Construction method of large-scale structure efficient dynamic time history calculation model based on equivalent boundary recognition
By using an equivalent boundary identification method, an efficient dynamic time history calculation model is constructed using response data from small and medium-sized earthquakes. This solves the problems of high calculation cost and low accuracy in seismic analysis of large structures, and achieves efficient and accurate structural dynamic response analysis.
Patent Information
- Application Number
- CN202511496038.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2025-08-15
- Filing Date
- 2025-10-20
- Publication Date
- 2026-01-23
AI Technical Summary
Existing seismic analysis methods for large structures are difficult to accurately simulate nonlinear soil behavior and complex foundation characteristics, resulting in high computational costs and unreliable seismic randomness assessments. Traditional direct SSI analysis methods for large structures are computationally inefficient.
By establishing an efficient dynamic time history calculation model based on equivalent boundary identification, and using small and medium-sized earthquake response data to identify high-precision equivalent boundary conditions, a new calculation model with both computational efficiency and accuracy is constructed, replacing the large foundation degrees of freedom in the traditional model.
It effectively resolves the contradiction between computational cost and accuracy, provides a more efficient and accurate method for structural dynamic response analysis, significantly reduces computation time and storage requirements, and improves the reliability of seismic stochastic assessment.
Smart Images
Figure CN121389749A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to a construction method of a large structure efficient dynamic time-history calculation model based on equivalent boundary identification, and belongs to the technical field of civil engineering structure safety evaluation. BACKGROUND
[0002] The safety of large complex structures such as concrete dams and nuclear power plants under earthquake disasters is crucial to social and economic stability and public safety. The existing large structure seismic analysis method generally uses soil-structure interaction models to calculate the structure response. The existing technology studies the influence of spatial variability of concrete material on the seismic response of the dam, evaluates the safety of high concrete arch dams using different seismic characteristic parameters, and studies the response characteristics of the buried nuclear power plant under different site conditions. However, these studies mainly use linear elastic isotropic assumption to simulate the foundation, and do not fully consider the complex mechanical properties of joint fissures in the rock foundation, resulting in significant differences between the predicted and measured values of the structure dynamic response.
[0003] On the other hand, the existing technology emphasizes the importance of fine simulation of the internal structure of the foundation, analyzes the influence of soil nonlinear dynamic characteristics on the safety of the nuclear island plant through a large model with millions of degrees of freedom, and accurately predicts the seismic response of the Dagangshan arch dam by simulating the propagation path from the source to the structure. However, precise simulation of complex foundations will produce tens of millions of degrees of freedom, combined with the dynamic iteration process of seismic analysis for thousands of steps, resulting in a dramatic increase in calculation cost, leading to a huge amount of seismic analysis calculation (a single seismic record processing may take several hours to several days. Limited by the computational burden, seismic randomness, material parameter uncertainty, structure demand parameters and oblique incidence seismic effects are usually evaluated using only tens of seismic records, which is much less than the hundreds of seismic records commonly used in building structure analysis, severely weakening the reliability of seismic randomness evaluation. Therefore, the current large structure seismic safety research faces two key challenges: (1) it is difficult to accurately simulate the nonlinear soil behavior and complex foundation characteristics; (2) the direct SSI analysis method for large structures is low in computational efficiency, and a solution that balances accuracy and computational cost is urgently needed. SUMMARY
[0004] The application provides a construction method of a large structure efficient dynamic time-history calculation model based on equivalent boundary identification, which overcomes the deficiencies in the prior art. The method uses the small and medium earthquake response data accumulated during the operation of the large structure, establishes a high-precision equivalent boundary condition identification algorithm, and uses optimized equivalent boundary conditions to replace the large foundation degrees of freedom in the traditional model, thereby constructing a new calculation model with both computational efficiency and accuracy.
[0005] The construction method of the large structure efficient dynamic time-history calculation model based on equivalent boundary identification comprises the following steps: Step 1: Establish the finite element model of the structure; Step 2: Extract the stiffness matrix, damping matrix and mass matrix of the finite element model; Step 3: Assume the equivalent boundary conditions and polynomial coefficients of the structure according to the boundary shape of the structure model; Step 4: Solve the equivalent boundary conditions of the structure according to the monitoring response signal, and obtain the corrected polynomial coefficients; Step 5: Calculate the diagonal vector and sub-diagonal vector curves according to the polynomial coefficients; Step 6: Reorganize each diagonal vector into the stiffness, damping and mass matrices of the equivalent boundary conditions; Step 7: Assemble the stiffness, damping and mass matrices corresponding to the boundary node degrees of freedom of the equivalent boundary conditions and the structure model together to generate a high-efficiency calculation model.
[0006] As preferred, the finite element model in step 1 is: , K wherein, C and M are the stiffness, damping and mass matrices, U is the displacement response, F is the external force of the structure.
[0007] As preferred, the stiffness matrix, damping matrix and mass matrix of the finite element model in step 2 are extracted: ; Equation 2 is the dynamic equilibrium equation of the finite element model, in which the superscript s represents the relevant matrix of the structure, and the subscripts B and I represent the boundary nodes and internal nodes, K , C and M are the stiffness, damping and mass matrices, U is the displacement response, F is the external force of the structure, represents the stiffness matrix corresponding to the node degrees of freedom on the boundary of the structure, represents the damping matrix corresponding to the internal node degrees of freedom of the structure.
[0008] As preferred, the mechanical parameters of the matrix diagonal, stiffness, damping and mass, are assumed to be continuously distributed along the spatial coordinates, and a quadratic polynomial is used to fit the distribution curve. Taking the stiffness matrix x-direction main diagonal as an example, the polynomial form is k x0 =a1x2 + a2x + a3, the polynomial coefficient vector S is preliminarily defined, which contains the polynomial coefficients, the stiffness coefficient vector S k , the damping coefficient vector Sc , mass coefficient vector S m ; ; ; ; .
[0009] As preferred, the step 4 is specifically: target response: measured response of structure or calculated response of high-precision global model; target function: minimizing mean square error (MSE) of equivalent model and target response, formula as follows: ; Solve polynomial coefficients S by using river horse algorithm.
[0010] As preferred, the step 5 calculates diagonal vector and sub-diagonal vector curve according to polynomial coefficients: ; ; As preferred, the step 6 reorganizes each diagonal vector into stiffness, damping and mass matrix of equivalent boundary condition: ; ; ; As preferred, the step 7 assembles stiffness, damping and mass matrix of equivalent boundary condition and boundary node freedom degree of structure model together to generate high-efficiency calculation model: ; ; ; .
[0011] Beneficial effects: the large structure high-efficiency calculation model construction method based on boundary condition correction, the method innovatively uses small and medium earthquake response data accumulated during operation of large structure, establishes high-precision equivalent boundary condition identification algorithm, replaces huge foundation freedom degree in traditional model by using optimized equivalent boundary condition, and thus constructs new calculation model with calculation efficiency and precision; the method effectively solves inherent contradiction between calculation cost and precision in soil-structure interaction analysis, and provides new technical approach for large structure dynamic response analysis. BRIEF DESCRIPTION OF DRAWINGS
[0012] Figure 1This is an example of the gravity dam structure and monitoring point layout used in this invention.
[0013] Figure 2 These are the maximum and minimum principal stress envelopes of the efficient calculation model proposed in this invention under seismic excitation.
[0014] Figure 3 This is a schematic diagram of the efficient computational model construction method based on modified equivalent boundary conditions proposed in this invention.
[0015] Figure 4 This is a schematic diagram of the equivalent boundary spring-damped mass system used in this invention.
[0016] Figure 5 This is a schematic diagram of the tridiagonal sparse stiffness matrix of the equivalent boundary conditions used in this invention.
[0017] Figure 6 This is a time history curve of the displacement response and acceleration response at a local observation point using the efficient calculation model proposed in this invention. Detailed Implementation
[0018] The invention will now be further described with reference to the accompanying drawings.
[0019] like Figures 1 to 6 As shown, Figure 1 The gravity dam structure in the text is the object. Figure 1 A finite element model of a gravity dam is presented. The structure has eight nodes at its base, and each node has an equivalent boundary system consisting of springs, dampers, and masses. Five monitoring points, designated AE points, are located on the gravity dam. The responses at these monitoring points serve as the basis for calibrating the equivalent boundary conditions. The meanings of the various parameters are as follows: like Figure 3 As shown, the present invention provides a method for constructing an efficient dynamic time history calculation model for large structures based on equivalent boundary identification, comprising the following steps: Step 1: Establish the finite element model of the structure: ; Step 2: Extract the stiffness matrix, damping matrix, and mass matrix of the finite element model: ; Step 3: Assuming the mechanical parameters stiffness, damping, and mass along the diagonal of the matrix are continuously distributed along the spatial coordinates, a quadratic polynomial is used to fit the distribution curve. Taking the main diagonal of the stiffness matrix in the x-direction as an example, let the polynomial form be k. x0 = a1x 2+a2x + a3, preliminarily define a polynomial coefficient vector S containing polynomial coefficients, a stiffness coefficient vector S k , a damping coefficient vector S c , and a mass coefficient vector S m ; ; ; ; .
[0020] Step 4: Solve the equivalent boundary conditions of the structure according to the monitored response signal, and obtain the corrected polynomial coefficients, specifically: Target response: the measured monitoring response of the structure or the calculated response of the high-precision overall model; target function: minimize the mean square error MSE between the equivalent model and the target response, as follows: ; Solve the polynomial coefficients S using the Rhinoceros algorithm, specifically: 1. Initial parameter setting and population generation: set the core parameters of the algorithm, including population size N (value range 20-50, preferably 30), maximum number of iterations Tmax (value range 100-300, adjust according to the dimension of the polynomial coefficients, preferably 250-300 when the coefficient dimension is greater than 20), search space boundary [lbj, ubj] (determined based on the preliminarily defined polynomial coefficient vector S in step 3, i.e. lbj = Sj - |0.5*Sj|, ubj = Sj + |0.5*Sj|, to ensure a reasonable parameter fluctuation range); generate the initial population X = [X1, X2,..., XN] using random uniform distribution T , where the ith individual Xi = [xi1, xi2,..., xim] T , m is the total number of polynomial coefficients, i.e. the dimension of the vector S, and each dimension parameter xij satisfies xij = lbj + r_0*(ubj-lbj), r0 is a random number between 0 and 1.
[0021] 2. Fitness function calculation: take the target function MSE as the algorithm fitness function, for each individual Xi in the initial population, substitute its corresponding polynomial coefficients into the equivalent model, calculate the displacement response ueq and acceleration response aeq of the equivalent model, and then combine the target responses utarget and atarget to calculate the fitness value f(Xi) = MSE(Xi) of each individual according to formula (7). The smaller the fitness value, the better the polynomial coefficients corresponding to the individual.
[0022] 3. Population update and optimization search: update the population according to the "foraging-moving" behavior mechanism of the conventional Rhinoceros algorithm, specifically including: (1) For each individual Xi, randomly select another individual Xk in the population, if f(Xk) < f(Xi), then individual Xi moves to Xk direction, update formula is Xi new = Xi + r1*(Xk - Xi); if f(Xk) >= f(Xi), then individual Xi moves randomly, update formula is Xi new = lb + r2*(ub - lb), where r1, r2 are random numbers between 0-1, used to simulate the position fluctuation of the hippo random foraging.
[0023] 2. Population optimization stage: calculate the optimal individual Xbest of the current population (the individual with the smallest fitness value), for all individuals Xi, update twice according to the formula Xi new = Xi + r3*(Xbest - Xi), where r3 is a random number between 0-0.8 (regular value, to ensure the population converges to the optimal direction), simulating the behavior of the hippo group gathering in the food-rich area.
[0024] 3. Boundary constraint processing: if the updated individual parameter xij new exceeds the search space [lbj, ubj], adjust it through the boundary reflection mechanism, i.e. xij new = lbj + (ubj - xij new ) (if xij new < lbj) or xij new = ubj - (xij new - ubj) (if xij new > ubj), to ensure the physical rationality of the parameters.
[0025] 4. Iteration termination and optimal coefficient output: repeat the fitness calculation and population update process of steps 2-3 until the maximum iteration number Tmax is reached, or the optimal fitness value changes less than 10 -5 for 10 consecutive iterations (convergence criterion threshold, regular accuracy requirement), at this time output the optimal individual Xbest in the current population, which corresponds to the corrected polynomial coefficients S v .
[0026] Step 5: Calculate the diagonal vector and sub-diagonal vector curves according to the polynomial coefficients: ; ; Similarly, calculate other direction main diagonal (such as k v y0 , k v z0 ), sub-diagonal (such as k v x1 , kv y1 ) and the diagonal vectors of the damping, mass matrix, forming the spatial distribution curve corresponding to each vector pair.
[0027] Step 6: reorganize each diagonal vector into the stiffness, damping, mass matrix of the equivalent boundary condition: ; ; ; Step 7: Assemble the stiffness, damping, mass matrix of the equivalent boundary condition and the boundary node freedom degree of the structure model together to generate a high-efficiency calculation model: ; ; ; ; Step 9: Calculate the equivalent seismic load according to the boundary equivalent condition and the free field motion on the structure boundary, ; Step 10: Calculate the response of the high-efficiency calculation model under the equivalent calculation load, and compare the agreement degree with the benchmark model.
[0028] The present application establishes a high-efficiency calculation model based on the modified boundary condition. In order to illustrate the lightweight characteristics and accuracy of the high-efficiency calculation model in this paper, the present application compares the traditional soil-structure interaction overall model and a rigid restraint model ignoring soil-structure interaction from the aspects of storage advantage and calculation efficiency, as shown in Table 1. From the table, it can be seen that due to the reduction of node number, the equivalent model shows significant advantages in calculation time and memory occupation compared with the overall model, and the storage space is only 22% of the soil-structure interaction model, and the calculation time is shortened by about half.
[0029] Table 1 Advantage of high-efficiency calculation model in storage and calculation time Figure 6 The time history curve of displacement response and acceleration response of the high-efficiency calculation model at the local observation point is shown. From Figure 6 (a) Displacement time history can be seen, the equivalent model is highly consistent with the overall model, while the rigid restraint model appears significant horizontal error at 6 seconds, 8.4 seconds and 12 seconds (peak value reaches 48.6%). From Figure 6 (b) Acceleration time history can be seen, the peak amplitude error of the rigid restraint model is twice that of the overall model, while the equivalent model is only 23%. From Figure 6(c) It can be seen from the Fourier spectrum that the rigid constraint model has a large error in the frequency band above 8 Hz (especially in the vertical direction), while the equivalent model is consistent with the global model in the whole frequency band, which shows that the equivalent boundary condition proposed in this paper can more accurately capture the key interaction mechanisms such as foundation rocking and sliding and high-frequency energy dissipation phenomena, highlighting the key influence of boundary conditions on structural performance.
[0030] Figure 2 The maximum and minimum principal stress envelopes of the three models under seismic excitation are compared. All models exhibit similar stress distribution patterns and comparable stress extreme locations, but there are significant numerical differences. Figure 2 (a) shows that the maximum principal tensile stress of each model appears in the transition zone of the downstream slope. However, the calculated value of the rigid constraint model at this position is overestimated by 0.1 MPa compared to the global model, while the equivalent model is completely consistent with the global model. Similarly, Figure 2 (b) shows that the rigid constraint model underestimates the maximum principal compressive stress in the middle section of the upstream dam by 0.3 MPa compared to the global model, while the equivalent model exhibits excellent accuracy.
[0031] The above is only the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make several improvements and refinements, these improvements and refinements should also be considered within the scope of the present application.
Claims
1. A method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification, characterized in that, The method comprises the following steps: Step 1: establishing a finite element model of the structure; Step 2: extracting a stiffness matrix, a damping matrix and a mass matrix of the finite element model; Step 3: assuming equivalent boundary conditions and polynomial coefficients of the structure according to the boundary shape of the structure model; Step 4: solving the equivalent boundary conditions of the structure according to a monitored response signal, and obtaining modified polynomial coefficients; Step 5: calculating diagonal vectors and sub-diagonal vector curves according to the polynomial coefficients; Step 6: recombining the diagonal vectors into stiffness, damping and mass matrices of the equivalent boundary conditions; Step 7: assembling the stiffness, damping and mass matrices corresponding to the boundary node degrees of freedom of the equivalent boundary conditions and the structure model together to generate a high-efficiency calculation model.
2. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 1, characterized in that: The finite element model in step 1 is: , K where, C and M are the stiffness, damping, mass matrices, U is the displacement response, F is the external force to the structure.
3. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 2, characterized in that: The step 2 extracts the stiffness matrix, the damping matrix and the mass matrix of the finite element model; ； Equation 2 is a finite element dynamic equilibrium equation separating the internal nodes and the boundary nodes of the structure, where the superscript s represents the relevant matrix of the structure, the subscript B and I represent the boundary nodes and the internal nodes, respectively, K , C and M are the stiffness, damping, and mass matrices, respectively, U is the displacement response, F is the external force of the structure, represents the stiffness matrix corresponding to the node degrees of freedom on the boundary of the structure, represents the damping matrix corresponding to the node degrees of freedom inside the structure.
4. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 3, characterized in that: Assuming that the mechanical parameters of stiffness, damping and mass of the matrix diagonal line are continuously distributed along the spatial coordinates, the distribution curve is fitted by a quadratic polynomial. Taking the main diagonal line of the stiffness matrix in the x direction as an example, the polynomial form is k x0 = a1x 2 + a2x + a3, the polynomial coefficient vector S is defined, which contains the polynomial coefficients, the stiffness coefficient vector S k , the damping coefficient vector S c , and the mass coefficient vector S m ; ； ； ； 。 5. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 4, characterized in that: The step 4 is specifically: a target response is a measured monitoring response of the structure or a calculated response of a high-precision overall model; a target function is to minimize mean square error (MSE) between the equivalent model and the target response, and a formula is as follows: ； The hippo algorithm is used to solve the polynomial coefficients S.
6. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 5, characterized in that: The step 5 calculates the diagonal vectors and the sub-diagonal vector curves according to the polynomial coefficients; ； 。 7. The method for constructing a high-efficiency dynamic time-history calculation model of a large-scale structure based on equivalent boundary identification according to claim 6, characterized in that: The step 6 recombines the diagonal vectors into the stiffness, the damping and the mass matrices of the equivalent boundary conditions; ； ； 。 8. The method for constructing a high-efficiency dynamic time-history calculation model of a large structure based on equivalent boundary identification according to claim 7, characterized in that: The step 7 assembles the stiffness, the damping and the mass matrices corresponding to the boundary node degrees of freedom of the equivalent boundary conditions and the structure model together to generate the high-efficiency calculation model. ; ; ; 。