressure, temperature and time as influencing factors;

[0078] Step 2 The deformation monitoring model of the concrete face rockfill dam is shown in formula (2):

[0079]

[0080] Where: a0 is the regression constant coefficient; a i is the water pressure factor regression coefficient, i = 1 ~ 7; H i is the ith power of the upstream water depth; is the average water depth of the previous i days; c 1j 、c 2j is the regression coefficient 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 one cycle; if n = 2, it means that half a year is taken as one cycle; t is the number of days between the monitoring day and the initial monitoring day; d1, d2, d3 are the regression coefficients of the aging factor; D m It is the cumulative deformation in the previous seven days.

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

[0082] Step 4: The optimal joint distribution Copula function obtained in step 3 replaces the original uniform distribution hypothesis in the Bayesian model average system to form a Copula Bayesian model. The panel rockfill dam monitoring model and the settlement of the measuring point are substituted into the average calculation system of the Copula Bayesian model. The posterior probability of each influencing factor and the monitoring model is calculated by 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 sedimentation and influencing factors was determined by kernel density estimation method. Finally, the parameters in the Copula function were obtained by semi-parametric estimation method and fitted and optimized. The best Copula function form was selected according to 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 DE-MCMC algorithm is as follows:

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

[0089] If the number of parameters to be optimized is n, 2n Markov chains are randomly initialized, that is, 2n sets of samples of parameter vectors v to be optimized are generated, and the square sum of the difference between the measured value and the predicted value of the displacement of the observation point of the panel rockfill dam is used to calculate the posterior probability density f(v i), i=1,…,2n;

[0090] Step 2: Use differential evolution to implement mutation operations

[0091] For the sample v of the i-th chain i According to formula (3), the mutation operation is performed to obtain the corresponding mutation new chain, that is, the new candidate sample z i ;

[0092]

[0093] Where: 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 crossover operations

[0095] According to formula (4), determine whether to use the old sample v i Replace the new sample z i ;

[0096]

[0097] Where: CR is the crossover probability; U∈[0,1] is the random sampling value of uniform probability;

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

[0099] Calculate the posterior probability density f(z 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 keep the current point position of the parallel sequence, and return to the second step to evolve again;

[0102] Step 5: Remove useless chains

[0103] Calculate the average posterior probability density Ω of each chain, and then calculate the interquartile range IQR of the posterior probability density of these samples, that is, the difference between the 75% quantile Q3 and the 25% quantile Q1, and remove useless chains that meet 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, it returns to the second step and continues until the maximum number of iterations.

[0106] The calculation method of the posterior inclusion probability of the concrete face rockfill dam deformation monitoring model in step 4 is as follows:

[0107] There are two options for the influencing factors of the deformation monitoring model of the concrete face rockfill dam in the modeling process, namely, selection or non-selection, thus forming all the model spaces. The posterior probability of the model parameters is obtained by formula (6):

[0108]

[0109] Where: y is the parameter vector to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor of the concrete face rockfill dam deformation monitoring model; D is the observed dam settlement data sample; is the deformation monitoring model of the kth 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; is the posterior probability of the kth concrete face rockfill dam deformation monitoring model in the model space; is the parameter in the kth concrete face rockfill dam deformation monitoring model y The posterior probability of .

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

[0111] Example 5

[0112] The monitoring points on the panel rockfill dam are continuously monitored to obtain the settlement of the measuring points and the corresponding environmental data such as water level and temperature. The obtained data are interpolated and supplemented, and data preprocessing such as outliers are eliminated, and the deformation training set data of the measuring points are normalized.

[0113] The deformation monitoring model of the concrete face rockfill dam is constructed by taking water pressure, temperature and time as influencing factors. Table 1 shows the influencing factors of each component of the concrete face rockfill dam deformation prediction model.

[0114] Table 1. Impact factors

[0115]

[0116]

[0117] In Table 1, is the average water depth of the previous i days; is the average water depth of the previous i days; t is the number of days between the monitoring day and the initial monitoring day; δ i is the deformation on the i-th day; D m is the cumulative deformation in the previous seven days;

[0118] The Gongboxia Concrete Face Rockfill Dam was selected as the research object. The maximum dam height is 132.2m. Three vertical monitoring sections are 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 are arranged at three elevations in the 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 arrangement of this section is as follows: Figure 2 The data of measuring points 3, 4 and 7 are invalid and do not participate in the selection of measuring point objects.

[0119] In this application study, four representative measurement points were selected (such as Figure 2 As shown in Figure 1), the prediction model is established for measuring points 6, 8, 10 and 15. The normalized sequence of settlement at each measuring point is as follows: Figure 3 The sedimentation data monitored from September 1, 2004 to June 1, 2008 are used as the training set, and the sedimentation data monitored from June 1, 2008 to December 31, 2009 are 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) are the empirical distribution functions of the two and the cumulative probability diagrams of the kernel distribution estimation. This non-parametric method is used to determine the marginal distribution of the variable from a given data sample set.

[0121] After determining the marginal distribution, a preliminary selection of the Copula function is performed based on the frequency distribution histogram, skewness, and kurtosis analysis between the measurement point deformation and the factor. Figure 5(a) and Figure 5(b) are the frequency histograms of the measurement point deformation and the water pressure factor X1. Figure 6 is the binary frequency histogram of the marginal distribution of the two, and Table 2 is the kurtosis analysis data of the two. It can be seen from the chart that Figure 6The frequency distribution tails of the marginal distributions of the two are asymmetric and the distribution pattern is not obvious. After calculation, the pattern also conforms to the distribution pattern of other factors and the deformation of the measuring points. Therefore, the research scope of this application selects Gumbel, Clayton and Frank functions in the Archimedean-Copula function to describe the correlation structure between the original data samples of the variables. The specific function form is shown in Table 2.

[0122] Table 2 Copula function types used

[0123]

[0124] Table 3 shows the semi-parametric estimation and fitting test results of the binary joint distribution Copula function between each factor and the deformation of the measuring point. Figure 6 Comparison of the goodness of fit of different Copula functions for each factor. 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 14 adopt the Frank-Copula function form, and X12 and X13 adopt the Gumbel function form.

[0125] Table 3 Parameter estimates and squared Euclidean distances of Copula functions

[0126]

[0127] After determining the binary joint distribution Copula function of each variable and the deformation of the measured point of the face rockfill dam, the distribution replaces the assumption of uniform distribution of the original Bayesian model prior parameters, and the calculation preparation of the Copula Bayesian model (CBMA) is completed. In the Bayesian model calculation system, each influencing factor has two possibilities of selection and non-selection. In this embodiment, there are 14 potential factors, that is, the total number of models is 2 14 =16384. Taking the No. 8 measuring point as an example, Table 4 lists the statistical data of the selected influencing factor set. Since there are relatively large numerical differences between the influencing factor sets, in order to eliminate such differences as much as possible, data standardization is required before model selection. In order to find the best model for predicting the deformation of the rockfill dam measuring point, DE-MCMC is used to perform global exploration in the model space. DE-MCMC sampling is run until the number of unique models in the sample exceeds the total number of models or the number of iterations exceeds 2 times the number of models. The smaller of the two is taken by default. Before analyzing the rationality of the results, it is necessary to observe whether the spatial exploration has been run for a long enough time through the diagnostic function to ensure the convergence of the posterior probability.

[0128] Table 4 Statistics of impact factor set data

[0129]

[0130] In order to observe the distribution more clearly, the posterior distribution of these coefficients is plotted as shown in the figure. Figure 8 It can be seen that the probability distribution of X4, X5, X6, X7, and X10 has a very large point density at point 0, while the remaining X9, X12, X13, and X14 have only a very small point peak at point 0. Although this shows that the posterior inclusion probability of these four variables is not completely 1, it is also basically determined that X9, X12, X13, and X14 should be assigned more weight in the Bayesian model average. This result is consistent with Fig. 9 The marginal posterior probability results of different factors in the complete model are consistent. Fig. 9 The variables corresponding to the red columns have marginal posterior inclusion probabilities greater than 0.5, which means that X1, X2, X3, X8, X9, X12, X13 and X14 are more important for the deformation prediction of rockfill dams, while the remaining blue columns represent marginal posterior probabilities less than 0.5, that is, X4, X5, X6, X7, X10 and X11 have little influence on deformation prediction.

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

[0132] Table 5 shows the calculation results of the settlement evaluation indexes of each model measurement point. The results show that the RMSE and MAE indicators of the prediction model (CBMA) proposed in this invention are both maintained at around 1 to 3 mm, and R 2 Keeping it above 0.85 can clearly reflect the changing trend of the deformation sequence, has strong adaptability to different deformation sequences, and has good stability.

[0133] Table 5 Evaluation indicators of each measuring point of different models

[0134]

[0135] Example 6

[0136] Based on Example 5,

[0137] In order to demonstrate the improvement of the average modeling accuracy of the improved Copula Bayesian model compared with the original BMA, the uncertainty prediction of deformation and its application value in engineering, the Gongboxia concrete face rockfill dam was taken as an example, and the BMA before and after the improvement was used to predict the deformation of measuring point 8 on the left section of 0+130.00m of the dam. The training set used the monitoring data from December 31, 2004 to December 31, 2009, and a long-term deformation prediction of one year was carried out for this measuring point with December 31, 2009 as the starting point. Fig.10 The 95% prediction uncertainty of CBMA deformation at measuring point 8 is demonstrated. By characterizing the uncertainty of dam deformation, risks can be better dealt with and the credibility of prediction results can be improved.

[0138] Fig.11 In order to improve the monthly settlement deformation prediction results of the No. 8 measuring point before and after BMA, the prediction accuracy of BMA and CBMA was 82.89% and 92.48% respectively compared with the measured values. Compared with the original BMA, the accuracy of CBMA was improved by 11.56%, and the calculation efficiency was higher. For engineering applications, this measuring point is located at the bottom of the dam close to the panel, and its settlement deformation has the regular characteristics of a trend of step-by-step growth. The results show that under the influence of cyclic loading and unloading deformation caused by water level fluctuations, the settlement deformation of this measuring point continues to accumulate, and the cumulative amount reaches 15.63mm. The cumulative amount predicted by BMA and CBMA also reached 18.85mm and 16.59mm, indicating that the growth rate of dam deformation has not shown a trend of convergence, and the deformation development of the dam still needs to be closely monitored in the future.

Claims

1. The deformation prediction method of concrete face rockfill dam based on CBMA and DE-MCMC algorithm is characterized by: A deformation monitoring model for panel rockfill dam is constructed, and the uniform distribution assumption of the Bayesian model is replaced by the joint distribution of the Copula function between the settlement of the measuring point and the influencing factors. The panel rockfill dam monitoring model and the measuring point data are substituted into the average calculation system of the Copula Bayesian model, and the model is improved by combining the differential evolution Markov chain Monte Carlo algorithm. This method is then applied to the deformation monitoring of panel rockfill dam.

2. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 1, characterized in that: The specific operations are as follows: Step 1: Continuously monitor the monitoring points on the concrete face rockfill dam to obtain the settlement of the measuring points and the corresponding water level and temperature environmental data, pre-process the obtained environmental data, and normalize the settlement of the measuring points; Step 2: Construct a deformation monitoring model for the concrete face rockfill dam by taking water pressure, temperature and time as influencing factors; Step 3: Construct the optimal joint distribution Copula function between the settlement of the measuring point and each influencing factor; Step 4: The optimal joint distribution Copula function obtained in step 3 replaces the original uniform distribution hypothesis in the Bayesian model average system to form a Copula Bayesian model. The panel rockfill dam monitoring model and the settlement of the measuring point are substituted into the average calculation system of the Copula Bayesian model. The posterior probability of each influencing factor and the monitoring model is calculated by the DE-MCMC algorithm to complete the quantification of the uncertainty of the model.

3. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2 is characterized in that: The preprocessing in step 1 includes interpolation and supplementation, and removal of outliers.

4. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2, characterized in that: The specific expression of the normalization process in step 1 is as follows: In formula (1), C i is the normalized sedimentation data; x i is the input variable; x max and x min The input variables x are i The maximum and minimum values ​​of .

5. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2, characterized in that: The deformation monitoring model of the concrete face rockfill dam in step 2 is shown in formula (2): Where: a0 is the regression constant coefficient; a i is the water pressure factor regression coefficient, i = 1 ~ 7; H i is the upstream water depth to the power of i; is the average water depth of the previous i days; c 1j 、c 2j is the regression coefficient 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 one cycle; if n = 2, it means that half a year is taken as one cycle; t is the number of days between the monitoring day and the initial monitoring day; d1, d2, d3 are the regression coefficients of the aging factor; D m It is the cumulative deformation in the previous seven days.

6. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2, characterized in that: Step 3 is as follows: The marginal distribution of sedimentation and influencing factors was determined by kernel density estimation method. Finally, the parameters in the Copula function were obtained by semi-parametric estimation method and fitted and optimized. The best Copula function form was selected according to the squared Euclidean distance.

7. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2, characterized in that: The DE-MCMC algorithm is a combination of the adaptive differential evolution algorithm and the Markov chain Monte Carlo algorithm; the DE-MCMC algorithm is specifically as follows: Step 1: Generate initial samples and calculate posterior probability density If the number of parameters to be selected is n, 2n Markov chains are randomly initialized, that is, 2n sets of samples of parameter vectors v to be selected are generated, and the posterior probability density f(v) is calculated by the sum of squares of the difference between the measured value and the predicted value of the displacement of the observation point of the panel rockfill dam. i ), i=1,…,2n; Step 2: Use differential evolution to implement mutation operations For the sample v of the i-th chain i According to formula (3), the mutation operation is performed to obtain the corresponding mutation new chain, that is, the new candidate sample z i ; Where: 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; Step 3: Implement crossover operations According to formula (4), determine whether to use the old sample v i Replace the new sample z i ; Where: CR is the crossover probability; U∈[0,1] is the random sampling value of uniform probability; Step 4: Decide whether to accept the transfer Calculate the posterior probability density f(z 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; 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 keep the current point position of the parallel sequence, and return to the second step to evolve again; Step 5: Remove useless chains Calculate the average posterior probability density Ω of each chain, and then calculate the interquartile range IQR of the posterior probability density of these samples, that is, the difference between the 75% quantile Q3 and the 25% quantile Q1, and remove useless chains that meet the condition Ω<(Q1-2IQR); Step 6: Determine convergence 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, it returns to the second step and continues until the maximum number of iterations.

8. The method for predicting deformation of a concrete face rockfill dam based on CBMA and DE-MCMC algorithm according to claim 2, characterized in that: The calculation method of the posterior inclusion probability of the concrete face rockfill dam deformation monitoring model in step 4 is as follows: There are two options for the influencing factors of the deformation monitoring model of the concrete face rockfill dam in the modeling process, namely, selection or non-selection, thus forming all the model spaces. The posterior probability of the model parameters is obtained by formula (6): Where: y is the parameter vector to be estimated, i.e., the vector composed of the regression coefficients of each influencing factor of the concrete face rockfill dam deformation monitoring model; D is the observed dam settlement data sample; is the deformation monitoring model of the kth 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; is the posterior probability of the kth concrete face rockfill dam deformation monitoring model in the model space; is the parameter in the kth concrete face rockfill dam deformation monitoring model y The posterior probability of .

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