A method for constructing a statistical model of concrete dam deformation observation

Abstract

This invention discloses a method for constructing a statistical model of concrete dam deformation observation. The method includes preprocessing concrete dam deformation monitoring data; using a trial-and-error approach to determine the chi-square distribution degrees of freedom describing the weights of the influence of the dam surface temperature in the early stages; determining the optimal parameters of the LSTM network model using the GA algorithm based on the training sample set data; constructing a concrete dam deformation prediction model based on the optimal parameters obtained by iteratively solving the LSTM network model using the GA algorithm; and verifying the model's prediction accuracy. Based on the causal functional relationship between concrete dam deformation and its explanatory variables, this invention proposes a modeling method for concrete deformation prediction with good prediction accuracy by introducing the chi-square distribution and a GA-optimized LSTM network. This invention can effectively reduce the uncertainty in deformation prediction caused by upstream and downstream dam surface temperatures, quantitatively consider the influence of the lag effect of dam body temperature deformation, and fully explore the complex nonlinear functional relationship between concrete dam deformation and its explanatory variables, thus achieving good prediction accuracy.

Description

Technical Field

[0001] This invention relates to the field of dam operation safety monitoring and safety management technology, specifically, a method for constructing a concrete dam deformation monitoring model based on a genetically optimized long short-term memory neural network algorithm. Background Technology

[0002] Deformation, as one of the most important monitoring parameters for the service performance of concrete dams, directly reflects the comprehensive evolution of the structural performance of the dam body-foundation-reservoir system under multiple environmental loads. Monitoring models based on historical deformation data are the foundation for dam health status diagnosis, future behavior prediction, and the establishment of deformation alarm thresholds. Therefore, a safety monitoring model driven by measured deformation is an important scientific means for analyzing the operational performance of concrete dams.

[0003] Based on the causal relationship between dam deformation and its explanatory variables, statistical models established using mathematical analysis methods are currently the most commonly used deformation monitoring models. Classical modeling methods, such as multiple linear regression and stepwise regression, are convenient to apply, but they struggle to handle problems such as nonlinear function approximation and collinearity of model factors. With the development of artificial intelligence technology, machine learning methods, which have stronger nonlinear mapping capabilities, have gradually replaced linear regression methods as the mainstream modeling approach for deformation monitoring models, greatly improving the modeling accuracy of deformation monitoring models, and the resulting models have strong generalization capabilities. Summary of the Invention

[0004] The purpose of this invention is to overcome the deficiencies in the prior art and provide a method for constructing a statistical model for the deformation observation of concrete dams, specifically achieved through the following technical solution:

[0005] A method for constructing a statistical model for the observation of concrete dam deformation includes the following steps:

[0006] S1. Preprocessing of concrete dam deformation monitoring data;

[0007] S2. Use a trial-and-error method to determine the chi-square distribution degrees of freedom that describe the weights of the influence of the dam surface temperature in the early stage;

[0008] S3. Based on the training sample set data, use GA to determine the optimal parameters of the LSTM network model;

[0009] S4. Construct a concrete dam deformation prediction model based on an optimized LSTM network using the optimal parameters of the LSTM network model obtained from the GA iterative solution, and realize the prediction of concrete dam deformation.

[0010] S5. Verify the accuracy of the model's predictions.

[0011] Step S1, the preprocessing of concrete dam deformation monitoring data, is mainly based on the fundamental theory of dam deformation. It involves creating the dam deformation δ and its explanatory variable set based on deterministic function derivation and physical inference, and then normalizing the data before dividing it into a training set and a prediction set. When the modeling object is a gravity dam, the deformation explanatory variables include H and H0. 2 H 3 , The total number of θ and lnθ is equal to the number of selected water temperature measurement points plus six; when the modeling object is an arch dam, the deformation explanation variables include H and H1. 2 H 3 H 4 , θ and lnθ, the total number is equal to the number of available water temperature measuring points plus seven; where H is the upstream water depth on the monitoring day, which is equal to the upstream water level on the monitoring day minus the foundation elevation of the corresponding dam section; The temperature value is the temperature monitoring value i days prior to the monitoring day. Let be the water temperature monitoring value of the selected j-th water temperature monitoring point on the i-th day before the monitoring date; θ is the cumulative number of days from the start of the dam measurement to the monitoring date; f(x) is the chi-square probability density function, and its expression is:

[0012]

[0013] In the formula, x is the independent variable; n is the degree of freedom of the chi-square distribution; and Γ(n / 2) is the gamma function.

[0014] The formula for normalizing explanatory variables is:

[0015] x′=(xx min ) / (x max -x min (16)

[0016] In the formula x max x min These are the maximum and minimum values ​​of a monitoring sequence for a certain explanatory variable used in modeling.

[0017] The specific process for determining the chi-square distribution weights in step S2 is as follows: The classic multiple linear regression algorithm is used to determine the fitting parameters of the explanatory variable factors, a dam deformation prediction model is constructed, and then the coefficient of determination R is selected. 2 The model's performance is measured by the mean absolute error (MAE) and root mean square error (RMSE) of the model fitting and prediction results. The optimal model corresponds to the chi-square distribution degrees of freedom, which is the desired optimal value. The calculation formula is as follows:

[0018]

[0019]

[0020]

[0021] In the formula δ d The measured value of the deformation; δ d ′ represents the deformation fitting value; is the average value of the measured deformation; n is the number of samples.

[0022] After determining the optimal degrees of freedom for the chi-square distribution, the optimal parameters of the LSTM network model are determined using the training sample set data. The parameter determination method is as follows:

[0023] During the forward computation of the LSTM network, the explanatory variable matrix X of the dam deformation at time t... t =[x t1 x t2 , ..., x tm After processing by the input layer, the data is transformed into an input matrix with a dimension matching the number of units in the first LSTM hidden layer, and then distributed to each LSTM unit as input data. Through calculations via the forget gate, input gate, and output gate within each unit, the unit's output value at that moment is obtained, and then input into the next LSTM hidden layer for further calculation. The output value of the last LSTM hidden layer is then combined and calculated by a fully connected layer before being output through the output layer to obtain the deformed fitted value δ. t During the forward computation, the forget gate network inside the LSTM unit controls the selection and discarding of historical information. The input gate determines the weight when merging new and historical information, and the output gate determines the unit's response to external stimuli. The calculation functions for each gate are as follows:

[0024] F t =g(W f [x t h t-1 ]+b F (20)

[0025] I t =g(W1[x t h t-1 ]+b I ) (twenty one)

[0026]

[0027]

[0028] O t =g(W O [h t-1 x t ]+b O ) (twenty four)

[0029] h t=tanh(c t )×O t (25)

[0030] In the formula: F t I t O t Let be the vectors calculated by the forget gate, input gate, and output gate at time t, respectively; W and b are the corresponding weight and bias matrices, respectively; x t The current input variables of the LSTM unit; The current candidate cell state; c t-1 c t These represent the cell states at the previous and current time points, respectively; h t-1 The previous hidden state; h t This represents the hidden state at the current moment, and also the output of the LSTM unit at the current moment; g(x) = 1 / (1+e^x). -x ); tanh = (e x -e -x ) / (e x +e -x ).

[0031] The LSTM network model is trained using the backpropagation BPTT algorithm over time: the model provides a fitted value δ based on the deformation. t Then, the weight matrix of each unit within the network is updated based on the loss function calculation results and a gradient-based stochastic optimization method, thus completing one iteration of model training. When updating the weights, the weight optimization gradient can be dynamically calculated using the Adaptive Moments Estimation (ADAM) algorithm or the Stochastic Gradient Descent (SGD) algorithm; a Dropout layer is added after the hidden layer to control the number of iterations of network training.

[0032] Using dam deformation and its explanatory variables as the output and input variables of an LSTM network, respectively, the specific calculation steps for constructing a concrete dam deformation monitoring model based on a genetically optimized LSTM network are as follows:

[0033] Step 1: Data Preprocessing and GA Algorithm Parameter Settings. The matrix consisting of the dam deformation time series and its explanatory variables is normalized and scaled to the (0, 1) interval. Simultaneously, the population size N and the maximum number of iterations I for the GA algorithm are set. max Crossover rate and mutation rate, as well as the upper and lower bounds of the network parameters to be optimized;

[0034] Step 2: Initial Population Generation for the GA Algorithm. Multiple sets of LSTM network parameter combinations are randomly generated within the specified solution space and encoded into chromosomes using floating-point encoding. These chromosomes are then assigned to individuals within the initial population. To ensure the diversity of the initial population for the GA algorithm, the chromosome generation formula for each individual is as follows:

[0035] x ij =x j，min +(x j，max -x j，min )×R (26)

[0036] In the formula: x ij Let be the floating-point number at the j-th position of the chromosome of the i-th individual, where the first floating-point number of the chromosome represents the layer number, and the rest represent the number of nodes in the layer; min x j , max x j , which are the upper and lower bounds of the j-th bit floating-point number, respectively; R is a random number in the interval [0, 1];

[0037] Step 3: Calculate the fitness of individuals within the population. The reciprocal of the sum of the mean absolute errors (MAE1) and MAE2 of the LSTM network model in the training and prediction sets is used as the fitness value for the corresponding individual x. i Fitness Fit(x) i The calculation formula is:

[0038] Fit(x i ) = 1 / (MAE 1i +MAE 2i (27)

[0039] In the formula MAE 1i MAE 2i These represent the mean absolute errors of the LSTM network model on the fitted and predicted sets, respectively.

[0040] Step 4: Perform competition processing, i.e., select individuals. Use the roulette wheel selection method to repeatedly select N individuals for the generation of the offspring population. The probability of an individual being selected is P(x). i The calculation formula is:

[0041]

[0042] Step 5: Perform crossover and mutation on the N individuals obtained to generate a progeny population. When performing the crossover operation, the randomly selected floating-point number on the chromosome is exchanged with the corresponding floating-point number on the chromosome of other individuals in the population. When performing the mutation operation, the selected floating-point number on the chromosome is reset according to equation (26), but only the floating-point number representing the number of network nodes in the individual chromosome is subjected to crossover and mutation.

[0043] Step 6: Determine if the iteration has terminated. If the current iteration count is less than the maximum set iteration count, repeat Step 3 to Step 6; otherwise, terminate the iteration and output the network parameter combination represented by the best individual in the current population.

[0044] Step 7: The optimal combination of network parameters obtained by iterative search using the GA algorithm is used to determine the structure of the LSTM network model, and a concrete dam deformation monitoring model based on the GA-LSTM algorithm can be constructed accordingly.

[0045] Step 8: Input the explanatory variables of the predicted concentrated deformation into the prediction model to achieve the prediction of the deformation of the concrete dam.

[0046] After successfully establishing a dam deformation prediction model based on GA-LSTM, R... 2 The modeling and prediction accuracy of the model are tested using statistical indicators such as MAE and RMSE.

[0047] The beneficial effects of the method of the present invention are as follows:

[0048] By using an improved temperature component factor, the established model effectively reduces the uncertainty in deformation prediction caused by upstream and downstream dam surface temperatures, quantitatively considers the hysteresis effect of temperature deformation, and to some extent separates the temperature deformation component mixed with the water pressure deformation component. Compared with linear regression methods, the selected GA-LSTM algorithm shows significant improvements in approximating nonlinear functions and solving the multicollinearity problem among explanatory variables, thus achieving higher prediction accuracy. Thanks to the strong memory capacity of the LSTM network, the established model can consider the long-term correlation of dam deformation. Furthermore, considering the significant impact of network parameters on model accuracy, the genetic optimization algorithm used in this invention effectively avoids the adverse consequences of blindly selecting network parameters, improves the robustness of the algorithm, and provides a new method for high-precision prediction of dam deformation. Attached Figure Description

[0049] Figure 1 This invention describes the modeling process for a concrete dam deformation prediction model based on a genetically optimized long short-term memory neural network algorithm.

[0050] Figure 2 This refers to the layout of vertical monitoring instruments and water temperature measuring points for section 21 of a concrete arch dam.

[0051] Figure 3 These are the measured values ​​of horizontal displacement, upstream water level, air temperature, and water temperature of section 21 of a concrete arch dam.

[0052] Figure 4 It is the process of finding the optimal degrees of freedom for the chi-square distribution through trial and error.

[0053] Figure 5 It is the iterative optimization process of the GA algorithm to optimize the solution of the number of layers and nodes in an LSTM network;

[0054] Figure 6This is the fitting and prediction results of the GA-optimized LSTM network concrete dam deformation prediction model, along with the corresponding residuals. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and examples.

[0056] Reference Figure 1 The modeling process of the concrete dam deformation monitoring model based on the genetically optimized long short-term memory neural network algorithm of the present invention includes:

[0057] S1, Preprocessing of concrete dam deformation monitoring data:

[0058] The preprocessing of concrete dam deformation monitoring data is mainly based on the fundamental theory of dam deformation. A set of explanatory variables for dam deformation δ is created based on deterministic function derivation and physical inference. After normalization, the data is divided into training and prediction sets. Deformation δ is taken as the absolute value obtained from observation. When the modeling object is a gravity dam, the explanatory variables for deformation include H and H0. 2 H 3 , The total number of θ and lnθ is equal to the number of selected water temperature measurement points plus six; when the modeling object is an arch dam, the deformation explanation variables include H and H1. 2 H 3 H 4 , θ and 1nθ, the total number is equal to the number of available water temperature measuring points plus seven; where H is the upstream water depth on the monitoring day, which is equal to the upstream water level on the monitoring day minus the foundation elevation of the corresponding dam section; The temperature value is the temperature monitoring value i days prior to the monitoring day. Let be the water temperature monitoring value of the selected j-th water temperature monitoring point on the i-th day before the monitoring date; θ is the cumulative number of days from the start of the dam measurement to the monitoring date; f(x) is the chi-square probability density function, and its expression is:

[0059]

[0060] In the formula, x is the independent variable; n is the degree of freedom of the chi-square distribution; and Γ(n / 2) is the gamma function.

[0061] The formula for normalizing explanatory variables is:

[0062] x′=(xx min ) / (x max -x min (30)

[0063] In the formula x max x min These are the maximum and minimum values ​​of a monitoring sequence for a certain explanatory variable used in modeling;

[0064] S2. The chi-square distribution degrees of freedom describing the weights of the influence of the dam surface temperature in the early stages are determined using a trial-and-error method, as follows:

[0065] The classic multiple linear regression algorithm was used to determine the parameters to be fitted for the above explanatory variable factors, and a dam deformation prediction model was constructed; the coefficient of determination R was selected. 2 The mean absolute error (MAE) and root mean square error (RMSE) of the model fitting and prediction results are used to measure the quality of the model. The optimal model corresponds to the chi-square distribution degrees of freedom, which is the desired optimal value. The calculation formula is as follows:

[0066]

[0067]

[0068]

[0069] In the formula δ d The measured value of the deformation; δ d ′ represents the deformation fitting value; is the average value of the measured deformation; n is the number of samples;

[0070] S3. Based on the training sample set data, a genetic algorithm is used to determine the optimal parameters of the Long Short-Term Memory (LSTM) network model. The specific method is as follows:

[0071] During the forward computation of the LSTM network, the explanatory variable matrix X of the dam deformation at time t... t =[x t1 x t2 , ..., x tm After processing by the input layer, the data is transformed into an input matrix with a dimension matching the number of units in the first LSTM hidden layer, and then distributed to each LSTM unit as input data. Through calculations via the forget gate, input gate, and output gate within each unit, the unit's output value at that moment is obtained, and then input into the next LSTM hidden layer for further calculation. The output value of the last LSTM hidden layer is then combined and calculated by a fully connected layer before being output through the output layer to obtain the deformed fitted value δ. t During the forward computation, the forget gate network inside the LSTM unit controls the selection and discarding of historical information. The input gate determines the weight when merging new and historical information, and the output gate determines the unit's response to external stimuli. The calculation functions for each gate are as follows:

[0072] F t =g(W f [x t h t-1 ]+b F (34)

[0073] I t =g(WI [x t h t-1 ]+b I (35)

[0074]

[0075]

[0076] O t =g(W O [h t-1 x t ]+b O (38)

[0077] h t =tanh(c t )×O t (39)

[0078] In the formula: F t I t O t Let be the vectors calculated by the forget gate, input gate, and output gate at time t, respectively; W and b are the corresponding weight and bias matrices, respectively; x t The current input variables of the LSTM unit; The current candidate cell state; c t-1 c t These represent the cell states at the previous and current time points, respectively; h t-1 The previous hidden state; h t This represents the hidden state at the current moment, and also the output of the LSTM unit at the current moment; g(x) = 1 / (1+e^x). -x ); tanh = (e x -e -x ) / (e x +e -x ).

[0079] The LSTM network model is trained using the backpropagation BPTT algorithm over time: the model provides a fitted value δ based on the deformation. t Then, the weight matrix of each unit in the network is updated based on the loss function calculation results and the gradient-based stochastic optimization method, thereby completing one iteration of model training. When updating the weights, the weight optimization gradient is dynamically calculated using the Adaptive Moment Estimation (ADAM) algorithm or the Stochastic Gradient Descent (SGD) algorithm, and a Dropout layer is added after the hidden layer to control the number of iterations of the network training.

[0080] Using dam deformation and its explanatory variables as the output and input variables of an LSTM network, respectively, the specific calculation steps for constructing a concrete dam deformation monitoring model based on a genetically optimized LSTM network are as follows:

[0081] Step 1: Data Preprocessing and GA Algorithm Parameter Settings. The matrix consisting of the dam deformation time series and its explanatory variables is normalized and scaled to the (0, 1) interval. Simultaneously, the population size N and the maximum number of iterations I for the GA algorithm are set. max Crossover rate and mutation rate, as well as the upper and lower bounds of the network parameters to be optimized;

[0082] Step 2: Initial Population Generation for the GA Algorithm. Multiple sets of LSTM network parameter combinations are randomly generated within the specified solution space and encoded into chromosomes using floating-point encoding. These chromosomes are then assigned to individuals within the initial population. To ensure the diversity of the initial population for the GA algorithm, the chromosome generation formula for each individual is as follows:

[0083] x ij =x j，min +(x j，max -x j，min )×R (40)

[0084] In the formula: x ij Let be the floating-point number at the j-th position of the chromosome of the i-th individual, where the first floating-point number of the chromosome represents the layer number, and the rest represent the number of nodes in the layer; min x j , max x j , which are the upper and lower bounds of the j-th bit floating-point number, respectively; R is a random number in the interval [0, 1];

[0085] Step 3: Calculate the fitness of individuals within the population. The method of this invention uses the reciprocal of the sum of the mean absolute errors (MAE1 and MAE2) of the LSTM network model in the training and prediction sets as the corresponding individual x. i Fitness Fit(x) i The calculation formula is:

[0086] Fit(x i ) = 1 / (MAE 1i +MAE 2i (41)

[0087] In the formula MAE 1i MAE 2i These represent the mean absolute errors of the LSTM network model on the fitted and predicted sets, respectively.

[0088] Step 4: Perform competition processing, i.e., select individuals. Use the roulette wheel selection method to repeatedly select N individuals for the generation of the offspring population. The probability of an individual being selected is P(x). i The calculation formula is:

[0089]

[0090] Step 5: Perform crossover and mutation on the N individuals obtained to generate a progeny population. When performing the crossover operation, the randomly selected floating-point number on the chromosome is exchanged with the corresponding floating-point number on the chromosome of other individuals in the population. When performing the mutation operation, the selected floating-point number on the chromosome is reset according to equation (43), but only the floating-point number representing the number of network nodes in the individual chromosome is subjected to crossover and mutation.

[0091] Step 6: Determine if the iteration has terminated. If the current iteration count is less than the maximum set iteration count, repeat Step 3 to Step 6; otherwise, terminate the iteration and output the network parameter combination represented by the best individual in the current population.

[0092] Step 7: The optimal combination of network parameters obtained by iterative search using the GA algorithm is used to determine the structure of the LSTM network model, and a concrete dam deformation monitoring model based on the GA-LSTM algorithm is constructed accordingly.

[0093] S4, Substitute the explanatory variables from the prediction sample set into the prediction model to predict the deformation of the concrete dam;

[0094] S5. Verify the model's prediction accuracy. After establishing the dam deformation prediction model based on GA-LSTM, use R... 2 The modeling and prediction accuracy of the model are tested using statistical indicators such as MAE and RMSE.

[0095] The specific implementation process of this invention is as follows:

[0096] (1) Obtain measured deformation and environmental monitoring data of the dam for modeling, and preprocess the data. Taking the construction of a horizontal deformation prediction model of a concrete arch dam in Panzhihua City, Sichuan Province as an example, this dam project is huge in scale, with a crest length of 774.69 meters and a maximum height of 240 meters, consisting of 39 dam sections. To monitor the dam's operating status, various measuring instruments are arranged on the surface and inside the dam. For example... Figure 2 As shown, nine thermometers are installed on the surface of dam section 21 to monitor water temperature changes. Vertical monitoring instruments, such as the positive vertical instruments TCN08, TCN09, and TCN10, are also buried in this section to monitor the dam's horizontal deformation behavior. Observational data on dam deformation and environmental quantities from 2014 to 2018 are shown below. Figure 3 As shown.

[0097] We selected 912 sets of monitoring data from January 1, 2016 to June 30, 2018 as the training set, and 184 sets of monitoring data from July 1, 2018 to December 31, 2018 as the prediction set to test the model's predictive ability. Since the main structure of the project is a concrete arch dam with 9 available water temperature monitoring points, based on its deformation mechanism, the input variables of the prediction model are H and H0. 2 H 3 H 4 , θ and lnθ, the output variable is the dam deformation δ. After determining the input and output variables, the input variables are normalized according to equation (30).

[0098] (2) A trial-and-error method was used to obtain the optimal degrees of freedom for the chi-square distribution describing the weights of the influence of the previous temperature. Training data was used, and multiple linear regression was employed to determine the fitting parameters for the deformable explanatory variable factors under different degrees of freedom. Then, based on the R-squared value of the obtained model... 2 The optimal degrees of freedom are determined by the MAE and RMSE on the fitted and prediction sets. Statistical indicators of the model obtained during the trial-and-error process are as follows: Figure 4 As shown, R 2 The model remains relatively stable as the degrees of freedom n increases. However, when n is 6, the MAE and RMSE in both the training and prediction sets are lowest. Therefore, at the TCN09 test point, the optimal chi-square distribution degrees of freedom for the deformation prediction model is 6.

[0099] (3) The GA algorithm is used to determine the number of layers and nodes in each layer of the LSTM network. The input variable dimension of the LSTM is 16, and the output variable dimension is 1. To improve computational efficiency, the number of hidden layers in the LSTM network in this example is limited to the range of [1, 4], and the number of units is a multiple of 25 in the range of [25, 400]. To avoid overfitting, a dropout layer is added after the hidden layers, and the dropout rate is set to 0.2. In the genetic algorithm, the population size and the maximum number of iterations are both set to 60, the crossover rate is set to 0.75, and the mutation rate is set to 0.008. Taking TCN09 as an example, the iterative optimization process of GA is as follows: Figure 5 As shown.

[0100] like Figure 5 As shown, after 12 iterations, the fitness of GA converged to 1.373, corresponding to an average error of 0.3137 on the training set and an average error of 0.4108 on the prediction set for the concrete dam deformation monitoring model based on the GA-LSTM algorithm. At this point, the LSTM network has two hidden layers with 175 and 75 units respectively.

[0101] (4) Based on the optimal parameters of the LSTM network obtained through GA iterative optimization, a deformation prediction model for concrete dams based on a genetically optimized LSTM network (hereinafter referred to as the GA-LSTM model) can be established. To evaluate the effectiveness and generalization ability of the GA-LSTM model, data from TCN10 was also used to construct the prediction model. Furthermore, the Radial Basis Function Network (RBFN) algorithm and the Extreme Learning Machine (ELM) algorithm were also used to construct deformation prediction models for TCN09 and TCN10 (hereinafter referred to as the RBFN model and the ELM model, respectively). The fitted values, predicted values, and residuals of these models are as follows: Figure 6 As shown.

[0102] (5) To quantify the quality of the established model, the statistical index R is used. 2 The modeling accuracy was evaluated using MAE and RMSE, and the statistical results are shown in Table 1.

[0103] Table 1 Statistical Indicators of the Horizontal Deformation Prediction Model

[0104]

[0105] like Figure 6 As shown, the fitted values ​​of the constructed models are basically consistent with the measured deformation observations at the two measurement points, indicating that these models can well reflect the causal relationship between deformation and its explanatory variables. Compared with the MLR-based models, the models built using GA-LSTM networks, ELM, and RBFN algorithms have better prediction accuracy. Among them, the GA-LSTM model performs best in both fitting and prediction. Moreover, due to the significantly smaller residuals of the GA-LSTM model, the GA-LSTM network has a clear advantage in approximating nonlinear relationships and extracting deep features of dam deformation. The statistical indicators listed in Table 1 further demonstrate that the GA-LSTM models have the best prediction performance; their MAE and RMSE in the prediction set are significantly lower than those of the models built by the other three algorithms. Furthermore, according to Table 1, the statistical indicators of the GA-LSTM models in the training and prediction sets are close to each other. From a statistical perspective, this means that these models do not exhibit underfitting or overfitting. Therefore, the GA-LSTM network has good nonlinear mapping capabilities and the ability to learn implicit features of time series data, making it suitable for constructing concrete dam deformation prediction models.

[0106] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for constructing a statistical model for the observation of concrete dam deformation, characterized in that, Includes the following steps: S1, Preprocessing of concrete dam deformation monitoring data; S2, using a trial-and-error method to determine the chi-square distribution degrees of freedom that describe the weights of the influence of the dam surface temperature in the early stage; S3. Based on the training sample set data, the optimal parameters of the Long Short-Term Memory (LSTM) network model are determined using the Genetic Algorithm (GA). S4. Based on the optimal parameters of the LSTM network model obtained by iterative solution using the GA algorithm, a concrete dam deformation prediction model based on the optimized LSTM network is constructed, and the deformation of the concrete dam is predicted. S5, verify the model's prediction accuracy; The preprocessing of concrete dam deformation monitoring data in step S1 is mainly based on the basic theory of dam deformation, and the dam deformation is created according to deterministic function derivation and physical inference. The set of explanatory variables is divided into a training set and a prediction set after normalization. When the modeling object is a gravity dam, the deformation explanatory variables include , , , , , and The total number is equal to the number of selected water temperature measuring points plus six; When the modeling object is an arch dam, the deformation explanatory variables include , , , , , , and The total number equals the number of available water temperature measuring points plus seven; in, To monitor the upstream water depth on a given day, it is equal to the upstream water level on the monitoring day minus the elevation of the corresponding dam section foundation surface; For the monitoring date Early day temperature monitoring values; The selected first Each water temperature monitoring point was monitored before the date of the monitoring. Daily water temperature monitoring values; This represents the cumulative number of days from the start of the dam survey to the monitoring date. Let be the probability density function of the chi-square distribution, and its expression is: ， In the formula As the independent variable; represents the degrees of freedom of the chi-square distribution; It is a gamma function; The formula for normalizing explanatory variables is: ， In the formula These are the maximum and minimum values ​​of a monitoring sequence for a certain explanatory variable used in modeling.

2. The method for constructing a statistical model for the deformation observation of a concrete dam according to claim 1, characterized in that, In step S2, the determination of the chi-square distribution degrees of freedom uses the classic multiple linear regression algorithm to determine the fitting parameters of the deformation explanatory variables and construct a dam deformation prediction model; the coefficient of determination is selected. The model's performance is measured by its mean absolute error (MAE) and root mean square error (RMSE) of the fitting and prediction results. The optimal model corresponds to the chi-square distribution degrees of freedom, which is the desired optimal value. The calculation formula is as follows: ， ， ， In the formula These are the measured values ​​of deformation. These are the deformation-fitted values; This represents the average value of the measured deformation. This represents the number of samples.

3. The method for constructing a statistical model for the deformation observation of a concrete dam according to claim 1, characterized in that, In step S3, the optimal parameters of the LSTM network model are determined using GA based on the training sample set data. The parameter determination method is as follows: During the forward computation of the LSTM network Explanation variable matrix of dam deformation at any time After processing by the input layer, it is transformed into an input matrix with a dimension matching the number of units inside the first LSTM hidden layer, and then assigned to each LSTM unit as input data; After calculations through the forget gate, input gate, and output gate within the cell, the cell output value at that moment is obtained and then input into the next LSTM hidden layer for further calculation. The output value of the last LSTM hidden layer is merged and calculated by the fully connected layer, and then output through the output layer to obtain the deformed fitted value. ; During the forward computation, the forget gate network inside the LSTM unit controls the selection and discarding of historical information. The input gate determines the weight when merging new and historical information, and the output gate determines the unit's response to the external environment. The calculation functions for each gate are as follows: ， ， ， ， ， ， In the formula: They are respectively The vectors calculated by the forget gate, input gate, and output gate at different times; These are the corresponding weight and bias matrices, respectively; The current input variables of the LSTM unit; This represents the current candidate cell state. These are the cell states at the previous and current times, respectively; The previous hidden state; This represents the hidden state at the current moment, and also the output of the LSTM unit at the current moment. ; .

4. The method for constructing a statistical model for the deformation observation of a concrete dam according to claim 3, characterized in that, In step S3, the LSTM network model is trained using the backpropagation BPTT algorithm over time, after the model provides a deformed fitted value. Then, based on the loss function calculation results and the gradient-based stochastic optimization method, the weight matrix of each unit in the network is updated, thereby completing one iteration of model training.

5. The method for constructing a statistical model for the deformation observation of a concrete dam according to claim 4, characterized in that, When updating weights, the gradient optimization algorithm can be dynamically calculated using the Adaptive Moment Estimation (ADAM) algorithm or the Stochastic Gradient Descent (SGD) algorithm; a Dropout layer is added after the hidden layer to control the number of iterations of the network training.

6. A method for constructing a statistical model for the deformation observation of a concrete dam according to any one of claims 3 to 5, characterized in that, Step S4 involves using the dam deformation and its explanatory variables as the output and input variables of the LSTM network, respectively, to construct a concrete dam deformation monitoring model based on a genetically optimized LSTM network. The specific calculation steps are as follows: Step 1: Data preprocessing and GA algorithm parameter settings; The time series data of dam deformation and the matrix composed of its explanatory variables are normalized and scaled to the (0,1) interval; the population size of the GA algorithm is also set. Maximum number of iterations Crossover rate and mutation rate, as well as the upper and lower bounds of the network parameters to be optimized; Step 2: Initial population generation using the GA algorithm; After randomly generating multiple sets of LSTM network parameter combinations within a specified solution space, these combinations are encoded into chromosomes using a floating-point encoding method and assigned to individuals in the initial population. To ensure the diversity of the initial population in the GA algorithm, the chromosome generation formula for individuals in the initial population is as follows: ， In the formula: For the first The first chromosome of an individual The first floating-point number of the chromosome represents the number of layers, and the rest represent the number of nodes in the layer; The first Upper and lower bounds of 2-bit floating-point numbers; A random number within the interval [0,1]; Step 3: Calculate the fitness of individuals within the population; The mean absolute error of the LSTM network model within the training and prediction sets. , The reciprocal of the sum is used as the corresponding individual. fitness The calculation formula is: ， In the formula These represent the mean absolute errors of the LSTM network model on the fitted and predicted sets, respectively. Step 4: Perform competition processing, i.e., extract individuals; Repeated selection using roulette wheel selection method Each individual is used to generate the offspring population; the probability of an individual being selected is... The calculation formula is: ， Step 5: Extract the obtained Each individual undergoes crossover and mutation processes to generate a progeny population; When performing crossover, a randomly selected floating-point number on a chromosome is exchanged with the corresponding floating-point number on the chromosome of another individual in the population. When performing a mutation operation, the selected floating-point number on the chromosome is determined according to the formula. The settings are reset, but only the floating-point numbers representing the number of network nodes in the individual chromosomes are crossovered and mutated. Step 6: Determine if the iteration has terminated; If the current iteration count is less than the set maximum iteration count, then repeat Step 3 to Step 6. Conversely, the iteration terminates and outputs the combination of network parameters represented by the best individual in the current population; Step 7: The optimal combination of network parameters obtained by iterative search using the GA algorithm is used to determine the structure of the LSTM network model, and a concrete dam deformation prediction model based on the GA-LSTM algorithm can be constructed accordingly. Step 8: Input the predicted concentrated deformation explanatory variables into the concrete dam deformation prediction model to achieve the prediction of concrete dam deformation.

7. The method for constructing a statistical model for the deformation observation of a concrete dam according to claim 1, characterized in that, Step S5 mainly adopts The prediction accuracy of the GA-LSTM-based concrete dam deformation prediction model was verified by evaluating the MAE and RMSE indicators.

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