CN114330067A - Soft foundation sluice finite element model correction method - Google Patents
Soft foundation sluice finite element model correction method Download PDFInfo
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Abstract
The invention relates to a soft foundation sluice finite element model correction method, which comprises the following steps: performing vibration test on the target soft foundation sluice to obtain a sluice vibration acceleration or dynamic displacement response signal; identifying a soft foundation sluice vibration modal parameter based on an IVMD-SSI method; establishing a finite element model of the soft foundation sluice, and determining the soft foundation sluice structure and the to-be-corrected parameter partition of the foundation; constructing a GA-SVR agent model to replace a finite element model of the soft foundation sluice according to the vibration modal parameters of the sluice and the parameters to be corrected; and constructing an objective function corrected by the finite element model of the soft foundation sluice, and carrying out optimization solution on the objective function based on the BAS-PSO optimization algorithm to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice. The method for correcting the finite element model of the soft foundation sluice overcomes the limitation that static information is difficult to monitor on line, solves the problems of low calculation efficiency and difficult global convergence of individual algorithms in a group algorithm, has good correction effect, and provides a brand new thought for correcting the finite element model of the soft foundation sluice.
Description
Technical Field
The invention relates to the technical field of safety monitoring and performance evaluation of sluice structures, in particular to a method for correcting a finite element model of a soft foundation sluice.
Background
According to statistics, the flow rate of the Chinese current building is 5m3And/s and above water gates reach 103878, which play irreplaceable roles in flood control, irrigation, shipping and the like. However, the complicated service environment and the perennial erosion of water flow bring different degrees of potential safety hazards to the water gate in service for a long time, and particularly, the water gate (soft foundation water gate) located on a soft foundation is prone to problems of unstable gate chamber, structural damage, gate foundation seepage damage, bottom plate void and the like, and the performance of the working efficiency of the water gate is seriously influenced. Therefore, the health monitoring and performance evaluation research of the sluice structure has great significance for ensuring the long-term safe operation of the sluice. The accurate and reliable finite element model is the basis of structural health monitoring, but because of the existence of uncertain factors such as model parameters, boundary conditions and the like, the established finite element model cannot accurately reflect the real dynamic characteristics of the sluice structure, and further the precision of sluice damage identification and performance evaluation is influenced. At present, the sluice finite element model correction method based on the measured information is a reliable method.
In the field of engineering structures, related finite element model correction methods can be classified into a finite element model correction method based on static force information and a finite element model correction method based on modal parameters according to actual measurement information. The finite element model correction method based on the modal parameters overcomes the limitation that static information is difficult to monitor on line. In addition, the selection of a reasonable and reliable intelligent algorithm is crucial to the correction of the finite element model of the water gate, but various intelligent algorithms have certain limitations, for example, the group algorithm has a problem of low calculation efficiency, the individual algorithm has a problem of difficulty in realizing global convergence, and the like, and further improvement is needed.
In contrast, the method is based on the actually measured vibration response of the soft foundation sluice, and adopts a random subspace method (IVMD-SSI) based on improved variational modal decomposition to identify the vibration modal parameters of the sluice; establishing a genetic algorithm-based support vector regression (GA-SVR) proxy model representing the nonlinear relation between the parameters to be corrected and the modal parameters of the soft foundation sluice based on the Support Vector Regression (SVR) principle; calculating modal parameters and sluice vibration modal parameters based on a GA-SVR agent model, and constructing an optimized mathematical model modified by a soft foundation sluice finite element model; and solving the optimized mathematical model by adopting a particle swarm optimization (BAS-PSO) algorithm based on a longicorn whisker search algorithm, and inverting the optimal combination of the parameters to be corrected of the soft foundation sluice. The method provides a brand new idea for correcting the finite element model of the soft foundation sluice.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and establishes a soft foundation sluice finite element model correction method based on modal parameters and a BAS-PSO optimization algorithm; according to modal parameters identified by the response signals of the sluice actual measurement and the modal parameters output by the GA-SVR agent model, an objective function reflecting the minimum relative deviation among the modal parameters is established, and the BAS-PSO optimization algorithm is adopted to invert the optimal combination of the parameters to be corrected of the soft foundation sluice, so that a new thought is provided for correcting the finite element model of the soft foundation sluice.
In order to achieve the purpose, the invention adopts the following technical scheme:
a soft foundation sluice finite element model correction method comprises the following steps:
and 5, constructing an objective function corrected by a finite element model of the soft foundation sluice by using the minimum relative deviation between the vibration modal parameters of the sluice and the calculation modal parameters of the GA-SVR proxy model established in the step 4, and carrying out optimization solution on the objective function based on the BAS-PSO optimization algorithm to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice.
Identifying the vibration mode parameters of the soft foundation sluice based on the IVMD-SSI in the step 2, wherein the specific process is as follows:
a1. and (3) noise reduction treatment of the actually measured vibration response signal of the soft foundation sluice: the variational modal decomposition VMD, as a multi-component adaptive signal decomposition method, can decompose a vibration signal f into K eigenmode functions (IMF) with limited bandwidths by solving a constrained variational problem, which is described as follows:
in the above formula, δ (t) is dirac distribution; u. ofk′(t) is the kth' IMF; j is a complex unit; omegak′(t) is the center frequency of the kth' IMF; in order to solve the variation constraint model, a secondary penalty factor and a Langrange multiplier are introduced to convert the variation constraint model into an unconstrained variation problem, and the following steps are performed:
in the above formula, α is a secondary penalty factor; lambda (t) is a Langcange multiplier, the formula (2) is solved in the frequency domain through an alternating direction multiplier algorithm, saddle points of the augmented Langcange function, namely the optimal solution of the formula (1), are calculated, and the u is continuously updated and optimized in an iterative mannerk′、ωk′And λ, thereby achieving signal decomposition;
the K value needs to be preset when the traditional VMD algorithm is used for denoising, the selection of the K value directly influences the accuracy of signal decomposition, in order to avoid the deviation caused by the uncertainty of the K value, the VMD algorithm is improved by utilizing a mutual information method to realize the self-adaptive selection of the K value, and the expression is as follows:
I(XI,YI)＝H′(XI)+H′(YI)-H′(XIYI) (3)
in the above formula, I (XI, YI) is a mutual information coefficient of IMF components XI and YI; h '(XI) and H' (YI) are the entropy of IMF components XI and YI, respectively; h' (XIYI) is the joint entropy of IMF components XI and YI, a normalized mutual information coefficient NMIC of each IMF component is calculated, the threshold value of NMIC is set to be 0.02, when the component is decomposed to the extent that NMIC is smaller than the threshold value, the component is not related to the original signal, the signal is decomposed fully at the moment, and the K value is determined in a self-adaptive mode;
b1. identification of vibration modal parameters of the soft foundation sluice: SSI is a method for identifying structural modal parameters by establishing a random state discrete space model, and the basic principle is as follows:
for N measuring points and the data length of each measuring point is l, measuring point response data output by IVMD noise reduction can be formed into a block Hankel matrix of 2Nc multiplied by l:
in the above formula, Y0|c-1And the Hankle matrix block is formed by all measuring points of which the subscript of the 1 st row in the Hankle matrix has the starting time of 0 and the end time of c-1. According to the principle of statistical sequence, when l/c is large enough, it can be considered that l → ∞, divides the line space of the Hankel matrix into "past" line space and "future" line space, and matches H with HThe ankle matrix is subjected to QR decomposition by:
in the above formula, YpastAnd YfutureRespectively representing the "past" and "future" line spaces of the Hankel matrix; r is formed by R2Nc×lIs a lower triangular matrix; q ∈ Rl×lIs an orthogonal matrix; r11，R21，R22∈RNc×Nc；
According to the theory of spatial projection, YfutureLine space in YpastThe orthogonal projection matrix on the formed row space is as follows:
in the above formula, the first and second carbon atoms are,
Moore-Penrose pseudo-inverse as a matrix;
according to the random subspace identification theory, the projection matrix Oc can be decomposed into a considerable matrix Gamma c and a Kalman filtering state vector
The product of (a) is obtained by Singular Value Decomposition (SVD):
in the above formula, U1∈RNc×n；S1∈Rn×n；V1 T∈Rn×l；
The state space equation at this time is:
in the above formula, A1And C1Respectively representing a system matrix and an output matrix, W1And V1Representing the residual error.
Since the Kalman filtering state vector and output are known, and the residual matrix and estimation sequence
Uncorrelated, and the state space equation of equation (9) is solved by least squares to obtain the system matrix A1And output matrix C1。
From the system matrix A1And output matrix C1And identifying the vibration mode parameters of the soft foundation sluice.
And 3, constructing a GA-SVR agent model reflecting the nonlinear relation between the parameters to be corrected of the soft foundation sluice and the structural modal parameters, wherein the construction process of the GA-SVR agent model is as follows:
a2. determining the variable: setting the modal parameters as dependent variables and setting the parameters to be corrected of the soft foundation sluice as independent variables by taking two parameters of frequency and vibration mode in the working modal parameters of the sluice as modal parameter variables;
b2. generating a sample: generating a parameter sample to be corrected based on a Latin hypersonic sampling method (LHS), and calculating modal parameters of the sluice under different parameter sample combinations to be corrected based on a finite element model;
c2. constructing an optimal hyperplane function: the method comprises the following steps of mapping a parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between parameters to be corrected and modal parameters of the soft foundation sluice by utilizing a linear regressive hyperplane, wherein the basic principle of SVR is as follows:
hypothesis to be modified parameter training sample set
Wherein
The number of training samples is represented, and the optimal hyperplane function is constructed as f '(x) ═ ω'TPhi '(x) + b', wherein omega 'and b' are parameters of the regression model, so that the loss is calculated when the absolute value of the deviation between f '(x) and mop (x) exceeds a certain tolerance range epsilon', and a relaxation variable xi is introduced to avoid the existence of singular points and deviation pointsiAnd
then the SVR optimization problem can be formalized as:
in the above formula, C is a regularization parameter. Lagrange multipliers are introduced to obtain Lagrange functions, and according to optimization conditions, the dual problem of SVR can be converted into the following problem:
taking the radial basis function as the kernel function of the SVR, the regression equation of the SVR is as follows:
in the above formula, σ is a width parameter of the radial basis function;
d2. fitting GA-SVR proxy model: generating a smaller parameter sample set to be corrected by adopting LHS, inputting the sample set into a finite element model to obtain a corresponding modal parameter set, mapping the parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between a parameter to be corrected of the soft foundation sluice and a modal parameter by utilizing a linear regressive hyperplane, and optimizing and solving a regularization parameter C and a kernel function parameter g in the model by utilizing a genetic algorithm, thereby establishing a GA-SVR proxy model representing the nonlinear mathematical relationship between the parameter to be corrected of the soft foundation sluice and the modal parameter and replacing the finite element model with the GA-SVR proxy model.
And 5, correcting the target function of the soft foundation sluice finite element model constructed in the step 5, wherein the expression of the target function is as follows:
in the above formula, the first and second carbon atoms are,
ωi(x) Respectively representing the i-th order inherent frequency identification value and the GA-SVR agent model calculation value of the sluice structure;
φij(x) Respectively representing the ith order vibration mode identification value and the GA-SVR agent model calculation value of a measuring point j of the water gate structure; w is ai、wijWeight coefficients respectively representing the frequency and the mode shape coefficient; n is the number of measuring points of the vibration response test; MF is the identified modal order.
In the step 5, the BAS-PSO optimization algorithm is used for carrying out optimization solution on the objective function to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice, and the BAS-PSO optimization algorithm comprises the following basic steps:
a3. randomly generating a particle population, defining population parameters and determining a fitness function;
b3. regarding the population particles as longicorn individuals, calculating the fitness value of the current population particles by adopting a BAS algorithm, determining the optimal position of the longicorn individuals, and updating the optimal solution and the local optimal solution of the individuals;
c3. iteratively updating the position and the speed of the particle swarm by adopting a PSO algorithm, repeating the step b3, and calculating the optimal solution of the updated population;
d3. when the algorithm reaches the iteration number or the iteration condition is met, stopping searching and outputting the optimal solution, otherwise, continuously repeating the step c3 until the value meeting the convergence criterion is searched.
Compared with the prior art, the invention has the beneficial effects that:
the method is characterized in that the water gate vibration modal parameters are identified based on a random subspace method IVMD-SSI of improved variational modal decomposition; establishing a GA-SVR proxy model representing the nonlinear relation between the parameters to be corrected and the modal parameters of the soft foundation sluice according to the Support Vector Regression (SVR) principle, calculating the modal parameters and the sluice vibration modal parameters according to the GA-SVR proxy model, and constructing an optimized mathematical model for correcting the finite element model of the soft foundation sluice; the particle swarm BAS-PSO optimization algorithm based on the longicorn whisker search algorithm is adopted to solve the optimized mathematical model, and the optimal combination of parameters to be corrected of the soft foundation sluice is inverted.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a method for correcting a finite element model of a soft foundation sluice according to the present invention;
FIG. 2 is a schematic diagram of a soft foundation sluice model according to an embodiment of the present invention;
FIG. 3 is a layout diagram of a soft foundation sluice vibration sensor in an embodiment of the present invention;
FIG. 4 is a schematic time-course diagram of a signal component at the B7 measurement point in the embodiment of the present invention;
FIG. 5 is a comparison graph of time courses before and after noise reduction of the measurement point B7 in the embodiment of the present invention;
FIG. 6 is a plot of a power spectral density curve versus a ratio of power spectral density curves before and after noise reduction at the B7 test point in an example of the present invention;
FIG. 7 is a finite element model of the soft foundation sluice model of FIG. 2;
FIG. 8 is a comparison of the BAS-PSO algorithm with the adaptive inertial weight PSO Algorithm (AWPSO) and the BAS algorithm in accordance with an embodiment of the present invention;
FIG. 9 is a diagram illustrating a comparison result of the modified finite element model of the soft foundation sluice according to an embodiment of the present invention; (a) a first stage; (b) a second stage; (c) a third step; (d) and the fourth step.
In the figure: 1. a working bridge; 2. a gate pier; 3. a foundation; 4. a base plate; 5. and (4) side walls.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any inventive step, are within the scope of the present invention.
Example (b): see fig. 1-9.
As shown in fig. 1, a method for modifying a finite element model of a soft foundation sluice comprises the following steps:
and 5, constructing an objective function corrected by a finite element model of the soft foundation sluice by using the minimum relative deviation between the vibration modal parameters of the sluice and the calculation modal parameters of the GA-SVR proxy model established in the step 4, and carrying out optimization solution on the objective function based on the BAS-PSO optimization algorithm to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice.
Identifying the vibration mode parameters of the soft foundation sluice based on the IVMD-SSI in the step 2, wherein the specific process is as follows:
a1. and (3) noise reduction treatment of the actually measured vibration response signal of the soft foundation sluice: the variational modal decomposition VMD, as a multi-component adaptive signal decomposition method, can decompose a vibration signal f into K eigenmode functions (IMF) with limited bandwidths by solving a constrained variational problem, which is described as follows:
in the above formula, δ (t) is dirac distribution; u. ofk′(t) is the kth' IMF; j is a complex unit; omegak′(t) is the center frequency of the kth' IMF; in order to solve the variation constraint model, a secondary penalty factor and a Langrange multiplier are introduced to convert the variation constraint model into an unconstrained variation problem, and the following steps are performed:
in the above formula, α is a secondary penalty factor; lambda (t) is a Langcange multiplier, the formula (2) is solved in the frequency domain through an alternating direction multiplier algorithm, saddle points of the augmented Langcange function, namely the optimal solution of the formula (1), are calculated, and the u is continuously updated and optimized in an iterative mannerk′、ωk′And λ, thereby achieving signal decomposition;
the K value needs to be preset when the traditional VMD algorithm is used for denoising, the selection of the K value directly influences the accuracy of signal decomposition, in order to avoid the deviation caused by the uncertainty of the K value, the VMD algorithm is improved by utilizing a mutual information method to realize the self-adaptive selection of the K value, and the expression is as follows:
I(XI,YI)＝H′(XI)+H′(YI)-H′(XIYI) (3)
in the above formula, I (XI, YI) is a mutual information coefficient of IMF components XI and YI; h '(XI) and H' (YI) are the entropy of IMF components XI and YI, respectively; h' (XIYI) is the joint entropy of IMF components XI and YI, a normalized mutual information coefficient NMIC of each IMF component is calculated, the threshold value of NMIC is set to be 0.02, when the component is decomposed to the extent that NMIC is smaller than the threshold value, the component is not related to the original signal, the signal is decomposed fully at the moment, and the K value is determined in a self-adaptive mode;
b1. identification of vibration modal parameters of the soft foundation sluice: SSI is a method for identifying structural modal parameters by establishing a random state discrete space model, and the basic principle is as follows:
for N measuring points and the data length of each measuring point is l, measuring point response data output by IVMD noise reduction can be formed into a block Hankel matrix of 2Nc multiplied by l:
in the above formula, Y0|c-1And the Hankle matrix block is formed by all measuring points of which the subscript of the 1 st row in the Hankle matrix has the starting time of 0 and the end time of c-1. According to the principle of statistical sequence, when l/c is large enough, l → ∞, the line space of the Hankel matrix is divided into the "past" line space and the "future" line space, and QR decomposition is performed on the Hankle matrix by:
in the above formula, YpastAnd YfutureRespectively representing the "past" and "future" line spaces of the Hankel matrix; r is formed by R2Nc×lIs a lower triangular matrix; q ∈ Rl×lIs an orthogonal matrix; r11，R21，R22∈RNc×Nc；
According to the theory of spatial projection, YfutureLine space in YpastThe orthogonal projection matrix on the formed row space is as follows:
in the above formula, the first and second carbon atoms are,
Moore-Penrose pseudo-inverse as a matrix;
according to the random subspace identification theory, the projection matrix Oc can be decomposed into a considerable matrix Gamma c and a Kalman filtering state vector
The product of (a) is obtained by Singular Value Decomposition (SVD):
in the above formula, U1∈RNc×n；S1∈Rn×n；V1 T∈Rn×l；
The state space equation at this time is:
in the above formula, A1And C1Respectively representing a system matrix and an output matrix, W1And V1Representing the residual error.
Since the Kalman filtering state vector and output are known, and the residual matrix and estimation sequence
Uncorrelated, and the state space equation of equation (9) is solved by least squares to obtain the system matrix A1And output matrix C1。
From the system matrix A1And output matrix C1And identifying the vibration mode parameters of the soft foundation sluice.
And 3, constructing a GA-SVR agent model reflecting the nonlinear relation between the parameters to be corrected of the soft foundation sluice and the structural modal parameters, wherein the construction process of the GA-SVR agent model is as follows:
a2. determining the variable: setting the modal parameters as dependent variables and setting the parameters to be corrected of the soft foundation sluice as independent variables by taking two parameters of frequency and vibration mode in the working modal parameters of the sluice as modal parameter variables;
b2. generating a sample: generating a parameter sample to be corrected based on a Latin hypersonic sampling method (LHS), and calculating modal parameters of the sluice under different parameter sample combinations to be corrected based on a finite element model;
c2. constructing an optimal hyperplane function: the method comprises the following steps of mapping a parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between parameters to be corrected and modal parameters of the soft foundation sluice by utilizing a linear regressive hyperplane, wherein the basic principle of SVR is as follows:
hypothesis to be modified parameter training sample set
Wherein
The number of training samples is represented, and the optimal hyperplane function is constructed as f '(x) ═ ω'TPhi '(x) + b', wherein omega 'and b' are parameters of the regression model, so that the loss is calculated when the absolute value of the deviation between f '(x) and mop (x) exceeds a certain tolerance range epsilon', and a relaxation variable xi is introduced to avoid the existence of singular points and deviation pointsiAnd
then the SVR optimization problem can be formalized as:
in the above formula, C is a regularization parameter. Lagrange multipliers are introduced to obtain Lagrange functions, and according to optimization conditions, the dual problem of SVR can be converted into the following problem:
taking the radial basis function as the kernel function of the SVR, the regression equation of the SVR is as follows:
in the above formula, σ is a width parameter of the radial basis function;
d2. fitting GA-SVR proxy model: generating a smaller parameter sample set to be corrected by adopting LHS, inputting the sample set into a finite element model to obtain a corresponding modal parameter set, mapping the parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between a parameter to be corrected of the soft foundation sluice and a modal parameter by utilizing a linear regressive hyperplane, and optimizing and solving a regularization parameter C and a kernel function parameter g in the model by utilizing a genetic algorithm, thereby establishing a GA-SVR proxy model representing the nonlinear mathematical relationship between the parameter to be corrected of the soft foundation sluice and the modal parameter and replacing the finite element model with the GA-SVR proxy model.
And 5, correcting the target function of the soft foundation sluice finite element model constructed in the step 5, wherein the expression of the target function is as follows:
in the above formula, the first and second carbon atoms are,
ωi(x) Respectively representing the i-th order inherent frequency identification value and the GA-SVR agent model calculation value of the sluice structure;
φij(x) Respectively representing the ith order vibration mode identification value and the GA-SVR agent model calculation value of a measuring point j of the water gate structure; w is ai、wijWeight coefficients respectively representing the frequency and the mode shape coefficient; n is the number of measuring points of the vibration response test; MF is the identified modal order.
In the step 5, the BAS-PSO optimization algorithm is used for carrying out optimization solution on the objective function to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice, and the BAS-PSO optimization algorithm comprises the following basic steps:
a3. randomly generating a particle population, defining population parameters and determining a fitness function;
b3. regarding the population particles as longicorn individuals, calculating the fitness value of the current population particles by adopting a BAS algorithm, determining the optimal position of the longicorn individuals, and updating the optimal solution and the local optimal solution of the individuals;
c3. iteratively updating the position and the speed of the particle swarm by adopting a PSO algorithm, repeating the step b3, and calculating the optimal solution of the updated population;
d3. when the algorithm reaches the iteration number or the iteration condition is met, stopping searching and outputting the optimal solution, otherwise, continuously repeating the step c3 until the value meeting the convergence criterion is searched.
Referring to fig. 1-9, the method of the present invention will be further described by taking a prototype soft foundation sluice engineering as an example.
Introduction of background: as shown in fig. 2, taking a prototype soft foundation sluice engineering as an example, a scale is made to be 1: 10, a single-hole soft foundation sluice model; this sluice structure is formed by reinforced concrete pouring, and soft base adopts fine sand, gravel and clay to fill, and soft base sets up the restraint of concrete side wall all around, and its basic size is as follows: the length of the sluice is 1.44m, the width is 1.36m, the height is 1.60m, the thickness of the bottom plate is 0.16m, the thickness of the gate pier is 0.16m, the widths of the front working bridge and the rear working bridge are respectively 0.32m and 0.40m, the thickness of the working bridge is 0.04m, the length of the soft foundation is 3.04m, the width is 2.96m, and the height of the foundation is 0.54 m.
Carrying out a vibration response test under artificial pulse excitation on the soft foundation sluice physical model, symmetrically arranging radial acceleration sensors at the left side and the right side of the sluice, and arranging 4 measuring points from left to right at the top of a right side sluice pier, wherein the measuring points are numbered from B1 to B4; 6 measuring points are arranged at the measuring point B4 from top to bottom, the number of the measuring points is B5-B10, the sensor adopts a BY-S07 high-precision vibration sensor, a speed gear is adopted during vibration test, the test frequency response range is 1-100Hz, and the specific arrangement condition is shown in figure 3. In the embodiment, the vibration test is performed under two different manual excitations, and the two different manual excitations are used as a calculation working condition and a verification working condition.
1. Modal parameter identification
Taking the calculation condition as an example, the IVMD is used to perform signal decomposition on the typical measurement point (B7), the mode number is determined to be 4 by using a mutual information method, and the time course of 4 signal components obtained through the IVMD is shown in fig. 4, and the NMIC value thereof is shown in table 1 below.
Table 1B 7 NMIC values for the measured point signal components
As can be seen from table 1, the NMIC value of each signal component is greater than the threshold value of 0.02, which satisfies the decomposition requirement.
The typical measuring point signal components are reconstructed to obtain time-course lines and power spectral density curves before and after noise reduction of the measuring point B7, as shown in fig. 5 and 6, it can be known from fig. 6 that low-frequency noise in the original signal is effectively removed, and the SSI is used for performing modal identification on the noise-reduced signal to obtain vibration modal parameters of the soft foundation sluice, as shown in table 2 below.
TABLE 2 identification results of the parameters of the vibration mode of the sluice
Wherein the natural frequencies of the front fourth order of the sluice are respectively 20.43Hz, 24.78Hz, 60.85Hz and 70.41 Hz; the first order vibration mode is homodromous vibration, the second order vibration mode is reverse vibration, the third order vibration mode is homodromous twisting, and the fourth order vibration mode is reverse twisting; the damping ratios of the respective stages were 3.11%, 0.68%, 1.50% and 0.55%, respectively.
2. Soft foundation sluice finite element model establishment
The difference exists between the arrangement of the water gate reinforcing steel bars and the concrete curing, and the filling materials and the compactness in different areas of the foundation are different, so that the elastic modulus and the density (parameters to be corrected) of the foundation are different. Therefore, the sluice structure is divided into four areas of a bottom plate A, a left sluice pier B, a right sluice pier C and a working bridge D, and the foundation is divided into three areas of an upper layer E, a middle layer F and a lower layer G. The method is characterized in that an ANSYS finite element software is used for establishing a soft foundation sluice finite element model, as shown in figure 7, the periphery and the bottom of a foundation are subjected to normal constraint to simulate the action of a foundation side wall, a working bridge and a gate pier are connected in an overlapping mode, and the finite element model is divided into 91602 units and 106150 nodes.
3. Establishment of support vector machine proxy model
Detecting the elastic modulus and the density of the sluice working bridge D to obtain the elastic modulus and the density of 19.04GPa and 2512kg/m3 respectively, and determining the value ranges of the elastic modulus and the density of other areas of the sluice by taking the elastic modulus and the density as reference; the value ranges for determining the modulus of elasticity and the density of the foundation are shown in the following table 3.
TABLE 3 bullet mode and Density value Range
And (2) randomly generating 750 groups of sample data in the value range of the elastic modulus and the density by adopting LHS, inputting the sample data into a finite element model for modal calculation to obtain 750 groups of frequency and normalized mode-of-oscillation coefficients, wherein 700 groups of data are used as a sample set, and 50 groups of data are used as a test set, so as to establish a corresponding GA-SVR agent model. Taking the frequency and the typical measuring point as an example, the Mean Square Error (MSE), the Mean Absolute Percentage Error (MAPE) and the correlation coefficient (R2) are introduced as evaluation indexes to quantify the fitting accuracy of the GA-SVR proxy model, and the results are shown in tables 4 and 5 below.
TABLE 4 frequency evaluation index
TABLE 5 typical test point normalization vibration mode coefficient evaluation index
4. BAS-PSO optimization algorithm solving
An optimized mathematical model is established based on the formula (17), and is optimized and solved by adopting a BAS-PSO optimization algorithm to obtain elastic modulus and density of each partition of the soft foundation sluice, and the result is shown in the following table 6.
TABLE 6 results of model correction parameter calculation
Comparing the calculation result of the BAS-PSO algorithm with the PSO Algorithm (AWPSO) of the adaptive inertial weight and the BAS algorithm, wherein the comparison result is shown in FIG. 8; it can be seen that the BAS-PSO optimization algorithm has higher accuracy.
5. Finite element model correction result verification
To verify the accuracy of the method of the present invention, the results of the corrections of the elastic modulus and the density were input into a finite element model to obtain frequency comparison results, as shown in table 7 below.
TABLE 7 frequency comparison results
And analyzing by combining the vibration mode comparison result after the finite element model of the soft foundation sluice is corrected as shown in FIG. 9:
from the comparison result, the maximum relative error is-4.75% for the frequency, which indicates that the frequency calculated by the corrected parameters is matched with the frequency of the modal identification in numerical comparison; for the measured point normalized mode shape coefficient, most measured points are well matched in numerical value and rule, the relative error between the identification value and the calculated value is within 12.73%, only three measured point normalized mode shape coefficients are slightly larger, namely the relative error of a first-order B10 measured point is-16.95%, the relative error of a second-order B20 measured point is 22.93%, and the relative error of a fourth-order B19 measured point is-14.38%. In general, the soft foundation sluice calculation modal parameter based on the corrected parameter is well matched with the soft foundation sluice vibration modal parameter, which shows that the method is reasonable and reliable.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the structure of the present invention in any way. Any simple modification, equivalent change and modification of the above embodiments according to the technical spirit of the present invention are within the technical scope of the present invention.
Claims (5)
1. A soft foundation sluice finite element model correction method is characterized by comprising the following steps:
step 1, acquiring actual engineering data of a target soft foundation sluice, performing test point arrangement on the soft foundation sluice, and performing vibration test to obtain a sluice vibration acceleration or dynamic displacement response signal;
step 2, identifying the vibration mode parameters of the soft foundation sluice based on IVMD-SSI: carrying out noise reduction treatment on the sluice vibration response signal based on an improved variational modal decomposition method IVMD, separating and filtering the noise signal from the sluice vibration signal, and reserving structural working characteristic information in the signal; then, identifying the noise-reduced signal by using a random subspace method SSI to obtain a water gate vibration modal parameter;
step 3, establishing a finite element model of the soft foundation sluice by using finite element modeling software according to the actual engineering data of the target soft foundation sluice obtained in the step 1, and determining the structure of the soft foundation sluice and the to-be-corrected parameter partition of the foundation;
step 4, according to the water gate vibration modal parameters and the parameters to be corrected obtained in the step 2 and the step 3, partitioning, constructing a GA-SVR agent model reflecting the nonlinear relation between the parameters to be corrected and the structural modal parameters of the soft foundation water gate, and replacing a finite element model of the soft foundation water gate with the GA-SVR agent model;
and 5, constructing an objective function corrected by a finite element model of the soft foundation sluice by using the minimum relative deviation between the vibration modal parameters of the sluice and the calculation modal parameters of the GA-SVR proxy model established in the step 4, and carrying out optimization solution on the objective function based on the BAS-PSO optimization algorithm to obtain the optimal combination of the parameters to be corrected of the soft foundation sluice.
2. The finite element model modification method of the soft foundation sluice as claimed in claim 1, wherein the identification of the vibration mode parameters of the soft foundation sluice based on IVMD-SSI in the step 2 comprises the following specific steps:
a1. and (3) noise reduction treatment of the actually measured vibration response signal of the soft foundation sluice: the variational modal decomposition VMD, as a multi-component adaptive signal decomposition method, can decompose a vibration signal f into K eigenmode functions (IMF) with limited bandwidths by solving a constrained variational problem, which is described as follows:
in the above formula, δ (t) is dirac distribution; u. ofk′(t) is the kth' IMF; j is a complex unit; omegak′(t) is the center frequency of the kth' IMF; in order to solve the variation constraint model, a secondary penalty factor and a Langrange multiplier are introduced to convert the variation constraint model into an unconstrained variation problem, and the following steps are performed:
in the above formula, α is a secondary penalty factor; λ (t) is LangcangeThe multiplication operator is used for solving the formula (2) in a frequency domain through an alternating direction multiplier algorithm, calculating saddle points of the augmented Langcange function, namely the optimal solution of the formula (1), and continuously and iteratively updating and optimizing uk′、ωk′And λ, thereby achieving signal decomposition;
the K value needs to be preset when the traditional VMD algorithm is used for denoising, the selection of the K value directly influences the accuracy of signal decomposition, in order to avoid the deviation caused by the uncertainty of the K value, the VMD algorithm is improved by utilizing a mutual information method to realize the self-adaptive selection of the K value, and the expression is as follows:
I(XI，YI)＝H′(XI)+H′(YI)-H′(XIYI) (3)
in the above formula, I (XI, YI) is a mutual information coefficient of IMF components XI and YI; h '(XI) and H' (YI) are the entropy of IMF components XI and YI, respectively; h' (XIYI) is the joint entropy of IMF components XI and YI, a normalized mutual information coefficient NMIC of each IMF component is calculated, the threshold value of NMIC is set to be 0.02, when the component is decomposed to the extent that NMIC is smaller than the threshold value, the component is not related to the original signal, the signal is decomposed fully at the moment, and the K value is determined in a self-adaptive mode; b1. identification of vibration modal parameters of the soft foundation sluice: SSI is a method for identifying structural modal parameters by establishing a random state discrete space model, and the basic principle is as follows:
for N measuring points and the data length of each measuring point is l, measuring point response data output by IVMD noise reduction can be formed into a block Hankel matrix of 2Nc multiplied by l:
in the above formula, Y0|c-1And the Hankle matrix block is formed by all measuring points of which the subscript of the 1 st row in the Hankle matrix has the starting time of 0 and the end time of c-1. According to the principle of statistical sequence, when l/c is large enough, l → ∞, the line space of the Hankel matrix is divided into the "past" line space and the "future" line space, and QR decomposition is performed on the Hankle matrix by:
in the above formula, YpastAnd YfutureRespectively representing the "past" and "future" line spaces of the Hankel matrix; r is formed by R2Nc×lIs a lower triangular matrix; q ∈ Rl×lIs an orthogonal matrix; r11，R21，R22∈RNc×Nc；
According to the theory of spatial projection, YfutureLine space in YpastThe orthogonal projection matrix on the formed row space is as follows:
in the above formula, the first and second carbon atoms are,
Moore-Penrose pseudo-inverse as a matrix;
according to the random subspace identification theory, projecting a matrix OcCan be decomposed into a considerable matrix gammacAnd Kalman filtering state vector
The product of (a) is obtained by Singular Value Decomposition (SVD):
in the above formula, U1∈RNc×n；S1∈Rn×n；V1 T∈Rn×l；
The state space equation at this time is:
in the above formula, A1And C1Respectively representing a system matrix and an output matrix, W1And V1Representing the residual error.
Since the Kalman filtering state vector and output are known, and the residual matrix and estimation sequence
Uncorrelated, and the state space equation of equation (9) is solved by least squares to obtain the system matrix A1And output matrix C1。
From the system matrix A1And output matrix C1And identifying the vibration mode parameters of the soft foundation sluice.
3. The finite element model modification method of the soft foundation sluice as claimed in claim 1, wherein the step 3 of constructing the GA-SVR agent model reflecting the nonlinear relationship between the parameters to be modified of the soft foundation sluice and the structural modal parameters comprises the following steps:
a2. determining the variable: setting the modal parameters as dependent variables and setting the parameters to be corrected of the soft foundation sluice as independent variables by taking two parameters of frequency and vibration mode in the working modal parameters of the sluice as modal parameter variables;
b2. generating a sample: generating a parameter sample to be corrected based on a Latin hypersonic sampling method (LHS), and calculating modal parameters of the sluice under different parameter sample combinations to be corrected based on a finite element model;
c2. constructing an optimal hyperplane function: the method comprises the following steps of mapping a parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between parameters to be corrected and modal parameters of the soft foundation sluice by utilizing a linear regressive hyperplane, wherein the basic principle of SVR is as follows:
hypothesis to be modified parameter training sample set
Wherein
The number of training samples is represented, and the optimal hyperplane function is constructed as f '(x) ═ ω'TPhi '(x) + b', wherein omega 'and b' are parameters of the regression model, so that the loss is calculated when the absolute value of the deviation between f '(x) and mop (x) exceeds a certain tolerance range epsilon', and a relaxation variable xi is introduced to avoid the existence of singular points and deviation pointsiAnd
then the SVR optimization problem can be formalized as:
in the above formula, C is a regularization parameter. Lagrange multipliers are introduced to obtain Lagrange functions, and according to optimization conditions, the dual problem of SVR can be converted into the following problem:
taking the radial basis function as the kernel function of the SVR, the regression equation of the SVR is as follows:
in the above formula, σ is a width parameter of the radial basis function;
d2. fitting GA-SVR proxy model: generating a smaller parameter sample set to be corrected by adopting LHS, inputting the sample set into a finite element model to obtain a corresponding modal parameter set, mapping the parameter input space to a high-dimensional space according to a nonlinear mapping principle, fitting a nonlinear mathematical relationship between a parameter to be corrected of the soft foundation sluice and a modal parameter by utilizing a linear regressive hyperplane, and optimizing and solving a regularization parameter C and a kernel function parameter g in the model by utilizing a genetic algorithm, thereby establishing a GA-SVR proxy model representing the nonlinear mathematical relationship between the parameter to be corrected of the soft foundation sluice and the modal parameter and replacing the finite element model with the GA-SVR proxy model.
4. The method for correcting the finite element model of the soft foundation sluice as claimed in claim 1, wherein the finite element model of the soft foundation sluice constructed in the step 5 is used for correcting an objective function, and the expression is as follows:
in the above formula, the first and second carbon atoms are,
ωi(x) Respectively representing the i-th order inherent frequency identification value and the GA-SVR agent model calculation value of the sluice structure;
φij(x) Respectively representing the ith order vibration mode identification value and the GA-SVR agent model calculation value of a measuring point j of the water gate structure; w is ai、wijWeight coefficients respectively representing the frequency and the mode shape coefficient; n is the number of measuring points of the vibration response test; MF is the identified modal order.
5. The finite element model modification method of the soft foundation sluice as recited in claim 1, wherein in step 5, the optimization solution is performed on the objective function based on the BAS-PSO optimization algorithm to obtain the optimal combination of the parameters to be modified of the soft foundation sluice, and the BAS-PSO optimization algorithm comprises the following basic steps:
a3. randomly generating a particle population, defining population parameters and determining a fitness function;
b3. regarding the population particles as longicorn individuals, calculating the fitness value of the current population particles by adopting a BAS algorithm, determining the optimal position of the longicorn individuals, and updating the optimal solution and the local optimal solution of the individuals;
c3. iteratively updating the position and the speed of the particle swarm by adopting a PSO algorithm, repeating the step b3, and calculating the optimal solution of the updated population;
d3. when the algorithm reaches the iteration number or the iteration condition is met, stopping searching and outputting the optimal solution, otherwise, continuously repeating the step c3 until the value meeting the convergence criterion is searched.
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