A combined modeling method to improve the performance of arch dam displacement prediction model

Abstract

The invention discloses a combined modeling method for improving the performance of an arch dam displacement prediction model in the field of arch dam displacement monitoring technology. The method comprises the following steps: collecting arch dam displacement and environmental quantity monitoring data, taking the displacement causal component in the monitoring data as input and the measured displacement of the arch dam as output, establishing an MLR sub-model for arch dam displacement prediction, which is defined as a first-type sub-model, and adopting an improved parameter optimization method for integrating the time-varying law consistency degree of displacement of multiple measuring points of the arch dam as much as possible, respectively establishing NN, ELM, SVM and RVM machine learning sub-models for arch dam displacement prediction, which are defined as a second-type sub-model; according to the evaluation index of each sub-model and the improved parameter optimization method, establishing five-type, four-type, three-type and two-type combined models, comparing the displacement prediction accuracy of each combined model and the sub-model with the smallest prediction MSE increase ratio, and taking the optimal one as the final combined prediction model, which can effectively reduce the overfitting degree of the machine learning model and improve the prediction accuracy of the arch dam displacement prediction model.

Description

Technical Field

[0001] The invention belongs to the technical field of arch dam displacement monitoring, and in particular relates to a combined modeling method for improving the performance of an arch dam displacement prediction model. Background Art

[0002] In terms of modeling methods for dam safety monitoring models, machine learning provides a more efficient solution for processing massive monitoring data. Neural networks (NN), extreme learning machines (ELM), support vector machines (SVM) and relevance vector machines (RVM) have been widely used. However, there are certain differences in the performance of each method in different practical engineering problems. A single modeling method cannot take into account the comprehensiveness of the model performance. The scientific and reasonable combination of different modeling methods can maximize the advantages of various modeling methods. Summary of the invention

[0003] In order to solve the deficiencies in the prior art, the present invention provides a combined modeling method for improving the performance of an arch dam displacement prediction model, reduces the overfitting degree of the machine learning model, and improves the prediction accuracy of the arch dam displacement prediction model.

[0004] To achieve the above-mentioned purpose, the technical scheme adopted by the present invention is: a combined modeling method for improving the performance of an arch dam displacement prediction model, comprising: collecting monitoring data of arch dam displacement and environmental quantities, taking the displacement causal component in the monitoring data as input and the measured displacement of the arch dam as output, establishing an MLR sub-model for arch dam displacement prediction, which is defined as a first-class sub-model, and using an improved parameter optimization method to respectively establish an NN machine learning sub-model, an ELM machine learning sub-model, an SVM machine learning sub-model and an RVM machine learning sub-model for arch dam displacement prediction, which are defined as second-class sub-models; statistically analyzing the evaluation indexes of the sub-models established for arch dam displacement prediction, and sorting the predicted MSE increase ratio in the evaluation indexes according to the size of their values; selecting the second-class sub-models. The machine learning method used for the model with the smallest predicted MSE among the types was used to establish type-5, type-4, type-3 and type-2 combined models, where the input of the type-5 combined model was the output of the five sub-models, and the output of the type-5 combined model was the measured displacement of the arch dam; the model with the largest predicted MSE increase ratio among the five sub-models was eliminated, and the remaining four sub-models were used to establish a type-4 combined model, where the input of the type-4 combined model was the output of the remaining four sub-models, and the output of the type-4 combined model was the measured displacement of the arch dam; similarly, type-3 and type-2 combined models were established respectively; the displacement prediction accuracies of the type-5 combined model, type-4 combined model, type-3 combined model, type-2 combined model and the sub-model with the smallest predicted MSE increase ratio were compared, and the optimal one was taken as the final combined prediction model for the prediction of arch dam displacement.

[0005] Furthermore, the improved parameter optimization method is to adjust the original fitting MSE minimum target in the machine learning model parameter optimization to a fitting MSE as small as possible and a consistency degree of the time-varying law of the displacement of multiple measuring points of the arch dam as large as possible, and its purpose is to avoid relying solely on the constraints from a mathematical perspective and increase the constraints from an engineering structure perspective to reduce the overfitting degree of the machine learning model; including:

[0006] Step A1: Extract the time-varying regularity information of the displacement time series by sliding window method; for the displacement time series δ of a given measuring point i it , set the window length and sliding step size to w and s respectively, from δ i1 First, extract the time-varying trend of each subsequence in the sliding window from left to right, as shown below:

[0007] Δ i,t =δ i,t+w-1 -δ i,t ,1≤t≤T-w+1 (1)

[0008] Among them, i is the serial number of the measuring point, t is the monitoring time, and T is the total number of monitoring data samples of the displacement measuring point under a fixed sampling frequency;

[0009] Then, define the time-varying regularity information characterization function as follows:

[0010]

[0011] Original displacement time series δ it The time-varying regularity information of can be obtained by the vector S containing -1, 0, 1 i To describe, for two displacement time series of the same length δ it and δ jt , the consistency degree of the time-varying laws between the two is CDT ij It can be expressed as:

[0012]

[0013] in, For S i The transposed vector of , i and j are the measurement point numbers.

[0014] Step A2: Calculate the overall CDT of the displacement measurement point to be modeled and all other displacement measurement points in the same zone of the arch dam by weighted superposition method. i According to the principle that the higher the consistency of the time-varying law between the two measuring points, the greater the corresponding weight, the fusion weight ω ij It can be defined as:

[0015]

[0016] Where N is the total number of similar displacement measurement points in the same partition;

[0017] Furthermore, the overall consistency of the displacement time-varying law of measuring point i and all measuring points in the partition is defined as:

[0018]

[0019] Step A3: Construct the objective function in the improved parameter optimization method; introduce a new objective CDT. To ensure that the fitting MSE is as small as possible and CDT is as large as possible, the CDT should be taken inversely, that is, RC = 1 / CDT. Since the dimensions of the two are inconsistent, they need to be normalized separately:

[0020]

[0021]

[0022] Among them, MSE max , MSE min ,RC max and RC min They are the maximum and minimum values ​​of the fitted MSE and RC within the parameter optimization range, respectively;

[0023] In summary, the objective function in the improved parameter optimization method is defined as:

[0024]

[0025] Among them, θ is the weight of the CDT of the consistency target of the time-varying law of displacement at multiple measuring points;

[0026] Step A4: Use the improved parameter optimization method to optimize the key parameters of the second type of sub-model; among them, the key parameters of the NN machine learning sub-model and the ELM machine learning sub-model are the number of neurons, and the key parameters of the SVM machine learning sub-model and the RVM machine learning sub-model are the penalty factor and the kernel function parameter.

[0027] Furthermore, the same partition of the arch dam in step A2 means that according to the displacement time series of all similar displacement monitoring points of the arch dam body, the measuring points are divided into different categories according to the conventional clustering partitioning method based on incremental distance, and then all the measuring points in the same cluster are used to calculate the overall consistency of the time-varying law.

[0028] Furthermore, in step A2 and step A3, when extracting the time-varying law information of the displacement time series of the proposed modeling measuring point according to step A1, the displacement time series used in step A2 are all measured displacement time series; in step A3, the modeling measuring point uses the fitted displacement time series output by the machine learning model, and the other measuring points use the measured displacement time series.

[0029] Furthermore, the evaluation indicators include mean square error MSE, maximum absolute value of error MAE, complex correlation coefficient R 2 , predicted MSE increase ratio; the smaller the MSE, the smaller the overall error between the displacement monitoring value and the model prediction value; the smaller the MAE value, the more stable the prediction result; R 2 The closer the value is to 1, the higher the correlation between the two. The predicted MSE increase ratio represents the degree of overfitting of the model. The larger the value, the more serious the overfitting.

[0030] Furthermore, when establishing the five-type combination model, the four-type combination model, the three-type combination model, and the two-type combination model, the improved parameter optimization method is used to optimize the key parameters in the machine learning combination model.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) The present invention adjusts the parameter optimization target of the machine learning model from minimizing the fitting MSE to minimizing the fitting MSE as much as possible and maximizing the consistency of the time-varying law of the displacement of multiple measuring points of the arch dam, which can effectively reduce the overfitting degree of the machine learning model and improve the prediction accuracy of the arch dam displacement prediction model;

[0033] (2) The present invention combines the traditional MLR model with a variety of machine learning models to construct a combined model, which can give full play to the advantages of each modeling method and significantly improve the prediction accuracy of arch dam displacement. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a combined modeling method for improving the performance of an arch dam displacement prediction model provided by an embodiment of the present invention;

[0035] Figure 2 It is the layout diagram of the arch dam vertical monitoring system and the incremental distance partition diagram of the measured radial displacement field;

[0036] Figure 3 Evolution of the fitted MSE and CDT obtained by the improved parameter optimization method for the measuring point PL11-1: (a) NN, (b) ELM, (c) SVM, (d) RVM;

[0037] Figure 4 The displacement time series obtained by five submodels: (a) NN, (b) ELM, (c) SVM, and (d) RVM;

[0038] Figure 5 The prediction performance evaluation indicators of the sub-model are: (a) MSE, (b) R 2 , (c) MAE, (d) predicted MSE increase ratio;

[0039] Figure 6 This is the evolution law of the prediction MSE of the combined model in the process of gradually eliminating sub-models. DETAILED DESCRIPTION

[0040] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0041] A combined modeling method for improving the performance of an arch dam displacement prediction model comprises collecting monitoring data of arch dam displacement and environmental quantities, taking the displacement causal component in the monitoring data as input and the measured displacement of the arch dam as output, establishing an MLR sub-model for arch dam displacement prediction, which is defined as a first-type sub-model, and using an improved parameter optimization method to respectively establish an NN machine learning sub-model, an ELM machine learning sub-model, an SVM machine learning sub-model and an RVM machine learning sub-model for arch dam displacement prediction, which are defined as second-type sub-models; statistically analyzing the evaluation indexes of the sub-models for arch dam displacement prediction, and sorting the predicted MSE increase ratios in the evaluation indexes according to their values; selecting the sub-model with the smallest predicted MSE in the second-type sub-model as the first-type sub-model. The machine learning method is used to establish five-type, four-type, three-type and two-type combination models respectively, among which the input of the five-type combination model is the output of the five sub-models, and the output of the five-type combination model is the measured displacement of the arch dam; the one with the largest predicted MSE increase ratio among the five sub-models is eliminated, and the four-type combination model is established using the remaining four sub-models, among which the input of the four-type combination model is the output of the remaining four sub-models, and the output of the four-type combination model is the measured displacement of the arch dam; similarly, three-type and two-type combination models are established respectively; the displacement prediction accuracies of the five-type combination model, the four-type combination model, the three-type combination model, the two-type combination model and the sub-model with the smallest predicted MSE increase ratio are compared, and the optimal one is used as the final combined prediction model for the prediction of arch dam displacement.

[0042] Step A: Based on the conventional causal model for explaining the deformation behavior of arch dams, the modeling factors in the displacement components such as water pressure, temperature and time are taken as the input of the sub-model, and the measured displacement of the arch dam is taken as the output. After the monitoring data is preprocessed according to the conventional method, the traditional MLR sub-model is established, and the improved parameter optimization method is used to establish four machine learning sub-models such as NN, ELM, SVM and RVM.

[0043] The improved parameter optimization method is to adjust the original fitting MSE minimum target in the machine learning model parameter optimization to make the fitting MSE as small as possible and the consistency degree of time-varying law (CDT) of the displacement of multiple measuring points of the arch dam as large as possible. Its purpose is to avoid relying solely on the constraints from the mathematical perspective and increase the constraints from the engineering structure perspective to reduce the overfitting degree of the machine learning model; including:

[0044] Step A1: Extract the time-varying regularity information of the displacement time series by sliding window method; for the displacement time series δ of a given measuring point i it , set the window length and sliding step size to w and s respectively. When the sampling frequency is once a day, it is more reasonable to take w as 7 days and s as 1 day. i1 First, extract the time-varying trend of each subsequence in the sliding window from left to right, as shown below:

[0045] Δ i,t =δ i,t+w-1 -δ i,t ,1≤t≤T-w+1 (1)

[0046] Among them, i is the serial number of the measuring point, t is the monitoring time, and T is the total number of monitoring data samples of the displacement measuring point under a fixed sampling frequency;

[0047] Then, define the time-varying regularity information characterization function as follows:

[0048]

[0049] Original displacement time series δ it The time-varying regularity information of can be obtained by the vector S containing -1, 0, 1 i To describe, for two displacement time series of the same length δ it and δ jt , the consistency degree of the time-varying laws between the two is CDT ij It can be expressed as:

[0050]

[0051] in, For S i The transposed vector of .

[0052] Step A2: Calculate the overall CDT of the displacement measurement point to be modeled and all other displacement measurement points in the same zone of the arch dam by weighted superposition method. i The same partition of the arch dam refers to dividing the measuring points into different categories according to the displacement time series of all similar displacement monitoring points of the arch dam body, according to the conventional cluster partitioning method based on incremental distance, and then using all the measuring points in the same cluster to calculate the overall consistency of the time-varying law. According to the principle that the higher the consistency of the time-varying law between two measuring points, the greater the corresponding weight, the fusion weight ω ij It can be defined as:

[0053]

[0054] Where N is the total number of similar displacement measurement points in the same partition;

[0055] Furthermore, the overall consistency of the displacement time-varying law of measuring point i and all measuring points in the partition is defined as:

[0056]

[0057] Step A3: Construct the objective function in the improved parameter optimization method; in the traditional optimization method of machine learning model parameters, the objective function is only to minimize the MSE of model fitting, where MSE is defined as follows:

[0058]

[0059] Among them, δ t and are the measured displacement value and fitted value of the measuring point at time t respectively;

[0060] In the improved parameter optimization method, a new target CDT is introduced on the basis of the original target. In order to ensure that the fitting MSE is as small as possible and CDT is as large as possible, the CDT is reciprocally processed, that is, RC = 1 / CDT. Since the two dimensions are inconsistent, they need to be normalized separately:

[0061]

[0062]

[0063] Among them, MSE max , MSE min ,RC max and RC min They are the maximum and minimum values ​​of the fitted MSE and RC within the parameter optimization range, respectively;

[0064] In summary, the objective function in the improved parameter optimization method is defined as:

[0065]

[0066] Among them, θ is the weight of the CDT of the consistency target of the time-varying law of displacement at multiple measuring points.

[0067] When extracting the time-varying regularity information of the displacement time series of the proposed modeling measuring points according to step A1, the displacement time series used in step A2 are all measured displacement time series; in step A3, the modeling measuring points use the fitted displacement time series output by the machine learning model, and the other measuring points use the measured displacement time series.

[0068] Step A4: Use the improved parameter optimization method to optimize the key parameters of the second type of sub-model; the key parameters of the NN machine learning sub-model and the ELM machine learning sub-model are the number of neurons c, and the key parameters of the SVM machine learning sub-model and the RVM machine learning sub-model are the penalty factor and the kernel function parameter. When the improved parameter optimization method is used to optimize the parameters of different machine learning models, the core idea and steps are exactly the same. Taking NN and ELM as examples, the specific implementation process is as follows:

[0069] (a) The CDT weight θ ranges from [0, 1] with a step size of 0.01. For each given θ m , a corresponding objective function can be determined And use it to optimize the number of hidden layer neurons c;

[0070] (b) The initial search range of parameter c is set to [1,50] and is an integer. The parameter for the nth optimization is c n ;

[0071] (c) For each determined θ m and parameter c n , the corresponding objective function value can be obtained

[0072] (d) At a given θ m Next, compare all The size of the minimum objective function value And calculate the corresponding and

[0073] (e) Repeat steps (a) to (d) to obtain all θ m Corresponding and And normalized them respectively.

[0074] (f) Determine the optimal model parameters. Generally speaking, the range of the number of neurons in the NN and ELM models is small, and the number of neurons that can be reduced in the process of simplifying the model structure is also very limited. Therefore, under the premise of ensuring that the model prediction performance is not reduced, in order to simplify the structure of the NN and ELM models as much as possible, the model with the least number of neurons can be selected, and the corresponding weights θ and c are the optimal parameters. For SVM and RVM, the parameter value range is large, and the sensitivity to the weight θ is large. Therefore, according to the principle of minimizing the fitting MSE and maximizing the consistency of the time-varying law of the displacement of multiple measuring points of the arch dam, when formulating the optimal weights and parameters, according to the principle that the weight θ is roughly small, the model corresponding to the first largest gap between the two target values ​​CDT′ and MSE′ after normalization is selected as the optimal model parameter.

[0075] Step B: Statistically establish the evaluation indicators of each sub-model for arch dam displacement prediction, including: prediction MSE, MAE, R 2 And the predicted MSE increase ratio. The predicted MSE increase ratio in the evaluation index is sorted according to its value. The predicted MSE increase ratio is used as an evaluation index for screening sub-models. The larger its value, the higher the degree of overfitting of the sub-model, and it is preferred to be eliminated in the combined modeling process.

[0076] Step C: Select the machine learning method used by the model with the smallest predicted MSE in the second category to establish five-type, four-type, three-type and two-type combination models, where the input of the five-type combination model is the output of the five sub-models, and the output of the five-type combination model is the measured displacement of the arch dam; remove the model with the largest predicted MSE increase ratio among the five sub-models, and use the remaining four sub-models to establish a four-type combination model, where the input of the four-type combination model is the output of the remaining four sub-models, and the output of the four-type combination model is the measured displacement of the arch dam; similarly, establish three-type and two-type combination models respectively. When establishing the five-type combination model, the four-type combination model, the three-type combination model and the two-type combination model, the improved parameter optimization method is used to optimize the key parameters in the machine learning combination model.

[0077] Step D: Compare the displacement prediction accuracy of the five-type combination model, the four-type combination model, the three-type combination model, the two-type combination model and the sub-model with the smallest predicted MSE increase ratio, and take the best one as the final combined prediction model for the prediction of arch dam displacement.

[0078] In this embodiment, the model performance evaluation indicators include mean square error MSE, maximum absolute value of error MAE, and multiple correlation coefficient R 2 , predicted MSE increase ratio; the smaller the MSE, the smaller the overall error between the displacement monitoring value and the model prediction value; the smaller the MAE value, the more stable the prediction result; R 2 The closer the value is to 1, the higher the correlation between the two. The predicted MSE increase ratio represents the degree of overfitting of the model. The larger the value, the more serious the overfitting. The calculation expression of the above indicators is as follows:

[0079]

[0080]

[0081]

[0082] in, and They are δ t and The average value of .

[0083] like Figure 1 to Figure 6As shown, this embodiment is further explained by taking a concrete dam as an example. The maximum dam height of a concrete hyperbolic arch dam is 305m, which is the highest concrete dam built in the world. The project started in 2005 and was fully poured to the dam top elevation of 1885m on December 23, 2013. After the first water storage to the normal water storage level of 1880m on August 24, 2014, the water level of the upstream reservoir has an annual cycle between 1880m and the dead water level of 1800m. The layout of the arch dam vertical monitoring system and the incremental distance partition results of the measured radial displacement field are shown in Figure 1. Figure 2 As shown in the figure, it contains 4 partitions, in which the number of displacement measurement points in the 1st, 2nd, 3rd and 4th partitions are 6, 9, 2 and 16 respectively. The radial displacement monitoring data of each measuring point were collected from June 5, 2014 to December 31, 2018, with a sampling frequency of once a day, with June 13, 2018 as the boundary, and the two segments before and after were used as training set and test set respectively.

[0084] (1) Sub-model causal input factors

[0085] The arch dam has a very obvious viscoelastic hysteresis deformation behavior during the stable period of high water level of 1880m per year. Therefore, it is necessary to add a hysteresis water pressure component represented by a step exponential function on the basis of the traditional HST model. Its mathematical expression is:

[0086]

[0087]

[0088] Among them, H is the upstream reservoir water depth on the day of displacement monitoring, t is the cumulative number of days from the displacement monitoring day to the start monitoring day, φ = t / 100, τ is the duration of the current 1880m reservoir water level stable period, a i 、b 1i 、b 2i , c1, c2, d1, d2 are the regression coefficients of water pressure, temperature, aging and hysteresis water pressure components respectively, α=E K1 / η K1 , β=E K2 / η K2 , where E K1 and E K2 is the hysteresis elastic modulus in the 5-parameter generalized Kelvin model of the dam concrete, η K1 and η K2 are the viscosity coefficients respectively.

[0089] (2) Constructing sub-models

[0090] Taking the measuring point PL11-1 as an example, the model obtained by the improved parameter optimization method is used to fit the change of the consistency target weight θ of MSE′ and CDT′ with the changing rules as shown in the following figure. Figure 3As shown in the figure, as the CDT weight θ increases, the evaluation indexes of the four machine learning models have similar trends, and the fitting MSE′ and CDT′ both increase accordingly. The main difference is that NN and ELM have only one-level step-by-step growth within the value range, while SVM and RVM have multi-level step-by-step growth. This is caused by the difference in the value range of the model optimization parameters between the former two and the latter two. Among them, the optimization parameters of NN and ELM are the number of neurons, and the value range is small, so the sensitivity to the CDT weight is low. According to the parameter determination criteria proposed in the present invention, the optimal weights θ of the two can be determined as 0.39 and 0.14 respectively; while SVM and RVM both need to optimize the penalty factors and kernel function parameters with a larger value interval, so they are more sensitive to the change of CDT weight. According to the principle that the maximum gap first appears in the normalized values ​​of the two optimization targets during the weight θ changes from roughly small to large, the optimal weights θ of the SVM and RVM models are determined to be 0.41 and 0.61 respectively.

[0091] Taking one measuring point in each of the four partitions of the radial displacement field of the dam as an example, the displacement time series obtained by the five seed models are as follows: Figure 4 As shown. It can be seen from the figure that although the peak values ​​of the radial displacement time series of the four measuring points are different, their time-varying laws show obvious consistency. This is also the reason why the present invention introduces the optimization constraint condition that the consistency of the time-varying laws of the displacements of multiple measuring points is as large as possible. The prediction performance of each model shows obvious differences. The models constructed using the improved parameter optimization method (marked as NN2, ELM2, SVM2 and RVM2; the traditional method only takes the minimum fitting MSE as the optimization goal, and the constructed models are marked as NN1, ELM1, SVM1 and RVM1) have higher prediction accuracy, especially the NN and RVM models. The prediction results of the NN1 model are more volatile, and the displacement prediction values ​​of the RVM1 model are lower than the monitoring values ​​during the stable period of the 1880m high water level. After using the improved parameter optimization method, the prediction values ​​of the two models are closer to the monitoring values.

[0092] The statistical box plots of the prediction evaluation indicators of the 26 measuring points of the dam body using the 5 seed models are shown in the figure. Figure 5 As shown in the figure, the four evaluation indicators of the MLR model are the best and relatively stable; among the four machine learning models, the prediction accuracy of the NN1 and RVM1 models is significantly poorer, and their prediction evaluation indicators are significantly inferior to other models, and some measurement points have serious abnormalities, indicating that the overfitting problem is very serious; the improved parameter optimization method can improve the prediction performance of the four machine learning models for most of the measurement points, and the prediction MSE, MAE and MSE increase ratio are significantly reduced, and R 2The average improvement effect statistics of the 26 test points are shown in Table 1, among which the predicted MSE and its increase ratio of the RVM model decreased the most, reaching 73.12% and 89.82% respectively, indicating that the improved parameter optimization method has the best performance improvement effect on the RVM model, followed by NN, ELM and SVM slightly behind; among the 26 test points, the improved parameter optimization method has the highest effective optimization ratio for RVM, reaching 92.31%, NN and SVM are both 73.08%, and ELM is the smallest, only 26.92%.

[0093] Table 1 Average improvement effect of the improved parameter optimization method on the prediction performance of the machine learning model at 26 measuring points on the dam body

[0094] Evaluation indicators NN ELM SVM RVM Predicted MSE reduction 66.92％ 45.37％ 35.45％ 73.12％ Predicted MSE increase / decrease 79.63％ 59.90％ 62.36％ 89.82％ Effective optimization ratio 73.08％ 26.92％ 73.08％ 92.31％

[0095] In Table 1, the effective optimization ratio refers to the proportion of the number of measurement points that have an improvement effect on the improved parameter optimization method to the total number of modeling measurement points, which is 26 this time.

[0096] However, compared with the MLR model, the prediction performance of the four machine learning models built by the improved parameter optimization method still needs to be improved. Therefore, the present invention establishes a combined model to give full play to the advantages of various modeling methods, further reduce the overfitting degree of the model, and improve the prediction accuracy of the machine learning model.

[0097] (3) Building a combined model

[0098] Among the four machine learning models, the prediction MSE of the SVM model built by the improved parameter optimization method is the smallest, indicating that its performance is the best. Therefore, the combined model in the present invention is established using SVM and the improved parameter optimization method. The MLR model and the four machine learning models are used as sub-models. By successively eliminating the sub-models with the largest prediction MSE increase ratio, 5, 4, 3 and 2 sub-models are used to respectively establish the five-type, four-type, three-type and two-type combined models. The combined model modeling process of some measurement points is shown in the figure. Figure 6 As shown in the figure, taking PL5-1 as an example, among the five-type combination models, the NN sub-model has the largest increase in the prediction MSE ratio, so it can be eliminated first, and then the remaining four sub-models are used to establish a four-type combination model. According to this rule, the order of sub-model elimination is NN, RVM, ELE and SVM, indicating that the optimal sub-model of this measurement point is the MLR model, but the prediction MSE of the two-type combination model built with SVM and MLR as sub-models is the smallest, so it can be determined as the optimal combination model. For the PL19-2 measurement point, after eliminating the NN, ELE, SVM and MLR sub-models in turn, the prediction MSE when only the RVM sub-model is left is the smallest, indicating that the optimal combination model and the optimal sub-model of this measurement point are the same, which is the RVM model.

[0099] The sub-models included in the optimal combined model and their predicted MSE reduction relative to the optimal sub-model are shown in Table 2. The average predicted MSE reduction in the first partition is the largest, reaching 40.08%, the second and third partitions are 26.15% and 37.52% respectively, and the average predicted MSE reduction in the fourth partition is the lowest, at 7.53%. Overall, the average predicted MSE reduction of the 26 measuring points on the dam body is 23.79%, indicating that the combined model can effectively improve the prediction accuracy of the arch dam displacement.

[0100] Table 2 Composition of the optimal combination model at each measuring point and its predicted MSE reduction

[0101]

[0102]

[0103] In Table 2, M, N, E, S and R represent MLR, NN2, ELM2, SVM2 and RVM2 sub-models respectively; the reduction is the percentage reduction of the prediction MSE of the optimal combination model relative to the optimal sub-model.

[0104] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A combined modeling method for improving the performance of an arch dam displacement prediction model, characterized in that: include: The monitoring data of arch dam displacement and environmental quantity are collected, and the displacement causal component in the monitoring data is used as input and the measured displacement of the arch dam is used as output. The MLR sub-model for arch dam displacement prediction is established, which is defined as the first type of sub-model. The NN machine learning sub-model, ELM machine learning sub-model, SVM machine learning sub-model and RVM machine learning sub-model for arch dam displacement prediction are established by using the improved parameter optimization method, which are defined as the second type of sub-model. The evaluation indexes of each sub-model established for arch dam displacement prediction are statistically analyzed, and the predicted MSE increase ratios in the evaluation indexes are sorted according to their values; The machine learning method used by the model with the smallest predicted MSE in the second type of sub-model is selected to establish type 5, type 4, type 3 and type 2 combined models, where the input of the type 5 combined model is the output of the five sub-models, and the output of the type 5 combined model is the measured displacement of the arch dam; Eliminate the model with the largest predicted MSE increase ratio among the five sub-models, and use the remaining four sub-models to establish a four-type combination model, where the input of the four-type combination model is the output of the remaining four sub-models, and the output of the four-type combination model is the measured displacement of the arch dam; similarly, establish a three-type combination model and a two-type combination model respectively; The displacement prediction accuracy of the five-type combined model, the four-type combined model, the three-type combined model, the two-type combined model and the sub-model with the smallest predicted MSE increase ratio were compared, and the best one was used as the final combined prediction model for the prediction of arch dam displacement. The improved parameter optimization method is to adjust the original fitting MSE minimum target in the machine learning model parameter optimization to a fitting MSE as small as possible and a consistency degree of the time-varying law of displacement of multiple measuring points of the arch dam as large as possible, and its purpose is to avoid relying solely on the constraints from a mathematical perspective and increase the constraints from an engineering structure perspective to reduce the overfitting degree of the machine learning model; including: Step A1: Extract the time-varying regularity information of the displacement time series by sliding window method; for the displacement time series of a given measuring point i , set the window length and sliding step size to w and s respectively, from First, extract the time-varying trend of each subsequence in the sliding window from left to right, as shown below: （1） Among them, i is the measurement point number, To monitor the time, is the total number of monitoring data samples of displacement measurement points at a fixed sampling frequency; Then, define the time-varying regularity information characterization function as follows: （2） Original displacement time series The time-varying regularity information of To describe, for two displacement time series of the same length and , the consistency of the time-varying laws of the two It is expressed as: （3） in, for The transposed vector of , i and j are the measurement point numbers; Step A2: Calculate the overall displacement of the proposed modeling point and all other displacement points in the same zone of the arch dam by weighted superposition method. ; According to the principle that the higher the consistency of the time-varying law between the two measuring points, the greater the corresponding weight, the fusion weight Defined as: （4） in, is the total number of similar displacement measurement points in the same partition; and then, The overall consistency of the displacement time-varying law of the measuring point and all measuring points in the partition is defined as: （5） Step A3: Construct the objective function in the improved parameter optimization method; introduce a new objective CDT. To ensure that the fitting MSE is as small as possible and the CDT is as large as possible, the CDT should be reciprocated, that is, , because the dimensions of the two are inconsistent, they need to be normalized separately: （7） （8） in, , , and They are the maximum and minimum values ​​of the fitted MSE and RC within the parameter optimization range, respectively; In summary, the objective function in the improved parameter optimization method is defined as: （9） in, is the weight of the target CDT of the consistency of the time-varying law of displacement at multiple measuring points; Step A4: Use the improved parameter optimization method to optimize the key parameters of the second type of sub-model; among them, the key parameters of the NN machine learning sub-model and the ELM machine learning sub-model are the number of neurons, and the key parameters of the SVM machine learning sub-model and the RVM machine learning sub-model are the penalty factor and the kernel function parameter.

2. The combined modeling method for improving the performance of the arch dam displacement prediction model according to claim 1 is characterized in that: The same partition of the arch dam in step A2 means that according to the displacement time series of all similar displacement monitoring points of the arch dam body, the measuring points are divided into different categories according to the conventional clustering partitioning method based on incremental distance, and then all the measuring points in the same cluster are used to calculate the overall consistency of the time-varying law.

3. The combined modeling method for improving the performance of the arch dam displacement prediction model according to claim 1 is characterized in that: When extracting the time-varying regularity information of the displacement time series of the proposed modeling measuring points according to step A1, the displacement time series used in step A2 are all measured displacement time series; in step A3, the modeling measuring points use the fitted displacement time series output by the machine learning model, and the other measuring points use the measured displacement time series.

4. The combined modeling method for improving the performance of the arch dam displacement prediction model according to claim 1 is characterized in that: The evaluation indicators include mean square error (MSE), maximum absolute value of error (MAE), and complex correlation coefficient. , predicted MSE increase ratio; the smaller the MSE, the smaller the overall error between the displacement monitoring value and the model prediction value; the smaller the MAE value, the more stable the prediction result; The closer the value is to 1, the higher the correlation between the two. The predicted MSE increase ratio represents the degree of overfitting of the model. The larger the value, the more serious the overfitting.

5. The combined modeling method for improving the performance of the arch dam displacement prediction model according to claim 1 is characterized in that: When establishing the five-type combination model, the four-type combination model, the three-type combination model, and the two-type combination model, the improved parameter optimization method is used to optimize the key parameters in the machine learning combination model.

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