CN115688253A - Bridge full-field dynamic displacement reconstruction method - Google Patents

Bridge full-field dynamic displacement reconstruction method Download PDF

Info

Publication number
CN115688253A
CN115688253A CN202211712377.0A CN202211712377A CN115688253A CN 115688253 A CN115688253 A CN 115688253A CN 202211712377 A CN202211712377 A CN 202211712377A CN 115688253 A CN115688253 A CN 115688253A
Authority
CN
China
Prior art keywords
displacement
bridge
full
strain
field
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202211712377.0A
Other languages
Chinese (zh)
Other versions
CN115688253B (en
Inventor
沈国栋
高傲
程华才
贺文宇
李子兵
束冬林
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Anhui Expressway Engineering Test And Research Center LLC
Hefei University of Technology
Anhui Transport Consulting and Design Institute Co Ltd
Original Assignee
Anhui Expressway Engineering Test And Research Center LLC
Hefei University of Technology
Anhui Transport Consulting and Design Institute Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Anhui Expressway Engineering Test And Research Center LLC, Hefei University of Technology, Anhui Transport Consulting and Design Institute Co Ltd filed Critical Anhui Expressway Engineering Test And Research Center LLC
Priority to CN202211712377.0A priority Critical patent/CN115688253B/en
Publication of CN115688253A publication Critical patent/CN115688253A/en
Application granted granted Critical
Publication of CN115688253B publication Critical patent/CN115688253B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a bridge full-field dynamic displacement reconstruction method, which comprises the following steps: s1, collecting dynamic response data of a bridge; s2, deriving a strain-displacement conversion expression; s3, constructing a displacement modal shape; s4, initializing parameters of the improved particle swarm algorithm; s5, training parameters; s6, order
Figure 124933DEST_PATH_IMAGE001
Is assigned to
Figure 68618DEST_PATH_IMAGE003
Repeating S5 until
Figure 893355DEST_PATH_IMAGE004
To obtain the first
Figure 356828DEST_PATH_IMAGE006
At the time of next iteration
Figure 77659DEST_PATH_IMAGE007
A fitness value of the individual particle; s7, order
Figure 508641DEST_PATH_IMAGE008
Assign to
Figure 605910DEST_PATH_IMAGE006
Repeating the process of S5-S6 until
Figure DEST_PATH_IMAGE009
Obtaining the optimal value of the parameter, namely obtaining the trained first 6-order displacement vibration mode function, and then substituting the function into a strain-displacement conversion expression to predict the full-field displacement; and S8, predicting and evaluating. The bridge full-field dynamic displacement reconstruction method is adopted, and the full-field displacement is indirectly measured through the finite strain sensor, so that the problems that the traditional displacement measurement is limited to finite point measurement and environmental influence, the precision is insufficient, the price is high and the like are effectively solved.

Description

Bridge full-field dynamic displacement reconstruction method
Technical Field
The invention relates to the technical field of bridge monitoring, in particular to a full-field dynamic displacement reconstruction method for a bridge.
Background
In bridge health monitoring, displacement is one of the important indicators reflecting structural stiffness, and is a more common monitoring object, because it provides key information about structural integrity and bridge condition. The existing displacement monitoring mainly comprises two types, the first type is direct measurement technology, such as a linear variable differential sensor, a real-time dynamic global navigation satellite system, an interferometric radar and the like, but the first type is generally limited by factors of environmental influence, insufficient precision, high price and the like, and is difficult to be applied on a large scale. The second category is indirect measurement techniques, such as estimating displacement by strain, etc., however, the technique based on strain-displacement conversion still has the following two problems:
(1) Considering the cost factor, usually only a small number of sensors are used for displacement measurement in a small part of areas, and the displacement of the whole field cannot be obtained, and the measurement of the limited points cannot carry out the whole-field monitoring on the bridge;
(2) The change of the environment of the bridge affects the vibration mode, thereby affecting the relation between strain and displacement. Therefore, the traditional strain-displacement conversion cannot be well adapted to the change of the environment of the bridge.
Disclosure of Invention
The invention aims to provide a bridge full-field dynamic displacement reconstruction method, which is used for indirectly measuring full-field displacement through a limited strain sensor and effectively solving the problems that the traditional displacement measurement is limited to limited point measurement and environmental influence, the precision is insufficient, the price is high and the like. The displacement modal shape is adjusted through modal shape self-learning to adapt to different environments, and the accuracy and robustness of bridge dynamic displacement prediction are improved.
In order to achieve the aim, the invention provides a bridge full-field dynamic displacement reconstruction method, which comprises the following steps:
s1, collecting bridge dynamic response data, wherein the bridge dynamic response data comprises strain, displacement and acceleration response;
s2, deriving a strain-displacement conversion expression;
s3, constructing a displacement modal shape;
s4, initializing parameters of the improved particle swarm algorithm, wherein the parameters comprise the current iteration time T, the population size N, the maximum iteration time T and the particle space dimension D;
s5, training parameters;
s6, order
Figure 552645DEST_PATH_IMAGE001
Assign to
Figure 15463DEST_PATH_IMAGE003
Repeating S5 until
Figure 854106DEST_PATH_IMAGE004
To obtain the first
Figure 338177DEST_PATH_IMAGE006
At the time of next iteration
Figure 604073DEST_PATH_IMAGE007
A fitness value of the individual particle; wherein d is the d-th particle;
s7, order
Figure 478488DEST_PATH_IMAGE008
Assign to
Figure 730609DEST_PATH_IMAGE006
Repeating the process of S5-S6 until
Figure 944553DEST_PATH_IMAGE009
Obtaining an optimal parameter value, namely obtaining a trained first 6-order displacement vibration mode function, and substituting a strain-displacement conversion expression to predict the full-field displacement;
and S8, predicting and evaluating.
Preferably, the S1 specifically includes the following steps:
s11, obtaining bridge parameters, namely the bridge length L, the elastic modulus E, the section moment of inertia I and the linear density rho; dividing the bridge into n units, and numbering 1 node between each unit from left to right in sequence; wherein n is a multiple of 20;
an acceleration sensor and a displacement sensor are arranged at two arbitrary nodes of the bridge for training, and the node positions of the displacement sensors are
Figure 592135DEST_PATH_IMAGE010
,
Figure 94792DEST_PATH_IMAGE011
(ii) a Respectively arranging a displacement sensor at a first node of the bridge and a node where a quartering point is located for verification; on a bridge
Figure 540817DEST_PATH_IMAGE012
A strain sensor is arranged at each node of the position, and the number of the strain sensors is 7;
s12, collecting by adopting an acceleration sensor, a displacement sensor and a strain sensor
Figure 15791DEST_PATH_IMAGE013
Dynamic phase response of seconds, wherein
Figure 498856DEST_PATH_IMAGE014
The response in seconds is: acceleration sensor data at any node in S11
Figure 144601DEST_PATH_IMAGE015
Data of displacement sensor
Figure 128738DEST_PATH_IMAGE016
The data of the strain sensor are sequentially from left to right
Figure 379591DEST_PATH_IMAGE017
(ii) a Finally, the step of
Figure 968310DEST_PATH_IMAGE018
The response in seconds is: displacement data at a first node and at a node at which a bridge quartile is located
Figure 242297DEST_PATH_IMAGE019
The data of the 7 strain sensors are sequentially from left to right
Figure 374332DEST_PATH_IMAGE020
。
Preferably, S2 is specifically:
according to the modal stacking theory, the full-field displacement and strain of the bridge can be represented by mode shape stacking weighted by modal coordinates, as shown in formulas (1) and (2)
Figure 682954DEST_PATH_IMAGE021
（1）
Figure 835718DEST_PATH_IMAGE022
（2）
Wherein the content of the first and second substances,
Figure 190476DEST_PATH_IMAGE023
is the full-field displacement of the bridge,
Figure 250835DEST_PATH_IMAGE024
is the full-field strain of the bridge,
Figure 476280DEST_PATH_IMAGE025
is the full-field displacement mode vibration mode of the bridge,
Figure 960132DEST_PATH_IMAGE026
is the full-field strain mode vibration mode of the bridge,
Figure 474290DEST_PATH_IMAGE027
is a modal coordinate;
the strain of a finite point of a bridge can be represented by mode shape-coordinate-weighted mode shape superposition, as shown in equation (3):
Figure 197396DEST_PATH_IMAGE028
（3）
wherein
Figure 480609DEST_PATH_IMAGE029
Is the strain information of the measuring point(s),
Figure 301409DEST_PATH_IMAGE030
is the modal shape of the strain measurement point;
{ q } yields a compound of formula (4):
Figure 37283DEST_PATH_IMAGE031
（4）
substituting formula (4) into formula (1) results in a strain-displacement transformation as shown in formula (5):
Figure 564080DEST_PATH_IMAGE032
（5）
the relation between the full-field displacement modal shape and the full-field strain modal shape is shown as the formula (6):
Figure 701800DEST_PATH_IMAGE033
（6）
therefore, only the parameter of the displacement modal shape needs to be trained, and the strain data of the measuring point can be realized
Figure 790104DEST_PATH_IMAGE029
Predicting full field displacement of a bridge
Figure 810013DEST_PATH_IMAGE023
。
Preferably, S3 specifically is:
the ith order displacement mode vibration mode is shown as the formula (7);
Figure 281445DEST_PATH_IMAGE034
（7）
in the formula
Figure 398306DEST_PATH_IMAGE035
Is a parameter that needs to be trained and,
Figure 31412DEST_PATH_IMAGE036
is a fixed coefficient in different structures, as shown in formula (8);
Figure 614316DEST_PATH_IMAGE037
（8）
in the formula
Figure 420598DEST_PATH_IMAGE038
Is the ith order natural frequency of the structure; based on the acceleration data measured in S12
Figure 408277DEST_PATH_IMAGE015
Performing fast Fourier transform to obtain a spectrogram, taking the first 6-order natural vibration frequency, and substituting the natural vibration frequency into the formula (7) to obtain the first 6-order displacement mode vibration mode;
for a simply supported beam bridge, the displacement at both ends of the beam is zero according to the boundary conditions, and equations (9) and (10) can be obtained:
Figure 477864DEST_PATH_IMAGE039
（9）
Figure 737944DEST_PATH_IMAGE040
（10）
Figure 426545DEST_PATH_IMAGE041
、
Figure 127785DEST_PATH_IMAGE042
can be composed of
Figure 40377DEST_PATH_IMAGE043
、
Figure 584491DEST_PATH_IMAGE044
Obtaining, therefore, the parameter of the i-th order displacement mode shape to be trained is
Figure 282976DEST_PATH_IMAGE045
First 6 order shift modesThe parameters of the vibration form required to be trained are
Figure 166618DEST_PATH_IMAGE046
。
Preferably, S4 specifically is:
setting the value ranges of the position and the speed of the parameters needing to be trained of the first 6 orders of displacement mode shape in the S3, and randomly initializing the first order
Figure 453374DEST_PATH_IMAGE006
Position of each particle at sub-iteration
Figure 360150DEST_PATH_IMAGE047
And velocity
Figure 639822DEST_PATH_IMAGE048
(ii) a Wherein the content of the first and second substances,
Figure 315654DEST_PATH_IMAGE049
is shown as
Figure 507732DEST_PATH_IMAGE006
At the time of the next iteration
Figure 901804DEST_PATH_IMAGE003
Information on the position of the individual particles,
Figure 719587DEST_PATH_IMAGE050
is shown as
Figure 515505DEST_PATH_IMAGE006
At the time of the next iteration
Figure 878484DEST_PATH_IMAGE003
Velocity information of individual particles, and
Figure 556590DEST_PATH_IMAGE051
，
Figure 787852DEST_PATH_IMAGE052
and
Figure 562910DEST_PATH_IMAGE053
is shown as
Figure 283741DEST_PATH_IMAGE006
At the time of the next iteration
Figure 386826DEST_PATH_IMAGE003
The first particle corresponds to
Figure 28636DEST_PATH_IMAGE054
Two parameters of order displacement mode shape to be trained;
Figure 799145DEST_PATH_IMAGE055
，
Figure 18774DEST_PATH_IMAGE056
。
preferably, the S5 specifically includes the following steps:
s51, initialization
Figure 874735DEST_PATH_IMAGE057
；
S52, initialization
Figure 588744DEST_PATH_IMAGE058
；
First, the
Figure 213760DEST_PATH_IMAGE006
At the time of the next iteration
Figure 807553DEST_PATH_IMAGE003
The first particle corresponds to
Figure 760596DEST_PATH_IMAGE054
Order displacement mode shape
Figure 934089DEST_PATH_IMAGE059
As shown in formula (11):
Figure 148032DEST_PATH_IMAGE060
Figure 256934DEST_PATH_IMAGE061
（11）
thus it is first
Figure 946541DEST_PATH_IMAGE006
At the time of the next iteration
Figure 126987DEST_PATH_IMAGE003
The full-field displacement mode shape and the full-field strain mode shape corresponding to each particle are shown as formulas (12) and (13):
Figure 796435DEST_PATH_IMAGE062
（12）
Figure 997609DEST_PATH_IMAGE063
（13）
in the formula
Figure 659666DEST_PATH_IMAGE064
、
Figure 643802DEST_PATH_IMAGE065
Respectively represent
Figure 956972DEST_PATH_IMAGE006
At the time of the next iteration
Figure 735572DEST_PATH_IMAGE003
The full-field displacement mode vibration mode and the full-field strain mode vibration mode corresponding to each particle;
Figure 71875DEST_PATH_IMAGE066
is m points from left to right on the beam,
Figure 469490DEST_PATH_IMAGE067
；
Figure 778111DEST_PATH_IMAGE068
is the first on the bridge
Figure DEST_PATH_IMAGE069
The location of the individual strain sensors at the location of the strain sensors,
Figure 321088DEST_PATH_IMAGE070
；
bringing the formulae (11) to (13) into the formula (5) to obtain a full-field displacement, wherein in S11
Figure 957737DEST_PATH_IMAGE071
Figure 421692DEST_PATH_IMAGE072
The predicted displacement data of (a) is as shown in equation (14):
Figure 850399DEST_PATH_IMAGE073
（14）；
s53, calculating the first time by using the root mean square error of the following formula (15)
Figure 95436DEST_PATH_IMAGE006
At the time of the next iteration
Figure 344014DEST_PATH_IMAGE003
Fitness function of individual particle
Figure 83431DEST_PATH_IMAGE074
：
Figure 163383DEST_PATH_IMAGE075
（15）
Preferably, S6 specifically is:
improving particle swarm optimization by adopting a compression factor method, wherein individual learning factors
Figure 189108DEST_PATH_IMAGE076
And social learning factor
Figure 49616DEST_PATH_IMAGE077
As shown in formulas (16) and (17):
Figure 514096DEST_PATH_IMAGE078
（16）
Figure 386237DEST_PATH_IMAGE079
（17）
compression factor
Figure 723808DEST_PATH_IMAGE080
As shown in equation (18):
Figure 946979DEST_PATH_IMAGE081
（18）
wherein the content of the first and second substances,
Figure 949570DEST_PATH_IMAGE082
;
improving a particle swarm algorithm by adopting an adaptive inertia weight method shown in the following formula (19);
Figure 613901DEST_PATH_IMAGE083
（19）
in the formula (I), the compound is shown in the specification,
Figure 309325DEST_PATH_IMAGE084
and
Figure 19792DEST_PATH_IMAGE085
respectively represent
Figure 888391DEST_PATH_IMAGE086
The minimum value and the maximum value of (d),
Figure 800370DEST_PATH_IMAGE087
indicating particleThe current fitness value of the child is,
Figure 994591DEST_PATH_IMAGE088
and
Figure 192355DEST_PATH_IMAGE089
average and minimum fitness values for all particles, respectively;
update the second using equations (20) and (21), respectively
Figure 349797DEST_PATH_IMAGE006
At the time of next iteration
Figure 113354DEST_PATH_IMAGE007
The velocity and position of the particles, thereby obtaining
Figure 353843DEST_PATH_IMAGE090
At the time of next iteration
Figure 725654DEST_PATH_IMAGE007
The velocity and position of the particle;
Figure 483526DEST_PATH_IMAGE091
（20）
Figure 304851DEST_PATH_IMAGE092
（21）
in the formula
Figure 840875DEST_PATH_IMAGE093
Is the first
Figure 482072DEST_PATH_IMAGE006
At the time of the next iteration
Figure 246897DEST_PATH_IMAGE003
The updated position and velocity of the individual particles;
Figure 985045DEST_PATH_IMAGE094
is at the first
Figure 567336DEST_PATH_IMAGE006
At the time of the next iteration
Figure 820463DEST_PATH_IMAGE003
Random vectors generated during updating of the particles;
Figure 513613DEST_PATH_IMAGE095
is the first
Figure 919317DEST_PATH_IMAGE003
The best position that the individual particles experience,
Figure 469247DEST_PATH_IMAGE096
is the best position experienced globally.
Preferably, S8 specifically is:
defining a prediction evaluation index
Figure 350616DEST_PATH_IMAGE097
As shown in equation (22):
Figure 706511DEST_PATH_IMAGE098
（22）
in the formula
Figure 356935DEST_PATH_IMAGE099
And
Figure 887886DEST_PATH_IMAGE101
respectively representing the predicted displacement and the displacement reference value; will be last in S1
Figure 53288DEST_PATH_IMAGE018
Data of strain sensor on second bridge
Figure 88240DEST_PATH_IMAGE020
Substituting the trained first 6 th order displacement mode function into formula (5) to predict the first nodeAnd the displacement of the node where the quartet point is located
Figure 983384DEST_PATH_IMAGE102
And calculating a prediction evaluation index, and if the prediction evaluation index meets the requirement, predicting the full-field dynamic displacement.
The bridge full-field dynamic displacement reconstruction method has the advantages and positive effects that:
1. according to the invention, the full-field displacement is accurately predicted through the response of the 7 strain sensors uniformly arranged on the beam bridge, and the problems that the traditional displacement measurement is limited to the measurement of a limited point and is limited by environmental influence, insufficient precision, high price and the like are effectively solved.
2. Under the condition of not interrupting measurement, parameters of displacement modal shape are self-learned and adjusted to adapt to the change of the surrounding environment of the bridge, so that adaptive displacement-strain transformation under the changing environment is obtained, and the displacement prediction has higher accuracy and robustness.
3. Compared with the traditional particle swarm optimization, the improved particle swarm optimization adopts the self-adaptive inertia weight and compression factor method to ensure that the algorithm achieves the effective balance between the global search and the local search, and improves the optimization capability of the population.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a diagram illustrating an embodiment of a bridge full-field dynamic displacement reconstruction method according to the present invention;
FIG. 2 is a schematic diagram of a simply supported bridge according to an embodiment of the full-field dynamic displacement reconstruction method of the present invention;
FIG. 3 is a diagram of an acceleration data spectrum at a 1/4 span position node of a simply supported beam according to an embodiment of a bridge full-field dynamic displacement reconstruction method of the present invention;
FIG. 4 is a diagram illustrating an optimal fitness change according to an embodiment of a bridge full-field dynamic displacement reconstruction method of the present invention;
FIG. 5 is a diagram illustrating a comparison between a reconstructed displacement and a theoretical displacement at a first node on a simply supported beam according to an embodiment of a full-field dynamic displacement reconstruction method for a bridge of the present invention;
FIG. 6 is an enlarged view of a portion of FIG. 5;
FIG. 7 is a diagram illustrating a comparison between a reconstructed displacement and a theoretical displacement at a node where a left quartet point on a simply supported beam is located according to an embodiment of a full-field dynamic displacement reconstruction method for a bridge of the present invention;
FIG. 8 is an enlarged view of a portion of FIG. 7;
FIG. 9 is a diagram illustrating a comparison between a reconstructed displacement and a theoretical displacement at a node at a mid-span position of a simply supported beam in an embodiment of a full-field dynamic displacement reconstruction method for a bridge according to the present invention;
FIG. 10 is an enlarged view of a portion of FIG. 9;
FIG. 11 is a diagram illustrating a comparison between a reconstructed displacement and a theoretical displacement at a node where a right quartet of a simply supported beam is located according to an embodiment of a full-field dynamic displacement reconstruction method for a bridge of the present invention;
fig. 12 is a partially enlarged view of fig. 11.
Detailed Description
The technical solution of the present invention is further illustrated by the accompanying drawings and examples.
Examples
As shown in fig. 1, a method for reconstructing a full-field dynamic displacement of a bridge includes the following steps:
s1, collecting bridge dynamic response data, wherein the bridge dynamic response data comprises strain, displacement and acceleration response.
S1 specifically comprises the following steps:
s11, obtaining bridge parameters, namely the bridge length L, the elastic modulus E, the section moment of inertia I and the density rho; dividing the bridge into n units, and numbering 1 node between each unit from left to right in sequence; wherein n is a multiple of 20.
As shown in FIG. 2, the bridge in this embodiment is a simple-supported bridge with an equal rectangular cross section, the span length of the bridge is 3m, the elastic modulus is 70GPa, and the density is 2700kg/m 3 The linear density is 6.75kg/m, the section width is 0.1m, the height is 0.025m, and the inertia moment is 1.302e-07m 4 . The bridge is divided into 20 plane euler beam units at equal intervals, and 1 node between each unit is numbered from left to right in sequence.
A node at the 1/4 span position of the bridge is provided with aAn acceleration sensor; a displacement sensor is respectively arranged at a node of a 1/4 span position of the bridge; on said bridgex 1 =0.15，x 2 =0.6，x 3 =1.05，x 4 =1.5，x 5 =1.95，x 6 =2.4，x 7 And 7 strain sensors are arranged at nodes of =2.85 respectively.
S12, applying a random load which follows Gaussian distribution at a node at a 1/4 span position for 23 seconds, and collecting by adopting an acceleration sensor, a displacement sensor and a strain sensor
Figure 812800DEST_PATH_IMAGE013
A dynamic phase response of seconds, wherein the response of the first 20 seconds is: acceleration sensor data at 1/4-span node in S11
Figure 278547DEST_PATH_IMAGE104
Figure 278547DEST_PATH_IMAGE104
1/4 node-spanning displacement sensor data
Figure 913928DEST_PATH_IMAGE105
The data of the bridge strain sensor are sequentially from left to right
Figure 273365DEST_PATH_IMAGE017
(ii) a The last 3 seconds response was: displacement data at a first node and at a node at which a bridge quartile is located
Figure 398316DEST_PATH_IMAGE106
(ii) a The data of the 7 strain sensors are sequentially from left to right
Figure 475993DEST_PATH_IMAGE107
。
And S2, deriving a strain-displacement conversion expression.
S2 specifically comprises the following steps:
according to the modal stacking theory, the full-field displacement and strain of the bridge can be represented by mode-coordinate-weighted mode-shape stacking, as shown in formulas (1) and (2)
Figure 915065DEST_PATH_IMAGE021
（1）
Figure 269954DEST_PATH_IMAGE022
（2）
Wherein the content of the first and second substances,
Figure 706751DEST_PATH_IMAGE023
is the full-field displacement of the bridge,
Figure 130780DEST_PATH_IMAGE024
is the full-field strain of the bridge,
Figure 311225DEST_PATH_IMAGE025
is the full-field displacement mode vibration mode of the bridge,
Figure 520621DEST_PATH_IMAGE026
is the full-field strain mode vibration mode of the bridge,
Figure 925057DEST_PATH_IMAGE027
is a modal coordinate;
the strain of a finite point of a bridge can be represented by mode shape-coordinate-weighted mode shape superposition, as shown in equation (3):
Figure 977327DEST_PATH_IMAGE028
（3）
wherein
Figure 820518DEST_PATH_IMAGE029
Is the strain information of the measurement point(s),
Figure 356191DEST_PATH_IMAGE030
is the modal shape of the strain measurement point;
{ q } yields a compound of formula (4):
Figure 134791DEST_PATH_IMAGE031
（4）
substituting formula (4) into formula (1) results in a strain-displacement transformation as shown in formula (5):
Figure 798991DEST_PATH_IMAGE032
（5）
the relation between the full-field displacement modal shape and the full-field strain modal shape is shown as the formula (6):
Figure 321239DEST_PATH_IMAGE033
（6）
therefore, only the parameter of the displacement modal shape needs to be trained, and the strain data of the measuring point can be realized
Figure 505227DEST_PATH_IMAGE029
Predicting full field displacement of a bridge
Figure 251466DEST_PATH_IMAGE023
。
And S3, constructing a displacement mode shape.
S3 specifically comprises the following steps:
the ith order displacement mode vibration mode is shown as the formula (7);
Figure 12749DEST_PATH_IMAGE034
（7）
in the formula
Figure 197742DEST_PATH_IMAGE035
Is a parameter that needs to be trained and,
Figure 718460DEST_PATH_IMAGE036
is a fixed coefficient in different structures, as shown in formula (8);
Figure 838863DEST_PATH_IMAGE037
（8）
in the formula
Figure 477655DEST_PATH_IMAGE038
Is the ith order natural frequency of the structure; acceleration data at the node of the 1/4 span position measured according to S12
Figure DEST_PATH_IMAGE108
Then, a fast fourier transform is performed to obtain a spectrogram, and as shown in fig. 3, the first 6-order natural frequency is taken and the expression (7) is substituted to obtain the first 6-order displacement mode shape.
For a simply supported beam bridge, the displacement at both ends of the beam is zero according to the boundary conditions, and equations (9) and (10) can be obtained:
Figure 420334DEST_PATH_IMAGE039
（9）
Figure 437969DEST_PATH_IMAGE040
（10）
Figure 119486DEST_PATH_IMAGE041
、
Figure 652098DEST_PATH_IMAGE042
can be composed of
Figure 319840DEST_PATH_IMAGE043
、
Figure 67347DEST_PATH_IMAGE044
The parameters required to train the i-th order displacement mode shape are obtained
Figure 529553DEST_PATH_IMAGE045
The first 6 th order displacement mode shape needs to be trained by the parameters
Figure 549461DEST_PATH_IMAGE046
。
S4, initializing parameters of the improved particle swarm algorithm, wherein the parameters comprise the current iteration time T, the population size N =50, the maximum iteration time T =200, and the particle space dimension D =12.
S4 specifically comprises the following steps:
setting the value ranges of the position and the speed of the parameters needing to be trained of the first 6 orders of displacement mode shape in the S3, and randomly initializing the first order
Figure 879948DEST_PATH_IMAGE006
Position of each particle at sub-iteration
Figure 606596DEST_PATH_IMAGE047
And velocity
Figure 302019DEST_PATH_IMAGE048
(ii) a Wherein the content of the first and second substances,
Figure 622274DEST_PATH_IMAGE049
is shown as
Figure 631818DEST_PATH_IMAGE006
At the time of the next iteration
Figure 603185DEST_PATH_IMAGE003
Information on the position of the individual particles,
Figure 407193DEST_PATH_IMAGE050
is shown as
Figure 401694DEST_PATH_IMAGE006
At the time of the next iteration
Figure 815927DEST_PATH_IMAGE003
Velocity information of individual particles, and
Figure 517167DEST_PATH_IMAGE051
，
Figure 616710DEST_PATH_IMAGE052
and
Figure 98507DEST_PATH_IMAGE053
is shown as
Figure 449853DEST_PATH_IMAGE006
At the time of the next iteration
Figure 880966DEST_PATH_IMAGE003
The first particle corresponds to
Figure 292356DEST_PATH_IMAGE054
Two parameters of order displacement mode shape to be trained;
Figure 995869DEST_PATH_IMAGE109
，
Figure 9962DEST_PATH_IMAGE110
。
and S5, training parameters.
S5 specifically comprises the following steps:
s51, initialization
Figure 685794DEST_PATH_IMAGE057
；
S52, initialization
Figure 877872DEST_PATH_IMAGE058
；
First, the
Figure 68682DEST_PATH_IMAGE006
At the time of the next iteration
Figure 761831DEST_PATH_IMAGE003
The first particle corresponds to
Figure 416804DEST_PATH_IMAGE054
Order displacement mode shape
Figure 169996DEST_PATH_IMAGE059
As shown in formula (11):
Figure 926730DEST_PATH_IMAGE060
Figure 954729DEST_PATH_IMAGE061
（11）
thus it is first
Figure 605154DEST_PATH_IMAGE006
At the time of the next iteration
Figure 388302DEST_PATH_IMAGE003
The full-field displacement mode shape and the full-field strain mode shape corresponding to each particle are shown as formulas (12) and (13):
Figure 553704DEST_PATH_IMAGE062
（12）
Figure 588656DEST_PATH_IMAGE063
（13）
in the formula
Figure 700444DEST_PATH_IMAGE064
、
Figure 795439DEST_PATH_IMAGE065
Respectively represent
Figure 448137DEST_PATH_IMAGE006
At the time of the next iteration
Figure 145835DEST_PATH_IMAGE003
The full-field displacement mode vibration mode and the full-field strain mode vibration mode corresponding to each particle;
Figure 505272DEST_PATH_IMAGE066
is m points from left to right on the beam,
Figure 567906DEST_PATH_IMAGE067
；
Figure DEST_PATH_IMAGE111
Figure 724212DEST_PATH_IMAGE112
is the first on the bridge
Figure 491179DEST_PATH_IMAGE114
Figure 767440DEST_PATH_IMAGE116
The location of the individual strain sensors at the location of the strain sensors,
Figure 204238DEST_PATH_IMAGE117
。
substituting the expressions (11) - (13) into the expression (5) to obtain the full-field displacement, wherein the predicted displacement data at the node of 1/4 across positions is shown as the expression (14):
Figure 644577DEST_PATH_IMAGE118
Figure DEST_PATH_IMAGE119
（14）；
s53, calculating the second step by using the following formula (15)
Figure 152919DEST_PATH_IMAGE006
At the time of the next iteration
Figure 752528DEST_PATH_IMAGE003
Fitness function of individual particle
Figure 235593DEST_PATH_IMAGE074
：
Figure 22283DEST_PATH_IMAGE075
（15）
S6, order
Figure 537578DEST_PATH_IMAGE001
Is assigned to
Figure 116327DEST_PATH_IMAGE003
Repeating S5 until
Figure 894927DEST_PATH_IMAGE120
To obtain the first
Figure 312789DEST_PATH_IMAGE006
Fitness value of 50 particles at the time of the second iteration.
S6 specifically comprises the following steps:
improving particle swarm optimization by adopting a compression factor method, wherein individual learning factors
Figure 569458DEST_PATH_IMAGE076
And social learning factor
Figure 2713DEST_PATH_IMAGE077
As shown in formulas (16) and (17):
Figure 748952DEST_PATH_IMAGE078
（16）
Figure 510235DEST_PATH_IMAGE079
（17）
compression factor
Figure 445961DEST_PATH_IMAGE080
As shown in equation (18):
Figure 609089DEST_PATH_IMAGE081
（18）
wherein the content of the first and second substances,
Figure 854126DEST_PATH_IMAGE082
;
improving a particle swarm algorithm by adopting an adaptive inertia weight method shown in the following formula (19);
Figure 165021DEST_PATH_IMAGE083
（19）
in the formula (I), the compound is shown in the specification,
Figure 29072DEST_PATH_IMAGE121
Figure DEST_PATH_IMAGE122
、
Figure 125335DEST_PATH_IMAGE123
Figure 478956DEST_PATH_IMAGE124
respectively represent
Figure 339465DEST_PATH_IMAGE086
The minimum value and the maximum value of (d),
Figure 741627DEST_PATH_IMAGE087
representing the current fitness value of the particle,
Figure 489134DEST_PATH_IMAGE088
and
Figure 13657DEST_PATH_IMAGE089
average and minimum fitness values for all particles, respectively;
update the first and second data using equations (20) and (21), respectively
Figure 971248DEST_PATH_IMAGE006
The velocities and positions of 50 particles in the second iteration, thereby obtaining the second
Figure 567315DEST_PATH_IMAGE090
The velocities and positions of 50 particles at the second iteration;
Figure 293962DEST_PATH_IMAGE091
（20）
Figure 799506DEST_PATH_IMAGE092
（21）
in the formula
Figure 306710DEST_PATH_IMAGE093
Is the first
Figure 316255DEST_PATH_IMAGE006
At the time of the next iteration
Figure 287622DEST_PATH_IMAGE003
The updated position and velocity of the individual particles;
Figure 91630DEST_PATH_IMAGE125
is at the first
Figure 899180DEST_PATH_IMAGE006
At the time of the next iteration
Figure 509153DEST_PATH_IMAGE003
Random vectors generated during updating of the particles;
Figure 475972DEST_PATH_IMAGE095
is the first
Figure 575515DEST_PATH_IMAGE003
The best position that the individual particles experience,
Figure 994995DEST_PATH_IMAGE096
is the best position experienced globally.
S7, order
Figure 143079DEST_PATH_IMAGE008
Is assigned to
Figure 839771DEST_PATH_IMAGE006
Repeating the process of S5-S6 untilTo
Figure 720002DEST_PATH_IMAGE126
Thus, the optimal value of the parameter is obtained, and the trained first 6 orders displacement vibration type functions can be obtained. In the iterative process, the variation of the optimal fitness value is shown in fig. 4. Then, the strain-displacement conversion expression is introduced to predict the full-field displacement.
And S8, predicting and evaluating.
S8 specifically comprises the following steps:
defining a prediction evaluation index
Figure 751412DEST_PATH_IMAGE097
As shown in equation (22):
Figure 906450DEST_PATH_IMAGE098
（22）
in the formula
Figure 379020DEST_PATH_IMAGE099
And
Figure 836677DEST_PATH_IMAGE101
respectively representing the predicted displacement and the displacement reference value; data of the last 3 seconds of the strain sensor on the bridge in the S1
Figure 965170DEST_PATH_IMAGE020
And substituting the trained first 6 th order displacement vibration type function into formula (5) to predict the displacement at the first node and the node at the quartet point
Figure 455057DEST_PATH_IMAGE127
Response to displacement
Figure 375609DEST_PATH_IMAGE106
As a reference value, the reconstructed displacement is compared with the theoretical value, as shown in fig. 5 to 12.
Therefore, the bridge full-field dynamic displacement reconstruction method is adopted, the full-field displacement is indirectly measured through the limited strain sensor, and the problems that the traditional displacement measurement is limited to limited point measurement and environmental influence, the precision is insufficient, the price is high and the like are effectively solved.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.

Claims (8)

1. A bridge full-field dynamic displacement reconstruction method is characterized by comprising the following steps: the method comprises the following steps:
s1, collecting bridge dynamic response data, wherein the bridge dynamic response data comprises strain, displacement and acceleration response;
s2, deriving a strain-displacement conversion expression;
s3, constructing a displacement modal shape;
s4, initializing parameters of the improved particle swarm algorithm, wherein the parameters comprise the current iteration time T, the population size N, the maximum iteration time T and the particle space dimension D;
s5, training parameters;
s6, order
Figure 972871DEST_PATH_IMAGE001
Is assigned to
Figure 864603DEST_PATH_IMAGE003
Repeating S5 until
Figure 48460DEST_PATH_IMAGE004
To obtain the first
Figure 700152DEST_PATH_IMAGE006
At the time of next iteration
Figure 653065DEST_PATH_IMAGE007
A fitness value of the individual particle; wherein d is the d-th particle;
s7, order
Figure 715699DEST_PATH_IMAGE008
Is assigned to
Figure 872005DEST_PATH_IMAGE006
Repeating the process of S5-S6 until
Figure 576655DEST_PATH_IMAGE009
Obtaining the optimal value of the parameter, namely obtaining the trained first 6-order displacement vibration mode function, and then substituting the function into a strain-displacement conversion expression to predict the full-field displacement;
and S8, predicting and evaluating.
2. The bridge full-field dynamic displacement reconstruction method according to claim 1, wherein the S1 specifically comprises the following steps:
s11, obtaining bridge parameters, namely the bridge length L, the elastic modulus E, the section moment of inertia I and the linear density rho; dividing the bridge into n units, and numbering 1 node between each unit from left to right in sequence; wherein n is a multiple of 20;
an acceleration sensor and a displacement sensor are arranged at two arbitrary nodes of the bridge for training, and the node positions of the displacement sensors are
Figure 118495DEST_PATH_IMAGE010
,
Figure 820872DEST_PATH_IMAGE011
(ii) a Respectively arranging a displacement sensor at a first node of the bridge and a node where a quartering point is located for verification; on a bridge
Figure 995632DEST_PATH_IMAGE012
One strain sensor is arranged at each node of the position7 in total;
s12, collecting by adopting an acceleration sensor, a displacement sensor and a strain sensor
Figure 441657DEST_PATH_IMAGE013
Dynamic phase response of seconds, wherein
Figure 838004DEST_PATH_IMAGE014
The response in seconds is: acceleration sensor data at any node in S11
Figure 508019DEST_PATH_IMAGE015
Data of displacement sensor
Figure 184724DEST_PATH_IMAGE016
The data of the strain sensor are sequentially from left to right
Figure 168861DEST_PATH_IMAGE017
(ii) a Finally, the step of
Figure 685293DEST_PATH_IMAGE018
The response in seconds is: displacement data at a first node and at a node at which a bridge quartile is located
Figure 526210DEST_PATH_IMAGE019
The data of the 7 strain sensors are sequentially from left to right
Figure 128093DEST_PATH_IMAGE020
。
3. The bridge full-field dynamic displacement reconstruction method according to claim 2, wherein the S2 specifically is:
according to the modal stacking theory, the full-field displacement and strain of the bridge can be represented by mode shape stacking weighted by modal coordinates, as shown in formulas (1) and (2)
Figure 463390DEST_PATH_IMAGE021
（1）
Figure 834329DEST_PATH_IMAGE022
（2）
Wherein the content of the first and second substances,
Figure 846147DEST_PATH_IMAGE023
is the full-field displacement of the bridge,
Figure 935326DEST_PATH_IMAGE024
is the full-field strain of the bridge,
Figure 74314DEST_PATH_IMAGE025
is the full-field displacement mode vibration mode of the bridge,
Figure 503021DEST_PATH_IMAGE026
is the full-field strain mode vibration mode of the bridge,
Figure 685741DEST_PATH_IMAGE027
is a modal coordinate;
the strain of a finite point of a bridge can be represented by mode shape superposition weighted by mode coordinates, as shown in equation (3):
Figure 262216DEST_PATH_IMAGE028
（3）
wherein
Figure 188584DEST_PATH_IMAGE029
Is the strain information of the measurement point(s),
Figure 19267DEST_PATH_IMAGE030
is the modal shape of the strain measurement point;
{ q } yields a compound of formula (4):
Figure 638468DEST_PATH_IMAGE031
（4）
substituting formula (4) into formula (1) results in a strain-displacement transformation as shown in formula (5):
Figure 702239DEST_PATH_IMAGE032
（5）
the relation between the full-field displacement modal shape and the full-field strain modal shape is shown as the formula (6):
Figure 432297DEST_PATH_IMAGE033
（6）
therefore, only the parameter of the displacement modal shape needs to be trained, and the strain data of the measuring point can be realized
Figure 570018DEST_PATH_IMAGE029
Predicting full field displacement of a bridge
Figure 107922DEST_PATH_IMAGE023
。
4. The bridge full-field dynamic displacement reconstruction method according to claim 3, wherein S3 specifically comprises:
the ith order displacement mode vibration mode is shown as the formula (7);
Figure 393410DEST_PATH_IMAGE034
（7）
in the formula
Figure 927159DEST_PATH_IMAGE035
Is a parameter that needs to be trained and,
Figure 981703DEST_PATH_IMAGE036
is a fixed coefficient in different structures, as shown in formula (8);
Figure 693438DEST_PATH_IMAGE037
（8）
in the formula
Figure 200643DEST_PATH_IMAGE038
Is the ith order natural frequency of the structure; based on the acceleration data measured in S12
Figure 272504DEST_PATH_IMAGE015
Performing fast Fourier transform to obtain a spectrogram, taking the first 6 orders of natural vibration frequency, and substituting the natural vibration frequency into the formula (7) to obtain the first 6 orders of displacement mode vibration modes;
for a simply supported beam bridge, the displacement at both ends of the beam is zero according to the boundary conditions, and equations (9) and (10) can be obtained:
Figure 447133DEST_PATH_IMAGE039
（9）
Figure 516720DEST_PATH_IMAGE040
（10）
Figure 527533DEST_PATH_IMAGE041
、
Figure 137506DEST_PATH_IMAGE042
can be composed of
Figure 432221DEST_PATH_IMAGE043
、
Figure 469447DEST_PATH_IMAGE044
The parameters required to train the i-th order displacement mode shape are obtained
Figure 967556DEST_PATH_IMAGE045
The first 6 th order displacement mode shape needs to be trained by the parameters
Figure 381219DEST_PATH_IMAGE046
。
5. The bridge full-field dynamic displacement reconstruction method according to claim 4, wherein S4 specifically is:
setting the value ranges of the position and the speed of the parameters needing to be trained of the first 6 orders of displacement mode shape in the S3, and randomly initializing the first order
Figure 468124DEST_PATH_IMAGE006
Position of each particle at the time of sub-iteration
Figure 941831DEST_PATH_IMAGE047
And velocity
Figure 910924DEST_PATH_IMAGE048
(ii) a Wherein the content of the first and second substances,
Figure 147520DEST_PATH_IMAGE049
is shown as
Figure 151248DEST_PATH_IMAGE006
At the time of the second iteration
Figure 530277DEST_PATH_IMAGE003
Information on the position of the individual particles,
Figure 2977DEST_PATH_IMAGE050
is shown as
Figure 758444DEST_PATH_IMAGE006
At the time of the next iteration
Figure 616678DEST_PATH_IMAGE003
Velocity information of individual particles, and
Figure 432188DEST_PATH_IMAGE051
，
Figure 126605DEST_PATH_IMAGE052
and
Figure 623446DEST_PATH_IMAGE053
is shown as
Figure 336187DEST_PATH_IMAGE006
At the time of the second iteration
Figure 588177DEST_PATH_IMAGE003
The first particle corresponds to
Figure 19158DEST_PATH_IMAGE054
Two parameters of order displacement mode shape to be trained;
Figure 867159DEST_PATH_IMAGE055
，
Figure 637669DEST_PATH_IMAGE056
。
6. the bridge full-field dynamic displacement reconstruction method according to claim 5, wherein the S5 specifically comprises the following steps:
s51, initialization
Figure 794981DEST_PATH_IMAGE057
；
S52, initialization
Figure 978838DEST_PATH_IMAGE058
；
First, the
Figure 614218DEST_PATH_IMAGE006
At the time of the second iteration
Figure 504814DEST_PATH_IMAGE003
The first particle corresponds to
Figure 580830DEST_PATH_IMAGE054
Order displacement mode shape
Figure 986404DEST_PATH_IMAGE059
As shown in formula (11):
Figure 691054DEST_PATH_IMAGE060
Figure 436156DEST_PATH_IMAGE061
（11）
thus it is first
Figure 935271DEST_PATH_IMAGE006
At the time of the next iteration
Figure 313294DEST_PATH_IMAGE003
The full-field displacement mode shape and the full-field strain mode shape corresponding to each particle are shown as formulas (12) and (13):
Figure 556056DEST_PATH_IMAGE062
（12）
Figure 217982DEST_PATH_IMAGE063
（13）
in the formula
Figure 887998DEST_PATH_IMAGE064
、
Figure 205846DEST_PATH_IMAGE065
Respectively represent
Figure 737453DEST_PATH_IMAGE006
At the time of the next iteration
Figure 253885DEST_PATH_IMAGE003
The full-field displacement mode vibration mode and the full-field strain mode vibration mode corresponding to each particle;
Figure 360381DEST_PATH_IMAGE066
is m points from left to right on the beam,
Figure 962264DEST_PATH_IMAGE067
；
Figure 750091DEST_PATH_IMAGE068
is the first on the bridge
Figure 871762DEST_PATH_IMAGE069
The location of the individual strain sensors at the location of the strain sensors,
Figure 149160DEST_PATH_IMAGE070
；
bringing the formulae (11) to (13) into the formula (5) to obtain a full-field displacement, wherein in S11
Figure 972759DEST_PATH_IMAGE071
Figure 564278DEST_PATH_IMAGE072
The predicted displacement data of (a) is as shown in equation (14):
Figure 789723DEST_PATH_IMAGE073
（14）；
s53, calculating the first time by using the root mean square error of the following formula (15)
Figure 714386DEST_PATH_IMAGE006
At the time of the next iteration
Figure 290860DEST_PATH_IMAGE003
Fitness function of individual particle
Figure 482807DEST_PATH_IMAGE074
：
Figure 562759DEST_PATH_IMAGE075
（15）。
7. The bridge full-field dynamic displacement reconstruction method according to claim 6, wherein S6 specifically is:
improving particle swarm optimization by adopting a compression factor method, wherein individual learning factors
Figure 932691DEST_PATH_IMAGE076
And social learning factor
Figure 730883DEST_PATH_IMAGE077
As shown in formulas (16) and (17):
Figure 195363DEST_PATH_IMAGE078
（16）
Figure 395400DEST_PATH_IMAGE079
（17）
compression factor
Figure 936234DEST_PATH_IMAGE080
As shown in equation (18):
Figure 159405DEST_PATH_IMAGE081
（18）
wherein the content of the first and second substances,
Figure 693154DEST_PATH_IMAGE082
;
improving a particle swarm algorithm by adopting an adaptive inertia weight method shown in the following formula (19);
Figure 544435DEST_PATH_IMAGE083
（19）
in the formula (I), the compound is shown in the specification,
Figure 443121DEST_PATH_IMAGE084
and
Figure 763375DEST_PATH_IMAGE085
respectively represent
Figure 100816DEST_PATH_IMAGE086
The minimum value and the maximum value of (c),
Figure 554406DEST_PATH_IMAGE087
representing the current fitness value of the particle,
Figure 296097DEST_PATH_IMAGE088
and
Figure 290598DEST_PATH_IMAGE089
average and minimum fitness values for all particles, respectively;
update the second using equations (20) and (21), respectively
Figure 916883DEST_PATH_IMAGE006
At the time of next iteration
Figure 211598DEST_PATH_IMAGE007
The velocity and position of the particles, thereby obtaining
Figure 248824DEST_PATH_IMAGE090
At the time of next iteration
Figure 996200DEST_PATH_IMAGE007
The velocity and position of the particle;
Figure 895017DEST_PATH_IMAGE091
（20）
Figure 44239DEST_PATH_IMAGE092
（21）
in the formula
Figure 252366DEST_PATH_IMAGE093
Is the first
Figure 424722DEST_PATH_IMAGE006
At the time of the second iteration
Figure 642076DEST_PATH_IMAGE003
The updated position and velocity of each particle;
Figure 133887DEST_PATH_IMAGE094
is at the first
Figure 840812DEST_PATH_IMAGE006
At the time of the next iteration
Figure 47934DEST_PATH_IMAGE003
Random direction generated when particles are updatedAn amount;
Figure 68979DEST_PATH_IMAGE095
is the first
Figure 927214DEST_PATH_IMAGE003
The best position that the individual particles experience,
Figure 945985DEST_PATH_IMAGE096
is the best position experienced globally.
8. The bridge full-field dynamic displacement reconstruction method according to claim 7, wherein the S8 specifically is:
defining a prediction evaluation index
Figure 889671DEST_PATH_IMAGE097
As shown in equation (22):
Figure 199560DEST_PATH_IMAGE098
（22）
in the formula
Figure 115564DEST_PATH_IMAGE099
And
Figure 101974DEST_PATH_IMAGE101
respectively representing the predicted displacement and the displacement reference value; will be last in S1
Figure 798535DEST_PATH_IMAGE018
Data of strain sensor on second bridge
Figure 895804DEST_PATH_IMAGE020
Substituting the trained first 6-order displacement vibration mode function into formula (5), and predicting the displacement of the first node and the node where the quartet point is located
Figure 666314DEST_PATH_IMAGE102
And calculating a prediction evaluation index, and if the prediction evaluation index meets the requirement, predicting the full-field dynamic displacement.
CN202211712377.0A 2022-12-30 2022-12-30 Bridge full-field dynamic displacement reconstruction method Active CN115688253B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211712377.0A CN115688253B (en) 2022-12-30 2022-12-30 Bridge full-field dynamic displacement reconstruction method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211712377.0A CN115688253B (en) 2022-12-30 2022-12-30 Bridge full-field dynamic displacement reconstruction method

Publications (2)

Publication Number Publication Date
CN115688253A true CN115688253A (en) 2023-02-03
CN115688253B CN115688253B (en) 2023-03-17

Family

ID=85055834

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211712377.0A Active CN115688253B (en) 2022-12-30 2022-12-30 Bridge full-field dynamic displacement reconstruction method

Country Status (1)

Country Link
CN (1) CN115688253B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104457681A (en) * 2014-09-18 2015-03-25 合肥工业大学 Girder structure dynamic deflection monitoring method based on strain mode
US20180246006A1 (en) * 2017-02-27 2018-08-30 Pile Dynamics, Inc. Non-Contact Strain Measurement System And Method For Using The Same
CN113283130A (en) * 2021-04-21 2021-08-20 中国铁路设计集团有限公司 Method for monitoring dynamic deflection of standard beam of 32 meters of high-speed railway based on strain mode
CN114896672A (en) * 2022-06-09 2022-08-12 合肥工业大学 Bridge dynamic displacement reconstruction method based on CSO-BilSTM network

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104457681A (en) * 2014-09-18 2015-03-25 合肥工业大学 Girder structure dynamic deflection monitoring method based on strain mode
US20180246006A1 (en) * 2017-02-27 2018-08-30 Pile Dynamics, Inc. Non-Contact Strain Measurement System And Method For Using The Same
CN113283130A (en) * 2021-04-21 2021-08-20 中国铁路设计集团有限公司 Method for monitoring dynamic deflection of standard beam of 32 meters of high-speed railway based on strain mode
CN114896672A (en) * 2022-06-09 2022-08-12 合肥工业大学 Bridge dynamic displacement reconstruction method based on CSO-BilSTM network

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
邓华夏等: "利用有限测点的振动位移预测全局应变的研究" *

Also Published As

Publication number Publication date
CN115688253B (en) 2023-03-17

Similar Documents

Publication Publication Date Title
Zhang Statistical damage identification for bridges using ambient vibration data
CN109145464B (en) Structural damage identification method integrating multi-target ant lion optimization and trace sparse regularization
CN111324949B (en) Engineering structure flexibility recognition method considering noise influence
Lu et al. Identification of prestress force from measured structural responses
CN112242060B (en) Traffic flow prediction method and apparatus, computer device, and readable storage medium
CN111414977A (en) Weighted integration temperature sensitive point combination selection method for machine tool spindle thermal error modeling
CN104598753A (en) Bridge moving vehicle load recognition method based on Brakhage V method
US20120296616A1 (en) Three-dimensional fluid simulation method
CN110069822B (en) Sensor arrangement method for blade dynamic strain measurement
CN117291072B (en) Bridge damage identification method
CN110533239A (en) A kind of smart city air quality high-precision measuring method
CN107862170A (en) A kind of correction method for finite element model based on dynamic condensation
CN109598027A (en) A kind of algorithm based on frequency response function correcting principle model parameter
JPWO2020065806A1 (en) Processing equipment, processing methods, and programs
Liu et al. A semi-convex function for both constant and time-varying moving force identification
CN116958933A (en) Multi-lane load identification method, system, electronic equipment and storage medium
Shi et al. Damage detection in shear buildings using different estimated curvature
CN115688253B (en) Bridge full-field dynamic displacement reconstruction method
Xiang et al. Vibration-based structural damage identification using P-CNN and time-frequency hybrid index under the conditions of uncertainties and incomplete measurements
Guo et al. Dynamic parameter identification of a high g accelerometer based on BP-PSO algorithm
CN117035001A (en) Conversion force sensor temperature compensation method based on Kriging interpolation
CN115809595A (en) Digital twin model construction method reflecting rolling bearing defect expansion
JP7207531B2 (en) Traffic volume estimation device for each route, traffic volume estimation method for each route, and traffic volume estimation program for each route
JP6578973B2 (en) Tire vibration performance evaluation method and tire simulation apparatus
CN113128053A (en) Nonlinear system parameter identification method, device, equipment and medium

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant