CN111324949B - Engineering structure flexibility recognition method considering noise influence - Google Patents
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Abstract
The invention provides an engineering structure flexibility recognition method considering noise influence, which utilizes a deterministic-stochastic subspace recognition algorithm to obtain modal parameters of input and output signals with noise interference in a bridge impact test at different calculation orders; then, calculating the relative deviation of modal parameters between adjacent calculation orders by using a stable graph method, and marking the mode with the relative deviation smaller than a preset threshold value as a stable mode; judging the modal orders of the structure by using the stability diagram and determining modal parameters corresponding to each order; calculating a structural frequency response function and a frequency response function covariance matrix by using input and output data; constructing an error function by taking the modal parameters of each order as initial values and an actually measured frequency response function together, and weighting the error function by using a covariance matrix of the frequency response function; iteratively solving a minimum value of an error function by taking the modal parameter as an independent variable; and (3) constructing a structure flexibility matrix by using the modal parameter values after iterative convergence, and achieving the purpose of predicting the displacement of the structure under the action of any static load.
Description
Technical Field
The invention belongs to the technical field of bridge safety detection, and relates to an engineering structure flexibility identification method considering noise influence.
Background
A structure health monitoring technology based on vibration information has attracted much attention in the civil engineering field, and is considered to be one of the most effective methods for improving the safety of an engineering structure, achieving a long life of the structure, and sustainable management. The rapid detection technology for structure identification through structure excitation load information and response information is an important way for evaluating the condition of the bridge. The flexibility is used as a deep level parameter in structure identification, and can be used for predicting the deformation of the bridge structure under any vehicle load. The structural deformation information directly reflects the rigidity and bearing capacity information of the bridge. The bearing capacity evaluation is an important component of bridge state evaluation and is also a foundation for bridge maintenance, reinforcement and technical transformation. Truck load testing is the most common method for evaluating the load-bearing capacity of bridges, and load-bearing capacity information of bridges is analyzed and evaluated by applying loads of different levels at different positions of the bridges by trucks and measuring strain and deflection information of the bridges. However, the truck load test is very complicated to implement, and the bridge to be tested must be closed, inevitably affecting traffic. A rapid detection technology based on an impact vibration test is developed, and an impact device is utilized to excite a bridge and simultaneously acquire, process and analyze an impact signal and a bridge response signal. As the input is known, the flexibility information of the structure can be further obtained besides the basic modal parameters (frequency, damping and mode shape) of the bridge, and the traditional truck load test can be effectively replaced.
In bridge compliance identification based on impact vibration testing, accurate structural modal parameter identification is the key to constructing an accurate structural compliance matrix. Many researchers have developed studies on the method of identifying the compliance based on input and output data. In a frequency domain method, Moon proposes an improved PolyMAX method, divides a frequency response function into a plurality of narrow frequency bands, respectively identifies parameters, and finally constructs a structural flexibility matrix. Zhang J utilizes a complex mode indication function method and a block testing technology to efficiently identify the structural flexibility. In the time domain method, the Li PJ utilizes a time domain signal to construct a Henkel matrix and identifies the flexibility information of the structure by determining a random subspace method. The method effectively identifies the algorithm and the impact equipment, improves the bridge detection efficiency and reduces the bridge detection cost. However, in actual testing, the collected data is inevitably contaminated by noise, which affects the accuracy of compliance identification, thereby preventing correct bridge bearing capacity evaluation. Therefore, it is necessary to overcome the noise effect in the compliance identification process.
Disclosure of Invention
The invention aims to provide an engineering structure flexibility identification method considering noise influence, and solves the problem that the flexibility identification is inaccurate due to noise interference in actual bridge test, so that the bridge bearing capacity evaluation is influenced.
The technical scheme of the invention is as follows:
firstly, acquiring modal parameters (frequency, damping, vibration mode and modal scaling coefficient) of input and output signals with noise interference in a bridge impact test at different calculation orders by using a deterministic-random subspace identification algorithm; then, calculating relative deviation of modal parameters between adjacent calculation orders by using a stable graph method, setting a deviation threshold value, and marking the mode with the relative deviation smaller than a preset threshold value as a stable mode; judging the structural modal orders by using the obtained stable graph and determining physical modal parameters corresponding to each order; calculating a structural frequency response function and a frequency response function covariance matrix by using input and output data; constructing an error function by taking the obtained physical modal parameters of each order as initial values and an actually measured frequency response function together, and weighting the error function by using a covariance matrix of the frequency response function; iteratively solving the minimum value of the error function by using a Levenberg-Marquardt method by taking the modal parameters as independent variables; and constructing a structure flexibility matrix by using the modal parameter values after iterative convergence.
An engineering structure flexibility recognition method considering noise influence comprises the following steps:
firstly, collecting single-input multi-output data and calculating modal parameters under different orders
(1) Acquiring excitation information and multi-point response information of one point of a structure, and constructing a Hankel matrix in the following way:
in the formula of U 0|v-1 And U v|2v-1 Is to form a matrix U 0|2v-1 Divided into an upper part and a lower part; u shape 0|2v-1 、U 0|v-1 And U v|2v-1 The subscripts of (a) represent the subscripts of the first and last elements of the first column of the hankel matrix; u. of v Is the input vector at the v-th moment; the hankel matrix Y of the output data is constructed in the same way 0|2v-1 ；
(2) Computing a projection matrix O by using the constructed Hankel matrix v ：
(3) Performing singular value decomposition on the projection matrix:
in the formula, S 1 Is a singular value matrix; u shape 1 And V 1 Is a unitary matrix; weight matrix W 1 And W 2 Is defined as follows: w 1 Is a full rank matrix, W 2 Satisfies the following conditions:
(4) the calculation order k is increased by 2 from 2 to the maximum calculation order n max (ii) a Making a matrix S of singular values 1 The number of rows and columns is equal to the set calculation order, and the frequency corresponding to each order k is calculated by using a deterministic-stochastic subspace identification algorithm
Damping
Vibration mode
And modal scaling factor
Wherein the corner mark represents the i-th mode under the calculation order k;
second, judging the order of the model and determining the initial value of each order of modal parameter
(5) By usingFrequency correlation difference between mode i at order k and mode j at adjacent calculation order k +1 calculated by the stable graph method
Damping correlation difference
And modal confidence factor
When the frequency correlation difference, the damping correlation difference and the modal confidence factor are lower than a set response threshold value, judging as a stable point; marking the frequency corresponding to the stable point as a horizontal axis and the corresponding calculation order as a vertical axis in the stable graph; finally, selecting a stable axis from the stable graph and determining the order number N of the model r ；
(6) Determining each order modal parameter corresponding to each stable axis as an iteration initial value theta
In the formula:
in the formula, o represents a measuring point corresponding to the output point; lambda r Being the mode pole point,
thirdly, constructing an error function, and iteratively calculating modal parameters corresponding to minimum values of the error function
(7) Calculating the accumulated error function at each frequency point under the condition of considering noise:
in the formula, N o Counting the number of output measurement points; n is a radical of f Is the number of spectral lines in the frequency band; omega f The frequency is corresponding to the f spectral line; e o The difference value of the actually measured frequency response function and the reconstructed frequency response function corresponding to the excitation point and the o-th output measuring point at each spectral line is as follows:
in the formula, the frequency response function H is actually measured o Determined by the H1 method; reconstructed frequency response function
Calculated in the following way:
in the formula, s represents a measuring point corresponding to the excitation point;
frequency response function covariance C in error function M (theta) o The calculation formula is as follows:
in the formula, N a The average times of the frequency response function is obtained by using an H1 method; g uu 、
And
the input self-power spectral density, the output self-power spectral density and the output and input cross-power spectral density are respectively;
(8) an iterative formula is constructed to minimize the error function to optimize the modal parameters:
in the formula, h represents the number of iterations; delta theta h The modal parameter change amount corresponding to the h iteration;
a Jacobian matrix corresponding to the h iteration;
for the weighted error vector corresponding to the h-th iteration:
in the formula (I), the compound is shown in the specification,
iteratively solving the minimum value of the error function by using a Levenberg-Marquardt method; and using the parameter change delta theta obtained by each iteration h Update parameter θ:
θ h+1 ＝θ h +Δθ h
the fourth step, construct the structural compliance matrix
(9) Constructing a flexibility matrix by using modal parameters of each order contained in theta obtained by the last iteration step;
the invention has the beneficial effects that: by utilizing the excitation and response data and finding the minimum value of the error function through iteration, more accurate modal parameters than the traditional determination-random subspace method can be obtained, and an accurate flexibility matrix can be constructed. The deflection of the bridge under any static load can be predicted by using the accurate flexibility matrix to evaluate the bearing capacity of the bridge.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph of the predicted bridge deflection.
Detailed Description
The embodiments of the present invention will be further explained with reference to the drawings and technical solutions.
A numerical example of a 5-degree-of-freedom concentrated mass simple beam model is adopted. The length of the simply supported beam is 6 meters. The concentrated mass of each point is 36.4kg, and the mass blocks are distributed on the beam at equal intervals. The flexural rigidity of the beam is 7.3542 x 10 6 N·m 2 . The rayleigh damping ratio of the first-order mode and the last-order mode is 5%. Multiple hammering is applied to node 5. The response of 5 nodes is calculated by a Newmark-beta method. 30% noise was added to the excitation data and response data.
The method is implemented as follows (the overall flow is shown in fig. 1):
(1) acceleration responses of node 1 to node 5 are collected along with input force data for node 5. And establishing a Hankel matrix U using the input and output data 0|2v-1 And Y 0|2v-1 。
(2) Computing a projection matrix O using a Hankel matrix v And performing singular value decomposition on the projection matrix:
in the formula S 1 Is a singular value matrix; u shape 1 And V 1 Is a unitary matrix.
(3) The initial calculation order k is set to 2. Making a matrix S of singular values 1 The number of rows and columns of (c) is equal to the set calculation order. Then calculating the frequency by using the method of determining random subspace
Damping
Vibration mode
And modal scaling factor
(4) Sequentially incrementing the calculation order by step 2 up to the maximum calculation order 150 (n) max 150) and repeating step (3) to calculate the modal parameters at different calculation orders.
(5) Calculating the relative difference of adjacent calculated order modes (
and
). Selection satisfies a threshold condition (e) ω ＝0.05,e ξ ＝0.2and e MAC 0.05) is the stable point.
(6) Determining model order N in a stability map r And determining each order modal parameter corresponding to each stable axis as an iteration initial value theta.
(7) Calculating an actual measurement frequency response function H by using input and output data o While reconstructing the frequency response function using the iteration initial value theta
Calculating an error matrix E by subtracting the actually measured frequency response function and the reconstructed frequency response function o And a frequency response function covariance C o The error function M (θ) is constructed as a weight.
(8) Calculating a Jacobian matrix J and constructing an iteration form as follows:
iteratively solving the minimum value of the error function by using a Levenberg-Marquardt method, and using delta theta obtained by each iteration h Update parameter θ:
θ h+1 ＝θ h +Δθ h
(9) the modal parameters contained in the parameter theta obtained by the last iteration update are used for constructing a flexibility matrix, and the comparison result of the predicted flexibility and the real flexibility when each measuring point applies 10kN load is shown in figure 2.
Claims (1)
1. An engineering structure flexibility recognition method considering noise influence is characterized by comprising the following steps:
firstly, collecting single-input multi-output data and calculating modal parameters under different orders
(1) Acquiring excitation information and multi-point response information of one point of a structure, and constructing a Hankel matrix in the following way:
in the formula of U 0|v-1 And U v|2v-1 Is to form a matrix U 0|2v-1 Divided into an upper part and a lower part; u shape 0|2v-1 、U 0|v-1 And U v|2v-1 The subscripts of (a) represent the subscripts of the first and last elements of the first column of the hankel matrix; u. u v Is the input vector at the v-th moment; the hankel matrix Y of the output data is constructed in the same way 0|2v-1 ；
(2) Computing a projection matrix O by using the constructed Hankel matrix v ：
(3) Performing singular value decomposition on the projection matrix:
in the formula, S 1 Is a singular value matrix; u shape 1 And V 1 Is a unitary matrix; weight matrix W 1 And W 2 Is defined as follows: w 1 Is a full rank matrix, W 2 Satisfies the following conditions:
(4) the calculation order k is increased by 2 from 2 to the maximum calculation order n max (ii) a Making a matrix S of singular values 1 Is equal to the set calculation order, and calculates the frequency corresponding to each order k by using a deterministic-stochastic subspace identification algorithm
Damping
Vibration mode
And modal scaling factor
Wherein the corner mark represents the i-th mode under the calculation order k;
second, judging the order of the model and determining the initial value of each order of modal parameter
(5) Calculating the frequency correlation difference between the mode i at the order k and the mode j at the adjacent calculation order k +1 by using a stability graph method
Damping correlation difference
And modal confidence factor
When the frequency correlation difference, the damping correlation difference and the modal confidence factor are lower than a set response threshold value, judging as a stable point; marking the frequency corresponding to the stable point as a horizontal axis and the corresponding calculation order as a vertical axis in the stable graph; finally, selecting a stable axis from the stable graph and determining the order number N of the model r ；
(6) Determining each order modal parameter corresponding to each stable axis as an iteration initial value theta
In the formula:
in the formula, o represents a measuring point corresponding to the output point; lambda [ alpha ] r Is the mode pole point, and the mode pole point,
thirdly, constructing an error function, and iteratively calculating modal parameters corresponding to minimum values of the error function
(7) Calculating the accumulated error function at each frequency point under the condition of considering noise:
in the formula, N o Counting the number of output measurement points; n is a radical of hydrogen f Is the number of spectral lines in the frequency band; omega f The frequency is corresponding to the f spectral line; e o The difference value of the actually measured frequency response function and the reconstructed frequency response function corresponding to the excitation point and the o-th output measuring point at each spectral line is as follows:
in the formula, the frequency response function H is actually measured o Determined by the H1 method; reconstructed frequency response function
Calculated in the following way:
in the formula, s represents a measuring point corresponding to the excitation point;
frequency response function covariance C in error function M (theta) o The calculation formula is as follows:
in the formula, N a The average times of the frequency response function is obtained by using an H1 method; g uu 、
And
the input self-power spectral density, the output self-power spectral density and the output and input cross-power spectral density are respectively;
(8) an iterative formula is constructed to minimize the error function to optimize the modal parameters:
in the formula, h represents the number of iterations; delta theta h The modal parameter change amount corresponding to the h iteration;
a Jacobian matrix corresponding to the h iteration;
for the weighted error vector corresponding to the h-th iteration:
in the formula (I), the compound is shown in the specification,
iteratively solving the minimum value of the error function by using a Levenberg-Marquardt method; and using the parameter change delta theta obtained for each iteration h Updating the parameter theta:
θ h+1 ＝θ h +Δθ h
the fourth step, construct the structural compliance matrix
(9) Constructing a flexibility matrix by using modal parameters of each order contained in theta obtained by the last iteration step;
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