CN114036605A - Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control - Google Patents
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Abstract
The invention discloses a Kalman filtering steel truss bridge structure parameter monitoring method based on adaptive control, which comprises the steps of firstly determining mechanical parameters such as the quality and the rigidity of a steel truss bridge structure; secondly, acquiring truss speed, acceleration, displacement and ground acceleration vibration response data of the steel truss bridge structure; and then tracking the change of the speed, the acceleration, the displacement and the rigidity of the structure by using a Kalman filtering algorithm, carrying out envelope control by combining a dynamic statistical process algorithm, and realizing automatic alarm when the rigidity generates a change value and exceeds an envelope control line. The method optimizes the Kalman filtering algorithm to enable the Kalman filtering algorithm to achieve the change of the predicted rigidity on the steel truss bridge structure, and accords with the actual engineering requirement; compared with the traditional single threshold algorithm, the method improves the defect of fixed threshold, optimizes the fixed threshold into dynamic control, provides reference for performance evaluation of the steel truss bridge structure, and can effectively serve management and maintenance work of the steel truss bridge structure.
Description
Technical Field
The invention discloses a method for monitoring structural parameters of a steel truss bridge, and particularly relates to the field of health monitoring and safety early warning of bridge structures.
Background
At present, the number of super bridges in China is continuously increased, steel truss continuous beam bridges are widely applied due to reasonable structural form, clear stress, economic manufacturing cost and attractive appearance, and steel truss bridges gradually move to standardized and assembled roads. The assembled steel truss bridge structure is degraded due to construction and installation and corrosion, and the components are damaged to different degrees. The damage can not be detected and maintained in time, the bearing capacity and the use safety of the assembled steel truss bridge structure can be directly influenced, and a series of problems occur in the process from design and construction to final bridge formation. Therefore, in order to guarantee the safety and the durability of the assembled steel truss bridge structure, the health monitoring of the steel truss bridge structure is enhanced, the safety of the steel bridge structure is evaluated accurately in real time, early warning is provided in time according to structural response, the service life of the steel truss bridge is prolonged, potential disastrous events are avoided, and the steel truss bridge has important significance in ensuring the use safety of the steel truss bridge.
The current common structural parameter identification method is mainly based on a known system and a power output signal thereof, utilizes response data acquired by a monitoring sensor to identify structural parameters by methods such as a time domain analysis method, a frequency domain analysis method, an HHT method and the like, and mainly comprises the following research methods:
the frequency domain identification method mainly includes a peak method, a frequency domain decomposition method and the like. The peak method is realized according to the principle that the frequency response function of the structure has an extreme value at the natural frequency, the frequency response function of the structure can be easily obtained under the condition that the input and the output can be known, the frequency response function can not be obtained under the condition of natural environment excitation, and the precision of the method is not very high. A frequency domain decomposition method is a method for identifying structural parameters under environmental excitation, the method assumes that input is white noise, carries out singular value decomposition on a power spectral density matrix of structural response, replaces a frequency response function curve with a singular value curve, and has better noise immunity and capability of identifying dense modes.
The time domain identification method comprises the following steps: least squares, ITD, STD, complex exponentiation, random subspace, and eigensystem implementation. The stochastic subspace method consists in determining the order of the equation by means of the singular value decomposition of the Toepliz matrix obtained from the covariance matrix of the structural response, the order determined due to noise interference, the possible presence of spurious modes, and the accuracy of the identification is reduced.
The HHT method is characterized in that each component of a non-stationary signal subjected to empirical mode decomposition is assumed to be stationary, so that the signal is converted to obtain Hilbert conversion, and the obtained Hilbert spectrum can accurately reflect the distribution of energy in various frequency scales and time in a physical process, so that the purpose of identifying structural parameter change is achieved. However, the harmonic component does not necessarily exist for the entire duration of the time series, and cannot be captured in real time.
Therefore, there is a lack of a method for continuous and automatic structural damage detection with real-time parameter estimation and capture of parameter mutations, by dynamically controlling the range to detect anomalies of selected features.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: based on the defects of frequency domain and time domain methods, the invention provides a Kalman filtering steel truss bridge structure parameter monitoring method based on adaptive control, and solves the calculation problem that the selected characteristics are screened through a dynamic control range without real-time parameter estimation and parameter mutation capture.
The invention adopts the following technical scheme for solving the problems:
the invention provides a Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control, which comprises the following steps:
the method comprises the steps of firstly, measuring or looking up basic mechanical parameters of the steel truss bridge structure, and collecting response data of speed, acceleration and displacement of vibration of the steel truss bridge structure.
And secondly, preprocessing acceleration, speed and displacement response data, and setting a state equation and an observation equation through a multi-degree-of-freedom structure dynamic system.
y(t)＝h(x(t))+w(t)
In the formula
F (x (t)) is a discretized state parameter, and v (t) is noise of the state equation; y (t) is the monitor equation, h (x (t)) is the observed state parameter, and w (t) is the noise of the observation equation.
And step three, linearizing the state equation and the measurement equation obtained in the step two through discrete time, importing the speed, acceleration and displacement response data processed in the step two, and obtaining estimated values of the displacement, the speed, the acceleration and the rigidity at each moment through recursion of a time updating equation and the state updating equation, wherein the estimated values represent the estimation of real values at each moment. .
In the formula
For the predicted value of the state parameter at the time k +1, phi (k) is a state transition matrix,
the true value at time k.
And H (k +1) observation matrix is used as the observation parameter prediction value at the k +1 moment.
For the state parameter estimate at time k +1,
for the predicted value of the state parameter at the time K +1, KgIs a kalman gain matrix.
The estimated value of the observation parameter at the time k +1, and y (k +1| k +1) is the observed value at the time k + 1.
And step four, setting a dynamic envelope curve through an improved statistical control process control method, wherein the limit of the statistical process control method generates an iterative control limit by each time step obtained in the step three, the limit represents displacement, speed, acceleration and rigidity estimated values generated in each step in the step three, the mean value and standard deviation of the set envelope curve represent the current state of an estimated state, when the rigidity is kept in the envelope curve range, the algorithm does not give an alarm, and when the rigidity exceeds the envelope curve, the rigidity is forecasted to generate sudden damage.
Wherein
Is the normal value of the state parameter at the moment k, which is equal to the normal value at k points in the pastEstimating an average value of the parameter;
is the mean standard deviation of time k, equal to the mean of the estimated parameters over k points in the past.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the method optimizes the Kalman filtering algorithm to enable the Kalman filtering algorithm to achieve the change of the predicted rigidity on the steel truss bridge structure, and accords with the actual engineering requirement; compared with the traditional single threshold algorithm, the method improves the defect of fixed threshold, optimizes the fixed threshold into dynamic control, provides reference for performance evaluation of the steel truss bridge structure, and can effectively serve management and maintenance work of the steel truss bridge structure.
Drawings
FIG. 1 is a schematic diagram of the engineering application of the method of the present invention.
FIG. 2 is a diagram of the first and second order mode shapes of a cable-stayed bridge in the numerical simulation process of the invention.
Fig. 3 is a diagram of the effect of displacement filtering in the present invention.
Fig. 4 is a graph of the effect of the velocity filtering in the present invention.
Fig. 5 is a graph of the effect of the stiffness filtering in the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
in the long-term service process, due to the effects of natural factors such as climate and environment and the increasing traffic flow and the increasing bridge passing number of heavy vehicles and overweight vehicles, the safety and the service performance of the bridge structure are necessarily degraded along with the increasing bridge age. The invention provides a Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control. Based on historical measurements of the impairment-sensitive features involved in the state space dynamic model, the method is used to generate real-time estimates and standard derivations of these features, which can then be used to form a statistically controlled control range to detect any anomalies of the selected features.
The invention provides a steel truss bridge structure rigidity monitoring method based on statistical process control and Kalman filtering, which comprises the following specific steps of:
the method comprises the steps of measuring or looking up basic mechanical parameters of the steel truss structure, and collecting response data of speed, acceleration and displacement of vibration of the steel truss bridge structure.
And secondly, preprocessing acceleration, speed and displacement response data, and setting a state equation and an observation equation through a multi-degree-of-freedom structure dynamic system.
And step three, linearizing the state equation and the measurement equation obtained in the step two through discrete time, importing the speed, acceleration and displacement response data processed in the step two, and obtaining estimated values of the displacement, the speed, the acceleration and the rigidity at each moment through recursion of a time updating equation and the state updating equation, wherein the estimated values represent the estimation of real values at each moment.
And step four, setting a dynamic envelope curve through an improved statistical control process control method, wherein the limit of the statistical process control method generates an iterative control limit by each time step obtained in the step three, the limit represents displacement, speed, acceleration and rigidity estimated values generated in each step in the step three, the mean value and standard deviation of the set envelope curve represent the current state of an estimated state, when the rigidity is kept in the envelope curve range, the algorithm does not give an alarm, and when the rigidity exceeds the envelope curve, the rigidity is forecasted to generate sudden damage.
As an embodiment of the present invention, the specific calculation manner of step two is as follows:
civil structures such as buildings and bridges can be modeled as multiple degrees of freedom (MDOF) power systems. Their equations of motion can be expressed as
Wherein M is a mass matrix, C is a mass matrix, K is a stiffness matrix, B is an excitation influence matrix,
u (t) are responses of the acceleration, velocity and displacement of the structure respectively,
is the ground acceleration. The extended state vector of the dynamic system is set by the equation to be defined as:
wherein α (t) ═ α1(t)，α2(t)，…，αn(t)]TThe vector is the vector of unknown structural parameters such as rigidity and damping value.
The state equation and the observation equation are:
y(t)＝h(x(t))+w(t)
where x (t) is the equation of state, f (x (t)) is the discretized state parameter, and v (t) is the noise of the equation of state. Where y (t) is the observation equation, h (x (t)) is the observed state parameter, and w (t) is the noise of the observation equation.
As an embodiment of the present invention, the implementation of step three is as follows:
since the state equation is in a continuous time form, conversion to discrete time is required when linearizing the state equation and the observation equation.
φ(tk，tk-1)＝I+Δt×Fk-1
Fk、HkIs a linearized Jacobian matrix, phi (t)k，tk-1) State transition matrix for linearized systems
The time update equation:
the state update equation:
Fp＝Fk(I-KgH)
Kg＝PHT(HPHT+R)-1
P＝FpPFp T+FkKgRKg TFk T+Q
in the formula
For the predicted value of the state parameter at the time k + 1, phi (k) is a state transition matrix,
the true value at time k.
And H (k +1) is an observation matrix, and is an observation parameter predicted value at the moment of k + 1. Wherein
Is pair kThe state parameter estimate at time +1,
for the predicted value of the state parameter at the time K + 1, KgIs a kalman gain matrix.
The estimated value of the observation parameter at the time k + 1, and y (k +1| k +1) is the observed value at the time k + 1. P is an error covariance matrix, FpTo update the matrix.
As an embodiment of the present invention, the implementation of step four is as follows:
adaptive statistical process control limits are used instead of static limits. It generates an iterative control limit at each time step according to the method of the invention, so the mean and standard deviation represent the current state of the estimated state. Sigma rules are applied and the range of use is determined to guarantee a 95% confidence level. Thus, the range around the normal value is defined as the adaptive statistical process control limit.
Wherein
The normal value of the state parameter at the moment k is equal to the average value of the estimated parameters at k points in the past;
is the mean standard deviation of time k, equal to the mean of the estimated parameters over k points in the pastThe value is obtained.
The following detailed description will be given with reference to specific examples.
The method is implemented as numerical simulation of a highway and railway dual-purpose cable-stayed bridge in Jiangsu province, and comprises the following detailed calculation steps:
the frequency of the first-order vibration mode and the second-order vibration mode of the numerical model of the cable-stayed bridge is similar to the real bridge data through numerical modeling, so that the damage condition of the real bridge is simulated by approximation. The mode diagram is shown in fig. 2.
Step one, acting on a finite element model of a highway-railway dual-purpose cable-stayed bridge by applying seismic load, setting a bridge span middle node to generate rigidity damage and change, and setting the local rigidity of the bridge span middle node to be reduced by 50%. And extracting the speed, acceleration and displacement response data of the node under the action of the seismic load.
And step two, importing the data into an algorithm to obtain a displacement filtering effect graph as shown in figure 3, a speed filtering effect graph as shown in figure 4, and a rigidity change filtering effect graph as shown in figure 5.
The filtering effect graph can be used for effectively tracking when the rigidity changes, and the dynamic capture effect can be achieved by fast convergence in a short time. When the change exceeds the statistical control line, the change can be found in time.
The above description is only a preferred embodiment of the present patent, and it should be noted that, for those skilled in the art, several modifications and decorations can be made without departing from the inventive concept, and these modifications and decorations should also be regarded as the protection scope of the present patent.
Claims (4)
1. A Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control is characterized by comprising the following steps:
measuring or looking up basic mechanical parameters of a steel truss structure, and acquiring response data of speed, acceleration and displacement of vibration of the steel truss bridge structure;
secondly, preprocessing acceleration, speed and displacement response data, and setting a state equation and an observation equation through a multi-degree-of-freedom structure dynamic system;
step three, linearizing the state equation and the measurement equation obtained in the step two through discrete time, importing the speed, the acceleration and the displacement response data processed in the step two, and obtaining the estimated values of the displacement, the speed, the acceleration and the rigidity of each moment through recursion of a time updating equation and a state updating equation, wherein the estimated values represent the estimation of the real values of each moment;
and step four, setting a dynamic envelope curve through a statistical control process control method, wherein the limit of the statistical process control method generates an iterative control limit by each time step obtained in the step three, the limit represents displacement, speed, acceleration and rigidity estimated values generated in each step in the step three, the mean value and standard deviation of the set envelope curve represent the current state of the estimated state, and when the mean value and the standard deviation exceed the envelope curve, the rigidity is judged to generate sudden damage.
2. The Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control according to claim 1, characterized in that in step two,
expressing the motion equation of the multi-freedom structure power system as
Wherein M is a mass matrix, C is a mass matrix, K is a stiffness matrix, B is an excitation influence matrix,
u (t) are responses of the acceleration, velocity and displacement of the structure respectively,
is the ground acceleration;
the expansion state vector of the dynamic system is set through the motion equation of the multi-degree-of-freedom power system, and is defined as:
wherein α (t) ═ α1(t),α2(t),…,αn(t)]TThe vector is the vector of unknown structural parameters such as rigidity and damping value;
the set state equation and the observation equation are as follows:
y(t)＝h(x(t))+w(t)
wherein,
f (x (t)) is a discretized state parameter, and v (t) is noise of the state equation; y (t) is the observation equation, h (x (t)) is the observed state parameter, and w (t) is the noise of the observation equation.
3. The Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control according to claim 1, characterized in that the third step is as follows:
linearizing the state equation and the observation equation, and converting into discrete time:
φ(tk，tk-1)＝I+Δt×Fk-1
Fk、Hkis a linearized Jacobian matrix, phi (t)k，tk-1) A state transition matrix for a linearized system;
the time update equation:
the state update equation:
Fp＝Fk(I-KgH)
Kg＝PHT(HPHT+R)-1
p＝FppFp T+FkKgRKg TFk T+Q
in the formula,
for the predicted value of the state parameter at the time k +1, phi (k) is a state transition matrix,
is the true value at time k and,
the predicted value of the observation parameter at the moment of k +1 is H (k +1) is an observation matrix;
for the state parameter estimate at time k +1,
for the predicted value of the state parameter at the time K +1, KgIs a Kalman gain matrix;
the estimated value of the observation parameter at the moment k +1 is obtained, and y (k +1| k +1) is the observed value at the moment k + 1; p is an error covariance matrix, FpTo update the matrix.
4. The Kalman filtering steel truss bridge structural parameter monitoring method based on adaptive control according to claim 1, characterized in that the calculation process in the fourth step is as follows:
wherein,
the normal value of the state parameter at the moment k is equal to the average value of the estimated parameters at k points in the past;
is the mean standard deviation of time k, equal to the mean of the estimated parameters over k points in the past.
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| CN114692279A (en) * | 2022-04-15 | 2022-07-01 | 石家庄铁道大学 | Time-varying stiffness parameter identification method resisting boundary constraint interference, storage medium and equipment |
| CN114692279B (en) * | 2022-04-15 | 2023-09-15 | 石家庄铁道大学 | Time-varying stiffness parameter identification method, storage medium and equipment for resisting boundary constraint interference |
| CN114912551A (en) * | 2022-07-18 | 2022-08-16 | 中国铁路设计集团有限公司 | GNSS and accelerometer real-time fusion algorithm for bridge deformation monitoring |
| CN116804534A (en) * | 2023-06-29 | 2023-09-26 | 中交第二航务工程局有限公司 | Auxiliary determination method for continuous beam bridge construction process |
| CN116804534B (en) * | 2023-06-29 | 2024-03-12 | 中交第二航务工程局有限公司 | Auxiliary determination method for continuous beam bridge construction process |
| CN116561535A (en) * | 2023-07-11 | 2023-08-08 | 安徽建筑大学 | Individualized building interaction design processing method |
| CN116561535B (en) * | 2023-07-11 | 2023-09-19 | 安徽建筑大学 | Individualized building interaction design processing method |
| CN118332232A (en) * | 2024-06-14 | 2024-07-12 | 一开控股(青岛)集团有限公司 | Rigidity change data algorithm and analysis system |
| CN118332232B (en) * | 2024-06-14 | 2024-09-03 | 一开控股(青岛)集团有限公司 | Rigidity change data algorithm and analysis system |
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