CN109858064A - A kind of dam and foundation elasticity modulus dynamic inversion method based on field test response - Google Patents
A kind of dam and foundation elasticity modulus dynamic inversion method based on field test response Download PDFInfo
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Abstract
The present invention relates to the monitorings of dam operational safety and administrative skill field, in particular to a kind of dam and foundation elasticity modulus dynamic inversion method based on field test response.Vibratory response is surveyed based on dam prototype, the operational modal parameter of dam runtime is identified using the Stochastic subspace identification method for determining rank based on singular entropy, and it is theoretical based on response surface, the response surface model between induced joint and ground subregion bullet mould and modal parameter is constructed, and finite element model is replaced with response surface model；The modal parameter that modal parameter and response surface model based on prototype observation response identification calculate, establish the mathematical model of optimization of dam and ground subregion bullet mould dynamic inversion, optimizing solution is carried out to the mathematical model using genetic algorithm, is finally inversed by each subregion bullet mould optimum combination；This method provides a kind of completely new thinking for the inverting of runtime dam and ground subregion bullet mould.
Description
Technical field
The present invention relates to the monitorings of dam operational safety and administrative skill field, in particular to a kind of be based on prototype
The dam and foundation elasticity modulus dynamic inversion method of vibratory response.
Background technique
The arch dam of the flood relief through dam of China has the characteristics that high water head, big flow, and in flood discharge, high-velocity flow is for arch dam
The influence of operational safety be it is very huge, will cause structural failure when serious.Therefore, the detection of dam reliability and safety evaluation
It studies and is just of great significance for the long-term safety operation for guaranteeing dam.It is examined in induced joint military service condition safety monitoring with health
Disconnected field, the determination of the material parameter of runtime is most important, is the important parameter for measuring structure safe operation.Currently, sharp
It is a kind of reliable method with dam prototype field data inverting runtime dam body and its basement rock material parameter.
Method in relation to carrying out dam parameters inverting using prototype observation data is broadly divided into two kinds: based on static prison
The dam parameters inverting of survey data and material parameter dynamic inversion method based on vibration-testing.Wherein mode of oscillation data
It can preferably reflect structure entirety mechanical characteristics, but for the induced joint of big rigidity, live vibration-testing is more difficult,
And influenced by environmental background noise, the mode of oscillation data of only lower a few ranks are that reliably, still have there are many key technology
Wait break through.In addition, the research for subregion Material Parameters Inversion, relies primarily on numerical simulation and intelligent algorithm to realize, this is logical
A large amount of FEM calculation is often needed, it is computationally intensive, although as the development of concurrent technique, finite element meter has been significantly increased
The efficiency of calculation, but numerical simulation and intelligent algorithm still need many times to complete, and improve meter by response phase method thus
It calculates efficiency and reduces workload.
The invention patent is based on dam prototype and surveys vibratory response, using the Stochastic subspace identification method for determining rank based on singular entropy
Identify the operational modal parameter of dam runtime, and theoretical based on response surface, construct induced joint and ground subregion bullet mould and
Response surface model between modal parameter, and finite element model is replaced with response surface model；Based on prototype observation response identification
The modal parameter that modal parameter and response surface model calculate, establishes the optimization number of dam and ground subregion bullet mould dynamic inversion
Model is learned, optimizing solution is carried out to the mathematical model using genetic algorithm, is finally inversed by each subregion bullet mould optimum combination；This method is
The inverting of runtime dam and ground subregion bullet mould provides a kind of completely new thinking.
Summary of the invention
The purpose of the present invention is to overcome the defects in the prior art, vibratory response is surveyed based on dam prototype, using base
The operational modal parameter of the Stochastic subspace identification method identification dam runtime of rank is determined in singular entropy, and theoretical based on response surface,
The response surface model between induced joint and ground subregion bullet mould and modal parameter is constructed, and finite element is replaced with response surface model
Model；The modal parameter that modal parameter and response surface model based on prototype observation response identification calculate, establishes dam and ground
The mathematical model of optimization of base subregion bullet mould dynamic inversion carries out optimizing solution, inverting to the mathematical model using genetic algorithm
Each subregion bullet mould optimum combination out；This method provides a kind of completely new think of for the inverting of runtime dam and ground subregion bullet mould
Road.
The present invention provides a kind of dam based on prototype observation vibratory response and ground subregion bullet mould dynamic inversion method, leads to
Cross following proposal realization:
A kind of dam and ground subregion bullet mould dynamic inversion method based on prototype observation vibratory response, including walk as follows
It is rapid:
1) field test test is carried out to dam, obtains dam vibration acceleration or dynamic displacement response, by based on unusual
The Stochastic subspace identification method that entropy determines rank carries out Modal Parameter Identification, determines arch dam operational modal parameter；
2) according to prototype engineering design and operational data, dam structure and foundation elasticity modulus subregion are determined, and utilizes finite element
Software establishes dam and ground finite element model；
3) building reflects the response of non-linear relation between dam and each subregion bullet mould parameter of ground and modal parameters
Surface model；
Construction method is as follows:
A. variable is determined: using two parameters of frequency and the vibration shape in dam operational modal parameter as modal parameter variable,
Modal parameter is set as dependent variable, dam and each subregion bullet mould of ground are set as independent variable；
B. it generates sample: being generated based on Latin hypercube experimental method and play mould parameter sample, and based on finite element model
Calculate the dam modal parameter under different bullet this combination of apperance；
C. it constructs Response Face Function: being fitted each subregion bullet mould parameter and dam structure modal parameter using polynomial function
Between non-linear relation, it is as follows to establish response surface equation:
In formula, f (E), φ (E) respectively indicate the intrinsic frequency of dam, node vibration shape value；E indicates to play modulus value；It indicates to become
Number is measured, i.e. bullet mould subregion number.By equation (1) and (2) in pointIt is unfolded with Taylor series formulas,
Then have:
Fully consider the nonlinear function between accurate expression dam and foundation elasticity modulus parameter and modal parameter with
And under the premise of computational efficiency, three rank multinomial response surface models are constructed, which is first four of above-mentioned Taylor series expansion
And do not consider three rank cross terms, it may be expressed as:
In formula,Indicate the bullet modulus value to inverting；For the value bound for playing mould；P indicates big
The pth rank mode on dam, q indicate q-th of measuring point on dam；α and β is response surface equation undetermined coefficient；
D. it is fitted response surface model: based on the response surface equation group played between mould sample value and dam vibration frequency, the vibration shape,
Using Latin Hypercube Sampling experimental design method in the value range for playing mouldInside apperance is rationally effectively played to obtain
This Ei′, inputted as the material parameter of FEM of dam modal calculation, corresponding intrinsic frequency can be acquired by carrying out FEM calculation
Rate fp(Ei′) and node vibration shape value φpq(Ei′), equation (5) and formula (6) are solved using Multiple Regression Analysis Method,
It can be fitted undetermined coefficient α and β, so that it is determined that playing the response surface model of mould dynamic inversion, and finite element model is replaced with this；
E. response surface model precision checking: when being fitted response surface equation, response surface model precision evaluation is to respond face mould
Relative error between type and finite element model is measured, and is chosen that finite element model calculates and response surface model output intrinsic
Frequency fpWith node vibration shape value φpqThe precision of response surface model is calculated, expression formula is as follows:
In formula, e indicates the precision of response surface model, within required precision control 5 ‰；yRSIndicate response surface model mode ginseng
Several output valves；yFEMIndicate the calculated value of finite element model modal parameter.
5) optimization objective function and its solution of mould dynamic inversion are played；
When seeking optimal dam and ground subregion bullet mould parameter inverting, it is based on response surface equation, by constructing target letter
Number J*The relative deviation of modal parameter is calculated to reflect dam on-the-spot test identification mode with response surface model, mould ginseng will be played
Number inverting is expressed as optimization problem, and expression formula is as follows:
In formula,fpRespectively indicate dam structure pth order frequency discre value and response surface model calculated value；φpq
The pth first order mode discre value and response surface equation calculated value of dam structure measuring point q are respectively indicated, N is field test response test
Measuring point number, M is the rank number of mode that is identified.
Objective function is 8. constructed based on formula, carries out optimizing solution in conjunction with genetic algorithm, obtains each subregion bullet of dam and area
Mould optimum combination.
The invention proposes a kind of dams and foundation elasticity modulus dynamic inversion method based on field test response, in conjunction with dam
Field test test, obtain actual measurement modal parameters, and by establish reflection structural division modal parameter and material parameter it
Between response surface model, be based on genetic algorithm, thus obtain most closing to reality operating condition subregion material parameter.The invention is not
More really reflect that the body force scholarship and moral conduct of structure is characterized merely with field test response signal, constructs response surface model also to mention
High inverting efficiency and precision provide a kind of new thinking for the subregion Material Parameters Inversion of runtime dam and ground.
Detailed description of the invention
Fig. 1 is dam and ground subregion bullet mould inversion process figure；
Fig. 2 is arch dam photo；
Fig. 3 is dam prototype vibrating sensor layout drawing in Fig. 2；
Fig. 4 is the dynamic displacement time-histories line of the lower B1 measuring point of operating condition 1 and power spectrum；
Fig. 5 is the dynamic displacement time-histories line of the lower B4 measuring point of operating condition 1 and power spectrum；
Fig. 6 is the dynamic displacement time-histories line of the lower B8 measuring point of operating condition 1 and power spectrum；
Fig. 7 is that 1 lower frequency of operating condition stablizes figure；
Fig. 8 is that 2 lower frequency of operating condition stablizes figure；
Fig. 9 is dam and foundation elasticity modulus block plan；
Figure 10 is FEM of dam model；
Figure 11 is frequency response face precision；
Figure 12 is B1 measuring point vibration shape response surface precision；
Figure 13 is B4 measuring point vibration shape response surface precision；
Figure 14 is B8 measuring point vibration shape response surface precision；
Figure 15 is the first first order mode calculated value and measured value comparison diagram；
Figure 16 is the second first order mode calculated value and measured value comparison diagram；
Figure 17 is third first order mode calculated value and measured value comparison diagram.
Specific embodiment
The preferred embodiment of the invention is further illustrated with reference to the accompanying drawing:
Embodiment one: referring to Fig. 1, Fig. 2.
Fig. 1 is a kind of process that corresponding dam and ground subregion bullet mould inversion method are vibrated based on prototype observation of the present invention
Figure, the present embodiment is by taking certain arch dam as an example, which is the concrete hyperboloid arched dam of dam body aerial drainage, as shown in Figure 2.Arch dams are risen
Journey is 1205m, and maximum height of dam is 240m, and dam crest arc length is 774.65m, and vault subsidence top thickness is 11m, base thickness 55.74m, camber
Than being 3.23, span-depth radio 2.83, thickness high ratio 0.232.In dam crest 2#~38# monolith, a radial direction is arranged every 5 monoliths
Dynamic displacement sensor, number is followed successively by B1~B7 from left to right, for testing radial vibration dynamic respond on arch ring；On the dam 20#
Section is sequentially arranged four sensors along elevation from top to bottom, and number is followed successively by B8~B11, for testing radial vibration on vault subsidence
Dynamic respond, sensor arrangement situation are as shown in Figure 3.Sensor is dynamic displacement sensor, 0.35~150Hz of Hz-KHz, spirit
Sensitivity is 15mv/.00M measurement direction is radial (Y-direction).Signal sampling frequencies 200Hz.Signal acquisition is to motivate condition in aerial drainage
Lower progress, measurement condition is as shown in table 1, and the test data of operating condition 1 is used for dam and each subregion bullet mould parameter inverting of ground, operating condition
2 test data is for the contrast verification with inversion result.
1. field test measurement condition table of table
1) modal idenlification
By taking operating condition 1 as an example, field test test is carried out to dam, obtains dam vibration acceleration or dynamic displacement response, greatly
Dam structure measuring point is distributed in T-shape, and measuring point B8 etc. is typical at centre measuring point B4 at dam abutment measuring point B1, arch ring and vault subsidence surveys
The time-histories line and power spectral density plot figure of point are as shown in figures 4-6.
Modal idenlification is carried out to dam using the stochastic subspace modal identification method for determining rank based on singular entropy, determines arch dam
Operational modal parameter, the modal frequency for obtaining operating condition 1 and the lower dam of operating condition 2 is as shown in table 2, and Mode Shape is as seen in figs. 15-17.
From the point of view of recognition result, under operating condition 1, as shown in frequency stabilization Fig. 7, first three rank working frequency is respectively frequency identification result
1.43Hz, 1.51Hz and 2.13Hz；Under operating condition 2, frequency identification result is as shown in frequency stabilization Fig. 8, first three rank working frequency
Respectively 1.44Hz, 1.52Hz and 2.19Hz.And the first first order mode is along the just symmetrical of vault subsidence direction second under two groups of operating conditions
First order mode is the antisymmetry along vault subsidence direction, and third first order mode is along the just symmetrical of vault subsidence direction, and each rank damping ratio exists
Within 10%.
2. dam operation mode frequency identification result of table
2) according to prototype engineering design and operational data, dam structure and foundation elasticity modulus subregion are determined, and utilizes finite element
Software establishes dam and ground finite element model
According to the dam concrete zoning design figure and dam foundation geology data, the bullet mould entirety subregion of the dam and ground is such as
Shown in Fig. 9, wherein dam body concrete is divided into tri- regions A, B, C, dam Rock be divided into five areas D, E, F, G, H
Domain.Dam concrete density is 2400kg/m3, ground Rock is in FEM calculation by the consideration of massless elastic foundation, dam body
It is as shown in table 3 with the bullet mould parameter design value of each subregion of ground.The finite element model foundation of structure is counted using additional mass method
The influence of the fluid-structure interaction between library water and dam body is calculated, finite element is as shown in Figure 10, and wherein model ground simulation takes
It is worth range and constraint are as follows: depth takes 200m, and upstream takes 124m, and downstream is simulated to cushion pool end, takes 534m, left and right dam abutment takes
100m, finite element model divides altogether 313121 units and 230567 nodes.
3. dam of table and foundation elasticity modulus design value partition table
3) non-thread between building reflection dam and each subregion bullet mould parameter of ground and modal parameters
The response surface model of sexual intercourse；
Construction method is as follows:
A. variable is determined: using two parameters of frequency and the vibration shape in dam operational modal parameter as modal parameter variable,
Modal parameter is set as dependent variable, dam and each subregion bullet mould of ground are set as independent variable；
B. it generates sample: being generated based on Latin hypercube experimental method and play mould parameter sample, and based on finite element model
Calculate the dam modal parameter under different bullet this combination of apperance；
500 groups are randomly selected in 8 subregion bullet mould value intervals using the test design method of Latin Hypercube Sampling
Data refer to each subregion in sampling to extract the parameter combination as close possible to true Dynamic Elastic Module and guarantee fitting precision
It plays mould design value and plays mould with the related literatures of change of external conditions, drafting 8 subregion Dynamic Elastic Module value ranges is
[28.3,42.5], [27.4,41], [26.4,39.6], [28,42], [20,30], [28,42], [16,24], [8,12] are (single
Position: GPa).
C. it constructs Response Face Function: being fitted each subregion bullet mould parameter and dam structure modal parameter using polynomial function
Between non-linear relation, it is as follows to establish response surface equation:
In formula, f (E), φ (E) respectively indicate the intrinsic frequency of dam, node vibration shape value；E indicates to play modulus value；It indicates to become
Number is measured, i.e. bullet mould subregion number.By equation (1) and (2) in pointIt is unfolded with Taylor series formulas,
Then have:
Fully consider the nonlinear function between accurate expression dam and foundation elasticity modulus parameter and modal parameter with
And under the premise of computational efficiency, three rank multinomial response surface models are constructed, which is first four of above-mentioned Taylor series expansion
And do not consider three rank cross terms, it may be expressed as:
In formula,Indicate the bullet modulus value to inverting；For the value bound for playing mould；P indicates big
The pth rank mode on dam, q indicate q-th of measuring point on dam；α and β is response surface equation undetermined coefficient；
D. it is fitted response surface model: based on the response surface equation group played between mould sample value and dam vibration frequency, the vibration shape,
Using Latin Hypercube Sampling experimental design method in the value range for playing mouldInside apperance is rationally effectively played to obtain
This Ei′, inputted as the material parameter of FEM of dam modal calculation, corresponding intrinsic frequency can be acquired by carrying out FEM calculation
Rate fp(Ei′) and node vibration shape value φpq(Ei′), equation (5) and formula (6) are solved using Multiple Regression Analysis Method,
It can be fitted undetermined coefficient α and β, so that it is determined that playing the response surface model of mould dynamic inversion, and finite element model is replaced with this；
500 groups of 8 subregion bullet apperance notebook datas input dam finite model that Latin Hypercube Sampling generates is had
First modal calculation is limited, corresponding 500 groups of first three order frequencies and Data of Mode is extracted, is fitted each point according to the form of formula (5) and (6)
Area bullet mould Ei′With intrinsic frequency fpWith node vibration shape value φpqBetween Response Face Function equation group, acquire response surface equation to
Determine factor alpha and β, and optimal bullet die combination is carried out with the response surface model of fitting substitution finite element model and is solved.
E. response surface model precision checking: when being fitted response surface equation, response surface model precision evaluation is to respond face mould
Relative error between type and finite element model is measured, and is chosen that finite element model calculates and response surface model output intrinsic
Frequency fpWith node vibration shape value φpqThe precision of response surface model is calculated, expression formula is as follows:
In formula, e indicates the precision of response surface model, within required precision control 5 ‰；yRSIndicate response surface model mode ginseng
Several output valves；yFEMIndicate the calculated value of finite element model modal parameter.
4) optimization objective function and its solution of mould dynamic inversion are played；
When seeking optimal dam and ground subregion bullet mould parameter inverting, it is based on response surface equation, by constructing target letter
Number J*The relative deviation of modal parameter is calculated to reflect dam on-the-spot test identification mode with response surface model, mould ginseng will be played
Number inverting is expressed as optimization problem, and expression formula is as follows:
In formula,fpRespectively indicate dam structure pth order frequency discre value and response surface model calculated value；φpq
The pth first order mode discre value and response surface equation calculated value of dam structure measuring point q are respectively indicated, N is field test response test
Measuring point number, M is the rank number of mode that is identified.
Objective function is 8. constructed based on formula, carries out optimizing solution in conjunction with genetic algorithm, obtains each subregion bullet of dam and area
Mould optimum combination.
Response surface model effect in order to guarantee fitting is good, calculates finite element model and response surface model according to formula (7)
Relative error between frequency and the vibration shape evaluates response surface precision, guarantees each order frequency and measuring point vibration shape response surface fitting precision
Within 5 ‰.
Figure 11 indicates the response surface precision of first three rank intrinsic frequency of the arch dam, as seen from the figure, the sound of first three rank intrinsic frequency
The face precision of answering is within 0.5 ‰, and the frequency response surface model of fitting is close to finite element model；Typical position B1, B4 and B8's
As shown in figs. 12-14, within 4 ‰, the vibration shape response surface model of fitting is close to be had precision first three first order mode response surface precision
Limit meta-model；Therefore, the response surface model based on frequency and the vibration shape can replace finite element model for playing mould parameter inverting.
Inversion result:
Inversion process according to figure 1, the dam and ground subregion bullet mould inversion result are as shown in table 4.In order to verify
The accuracy of inversion result will play mould inversion result and input finite element model, is foundation, comparing calculation with dam measurement condition 2
FEM of dam under the operating condition based on inverted parameters calculates modal parameter and dam actual measurement identification modal parameter result.Frequency pair
Than the results are shown in Table 5, vibration shape comparing result is as seen in figs. 15-17.
Table 4. plays mould inversion result
First three the order frequency inverting value of table 5. and calculated value compare
Although having done more detailed elaboration to technical solution of the present invention and having enumerated, it should be understood that for ability
For field technique personnel, modifications to the embodiments described above may be made or uses equivalent alternative solution, this is to those skilled in the art
It is it is clear that these modifications or improvements without departing from theon the basis of the spirit of the present invention, belong to the present invention for member
Claimed range.
Claims (1)
1. a kind of dam and foundation elasticity modulus dynamic inversion method based on field test response, which is characterized in that including walking as follows
It is rapid:
1) field test test is carried out to dam, obtains dam vibration acceleration or dynamic displacement response, by fixed based on singular entropy
The Stochastic subspace identification method of rank carries out Modal Parameter Identification, determines arch dam operational modal parameter；
2) according to prototype engineering design and operational data, dam structure and foundation elasticity modulus subregion are determined, and utilizes finite element software
Establish dam and ground finite element model；
3) building reflects the response face mould of non-linear relation between dam and each subregion bullet mould parameter of ground and modal parameters
Type；
Construction method is as follows:
A. variable is determined: using two parameters of frequency and the vibration shape in dam operational modal parameter as modal parameter variable, by mould
State parameter is set as dependent variable, and dam and each subregion bullet mould of ground are set as independent variable；
B. it generates sample: being generated based on Latin hypercube experimental method and play mould parameter sample, and calculated not based on finite element model
With the dam modal parameter played under this combination of apperance；
C. it constructs Response Face Function: being fitted using polynomial function between each subregion bullet mould parameter and dam structure modal parameter
Non-linear relation, it is as follows to establish response surface equation:
In formula, f (E), φ (E) respectively indicate the intrinsic frequency of dam, node vibration shape value；E indicates to play modulus value；Indicate variable
Number, i.e. bullet mould subregion number.By equation (1) and (2) in pointIt is unfolded with Taylor series formulas, then
Have:
Fully considering nonlinear function and meter between accurate expression dam and foundation elasticity modulus parameter and modal parameter
Under the premise of calculating efficiency, three rank multinomial response surface models are constructed, which is first four of above-mentioned Taylor series expansion and not
Consider three rank cross terms, may be expressed as:
In formula,Indicate the bullet modulus value to inverting；For the value bound for playing mould；P indicates dam
Pth rank mode, q indicate q-th of measuring point on dam；α and β is response surface equation undetermined coefficient；
D. it is fitted response surface model: based on the response surface equation group played between mould sample value and dam vibration frequency, the vibration shape, using
Latin Hypercube Sampling experimental design method is in the value range for playing mouldInside apperance sheet is rationally effectively played to obtain
Ei′, inputted as the material parameter of FEM of dam modal calculation, corresponding intrinsic frequency can be acquired by carrying out FEM calculation
fp(Ei′) and node vibration shape value φpq(Ei′), equation (5) and formula (6) are solved using Multiple Regression Analysis Method, i.e.,
It can be fitted undetermined coefficient α and β, so that it is determined that playing the response surface model of mould dynamic inversion, and finite element model is replaced with this；
E. response surface model precision checking: when being fitted response surface equation, response surface model precision evaluation with response surface model with
Relative error between finite element model is measured, and chooses intrinsic frequency that finite element model calculates and response surface model output
fpWith node vibration shape value φpqThe precision of response surface model is calculated, expression formula is as follows:
In formula, e indicates the precision of response surface model, within required precision control 5 ‰；yRSIndicate response surface model modal parameter
Output valve；yFEMIndicate the calculated value of finite element model modal parameter.
4) optimization objective function and its solution of mould dynamic inversion are played；
When seeking optimal dam and ground subregion bullet mould parameter inverting, it is based on response surface equation, by constructing objective function J*Come
The relative deviation of modal parameter is calculated in reflection dam on-the-spot test identification mode and response surface model, will play mould parameter inverting
It is expressed as optimization problem, expression formula is as follows:
In formula,fpRespectively indicate dam structure pth order frequency discre value and response surface model calculated value；φpqRespectively
Indicate that the pth first order mode discre value and response surface equation calculated value of dam structure measuring point q, N are the survey of field test response test
Point number, M are the rank number of mode that is identified.
Objective function is 8. constructed based on formula, carries out optimizing solution in conjunction with genetic algorithm, obtains each subregion bullet mould of dam and area most
Excellent combination.
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| CN110750928A (en) * | 2019-10-10 | 2020-02-04 | 中冶京诚工程技术有限公司 | Finite element model optimization method and device and electronic equipment |
| CN111090960A (en) * | 2020-01-07 | 2020-05-01 | 中冶京诚工程技术有限公司 | Engineering structure finite element model processing method and device |
| CN111695177A (en) * | 2020-05-14 | 2020-09-22 | 河海大学 | Dam mechanics parameter random inversion method and system based on displacement field monitoring data |
| CN111695177B (en) * | 2020-05-14 | 2022-10-14 | 河海大学 | Dam mechanics parameter random inversion method and system based on displacement field monitoring data |
| CN113033054A (en) * | 2021-03-29 | 2021-06-25 | 河海大学 | PCE _ BO-based structural performance parameter rapid inversion method |
| CN113033054B (en) * | 2021-03-29 | 2022-07-19 | 河海大学 | PCE-BO-based dam structure performance parameter rapid inversion method |
| CN114330067A (en) * | 2021-12-30 | 2022-04-12 | 南昌大学 | Soft foundation sluice finite element model correction method |
| CN115983062A (en) * | 2022-12-08 | 2023-04-18 | 武汉大学 | High arch dam earthquake damage assessment method and system based on finite element model correction |
| CN115983062B (en) * | 2022-12-08 | 2023-09-12 | 武汉大学 | High arch dam seismic damage assessment method and system based on finite element model correction |
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