A method and system for inverse analysis of mechanical parameters of roller compacted concrete dams

Abstract

The present invention discloses a method and system for inverse analysis of mechanical parameters of roller compacted concrete dams, which relates to the technical field of deformation monitoring of roller compacted concrete dams. It includes: obtaining a data sample set; establishing an MLSSVR model according to the data sample set; obtaining the displacements of each monitoring point of the roller compacted concrete dam by using the data sample set according to the MLSSVR model; calculating the fitness value g(x) of the objective function and taking the minimum value; obtaining the inverse value x of the mechanical parameters that makes the objective function g(x) the minimum value. The inverse analysis method of mechanical parameters of roller compacted concrete dams based on MLSSVR in the present invention shows good results in inverse analysis of mechanical parameters of roller compacted concrete dams; the MLSSVR model can replace the finite element method to reflect the non-linear mapping relationship between mechanical parameters and dam displacements, and can perform reliable inverse analysis on the mechanical parameters of roller compacted concrete dams, improving the accuracy and efficiency of inverse analysis of mechanical parameters of roller compacted concrete dams.

Description

Technical Field

[0001] The present invention relates to the technical field of deformation monitoring of roller compacted concrete dams, and more particularly to a method and system for inverse analysis of mechanical parameters of roller compacted concrete dams. Background Art

[0002] Currently, the inverse analysis method of using monitoring data to inverse the mechanical parameters of dams is the most popular method. The basic idea of this method is to construct an objective function by using the displacement values calculated by the finite element method under the assumption of parameters and the measured displacement values, and search for the mechanical parameters corresponding to the minimum objective function value through an optimization algorithm. In recent years, various optimization algorithms have been widely used in the inverse analysis process, such as genetic algorithms, particle swarm algorithms, ant colony algorithms, simulated annealing algorithms, and so on.

[0003] In order to improve the efficiency of inverse analysis, various machine learning models such as artificial neural networks, Gaussian process regression, kernel extreme learning machines, support vector regression, and response surface models have been used to establish a non-linear mapping relationship between mechanical parameters and dam displacements to replace the finite element method. Even so, there are still some problems in the inverse analysis process, such as poor algorithm convergence and weak model generalization ability.

[0004] For a dam that has been in operation for many years, the initial design values of mechanical parameters cannot represent the material properties of the dam, and affected by various factors, the test values of mechanical parameters usually have a large difference from the actual values. The existence of these limitations has accelerated the exploration of new methods for obtaining reliable mechanical parameters of dams.

[0005] Therefore, how to provide a new method for obtaining reliable mechanical parameters of dams is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for inverse analysis of mechanical parameters of roller compacted concrete dams, which perform reliable inverse analysis on the mechanical parameters of roller compacted concrete dams and improve the accuracy and efficiency of inverse analysis of mechanical parameters of roller compacted concrete dams.

[0007] To achieve the above object, the present invention adopts the following technical scheme: A method for inverse analysis of mechanical parameters of roller compacted concrete dams, comprising the following steps:

[0008] Step 1: Obtain a data sample set;

[0009] Step 2: Establish an MLSSVR model according to the data sample set;

[0010] Step 3: According to the MLSSVR model, use the data sample set to obtain the displacements y of each monitoring point of the roller compacted concrete dam j ;

[0011] Step 4: Calculate the fitness value g(x) of the objective function and take the minimum value;

[0012] Step 5: Obtain the inversion value x of the mechanical parameters that makes the objective function g(x) minimum.

[0013] Preferably, divide the data sample set into a training set and a test set; train the MLSSVR model according to the training set, and test the trained MLSSVR model using the test set.

[0014] Preferably, the specific steps of step 2 include:

[0015] Construct the basic mathematical model for mechanical parameter inversion analysis, and determine the objective function and constraint equations of the MLSSVR model according to the output defined by the MLSSVR principle.

[0016] Preferably, the basic mathematical model of the mechanical parameter inversion analysis is expressed as:

[0017]

[0018] where g(x) is the objective function, x is the parameter to be inverted, n is the number of observations, δ c represents the displacement value calculated by the finite element method under the assumed mechanical parameter condition, and δ m represents the measured displacement value obtained from the measured data, K is the global stiffness matrix, δ is the nodal displacement matrix, R is the equivalent load matrix, x max and x min represent the upper and lower limits of the mechanical parameters to be inverted, respectively.

[0019] Preferably, the specific steps of determining the objective function and constraint equations of the MLSSVR model include:

[0020] For a series of data {(x1, y1), (x2, y2), …, (x n , y n )}, N is the number of samples, x i ∈R n is an n-dimensional input variable, and y i ∈R m is an m-dimensional output variable, where i ∈ N, and y ij represents the i-th sample value of the j-th dimension output, where j = 1, 2, …, m; represents the non-linear mapping relationship between the input and output variables, and the output of the j-th dimension is expressed as:

[0021]

[0022] where w j and b jThe weight vector and bias coefficient vector for the j-th dimensional output respectively;

[0023] The objective function and constraint equations of the MLSSVR model are obtained and expressed as:

[0024]

[0025] where e ij is the fitting error of the single-dimensional output variable, and E i is the overall fitting error of the samples. c and c' are regularization model parameters greater than zero.

[0026] Preferably, the displacements y of each monitoring point of the roller-compacted concrete dam are obtained using the data sample set j :

[0027] Optimize the objective function and constraint equations of the MLSSVR model:

[0028]

[0029] where α and β are Lagrange multipliers;

[0030] According to the optimal conditions, the following formula is obtained:

[0031]

[0032] Obtain the output variable of the j-th dimension:

[0033]

[0034] Preferably, in step 4, according to the displacements y of each monitoring point of the roller-compacted concrete dam j replace δ in the basic mathematical model c , and calculate the fitness value g(x) of the objective function to obtain the minimum value of the fitness value g(x).

[0035] Preferably, a mechanical parameter inversion analysis system for a roller-compacted concrete dam includes:

[0036] A data acquisition module for acquiring data samples;

[0037] A model establishment module for establishing an MLSSVR model according to the data samples;

[0038] A model optimization module for optimizing the MLSSVR model;

[0039] A displacement acquisition module for monitoring points, which is used to obtain the displacements of each monitoring point of the roller-compacted concrete dam according to the optimized MLSSVR model;

[0040] A calculation module, configured to calculate the fitness value of the objective function according to the displacements of the monitoring points and take the minimum value;

[0041] An output module, configured to output the inverse value of the mechanical parameter corresponding to the minimum value of the fitness value of the objective function.

[0042] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a method and system for inverse analysis of mechanical parameters of a roller compacted concrete dam, including: obtaining a data sample set; establishing an MLSSVR model according to the data sample set; obtaining the displacements of each monitoring point of the roller compacted concrete dam according to the MLSSVR model; calculating the fitness value g(x) of the objective function and taking the minimum value; obtaining the inverse value x of the mechanical parameter that makes the objective function g(x) the minimum value. The method for inverse analysis of mechanical parameters of a roller compacted concrete dam based on MLSSVR in the present invention shows good results in inverse analysis of mechanical parameters of a roller compacted concrete dam; the MLSSVR model can replace the finite element method to reflect the non-linear mapping relationship between mechanical parameters and dam displacements, and can perform reliable inverse analysis on mechanical parameters of a roller compacted concrete dam, improving the accuracy and efficiency of inverse analysis of mechanical parameters of a roller compacted concrete dam. Description of the Drawings

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the provided drawings.

[0044] Figure 1 It is a schematic diagram of the overall process of inverse analysis of mechanical parameters of a roller compacted concrete dam proposed by the present invention;

[0045] Figure 2 It is a schematic diagram of the distribution of vertical line monitoring equipment of a certain roller compacted concrete dam in the embodiment of the present invention;

[0046] Figure 3 It is a comparison diagram of the results of the MLSSVR model and the finite element method. Detailed Embodiments

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0048] The object of the present invention is to perform a reliable inverse analysis on the mechanical parameters of a roller compacted concrete dam. For a dam that has been in operation for many years, the initial design values of the mechanical parameters cannot represent the material properties of the dam. And affected by various factors, there are usually large differences between the test values of the mechanical parameters and the actual values. In order to obtain more accurate mechanical parameters of the dam material, it is necessary to explore a reliable method. The inverse analysis method is based on the prototype observation data and combines mathematical theories to solve the parameters required in the forward calculation, which is an effective way.

[0049] An embodiment of the present invention discloses a method for inverse analysis of the mechanical parameters of a roller compacted concrete dam, which adopts an inverse analysis method for the mechanical parameters of an RCC (roller compacted concrete dam) based on an MLSSVR model (multi-output least squares support vector regression model), as Figure 1 shown, and includes the following steps:

[0050] Step 1: Obtain a data sample set;

[0051] Step 2: According to the data sample set, establish an MLSSVR model; divide the data sample set into a training set and a test set; train the MLSSVR model according to the training set, and test the trained MLSSVR model using the test set;

[0052] Step 3: According to the MLSSVR model, use the data sample set to obtain the displacements y of each monitoring point of the roller compacted concrete dam j ;

[0053] Step 4: Calculate the fitness value g(x) of the objective function and take the minimum value;

[0054] Step 5: Obtain the inverse value x of the mechanical parameters that makes the objective function g(x) the minimum value.

[0055] Specifically, the specific content of step 2 includes:

[0056] Construct the basic mathematical model for inverse analysis of mechanical parameters, and determine the objective function and constraint equations of the MLSSVR model according to the output defined by the MLSSVR principle.

[0057] Specifically, the basic mathematical model for inverse analysis of mechanical parameters starts from the basic principle of inverse analysis of mechanical parameters, takes the overall control equation for calculating node displacements by the finite element theory as the constraint condition, and takes the error between the displacements corresponding to the assumed mechanical parameters calculated by the finite element method and the measured displacements as the objective function, and constructs the basic mathematical model for inverse analysis of mechanical parameters, which is expressed as:

[0058]

[0059] Among them, g(x) is the objective function, x is the parameter to be inverted, n is the number of observations, and δ c represents the displacement value calculated by the finite element method under the assumed mechanical parameters, and δ m represents the measured displacement value obtained from the measured data. K is the global stiffness matrix, δ is the nodal displacement matrix, R is the equivalent load matrix, x max and x min represent the upper and lower limits of the mechanical parameters to be inverted, respectively;

[0060] Specifically, the MLSSVR model is used to replace the finite element method to solve for δ in formula (1) c ; the MLSSVR principle is expressed as: for a series of data {(x1, y1), (x2, y2), …, (x n , y n )}, N is the number of samples, x i ∈R n is an n-dimensional input variable, and y i ∈R m is an m-dimensional output variable, where i ∈ N, and y ij represents the i-th sample value of the j-th dimension output, where j = 1, 2, …, m; the output of the j-th dimension is expressed as:

[0061]

[0062] where, w j and b j are the weight vector and bias coefficient vector of the j-th dimension output, respectively; represents the non-linear mapping relationship between the input and output variables, and non-linearly maps the samples to a high-dimensional feature space, so that the non-linear function problem in the original sample space can be transformed into a linear function problem in the high-dimensional feature space.

[0063] The objective function and constraint equations corresponding to the multi-output least squares support vector regression model (MLSSVR model) obtained according to the MLSSVR principle are expressed as:

[0064]

[0065] where e ij is the fitting error of the single-dimensional output variable, E i is the overall fitting error of the samples, and c and c' are regularization model parameters greater than zero; selecting appropriate values can ensure the accuracy of model fitting and prediction;

[0066] Specifically, by establishing a Lagrange function equation, formula (3) is transformed into an unconstrained optimization problem:

[0067]

[0068] Among them, α and β are Lagrange multipliers; e represents the fitting error of the single-dimensional output variable, and E represents the overall fitting error of the samples.

[0069] According to the optimal conditions, the following formula is obtained:

[0070]

[0071] Eliminate w in formula (5) j , e ij , E i , then there is:

[0072]

[0073] Specifically, by solving b j , α ij and β i , the output variable of the j-th dimension is obtained:

[0074]

[0075] In formulas (6) and (7), is defined as k(x, x i ), that is, a kernel function is introduced in the model derivation process. In the embodiment of the present invention, the radial basis function is selected as the kernel function, that is, k(x, x i ) = exp(-||x i - x|| 2 / 2σ 2 ), where σ > 0 is the kernel width. The prediction accuracy of the multi-output least squares support vector regression model based on the radial basis function is mainly affected by the regularization parameters c, c' and the kernel parameter σ.

[0076] In an embodiment of the present invention, in step 3, using the mechanical parameter population in Table 1, the displacements y of each monitoring point of the roller compacted concrete dam are obtained according to formula (7) j .

[0077] In step 4, the displacements y of each monitoring point of the roller compacted concrete dam obtained in step 3 j are used to replace δ in formula (1) solved by the finite element method c ; according to the solution formula (1), the fitness value g(x) of the objective function is calculated, and the minimum value is taken.

[0078] Record the mechanical parameter x that makes the objective function take the minimum value in step 4; output the mechanical parameter x.

[0079] A system for inverse analysis of mechanical parameters of a roller compacted concrete dam, characterized by comprising:

[0080] A data acquisition module for acquiring data samples;

[0081] A model establishment module for establishing an MLSSVR model based on the data samples;

[0082] A model optimization module for optimizing the MLSSVR model;

[0083] A displacement acquisition module for monitoring points, which acquires the displacements of each monitoring point of the roller compacted concrete dam according to the optimized MLSSVR model;

[0084] A calculation module for calculating the fitness value of the objective function according to the displacements of each monitoring point and taking the minimum value;

[0085] An output module for outputting the inverse value of the mechanical parameters corresponding to the minimum value of the fitness value of the objective function.

[0086] In an embodiment of the present invention, as Figure 2 shown, a schematic diagram of the distribution of the vertical line monitoring equipment of a certain roller compacted concrete dam selected in the embodiment of the present invention is shown. The dam body is divided into six dam sections, among which ①, ②, ⑤ and ⑥ are non-overflow dam sections, and ③ and ④ are overflow dam sections, with a dam length of 308.5 m. According to the actual situation of the project, a complete set of horizontal displacement monitoring instruments is designed and installed, including sensors buried in each dam section and the corresponding data acquisition devices. To monitor the change of the horizontal displacement operation state of the dam top and the dam body interior, the dam safety monitoring and management department places the vertical line horizontal displacement monitoring system including seven plumb lines (PL1, PL2, PL3, PL4, PL5, PL6, PL7) and three inverted plumb lines (IP1, IP2, IP3) on three dam sections and their corresponding dam foundations;

[0087] As Figure 3 shown, Figure 3 Thirty-seven data samples in Table 1 are randomly divided into 30 training sets and 7 test sets to establish a multi-output least squares support vector regression model. The multi-output least squares support vector regression model is tested through the test sets, and the test results of the model are compared and analyzed with the results calculated by the finite element software. Figure 3 In, the test results of testing with 7 test sets in the trained multi-output least squares support vector regression model are respectively shown. Generally speaking, the errors between the model test results and the finite element calculation results at the monitoring points of the seven plumb lines PL1, PL2, PL3, PL4, PL5, PL6, and PL7 are all small, indicating that the multi-output least squares support vector regression model can well represent the non-linear mapping relationship between the material parameters and the dam displacement values, and can be used to replace the finite element method for calculation and application in the optimization inversion analysis. Among them, Table 1 shows five parameters to be inverted E 1x , E 1z , E2x , E 2z , E3 and the calculated horizontal displacement difference Δδ' at each monitoring point H .

[0088] Table 1. Mechanical parameter combinations (GPa) and calculated horizontal displacement difference Δδ' H (mm)

[0089]

[0090]

[0091] Based on the research on the analysis of the mechanical parameters of roller-compacted concrete dams, the present invention proposes a new method for inverse analysis of the mechanical parameters of roller-compacted concrete dams. This method uses the inverse analysis method of the mechanical parameters of roller-compacted concrete dams based on MLSSVR and shows good results in inverse analysis of the mechanical parameters of roller-compacted concrete dams. The multi-output least squares support vector regression model (MLSSVR model) can replace the finite element method to reflect the non-linear mapping relationship between mechanical parameters and dam displacement. Since the deformation between dam sections affects each other, the deformation information collected by the monitoring points on different dam sections is cross-correlated. Therefore, from the perspective of the model accuracy, the multi-output least squares support vector regression model uses the deformation information of multiple monitoring points to establish the relationship with the material mechanical parameters, while in the single-output least squares support vector regression model, only the deformation information of a certain monitoring point is used, thus ignoring the correlation between the monitoring point information and increasing the error of the single-output least squares support vector regression model. In addition, in terms of the model calculation efficiency, only one model needs to be established for the multi-output least squares support vector regression model, while the single-output least squares support vector regression model needs to be modeled multiple times according to the number of monitoring points. Based on the above analysis, the multi-output least squares support vector regression model shows better performance than the single-output least squares support vector regression model. The method for inverse analysis of the mechanical parameters of roller-compacted concrete dams based on MLSSVR in the present invention shows good results in inverse analysis of the mechanical parameters of roller-compacted concrete dams; it can perform reliable inverse analysis on the mechanical parameters of roller-compacted concrete dams, improving the accuracy and efficiency of the inverse analysis of the mechanical parameters of roller-compacted concrete dams.

[0092] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0093] The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for inverse analysis of mechanical parameters of a roller compacted concrete dam, characterized in that, It includes the following steps: Step 1: Obtain a data sample set; Step 2: Establish an MLSSVR model according to the data sample set; The specific content of Step 2 includes: Construct a basic mathematical model for mechanical parameter inversion analysis, and determine the objective function and constraint equations of the MLSSVR model according to the output defined by the MLSSVR principle; The basic mathematical model for mechanical parameter inversion analysis is expressed as: where \(g(x)\) is the objective function, \(x\) is the parameter to be inverted, \(n\) is the number of observations, and \(\delta\) c represents the displacement value calculated by the finite element method under the assumed mechanical parameters, and \(\delta\) m represents the measured displacement value obtained from the measured data, \(K\) is the global stiffness matrix, \(\delta\) is the nodal displacement matrix, \(R\) is the equivalent load matrix, \(x\) max and \(x\) min represent the upper and lower limits of the mechanical parameters to be inverted, respectively; The specific content of determining the objective function and constraint equations of the MLSSVR model includes: For a series of data \(\{(x_1,y_1),(x_2,y_2),\ldots,(x n ,y n )\}\), \(N\) is the number of samples, \(x i \in\mathbb{R} n \) is an \(n\)-dimensional input variable, \(y i \in\mathbb{R} m \) is an \(m\)-dimensional output variable, where \(i\in N\), \(y ij \) represents the \(i\)-th sample value of the \(j\)-th dimension output, where \(j = 1,2,\ldots,m\); represents the non - linear mapping relationship between the input and output variables. The output of the \(j\)-th dimension is expressed as: where, w j and b j are the weight vector and the bias coefficient vector of the j-th dimension output, respectively; The obtained objective function and constraint equations of the MLSSVR model are expressed as: where e ij is the fitting error of the one-dimensional output variable, and E i is the overall fitting error of the samples, and c and c' are regularization model parameters greater than zero respectively; Step 3: According to the MLSSVR model, obtain the displacements y of each monitoring point of the roller compacted concrete dam by using the data sample set j ; Step 4: Calculate the fitness value g(x) of the objective function and take the minimum value; Step 5: Obtain the mechanical parameter inversion value x that makes the objective function g(x) the minimum value.

2. The mechanical parameter back-analysis method for a roller-compacted concrete dam according to claim 1, characterized in that Divide the data sample set into a training set and a test set; train the MLSSVR model according to the training set, and test the trained MLSSVR model using the test set.

3. A back analysis method for mechanical parameters of a roller compacted concrete dam according to claim 1, characterized in that, Obtaining the displacements y of each monitoring point of the roller compacted concrete dam by using a data sample set j : Optimize the objective function and constraint equations of the MLSSVR model: where α and β are Lagrange multipliers; According to the optimal conditions, the following formula is obtained: Obtain the output variable of the j-th dimension:

4. A method for inverse analysis of mechanical parameters of a roller compacted concrete dam according to claim 3, characterized in that, In step 4, according to the displacements y of each monitoring point of the roller compacted concrete dam j replace δ in the basic mathematical model c , and calculate the fitness value g(x) of the objective function to obtain the minimum value of the fitness value g(x).

5. A mechanical parameter back-analysis system for a roller-compacted concrete dam, characterized in that, It includes: A data acquisition module for obtaining data samples; A model establishment module for establishing an MLSSVR model according to the data samples; Specifically includes: constructing a basic mathematical model for mechanical parameter inversion analysis, and determining the objective function and constraint equations of the MLSSVR model according to the output defined by the MLSSVR principle; The basic mathematical model for mechanical parameter inversion analysis is expressed as: Among them, g(x) is the objective function, x is the parameter to be inverted, n is the number of observations, and δ c represents the displacement value calculated by the finite element method under the assumed mechanical parameters, and δ m represents the measured displacement value obtained from the measured data, K is the global stiffness matrix, δ is the nodal displacement matrix, R is the equivalent load matrix, x max and x min represent the upper and lower limits of the mechanical parameters to be inverted, respectively; The specific content of determining the objective function and constraint equations of the MLSSVR model includes: For a series of data \(\{(x_1,y_1),(x_2,y_2),\cdots,(x n ,y n )\}\), \(N\) is the number of samples, \(x i \in\mathbb{R} n \) is an \(n\)-dimensional input variable, \(y i \in\mathbb{R} m \) is an \(m\)-dimensional output variable, where \(i\in N\), \(y ij \) represents the \(i\)-th sample value of the \(j\)-th dimension output, where \(j = 1,2,\cdots,m\); represents the non - linear mapping relationship between the input and output variables. The output of the \(j\)-th dimension is expressed as: where w j and b j are the weight vector and the bias coefficient vector of the j-th dimension output, respectively; The obtained objective function and constraint equations of the MLSSVR model are expressed as: where e ij is the fitting error of the single-dimensional output variable, and E i is the overall fitting error of the sample, and c and c' are regularization model parameters greater than zero respectively; A model optimization module for optimizing the MLSSVR model; A detection point displacement acquisition module for obtaining the displacements of each monitoring point of the roller compacted concrete dam according to the optimized MLSSVR model; A calculation module for calculating the fitness value of the objective function according to the displacements of each monitoring point and taking the minimum value; An output module for outputting the mechanical parameter inversion value corresponding to the minimum value of the fitness value of the objective function.

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