CN103246890B - Modal Parameters Identification based on multi-input multi-output signal noise reduction - Google Patents

Abstract

The present invention relates to a kind of Modal Parameters Identification based on multi-input multi-output signal noise reduction, it is characterized in that, comprise the following steps: step 1, noisy multiple spot impulse response signal is carried out block-Hankel matrixing, obtains a block-Hankel matrix；Step 2, utilizes structure low-rank to approach obtaining the non-block-Hankel matrix of first after low-rank approaches after described first matrix disposal according to described first rank of matrix；Step 3, is replaced the element of each piece in described second matrix by the mathematical mean of the block element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix；Step 4, repeats step 2 and step 3 until restraining, thus obtaining the multiple spot impulse response signal after noise reduction；Step 5, carries out Modal Parameter Identification.When the present invention can save machine, improve accuracy of identification.

Description

Modal Parameters Identification based on multi-input multi-output signal noise reduction

Technical field

The present invention relates to signal processing field, particularly relate to a kind of Modal Parameters Identification based on multi-input multi-output signal noise reduction.

Background technology

Traditional mould measurement and analysis are built upon on the basis of system input and output data, thus estimated frequency response function (frequency domain) or impulse response function (time domain), then carry out Modal Parameter Identification.But, for actual large and complex structure, artificial excitation (input) is not a nothing the matter, and difficulty is big, cost is high in experiment enforcement, often cannot obtain the input information of structural system, so the response message only with output carries out Modal Parameter Identification.

Number based on input, output reference point is different, is divided into the Modal Parameters Identification of single-input single-output (SISO), single input and multi-output (SIMO), multiple-input and multiple-output (MIMO).For large and complex structure, single-point-excitation seems that energy is inadequate, and loss is very big in transmittance process, and therefore from point of excitation place farther out, response signal is more weak, and noise is smaller.If increasing exciting force, then easily produce local acknowledgement excessive, cause non-linear phenomena.Additionally during single-point-excitation, if point of excitation is exactly in the node location of certain order mode state, for this order mode state, system will become uncontrollable and inconsiderable, therefore will be unable to this order mode state of identification, and the phenomenon of leakage mode will occur.

For single-input multiple output, Modal Parameter Identification generally only utilizes the column data in frequency response function matrix, and the quantity of information being therefore provided that is limited, affects identification precision, and the situation that mode is intensive, identification capability is more weak.

For these situations, from the eighties in 20th century, occur in that the Modal Parameters Identification of some multi-input multi-output systems successively, be called for short MIMO method.Traditional MIMO method is directly to adopt the signal of all response point to carry out Modal Parameter Identification, but, owing to the signal of actual measurement is inevitably subject to the interference of the background noise such as test environment, electronic equipment, therefore the precision of recognition result will necessarily be affected.

In order to obtain recognition result more accurately, in conventional Time-Domain Modal recognition methods and software, mostly adopt the method stablizing figure.In theory, along with computation model order is gradually increased, will recognise that increasing modal parameter, but, only real modal parameter just can tend towards stability gradually, and false mode parameter then will not.Owing to calculating the model order adopted higher than real model order, thus having allowed the existence of noisy modt.And noisy modt can not be got rid of completely by stablizing figure method, particular with the rising of model order, some false modes tend to tend towards stability, and are difficult to correctly identify the true modal parameter of structure with stable figure.And stablize figure method and be largely dependent upon the micro-judgment of user, so owing to the impact of anthropic factor can cause the reduction of computational efficiency, particularly when the signal to noise ratio of signal is low time, how to distinguish substantial amounts of false mode and true mode will become highly difficult.

Summary of the invention

It is an object of the invention to provide and a kind of save the calculating time, improve the Modal Parameters Identification based on multi-input multi-output signal noise reduction of work efficiency and accuracy of identification.

For solving above-mentioned technical problem, as one aspect of the present invention, provide a kind of Modal Parameters Identification based on multi-input multi-output signal noise reduction, it is characterized in that, comprise the following steps: step 1, noisy multiple spot impulse response signal is carried out block-Hankel matrixing, obtains a block-Hankel matrix；Step 2, utilizes structure low-rank to approach obtaining the non-block-Hankel matrix of first after low-rank approaches after described first matrix disposal according to described first rank of matrix；Step 3, is replaced the element of each piece in described second matrix by the mathematical mean of the block element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix；Step 4, repeats step 2 and step 3 until restraining, thus obtaining the multiple spot impulse response signal after noise reduction；Step 5, carries out Modal Parameter Identification according to a described block-Hankel rank of matrix to the multiple spot impulse response signal after described noise reduction.

Further, described method adopts the mode of singular value decomposition (SVD) to determine described order.

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

The present invention solves that existing multiple-input and multiple-output Time-Domain Modal parameter identification technology causes the problems such as computational efficiency and accuracy of identification are not high because signal is affected by noise, before Modal Parameter Identification, the method that structure low-rank approaches is adopted to unify to eliminate the noise in multichannel response signal, it is then based on the signal after noise reduction and carries out Modal Parameter Identification, when can save machine, improve accuracy of identification.

Accompanying drawing explanation

Fig. 1 diagrammatically illustrates the flow chart of the Modal Parameters Identification in the present invention；

Fig. 2 diagrammatically illustrates jacket offshore platform FEM (finite element) model figure；

Fig. 3 diagrammatically illustrates signals and associated noises model and determines rank figure；

Fig. 4 diagrammatically illustrates the comparison diagram before and after signal de-noising；And

Fig. 5 diagrammatically illustrates the comparison diagram after precise signal and signal de-noising.

Detailed description of the invention

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

As it is shown in figure 1, the Modal Parameters Identification based on multi-input multi-output signal noise reduction in the present invention, comprise the following steps:

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

Step 2, utilizes structure low-rank to approach obtaining the non-block-Hankel matrix of first after low-rank approaches after described first matrix disposal according to described first rank of matrix；

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

Step 4, repeats step 2 and step 3 until restraining, thus obtaining the multiple spot impulse response signal after noise reduction；

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

The present invention solves that existing multiple-input and multiple-output Time-Domain Modal parameter identification technology causes the problems such as computational efficiency and accuracy of identification are not high because signal is affected by noise, before Modal Parameter Identification, the method that structure low-rank approaches is adopted to unify to eliminate the noise in multichannel response signal, it is then based on the signal after noise reduction and carries out Modal Parameter Identification, when can save machine, improve accuracy of identification.

Below each details is described in detail.

(1) block-Hankel matrix is built

First, the impulse response data of the multiple-input and multiple-output surveyed by sensor is stored in private memory.The impulse response function that the dynamical system of one N degree of freedom obtains q point in the applying pulse excitation of p point 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_outThe respectively quantity of point of excitation (input) and response point (output)

s_r=-ω_rξ_r+iω′_r,It it is damped frequency

ω_rAnd ξ_rRepresent r rank natural frequency and damping ratio,

A_{Pq, r}Representing multiple amplitude, e is the end of natural logrithm.

Impulse response function h when actual measurement structure_pqT () comprises the M order mode state of the unknown, and when being expressed as discrete form with sampling interval Δ t, then t_kThe impulse response function matrix of=k Δ t is represented by:

h_k=WZ^kΦ^T(2)

Wherein,

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

$W\∈R^{N_{\mathrm{in}}\×2M}$

$Z=\mathrm{diag}\{e^{s_1\mathrm{\Δt}},\·\·\·,e^{s_{2M}\mathrm{\Δt}}\}$ For diagonal matrix

$\mathrm{\Φ}\∈R^{N_{\mathrm{out}}\×2M}$

K=0,1,2 ...

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

Then, based on h_kBuild mN_in×nN_outOneth block-Hankel matrix of dimension(hereinafter referred to as H).Wherein, matrixIn each independent block (block, i.e. h_k) it is all by t_kMoment correspondence N_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.

$H_{{\mathrm{mN}}_{\mathrm{in}}\×{\mathrm{nN}}_{\mathrm{out}}}=\left[\begin{array}{cccc}{h}_0& h_1& \·\·\·& h_{n-1}\\ h_1& h_2& \·\·\·& h_n\\ \·& \·& & \·\\ \·& \·& \·\·\·& \·\\ \·& \·& & \·\\ h_{m-1}& h_m& \·\·\·& h_x\end{array}\right]---\left(3\right)$

(2) order is determined

Application singular value decomposition determines a block-Hankel rank of matrix.The singular value decomposition (SVD) of matrix H is represented by:

H=U ∑ V^T(4)

Wherein, $U\∈R^{{\mathrm{mN}}_{\mathrm{in}}\×{\mathrm{mN}}_{\mathrm{in}}},$ $V^T\∈R^{{\mathrm{nN}}_{\mathrm{out}}\×{\mathrm{nN}}_{\mathrm{out}}}$ Being orthogonal matrix, its subscript T represents the transposition of matrix,Being diagonal matrix, its diagonal element is the singular value of descending.And ∑ can be analyzed to g non-zero singular value submatrix ∑_gWith several zero submatrixs:

$\mathrm{\Σ}=\left[\begin{array}{cc}{\mathrm{\Σ}}_g& 0\\ 0& 0\end{array}\right]---\left(5\right)$

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

In theory, those should be equal to zero beyond the singular value of rank of matrix, i.e. σ₁≥σ₂≥…≥σ_g> 0, σ_g+1=...=σ_l=0, l=min{mN in formula_in, nN_out}.For measured signal, due to the impact of random noise, these singular values are also not equal to zero, but can become only small, if selecting a suitable marginal value ε so that σ₁≥σ₂≥…≥σ_g> ε, σ_g+1< ε sets up, and namely can determine that model order (i.e. order).

Introduce model order indexJ=1,2 ..., l-1, owing to singular value is descending, Definition Model order index MOC_jThe order that order is model that maximum is corresponding, this is a block-Hankel rank of matrix, is also the twice comprising mode number in signal.

(3) signal de-noising

The basic thought of signal de-noising of the present invention is: noisy impulse response signal is built a block-Hankel matrix, by truncated singular value decomposition (TSVD) technology, the true mode in signal is decomposed in the subspace that a series of singular value is corresponding with singular value vector with noisy modt；And according to the order determined, carry out structure low-rank approximation computation, only retain singular value corresponding to true mode and singular value vector, and singular value corresponding for noisy modt and singular value vector are filtered, thus reaching the purpose of signal de-noising.

In theory, by the signals and associated noises h comprising M order mode state_kThe block-Hankel matrix H built 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,Representing the block-Hankel matrix that actual signal builds, E represents noise matrix.By above-mentioned discussion, it may be determined that matrixOrder equal to 2M.

Employing structure low-rank approximation technique carries out the basic thought of signal de-noising calculating: obtain based on HNamely by block-Hankel matrix immediate with H(order is 2M) approachesMake matrix H andThe Frobenius Norm minimum of difference.

Concrete noise reduction step is as follows:

A oneth block-Hankel matrix H is carried out truncated singular value decomposition (TSVD) by (), i.e. H=U ∑ V^T, based on the above-mentioned order g determined, obtain $\widehat{\mathrm{\&Sigma;}}=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_g& 0\\ 0& 0\end{array}\right],$ Then by formulaObtain the matrix that low-rank approachesNote: nowIt it not the form of block-Hankel matrix.

B () is by matrixIn the element of each piece (block) replaced by the mathematical mean of block (block) element on the back-diagonal at its place, just obtain block-Hankel matrixNote: nowOrder be not g.

C () repeats step (a) and (b), until 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 after noise reduction.

Refer to Fig. 2 to Fig. 5, below, in conjunction with this specific embodiment of jacket offshore platform, the present invention is further illustrated.

1, jacket offshore platform finite element numerical model is set up

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 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 FEM (finite element) model, and obtained front two order frequencies of model and the theoretical value of damping ratio by FEM calculation.First x is applied at node 1 place of model to pulse excitation, record node 1,2,3,4 place x is to dynamic respond time-histories respectively, then apply x at node 2 place of model to pulse excitation, again record node 1,2,3,4 place x respectively to dynamic respond time-histories, wherein sampling time interval 0.005 second.With two inputs and four outputs of corresponding each input, eight sections of sampled signals altogether, 601 data points of every segment signal are as object of study (excitation of other position, response signal similar).Precise signal (not Noise) is simulated with eight sections of sampled signals；On every 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.

2, rank determined by model:

First the model order of signals and associated noises is determined.With 8 segment signal (N_in×N_out=2 × 4), 601 every section data points (m=n=301) build dimension is mN_in×nN_outAn i.e. block-Hankel matrix H of 602 × 1204_602x1204, then to H_602x1204Carry out singular value decomposition, by descending for singular value arrangement, computation model order index MOC_j, such as Fig. 3, it can be seen that the MOC value that model order is corresponding when being 4 is maximum, thus can determine that this model order is 4, namely this signals and associated noises include 2 rank modal informations.

3, signal de-noising:

Based on a determination that model order 4, (a) low-rank in signal de-noising step is approached and (b) back-diagonal element is average, alternating iteration, until meeting convergence, signal now is the signal after noise reduction.Fig. 4 is the contrast before and after signal de-noising, it is possible to be apparent from, and the curve after noise reduction becomes very smooth.Fig. 5 is the signal contrast after precise signal and noise reduction, it can be seen that the signal curve after precise signal curve and noise reduction almost overlaps, and this illustrates that signal de-noising effect is fine.

4, Modal Parameter Identification:

Adopt existing multiple-input and multiple-output Modal Parameter Identification technology, such as multiple reference points complex exponential method, the signal after precise signal, signals and associated noises and noise reduction is carried out respectively Modal Parameter Identification, obtains 2 rank model frequency and damping ratios, and compare with theoretical value, in Table 1, table 2.

Table 1: model frequency theoretical value compares 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 the table: compared with signals and associated noises, adopt de-noising signal to carry out Modal Parameter Identification, improve accuracy of identification.

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

The present invention is by building a block-Hankel matrix to the impulse response signal of multiple-input and multiple-output, adopt singularity value decomposition, rank index is determined to determine model order in conjunction with what quantify, based on model order, block-Hankel matrix carried out structure low-rank approximation computation, only retain singular value corresponding to true mode and singular value vector, thus reaching the purpose of signal de-noising.It is based ultimately upon the model order determined, and adopts the signal after noise reduction to carry out the Modal Parameter Identification of multiple-input and multiple-output.

The present invention is embodied in following aspect from the different of multiple-input and multiple-output Modal Parameters Identification of the prior art.At present, traditional multiple-input and multiple-output Modal Parameters Identification is but without the special algorithm considering to eliminate noise, common practice is to calculate the model order adopted higher than real model order, thus " having allowed " existence of noisy modt, then " stable figure " technology is adopted to determine real model order, and reject the false mode in recognition result, to retain true mode.

But this method needs to incrementally increase model order, repeatedly " tentative calculation ", and depend on the micro-judgment of user, reduce computational efficiency；And noisy modt can not be got rid of completely, particular with the increase of model order, some false modes also easily tend towards stability, and bring difficulty to accurately identifying of modal parameter.Compared with traditional technology, the Modal Parameters Identification based on multi-input multi-output signal noise reduction in the present invention, save the calculating time, improve work efficiency, and improve the accuracy of identification of modal parameter, thus have more actual application value.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.

Claims (1)

1. the Modal Parameters Identification based on multi-input multi-output signal noise reduction, it is characterised in that comprise the following steps:

Step 1, carries out block-Hankel matrixing to noisy multiple spot impulse response signal, obtains a block-Hankel matrix；Specific as follows:

First, the impulse response data of the multiple-input and multiple-output surveyed by sensor is stored in private memory, and the impulse response function that the dynamical system of a N degree of freedom obtains q point in the applying pulse excitation of p point is expressed as:

Wherein

P ∈ 1 ..., N_in}

Q ∈ 1 ..., N_out}

N_inAnd N_outThe respectively quantity of point of excitation (input) and response point (output)；

s_r=-ω_rξ_r+iω′_r,It is damped frequency,

ω_rAnd ξ_rRepresent r rank natural frequency and damping ratio,

A_{Pq, r}Representing multiple amplitude, e is the end of natural logrithm,

Impulse response function h when actual measurement structure_pqT () comprises the M order mode state of the unknown, and when being expressed as discrete form with sampling interval Δ t, then t_kThe impulse response function matrix of=k Δ t is represented by:

h_k=WZ^kΦ^T(2)

Wherein,

For diagonal matrix,

K=0,1,2 ...,

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

Then, based on h_kBuild mN_in×nN_outOneth block-Hankel matrix of dimensionIt is called for short H, wherein, matrixIn each independent block block, i.e. h_kIt is all by t_kMoment correspondence N_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；

Step 2, utilizes structure low-rank to approach obtaining the non-block-Hankel matrix of first after low-rank approaches after described first matrix disposal according to described first rank of matrix；Specifically comprise the following steps that

The singular value decomposition of matrix H is represented by:

H=U ∑ V^T(4)

Wherein,Being orthogonal matrix, its subscript T represents the transposition of matrix,Being diagonal matrix, its diagonal element is the singular value of descending, and ∑ can be analyzed to g non-zero singular value submatrix ∑_gWith several zero submatrixs:

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

In theory, those should be equal to zero beyond the singular value of rank of matrix, i.e. σ₁≥σ₂≥…≥σ_g> 0, σ_g+1=...=σ_l=0, l=min{mN in formula_in, nN_out}；For measured signal, due to the impact of random noise, these singular values are also not equal to zero, but can become only small, if selecting a suitable marginal value ε so that σ₁≥σ₂≥…≥σ_g> ε, σ_g+1< ε sets up, and namely can determine that model order；

For measured signal, based on the above-mentioned order g determined, obtainThen by formulaObtain the non-block-Hankel matrix of first after low-rank approaches

Step 3, by described first non-block-Hankel matrix, namely in the second matrix, the element of each piece is replaced by the mathematical mean of the block element on the back-diagonal at its place, just obtains the 2nd block-Hankel matrix；Specifically comprise the following steps that

By matrixIn the element of each piece of block replaced by the mathematical mean of the block block element on the back-diagonal at its place, just obtain the 2nd block-Hankel matrix

Step 4, repeats step 2 and step 3 until restraining, thus obtaining the multiple spot impulse response signal after noise reduction；

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

Described method adopts the mode of singular value decomposition to determine described order；

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