CN103246890A - Modal parameter recognizing method based on multi-input multi-output signal noise reduction - Google Patents

Abstract

The invention relates to a modal parameter recognizing method based on multi-input multi-output signal noise reduction. The method is characterized by comprising the steps of step 1, performing block-Hankel matrix conversion on noise-containing multi-point pulse responding signals to obtain a first block-Hankel matrix; step 2, processing the first matrix by utilizing structural low rank approximating according to the rank of the first matrix to obtain a first non-block-Hankel matrix after the low rank approximating; step 3, replacing the elements of each block in a second matrix with math average values of the block elements on a back-diagonal to obtain a second block-Hankel matrix; step 4, repeating the steps 2 and 3 until convergence, thus obtaining the noise-reduced multi-point pulse responding signal; and step 5, performing modal parameter recognizing. The modal parameter recognizing method based on multi-input multi-output signal noise reduction can save machine time and improve recognizing accuracy.

Description

Modal Parameters Identification based on the MIMO signal noise reduction

Technical field

The present invention relates to the signal process field, particularly relate to a kind of Modal Parameters Identification based on the MIMO signal noise reduction.

Background technology

Traditional mode test and analysis are to be based upon on the basis of system's input and output data, and estimated frequency response function (frequency domain) or impulse response function (time domain) carry out Modal Parameter Identification more thus.Yet for actual large and complex structure, artificial excitation (input) is not a nothing the matter, and experiment enforcement difficulty is big, cost is high, often can't obtain the input information of structural system, so can only utilize the response message of output to carry out Modal Parameter Identification.

Based on the number difference of input, output reference point, be divided into the Modal Parameters Identification of single single output of input (SISO), single many outputs of input (SIMO), multiple-input and multiple-output (MIMO).For large and complex structure, single-point excitation seems that energy is not enough, and loss is very big in transmittance process, therefore from the place of point of excitation away from, response signal a little less than, signal to noise ratio (S/N ratio) is less.If strengthen exciting force, it is excessive then to be easy to generate local acknowledgement, causes non-linear phenomena.In addition single-point when excitation, if point of excitation just in time is in the node location of certain rank mode, concerning this rank mode, system will become uncontrollable and inconsiderable, so can't this rank mode of identification, will miss the phenomenon of mode.

For single input multiple output system, the modal parameter identification generally only utilizes the columns certificate in the frequency response function matrix, and therefore the quantity of information that can provide is limited, influences identification precision, to the intensive situation of mode, identification capability a little less than.

At these situations, since the eighties in 20th century, the modal parameter discrimination method of some multi-input multi-output systems has appearred successively, be called for short the MIMO method.Traditional MIMO method is directly to adopt the signal of all response point to carry out Modal Parameter Identification, yet because the signal of actual measurement is subjected to the interference of ground unrests such as test environment, electronic equipment inevitably, so the precision of recognition result will inevitably be affected.

In order to obtain recognition result more accurately, in time domain modal identification method and software in the past, adopt the method for stability diagram mostly.In theory, along with the computation model order increases gradually, can identify increasing modal parameter, still, have only real modal parameter just can tend towards stability gradually, false modal parameter then can not.Be higher than real model order owing to calculate the model order that adopts, thereby allowed the existence of noisy modt.And can not get rid of noisy modt fully by the stability diagram method, particularly along with the rising of model order, some false mode often tend towards stability easily, are difficult to correctly identify the true modal parameter of structure with stability diagram.And the stability diagram method depends on user's experience judgement to a great extent, like this because artificial factor can cause the reduction of counting yield, particularly when the signal to noise ratio (S/N ratio) of signal is low, how to distinguish a large amount of false mode and true mode will become very difficult.

Summary of the invention

The purpose of this invention is to provide a kind of Modal Parameters Identification based on the MIMO signal noise reduction of saving computing time, having improved work efficiency and accuracy of identification.

For solving the problems of the technologies described above, as one aspect of the present invention, a kind of Modal Parameters Identification based on the MIMO signal noise reduction is provided, it is characterized in that, may further comprise the steps: step 1, noisy multiple spot impulse response signal is carried out the block-Hankel matrixing, obtain a block-Hankel matrix; Step 2, the first non-block-Hankel matrix after obtaining low-rank after utilizing the structure low-rank to approach described first matrix handled according to described first rank of matrix and approaching; Step 3 replaces the element of each piece in described second matrix mathematical mean by the piece element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix; Step 4, repeating step 2 and step 3 be up to convergence, thereby obtain the multiple spot impulse response signal behind the noise reduction; Step 5 is carried out Modal Parameter Identification according to the multiple spot impulse response signal of a described block-Hankel rank of matrix after to described noise reduction.

Further, described method adopts the mode of svd (SVD) to determine described order.

Further, the Modal Parameters Identification in the described step 5 is the multiple reference points complex exponential method.

The present invention causes problems such as counting yield and accuracy of identification are not high for solving existing multiple-input and multiple-output time domain modal parameter recognition technology because signal is affected by noise, before Modal Parameter Identification, the method that adopts the structure low-rank to approach unifies to eliminate the noise in the hyperchannel response signal, carry out Modal Parameter Identification based on the signal behind the noise reduction then, in the time that machine can being saved, improve accuracy of identification.

Description of drawings

Fig. 1 has schematically shown the process flow diagram of the Modal Parameters Identification among the present invention;

Fig. 2 has schematically shown jacket offshore platform finite element model figure;

Fig. 3 has schematically shown the signals and associated noises model and has decided rank figure;

Fig. 4 has schematically shown the comparison diagram before and after the signal de-noising; And

Fig. 5 has schematically shown the comparison diagram behind accurate signal and the signal de-noising.

Embodiment

Below in conjunction with accompanying drawing embodiments of the invention are elaborated, but the multitude of different ways that the present invention can be defined by the claims and cover is implemented.

As shown in Figure 1, the Modal Parameters Identification based on the MIMO signal noise reduction among the present invention may further comprise the steps:

Step 1 is carried out the block-Hankel matrixing to noisy multiple spot impulse response signal, obtains a block-Hankel matrix;

Step 2, the first non-block-Hankel matrix after obtaining low-rank after utilizing the structure low-rank to approach described first matrix handled according to described first rank of matrix and approaching;

Step 3 replaces the element of each piece in described second matrix mathematical mean by the piece element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix; Preferably, described method adopts the mode of svd to determine described order.

Step 4, repeating step 2 and step 3 be up to convergence, thereby obtain the multiple spot impulse response signal behind the noise reduction;

Step 5 is carried out Modal Parameter Identification according to the multiple spot impulse response signal of a described block-Hankel rank of matrix after to described noise reduction.Preferably, the Modal Parameters Identification in the described step 5 is the multiple reference points complex exponential method.

The present invention causes problems such as counting yield and accuracy of identification are not high for solving existing multiple-input and multiple-output time domain modal parameter recognition technology because signal is affected by noise, before Modal Parameter Identification, the method that adopts the structure low-rank to approach unifies to eliminate the noise in the hyperchannel response signal, carry out Modal Parameter Identification based on the signal behind the noise reduction then, in the time that machine can being saved, improve accuracy of identification.

Below each details is elaborated.

(1) makes up the block-Hankel matrix

At first, the impulse response data of the multiple-input and multiple-output that sensor is surveyed is stored in the private memory.The power system of a N degree of freedom applies pulse excitation at the p point and obtains the impulse response function that q orders and can be expressed as:

$h_{\mathrm{pq}}\left(t\right)=\underset{r=1}{\overset{2N}{\mathrm{\Σ}}}{A}_{\mathrm{pq},r}{e}^{s_{r}t}---\left(1\right)$

Wherein

p∈{1，…，N _in}

q∈{1，…，N _out}

N _InAnd N _OutBe respectively the quantity of point of excitation (input) and response point (output)

s _r=-ω _rξ _r+ i ω ' _r,

It is damped frequency

ω _rAnd ξ _rRepresent r rank free-running frequency and damping ratio,

A _{Pq, r}The multiple amplitude of representative, e is the end of natural logarithm.

Impulse response function h when the actual measurement structure _Pq(t) comprise unknown M rank mode in, and when being expressed as discrete form with sampling interval Δ t, then t _k=k Δ t impulse response function matrix constantly can be expressed as:

h _k＝WZ ^kΦ ^T (2)

Wherein,

$h_k\∈R^{N_{\mathrm{in}}\×N_{\mathrm{out}}}$

$W\∈R^{N_{\mathrm{in}}\×2M}$

$Z=\mathrm{diag}\{{\mathrm{<figure-callout\; id="1"\; label="e\; s"\; filenames="HSA00000896119700012.png,HSA00000896119700031.png"\; state="\{\{state\}\}">e</figure-callout>}}^{s_{}},\&CenterDot;\&CenterDot;\&CenterDot;,e^{s_{2M}\mathrm{\&Delta;t}}\}$ Be diagonal matrix

$\mathrm{\&Phi;}\&Element;R^{N_{\mathrm{out}}\&times;2M}$

k＝0，1，2，…

R represents real number matrix, and its subscript represents matrix dimension.

Then, based on h _kMake up mN _In* nN _OutThe one block-Hankel matrix of dimension

(hereinafter to be referred as H).Wherein, matrix

In each piece (block, i.e. h independently _k) all be by t _kCorresponding N of the moment _InIndividual point of excitation N _OutThe N that the signal of individual response point is built into _In* N _OutThe matrix of dimension, mN _In, nN _Out〉=2M, x=m+n-2.

$H_{{\mathrm{mN}}_{\mathrm{in}}\&times;{\mathrm{nN}}_{\mathrm{out}}}=\left[\begin{array}{cccc}{h}_0& {\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000896119700012.png,HSA00000896119700031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1& \&CenterDot;\&CenterDot;\&CenterDot;& h_{n-1}\\ h_1& h_2& \&CenterDot;\&CenterDot;\&CenterDot;& h_n\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ h_{m-1}& h_m& \&CenterDot;\&CenterDot;\&CenterDot;& h_x\end{array}\right]---\left(3\right)$

(2) determine order

Use svd and determine a block-Hankel rank of matrix.The svd of matrix H (SVD) can be expressed as:

H＝U∑V ^T (4)

Wherein, $U\&Element;R^{{\mathrm{mN}}_{\mathrm{in}}\&times;{\mathrm{mN}}_{\mathrm{in}}},$ $V^T\&Element;R^{{\mathrm{nN}}_{\mathrm{out}}\&times;{\mathrm{nN}}_{\mathrm{out}}}$ Be orthogonal matrix, its subscript T represents transpose of a matrix,

Be diagonal matrix, its diagonal element is the singular value of descending sort.And ∑ can be decomposed into g non-zero singular value submatrix ∑ _gWith several zero submatrixs:

$\mathrm{\&Sigma;}=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="HSA00000896119700022.png,HSA00000896119700031.png"\; state="\{\{state\}\}">g</figure-callout>}}& 0\\ 0& 0\end{array}\right]---\left(5\right)$

This decomposition shows that the order of matrix H is g.

In theory, those singular values that exceed rank of matrix should equal zero, i.e. σ ₁〉=σ ₂〉=... 〉=σ _g＞0, σ _G+1=...=σ _l=0, l=min{mN in the formula _In, nN _Out.For measured signal, because the influence of random noise, these singular values do not equal zero, but can become very little, if select a suitable critical value ε, make σ ₁〉=σ ₂〉=... 〉=σ _g＞ε, σ _G+1＜ε sets up, and can determine model order (being order).

Introduce the model order index

J=1,2 ..., l-1, because singular value is descending sort, definition model order index MOC _jThe order of maximal value correspondence is the order of model, and this i.e. a block-Hankel rank of matrix, also is the twice that comprises the mode number in the signal.

(3) signal de-noising

The basic thought of signal de-noising of the present invention is: noisy impulse response signal is made up a block-Hankel matrix, by truncated singular value decomposition (TSVD) technology, the true mode in the signal and noisy modt are decomposed in the subspace of a series of singular values and singular value vector correspondence; And according to the order of determining, carry out the structure low-rank and approach calculating, only keep singular value and the singular value vector of true mode correspondence, and singular value and the singular value vector of noisy modt correspondence filtered, thereby reach the purpose of signal de-noising.

In theory, by the signals and associated noises h that comprises M rank mode _kA block-Hankel matrix H that makes up can be divided into two parts:

$H_{m{N}_{\mathrm{in}}\&times;{\mathrm{nN}}_{\mathrm{out}}}={\stackrel{\&OverBar;}{H}}_{{\mathrm{mN}}_{\mathrm{in}}\&times;{\mathrm{nN}}_{\mathrm{out}}}+E_{{\mathrm{mN}}_{\mathrm{in}}\&times;{\mathrm{nN}}_{\mathrm{out}}}---\left(6\right)$

Wherein,

Represent the block-Hankel matrix that actual signal makes up, E represents noise matrix.By above-mentioned argumentation, can determine matrix

Order equal 2M.

The basic thought that adopts structure low-rank approximation technique to carry out signal de-noising calculating is: obtain based on H Namely by with the immediate block-Hankel matrix of H

(order is 2M) approaches Make matrix H and

The Frobenius norm minimum of difference.

Concrete noise reduction step is as follows:

(a) a block-Hankel matrix H is carried out truncated singular value decomposition (TSVD), i.e. H=U ∑ V ^T, based on above-mentioned definite order g, obtain $\widehat{\mathrm{\&Sigma;}}=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="g"\; filenames="HSA00000896119700022.png,HSA00000896119700031.png"\; state="\{\{state\}\}">g</figure-callout>}}& 0\\ 0& 0\end{array}\right],$ Then by formula

Obtain the matrix that low-rank approaches Attention: at this moment

It or not the form of block-Hankel matrix.

(b) with matrix In the element of each piece (block) replaced by the mathematical mean of the piece on the back-diagonal at its place (block) element, just obtain the block-Hankel matrix

Attention: at this moment

Order be not g.

(c) repeating step (a) and (b) is up to convergence.

(4) Modal Parameter Identification

Adopt fixed model order and carry out Modal Parameter Identification by the multiple-input and multiple-output impulse response signal behind the noise reduction.

Please refer to Fig. 2 to Fig. 5, below, this specific embodiment of uniting conduit posture ocean platform further illustrates the present invention.

1, sets up the jacket offshore platform finite element numerical model

Embodiments of the invention are jacket offshore platform models, as shown in Figure 2.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 the jacket offshore platform finite element model, and obtain preceding two order frequencies of model and the theoretical value of damping ratio by FEM (finite element) calculation.At first apply x to pulse excitation at node 1 place of model, record node 1,2,3 respectively, 4 x of place respond time-histories to displacement, apply x to pulse excitation at node 2 places of model then, record node 1,2,3 again respectively, 4 x of place respond time-histories to displacement, wherein sampling time interval is 0.005 second.Four outputs with two inputs and corresponding each input amount to eight sections sampled signals, and 601 data points of every segment signal are as research object (excitation of other position, response signal are similarly).Simulate accurate signal (not containing noise) with eight sections sampled signals; The superimposed noise level is 5% white Gaussian noise on every section accurate basis of signals, simulates signals and associated noises.Wherein noise level is defined as the ratio of standard deviation with the standard deviation of accurate signal of white Gaussian noise.

2, model is decided rank:

At first determine the model order of signals and associated noises.With 8 segment signal (N _In* N _Out=2 * 4), 601 every section data points (m=n=301) structure dimension is mN _In* nN _OutAn i.e. block-Hankel matrix H of 602 * 1204 _602x1204, then to H _602x1204Carry out svd, with the descending arrangement of singular value, computation model order index MOC _j, as Fig. 3, model order is that the MOC value of 4 o'clock correspondences is maximal value as can be seen, can determine that thus this model order is 4, namely includes 2 rank modal informations in this signals and associated noises.

3, signal de-noising:

Based on the model order of determining 4, (a) low-rank in the signal de-noising step is approached with (b) the back-diagonal element is average, replace iteration, up to satisfying convergence, the signal of this moment is the signal behind the noise reduction.Fig. 4 is the contrast before and after the signal de-noising, can find out significantly that it is very level and smooth that the curve behind the noise reduction becomes.Fig. 5 is the signal contrast behind accurate signal and the noise reduction, and as can be seen, accurately the signal curve behind signal curve and the noise reduction almost overlaps, and this explanation signal de-noising effect is fine.

4, Modal Parameter Identification:

Adopt existing multiple-input and multiple-output Modal Parameter Identification technology, as the multiple reference points complex exponential method, the signal behind accurate signal, signals and associated noises and the noise reduction is carried out Modal Parameter Identification respectively, obtain 2 rank model frequency and damping ratios, and with theoretical value relatively, see Table 1, table 2.

Table 1: the model frequency theoretical value with based on the discre value of accurate signal, signals and associated noises and de-noising signal relatively.

Table 2 modal damping than theoretical value with based on the discre value of accurate signal, signals and associated noises and de-noising signal relatively.

As can be seen from the table: compare with signals and associated noises, adopt de-noising signal to carry out Modal Parameter Identification, improved accuracy of identification.

Adopt the block-Hankel matrix that multiple-input and multiple-output (MIMO) signal is carried out noise reduction process, carry out Modal Parameter Identification then, can improve accuracy of identification.

The present invention makes up a block-Hankel matrix by the impulse response signal to multiple-input and multiple-output, adopt the svd technology, decide the rank index to determine model order in conjunction with what quantize, based on model order the block-Hankel matrix is carried out the structure low-rank and approach calculating, only keep singular value and the singular value vector of true mode correspondence, thereby reach the purpose of signal de-noising.Final based on the model order of determining, and the signal behind the employing noise reduction carries out the Modal Parameter Identification of multiple-input and multiple-output.

The different embodiments of the present invention and multiple-input and multiple-output Modal Parameters Identification of the prior art in the following areas.At present, traditional multiple-input and multiple-output Modal Parameters Identification does not also have the special algorithm of considering to eliminate noise, common way is to calculate the model order that adopts to be higher than real model order, thereby " allowed " existence of noisy modt, adopt " stability diagram " technology to determine real model order then, and the false mode in the rejecting recognition result, to keep true mode.

But this method need progressively increase model order, repeatedly " tentative calculation ", and the experience that depends on the user judges, reduced counting yield; And can not get rid of noisy modt fully, particularly along with the increase of model order, some false mode also tend towards stability easily, bring difficulty for the accurate identification of modal parameter.Compare with traditional technology, the Modal Parameters Identification based on the MIMO signal noise reduction among the present invention has been saved computing time, has improved work efficiency, and has improved the accuracy of identification of modal parameter, thereby has more actual application value.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various changes and variation.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. the Modal Parameters Identification based on the MIMO signal noise reduction is characterized in that, may further comprise the steps:

Step 1 is carried out the block-Hankel matrixing to noisy multiple spot impulse response signal, obtains a block-Hankel matrix;

Step 2, the first non-block-Hankel matrix after obtaining low-rank after utilizing the structure low-rank to approach described first matrix handled according to described first rank of matrix and approaching;

Step 3 replaces the element of each piece in described second matrix mathematical mean by the piece element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix;

Step 4, repeating step 2 and step 3 be up to convergence, thereby obtain the multiple spot impulse response signal behind the noise reduction;

Step 5 is carried out Modal Parameter Identification according to the multiple spot impulse response signal of a described block-Hankel rank of matrix after to described noise reduction.

2. Modal Parameters Identification according to claim 1 is characterized in that, described method adopts the mode of svd to determine described order.

3. Modal Parameters Identification according to claim 1 is characterized in that, the Modal Parameters Identification in the described step 5 is the multiple reference points complex exponential method.

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