CN105205461A - Signal noise reducing method for modal parameter identification - Google Patents
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Abstract
The invention discloses a signal noise reducing method for modal parameter identification. The signal noise reducing method for modal parameter identification comprises the steps that 1, a Hankel matrix is built through a pulse response signal of a noise-containing structure; 2, a rank of the Hankel matrix is resolved, an order determination index is resolved according to the rank of the Hankel matrix, and a model order is determined through the order determination index; 3, the Hankel matrix is processed through the order determination index and structure low rank approximation to obtain a rebuilt matrix processed through low rank approximation; 4, the step 2 and the step 3 are repeatedly performed until the convergent standard is met, and therefore a noise reducing signal is obtained; 5, modal parameter identification is performed through the noise reducing signal. The signal noise reducing method for modal parameter identification has the advantages that the fact that a Frobenius norm of a difference between the Hankel matrix before being processed through noise reducing and the Hankel matrix after being processed through noise reducing approaches to be the minimum can be achieved by setting the mode of the convergent standard and structure low rank approximation, that is, the improvement of the precision of the noise reducing signal can be achieved.
Description
Technical field
The present invention relates to signal transacting field, especially a kind of signal de-noising method for Modal Parameter Identification.
Background technology
At present, in order to ensure that the safety of the heavy construction such as bridge, ocean platform structure is on active service, the structural health detection technique development of structure based impulse response signal rapidly.And Modal Parameter Identification is the basic and critical link of this detection technique.Therefore, the precision improving Modal Parameter Identification is most important.
Due to the impact of test condition, instrument and equipment, manual operation etc., always there are some uncertain factors in on-the-spot vibration experiments process, the signal of actual measurement is inevitably subject to the interference of ground unrest.Although the measures such as such as average, filtering and shielding can be taked in data acquisition to reduce noise, expect not to be unpractical by the signal of noise pollution completely.In order to identify the modal parameter of structure more accurately, the noise in erasure signal just becomes very urgent.Current, signal de-noising problem mainly concentrates on acoustics, Based Intelligent Control, electronics, image and the field such as signal transacting and linear math, and also lacks relevant signal de-noising technical research for the Modal Parameter Identification problem of structure.When carrying out model analysis, the way usually adopted calculates the model order that adopts higher than real model order, thus allowed the impact of " noisy modt ".But the result identified like this can produce false mode, and can cause the reduction of counting yield, particularly when the signal to noise ratio (S/N ratio) of signal is low time, how to distinguish a large amount of false modes and true mode will become very difficult.
At present, propose in prior art to carry out signal de-noising based on low-rank approximation technique, the Hankel matrix counter-diagonal method of average should be utilized based on low-rank approximation technique, signal after de-noising carries out Modal Parameter Identification, the method improves the precision of Modal Parameter Identification to a certain extent, but before and after noise reduction, the Frobenius norm of Hankel matrix deviation is not minimum value in this noise-eliminating method, what namely finally obtain is not mathematical optimum solution, that is, signal de-noising effect also has the space of improving.
Summary of the invention
The object of the invention is for overcoming above-mentioned the deficiencies in the prior art, a kind of signal de-noising method for Modal Parameter Identification improving noise reduction precision is provided.
For achieving the above object, the present invention adopts following technical proposals:
For a signal de-noising method for Modal Parameter Identification, comprise the following steps:
Step one: build Hankel matrix according to noisy structure impulse response signal;
Step 2: ask Hankel rank of matrix, tries to achieve according to Hankel rank of matrix and determines rank index, utilizes and determines rank index Confirming model order;
Step 3: utilize and determine rank index and structure low-rank and approach Hankel matrix is processed, obtain low-rank approach after restructuring matrix;
Step 4: repetition step 2 and step 3 until meet convergence, thus obtain de-noising signal.
Step 5: utilize described de-noising signal to carry out Modal Parameter Identification.
Preferably, in step one, described noisy structure impulse response signal is acceleration or speed or displacement.
Preferably, in step 2, the mode of svd is adopted to ask for Hankel rank of matrix.
Preferably, in step 3, the mode obtaining restructuring matrix is:
If Hankel matrix is H in step one
m × n, restructuring matrix is H
p × (k+q)model order is k, l is signals and associated noises data point, p and q meets p+k+q-1=l, q=1,2 ..., n-k; Restructuring matrix H
p × (k+q)first be classified as front p in l data point, matrix H
p × (k+q)last column be rear k+q in l data point, the design feature of Hankel matrix is that the element on counter-diagonal is equal, and the first row of known matrix and last column, can obtain restructuring matrix H
p × (k+q)the data that 2nd row arrange to kth+q.
Preferably, in step 3, the structure low-rank mode of approaching is: q initial value is 1, restructuring matrix determined rank index according to descending sort, relatively determine maximal value and the second largest value of rank index, if maximal value is more than or equal to K (K>=4, K ∈ Z) times second largest value, then structure low-rank approaches end, the restructuring matrix after acquisition low-rank approaches; Otherwise, q=q+ Δ t, wherein Δ t ∈ N
*, Hankel matrix is reconstructed, until meet above-mentioned condition.Δ t represents the speed that structure low-rank approaches, if Δ t value is selected less, then structure low-rank velocity of approch is fast, if Δ t value is selected comparatively large, then structure low-rank velocity of approch is slow.
Preferably, in step 3, K=4, Δ t=1.
Preferably, in step 4, convergence is:
To reconstruct matrix H
p × (k+q)carry out svd and carry out descending sort to singular value, singular value is expressed as λ
i(i=1,2 ..., k+q), λ
1> λ
2> λ
3> λ
k+q, convergence is that kth+1 singular value and the 1st singular value ratio level off to zero.By arranging this convergence, make Hankel matrix H
m × nthe Frobenius norm of the deviation before and after low-rank approaches levels off to minimum, improves the precision of de-noising signal.
The selection of this convergence is not unique, needs according to restructuring matrix H
p × (k+q)singular value judge, as another possibility, convergence can be set to kth+1 singular value and level off to 0, i.e. λ
k+1< 1 × 10
-15, now, make Hankel matrix H
m × nthe Frobenius norm of the deviation before and after low-rank approaches levels off to minimum.
Preferably, in step 4, convergence function expression is:
Preferably, in step 5, Modal Parameters Identification is complex exponential method.
Wherein, the concrete mode of step one is as follows:
Based on the noisy structure impulse response signal comprising l data point of sensor actual measurement, build square formation or the Hankel matrix H close to box formation
m × n, wherein, if l is even number, then
if l is odd number, then
The concrete mode of step 2 is as follows:
To Hankel matrix H
m × ncarry out svd, obtain the singular value λ by descending sort
i(i=1,2 ..., n), λ
1> λ
2> λ
3> λ
n.
Determine rank index MOC, function expression is
j represents order, j=1,2 ..., n-1.
Ask and determine rank index maximal value, and using the order of order k corresponding for this maximal value as model, the mode number namely comprised in signal is
The concrete mode of step 3 is as follows:
In order to improve the counting yield of noise reduction algorithm, to the Hankel matrix H in step 2
m × nbe reconstructed and obtain restructuring matrix H
p × (k+q);
Because matrix dimension is very large on the impact of iteration convergence efficiency, if Hankel matrix adopts square formation or close to box formation, calculation of complex and consuming time; If Hankel matrix adopts matrix dimension to be p × (k+1), then convergence efficiency is the highest, but owing to adopting matrix dimension to be p × (k+1), cause matrix dimension less, cause true modal information to occur partial loss after noise reduction, while namely carrying out noise reduction, true modal information goes out active.
For this reason, COMPREHENSIVE CALCULATING efficiency and noise reduction two aspect, setting iterated conditional.Iterated conditional is that the maximal value of determining rank index is more than or equal to the second largest value that four times are determined rank index, and this iterated conditional act as: ensure that de-noising signal there will not be loss or the omission of true modal information; Meanwhile, with Hankel matrix adopt square formation or close to square formation mode compared with, calculate simple, improve counting yield, make convergence efficiency high as far as possible.
The iterated conditional determining rank index is that the maximal value of determining rank index is more than or equal to the second largest value that four times are determined rank index, reason is: determine the corresponding model order of rank index maximal value, and model order equals the twice of the mode number comprised in signal, if determine rank index maximal value and second largest value difference little, illustrate that model order judges not obvious, de-noising signal can be caused still to be subject to noise effect, or to there is the situation of omitting true modal information.
If determine rank index maximal value and larger difference appears in second largest value, illustrate that model order judges obviously, for this reason, the maximal value of determining rank index is more than or equal to K (K >=4, K ∈ Z) times and determines the second largest value of rank index as iterated conditional.
Hankel matrix H
m × nconcrete reconstruct mode is as follows:
If p+k+q-1=l, q=1,2 ..., n-k:
Make q=1, then p=l-k;
A. to Hankel matrix H
m × nbe reconstructed and obtain restructuring matrix H
p × (k+q), restructuring matrix H
p × (k+q)first be classified as front p in l data point, restructuring matrix H
p × (k+q)last column be rear k+q in l data point, the design feature of Hankel matrix is that the element on counter-diagonal is equal, and the first row of known matrix and last column, can obtain restructuring matrix H
p × (k+q)the data that 2nd row arrange to kth+q.
B. to reconstruct matrix H
p × (k+q)carry out the singular value that svd obtains this matrix, and to this singular value by descending sort, be expressed as λ
i(i=1,2 ..., k+q), λ
1> λ
2> λ
3> λ
k+q.
C. ask according to above-mentioned singular value and determine rank index MOC
j(j=1,2 ..., k+q-1), store M OC
jmaximal value MOC
mAXwith second largest value MOC
sUB;
D. K=4 is got, Δ t=1, if determine rank index maximal value and second largest value meets following funtcional relationship
MOC
mAX>=4MOC
sUB, then matrix dimension is defined as p × (k+q);
If determine rank index maximal value and second largest value does not meet above-mentioned funtcional relationship, i.e. MOC
mAX< 4MOC
sUB, then q=q+1, and return execution above-mentioned steps a to step c, until when meeting q=t, MOC
mAX>=4MOC
sUB, then calculate end, determine H
p × (k+q)matrix dimension is p × (k+t), wherein p+k+t-1=l.
The concrete mode of step 4 is as follows:
(1) to H in step 3
p × (k+t)matrix carries out svd, obtains orthogonal vector
wherein R represents real number matrix, and presses the singular value of descending sort, is expressed as λ
i, i=1,2 ..., k+t, wherein λ
1>=...>=λ
k+t.
(2) equation is built
Wherein, i=1 ..., k+t, j=1 ..., p, subscript T represents transpose of a matrix, and e is the Standard basis vector of Line independent,
form H
p × (k+t)a series of basis matrixs of the linear space of matrix.
C
srepresenting de-noising signal, is signal to be asked.
Order
w＝ij，
Then
Be expressed as
Will
Be expressed as matrix form, i.e. Gc=d, wherein, G ∈ R
p (k+t) × l, c ∈ R
l, d ∈ R
p × (k+t).
(3) carry out svd to matrix G, namely matrix G is decomposed into
Wherein, Y ∈ R
p (k+t) × p (k+t), Z
t∈ R
l × l, Y and Z is orthogonal matrix, Λ ∈ R
p (k+t) × lbe diagonal matrix, Λ can be analyzed to a non-zero singular value submatrix Λ
awith some null matrix, wherein Λ
afor diagonal line comprises the submatrix of a nonzero value, namely
Y
aand Z
afor a row before Y and Z.
(4) convergence is set
if restructuring matrix H in step 3
p × (k+q)singular value meets following funtcional relationship
then utilize
and c=G
-1d tries to achieve de-noising signal;
Otherwise return and perform step 2 and step 3 until meet convergence.
The reason of choosing of above-mentioned convergence mark standard is:
To reconstruct matrix H
p × (k+q)svd obtains the singular value by descending sort, and tries to achieve restructuring matrix H
p × (k+q)order, when meeting kth+1 singular value and the 1st singular value ratio is less, can noise reduction be realized, in theoretical research, when kth+1 singular value and the 1st singular value ratio level off to zero time, the raising of noise reduction precision can be realized, in actual computation, can arrange ultimate value is 1 × 10
-15.
According to above-mentioned principle, convergence employing function expression is
Step 5: the de-noising signal utilizing step 4 to obtain carries out Modal Parameter Identification.
The invention has the beneficial effects as follows, by adopting above-mentioned computing method, compared with the prior art mentioned in background technology, noise-reduction method adopts the mathematic(al) mean of getting Hankel matrix counter-diagonal element, the Frobenius norm that cannot reach matrix deviation before and after noise reduction levels off to minimum value, the application can make the Frobenius norm of the Hankel matrix deviation before and after noise reduction level off to minimum by the mode arranging convergence and structure low-rank and approach, and namely can realize the raising of de-noising signal precision.
Accompanying drawing explanation
The process flow diagram of Fig. 1 signal de-noising method for Modal Parameter Identification of the present invention;
Fig. 2 is embodiments of the invention jacket offshore platform model;
Fig. 3 is embodiments of the invention square formation H
201 × 201determine rank index;
Fig. 4 is embodiments of the invention matrix H
390 × 12determine rank index;
Fig. 5 is that embodiments of the invention signals and associated noises and de-noising signal contrast;
Fig. 6 is that embodiments of the invention precise signal and de-noising signal contrast.
Embodiment
Below in conjunction with drawings and Examples, the present invention is further described.
Embodiments of the invention are jacket offshore platform models, referring to figs. 2 to Fig. 6.
Set up jacket offshore platform finite element numerical model:
Jacket offshore platform finite element numerical model parameter is as follows:
The external diameter of stake is 24mm, and wall thickness is 2.5mm; The external diameter of stull and diagonal brace is 16mm, and wall thickness is 1.5mm; Bosun 0.6m, wide 0.3m, thick 0.01m; From bottom to top, every layer height is respectively 0.5m, 0.9m, 1.35m, 1.5m, 1.7m; The gradient of stake is 1/10.
Utilize Ansys software to set up jacket offshore platform finite element model, and obtain the theoretical value of 2 order frequencies and damping ratio before model by FEM (finite element) calculation.Apply x at node 1 place of model to pulse excitation, measuring point 1,2,3,4 place x is to dynamic respond time-histories respectively, wherein sampling time interval 0.005 second.Using the response signal at measuring point 1 place as research object (excitation, the response signal of other positions are similar).
With this section of sampled signal simulation precise signal, this precise signal not Noise; On this section of precise signal basis, superimposed noise level is the white Gaussian noise of 5%, simulates signals and associated noises.Wherein noise level is defined as the ratio of the standard deviation of white Gaussian noise and the standard deviation of precise signal.
Step one: build Hankel matrix according to noisy structure impulse response signal:
One section that gets noisy structure impulse response signal, totally 401 data points, i.e. l=401, analyze for these 401 data points.
By l=401, calculate
The Hankel square formation H that dimension is 201 × 201 is built according to above-mentioned 401 data points
201 × 201.
Step 2: to Hankel square formation H
201 × 201carry out svd, try to achieve the maximal value MOC determining rank index
k, as shown in Figure 3, determine rank figure according to signals and associated noises model and obtain determining model order corresponding to rank index being 4, i.e. k=4, this shows that the mode number comprised in this signals and associated noises is 2.
Step 3: to the Hankel matrix H in step 2
201 × 201carry out utilizing structure low-rank to approach and obtain restructuring matrix H
p × (4+q), in order to improve counting yield, structure low-rank approaches by reconstruct Hankel matrix H
201 × 201realize.
Hankel matrix H
201 × 201reconstruct mode is as follows:
If p+k+q-1=l, wherein q=1,2 ..., n-k;
By l=401, k=4, obtain p+q=398.
Make K=4, q initial value is 1:
A. restructuring matrix H
p × (4+q)first is classified as front p in l data point, restructuring matrix H
p × (4+q)last column be rear 4+q in l data point, according to the feature of Hankel matrix, obtain this matrix the 2nd and arrange to 4+q column data.
B. to reconstruct matrix H
p × (4+q)carry out svd, obtain the singular value λ by descending sort
i(i=1,2 ..., 4+q), λ
1> λ
2> λ
3> λ
4+q, ask for according to above-mentioned singular value and determine rank index by descending sort, determine to determine rank index maximal value MOC
mAXwith second largest value MOC
sUB.
If c. MOC
mAX< 4MOC
sUB, then q=q+1, order performs above-mentioned steps a to b;
As shown in Figure 4, as q=8, maximal value MOC
mAXbe 12.02, second largest value MOC
sUBbe 2.80, meet MOC
mAX>=4MOC
sUB, now p=l-k-q+1=390, t=8, then determine matrix H
p × (4+q)dimension is p × (k+t), namely 390 × 12.
Step 4: to reconstruct matrix H
390 × 12carry out svd, obtain the singular value according to descending sort, whether inspection singular value meets convergence
if do not meet this formula, then return and perform step 2 and step 3 until meet convergence, and according to c=G
-1d tries to achieve de-noising signal.
Fig. 5 is the signal contrast before and after structure impulse response signal noise reduction, can find out significantly, and the structure impulse response signal curve after noise reduction becomes very level and smooth.
Fig. 6 is that the structure impulse response signal after precise signal and noise reduction contrasts, and can find out, the structure impulse response signal curve after precise signal curve and noise reduction almost overlaps completely, and this illustrates that noise reduction is very good.
Step 5: Modal Parameter Identification: adopt existing Modal Parameter Identification technology, as complex exponential method, respectively Modal Parameter Identification is carried out to the signal after precise signal, signals and associated noises and noise reduction, obtain 2 rank model frequency and damping ratios, and compare with theoretical value, in table 1, table 2.
Table 1: model frequency theoretical value compares (Hz) with the discre value based on precise signal, signals and associated noises and de-noising signal.
Table 2: damping ratios theoretical value compares with the discre value based on precise signal, signals and associated noises and de-noising signal.
As can be seen from Table 1 and Table 2: compared with signals and associated noises, adopt de-noising signal to carry out Modal Parameter Identification, significantly improve accuracy of identification.
By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.
Claims (10)
1., for a signal de-noising method for Modal Parameter Identification, it is characterized in that:
Step one: the structure impulse response signal utilizing sensor to survey builds Hankel matrix;
Step 2: ask for Hankel rank of matrix, tries to achieve according to Hankel rank of matrix and determines rank index, utilizes and determines rank index Confirming model order;
Step 3: utilize and determine rank index and structure low-rank and approach Hankel matrix is processed, obtain low-rank approach after restructuring matrix;
Step 4: repetition step 2 and step 3 until meet convergence, thus obtain de-noising signal;
Step 5: utilize described de-noising signal to carry out Modal Parameter Identification.
2. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 1, it is characterized in that, in step one, described structure impulse response signal is acceleration, or speed, or displacement.
3. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 1, is characterized in that, in step 2, adopts the mode of svd to ask for Hankel rank of matrix.
4. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 3, is characterized in that, in step 3, the mode obtaining restructuring matrix is:
If Hankel matrix H
m × n, model order is k, l is signals and associated noises data point, and restructuring matrix is H
p × (k+q), wherein p+k+q-1=l, q=1,2 ..., n-k; Restructuring matrix H
p × (k+q)first be classified as front p in l signals and associated noises data point, last column of restructuring matrix is that the rear k+q in l data point is individual.
5. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 4, it is characterized in that, in step 3, the structure low-rank mode of approaching is: q initial value is 1, restructuring matrix determined rank index according to descending sort, relatively determine maximal value and the second largest value of rank index, if maximal value is more than or equal to K second largest value doubly, then structure low-rank approaches end, restructuring matrix after acquisition low-rank approaches, otherwise, q=q+ Δ t, wherein Δ t ∈ N
*, Hankel matrix is reconstructed, until meet above-mentioned condition, wherein, K>=4, K ∈ Z.
6. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 5, is characterized in that, in step 3, and K=4, Δ t=1.
7. a kind of signal de-noising method for Modal Parameter Identification as described in claim 5 or 6, it is characterized in that, in step 4, convergence is:
Be H to restructuring matrix
p × (k+q)carry out svd and carry out descending sort to singular value, singular value is expressed as λ
i(i=1,2 ..., k+q), λ
1> λ
2> λ
3> λ
k+q, convergence meets kth+1 singular value and the 1st singular value ratio levels off to zero.
8. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 7, it is characterized in that, in step 4, convergence function expression is:
9. a kind of signal de-noising method for Modal Parameter Identification as described in claim 5 or 6, is characterized in that, in step 4, to reconstruct matrix H
p × (k+q)carry out svd and carry out descending sort to singular value, singular value is expressed as λ
i(i=1,2 ..., k+q), wherein λ
1> λ
2> λ
3> λ
k+q, convergence is that kth+1 singular value levels off to 0.
10. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 1, it is characterized in that, in step 5, Modal Parameters Identification is complex exponential method.
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| CN107943757B (en) * | 2017-12-01 | 2020-10-20 | 大连理工大学 | Order determination method based on sparse component analysis modal identification |
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| CN108399385B (en) * | 2018-02-23 | 2021-10-15 | 中国石油大学(华东) | Noise reduction method for vibration monitoring signal of wind generating set |
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