Dangerous rock slope long-term deformation prediction method based on data-mechanism dual drive

Abstract

The invention discloses a dangerous rock mass slope long-term deformation prediction method based on data-mechanism dual drive. The method comprises the following steps: collecting dangerous rock mass slope long-term deformation monitoring data as an observation value; a Burgers rheological mechanical model used for prediction and rheological mechanical parameters to be inverted are determined; determining prior distribution of the rheological mechanical parameters, and updating the rheological mechanical parameters by using Bayesian reasoning to obtain updated posterior distribution of the rheological mechanical parameters; correlation and sensitivity analysis is conducted on the rheological mechanical parameters, and long-term deformation of the dangerous rock mass slope is predicted through the updated rheological mechanical parameters. According to the method, a driving method based on long-term monitoring data and a driving method based on a rheological mechanical mechanism are fused, the long-term deformation of the rock slope is predicted by continuously iterating and updating rheological mechanical parameters, a basis is provided for making prevention and control measures for slope deformation, and the method has practical value.

Description

Technical Field

[0001] The present invention relates to the interdisciplinary field of water conservancy and hydropower rock slope engineering and data-driven, and in particular to a method for predicting long-term deformation of dangerous rock slopes based on data-mechanism dual-drive. Background Art

[0002] For dangerous rock slopes in hydropower projects, external factors such as natural rainfall, water level fluctuations, and dam discharge vibrations can lead to geological hazards such as rock collapse, collapse, and sliding. Many slope engineering failures are caused by gradual deformation accumulation over time, reaching a critical threshold for instability. Rock creep is a time-dependent deformation mechanism. Creep must be considered a key factor during the engineering design phase. Extensive engineering geological surveys have shown that the geological conditions of large rock slopes in hydropower projects in Southwest China are extremely complex, posing considerable challenges to predicting long-term deformation of the slope rock mass.

[0003] According to the theory of rock rheology, the long-term deformation of rock slopes is caused by the degradation of parameters. By selecting a suitable rheological model and calibrating the rheological parameters by solving the inverse problem, the overall deformation characteristics of the slope within a certain period of time can be accurately evaluated.

[0004] Current parameter inversion methods fall into two categories: deterministic and nondeterministic. Deterministic methods have evolved from local optimization (Newton's method, gradient descent) to global optimization (genetic algorithms, particle swarm optimization). Among nondeterministic methods, Bayesian methods are commonly used. These methods reveal and evaluate parameter uncertainty, providing corresponding probability distribution intervals. Probabilistic inversion analysis provides a reasonable and feasible approach for fully utilizing monitoring data, quantifying and reducing parameter uncertainty, and improving prediction accuracy.

[0005] With the development of digital technology, data assimilation is becoming a promising predictive technology. This method consists of three main components: Bayesian reasoning, computational models, and observational data. The principle of data modeling based on Bayesian reasoning is to model all variables as random variables with a certain probability distribution. The influence of observations on parameters is incorporated into the posterior distribution, from which updated model estimates can be obtained. Due to the complex geological environment of dangerous rock slope engineering, a large number of visual monitoring points are deployed on the rock surface. This provides valuable observational data for long-term rock deformation prediction based on data assimilation methods.

[0006] How to apply data assimilation methods to the long-term deformation prediction and analysis of dangerous rock slopes, and combine them with deformation monitoring data from actual projects to achieve long-term deformation prediction of dangerous rock slopes that combines mechanism analysis and data-driven, is a technical problem that needs to be solved urgently. Summary of the Invention

[0007] Purpose of the invention: In response to the shortcomings of the existing technology, the present invention proposes a method for predicting the long-term deformation of dangerous rock slopes based on data-mechanism dual drive. The method combines slope engineering deformation monitoring data, rheological mechanics model and Bayesian reasoning to perform data assimilation on the rheological mechanics parameters of the slope rock mass, and realizes the long-term deformation prediction of dangerous rock slopes combined with mechanism analysis and data drive, providing a basis for taking preventive measures for dangerous rock slopes.

[0008] Technical solution: The present invention is based on a data-mechanism dual-driven long-term deformation prediction method for dangerous rock slopes, which includes the following steps:

[0009] Step (1) collects monitoring data of the dangerous rock mass slope as observation values, including deformation values of the dangerous rock mass surface monitoring and corresponding monitoring time.

[0010] Step (2) inverting the rheological parameters of the Burgers rheological model used for prediction: the external pressure σ0 of the dangerous rock mass at the apparent monitoring point, the delayed elastic modulus η1, the viscous flow rate η2, and the elastic shear modulus E2 at the apparent monitoring point of the dangerous rock mass to obtain the deformation value;

[0011] In step (3), based on the monitoring data of the dangerous rock mass slope, the four rheological parameters σ0, η1, E2 and η2 are updated in a Bayesian manner to realize the data assimilation of the apparent monitoring deformation value of the dangerous rock mass. The data assimilation process is as follows:

[0012] Step (3.1) determines the rheological parameters based on Bayesian update. Under the Burgers rheological model, Bayesian update allows the prior distribution of the parameters to be inverted to be improved according to the newly obtained apparent monitoring deformation value of the dangerous rock mass, thereby generating a posterior distribution that reflects the prior information and monitoring evidence. Given the apparent monitoring deformation value of the dangerous rock mass is ε=[ε1,=,ε n ], n is the number of observation points, then the posterior distribution f(θ|ε) of the rheological parameters to be inverted θ=[σ0,η1,E2,η2] is:

[0013]

[0014] Where p(θ) is the prior probability distribution of the parameter, p(ε|θ) is the likelihood function, and p(ε) is the normalization constant.

[0015] Step (3.2), determine the likelihood function and prior probability distribution. First, assume that based on the updated rheological parameters The predicted displacement value is Then the error vector between the predicted value and the monitored value is e=[e1,…,e n ]for:

[0016]

[0017] When the error value is 0, it means the rheological parameters are updated based on Bayesian Completely predict the apparent monitoring deformation value of the dangerous rock mass. Assuming that the error follows a Gaussian distribution, the joint probability density function of the error is:

[0018]

[0019] Where ∑ is the covariance matrix of the error vector e, ∑ = σ 2 I, where σ is the standard deviation of the Gaussian distribution and I is the identity matrix.

[0020] According to the error probability density function, the logarithmic form of the likelihood function is:

[0021]

[0022] In order to avoid deviation, the rheological parameters to be inverted in the present invention are all used as independent variables, and their prior distribution adopts the form of uniform distribution, which is expressed as:

[0023]

[0024] The posterior distribution is then calculated using Equation (2). Since the posterior distribution is difficult to process analytically, samples are generated by exploring the parameter space from the posterior distribution. The prior distribution reflects the initial understanding of the parameter values, the likelihood function captures the difference between the monitored and predicted values, and the posterior distribution is generated through Monte Carlo Markov Chain (MCMC) sampling.

[0025] Step (3.3) uses the MCMC method to iteratively update and preliminarily predict the rheological parameters to be inverted; a set of parameters θ current Make a jump to generate a new set of parameters θ new By comparing the likelihood function in step (3.2) with the value after the jump, the error between the predicted result of the current parameter value and the monitored value is determined and the acceptance probability α is solved as:

[0026]

[0027] Step (4): Determine whether to retain the current parameter θ based on the acceptance probability α current If the value of α is not 1, the current parameters are retained and the iteration is repeated until samples are generated to ensure that the Markov chain converges to the posterior distribution of the target.

[0028] Step (4.1), for the posterior parameters of the four rheological parameters σ0, η1, E2 and η2, establish a one-dimensional marginal probability density map and a two-dimensional scatter density map, calculate the Pearson correlation coefficient for the scatter density map, and determine the collinearity between the posterior parameters;

[0029] In step (4.2), in order to analyze the differences in the rheological parameters σ0, η1, E2, and η2 and explain the shape of the posterior distribution, the Sobol sensitivity analysis method is used to uniformly sample the rheological parameters σ0, η1, E2, and η2 within the prior range to analyze the influence of each parameter on the displacement value ε. The output displacement value ε of the Burgers model is expressed as a function ε = f(x) of the input parameters x = [x1, x2, x3, x4], and the total variance V(ε) of ε is decomposed into the variance contribution of each input variable and its interaction term:

[0030]

[0031] Where, f i =f i (x i ),f ij =f ij (x i ,x j ),…,f 1234 =f 1234 (x1,x2,x3,x4), the total variance is:

[0032]

[0033] Where V i (ε) is x i The resulting variance, V ij (ε) is x i and x j The variance due to the interaction, V 1234 (ε) is the variance produced by the effects of x1, x2, x3, and x4.

[0034] V i (ε)=V(f i (xi))#(25)

[0035] V ij (ε)=V(f ij (x i ,x j ))#(26)

[0036] V 1234 (ε)=V(f 1234 (x1,x2,x3,x4))#(27)

[0037] Then the global sensitivity index of each variable is:

[0038]

[0039] Where, ST i is the global Sobol sensitivity index; is the conditional expectation of the output of the Burgers rheological model; i Divide by x i All input variables except .

[0040] (5) Substitute the parameters that converge to the target posterior distribution into formula (1) to obtain the deformation prediction value. Compare the deformation prediction value with the monitored deformation value and calculate the root mean square error (RMSE) and mean absolute error (MAE).

[0041] In step (2), the Burgers rheological model is used to invert and obtain ε:

[0042]

[0043] Where ε represents the deformation of the dangerous rock mass as a function of time t; σ0 represents the external pressure exerted on the surrounding rock mass at the apparent monitoring point; E1 is the elastic modulus of the rock mass at the monitoring point, which is used to control the elastic deformation of the rock mass and is set to a constant value during the prediction process; E2 is the elastic shear modulus of the rock mass at the apparent monitoring point of the dangerous rock mass; η1 and η2 are viscosity coefficients, where η1 is the delayed elastic modulus and η2 is the viscous flow rate. The rheological parameters to be inverted are σ0, η1, E2, and η2.

[0044] In step (4.1), the Pearson correlation coefficient is:

[0045]

[0046] Where p and q are two parameters of the two-dimensional scatter density map, and is the mean of the corresponding parameter. The range of the correlation coefficient R is [-1, 1]. When |R| approaches 1, it indicates that there is a strong linear correlation between the two parameters. When |R| approaches 0, it indicates that the two parameters are linearly independent.

[0047] In step (5), the root mean square error RMSE is calculated as follows:

[0048]

[0049] Where, represents the predicted deformation value of the i-th day calculated based on the posterior parameters, ε iRefers to the measured deformation value corresponding to day i, and n is the total number of samples. The smaller the RMSE and MAE values, the higher the prediction accuracy.

[0050] In step (5), the mean absolute error (MAE) is calculated as follows:

[0051]

[0052] Where, is the predicted deformation value of the i-th day calculated from the posterior parameters, ε i is the measured deformation value corresponding to the i-th day, and n is the total number of samples.

[0053] Working principle: The present invention first collects long-term deformation monitoring data of dangerous rock slopes as observation values; determines the Burgers rheological mechanics model used for prediction and the rheological mechanics parameters to be inverted; clarifies the prior distribution of the rheological mechanics parameters, uses Bayesian reasoning to update the rheological mechanics parameters, and obtains the updated posterior distribution of the rheological mechanics parameters; performs correlation and sensitivity analysis on the rheological mechanics parameters, and uses the updated rheological mechanics parameters to predict the long-term deformation of the dangerous rock slope.

[0054] Beneficial effects: Compared with the existing technology, the present invention has the following advantages: the present invention integrates the driving method based on long-term monitoring data and the driving method based on rheological mechanics mechanism, combines the slope engineering deformation monitoring data, rheological mechanics model and Bayesian reasoning to perform data assimilation on the rheological mechanics parameters of the slope rock mass, and realizes the long-term deformation prediction of dangerous rock slopes combined with mechanism analysis and data driving, providing a basis for taking prevention and control measures for dangerous rock slopes. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of the method for predicting long-term deformation of dangerous rock slopes based on data-mechanism dual drive of the present invention;

[0056] Figure 2 This is a diagram showing the apparent deformation change of a dangerous rock mass slope in one embodiment of the present invention;

[0057] Figure 3 Schematic diagram of the Burgers rheological model in the present invention;

[0058] Figure 4 is a priori distribution diagram of rheological parameters in one embodiment of the present invention;

[0059] Figure 5 1 is a graph showing the correlation analysis results of posterior parameters in one embodiment of the present invention;

[0060] Figure 6 A graph showing sensitivity results of rheological parameters obtained by uniformly sampling within a priori range in one embodiment of the present invention;

[0061] Figure 7 This is a diagram showing the results of long-term deformation prediction based on a posteriori rheological parameters in one embodiment of the present invention;

[0062] Figure 8 Graph showing calculation results of error indicators in one embodiment of the present invention. DETAILED DESCRIPTION

[0063] like Figure 1 As shown, the process of the long-term deformation prediction method of dangerous rock slope based on data-mechanism dual drive in the embodiment of the present invention is as follows:

[0064] (1) Collect long-term deformation monitoring data of dangerous rock slopes as observation values. This implementation case uses the deformation monitoring values of a surface monitoring point of Dr2 dangerous rock slope of Suofengying Hydropower Station from November 18, 2021 to September 15, 2023, a total of about 600 days, as shown in the following example: Figure 2 shown.

[0065] (2) Determine the Burgers rheological model used for prediction and the rheological parameters to be inverted. The schematic diagram of the Burgers rheological model is as follows: Figure 3 The Burgers rheological model is composed of a Maxwell body and a Kelvin body. The deformation ε is represented by six parameters: σ0, E1, η1, E2, η2, and t. The four rheological parameters σ0, η1, E2, and η2 are determined for inversion. Parameter E1, which represents the elastic deformation property, is set to the elastic modulus of the target rock mass and is set to a constant value.

[0066] (3) Clarify the prior distribution of rheological parameters, use Bayesian reasoning to update the rheological parameters, and obtain the updated posterior distribution of the rheological parameters. The rheological parameters and their prior distribution ranges for this implementation case are shown in Appendix 1.

[0067] Appendix 1 Prior distribution range of rheological parameters

[0068] Rheological parameters <![CDATA[σ0(Pa)]]> <![CDATA[η1(Pa·s)]]> <![CDATA[E2(Pa)]]> <![CDATA[η2(Pa·s)]]> Prior range 5e6~5e7 1e11~5e12 1e10~2e11 5e8~1e9 Distribution Uniform distribution Uniform distribution Uniform distribution Uniform distribution

[0069] The rheological parameters are updated using the MCMC algorithm. The posterior distribution of the rheological parameters is as follows: Figure 4 As shown in the figure, the posterior distributions of σ0 and η1 are more concentrated than the prior results, with η1 showing the most significant change and a significant decrease in the distribution range, indicating a significant reduction in the uncertainty of these two rheological parameters. However, the posterior distributions of E2 and η2 show less change, with a larger overlap between the prior and posterior distributions, and η2 showing the smallest change, indicating that the uncertainties of these two rheological parameters are higher than those of other parameters.

[0070] (4) After obtaining the posterior parameters, the linear correlation of each rheological parameter is analyzed using the Pearson correlation coefficient, such as Figure 5 shown. Figure 5 The two-dimensional scatter plots and posterior distributions of each parameter are given. In order to standardize the calculation of correlation coefficients, all posterior parameters are normalized. Figure 5 It can be seen that σ0 and η1 have a strong positive linear correlation, and the Pearson correlation coefficient reaches 0.99, while the correlation of other parameters is not obvious. The sensitivity analysis of the rheological parameters of the prior uniform sampling is carried out using the Sobol method. The results of the global sensitivity index are as follows Figure 6 As shown. Figure 6 It can be seen that with the increase of simulation time, the global sensitivity index of σ0 and E2 shows a trend of first decreasing and then stabilizing, and finally reaches 0.25 and 0.02 respectively, while η1 shows a trend of initially increasing and then stabilizing, and finally stabilizes at 0.92. In contrast, the global sensitivity index of η2 shows a continuous minimum value, which indicates that η2 has little effect on the deformation ε. It is worth noting that, compared with Figure 3 and Figure 6 The results show that the global sensitivity index of the parameter with low uncertainty is larger, while the parameter with high uncertainty shows a smaller global sensitivity index. This further shows that the results of sensitivity analysis are consistent with those of uncertainty analysis.

[0071] (5) The updated rheological parameters are used to predict the long-term deformation of the dangerous rock slope and perform error analysis, using the root mean square error (RMSE) and mean absolute error (MAE) as error indicators. The prediction results are as follows: Figure 7 As shown in Figure 2, the calculation results of the prior parameters (grey lines) are widely distributed around the observed data, indicating that the prior range is reasonable. At the same time, the calculation results of the posterior parameters (green lines) are clustered near the observed data, which indicates that the prediction has been successfully achieved. The calculation results of the error indicators are shown in Figure 2. Figure 8 As shown, regardless of Figure 7 The error situation shown is still based on the actual error calculation results. The error between the a posteriori calculation results and the observed data is very small, less than 10%, which shows the effectiveness of the data-mechanism dual-driven long-term deformation prediction method of dangerous rock slopes in this invention.

Claims

1. A data-mechanism dual-driven method for predicting long-term deformation of dangerous rock slopes, characterized by: The following steps are involved: Step (1), collecting deformation value and monitoring time of the dangerous rock mass surface monitoring as observation values; Step (2) inverting the rheological parameters of the Burgers rheological model used for prediction: the external pressure σ0 of the dangerous rock mass at the apparent monitoring point, the delayed elastic modulus η1, the viscous flow rate η2, and the elastic shear modulus E2 at the apparent monitoring point of the dangerous rock mass to obtain the deformation value; Step (3) performs Bayesian update on σ0, η1, E2 and η2, and assimilates the apparent monitoring deformation data of the dangerous rock mass: Step (3.1), set the apparent monitoring deformation value of the dangerous rock mass to be ε=[ε1,…,ε n ], n is the number of observation points; then the posterior distribution f(θ|ε) of the rheological parameters to be inverted θ=[σ0,η1,E2,η2] is: Where p(θ) is the prior probability distribution of the parameter, p(ε|θ) is the likelihood function, and p(ε) is the normalization constant; Step (3.2), determine the likelihood function and prior probability distribution; first, set the updated rheological parameters The predicted displacement value is Then the error vector between the predicted value and the monitored value is e=[e1,…,e n ]for: The error obeys Gaussian distribution, and the probability density function of the error is: Where ∑ is the covariance matrix of the error vector e, ∑ = σ 2 I, where σ is the standard deviation of the Gaussian distribution and I is the identity matrix; According to the probability density function of the error, the logarithmic form of the likelihood function is derived as follows: Prior distribution of rheological parameters to be inverted: Step (3.3) uses the MCMC method to iteratively update and preliminarily predict the rheological parameters to be inverted; a set of parameters θ current Make a jump to generate a new set of parameters θ new , by comparing the likelihood function in step (3.2) with the value after the jump, determine the error between the result predicted by the current parameter value and the monitored value and solve the acceptance probability α as: (4) Determine whether to retain the current parameter θ based on the acceptance probability α current , repeated iterations make the Markov chain converge to the posterior distribution of the target; Step (4.1), for the posterior parameters of rheological parameters σ0, η1, E2 and η2, establish a one-dimensional marginal probability density map and a two-dimensional scatter density map, calculate the Pearson correlation coefficient for the scatter density map, and determine the collinearity between the posterior parameters; In step (4.2), the Sobol sensitivity analysis method is used to uniformly sample the rheological parameters σ0, η1, E2 and η2 within the prior. The Burgers output displacement value ε is a function ε = f(x) of the input parameters x = [x1, x2, x3, x4]. The total variance V(ε) of ε is decomposed into the variance contributions of the input variables and the interaction terms: Where, The total variance is: Where V i (ε) is x i The resulting variance, V ij (ε) is x i and x j The variance due to the interaction, V 1234 (ε) is the variance produced by the effects of x1, x2, x3, and x4; V i (ε)=V(f i (x i ))#(9) V ij (ε)=V(f ij (x i ,x j ))#(10) V 1234 (ε)=V(f 1234 (x1,x2,x3,x4))#(11) Then the global sensitivity index of each variable is: Where, ST i is the global Sobol sensitivity index; is the conditional expectation of the output of the Burgers rheological model; i Divide by x i All input variables except (5) Substitute the parameter group that converges to the target posterior distribution into formula (1) to obtain the deformation prediction value. The deformation prediction value is compared with the monitored deformation value, and the root mean square error (RMSE) and mean absolute error (MAE) are calculated.

2. The method for predicting long-term deformation of dangerous rock slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (2), the Burgers rheological model is used to invert and obtain ε: Where ε is the deformation value of the dangerous rock mass at the apparent monitoring point changing with time t; σ0 is the external pressure on the rock mass at the apparent monitoring point; E1 is the elastic modulus of the rock mass at the monitoring point; E2 is the elastic shear modulus of the rock mass at the apparent monitoring point of the dangerous rock mass; η1 is the delayed elastic modulus, and η2 is the viscous flow rate.

3. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 2 is characterized by: In step (2), E1 is the elastic modulus of the rock mass at the monitoring point, and E1 is a constant value during the prediction process.

4. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (3.2), when the error value is 0, the rheological parameters after Bayesian update are Predict the apparent monitoring deformation value of dangerous rock mass.

5. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (3.3), the MCMC method is used to iteratively update the rheological parameters to be inverted, the number of iterations and the number of Markov chains of the MCMC process are determined, and a preliminary prediction is made on the rheological parameters to be inverted.

6. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (3.3), the jump process is governed by the prior distribution in step (3.2). By comparing the likelihood function in step (3.2) with the value after the jump, the error between the predicted result of the current parameter value and the monitored value is determined and the acceptance probability α is solved.

7. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (4), determine whether to retain the current parameter θ based on the acceptance probability α current If the value of α is not 1, the current parameters are retained and the iteration is repeated so that the Markov chain converges to the posterior distribution of the target.

8. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (4.1), the Pearson correlation coefficient is: Where p and q are two parameters of the two-dimensional scatter density map, and is the mean of the corresponding parameter.

9. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1 is characterized by: In step (5), the root mean square error RMSE is calculated as follows: Where, is the predicted deformation value of the i-th day calculated from the posterior parameters, ε i is the measured deformation value corresponding to the i-th day, and n is the total number of samples.

10. The method for predicting long-term deformation of dangerous rock mass slopes based on data-mechanism dual drive according to claim 1, characterized in that: In step (5), the mean absolute error (MAE) is calculated as follows: Where, is the predicted deformation value of the i-th day calculated from the posterior parameters, ε i is the measured deformation value corresponding to the i-th day, and n is the total number of samples.

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