CN113076879A - Asynchronous sampling structure modal parameter identification method based on random subspace - Google Patents

Abstract

The invention discloses a random subspace-based method for identifying modal parameters of an asynchronous sampling structure, which comprises the following steps: asynchronous sampling is carried out on the bridge structure measuring point to obtain original acceleration response data; selecting acceleration response data of a certain measuring point as a reference signal, using acceleration response data of the other measuring points as translation signals, and determining actual time delay between the two measuring points by analyzing error functions at different time intervals; after actual time delay between different translation signals and reference signals is determined, data reduction is calculated according to the sampling frequency of the signals, and corrected acceleration response data are obtained by processing original acceleration response data after the data reduction is obtained; and finally, identifying the vibration mode modal parameters of the bridge structure by the corrected acceleration response data through a random subspace method. The method can identify the actual time delay among different measuring points, so as to obtain the frequency modal parameter and the high-precision vibration mode modal parameter under the asynchronous sampling data of the bridge structure.

Description

Asynchronous sampling structure modal parameter identification method based on random subspace

Technical Field

The invention belongs to the field of bridge safety detection, and particularly relates to an asynchronous sampling structure modal parameter identification method based on a random subspace.

Background

The identification of modal parameters of a structure is the key point of research in the field of structural health monitoring, modal analysis plays an important role in health monitoring of large-scale engineering structures, and important modal parameters in a bridge structure comprise natural frequency and modal vibration modes, so that one of important tasks of modal parameter identification is to identify the frequency and the vibration modes of the bridge structure. The random subspace method is a linear system identification method developed in recent years, the method does not need manual excitation, and modal parameters of the structure are directly extracted from corresponding output signals of environment excitation, and the modal parameters are used as the basis or input of structure health monitoring, finite element model correction, damaged structure evaluation and structure control;

at present, increasingly large bridges are put into use, the synchronism of sampling time of all measuring points of the whole bridge is difficult to guarantee when the measuring points are arranged, and because response data in a random subspace identification method requires simultaneous synchronous sampling among different measuring points, a great error is caused to identification of mode shape parameters in actual monitoring.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides a random subspace-based asynchronous sampling structure modal parameter identification method, so that the actual time delay between different measuring points of a bridge structure can be accurately identified, asynchronous sampling data can be corrected, the corrected sampling data can be subjected to random subspace parameter identification, and a frequency modal parameter and a high-precision vibration mode modal parameter can be obtained.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention relates to a random subspace-based asynchronous sampling structure modal parameter identification method which is characterized by comprising the following steps:

step 1: in thatAcceleration response data { a) of i measuring points on bridge structure _r1,2, …, i }; wherein, a_rRepresenting acceleration response data of an r measuring point;

step 2: acceleration response data a of the r measuring point is selected_rAcceleration response data of the rest measuring points as reference signals { a_t1,2, …, i-1 as a translation signal, where a_tRepresents the t-th translation signal; determining an actual time delay by analyzing error functions at different time intervals;

step 2.1: defining the total time axis as NxDeltat; reference signal a_rThe time axis of the device is fixed and unchanged; the t translation signal a_tThe time axis of (a) is translated at certain time intervals Δ t;

step 2.2: for the k translation time instant, the reference signal a_rAnd the t-th translation signal a_tConstituent output vector y_tObtaining a state matrix A of the bridge structure by using a random subspace method based on data driving_tOutput matrix C_tAnd the state vector x at the kth translation time_k,t；

Step 2.3: predicting to obtain an output vector y of the k translation moment by using a state space equation shown in formula (1)_k,t；

In formula (1): v and w are different zero mean Gaussian white noises respectively; x is the number of_k+1,tState vectors representing the (k + 1) th translation time instant;

step 2.4: the prediction error vector sequence z at the k-th translation time is obtained by using the formula (2)_k,t：

z_k,t＝y_t-y_k,t (2)

Step 2.5: an error function value D of the k translation time is obtained by using the formula (3)_k,t：

In formula (3): det is determinant, (.)^TRepresents a transpose of a matrix;

step 2.6: after k +1 is assigned to k, steps 2.1-2.5 are repeated until k equals nxat, thereby matching the actual output vector y_tWhen the value of the error function is minimum, the corresponding translation time is the reference signal a_rAnd the output vector y_tIs delayed by an actual time n_t·Δt；

And step 3: performing data processing on the acceleration response data on the premise of knowing the signal sampling frequency fs to obtain corrected acceleration response data Y;

step 3.1: obtaining the t translation signal a by using the formula (4)_tData deletion amount T of_t：

T_t＝n_t·Δt·fs (4)

Step 3.2: using the data reduction amount T_tFor the t translation signal a_tData deleting processing is carried out, so that the deleted acceleration response data Y is obtained_t；

Step 3.3: repeating the step 3.1 and the step 3.2, so as to obtain corrected acceleration response data Y;

and 4, step 4: and identifying modal parameters of the corrected acceleration response data Y by using a random subspace method, thereby obtaining frequency modal parameters and high-precision mode shape modal parameters.

Compared with the prior art, the invention has the beneficial effects that:

according to the method, the measuring point acceleration response data are processed on a time domain, the actual time delay between two signal sequences is determined according to the error function values of the reference signal and the translation signal, the corrected acceleration sampling data are obtained through processing, the modal parameters are identified through a random subspace method for the corrected acceleration sampling data, and the frequency modal parameters and the high-precision mode modal parameters are obtained, so that the problem that the measuring point signal acquisition time is not synchronous in the process of monitoring the health of a large-span bridge in the actual engineering, namely the time delay problem among sensors is solved, and the existing random subspace identification method based on data driving is supplemented and perfected.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a measuring point layout diagram of the uniform-section simply supported beam bridge;

FIG. 3 is a white noise excitation time-course diagram applied to a measurement point according to the present invention;

FIG. 4 is a time-course diagram of acceleration response extracted from measured points according to the present invention;

FIG. 5 is a graph of the error function of the response signals of the measuring points No. 3 and No. 4 according to the present invention;

FIG. 6 is a graph of the error function of the response signals of the measuring points No. 3 and No. 5 of the present invention;

FIG. 7 is a graph of the error function of the response signals of the measuring points No. 3 and No. 6 according to the present invention;

FIG. 8 is a graph of the error function of the response signals of the measuring points No. 3 and No. 7 of the present invention;

FIG. 9 is a graph of the error function of the response signals of the measuring points No. 3 and No. 8 according to the present invention;

FIG. 10 is a graph of the error function of the response signals of the measuring points No. 3 and No. 9 according to the present invention;

FIG. 11 is a graph of the first-order vibration pattern recognition result of the uniform-section simply supported beam bridge of the present invention;

FIG. 12 is a diagram showing the second-order mode of vibration identification result of the uniform-section simply-supported girder bridge according to the present invention;

FIG. 13 is a diagram showing the result of the recognition of the third vibration mode of the uniform-section simply supported girder bridge according to the present invention.

Detailed Description

In this embodiment, the bridge with the uniform-section simply-supported beam shown in fig. 2 has a span length of 10m, an elastic modulus of 21Gpa, a poisson's ratio of 0.3, and a density of 8.0 × 10³Kg/m³When the finite element method is adopted for simulation, 8 plane Euler beam units are equidistantly divided by the bridge, and the bridge comprises 9 nodes of two supports; sequentially applying white noise excitation shown in fig. 3 to the total 7 nodes from 2 nd to 8 th, and calculating the dynamic response of the bridge by a Newmark-beta method, wherein the signal sampling method comprises the following steps: 2. synchronously sampling the 3 and 4 nodes at the same time, starting sampling at the 5 and 6 nodes after 1s, and starting at the 7 and 8 nodes after 2sSampling is started, and the sampling frequency is 400 Hz; as shown in fig. 1, a method for identifying modal parameters of an asynchronous sampling structure based on a random subspace includes the following steps:

step 1: acceleration response data { a) of 7 measuring points in total are collected on the bridge structure _r2,3, …,8 }; wherein a is_rAcceleration response data representing the r-th measurement point, { a_rThe | r ═ 2,3, …,8} is arranged in sequence from top to bottom as shown in fig. 4;

step 2: acceleration response data a of the 2 nd measuring point is selected₂Acceleration response data of the rest measuring points as reference signals { a_t L t 3,4, …,8 as a translation signal, where a_tRepresents the t-th translation signal; determining an actual time delay by analyzing error functions at different time intervals;

step 2.1: defining the total time axis as NxDeltat; reference signal a₃The time axis of the device is fixed and unchanged; the t translation signal a_tThe time axis of (a) is translated at a certain time interval Δ t of 1 s;

step 2.2: for the k translation time instant, the reference signal a₂And the t-th translation signal a_tConstituent output vector y_tObtaining a state matrix A of the bridge structure by using a random subspace method based on data driving_tOutput matrix C_tAnd the state vector x at the kth translation time_k,t；

Step 2.3: predicting to obtain an output vector y of the k translation moment by using a state space equation shown in formula (1)_k,t；

In formula (1): v and w are different zero mean Gaussian white noises respectively; x is the number of_k+1,tState vectors representing the (k + 1) th translation time instant;

step 2.4: the prediction error vector sequence z at the k-th translation time is obtained by using the formula (2)_k,t：

z_k,t＝y_t-y_k,t (2)

Step 2.5: an error function value D of the k translation time is obtained by using the formula (3)_k,t：

In formula (3): det is determinant, (.)^TRepresents a transpose of a matrix;

step 2.6: after k +1 is assigned to k, steps 2.1-2.5 are repeated until k equals nxat, thereby matching the actual output vector y_tWhen the value of the error function is minimum, the corresponding translation time is the reference signal a_rAnd the output vector y_tIs delayed by an actual time n_tΔ t, the actual time delay between two measuring points 2 and 3 is 0s as shown in FIG. 5; from FIG. 6, the actual time delay between two measuring points 2 and 4 is 0 s; from FIG. 7, the actual time delay between two measuring points 2 and 5 is 1 s; from FIG. 8, the actual time delay between two measuring points 2 and 6 is 1 s; from fig. 9, the actual time delay between two measuring points 2 and 7 is 2 s; from fig. 10, the actual time delay between two measuring points 2 and 8 is 2 s;

and step 3: performing data processing on the acceleration response data on the premise that the known signal sampling frequency fs is 400Hz to obtain corrected acceleration response data Y;

step 3.1: obtaining the t translation signal a by using the formula (4)_tData deletion amount T of_t：

T_t＝n_t·Δt·fs (4)

Step 3.2: using data puncturing amount T_tFor the t translation signal a_tData deleting processing is carried out, so that the deleted acceleration response data Y is obtained_t；

Step 3.3: repeating the step 3.1 and the step 3.2, so as to obtain corrected acceleration response data Y;

and 4, step 4: the corrected acceleration response data Y is subjected to modal parameter identification using a random subspace method, so as to obtain frequency modal parameters and high-accuracy mode shape modal parameters, as shown in table 1.

TABLE 1

As can be seen from the results and errors of frequency identification in table 1, the error between the identified frequency modal parameter and the reference frequency modal parameter is small, and as can be seen from the results of vibration mode identification in fig. 11, 12, and 13, the method can identify the high-precision vibration mode modal parameter when the signal sampling is asynchronous.

Claims (1)

1. A method for identifying asynchronous sampling structure modal parameters based on random subspace is characterized by comprising the following steps:

step 1: acquiring acceleration response data { a) of i measuring points on bridge structure_r1,2, …, i }; wherein, a_rRepresenting acceleration response data of an r measuring point;

step 2: acceleration response data a of the r measuring point is selected_rAcceleration response data of the rest measuring points as reference signals { a_t1,2, …, i-1 as a translation signal, where a_tRepresents the t-th translation signal; determining an actual time delay by analyzing error functions at different time intervals;

step 2.1: defining the total time axis as NxDeltat; reference signal a_rThe time axis of the device is fixed and unchanged; the t translation signal a_tThe time axis of (a) is translated at certain time intervals Δ t;

step 2.2: for the k translation time instant, the reference signal a_rAnd the t-th translation signal a_tConstituent output vector y_tObtaining a state matrix A of the bridge structure by using a random subspace method based on data driving_tOutput matrix C_tAnd the state vector x at the kth translation time_k,t；

Step 2.3: predicting to obtain an output vector y of the k translation moment by using a state space equation shown in formula (1)_k,t；

In formula (1): v and w are different zero mean Gaussian white noises respectively; x is the number of_k+1,tState vectors representing the (k + 1) th translation time instant;

step 2.4: the prediction error vector sequence z at the k-th translation time is obtained by using the formula (2)_k,t：

z_k,t＝y_t-y_k,t (2)

Step 2.5: an error function value D of the k translation time is obtained by using the formula (3)_k,t：

In formula (3): det is determinant, (.)^TRepresents a transpose of a matrix;

step 2.6: after k +1 is assigned to k, steps 2.1-2.5 are repeated until k equals nxat, thereby matching the actual output vector y_tWhen the value of the error function is minimum, the corresponding translation time is the reference signal a_rAnd the output vector y_tIs delayed by an actual time n_t·Δt；

And step 3: performing data processing on the acceleration response data on the premise of knowing the signal sampling frequency fs to obtain corrected acceleration response data Y;

step 3.1: obtaining the t translation signal a by using the formula (4)_tData deletion amount T of_t：

T_t＝n_t·Δt·fs (4)

Step 3.2: using the data reduction amount T_tFor the t translation signal a_tData deleting processing is carried out, so that the deleted acceleration response data Y is obtained_t；

Step 3.3: repeating the step 3.1 and the step 3.2, so as to obtain corrected acceleration response data Y;

and 4, step 4: and identifying modal parameters of the corrected acceleration response data Y by using a random subspace method, thereby obtaining frequency modal parameters and high-precision mode shape modal parameters.

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