CN105205461B - A kind of signal de-noising method for Modal Parameter Identification - Google Patents
A kind of signal de-noising method for Modal Parameter Identification Download PDFInfo
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Abstract
The invention discloses a kind of signal de-noising method for Modal Parameter Identification, step 1：Hankel matrixes are built using noisy structure impulse response signal；Step 2：Hankel ranks of matrix are sought, is tried to achieve according to Hankel ranks of matrix and determines rank index, model order is determined using rank index is determined；Step 3：Using rank index is determined and structure low-rank approaches and Hankel matrixes are handled, the restructuring matrix after low-rank approaches is obtained；Step 4：Repeat step two and step 3 are until meet convergence, so as to obtain de-noising signal.Step 5：Modal Parameter Identification is carried out using the de-noising signal.The invention has the advantages that the Frobenius norms of the Hankel matrix deviations before and after noise reduction can be realized by way of setting convergence and structure low-rank approaches level off to minimum, you can to realize the raising of de-noising signal precision.
Description
Technical field
The present invention relates to field of signal processing, 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 structures such as bridge, ocean platform is on active service, believed based on structure impulse response
Number structural health detection technique quickly grow.And Modal Parameter Identification is the basic and critical ring of the detection technique
Section.Therefore, the precision for improving Modal Parameter Identification is most important.
Due to the influence of test condition, instrument and equipment, manual operation etc., it is constantly present during live vibration experiments
Some uncertain factors, the signal of actual measurement are inevitably disturbed be subject to ambient noise.Although in data acquisition
In the measures such as average, filtering and shielding can be taken to reduce noise, but to obtain completely from the letter of noise pollution
Number it is unpractical.In order to more accurately identify the modal parameter of structure, the noise eliminated in signal just becomes very urgent.When
Before, signal de-noising problem is concentrated mainly on the neck such as acoustics, intelligent control, electronics, image and signal processing and linear math
Domain, and also lack relevant signal de-noising technical research for the Modal Parameter Identification problem of structure.When carrying out model analysis,
The way of generally use is to calculate the model order used to be higher than real model order, so as to allow the shadow of " noisy modt "
Ring.But the result so identified can produce false mode, and the reduction of computational efficiency can be caused, particularly the letter when signal
Make an uproar than it is low when, how distinguishing substantial amounts of false mode and true mode will become highly difficult.
At present, propose to carry out signal de-noising based on low-rank approximation technique in the prior art, should be based on low-rank approximation technique profit
With the Hankel matrix counter-diagonal methods of average, the signal after de-noising carries out Modal Parameter Identification, and this method carries to a certain extent
The high precision of Modal Parameter Identification, but in the noise-eliminating method before and after noise reduction Hankel matrixes deviation Frobenius norms
It is not minimum value, that is, what is finally obtained is not optimal solution mathematically, that is to say, that signal de-noising effect also has improved sky
Between.
The content of the invention
The purpose of the present invention is to overcome above-mentioned the deficiencies in the prior art, there is provided it is a kind of improve noise reduction precision be used for mode
The signal de-noising method of parameter identification.
To achieve the above object, the present invention uses following technical proposals：
A kind of signal de-noising method for Modal Parameter Identification, comprises the following steps：
Step 1：Hankel matrixes are built according to noisy structure impulse response signal；
Step 2：Hankel ranks of matrix are sought, is tried to achieve according to Hankel ranks of matrix and determines rank index, rank index is true using determining
Determine model order；
Step 3：Using rank index is determined and structure low-rank approaches and Hankel matrixes are handled, obtain after low-rank approaches
Restructuring matrix；
Step 4：Repeat step two and step 3 are until meet convergence, so as to obtain de-noising signal.
Step 5：Modal Parameter Identification is carried out using the de-noising signal.
Preferably, in step 1, the noisy structure impulse response signal is acceleration or speed or displacement.
Preferably, in step 2, Hankel ranks of matrix are asked for by the way of singular value decomposition.
Preferably, in step 3, the mode for obtaining restructuring matrix is：
If Hankel matrixes are H in step 1m×n, restructuring matrix Hp×(k+q)Model order is k, and l is signals and associated noises data
Point, p and q meet p+k+q-1=l, q=1,2 ..., n-k；Restructuring matrix Hp×(k+q)First be classified as preceding p in l data point
It is a, matrix Hp×(k+q)Last column it is a for the rear k+q in l data point, Hankel matrixes are structurally characterized in that counter-diagonal
On element it is equal, it is known that the first row and last column of matrix, can obtain restructuring matrix Hp×(k+q)2nd arranges to kth+q row
Data.
Preferably, in step 3, the structure low-rank mode of approaching is：Q initial values are 1, and the rank index of determining of restructuring matrix is pressed
Arranged according to descending, compare the maximum and second largest value for determining rank index, if maximum is more than or equal to K (K >=4, K ∈ Z) times second largest value,
Then structure low-rank approaches end, obtains the restructuring matrix after low-rank approaches；Otherwise, q=q+ Δs t, wherein Δ t ∈ N*, it is right
Hankel matrixes are reconstructed, until meeting above-mentioned condition.Δ t represents the speed approached of structure low-rank, if Δ t values select compared with
Small, then structure low-rank velocity of approch is fast, if the selection of Δ t values is larger, structure low-rank velocity of approch is slow.
Preferably, in step 3, K=4, Δ t=1.
Preferably, convergence is in step 4：
To reconstructing matrix Hp×(k+q)Carry out singular value decomposition and descending arrangement is carried out to singular value, singular value is expressed as λi(i
=1,2 ..., k+q), λ1＞ λ2＞ λ3... ＞ λk+q, convergence is that+1 singular value of kth levels off to the 1st singular value ratio
Zero.By setting the convergence, make Hankel matrix Hsm×nThe Frobenius norms that low-rank approaches front and rear deviation level off to
Minimum, improves the precision of de-noising signal.
The selection of the convergence is not unique, it is necessary to according to restructuring matrix Hp×(k+q)Singular value judged, as another
One alternative, convergence may be configured as+1 singular value of kth and level off to 0, i.e. λk+1＜ 1 × 10-15, at this time, make Hankel
Matrix Hm×nThe Frobenius norms that low-rank approaches front and rear deviation level off to minimum.
Preferably, convergence function expression is in step 4：
Preferably, Modal Parameters Identification is complex exponential method in step 5.
Wherein, the concrete mode of step 1 is as follows：
Based on the noisy structure impulse response signal for including l data point of sensor actual measurement, square formation or close is built
The Hankel matrix Hs of box formationm×n, wherein, if l is even number,If l is odd number,
The concrete mode of step 2 is as follows：
To Hankel matrix Hsm×nCarry out singular value decomposition, the singular value λ arranged in descending orderi(i=1,2 ..., n),
λ1＞ λ2＞ λ3... ＞ λn。
Determine rank index MOC, function expression isJ represents order, j=1,2 ..., n-1.
Ask and determine rank index maximum, and using the corresponding order k of the maximum as the order of model, i.e., included in signal
Mode number is
The concrete mode of step 3 is as follows：
In order to improve the computational efficiency of noise reduction algorithm, to the Hankel matrix Hs in step 2m×nIt is reconstructed and is reconstructed
Matrix Hp×(k+q)；
Due to matrix dimension iteration convergence efficiency is influenced it is very big, if Hankel matrixes are using square formation or close to square matrix-shaped
Formula, calculates complicated and time-consuming；If Hankel matrixes use matrix dimension as p × (k+1), convergence efficiency highest, but due to
Matrix dimension is used to cause matrix dimension smaller for p × (k+1), cause true modal information partial loss occur after noise reduction, i.e.,
True modal information goes out active while carrying out noise reduction.
For this reason, COMPREHENSIVE CALCULATING efficiency and the aspect of noise reduction two, set iterated conditional.Iterated conditional is to determine rank index most
Big value is more than or equal to four times of second largest values for determining rank index, which act as：It is not in true mould to ensure de-noising signal
The loss of state information or omission；Meanwhile with Hankel matrixes compared with square formation or close to by the way of square formation, calculate letter
It is single, computational efficiency is improved, makes convergence efficiency as high as possible.
The iterated conditional for determining rank index is that the maximum for determining rank index is more than or equal to four times of second largest values for determining rank index, reason
It is：Determine rank index maximum and correspond to model order, and model order is equal to twice of the mode number included in signal, if determining rank
Index maximum and second largest value difference are little, illustrate that model order judges unobvious, de-noising signal can be caused to nevertheless suffer from noise
Influence, or there is a situation where to omit true modal information.
If determining rank index maximum and larger difference occurring in second largest value, it is obvious to illustrate that model order judges, for this reason, setting is fixed
The maximum of 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 Hsm×nSpecific reconstruct mode is as follows：
If p+k+q-1=l, q=1,2 ..., n-k：
Q=1 is made, then p=l-k；
A. to Hankel matrix Hsm×nIt is reconstructed and obtains restructuring matrix Hp×(k+q), restructuring matrix Hp×(k+q)First be classified as l
Preceding p in a data point, restructuring matrix Hp×(k+q)Last column it is a for the rear k+q in l data point, Hankel matrixes
It is structurally characterized in that the element on counter-diagonal is equal, it is known that the first row and last column of matrix, can obtain restructuring matrix
Hp×(k+q)The data that 2nd row are arranged to kth+q.
B. to reconstructing matrix Hp×(k+q)Carry out singular value decomposition and obtain the singular value of the matrix, and to the singular value in descending order
Arrangement, is expressed as λi(i=1,2 ..., k+q), λ1＞ λ2＞ λ3... ＞ λk+q。
C. asked according to above-mentioned singular value and determine rank index MOCj(j=1,2 ..., k+q-1), store MOCjMaximum MOCMAXWith
Second largest value MOCSUB；
D. K=4, Δ t=1 are taken, if determining rank index maximum and second largest value meets following functional relation
MOCMAX≥4MOCSUB, then matrix dimension be determined as p × (k+q)；
If determine rank index maximum and second largest value is unsatisfactory for above-mentioned functional relation, i.e. MOCMAX＜ 4MOCSUB, then q=q+1,
And return and perform above-mentioned steps a to step c, when meeting q=t, MOCMAX≥4MOCSUB, then calculate and terminate, determine Hp×(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 3p×(k+t)Matrix carries out singular value decomposition, obtains orthogonal vectors Wherein R represents real number matrix, and the singular value arranged in descending order, is expressed as λi, i=1,2 ...,
K+t, wherein λ1≥...≥λk+t。
(2) equation is built
Wherein, i=1 ..., k+t, j=1 ..., p, subscript T represent the transposition of matrix, and e is the standard base of Line independent
Vector,It is to form Hp×(k+t)A series of basic matrixs of the linear space of matrix.
csDe-noising signal is represented, for signal to be asked.
OrderW=ij,
ThenIt is expressed as
WillMatrix form, i.e. Gc=d are expressed as, wherein, G ∈ Rp(k+t)×l, c ∈ Rl, d ∈ Rp×(k+t)。
(3) singular value decomposition is carried out to matrix G, i.e. matrix G is decomposed into
Wherein, Y ∈ Rp(k+t)×p(k+t), ZT∈Rl×l, Y and Z are orthogonal matrixes, Λ ∈ Rp(k+t)×lIt is diagonal matrix, Λ can
It is decomposed into a non-zero singular value submatrix ΛaWith some null matrix, wherein ΛaThe submatrix of a nonzero value is included for diagonal,
I.e.YaAnd ZaArranged for the preceding a of Y and Z.
(4) convergence is setIf restructuring matrix H in step 3p×(k+q)Singular value meets following functions
RelationThen utilizeAnd c=G-1D tries to achieve de-noising signal；
Otherwise return and perform step 2 and step 3 until meeting convergence.
The selection of above-mentioned convergence mark standard the reason is that：
To reconstructing matrix Hp×(k+q)Singular value decomposition obtains the singular value arranged in descending order, and tries to achieve restructuring matrix Hp×(k+q)
Order, when meeting that+1 singular value of kth and the 1st singular value ratio are smaller, it can be achieved that noise reduction, in theoretical research, when kth+1
A singular value and the 1st singular value ratio level off to zero when, it can be achieved that the raising of noise reduction precision, it is actual to calculate, pole can be set
Limit value is 1 × 10-15。
According to above-mentioned principle, convergence use function expression for
Step 5：The de-noising signal obtained using step 4 carries out Modal Parameter Identification.
The invention has the advantages that by using above-mentioned computational methods, with the prior art phase referred in background technology
Than, noise-reduction method using the mathematic(al) mean for taking Hankel matrix counter-diagonal elements, matrix deviation before and after noise reduction is unable to reach
Frobenius norms level off to minimum value, and the application can make drop by way of setting convergence and structure low-rank approaches
The Frobenius norms for front and rear Hankel matrix deviations of making an uproar level off to minimum, you can to realize the raising of de-noising signal precision.
Brief description of the drawings
The flow chart of the signal de-noising method for Modal Parameter Identification of Fig. 1 present invention；
Fig. 2 is the embodiment of the present invention jacket offshore platform model；
Fig. 3 is the embodiment of the present invention square formation H201×201Determine rank index；
Fig. 4 is the embodiment of the present invention matrix H390×12Determine rank index；
Fig. 5 is that the embodiment of the present invention signals and associated noises are contrasted with de-noising signal；
Fig. 6 is that the embodiment of the present invention precise signal is contrasted with de-noising signal.
Embodiment
The present invention is further described with reference to the accompanying drawings and examples.
The embodiment of the present invention is a jacket offshore platform model, referring to figs. 2 to Fig. 6.
Establish jacket offshore platform finite element numerical model：
Jacket offshore platform finite element numerical model parameter is as follows：
The outside diameter of stake is 24mm, wall thickness 2.5mm；The outside diameter of stull and diagonal brace is 16mm, wall thickness 1.5mm；Bosun
0.6m, wide 0.3m, thick 0.01m；From bottom to top, it is respectively 0.5m, 0.9m, 1.35m, 1.5m, 1.7m per layer height；The gradient of stake
For 1/10.
Jacket offshore platform finite element model is established using Ansys softwares, and model is obtained by FEM calculation
Preceding 2 order frequency and damping ratio theoretical value.Apply x at the node 1 of model to pulse excitation, difference measuring point 1,2,3,4
Locate x to dynamic respond time-histories, wherein sampling time interval 0.005 second.Research object is used as using the response signal at measuring point 1
(excitation of other positions, response signal are similar).
Precise signal is simulated with this section of sampled signal, the precise signal not Noise；Folded on the basis of this section of precise signal
The white Gaussian noise that it is 5% that plus noise is horizontal, to simulate signals and associated noises.Wherein noise level is defined as the standard of white Gaussian noise
The ratio between difference and the standard deviation of precise signal.
Step 1：Hankel matrixes are built according to noisy structure impulse response signal：
One section of noisy structure impulse response signal is taken, totally 401 data points, i.e. l=401, with 401 data points
Exemplified by analyzed.
By l=401, it is calculated
The Hankel square formations H that dimension is 201 × 201 is built according to above-mentioned 401 data points201×201。
Step 2：To Hankel square formations H201×201Singular value decomposition is carried out, tries to achieve the maximum MOC for determining rank indexk, such as scheme
Shown in 3, it is 4, i.e. k=4 to obtain determining the corresponding model order of rank index according to signals and associated noises model order figure, this shows that this is noisy
The mode number included in signal is 2.
Step 3：To the Hankel matrix Hs in step 2201×201Carry out approaching to obtain restructuring matrix using structure low-rank
Hp×(4+q), in order to improve computational efficiency, structure low-rank is approached by reconstructing Hankel matrix Hs201×201Realize.
Hankel matrix Hs201×201Reconstruct mode is as follows：
If p+k+q-1=l, wherein q=1,2 ..., n-k；
By l=401, k=4, p+q=398 is obtained.
K=4 is made, q initial values are 1：
A. restructuring matrix Hp×(4+q)First is classified as preceding p in l data point, restructuring matrix Hp×(4+q)Last column be
Rear 4+q in l data point, according to the characteristics of Hankel matrixes, the matrix the 2nd row are obtained to 4+q column datas.
B. to reconstructing matrix Hp×(4+q)Carry out singular value decomposition, the singular value λ arranged in descending orderi(i=1,2 ..., 4
+q),λ1＞ λ2＞ λ3... ＞ λ4+q, determine rank index according to what above-mentioned singular value was asked for arranging in descending order, determine rank index maximum
Value MOCMAXWith second largest value MOCSUB。
If c. MOCMAX＜ 4MOCSUB, then q=q+1, order perform above-mentioned steps a to b；
As shown in figure 4, as q=8, maximum MOCMAXFor 12.02, second largest value MOCSUBFor 2.80, meet MOCMAX≥
4MOCSUB, p=l-k-q+1=390, t=8 at this time, it is determined that matrix Hp×(4+q)Dimension is p × (k+t), i.e., 390 × 12.
Step 4：To reconstructing matrix H390×12Singular value decomposition is carried out, obtains the singular value arranged according to descending, is examined strange
Whether different value meets convergenceIf being unsatisfactory for the formula, return 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, it is apparent that the structure arteries and veins after noise reduction
Rushing response signal graph becomes very smooth.
Fig. 6 is that precise signal is contrasted with the structure impulse response signal after noise reduction, it can be seen that precise signal curve and drop
Structure impulse response signal curve after making an uproar almost overlaps, this explanation noise reduction is very good.
Step 5：Modal Parameter Identification：Using existing Modal Parameter Identification technology, such as complex exponential method, to precise signal,
Signal after signals and associated noises and noise reduction carries out Modal Parameter Identification respectively, obtains 2 rank modal frequencies and damping ratio, and with theory
Value compares, and is shown in Table 1, table 2.
Table 1：Modal frequency theoretical value (Hz) compared with the discre value based on precise signal, signals and associated noises and de-noising signal.
Table 2：Damping ratios theoretical value is compared 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, Modal Parameter Identification is carried out using de-noising signal, is significantly carried
High accuracy of identification.
Although above-mentioned be described the embodiment of the present invention with reference to attached drawing, model not is protected to the present invention
The limitation enclosed, those skilled in the art should understand that, on the basis of technical scheme, those skilled in the art are not
Need to make the creative labor the various modifications that can be made or deformation still within protection scope of the present invention.
Claims (7)
1. a kind of signal de-noising method for Modal Parameter Identification, it is characterized in that：
Step 1：Hankel matrixes are built using the structure impulse response signal of sensor actual measurement；
Step 2：Hankel ranks of matrix are asked for, is tried to achieve according to Hankel ranks of matrix and determines rank index, are determined using rank index is determined
Model order；
Step 3：Using rank index is determined and structure low-rank approaches and Hankel matrixes are handled, the weight after low-rank approaches is obtained
Structure matrix；
Step 4：Repeat step two and step 3 are until meet convergence, so as to obtain de-noising signal；
Step 5：Modal Parameter Identification is carried out using the de-noising signal；
In step 2, Hankel ranks of matrix are asked for by the way of singular value decomposition；
In step 3, the mode for obtaining restructuring matrix is：
If Hankel matrix Hsm×n, model order k, l are signals and associated noises data point, restructuring matrix Hp×(k+q), wherein p+k+q-
1=l, q=1,2 ..., n-k；Restructuring matrix Hp×(k+q)First be classified as preceding p in l signals and associated noises data point, reconstruct square
Last column of battle array is rear k+q in l data point；
In step 3, the structure low-rank mode of approaching is：Q initial values are 1, and the rank index of determining of restructuring matrix is arranged according to descending,
Compare the maximum and second largest value for determining rank index, if maximum is more than or equal to K times of second largest value, structure low-rank approaches end,
Obtain the restructuring matrix after low-rank approaches, otherwise, q=q+ Δ t, wherein Δ t ∈ N*, Hankel matrixes are reconstructed, until
Meet above-mentioned condition, wherein, K >=4, K ∈ Z.
2. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 1, it is characterized in that, in step 1,
The 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, it is characterized in that, in step 3, K
=4, Δ t=1.
4. a kind of signal de-noising method for Modal Parameter Identification as described in claim 1 or 3, it is characterized in that, step 4
In, convergence is：
It is H to restructuring matrixp×(k+q)Carry out singular value decomposition and descending arrangement is carried out to singular value, singular value is expressed as λi(i=
1,2,…,k+q),λ1＞ λ2＞ λ3... ＞ λk+q, convergence meets that+1 singular value of kth levels off to the 1st singular value ratio
Zero.
5. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 4, it is characterized in that, received in step 4
Holding back canonical function expression formula is：
6. a kind of signal de-noising method for Modal Parameter Identification as described in claim 1 or 3, it is characterized in that, step 4
In, to reconstructing matrix Hp×(k+q) carry out singular value decomposition and descending arrangement is carried out to singular value, singular value is expressed as λi(i=1,
2 ..., k+q), wherein λ1＞ λ2＞ λ3... ＞ λk+q, convergence levels off to 0 for+1 singular value of kth.
7. a kind of signal de-noising method for Modal Parameter Identification as claimed in claim 1, it is characterized in that, mould in step 5
State parameter identification method is complex exponential method.
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| CN106096530B (en) * | 2016-06-07 | 2019-04-16 | 西安交通大学 | A kind of Modal Parameters Identification under strong background noise environment |
| CN106446829A (en) * | 2016-09-22 | 2017-02-22 | 三峡大学 | Hydroelectric generating set vibration signal noise reduction method based on mode autocorrelation analysis of SVD and VMD |
| CN107133195B (en) * | 2017-04-14 | 2019-08-09 | 大连理工大学 | A kind of Methodology of The Determination of The Order of Model of engineering structure modal idenlification |
| CN107345834B (en) * | 2017-07-11 | 2020-06-23 | 中国人民解放军空军工程大学 | Linear narrow-band filtering method based on resonance enhanced singular value decomposition |
| CN107727228B (en) * | 2017-07-11 | 2019-12-31 | 中国人民解放军空军工程大学 | Sound field modal analysis method based on resonance enhanced singular value decomposition |
| CN107679456B (en) * | 2017-09-06 | 2021-07-06 | 中国海洋大学 | Ocean platform vibration response noise elimination method based on extreme value-residue decomposition |
| CN107943757B (en) * | 2017-12-01 | 2020-10-20 | 大连理工大学 | Order determination method based on sparse component analysis modal identification |
| 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 |
| CN112215274A (en) * | 2020-03-02 | 2021-01-12 | 周红 | Signal processing method and signal recovery equipment based on drilling engineering |
| CN112347922B (en) * | 2020-11-06 | 2022-02-08 | 华北电力大学 | Power signal filtering method and system by using Hankerl matrix |
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| CN103246890A (en) * | 2013-05-15 | 2013-08-14 | 中国石油大学(华东) | Modal parameter recognizing method based on multi-input multi-output signal noise reduction |
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| CN103246890A (en) * | 2013-05-15 | 2013-08-14 | 中国石油大学(华东) | Modal parameter recognizing method based on multi-input multi-output signal noise reduction |
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