CN104154893A - Vibration displacement response reconstruction method based on discrete singular convolution - Google Patents

Abstract

The invention discloses a method of vibration displacement response reconstruction based on discrete singular convolution. The method comprises the steps of (1) establishing a minimum square error function for measuring acceleration and actual displacement second differential, (2) applying variation and Fourier transform to obtain the transfer function of a minimum value function control equation, (3) obtaining the precision function of a reconstruction displacement by using the transfer function of the control equation and determining the target precision of the displacement reconstruction, (4) applying a discrete singular convolution formula to obtain a control equation discrete singular feature matrix expression, and (5) calculating the acceleration vector expression of measurement point displacement according to the discrete singular expression of the control equation. The method has the advantages of high pertinence and high accuracy, a vibration acceleration signal can be effectively used to reconstruct a vibration displacement signal, and the application of the method is relatively wide.

Description

A kind of vibration displacement response reconstructing method based on discrete unusual convolution

Technical field

The invention belongs to vibration-testing signal processing technology field, especially a kind of vibration displacement response reconstructing method based on discrete unusual convolution.

Background technology

The vibration displacement response that accurately obtains structural key region contributes to grasp the running status of system architecture.Develop rapidly along with modern industrial technology, there is active demand in increasing field to the measuring technology of structural vibration displacement signal, as system control, to fields such as the evaluation of equipment dynamic perfromance, earthquake engineering research, science of bridge building research, Antiseismic building characteristic research, in this external auto industry, when the dynamic perfromance of research structure, vibration noise characteristic and riding comfort, the dynamic displacement signal of structure is also essential.But, in practical engineering application, utilize acceleration information reconfiguration system dynamic displacement comparatively extensive.Space constraint due to structure is often difficult to find suitable displacement transducer installation site on the one hand, even if inside configuration has enough spaces to arrange displacement transducer on the other hand, the also just relative displacement between installation site and tested point that displacement transducer test obtains.For large scale structure, as the vibration of the automotive interior in travelling, bridge vibration of beam, seismic event vibration etc., relative displacement is difficult to meet the needs of research, and the absolute displacement signal really needing is still difficult to Measurement accuracy.So vibration acceleration test is quite extensive in engineering application, displacement signal can be reconstructed and be obtained by the acceleration signal that test is obtained.So structure dynamic response reconstruct has been subjected to widely and has paid close attention to.

Utilizing acceleration information to carry out the displacement response of reconfiguration system is mainly by building the displacement of digital filter reconfiguration system, comprising finite impulse response filter and infinite impulse response filter.Utilize infinite impulse response filter to carry out initial displacement and initial velocity that displacement structure reconstruct needs known road system.But in actual engineering problem, the initial displacement of structural system and initial velocity are difficult to obtain, and As time goes on, the low-frequency component in measuring-signal will be exaggerated and propagate.Tradition finite impulse response filter carrys out the dynamic displacement of reconfiguration system structure by the linear combination of acceleration measurement, this method needs a known parsing transport function in frequency domain to obtain the coefficient of finite impulse wave filter.But, for finite impulse response filter, owing to resolving transport function, at zero frequency place, there is singular point, therefore, in low-frequency range, be conventionally difficult to carry out approximate analysis transport function accurately by limited Fourier series.Within a relatively short time interval, the acceleration of measuring is carried out to discrete Fourier transformation simultaneously, can cause serious discretization error.Have in addition that the finite difference utilized is discrete sets up finite impulse response filter and the methods such as impulse response filter based on finite element are carried out reconstruct displacement.But the former does not provide concrete reconstruction and controls the differential equation, and determining that the regularization factor of filter accuracies is not to define according to aimed at precision, but given according to experience, this will have a strong impact on stability and the accuracy of wave filter; Although the latter can utilize target frequency expectation quality to determine the regularization factor, the selection of its filter size there is no definite foundation.

For the problems referred to above, the object of this method is to overcome the needed initial displacement information of acceleration quadratic integral reconstruct displacement data of utilizing, utilize discrete unusual convolution to build finite impulse response filter, the vibration acceleration data reconstruction target vibration displacement recording by acceleration transducer according to needed displacement reconstruction accuracy has good inhibition ability to noise simultaneously.

Summary of the invention

In order to overcome the deficiencies in the prior art, the object of this invention is to provide a kind of specific aim and accuracy higher, can effectively utilize vibration acceleration signal reconstruct vibration displacement signal, and widely used vibration displacement reconstructing method.

The present invention realizes as follows: a kind of vibration displacement response reconstructing method based on discrete unusual convolution, comprises the following steps:

Step 1: the Minimum square error function of setting up acceleration measurement and actual displacement second differential;

Step 2: apply variation and Fourier transform, obtain the transport function of minimum value function governing equation;

Step 3: utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine the aimed at precision of displacement reconstruct;

Step 4: apply the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula;

Step 5: the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation.

Further, in step 1, the Minimum square error function of setting up acceleration measurement and actual displacement second differential comprises the following steps:

(1) measure the vibration acceleration signal of device target position;

(2) create the Minimum square error function of acceleration measurement and actual displacement second differential;

(3) in Minimum square error function, introduce regularization function, solve morbid state and order not enough.

Further, in step 2, application variation and Fourier transform, the transport function that obtains minimum value function governing equation comprises the following steps:

(1) Minimum square error function after transforming is carried out to variation computing, obtain governing equation and the Nuo Yiman boundary condition of this minimum value function;

(2) according to Nuo Yiman boundary condition, governing equation is carried out to Fourier transform, the transport function of controlled equation.

Further, in step 3, utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine that the aimed at precision of displacement reconstruct comprises the following steps:

(1) utilize transport function and the accurate transfer function of the governing equation of scale free frequency representation to obtain the precision function that reconstructed bit is moved;

(2) by precision function, determined the aimed at precision of displacement reconstruct, and then obtain regularization factor value in regularization function;

(3) transport function and the precision function of the displacement reconstruct governing equation that the substitution of the regularization factor is obtained to different target precision with reconstruct governing equation transport function and the precision function of scale free frequency representation.

Further, in step 4, apply the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula and comprise the following steps:

(1) apply discrete unusual Convolution Formula and obtain the discrete singularity characteristics matrix expression of second order, three rank and quadravalence of each sampled point displacement in a certain measurement point time window based on Delta type singular kernel and single order, the Second-Order Discrete singularity characteristics matrix expression of acceleration;

(2) can the discrete singularity characteristics matrix expression of controlled equation by displacement and the discrete singularity characteristics matrix expression of acceleration.

Further, in step 5, the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation comprises the following steps:

(1) displacement that calculates acceleration measurement reconstruct according to the discrete unusual expression formula of governing equation responds discrete singularity characteristics matrix expression;

(2), by window setting technique overlapping time, the reconstruct displacement of this measurement point is expressed as to the linear combination of each sampled point acceleration measurement;

(3) by the displacement discrete unusual expression formula of response of acceleration measurement reconstruct and the linear combination of each acceleration measurement, can be obtained the vector acceleration expression formula of this measurement point displacement.

The invention has the beneficial effects as follows: the method is difficult to obtain for the initial displacement information of utilizing acceleration transducer measurement gained acceleration quadratic integral reconstruct displacement to need, by the displacement response reconstructing method based on discrete unusual convolution method, can effectively utilize acceleration information, according to needed displacement reconstruction accuracy, reconstruct target vibration displacement data, and noise is had to stronger inhibition ability.

Accompanying drawing explanation

Fig. 1 is a kind of block diagram of the vibration displacement reconstructing method based on discrete unusual convolution.

Fig. 2 is example simple beam structure and measurement point arrangenent diagram.

Fig. 3 is free beam measuring point actual vibration accelerating curve.

Fig. 4 is free beam measuring point actual vibration displacement curve.

Fig. 5 utilizes discrete unusual convolution method by free beam vibration acceleration reconstruct displacement curve.

Fig. 6 is that the door frame vibration under certain fork truck idling operation adopts LMS system to carry out the site layout project figure that vibration acceleration is measured and high-speed camera equipment carries out vibration displacement measurement simultaneously.

Fig. 7 is the forklift door frame vibration acceleration curve that sensor measurement obtains.

Fig. 8 is the forklift door frame vibration displacement curve that high-speed camera measures.

Fig. 9 is the forklift door frame vibration displacement curve being obtained based on discrete unusual convolution reconstruct by acceleration information.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, further illustrate the present invention.

A kind of displacement reconstructing method based on discrete unusual convolution of the present invention, as shown in Figure 1, comprises the steps:

Step 1: the Minimum square error function of setting up acceleration measurement and actual displacement second differential;

Step 2: apply variation and Fourier transform, obtain the transport function of minimum value function governing equation;

Step 3: utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine the aimed at precision of displacement reconstruct;

Step 4: apply the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula;

Step 5: the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation.

In step 1, the Minimum square error function of setting up acceleration measurement and actual displacement second differential comprises the following steps:

(1) in device target position, one or more measurement points are set, gather the vibratory response acceleration signal of lower each measurement point of excitation, order for time interval T ₁< t < T ₂interior each sampled point vector acceleration, b is eigenmatrix.Make U={u ₀, u ₁, u ₂..., u _n-1be time interval T ₁< t < T ₂interior each sampled point reconstruct motion vector, U "=B ⁽²⁾u, U ⁽³⁾=B ⁽³⁾u,U ⁽⁴⁾=B ⁽⁴⁾u, B is eigenmatrix.

(2) provide the least squares error expression formula between acceleration measurement and the second differential of time window intrinsic displacement:

${\mathrm{Min\&Pi;}}_{E\left(u\right)}=\frac{1}{2}{\&Integral;}_{T_2}^{T_1}{(a\left(u\left(t\right)\right)-\stackrel{\&OverBar;}{a})}^2\mathrm{dt}$

Wherein, the acceleration that a (u (t)) obtains for actual displacement u (t) second differential, for the acceleration measuring.

(3) in order to overcome morbid state and the order deficiency of inverse problem, introduce regularization function:

${\mathrm{Min\&Pi;}}_{E\left(u\right)}=\frac{1}{2}{\&Integral;}_{T_1}^{T_2}{(a\left(u\left(t\right)\right)-\stackrel{\&OverBar;}{a})}^2\mathrm{dt}+\frac{{\mathrm{\&beta;}}^2}{2}{\&Integral;}_{T_1}^{T_2}u{\left(t\right)}^2\mathrm{dt}$

Wherein, for regularization function, β is the regularization factor.

In step 2, application variation and Fourier transform, the transport function that obtains minimum value function governing equation comprises the following steps:

(1) step 1 (3) gained Minimum square error function formula being carried out to variation computing obtains:

$\mathrm{\&delta;\&Pi;}\left(u\right)={\&Integral;}_{T_1}^{T_2}\frac{d^2\mathrm{\&delta;u}}{{\mathrm{dt}}^2}(\frac{d^{2}u}{{\mathrm{dt}}^2}-\stackrel{\&OverBar;}{a})\mathrm{dt}+\mathrm{\&beta;}{\&Integral;}_{T_1}^{T_2}\mathrm{\&delta;uudt}=0$

First of variation gained formula carried out to twice integration by parts, after arrangement abbreviation:

${\&Integral;}_{T_1}^{T_2}\mathrm{\&delta;u}{(\frac{d^{4}u}{{\mathrm{dt}}^4}+{\mathrm{\&beta;}}^{2}u-\frac{d^2\stackrel{\&OverBar;}{a}}{{\mathrm{dt}}^2})\mathrm{dt}+\frac{\mathrm{d\&delta;u}}{\mathrm{dt}}(\frac{d^{2}u}{{\mathrm{dt}}^2}-\stackrel{\&OverBar;}{a})|}_{T_1}^{T_2}{-\mathrm{\&delta;u}(\frac{d^{3}u}{{\mathrm{dt}}^3}-\frac{d\stackrel{\&OverBar;}{a}}{\mathrm{dt}})|}_{T_1}^{T_2}=0$

Making first of this equation is 0, can obtain the governing equation of minimum problems:

$\frac{d^{4}u}{{\mathrm{dt}}^4}+{\mathrm{\&beta;}}^{2}u=\frac{d^2\stackrel{\&OverBar;}{a}}{{\mathrm{dt}}^2}$

Making respectively second of this equation and the 3rd is 0, can obtain the Nuo Yiman boundary condition of minimum problems:

$\frac{d^{2}u}{{\mathrm{dt}}^2}=\stackrel{\&OverBar;}{a}$

$\frac{d^{3}u}{{\mathrm{dt}}^3}=\frac{d\stackrel{\&OverBar;}{a}}{\mathrm{dt}}$

(2) according to the Neumann boundary conditions of gained, can show that the solution of the governing equation of minimum problems exists and unique, to the every Fourier transform of carrying out in these governing equation both sides, can obtain the transport function based on reconstruction governing equation:

$H_{\mathrm{IP}}\left(\mathrm{\&omega;}\right)=-\frac{{\mathrm{\&omega;}}^2}{{\mathrm{\&omega;}}^4+{\mathrm{\&beta;}}^2}=-\frac{{\left(2\mathrm{\&pi;f}\right)}^2}{{\left(2\mathrm{\&pi;f}\right)}^4+{\mathrm{\&beta;}}^2}$

Wherein, ω is angular frequency, and f is the frequency corresponding with angular frequency.

In step 3, utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine that the aimed at precision of displacement reconstruct comprises the following steps:

(1) utilize the governing equation transport function of scale free frequency representation and accurate transfer function to obtain the precision function that reconstructed bit is moved:

Try to achieve the reconstruct governing equation transport function with scale free frequency representation:

$\begin{array}{c}{\tilde{H}}_{\mathrm{IP}}\left(\tilde{f}\right)=-{\left({2\mathrm{\&pi;f}}_T\right)}^2{H}_{\mathrm{IP}}\left(\mathrm{\&omega;}\right)\\ =\frac{{\left(2\mathrm{\&pi;f}\right)}^2/{\left({2\mathrm{\&pi;f}}_T\right)}^2}{({\left(2\mathrm{\&pi;f}\right)}^4+{\mathrm{\&beta;}}^2)/{\left({2\mathrm{\&pi;f}}_T\right)}^4}\\ =\frac{{\tilde{f}}^2}{({\tilde{f}}^4+{\mathrm{\&beta;}}^2/{\left({2\mathrm{\&pi;f}}_T\right)}^4)}\end{array}$

Wherein, for scale free frequency, f _tfor target frequency.

Because the pass of certain point of fixity acceleration and displacement is: for acceleration measurement, Fourier transform is carried out in these formula both sides can be obtained: $F\left(u\left(t\right)\right)=H_E\left(\mathrm{\&omega;}\right)F\left(\stackrel{\&OverBar;}{a}\left(t\right)\right)=-\frac{1}{{\mathrm{\&omega;}}^2}F\left(\stackrel{\&OverBar;}{a}\left(t\right)\right),$ Wherein, it is accurate transfer function.Take scale free frequency representation accurate transfer function as:

${\tilde{H}}_E\left(\tilde{f}\right)=-{\left({2\mathrm{\&pi;f}}_T\right)}^2{H}_E\left(\mathrm{\&omega;}\right)={\left(\frac{{2\mathrm{\&pi;f}}_T}{\mathrm{\&omega;}}\right)}^2=\frac{1}{{\tilde{f}}^2}$

The transport function of definition reconstruct governing equation and the ratio of accurate transfer function are the precision of reconstruct displacement, and the precision function of reconstruct displacement is:

$H_{\mathrm{IP}}^{\mathrm{acc}}\left(\mathrm{\&omega;}\right)=\frac{H_{\mathrm{IP}}}{H_E}=\frac{{\tilde{H}}_{\mathrm{IP}}}{{\tilde{H}}_E}=\frac{{\tilde{f}}^4}{({\tilde{f}}^4+{\mathrm{\&beta;}}^2/{\left({2\mathrm{\&pi;f}}_T\right)}^4)}$

Can find out, when time, displacement reconstruction accuracy is zero, when time, displacement reconstruction accuracy is tending towards 1, when time, displacement reconstruction accuracy is subject to the impact of regularization factor-beta.

(2) by precision function, determined the aimed at precision of displacement reconstruct, and then obtain regularization factor value in regularization function:

Will time reconstruct displacement accuracy be defined as and use α _tthe target expectation quality representing:

${\mathrm{\&alpha;}}_T=\frac{1}{1+{\mathrm{\&beta;}}^2/{\left({2\mathrm{\&pi;f}}_T\right)}^4}$

By above formula, can be obtained the value of regularization factor-beta:

$\mathrm{\&beta;}=-\sqrt{\frac{1-{\mathrm{\&alpha;}}_T}{{\mathrm{\&alpha;}}_T}}{\left({2\mathrm{\&pi;f}}_T\right)}^2={\mathrm{\&lambda;}}^2\left({\mathrm{\&alpha;}}_T\right){\left({2\mathrm{\&pi;f}}_T\right)}^2,0\&le;{\mathrm{\&alpha;}}_T\&le;1$

Wherein, ${\mathrm{\&lambda;}}^2\left({\mathrm{\&alpha;}}_T\right)=\sqrt{(1-{\mathrm{\&alpha;}}_T)/{\mathrm{\&alpha;}}_T}.$

(3) reconstruct governing equation transport function and the precision function with scale free frequency representation by the substitution of regularization factor-beta, can obtain transport function and the precision function of the displacement reconstruct governing equation of different target precision:

${\tilde{H}}_{\mathrm{IP}}\left(\tilde{f}\right)=\frac{{\tilde{f}}^2}{{\tilde{f}}^4+{\mathrm{\&lambda;}}^4\left({\mathrm{\&alpha;}}_T\right)}$

${\tilde{H}}_{\mathrm{IP}}^{\mathrm{acc}}\left(\tilde{f}\right)=\frac{{\tilde{f}}^4}{{\tilde{f}}^4+{\mathrm{\&lambda;}}^4\left({\mathrm{\&alpha;}}_T\right)}$

In step 4, apply the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula and comprise the following steps:

(1) according to the fundamental formular of discrete unusual convolution can obtain the discrete singularity characteristics matrix expression of second order, three rank and quadravalence of each sampled point displacement in a certain measurement point time window based on Delta type singular kernel and single order, the Second-Order Discrete singularity characteristics matrix expression of acceleration:

$u^{\&prime;\&prime;}\left(t_i\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{\mathrm{\&sigma;},\mathrm{\&Delta;}}^{\left(2\right)}(t_i-t_k)u\left(t_k\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{B}_{i,k}^{\left(2\right)}{u}_k$

$u^{\left(3\right)}\left(t_i\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{\mathrm{\&sigma;},\mathrm{\&Delta;}}^{\left(3\right)}(t_i-t_k)u\left(t_k\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{B}_{i,k}^{\left(3\right)}{u}_k$

$u^{\left(4\right)}\left(t_i\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{\mathrm{\&sigma;},\mathrm{\&Delta;}}^{\left(4\right)}(t_i-t_k)u\left(t_k\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{B}_{i,k}^{\left(4\right)}{u}_k$

$a^{-\&prime;}\left(t_i\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{\mathrm{\&sigma;},\mathrm{\&Delta;}}^{\left(1\right)}(t_i-t_k)\stackrel{\&OverBar;}{a}\left(t_k\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{B}_{i,k}^{\left(1\right)}{\stackrel{\&OverBar;}{a}}_k$

${\stackrel{\&OverBar;}{a}}^{\&prime;\&prime;}\left(t_i\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_{\mathrm{\&sigma;},\mathrm{\&Delta;}}^{\left(2\right)}(t_i-t_k)\stackrel{\&OverBar;}{a}\left(t_k\right)=\underset{k=-M}{\overset{M}{\mathrm{\&Sigma;}}}{B}_{i,k}^{\left(2\right)}{\stackrel{\&OverBar;}{a}}_k$

Wherein: σ is calculating parameter, Δ is node spacing, and 2M+1 is computation bandwidth (value of M generally should be less than along the nodes in a direction computational fields), the n order derivative of Delta type singular kernel, { t _kthe discrete point of a series of spaced sets in computational fields, with be respectively single order, second order, three rank and the quadravalence eigenmatrix of discrete unusual convolution.

(2) according to top offset and the discrete singularity characteristics expression matrix of acceleration, discrete unusual expression formula that can controlled equation based on reconstruct governing equation:

$[B^{\left(4\right)}+{\mathrm{\&beta;}}^2{\left(\mathrm{\&Delta;t}\right)}^{4}I]U={\left(\mathrm{\&Delta;t}\right)}^2{B}^{\left(2\right)}\stackrel{\&OverBar;}{A},T_1<t<T_2$

In above formula: wherein N is time window T ₁< t < T ₂interior sampling number, f _sfor sample frequency, I is unit matrix, and exponent number is N * N.

In step 5, the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation comprises the following steps:

(1) by the discrete unusual expression formula of governing equation and then can obtain the discrete unusual expression formula of displacement response by acceleration measurement reconstruct:

$U={\left(\mathrm{\&Delta;t}\right)}^2{[B^{\left(4\right)}+{\mathrm{\&beta;}}^2{\left(\mathrm{\&Delta;t}\right)}^{4}I]}^{-1}{B}^{\left(2\right)}\stackrel{\&OverBar;}{A}={\left(\mathrm{\&Delta;t}\right)}^{2}D\stackrel{\&OverBar;}{A}$

In formula: D=[B ⁽⁴⁾+ I β ²(Δ t) ⁴] ^-1b ⁽²⁾for matrix of coefficients, exponent number is N * N.

(2) according to window setting technique overlapping time, the displacement components u of central point in time window _k+1, be reconstruct displacement real in this time window, by the linear combination that is expressed as each acceleration measurement in this time window, be:

$u_{k+1}=u\left(t\right)={\left(\mathrm{\&Delta;t}\right)}^2{\mathrm{\&Sigma;}}_{p=1}^{2k+1}{c}_p{\stackrel{\&OverBar;}{a}}_p={\left(\mathrm{\&Delta;t}\right)}^2{\mathrm{\&Sigma;}}_{p=-k}^k{c}_{p+k+1}\stackrel{\&OverBar;}{a}(t+\mathrm{p\&Delta;t})$

In above formula: c _pfor the coefficient of wave filter, p represents wave filter item number, (Δ t) ²introducing be in order to make filter coefficient c _pfor scale free coefficient.

The size of time window take time representation filter size as:

Wherein, the filter size that the multiple with target period represents, during for discrete wave filter item number and coefficient point serialization curve zero crossing, the value of wave filter item number, this value is for being greater than 0 real number.

(3) by the displacement discrete unusual expression formula of response of acceleration measurement reconstruct and the linear combination of each acceleration measurement, can be obtained the vector acceleration expression formula of this measurement point displacement:

$u\left(t\right)=u_{k+1}={\left(\mathrm{\&Delta;t}\right)}^{2}d\stackrel{\&OverBar;}{a}={\left(\mathrm{\&Delta;t}\right)}^2{\mathrm{\&Sigma;}}_{p=-k}^k{c}_{p+k+1}\stackrel{\&OverBar;}{a}(t+\mathrm{p\&Delta;t})$

In formula: d is that the k+1 of matrix of coefficients D is capable, for acceleration measurement vector.D has determined the value of each filter coefficient.This formula filter coefficient is obtained by discrete unusual convolution method, is discrete unusual convolution finite impulse wave filter.

So far, above step can be by surveyed vibration acceleration response signal, by determining that target frequency, aimed at precision and filter size reconstruct obtain vibration displacement signal.

Simulation example:

A length take below as 600mm, and density and Young modulus are respectively: 7.827e ^-9tonne/mm ³, 199948MPa, the simple beam structure Vibration Simulation that Poisson ratio is 0.27 is the validity that example further illustrates vibration displacement reconstructing method of the present invention, structure as shown in Figure 2.

Be located at from beam left support point 140mm place as measurement point position and exciting force apply position, excitation load function definition is: Φ (t)=8.9sin15.4 π t-35.9sin31 π t+29.3sin56 π t, Fig. 3 has provided the acceleration responsive curve measuring, and Fig. 4 has provided free beam actual displacement response curve.If target frequency is required minimum frequency, from exciting force, can find out, minimum excitation frequency is 7.7Hz, target frequency f _t=7.7Hz, again sample frequency f _s=166.5Hz.The aimed at precision of setting displacement reconstruct is 0.97, filter size N _w=4.216.Fig. 5 has provided the reconstruct displacement based in discrete unusual convolution method 4～5s under this filter size.The displacement curve of comparison diagram 5 and Fig. 6 can obtain not occurring in reconstruction result phase error, and amplitude to change maximum relative error be only 3.65%, so displacement reconstructed error is very little.

Experiment embodiment:

The vibration of take below under on-the-spot forklift door frame idling operation further illustrates vibration displacement reconstructing method validity of the present invention as example.Fig. 6 measures for the door frame vibration under certain fork truck idling operation adopts LMS system to carry out vibration acceleration simultaneously the site layout project figure that carries out vibration displacement test with high-speed camera equipment.Acceleration information after test observe is found, because the sample frequency of LMS system is higher, recorded a plurality of test values within a short period of time, so we resample to the acceleration information gathering, the acceleration information obtaining as shown in Figure 7.Fig. 8 is the forklift door frame vibration displacement curve that high speed video process obtains.The parameter setting of discrete unusual convolution filter displacement reconstruct: target frequency is 23Hz, resampling frequency is 100Hz, aimed at precision is 0.97, filter size N _w=7.5916, Fig. 9 is the reconstruct displacement based on the inventive method, and with the vibration displacement data contrast that Fig. 8 high-speed camera equipment gathers, phase error, does not appear in displacement reconstruct amplitude relative error maximum only 3.87%.So the inventive method can be utilized vibration acceleration data reconstruction displacement data accurately.

The method that the present invention proposes is not limited to the embodiment described in embodiment, those skilled in the art's technical scheme according to the present invention draws other embodiment, so long as build wave filter by discrete unusual convolution method, realize vibratory response displacement reconstruct, also should belong to equally innovation scope of the present invention.

Claims (6)

1. the response of the vibration displacement based on a discrete unusual convolution reconstructing method, is characterized in that, comprises the following steps:

Step 1: the Minimum square error function of setting up acceleration measurement and actual displacement second differential;

Step 2: apply variation and Fourier transform, obtain the transport function of minimum value function governing equation;

Step 3: utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine the aimed at precision of displacement reconstruct;

Step 4: apply the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula;

Step 5: the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation.

2. a kind of vibration displacement response reconstructing method based on discrete unusual convolution according to claim 1, is characterized in that, in step 1, the Minimum square error function of setting up acceleration measurement and actual displacement second differential comprises the following steps:

(1) measure the vibration acceleration signal of device target position;

(2) create the Minimum square error function of acceleration measurement and actual displacement second differential;

(3) in Minimum square error function, introduce regularization function, solve morbid state and order not enough.

3. a kind of vibration displacement response reconstructing method based on discrete unusual convolution according to claim 1, is characterized in that, in step 2, and application variation and Fourier transform, the transport function that obtains minimum value function governing equation comprises the following steps:

(1) Minimum square error function after transforming is carried out to variation computing, obtain governing equation and the Nuo Yiman boundary condition of this minimum value function;

(2) according to Nuo Yiman boundary condition, governing equation is carried out to Fourier transform, the transport function of controlled equation.

4. a kind of vibration displacement based on discrete unusual convolution according to claim 1 responds reconstructing method, it is characterized in that, in step 3, utilize the transport function of governing equation to obtain the precision function of reconstruct displacement, determine that the aimed at precision of displacement reconstruct comprises the following steps:

(1) utilize transport function and the accurate transfer function of the governing equation of scale free frequency representation to obtain the precision function that reconstructed bit is moved;

(2) by precision function, determined the aimed at precision of displacement reconstruct, and then obtain regularization factor value in regularization function;

(3) transport function and the precision function of the displacement reconstruct governing equation that the substitution of the regularization factor is obtained to different target precision with reconstruct governing equation transport function and the precision function of scale free frequency representation.

5. a kind of vibration displacement response reconstructing method based on discrete unusual convolution according to claim 1, is characterized in that, in step 4, applies the discrete singularity characteristics matrix expression of the controlled equation of discrete unusual Convolution Formula and comprises the following steps:

(1) apply discrete unusual Convolution Formula and obtain the discrete singularity characteristics matrix expression of second order, three rank and quadravalence of each sampled point displacement in a certain measurement point time window based on Delta type singular kernel and single order, the Second-Order Discrete singularity characteristics matrix expression of acceleration;

(2) can the discrete singularity characteristics matrix expression of controlled equation by displacement and the discrete singularity characteristics matrix expression of acceleration.

6. a kind of vibration displacement based on discrete unusual convolution according to claim 1 responds reconstructing method, it is characterized in that, in step 5, the vector acceleration expression formula that calculates measurement point displacement according to the discrete unusual expression formula of governing equation comprises the following steps:

(1) displacement that calculates acceleration measurement reconstruct according to the discrete unusual expression formula of governing equation responds discrete singularity characteristics matrix expression;

(2), by window setting technique overlapping time, the reconstruct displacement of this measurement point is expressed as to the linear combination of each sampled point acceleration measurement;

(3) by the displacement discrete unusual expression formula of response of acceleration measurement reconstruct and the linear combination of each acceleration measurement, can be obtained the vector acceleration expression formula of this measurement point displacement.