CN117056789B - Method and system for confirming modal parameters of random subspace method under test of multiple test sets - Google Patents
Method and system for confirming modal parameters of random subspace method under test of multiple test sets Download PDFInfo
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Abstract
The invention provides a method and a system for confirming modal parameters of a random subspace method under a multi-test-set test, wherein the method comprises the following steps: performing multi-group single-reference-point environment excitation modal test; using covariance to drive a random subspace method to identify each group of system order modal parameters; setting allowable values among system steps to determine stable modal results of each system step; specifying a self-oscillation frequency sequence f 0 And a frequency tolerance sequence f d Recording system order id satisfying condition s The method comprises the steps of carrying out a first treatment on the surface of the If the mode is in the lower order id s If not, setting the set of modal order results as null, otherwise, carrying out averaging to obtain the set of modal order parameters; and respectively calculating the average value of the self-vibration frequency and the damping ratio of each group of the modal orders to obtain the final self-vibration frequency and the damping ratio of the order, writing each group of the vibration modes as column vectors, and carrying out interpolation processing and transverse splicing to obtain the final real vibration mode of the order. The method solves the problem that each group of results comprise inconsistent modal orders caused by the randomness of environmental excitation under the test of multiple test groups, does not need iteration, and has the advantages of practicality and high efficiency.
Description
Technical Field
The invention relates to the field of bridge health monitoring modal parameter identification, in particular to a method and a system for confirming modal parameters by a random subspace method under multi-test-set test.
Background
In bridge health monitoring, there are typically a large number of structural points, but the available sensors or acquisition channels are limited. Therefore, it is necessary to perform grouping test on the measurement points, each test group includes a part of the measurement points, and summarize and integrate the parameter identification result of each test group. However, due to the randomness of the environmental stimulus, certain test sets may not accurately identify parameters of a particular modal order. The current conventional method for multiple sets of tests is manual screening and adjustment, but this method is time consuming and labor intensive. In a single stable graph, parameter identification mainly depends on a clustering method, and repeated iterative updating is needed until an optimal result is obtained, so that the time cost is high.
Disclosure of Invention
The invention provides a method and a system for confirming modal parameters of a random subspace method under a multi-test-set test, which are used for solving the problems existing in the prior art. The technical scheme is as follows:
in one aspect, a method for confirming a random subspace method modal parameter under a multi-test-set test is provided, including the following steps:
S1, acquiring each group of time-course sequence data by performing environmental excitation modal test of multi-test group single reference point time-course data;
s2, identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the natural vibration frequency, damping ratio and real vibration mode of each modal order;
s3, setting the self-vibration frequency, damping ratio and vibration mode among system stepsThe allowable percentage, the stable mode result under each system order is determined;
s4, referring to the stable modal result, preliminarily designating a self-vibration frequency sequence f 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
S5, if the system order id of a certain test group under a certain modal order is judged s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
s6, for each mode order, calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group to obtain a final self-vibration frequency sequence and a damping ratio sequence, in each mode order, arranging the effective real vibration mode values of each test point of each test group into a column vector to obtain the integral effective real vibration mode of each mode order, carrying out interpolation treatment on the integral effective real vibration mode of each mode order to remove 'null' in vibration mode data, and transversely splicing to obtain a final integral real vibration mode matrix.
In another aspect, a system for validating a random subspace method modal parameter under a multi-test set test is provided, the system comprising:
the test module is used for obtaining each group of time-course sequence data by performing environmental excitation modal test of the multi-test group single reference point time-course data;
the identification module is used for identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the self-vibration frequency, damping ratio and real vibration mode of each modal order;
A determining module for setting the self-vibration frequency, damping ratio and vibration mode between system stepsThe allowable percentage, the stable mode result under each system order is determined;
a first processing module for preliminarily designating a self-oscillation frequency sequence f by referring to the stable mode result 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
A second processing module for determining the system order id of a test group under a certain mode order if the system order id is determined s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
and the third processing module is used for calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group for each mode order to obtain a final self-vibration frequency sequence and a damping ratio sequence, and in each mode order, the effective real vibration mode values of each test point of each test group are arranged into a column vector to obtain the integral effective real vibration mode of each mode order, the integral effective real vibration mode of each mode order is subjected to interpolation processing to remove 'null' in vibration mode data, and the integral real vibration mode matrix is obtained through transverse splicing.
In another aspect, an electronic device is provided, the electronic device including a processor and a memory, the memory storing instructions that are loaded and executed by the processor to implement the method for determining a random subspace method modal parameter under a multi-test set test described above.
In another aspect, a computer readable storage medium is provided, in which instructions are stored, the instructions being loaded and executed by a processor to implement the method for random subspace method modal parameter validation under multiple test set testing described above.
The technical scheme provided by the invention has the beneficial effects that at least:
the method can dynamically adjust, simply and conveniently select the effective parameters in the stable modal result (single stable graph), does not need time-consuming manual screening and adjusting processes, can rapidly integrate multiple groups of parameters, effectively improves the efficiency and accuracy of parameter identification, is simple and efficient, does not need iterative calculation, can automatically adapt to the condition of multiple groups of tests, and has good identification effect and reliability.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for determining modal parameters of a random subspace method under a multi-test-set test according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a bridge girder erection modal test under environmental excitation according to an embodiment of the present invention;
FIG. 3 is a diagram of a station layout of a viaduct under environmental excitation in accordance with an embodiment of the present invention;
FIG. 4 is a chart of group 41 accelerations of a viaduct group modal test under environmental excitation in accordance with an embodiment of the present invention;
FIG. 5 is a group 41 stability chart of a viaduct group modal test under environmental excitation of an embodiment of the present invention-original;
FIG. 6 is a group 43 stability chart of a packet modal test of a viaduct under environmental excitation in accordance with an embodiment of the present invention-original;
FIG. 7 is a group 41 stability chart of a viaduct group modal test under environmental excitation-screening stability points according to an embodiment of the present invention;
FIG. 8 is a final set 41 of stability diagrams of a viaduct group modal test under environmental excitation in accordance with an embodiment of the present invention;
FIG. 9 is a graph of a first order vibration pattern after interpolation of a packet modal test of a viaduct under environmental excitation in accordance with an embodiment of the present invention;
FIG. 10 is a graph of the second order vibration pattern of a viaduct after interpolation of packet modal testing under environmental excitation in accordance with an embodiment of the present invention;
FIG. 11 is a graph of a third order vibration pattern after interpolation of a packet modal test of a viaduct under environmental excitation in accordance with an embodiment of the present invention;
FIG. 12 is a block diagram of a system for determining modal parameters of a random subspace method under a multi-test set test according to an embodiment of the present invention;
fig. 13 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Reference numerals:
the test section of the 1-steel bridge, the accelerometer group of the 2-IEPE, the 3-data acquisition instrument, the 4-notebook computer, the 5-220V mobile power supply, the first cut-off section of the A-schematic drawing, the second cut-off section of the B-schematic drawing, the bridge plate of the 11-steel bridge, the 12-steel pipe column, the 21-test channel accelerometer and the 22-reference channel accelerometer.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the embodiment of the invention provides a method for confirming a random subspace method modal parameter under a multi-test-set test, which comprises the following steps:
s1, acquiring each group of time-course sequence data by performing environmental excitation modal test of multi-test group single reference point time-course data;
s2, identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the natural vibration frequency, damping ratio and real vibration mode of each modal order;
S3, setting the self-vibration frequency, damping ratio and vibration mode among system stepsThe allowable percentage, the stable mode result under each system order is determined;
s4, referring to the stable modal result, preliminarily designating a self-vibration frequency sequence f 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
S5, if the system order id of a certain test group under a certain modal order is judged s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
s6, for each mode order, calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group to obtain a final self-vibration frequency sequence and a damping ratio sequence, in each mode order, arranging the effective real vibration mode values of each test point of each test group into a column vector to obtain the integral effective real vibration mode of each mode order, carrying out interpolation treatment on the integral effective real vibration mode of each mode order to remove 'null' in vibration mode data, and transversely splicing to obtain a final integral real vibration mode matrix.
The following describes in detail a method for confirming a modal parameter of a random subspace method under a multi-test-set test, with reference to fig. 2-11, which includes the following steps:
s1, acquiring each group of time-course sequence data by performing environmental excitation modal test of multi-test group single reference point time-course data;
optionally, the specific step of S1 is:
s1-1, setting measuring points according to structural characteristics, and grouping the measuring points into test groups according to sensor and acquisition channel limitations;
s1-2, each test group consists of a reference point and a plurality of measuring points, the reference points of the test groups are the same reference point (the reference points need to avoid the node positions of the structure focusing on the vibration mode through experience), and modal tests are carried out on the test groups.
Each set of time sequence data includes: displacement or velocity or acceleration time course sequence data.
S2, identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the natural vibration frequency, damping ratio and real vibration mode of each modal order;
optionally, the specific step of S2 is:
s2-1, constructing a Hankel matrix under each test group, wherein the calculation process is carried out by the formula (1):
（1）
Wherein the method comprises the steps ofIs->The moment output vector block is formed by each measuring point in +.>Column vector of values of time of day, +.>For measuring point number, hankel matrix +.>Consists of an upper matrix and a lower matrix which respectively represent the past and the future +.>And->,/>Is +.>Each column of which is composed of->Personal->The block is formed;
s2-2, constructing an output covariance matrixAnd->To obtain the discrete system matrix +.>Discrete output matrixSupport is provided, the calculation process is performed by the formula (2):
（2）
wherein the method comprises the steps ofFor the output vector block->Covariance matrix of>To be from->To->Output covariance matrix of>For the observability matrix, +.>Is a controllable turnover matrix; />For discrete output matrix>Is a discrete system matrix>For the system order>For a one-step state vector and an output response covariance matrix, wherein->Representing mathematical expectations +.>Representing a transpose; />To be from->To->Is a covariance matrix of the output of the (b);
s2-3, pairSVD singular value decomposition of the matrix is performed by equation (3), and when no noise is present, the matrix is subjected to +.>By->The rank of the matrix directly gives the system order +.>In the presence of noise +.>The diagonal element is not strictly 0, and the system order is specified at this time>Is a positive integer, and then is taken as +. >And->The corresponding part is->：
（3）
Wherein the method comprises the steps ofIs an orthogonal array->Diagonal matrix of singular values, singular values in descending order,>is->The upper left part of the matrix is to be read,respectively->And->Left part of->The matrix is +.>And->Right lower, right side portion of (a);
s2-4, discrete system matrix of computing systemAnd discrete output matrix->And further obtaining a continuous system matrix +.>Decomposing the characteristic value to obtain a system characteristic vector matrix +.>And eigenvalue matrix->The calculation process is performed by the formula (4):
, />
, />
（4）
wherein,in general, reverse->For a continuous system matrix>Is conjugate (I)>Is a complex vibration type matrix, which is characterized in that,for the total number of measuring points in each group, +.>For the identified modality order, +.>Indicate->The column vector of the order-vibration type,is->Order conjugate complex eigenvalue->Is the +.>Order generalized damping ratio, < >>Is the firstOrder natural vibration circle frequency, < >>Is->The complex modal natural frequency; />Is a natural constant;
s2-5, testing the obtained vibration mode valuePlural, the amplitude ratio between the measurement points over time is not a constant value (i.e. the ratio between the measurement points over time is changing), and the value of the vibration pattern that maximizes the displacement is selected as the real vibration pattern +. >In each test group, performing normalization processing with respect to each order real vibration type value of the reference point, as shown in formula (5);
（5）
wherein the reference point vibration mode value is positioned atFirst,/-first>To take a plurality of angles>The representation takes the cosine +.>Representing sine +.>Representing absolute value>Representing taking absolute value and returning to its lower index position +.>Indicate->Mode order real mode,/->Representation->Is a first value of (a); />Is thatModal order complex vibration absolute cosine,>is->Modal order complex mode shape absolute sine.
S3, setting the self-vibration frequency, damping ratio and vibration mode among system stepsThe allowable percentage, the stable mode result under each system order is determined;
optionally, the specific step of S3 is:
by setting the self-vibration frequency, damping ratio and vibration mode between system stepsTolerance percentage, specified system orderIs a different positive integer value, based on which is again +.>Different +.>Under the values +.>Further calculation can obtain the system order +.>Mode parameters obtained by calculation when taking different values are calculated from system orderAnd (3) comparing the mode parameters calculated under a certain system order with the mode parameters calculated under the previous system order until the set maximum system order, so as to judge whether the certain mode order identified under the certain system order is stable or not, wherein the calculation process is carried out by the formula (6):
（6）
Wherein, superscriptRepresenting the system order in which the modal parameters are located, subscript +.>Representing modality order->Guaranteeing criteria for modality->Represents the conjugate transpose->Representing the inner product between vectors, +.>Representing modulo taking.
S4, referring to the stable modal result, preliminarily designating a self-vibration frequency sequence f 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
Optionally, the specific step of S4 is:
the self-vibration frequency sequence f is preliminarily determined by the self-vibration frequencies of each order obtained by identifying the stable mode results of each test group (the stable mode results of each test group can be directly obtained or the stable graph obtained by the stable mode results of each test group can be obtained) 0 Setting a frequency tolerance sequence f according to the density of the self-oscillation frequency d The method is used for screening and judging the effective data in the next step, and the screening and judging process is to traverse the primarily determined self-vibration frequency sequence f 0 Writing each order of natural vibration frequency identified by each test group into a two-dimensional matrix form, wherein each order of natural vibration frequency identified under one system order is used as a matrixThe method comprises the steps of carrying out a first treatment on the surface of the Writing the two-dimensional damping ratios of each order identified by each test group into a two-dimensional matrix form, wherein the two-dimensional damping ratios of each order identified under one system order of the matrix acts as +. >The method comprises the steps of carrying out a first treatment on the surface of the Writing the vibration modes of each step identified by each test group into a three-dimensional matrix form, wherein three dimensions are respectively measuring points, system steps and vibration mode values of each identification mode step, and recording the satisfaction f obtained by the identification of each system step of each test group d Frequency tolerance sequence value is located in system order id s As valid identification data for each test group.
S5, if the system order id of a certain test group under a certain modal order is judged s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal steps of the test group, and the system steps of all measuring points are takenNumber id s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
s6, for each mode order, calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group to obtain a final self-vibration frequency sequence and a damping ratio sequence, in each mode order, arranging the effective vibration mode values of each test point of each test group into a column vector to obtain the integral real vibration mode of each mode order (the vibration mode values of partial test points of certain mode orders are possible to be 'null'), carrying out interpolation treatment on the integral real vibration mode of each mode order to remove 'null' in vibration mode data, and transversely splicing to obtain a final integral real vibration mode matrix.
Specifically, a two-dimensional coordinate system is constructed based on a steel tube bundle concrete test surface by adopting double-tone and spline interpolation based on a green function, and the lower left corner is taken asCoordinate points according to the test points->The vibration mode value of each order is used as the original data, a reasonable interpolation grid is arranged in each order according to specific needs, and interpolation points are confirmed +.>And interpolating to obtain each order vibration type value at the interpolation point:
wherein,representing raw data points, +.>Is->The position of the measuring point->Is->Real vibration value of measuring point +.>Is->Point and->The point is->Euclidean distance of plane, +.>Representing the weight vector derived from the known data, < >>Representing the desired interpolated data point +.>To be evaluated.
Example 1
In this example, two IEPE accelerometers were used for testing. The test mode adopts a single reference channel and a single test channel, wherein the sensitivity of the two accelerometers is 1013.8mv/g and 986mv/g respectively. For data acquisition and processing, a blue-filled instrument LC-200 data acquisition instrument and a notebook computer were used and powered by a san xin long 220V mobile power supply with a capacity of 1600 wh. The object to be tested is a single-span steel bridge, and the mode test is carried out under the environmental excitation, and the specific configuration is shown in fig. 2.
The steel bridge testing section has the length of 7700mm, the width of 2200m and the thickness of 250mm. The test section consists of four steel pipe columns and bridge plates, the height of the steel pipe columns is 2500mm, and the inner and outer radiuses of the steel pipes are 150mm and 200mm respectively. The bridge plate is composed of a cross staggered steel frame and a C30 concrete surface layer with the thickness of 50mm, and the steel frame and the steel pipe column are welded together. The total number of the measuring points is 54, wherein 9 measuring points are distributed in the length direction, and the intervals are 1 0.7m and 7 1m respectively. 6 measuring points are distributed in the width direction, and the interval is 5 and 0.4m. The positions of the reference points and the test sequence of the measuring points are shown in fig. 3. The measurement precision and the experimental cost are comprehensively considered in the selection of the measuring point spacing, and the vibration mode distribution condition of the structure is considered, so that a more comprehensive mode test effect is obtained.
Modal testing for test segmentsIn total, 54 test sets were tested. And (3) placing one accelerometer at the reference point and not moving in the whole test process, sequentially moving the other accelerometer to each measuring point position according to the figure 3, and collecting acceleration data of each test group, wherein each group of data comprises an acceleration time sequence of the positions of the two accelerometers at the moment, and the sampling frequency is set to be 200Hz and the single sampling time length is set to be 150s for ensuring the data collection quality. The reference points and acceleration profiles of the points for the 41 st set of tests are shown in figure 4. From these data, a Hankel matrix is constructed by equation (1), taken 80, and constructs an output covariance matrix according to equation (2)>And->. Next, according to equation (3) pair +.>SVD singular value decomposition is performed and by setting the system order +.>From 1 to 40, the different system orders +.>The natural vibration frequency of each mode order (the complex mode natural vibration frequency of each mode order is equal to the natural vibration frequency of each mode order), the damping ratio (the generalized damping ratio of each mode order is equal to the damping ratio of each mode order) and the complex vibration mode are obtained through a formula (5). Finally, the stability of the modal parameters under the next system level is determined between the adjacent system levels through the formula (6), and the stable modal results under each system level are determined (the stable graphs of each group can be obtained according to the stable modal results of each test group). The stability diagrams for the test of groups 41 and 43 are shown in FIGS. 5 and 6, where "stability Point-type 1" indicates satisfactionThe vibration mode, the self-vibration frequency and the damping in the formula (6), "stable point-type 2" indicates that the vibration mode and the self-vibration frequency in the formula (6) are satisfied, and the rest is "unstable point", as can be seen in the figure, in some test groups, the modal parameters of some modal orders are not identified.
For ease of observation, two power spectra are plotted in the stability diagram of the present example, respectively performing auxiliary analysis for the first singular value power spectrum and the average power spectrum, by "performing singular value decomposition at each frequency value for cross power spectral density estimation of each set of test-point acceleration time courses" and taking the first singular value "and" averaging at each frequency value the self power spectrum of each set of test-point acceleration time courses ".
According to the stable modal results identified by each test group, the position of the stable point is found to be consistent with the position of the power spectrum peak, namely, the common sense of modal analysis is met. The position of the stable point is referenced, and each modal order frequency sequence f is designated preliminarily by manual work 0 And sets a proper frequency tolerance f according to the degree of the density d Sequence, in this example, f 0 =[3.3203, 5.8594, 9.7656, 16.9922]，f d =[0.5, 0.5, 0.5, 0.5]In Hz.
At the stable points of the stable mode results of each test group, the self-vibration frequency and f at the stable points of the group are sequentially judged 0 Whether the difference of the corresponding frequency values is f d Within the corresponding frequency tolerance range, the stable points meeting the tolerance condition are classified as effective stable point frequencies of the mode steps, and the effective stable point frequencies of the mode steps under the group are averaged to obtain f 0 And (3) corresponding to the intra-group effective self-vibration frequency of the modal order, similarly obtaining an intra-group effective damping ratio and an intra-group effective vibration mode value, and setting the intra-group effective self-vibration frequency, the intra-group effective damping ratio and the intra-group effective vibration mode value to be 'null' if the group does not have a stable point meeting the tolerance condition.
For each group of data, an intra-group effective self-vibration frequency sequence, an intra-group effective damping ratio sequence and an intra-group effective vibration mode value sequence are obtained. Then, for the same mode order natural vibration frequency and damping ratio of each test group, calculateAveraging to obtain the final self-oscillation frequency sequenceAnd damping ratio sequence. The process of screening effective stable points in the 41 st test group is shown in fig. 7 and 8, and the boxes in the figures indicate that the test group data pass the screening conditions and participate in the calculation of the effective self-vibration frequency, the damping ratio and the vibration type value of the test group.
The four vertical lines in fig. 8 represent the values of the final natural vibration frequency sequence f in order from left to right. Because each test group only tests part of the testing points, the common mode order vibration modes of each test group are put together to be written into a column vector formProcessing 'null' in each mode order, interpolating by adopting a mode of bi-tone and spline interpolation based on a green function, and adding the real vibration mode column vector of each mode order after interpolation >Transversely splicing to obtain the interpolated real vibration mode>The x and y interpolation points in this example are 12 and 18, respectively. The first, second, and third order modes after interpolation are shown in fig. 9, 10, and 11, in which circles represent mode points before interpolation. The mode parameters of the real vibration mode, the natural vibration frequency and the damping ratio are obtained, so that practical application and analysis are convenient. By the simple and efficient method, the confirmation of the modal test parameters under the environment excitation of multiple test groups is realized, and the manual screening and adjusting processes are avoided.
As shown in fig. 12, the embodiment of the present invention further provides a system for confirming a modal parameter of a random subspace method under a multi-test-set test, where the system includes:
the test module is used for obtaining each group of time-course sequence data by performing environmental excitation modal test of the multi-test group single reference point time-course data;
the identifying module 1210 is configured to identify each set of time-course sequence data by using a covariance driving random subspace method, so as to obtain modal parameters of each test set under each system order, where the modal parameters include a self-vibration frequency, a damping ratio and a real vibration mode of each modal order;
a determining module 1220 for setting the self-vibration frequency, damping ratio and vibration mode between system steps The allowable percentage, the stable mode result under each system order is determined;
a first processing module 1230 for preliminarily designating a natural vibration frequency sequence f with reference to the stable mode result 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
A second processing module 1240 for determining the system order id of a test group under a certain mode order if the test group is discriminated s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
and a third processing module 1250, configured to calculate, for each mode order, an average value of the effective natural vibration frequency and the effective damping ratio obtained by each test group, to obtain a final natural vibration frequency sequence and a damping ratio sequence, in each mode order, sort each measurement point effective real vibration mode value of each test group into a column vector, obtain an overall effective real vibration mode of each mode order, perform interpolation processing on the overall effective real vibration mode of each mode order to remove "null" in vibration mode data, and laterally splice to obtain a final overall real vibration mode matrix.
Optionally, the test module is specifically configured to:
s1-1, setting measuring points according to structural characteristics, and grouping the measuring points into test groups according to sensor and acquisition channel limitations;
s1-2, each test group consists of a reference point and a plurality of measuring points, the reference points of the test groups are the same reference point, and modal tests are carried out on the test groups.
Optionally, the identification module is specifically configured to:
s2-1, constructing a Hankel matrix under each test group, wherein the calculation process is carried out by the formula (1):
（1）
wherein the method comprises the steps ofIs->The moment output vector block is formed by each measuring point in +.>Column vector of values of time of day, +.>For measuring point number, hankel matrix +.>Consists of an upper matrix and a lower matrix which respectively represent the past and the futureAnd->,/>Is +.>Each column of which is composed of->Personal->The block is formed;
s2-2, constructing an output covariance matrixAnd->To obtain the discrete system matrix +.>Discrete output matrixSupport is provided, the calculation process is performed by the formula (2):
/>
（2）
wherein the method comprises the steps ofFor the output vector block->Covariance matrix of>To be from->To->Output covariance matrix of>For the observability matrix, +.>Is a controllable turnover matrix; />For discrete output matrix>Is a discrete system matrix >For the system order>For a one-step state vector and an output response covariance matrix, wherein->Representing mathematical expectations +.>Representing a transpose; />To be from->To->Is a covariance matrix of the output of the (b);
s2-3, pairSVD singular value decomposition of the matrix is performed by equation (3), and when no noise is present, the matrix is subjected to +.>By->The rank of the matrix directly gives the system order +.>In the presence of noise +.>The diagonal element is not strictly 0, and the system order is specified at this time>Is a positive integer, and then is taken as +.>And->The corresponding part is->：
（3）
Wherein the method comprises the steps ofIs an orthogonal array->Diagonal matrix of singular values, singular values in descending order,>is->The upper left part of the matrix is to be read,respectively->And->Left part of->The matrix is +.>And->Right lower, right side portion of (a);
s2-4, discrete system matrix of computing systemAnd discrete output matrix->And further obtaining a continuous system matrix +.>Decomposing the characteristic value to obtain a system characteristic vector matrix +.>And eigenvalue matrix->The calculation process is performed by the formula (4):
, />
, />
/>
（4）
wherein,in general, reverse->For a continuous system matrix>Is conjugate (I)>Is a complex vibration type matrix, which is characterized in that,for the total number of measuring points in each group, +. >For the identified modality order, +.>Indicate->The column vector of the order-vibration type,is->Order conjugate complex eigenvalue->Is the +.>Order generalized damping ratio, < >>Is->Order natural vibration circle frequency, < >>Is->The complex modal natural frequency; />Is a natural constant;
s2-5, testing the obtained vibration mode valueComplex number, the amplitude ratio of the vibration modes between the measuring points is not a constant value, and the vibration mode value which maximizes the displacement is selected as the real vibration mode +.>In each test group, performing normalization processing with respect to each order real vibration type value of the reference point, as shown in formula (5);
（5）
wherein the reference point vibration mode value is positioned atFirst,/-first>To take a plurality of angles>The representation takes the cosine +.>Representing sine +.>Representing absolute value>Representing taking absolute value and returning to its lower index position +.>Indicate->Mode order real mode,/->Representation->Is a first value of (a); />Is->Modal order complex vibration absolute cosine,>is->Modal order complex mode shape absolute sine.
Optionally, the determining module is specifically configured to:
by setting the self-vibration frequency, damping ratio and vibration mode between system stepsTolerance percentage, specified system orderIs a different positive integer value, based on which is again +. >Different +.>Under the values +.>Further calculation can obtain the system order +.>Mode parameters obtained by calculation when taking different values are calculated from system orderAnd (3) comparing the mode parameters calculated under a certain system order with the mode parameters calculated under the previous system order until the set maximum system order, so as to judge whether the certain mode order identified under the certain system order is stable or not, wherein the calculation process is carried out by the formula (6):
（6）
wherein, superscriptRepresenting the system order in which the modal parameters are located, subscript +.>Representing modality order->Guaranteeing criteria for modality->Represents the conjugate transpose->Representing the inner product between vectors, +.>Representing modulo taking. />
Optionally, the first processing module is specifically configured to:
each order of natural vibration frequency obtained by identifying stable modal results of each test group is preliminarily determined to be a natural vibration frequency sequence f 0 Setting a frequency tolerance sequence f according to the density of the self-oscillation frequency d The method is used for screening and judging the effective data in the next step, and the screening and judging process is to traverse the primarily determined self-vibration frequency sequence f 0 Writing each order of natural vibration frequency identified by each test group into a two-dimensional matrix form, wherein each order of natural vibration frequency identified under one system order is used as a matrix The method comprises the steps of carrying out a first treatment on the surface of the Writing the two-dimensional damping ratios of each order identified by each test group into a two-dimensional matrix form, wherein the two-dimensional damping ratios of each order identified under one system order of the matrix acts as +.>The method comprises the steps of carrying out a first treatment on the surface of the Writing the vibration modes of each step identified by each test group into a three-dimensional matrix form, wherein three dimensions are respectively measuring points, system steps and vibration mode values of each identification mode step, and recording the satisfaction f obtained by the identification of each system step of each test group d System level where frequency tolerance sequence values are locatedNumber id s As valid identification data for each test group.
The functional structure of the system for confirming the modal parameters of the random subspace method under the test of the multiple test sets provided by the embodiment of the invention corresponds to the method for confirming the modal parameters of the random subspace method under the test of the multiple test sets provided by the embodiment of the invention, and the description is omitted herein.
Fig. 13 is a schematic structural diagram of an electronic device 1300 according to an embodiment of the present invention, where the electronic device 1300 may have a relatively large difference due to different configurations or performances, and may include one or more processors (central processing units, CPU) 1301 and one or more memories 1302, where the memories 402 store instructions, and the instructions are loaded and executed by the processor 1301 to implement the steps of the method for determining a mode parameter of a random subspace method under the test set test described above.
In an exemplary embodiment, a computer readable storage medium, such as a memory comprising instructions executable by a processor in a terminal to perform the above-described method of random subspace method modal parameter validation under multiple test set testing is also provided. For example, the computer readable storage medium may be ROM, random Access Memory (RAM), CD-ROM, magnetic tape, floppy disk, optical data storage device, etc.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program for instructing relevant hardware, where the program may be stored in a computer readable storage medium, and the storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (10)
1. The method for confirming the modal parameters of the random subspace method under the test of the multiple test groups is characterized by comprising the following steps of:
S1, acquiring each group of time-course sequence data by performing environmental excitation modal test of multi-test group single reference point time-course data;
s2, identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the natural vibration frequency, damping ratio and real vibration mode of each modal order;
s3, setting the self-vibration frequency, damping ratio and vibration mode among system stepsThe allowable percentage, the stable mode result under each system order is determined;
s4, referring to the stable modal result, preliminarily designating a self-vibration frequency sequence f 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
S5, if the system order id of a certain test group under a certain modal order is judged s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
s6, for each mode order, calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group to obtain a final self-vibration frequency sequence and a damping ratio sequence, in each mode order, arranging the effective real vibration mode values of each test point of each test group into a column vector to obtain the integral effective real vibration mode of each mode order, carrying out interpolation treatment on the integral effective real vibration mode of each mode order to remove 'null' in vibration mode data, and transversely splicing to obtain a final integral real vibration mode matrix.
2. The method according to claim 1, wherein the specific step of S1 is:
s1-1, setting measuring points according to structural characteristics, and grouping the measuring points into test groups according to sensor and acquisition channel limitations;
s1-2, each test group consists of a reference point and a plurality of measuring points, the reference points of the test groups are the same reference point, and modal tests are carried out on the test groups.
3. The method according to claim 1, wherein the specific step of S2 is:
s2-1, constructing a Hankel matrix under each test group, wherein the calculation process is carried out by the formula (1):
（1）
Wherein the method comprises the steps ofIs->The moment output vector block is formed by each measuring point in +.>Column vector of values of time of day, +.>For measuring point number, hankel matrix +.>Consists of an upper matrix and a lower matrix which respectively represent the past and the future +.>And->,/>Is +.>Each column of which is composed of->Personal->The block is formed;
s2-2, constructing an output covariance matrixAnd->To obtain the discrete system matrix +.>And discrete output matrix->Support is provided, the calculation process is performed by the formula (2):
；
；
；
；
；
（2）
wherein the method comprises the steps ofFor the output vector block->Covariance matrix of>To be from->To->Is used to determine the output covariance matrix of the (c),for the observability matrix, +.>Is a controllable turnover matrix; />In the form of a discrete output matrix,is a discrete system matrix>For the system order>For a one-step state vector and an output response covariance matrix, wherein->Representing mathematical expectations +.>Representing a transpose; />To be from->To->Is a covariance matrix of the output of the (b);
s2-3, pairThe matrix is subjected to SVD singular value decomposition, the calculation process is performed by the formula (3), when no noise exists,by->The rank of the matrix directly gives the system order +.>In the presence of noise +.>The diagonal element is not strictly 0, and the system order is specified at this time>Is a positive integer, and then is taken as +. >And->The corresponding part is->：
；
；
（3）
Wherein the method comprises the steps ofIs an orthogonal array->Diagonal matrix of singular values, singular values in descending order,>is->Left upper part of matrix, ">Respectively->Andleft part of->The matrix is +.>And->Right lower, right side portion of (a);
s2-4, discrete system matrix of computing systemAnd discrete output matrix->And further obtaining a continuous system matrixDecomposing the characteristic value to obtain a system characteristic vector matrix +.>And eigenvalue matrix->The calculation process is performed by the formula (4):
；
；
；
；
，/>；
；
，/>；
；
（4）
wherein,in general, reverse->For a continuous system matrix>Is conjugate (I)>Is a complex vibration matrix->For each groupTotal number of measurement points>For the identified modality order, +.>Indicate->Order vibration column vector, ">Is the firstOrder conjugate complex eigenvalue->Is the +.>Order generalized damping ratio, < >>Is->The frequency of the order self-oscillation circle,is->The complex modal natural frequency; />Is a natural constant;
s2-5, testing the obtained vibration mode valueIs a complexThe value of the amplitude ratio between the measuring points is not a constant value, and the value of the amplitude ratio which maximizes the displacement is selected as the real amplitude +.>In each test group, performing normalization processing with respect to each order real vibration type value of the reference point, as shown in formula (5);
；
；
；
；
；
（5）
Wherein the reference point vibration mode value is positioned atFirst,/-first>To take a plurality of angles>The representation takes the form of a cosine,representing sine +.>Representing absolute value>Representing taking absolute value and returning to its lower index position +.>Indicate->Mode order real mode,/->Representation->Is a first value of (a); />Is->Modal order complex vibration absolute cosine,>is->Modal order complex mode shape absolute sine.
4. A method according to claim 3, wherein the specific step of S3 is:
by setting the self-vibration frequency, damping ratio and vibration mode between system stepsTolerance hundredFraction, designated system order +.>Is a different positive integer value, based on which is again +.>Different +.>Under the value ofFurther calculation can obtain the system order +.>The mode parameters calculated when taking different values are calculated from the system order +.>And (3) comparing the mode parameters calculated under a certain system order with the mode parameters calculated under the previous system order until the set maximum system order, so as to judge whether the certain mode order identified under the certain system order is stable or not, wherein the calculation process is carried out by the formula (6):
；
（6）
wherein, superscriptRepresenting the system order in which the modal parameters are located, subscript +.>Representing modality order- >Guaranteeing criteria for modality->Represents the conjugate transpose->Representing the inner product between vectors, +.>Representing modulo taking.
5. The method according to claim 4, wherein the specific step of S4 is:
each order of natural vibration frequency obtained by identifying stable modal results of each test group is preliminarily determined to be a natural vibration frequency sequence f 0 Setting a frequency tolerance sequence f according to the density of the self-oscillation frequency d The method is used for screening and judging the effective data in the next step, and the screening and judging process is to traverse the primarily determined self-vibration frequency sequence f 0 Writing each order of natural vibration frequency identified by each test group into a two-dimensional matrix form, wherein each order of natural vibration frequency identified under one system order is used as a matrixThe method comprises the steps of carrying out a first treatment on the surface of the Writing the two-dimensional damping ratios of each order identified by each test group into a two-dimensional matrix form, wherein each two-dimensional damping ratio of each order identified under one system order of a matrix behaviorThe method comprises the steps of carrying out a first treatment on the surface of the Writing the vibration modes of each step identified by each test group into a three-dimensional matrix form, wherein three dimensions are respectively measuring points, system steps and vibration mode values of each identification mode step, and recording the satisfaction f obtained by the identification of each system step of each test group d Frequency tolerance sequence value is located in system order id s As valid identification data for each test group.
6. A system for confirming modal parameters of a random subspace method under a multi-test-set test, the system comprising:
the test module is used for obtaining each group of time-course sequence data by performing environmental excitation modal test of the multi-test group single reference point time-course data;
the identification module is used for identifying each group of time-course sequence data by using a covariance driving random subspace method to obtain modal parameters of each test group under each system order, wherein the modal parameters comprise the self-vibration frequency, damping ratio and real vibration mode of each modal order;
a determining module for setting the self-vibration frequency, damping ratio and vibration mode between system stepsThe allowable percentage, the stable mode result under each system order is determined;
a first processing module for preliminarily designating a self-oscillation frequency sequence f by referring to the stable mode result 0 And sets a frequency tolerance sequence f d Traversing f of each modal order in the self-vibration frequency data identified by each test group 0 Recording each system order id meeting tolerance conditions s ；
A second processing module for determining the system order id of a test group under a certain mode order if the system order id is determined s If the test group does not exist, setting the self-vibration frequency, the damping ratio and the vibration mode of the test group at the modal order to be 'null'; if present, take the system order id s Taking the average value of the self-vibration frequencies identified at the position as the effective self-vibration frequency of the modal order of the test group, and taking the system order id s The average value of the damping ratios is identified as the effective damping ratio of the modal order of the test group, and the system order id of each measuring point is taken s Identifying an average value of the real mode shapes as an effective real mode shape of the modal orders of the test group;
and the third processing module is used for calculating the average value of the effective self-vibration frequency and the effective damping ratio obtained by each test group for each mode order to obtain a final self-vibration frequency sequence and a damping ratio sequence, and in each mode order, the effective real vibration mode values of each test point of each test group are arranged into a column vector to obtain the integral effective real vibration mode of each mode order, the integral effective real vibration mode of each mode order is subjected to interpolation processing to remove 'null' in vibration mode data, and the integral real vibration mode matrix is obtained through transverse splicing.
7. The system according to claim 6, wherein the test module is specifically configured to:
s1-1, setting measuring points according to structural characteristics, and grouping the measuring points into test groups according to sensor and acquisition channel limitations;
s1-2, each test group consists of a reference point and a plurality of measuring points, the reference points of the test groups are the same reference point, and modal tests are carried out on the test groups.
8. The system according to claim 6, wherein the identification module is specifically configured to:
s2-1, constructing a Hankel matrix under each test group, wherein the calculation process is carried out by the formula (1):
（1）
wherein the method comprises the steps ofIs->The moment output vector block is formed by each measuring point in +.>Column vector of values of time of day, +.>For measuring point number, hankel matrix +.>Consists of an upper matrix and a lower matrix which respectively represent the past and the future +.>And->,/>Is +.>Each column of which is composed of->Personal->The block is formed;
s2-2, constructing an output covariance matrixAnd->To obtain the discrete system matrix +.>And discrete output matrix->Support is provided, the calculation process is performed by the formula (2):
；
；
；
；
；
（2）
wherein the method comprises the steps ofFor the output vector block->Covariance matrix of>To be from->To->Is used to determine the output covariance matrix of the (c),for the observability matrix, +.>Is a controllable turnover matrix; />In the form of a discrete output matrix,is a discrete system matrix>For the system order>For a one-step state vector and an output response covariance matrix, wherein->Representing mathematical expectations +.>Representing a transpose; />To be from->To->Is a covariance matrix of the output of the (b);
s2-3, pairThe matrix is subjected to SVD singular value decomposition, the calculation process is performed by the formula (3), when no noise exists, By->The rank of the matrix directly gives the system order +.>In the presence of noise +.>The diagonal element is not strictly 0, and the system order is specified at this time>Is a positive integer, and then is taken as +.>And->The corresponding part is->：
；
；
（3）
Wherein the method comprises the steps ofIs an orthogonal array->Diagonal matrix of singular values, singular values in descending order,>is->Left upper part of matrix, ">Respectively->Andleft part of->The matrix is +.>And->Right lower, right side portion of (a);
s2-4, discrete system matrix of computing systemAnd discrete output matrix->And further obtaining a continuous system matrixDecomposing the characteristic value to obtain a system characteristic vector matrix +.>And eigenvalue matrix->The calculation process is performed by the formula (4):
；
；
；
；
，/>；
；
，/>；
；
（4）
wherein,in general, reverse->For a continuous system matrix>Is conjugate (I)>Is a complex vibration matrix->For the total number of measuring points in each group, +.>For the identified modality order, +.>Indicate->Order vibration column vector, ">Is the firstOrder conjugate complex eigenvalue->Is the +.>Order generalized damping ratio, < >>Is->The frequency of the order self-oscillation circle,is->Self-organizing complex modeA vibration frequency; />Is a natural constant;
s2-5, testing the obtained vibration mode value Complex number, the amplitude ratio of the vibration modes between the measuring points is not a constant value, and the vibration mode value which maximizes the displacement is selected as the real vibration mode +.>In each test group, performing normalization processing with respect to each order real vibration type value of the reference point, as shown in formula (5);
；
；
；
；
；
（5）
wherein the reference point vibration mode value is positioned atFirst,/-first>To take a plurality of angles>The representation takes the form of a cosine,representing sine +.>Representing absolute value>Representing taking absolute value and returning to its lower index position +.>Indicate->Mode order real mode,/->Representation->Is a first value of (a); />Is->Modal order complex vibration absolute cosine,>is->Modal order complex mode shape absolute sine.
9. The system according to claim 8, wherein the determining module is specifically configured to:
by setting the self-vibration frequency, damping ratio and vibration mode between system stepsTolerance percentage, specified system order->Is a different positive integer value, based on which is again +.>Different +.>Under the value ofFurther calculation can obtain the system order +.>The mode parameters calculated when taking different values are calculated from the system order +.>And (3) comparing the mode parameters calculated under a certain system order with the mode parameters calculated under the previous system order until the set maximum system order, so as to judge whether the certain mode order identified under the certain system order is stable or not, wherein the calculation process is carried out by the formula (6):
；
（6）
Wherein, superscriptRepresenting the system order in which the modal parameters are located, subscript +.>Representing modality order->Guaranteeing criteria for modality->Represents the conjugate transpose->Representing the inner product between vectors, +.>Representing modulo taking.
10. The system according to claim 9, wherein the first processing module is specifically configured to:
each order of natural vibration frequency obtained by identifying stable modal results of each test group is preliminarily determined to be a natural vibration frequency sequence f 0 Setting a frequency tolerance sequence f according to the density of the self-oscillation frequency d The method is used for screening and judging the effective data in the next step, and the screening and judging process is to traverse the primarily determined self-vibration frequency sequence f 0 Writing each order of natural vibration frequency identified by each test group into a two-dimensional matrix form, wherein each order of natural vibration frequency identified under one system order is used as a matrixThe method comprises the steps of carrying out a first treatment on the surface of the Writing the two-dimensional damping ratios of each order identified by each test group into a two-dimensional matrix form, wherein each two-dimensional damping ratio of each order identified under one system order of a matrix behaviorThe method comprises the steps of carrying out a first treatment on the surface of the Writing the vibration modes of each step identified by each test group into a three-dimensional matrix form, wherein three dimensions are respectively measuring points, system steps and vibration mode values of each identification mode step, and recording the satisfaction f obtained by the identification of each system step of each test group d Frequency tolerance sequence value is located in system order id s As valid identification data for each test group.
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