CN112485030B - Bridge structure dynamic monitoring method, system and equipment based on frequency coupling - Google Patents
Bridge structure dynamic monitoring method, system and equipment based on frequency coupling Download PDFInfo
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Abstract
The invention discloses a bridge structure dynamic monitoring method, a system and equipment based on frequency coupling, the frequency value under a non-damage state and an actually measured acceleration signal are calculated through a finite element model to invert an actually measured frequency value of a bridge structure, and the frequency value and the actually measured acceleration signal are compared, the method identifies the bridge structure as a whole, can effectively predict damage, quickly makes a judgment and timely makes an early warning, and ensures the safety of the bridge structure and the safety of life and property; the empirical mode decomposition can be quickly, simply and directly carried out on a section of unknown signal without pre-analysis and research, the unknown signal is automatically decomposed according to the inherent mode and levels without manual setting and intervention, errors and misjudgment caused by manual intervention are avoided, the high efficiency of real-time monitoring is guaranteed, the precision is not lost, the calculation process is simple, and the method can be applied to various damage prevention of bridge structures.
Description
Technical Field
The invention relates to the field of civil engineering, in particular to a bridge structure dynamic monitoring method, a bridge structure dynamic monitoring system and bridge structure dynamic monitoring equipment based on frequency coupling.
Background
With the progress of society and the development of civil engineering technology, the health monitoring and safety state evaluation of large civil engineering structures, especially large bridge structures, have become the focus of attention in academic and engineering circles at home and abroad at present.
How to invert the working state and health condition of the bridge structure according to the acquired data and signals, establish an accurate finite element model, accurately identify key safety control positions of the structure, and set safety early warning values to prevent structural damage, which is one of the most critical problems in bridge structure health monitoring.
At present, researches on structural damage early warning methods at home and abroad are mainly focused on two aspects of model-based data and data-driven data, wherein the data-driven damage early warning method is based on massive time-course data acquired by a structural health monitoring system, damage is recognized and a safety early warning value is set through nonlinear characteristics of data or structural units derived after relevant change, the main methods comprise a time sequence model method, a wavelet analysis method, hilbert-Huang transform (HHT), a Kalman filter method and the like, the recognition errors of the methods are large, and the calculated safety early warning value cannot truly reflect the actual safety limit of a structure.
Disclosure of Invention
The invention aims to provide a bridge structure dynamic monitoring method based on frequency coupling, and aims to solve the technical problems that in the prior art, the identification error of a structure damage early warning method is large, and the calculated and set safety early warning value cannot truly reflect the actual safety limit of a structure, so that unnecessary false alarm and error are caused.
The embodiment of the invention is realized in such a way that a bridge structure dynamic monitoring method based on frequency coupling comprises the following steps:
establishing a finite element model of a bridge structure, carrying out modal analysis on the finite element model, and obtaining a frequency value omega of the bridge structure in a non-damage state 0 ；
Actually measuring an acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t);
approximately fitting the fitting function u (t) to the natural mode function c (t) by coupling;
calculating an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
according to the frequency value omega of the bridge structure in the non-damage state 0 Obtaining an early warning value phi with the actually measured frequency value omega, and judging whether the bridge structure is damaged or not according to the early warning value phi;
the coupling pair fitting function u (t) is:
u(t)＝G+A sin(ω 0 )-B cos(ω 0 )＝G+H cos(ω 0 +φ 1 )；
wherein, the first and the second end of the pipe are connected with each other,
φ 1 ＝tan -1 (B/A), wherein A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to values of the parameters A and B; a sin (omega) 0 ) And B cos (. Omega.) of 0 ) Are coupled pair functions of each other;
preferably, the step of "actually measuring an acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t)" specifically includes:
actually measuring an acceleration signal a (t) of the bridge structure;
carrying out empirical mode decomposition on the acceleration signal a (t) to obtain an n-order intrinsic mode function;
preferably, the step of "performing empirical mode decomposition on the acceleration signal a (t) to obtain an n-order intrinsic mode function" specifically includes:
setting the actually measured acceleration signal a (t) as a current acceleration signal;
judging whether the number of the upper extreme points and the lower extreme points of the current acceleration signal is more than or equal to 2, if so, entering the next step;
respectively drawing an upper envelope line of an upper extreme point and a lower envelope line of a lower extreme point of the current acceleration signal, and acquiring the mean value of the upper envelope line and the lower envelope line and the mean envelope line thereof;
subtracting the envelope curve of the mean value of the current acceleration signal to obtain a middle signal;
judging whether the difference value between the number of local extreme points and the number of zero-crossing points of the intermediate signal in the whole time range is equal to 0 or 1, and whether the upper envelope line and the lower envelope line of the intermediate signal are locally symmetrical relative to a time axis, if so, entering the next step;
outputting the intermediate signal as an nth-order intrinsic mode function; subtracting the nth order intrinsic mode function from the current acceleration signal to serve as the current acceleration signal, and entering the step of judging whether the number of upper extreme points and lower extreme points of the current acceleration signal is more than or equal to 2;
preferably, the step of "approximately fitting the fitting function u (t) to the natural mode function c (t) by coupling" is specifically:
randomly selecting parameter values of parameters A and B, and approximately fitting a fitting function u (t) according to coupling to a first-order intrinsic mode function c 1 (t)；
Obtaining a coupling pair fitting function u (t) and a first-order intrinsic mode function c 1 Error value e between (t) error ；
Determining the error value e error Whether or not it is equal to or less than the first natural mode function c 1 (t), if the value is r times, entering the step of calculating an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
wherein r is 0.001;
preferably, an error value e is calculated error The formula of (1) is:
e error ＝[u(t)-c 1 (t)] 2 ；
preferably, the formula for calculating the measured frequency value ω is:
preferably, the formula for calculating the early warning value phi is as follows:
when the early warning value phi is larger than or equal to m, the damage of the bridge structure can be determined, and early warning is sent out;
when the early warning value phi is less than m, the bridge structure can be determined to be free of damage;
the value range of m is 3-6%.
Another objective of the embodiments of the present invention is to provide a dynamic monitoring system for a bridge structure based on frequency coupling, where the system includes a modal analysis module, a measured measurement module, a fitting module, a calculation module, and a determination module;
the modal analysis module is connected with the calculation module and the fitting module and used for establishing a finite element model of the bridge structure, carrying out modal analysis on the finite element model and obtaining a frequency value omega of the bridge structure in a non-damage state 0 And the frequency value omega in the non-damage state is used 0 Sending the data to the calculation module and the fitting module;
the actual measurement module is connected with the fitting module and is used for actually measuring the acceleration signal a (t) of the bridge structure, reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t), and sending the inherent modal function c (t) to the fitting module;
the fitting module is connected with the modal analysis module, the actual measurement module and the judgment module and is used for receiving the frequency value omega sent by the modal analysis module in the non-damage state 0 The frequency value acquisition module is also used for receiving the inherent mode function c (t) sent by the actual measurement module and matching the fitting function u (t) and the frequency value omega in the non-damage state through coupling 0 Approximately fitting the inherent modal function c (t), and sending an error value between a coupling pair fitting function u (t) and the inherent modal function c (t) to a judging module; the coupling pair fitting function u (t) is:
u(t)＝G+A sin(ω 0 )-B cos(ω 0 )＝G+H cos(ω 0 +φ 1 )；
wherein the content of the first and second substances,
φ 1 ＝tan -1 (B/A), wherein A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to values of the parameters A and B; a sin (omega) 0 ) And B cos (. Omega.) of 0 ) Are coupled as a function pair;
the calculation module is connected with the judgment module and the modal analysis module and is used for receiving the frequency value omega of the bridge structure in the non-damage state sent by the modal analysis module 0 And receiving the parameter values of the parameters A and B sent by the judging module, calculating the actual measurement frequency value omega of the bridge structure, and calculating the frequency value omega of the bridge structure under the non-damage state according to the frequency value omega of the bridge structure 0 Calculating an early warning value phi with the actually measured frequency value omega, and simultaneously sending the early warning value phi to a judging module;
the judging module is connected with the calculating module and the fitting module and is used for receiving the error value sent by the fitting module and judging whether the error value is less than or equal to r times of the inherent modal function, if so, the parameter values of the parameters A and B corresponding to the coupling pair fitting function u (t) are transmitted to the calculating module; the judgment module is also used for receiving the early warning value phi sent by the calculation module, judging whether the early warning value phi is larger than or equal to m, if so, determining that the bridge structure is damaged, and sending out early warning; if not, determining that the bridge structure is not damaged.
The third purpose of the embodiments of the present invention is to provide a bridge structure dynamic monitoring device based on frequency coupling, where the device includes the bridge structure dynamic monitoring system based on frequency coupling.
The invention has the beneficial effects that:
according to the method, the frequency value under a non-damage state and the actually-measured acceleration signal are calculated through the finite element model to invert the actually-measured frequency value of the bridge structure, and the frequency value and the actually-measured acceleration signal are compared, so that the bridge structure is identified on the whole, damage prediction can be effectively carried out, judgment can be rapidly made, early warning can be timely made, and the safety of the bridge structure and the safety of lives and properties can be ensured; the empirical mode decomposition can be rapidly, simply and directly carried out on a section of unknown signal without carrying out preliminary analysis and research, and the unknown signal is automatically decomposed according to the inherent mode and levels without manual setting and intervention, so that errors and misjudgment caused by manual intervention are avoided; the accuracy of calculation is ensured by selecting a first-order inherent modal function as a fitting object; accurately expressing the actually measured acceleration signal by a function through a signal fitting method; curve fitting is carried out through a least square method, so that the optimal function matching of the data is found, unknown data can be simply and conveniently obtained, the square sum of errors between the unknown data and actual data is minimum, and the calculation accuracy is further improved; according to the fitted parameter values, the actual measurement frequency value is calculated, the damage position and the damage time of the bridge structure can be quickly identified, even real-time damage identification can be realized, and the accuracy is high; the method can effectively and truly reflect the safety limit of the bridge structure, accurately predict the damage of the bridge structure, early warn in advance and prevent the damage in the future by calculating the early warning value phi through the frequency value and the actually measured frequency value in a non-damaged state.
Drawings
FIG. 1 is a flow chart of a dynamic monitoring method for a bridge structure based on frequency coupling according to the present invention;
FIG. 2 is a flow chart of empirical mode decomposition;
FIG. 3 is a flow chart of a coupling-to-fit function fitting a natural mode function;
FIG. 4 is a schematic diagram of an arrangement of acceleration sensors of a bridge structure;
FIG. 5 is a schematic structural diagram of a dynamic bridge structure monitoring system based on frequency coupling according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and examples, and for convenience of description, only parts related to the examples of the present invention are shown. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example one
Fig. 1 is a flow chart of a dynamic monitoring method for a bridge structure based on frequency coupling according to the present invention, and the method includes the following steps:
s101, establishing a finite element model of the bridge structure, carrying out modal analysis on the finite element model, and obtaining a frequency value omega of the bridge structure in a non-damage state 0 ；
The finite element model is a model established by using a finite element analysis method, is a group of element combinations which are only connected at nodes, only transmit force by virtue of the nodes and are only restrained at the nodes, is a discretization result of a mechanical model and is a digital model for numerical calculation;
a bridge structure finite element model can be established through analysis software such as ANSYS and the like, modal analysis is carried out on the bridge structure according to the finite element model, and therefore the frequency value omega of the bridge structure in a non-damage state is obtained through calculation 0 I.e. the calculated structural frequency characteristic omega 0 ；
S102, actually measuring an acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain a natural mode function c (t);
the method comprises the following steps of obtaining an acceleration signal a (t) of the bridge structure through actual measurement of a bridge health monitoring system, reconstructing the actual measurement acceleration signal a (t) based on a coupling pair decomposition method, and obtaining an inherent modal function c (t), wherein the specific method comprises the following steps:
s1021, actually measuring an acceleration signal a (t) of the bridge structure;
in the uniform variable speed linear motion, the ratio of the speed change v to the used time t is called the acceleration, is the ratio of the speed change amount to the time used for the change, is a physical quantity for describing the speed change speed of an object, is generally expressed by a, and has the international unit of meter/square second; the acceleration has magnitude and direction and is a vector; the acceleration is related to the speed change and the time length of the speed change, but is not related to the speed; in kinematics, the acceleration of an object is in direct proportion to the resultant force of a received external force, and is in inverse proportion to the mass of the object, and the direction of the acceleration is the same as the direction of the resultant external force;
s1022, carrying out empirical mode decomposition on the acceleration signal a (t) to obtain an n-order inherent mode function c 1 (t)、c 2 (t)、c 3 (t)……c n (t)；
Wherein n is more than or equal to 1;
fig. 2 is a flowchart of empirical mode decomposition, which includes the following specific steps:
step S1, setting an actually measured acceleration signal a (t) as a current acceleration signal;
the acceleration signal is a time-course frequency curve and comprises an upper extreme point and a lower extreme point;
step S2, judging whether the number of the upper extreme points and the lower extreme points of the current acceleration signal is more than or equal to 2, if so, entering step S3, and if not, entering step S8;
when the number of the upper extreme points and the lower extreme points is less than 2, the acceleration signal is a monotonous frequency curve, and has no significance of empirical mode decomposition and no value of judging damage of a bridge structure, so that the empirical mode decomposition is finished, and a next actually measured acceleration signal is waited to be obtained;
s3, respectively drawing an upper envelope line of an upper extreme point and a lower envelope line of a lower extreme point of the current acceleration signal, and acquiring the mean value of the upper envelope line and the lower envelope line and the mean envelope line thereof;
the mean envelope curve is an envelope curve corresponding to the mean value of the upper envelope curve and the lower envelope curve;
s4, subtracting the envelope curve of the mean value of the current acceleration signal to obtain an intermediate signal;
step S5, judging whether the difference value between the number of local extreme points and the number of zero-crossing points of the intermediate signal in the whole time range is equal to 0 or 1, and whether the upper envelope curve and the lower envelope curve of the intermediate signal are locally symmetrical relative to a time axis (namely, the average value of the upper envelope curve formed by the local extreme points and the lower envelope curve formed by the local minimum points of the intermediate signal at any time point is zero), if so, entering the step S7; if not, the step S6 is carried out;
step S6, taking the intermediate signal as a current acceleration signal, and entering step S2;
s7, outputting the intermediate signal as an nth order intrinsic mode function; subtracting the nth order intrinsic mode function from the current acceleration signal to serve as a current acceleration signal, and entering a step S2;
n is an ordered positive integer, the initial value is 1, and n is added with 1 every time the n is output;
wherein the inherent mode function of the first output is a first-order inherent mode function, the inherent mode function of the second output is a second-order inherent mode function, and so on, and the description is omitted;
s8, finishing the empirical mode decomposition;
in physics, if the instantaneous frequency is meaningful, the function must be symmetric, have a local mean of 0, and have the same number of zero crossings and extremal points;
after the empirical mode decomposition is finished, n-order intrinsic mode functions are output in sequence, namely c 1 (t)、c 2 (t)、c 3 (t)……c n (t)；
Each order of natural mode function represents a natural mode component present in the acceleration signal a (t), wherein c 1 (t) is a first order intrinsic mode function; c. C 2 (t) is the second order natural mode function, and so on, c n (t) is the nth order natural mode function;
in the empirical mode decomposition process, the empirical mode decomposition can be quickly, simply and directly carried out on a section of unknown signals without pre-analysis and study, and the empirical mode decomposition is automatically carried out according to the inherent mode and levels without manual setting and intervention; any signal can be split into the sum of a plurality of intrinsic mode functions;
s103, approximately fitting the fitting function u (t) with the inherent modal function c (t) through coupling;
the embodiment selects the fitting object as a first-order intrinsic mode function c 1 (t) (i.e. the first connotative modal component) to ensure the accuracy of the calculation, and accurately and functionally representing the measured acceleration signal by a signal fitting method;
fig. 3 is a flowchart illustrating the process of fitting the natural mode function to the fitting function by coupling, specifically:
s1031, randomly selecting parameter values of the parameters A and B, and approximately fitting a first-order intrinsic mode function c according to a coupling pair fitting function u (t) 1 (t), the coupling pair fitting function u (t) fitting formula is:
u(t)＝G+A sin(ω 0 )-B cos(ω 0 )＝G+H cos(ω 0 +φ 1 )
wherein the content of the first and second substances,
φ 1 ＝tan -1 (B/A), wherein A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to values of the parameters A and B; a sin (omega) 0 ) And B cos (. Omega.) of 0 ) Are coupled pair functions of each other;
s1032, acquiring a coupling pair fitting function u (t) and a first-order intrinsic mode function c 1 Error value e between (t) error The concrete formula is as follows:
e error ＝[u(t)-c 1 (t)] 2
s1033, determining the error value e error Whether or not it is equal to or less than first-order natural mode function c 1 (t), if r is multiple, go to step S104; if not, the step S1031 is carried out;
randomly selecting different arbitrary values A and B, and performing trial calculation continuously to enable a coupling pair fitting function u (t) and a first inherent modal function c 1 Error value e between (t) error ≤r×c 1 (t) where r is a number less than 0, preferably 0.001-0.002, most preferably r =0.001, when the error value e is error When the above conditions are met, the numerical values corresponding to A and B meeting the conditions are used as the parameter values of the actual measurement frequency value omega of the bridge structure;
in the step, different arbitrary values A and B can be randomly selected through a least square method, and trial calculation is continuously carried out, so that the optimal function matching of the data is found, and unknown data can be simply and conveniently obtained, so that the sum of squares of errors between the unknown data and actual data is minimum;
the least squares method (also known as the least squares method) is a mathematical optimization technique;
s104, calculating an actual measurement frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
the parameter values refer to parameter values of the parameters a and B which satisfy the judgment condition of step S1033;
the formula for calculating the measured frequency value ω is:
where dt is the increment of t;
s105, according to the frequency value omega of the bridge structure in the non-damage state 0 Obtaining an early warning value phi with the actually measured frequency value omega, and judging whether the bridge structure is damaged or not according to the early warning value phi;
according to ANSYS analysis software meterCalculating to obtain frequency value omega under non-damage state 0 And calculating an early warning value phi based on an actually measured frequency value omega obtained by the actually measured acceleration signal a (t), wherein the formula is as follows:
when the early warning value phi is larger than or equal to m, the damage of the bridge structure can be determined, and early warning is sent out;
when the early warning value phi is less than m, the bridge structure can be determined to be free of damage;
m is 3% -6%, preferably 5%, and a large number of experiments prove that the early warning value phi is 5%, so that the safety limit of the bridge structure can be effectively and truly reflected, the damage of the bridge structure can be accurately predicted, and early warning is carried out in advance;
if the bridge structure to be monitored is an arch bridge, as shown in fig. 4, a schematic layout diagram of acceleration sensors of the bridge structure is shown, where the acceleration sensors 1 (circle positions in the drawing) may be disposed on the tops of arch ribs, longitudinal beams or tie bars, wind braces, vertical bars, etc. of the arch bridge, the number of the acceleration sensors 1 may be set according to the situation, and other acceleration sensors may be added as needed.
The bridge structure dynamic monitoring method based on frequency coupling comprises the steps of establishing a bridge structure finite element model, carrying out modal analysis on the finite element model, and obtaining a frequency value omega of the bridge structure in a non-damage state 0 (ii) a Actually measuring an acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t); approximately fitting the fitting function u (t) to the natural mode function c (t) by coupling; calculating an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t); according to the frequency value omega of the bridge structure in the non-damage state 0 Obtaining an early warning value phi together with the actually measured frequency value omega, and judging whether the bridge structure is damaged or not according to the early warning value phi; the method comprises the steps of calculating a frequency value under a non-damage state and an actually measured frequency value of the bridge structure through a finite element model, inverting the actually measured frequency value and the actually measured acceleration signal to obtain an actually measured frequency value of the bridge structure, and comparing the actually measured frequency value and the actually measured acceleration signalThe bridge structure is identified on the body, damage prediction can be effectively carried out, judgment can be quickly made, early warning can be timely made, and the safety of the bridge structure and the safety of lives and properties can be ensured; the empirical mode decomposition can be rapidly, simply and directly carried out on a section of unknown signal without carrying out preliminary analysis and research, and the unknown signal is automatically decomposed according to the inherent mode and levels without manual setting and intervention, so that errors and misjudgment caused by manual intervention are avoided; the accuracy of calculation is ensured by selecting a first-order inherent modal function as a fitting object; accurately expressing the actually measured acceleration signal by a function through a signal fitting method; curve fitting is carried out through a least square method, so that the optimal function matching of the data is found, unknown data can be simply and conveniently obtained, the square sum of errors between the unknown data and actual data is minimum, and the calculation accuracy is further improved; according to the fitted parameter values, the actual measurement frequency value is calculated, the damage position and the damage time of the bridge structure can be quickly identified, even real-time damage identification can be realized, and the accuracy is high; the method can effectively and truly reflect the safety limit of the bridge structure, accurately predict the damage of the bridge structure, early warn in advance and prevent the damage in the future by calculating the early warning value phi through the frequency value in a non-damage state and the actually measured frequency value.
Example two
FIG. 5 is a schematic structural diagram of a dynamic bridge structure monitoring system based on frequency coupling according to the present invention, where the system includes a modal analysis module, an actual measurement module, a fitting module, a calculation module, and a determination module;
the modal analysis module is connected with the calculation module and the fitting module and is used for establishing a finite element model of the bridge structure, carrying out modal analysis on the finite element model and obtaining a frequency value omega of the bridge structure in a non-damage state 0 And the frequency value omega in the non-damage state is used 0 Sending the data to the calculation module and the fitting module;
the finite element model is a model established by using a finite element analysis method, is a group of element combinations which are only connected at nodes, only transmit force by virtue of the nodes and are only restrained at the nodes, is a discretization result of a mechanical model and is a digital model for numerical calculation;
a bridge structure finite element model can be established through ANSYS and other analysis software, modal analysis is carried out on the bridge structure according to the finite element model, and therefore the frequency value omega of the bridge structure in a non-damage state is calculated and obtained 0 (i.e., the structural frequency characteristic ω 0 )；
The actual measurement module is connected with the fitting module and used for actually measuring the acceleration signal a (t) of the bridge structure, reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t) and sending the inherent modal function c (t) to the fitting module; as shown in fig. 4, the actual measurement module may be disposed on the top of an arch rib, a longitudinal beam or a tie bar, a wind brace, a vertical rod, etc. of the arch bridge, the number of the acceleration sensors 1 may be disposed as appropriate, for example, at the position of a circle in fig. 4, and other acceleration sensors may be added as needed;
the method comprises the following steps of actually measuring and obtaining an acceleration signal a (t) of the bridge structure through a bridge health monitoring system, reconstructing the actually measured acceleration signal a (t) based on a coupling pair decomposition method, and thus obtaining an inherent modal function c (t), which specifically comprises the following steps:
actually measuring an acceleration signal a (t) of the bridge structure;
in the uniform variable speed linear motion, the ratio of the speed change v to the used time t is called the acceleration, is the ratio of the speed variation to the time used for the change, is a physical quantity for describing the speed change of an object, is usually expressed by a, and has the international unit of meter/quadratic second; the acceleration has magnitude and direction and is a vector; the acceleration is related to the speed change and the time length of the speed change, but is not related to the speed; in kinematics, the acceleration of an object is in direct proportion to the magnitude of resultant force of a received external force, and is in inverse proportion to the mass of the object, and the direction of the resultant force is the same as that of the external force;
performing empirical mode decomposition on the acceleration signal a (t) to obtain an n-order inherent mode function c 1 (t)、c 2 (t)、c 3 (t)……c n (t)；
Wherein n is more than or equal to 1;
in physics, if the instantaneous frequency is meaningful, the function must be symmetric, have a local mean of 0, and have the same number of zero crossings and extrema;
after the empirical mode decomposition is finished, n-order intrinsic mode functions are output in sequence, namely c 1 (t)、c 2 (t)、c 3 (t)……c n (t)；
Each order of natural mode function represents a natural mode component present in the acceleration signal a (t), wherein c 1 (t) is a first order intrinsic mode function; c. C 2 (t) is the second order natural mode function, and so on, c n (t) is the nth order natural mode function;
in the empirical mode decomposition process, the empirical mode decomposition can be quickly, simply and directly carried out on a section of unknown signals without pre-analysis and study, and the empirical mode decomposition is automatically carried out according to the inherent mode and levels without manual setting and intervention; any signal can be split into the sum of a plurality of intrinsic mode functions;
the fitting module is connected with the modal analysis module, the actual measurement module and the judgment module and is used for receiving the frequency value omega sent by the modal analysis module in the non-damage state 0 The frequency value acquisition module is also used for receiving the inherent mode function c (t) sent by the actual measurement module and matching the fitting function u (t) and the frequency value omega in the non-damage state through coupling 0 Approximately fitting the inherent modal function c (t), and sending an error value between a coupling pair fitting function u (t) and the inherent modal function c (t) to a judging module;
in this embodiment, the fitting module selects a fitting object as a first-order natural mode function c 1 (t) (i.e. the first content modal component) to ensure the accuracy of the calculation, and accurately functionally representing the measured acceleration signal by a signal fitting method;
the fitting module randomly selects parameter values of the parameters A and B, and approximately fits a first-order natural mode according to a coupling pair fitting function u (t)Function c 1 (t); the coupling pair fitting function u (t) is fitted by the following formula:
u(t)＝G+A sin(ω 0 )-B cos(ω 0 )＝G+Hcos(ω 0 +φ 1 )
wherein the content of the first and second substances,
φ 1 ＝tan -1 (B/A), wherein the parameters A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to the values of A and B; a sin (omega) 0 ) And B cos (ω) 0 ) Are coupled as a function pair;
the fitting module obtains a coupling pair fitting function u (t) and a first-order natural modal function c 1 Error value e between (t) error ，e error ＝[u(t)-c 1 (t)] 2 ；
The fitting module is further configured to apply an error value e error Transmitting to a judging module;
the judging module is connected with the calculating module and the fitting module and is used for receiving the error value sent by the fitting module and judging whether the error value is less than or equal to r times of the inherent modal function, if so, the parameter values of the parameters A and B corresponding to the coupling pair fitting function u (t) are transmitted to the calculating module;
in this embodiment, the determining module receives the coupling pair fitting function u (t) and the first-order intrinsic mode function c sent by the fitting module 1 Error value e between (t) error And determining the error value e error Whether the value is less than or equal to r times of the first-order inherent modal function, if so, transmitting the values of the parameters A and B corresponding to the coupling pair fitting function u (t) to a calculation module;
the fitting module randomly selects parameter values of the parameters A and B, and conducts trial calculation continuously to enable the fitting function u (t) and the first inherent modal function c to be coupled 1 Error value e between (t) error ≤r×c 1 (t) where r is a number less than 0, preferably 0.001-0.002, most preferably r =0.001, when the error value e error When the above conditions are satisfied, the composition satisfies the conditionsA. The numerical value corresponding to B is used as a parameter value of an actually measured frequency value omega of the bridge structure;
the fitting module randomly selects parameter values of the parameters A and B through a least square method, and conducts trial calculation continuously, so that the best function matching of the data is found, unknown data can be obtained simply and conveniently, and the square sum of errors between the unknown data and actual data is minimum;
the least squares method (also known as the least squares method) is a mathematical optimization technique;
the judgment module is also used for receiving the early warning value phi sent by the calculation module, judging whether the early warning value phi is larger than or equal to m, if so, determining that the bridge structure is damaged, and sending out early warning; if not, determining that the bridge structure is not damaged;
the calculation module is connected with the judgment module and the modal analysis module and is used for receiving the frequency value omega of the bridge structure in the non-damage state sent by the modal analysis module 0 And receiving the values of the parameters A and B sent by the judging module, calculating the actual measurement frequency value omega of the bridge structure, and calculating the frequency value omega of the bridge structure under the non-damage state according to the frequency value omega of the bridge structure 0 Calculating an early warning value phi with the actually measured frequency value omega, and simultaneously sending the early warning value phi to a judging module;
the calculation module calculates an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
the parameter values refer to values of the parameters a and B that satisfy the judgment condition of step S1033;
the formula for calculating the measured frequency value ω is:
where dt is the increment of t;
the calculation module is used for calculating the frequency value omega of the bridge structure in the non-damage state 0 Planning an early warning value phi with the actually measured frequency value omega, and sending the early warning value to a judging module;
the meterThe calculation module calculates and obtains a frequency value omega under a non-damage state according to ANSYS analysis software 0 And calculating an early warning value phi based on an actually measured frequency value omega obtained by the actually measured acceleration signal a (t), wherein the formula is as follows:
the judgment module judges whether the early warning value phi is larger than or equal to m after receiving the early warning value sent by the calculation module, if so, the bridge structure can be determined to be damaged, and early warning is sent out; when the early warning value phi is smaller than m, determining that the bridge structure is not damaged;
m is 3% -6%, preferably 5%, and a large number of experiments prove that the early warning value phi is 5%, the safety limit of the bridge structure can be effectively and truly reflected, the damage of the bridge structure can be accurately predicted, and early warning is carried out in advance.
The bridge structure dynamic monitoring system based on frequency coupling comprises a modal analysis module, an actual measurement module, a fitting module, a calculation module and a judgment module, wherein the frequency value omega of the bridge structure in a non-damage state is obtained through the modal analysis module 0 Actually measuring an acceleration signal a (t) of the bridge structure through an actually measuring module, reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t), approximately fitting the inherent modal function c (t) through a fitting module, obtaining an error value between a coupling pair fitting function u (t) and the inherent modal function c (t), calculating an actually measured frequency value omega and an early warning value phi of the bridge structure through a calculating module, and determining whether the bridge structure is damaged or not and needs early warning through a judging module; the modal analysis module of the embodiment acquires a frequency value in a non-damage state through a finite element model, and the actual measurement module actually measures an acceleration signal, so that the actual measurement frequency value of the bridge structure is inverted, the two are compared, the bridge structure is identified integrally, damage prediction can be effectively carried out, judgment can be rapidly made, early warning can be timely made, and the safety of the bridge structure and the safety of lives and properties can be ensured; for a section of unknown signal, the method can quickly carry out analysis and research in advanceThe empirical mode decomposition is simply and directly carried out, and the decomposition is automatically carried out according to the inherent mode and the layers without manual setting and intervention, so that errors and misjudgment caused by manual intervention are avoided; the fitting module ensures the calculation accuracy by selecting a first-order inherent modal function as a fitting object; accurately expressing the actually measured acceleration signal by a function through signal fitting; curve fitting is carried out by a least square method, so that the optimal function matching of the data is found, unknown data can be simply and conveniently obtained, the sum of squares of errors between the unknown data and actual data is minimum, and the calculation accuracy is further improved; the calculation module calculates the actual measurement frequency value according to the fitted parameter value, and the judgment module can quickly identify the damage position and the damage time of the bridge structure, even can identify the damage in real time, and has high accuracy; the calculation module calculates the early warning value phi through the frequency value in the non-damage state and the actually measured frequency value, and the judgment module can effectively and truly reflect the safety limit of the bridge structure, accurately predict the damage of the bridge structure, early warn in advance and prevent the damage.
Those of ordinary skill in the art will appreciate that embodiments one and two may be practiced by way of equipment, storage media, and the like.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
Claims (9)
1. A bridge structure dynamic monitoring method based on frequency coupling is characterized by comprising the following steps:
establishing a finite element model of a bridge structure, carrying out modal analysis on the finite element model, and obtaining a frequency value omega of the bridge structure in a non-damage state 0 ；
Actually measuring an acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t);
approximately fitting the fitting function u (t) to the natural modal function c (t) by coupling;
calculating an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
according to the frequency value omega of the bridge structure in the non-damage state 0 Obtaining an early warning value phi together with the actually measured frequency value omega, and judging whether the bridge structure is damaged or not according to the early warning value phi;
the coupling pair fitting function u (t) is:
u(t)＝G+Asin(ω 0 )-Bcos(ω 0 )＝G+Hcos(ω 0 +φ 1 )；
wherein, the first and the second end of the pipe are connected with each other,
φ 1 ＝tan -1 (B/A), wherein A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to values of the parameters A and B; asin (omega) 0 ) And Bcos (ω) 0 ) Are coupled pair functions of each other.
2. The dynamic monitoring method for the bridge structure based on the frequency coupling according to claim 1, wherein the step "actually measuring the acceleration signal a (t) of the bridge structure, and reconstructing the acceleration signal a (t) to obtain the natural mode function c (t)" specifically comprises:
actually measuring an acceleration signal a (t) of the bridge structure;
and carrying out empirical mode decomposition on the acceleration signal a (t) to obtain an n-order intrinsic mode function.
3. The dynamic monitoring method for the bridge structure based on the frequency coupling as recited in claim 2, wherein the step "performing empirical mode decomposition on the acceleration signal a (t) to obtain an n-order natural mode function" specifically includes:
setting the actually measured acceleration signal a (t) as a current acceleration signal;
judging whether the number of the upper extreme points and the lower extreme points of the current acceleration signal is more than or equal to 2, if so, entering the next step;
respectively drawing an upper envelope line of an upper extreme point and a lower envelope line of a lower extreme point of the current acceleration signal, and acquiring the mean value of the upper envelope line and the lower envelope line and the mean envelope line thereof;
subtracting the envelope curve of the mean value of the current acceleration signal to obtain a middle signal;
judging whether the difference value between the number of local extreme points and the number of zero-crossing points of the intermediate signal in the whole time range is equal to 0 or equal to 1, and whether the upper envelope line and the lower envelope line of the intermediate signal are locally symmetrical relative to a time axis, if so, entering the next step;
outputting the intermediate signal as an nth order intrinsic mode function; and subtracting the nth order intrinsic mode function from the current acceleration signal to serve as the current acceleration signal, and entering the step of judging whether the number of upper extreme points and lower extreme points of the current acceleration signal is more than or equal to 2 or not.
4. The dynamic monitoring method for a bridge structure based on frequency coupling according to any one of claims 1 to 3, wherein the step of "approximately fitting the fitting function u (t) by coupling to the natural mode function c (t)" is specifically:
randomly selecting parameter values of parameters A and B, and approximately fitting a fitting function u (t) according to coupling to a first-order intrinsic mode function c 1 (t)；
Obtaining a coupling pair fitting function u (t) and a first-order intrinsic mode function c 1 Error value e between (t) error ；
Determining the error value e error Whether or not it is less than or equal to the first natural mode function c 1 (t), if so, entering the step of calculating an actually measured frequency value omega of the bridge structure according to the parameter value of the coupling pair fitting function u (t);
wherein r is 0.001.
5. The dynamic bridge structure monitoring method based on frequency coupling as claimed in claim 4, wherein an error value e is calculated error The formula of (1) is:
e error ＝[u(t)-c 1 (t)] 2 。
6. the dynamic bridge structure monitoring method based on frequency coupling as claimed in claim 5, wherein a formula for calculating the measured frequency value ω is:
7. the dynamic bridge structure monitoring method based on frequency coupling of claim 6, wherein the formula for calculating the early warning value φ is as follows:
when the early warning value phi is larger than or equal to m, the damage of the bridge structure can be determined, and early warning is sent out;
when the early warning value phi is less than m, the bridge structure can be determined to be free of damage;
the value range of m is 3-6%.
8. A bridge structure dynamic monitoring system based on frequency coupling is characterized by comprising a modal analysis module, an actual measurement module, a fitting module, a calculation module and a judgment module;
the modal analysis module is connected with the calculation module and the fitting module and used for establishing a finite element model of the bridge structure, carrying out modal analysis on the finite element model and obtaining a frequency value omega of the bridge structure in a non-damage state 0 And the frequency value omega in the non-damage state is measured 0 Sending to a calculation module and a fitting modelA block;
the actual measurement module is connected with the fitting module and used for actually measuring the acceleration signal a (t) of the bridge structure, reconstructing the acceleration signal a (t) to obtain an inherent modal function c (t) and sending the inherent modal function c (t) to the fitting module;
the fitting module is connected with the modal analysis module, the actual measurement module and the judgment module and is used for receiving the frequency value omega sent by the modal analysis module in the non-damage state 0 The frequency value omega is also used for receiving the inherent mode function c (t) sent by the actual measurement module and matching the fitting function u (t) and the frequency value omega in the non-damage state through coupling 0 Approximately fitting the inherent modal function c (t), and sending an error value between the coupling pair fitting function u (t) and the inherent modal function c (t) to a judging module; the coupling pair fitting function u (t) is:
u(t)＝G+Asin(ω 0 )-Bcos(ω 0 )＝G+Hcos(ω 0 +φ 1 )；
wherein the content of the first and second substances,
φ 1 ＝tan -1 (B/A), wherein A and B are parameters of a coupling pair fitting function u (t), any numerical value is taken, and H is obtained through mathematical calculation according to values of the parameters A and B; asin (omega) 0 ) And Bcos (ω) 0 ) Are coupled pair functions of each other;
the calculation module is connected with the judgment module and the modal analysis module and is used for receiving the frequency value omega of the bridge structure in the non-damage state sent by the modal analysis module 0 And receiving the parameter values of the parameters A and B sent by the judging module, calculating the actual measurement frequency value omega of the bridge structure, and calculating the frequency value omega of the bridge structure under the non-damage state according to the frequency value omega of the bridge structure 0 Calculating an early warning value phi with the actually measured frequency value omega, and simultaneously sending the early warning value phi to a judging module;
the judging module is connected with the calculating module and the fitting module and is used for receiving the error value sent by the fitting module and judging whether the error value is less than or equal to r times of the inherent modal function, if so, the parameter values of the parameters A and B corresponding to the coupling pair fitting function u (t) are transmitted to the calculating module; the judgment module is also used for receiving the early warning value phi sent by the calculation module, judging whether the early warning value phi is larger than or equal to m, if so, determining that the bridge structure is damaged, and sending out early warning; if not, determining that the bridge structure is not damaged.
9. An apparatus comprising the frequency coupling based bridge structure dynamic monitoring system of claim 8.
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