CN105277938A - Vibration amplitude high-precision microwave measurement method based on least squares estimation - Google Patents

Abstract

The invention provides a non-contact vibration amplitude measurement method based on a least squares method. The method comprises the steps that the complex baseband echo spectrum of a radar is analyzed, and the amplitude of each harmonic is extracted; the ratio of different harmonic pairs is calculated to acquire an observation harmonic pair vector; the assumption that target amplitude is within the intersection of a detectable range of different harmonic pairs in the harmonic pair vector is made, wherein the intersection is between Ab and Ae; according to a vibration amplitude step value A0, from Ab to Ae is discretized to from A1 to Am; A1, A2, A3...Am are orderly used as target vibration amplitude estimation values; the harmonic pair vector in each case is calculated to acquire a harmonic pair matrix Jm; the mean square error sum of the sum of each row of Jm is calculated; and according to least squares estimation, the final target vibration amplitude estimation value is acquired based on the minimum Ji(A). According to the method which is directly based on a pair of harmonic ratio is used to acquire high vibration amplitude precision, and has an important significance for radar high-precision target vibration amplitude measurement.

Description

A kind of Oscillation Amplitude High-precision Microwave measuring method based on least-squares estimation

Technical field

The invention belongs to radar high precision vibration measurement technique field, be specifically related to a kind of Oscillation Amplitude High-precision Microwave measuring method based on least-squares estimation.

Background technology

Traditional vibration survey device comprises displacement and speed pickup.One of them is the most widely used is accelerometer, and piezoelectric accelerometer can export the electric signal that is proportional to the acceleration of its contact target.Another kind of instrument with contacts is linear variable difference transformer, can be used as the displacement of the direct measuring vibrations target of displacement transducer.But being limited to contact type measurement, the application of these instruments has limitation.

Some non-contacting vibration surveying instruments based on laser, as laser vibration measurer, laser interferometer and laser displacement sensor etc.These equipment costs are high, and have limitation, as inevitably calibrated and narrow sensing range.On the other hand, owing to having high precision, target can be isolated from clutter, the advantage such as cost is lower, the vibration survey based on radar had attracted the interest of Many researchers in recent years.The main application of radar vibration measuring comprises vital sign parameter signals measurement, physical construction fault detect, engineering structure monitoring etc.Correlative study person utilizes heart rate and the respiratory rate of radargrammetry human body, vibration parameters when normally being worked by contrast physical construction detects its health status, and monitors their state by the vibration parameters measured as the engineering structure of floor, high building and bridge.

Published a kind of radar Oscillation Amplitude extracting method is based on nonlinear Doppler phase-modulation, after Vibration Targets scattering, radar base band echoed signal can be analyzed to the harmonic wave that a series of amplitude is determined by intended vibratory amplitude, carrys out inverting target amplitude by the Amplitude Ration obtaining a pair harmonic wave.But noise can cause the skew of harmonic amplitude, because the amplitude of inverting is very sensitive to harmonic amplitude, thus no small error can be introduced.

Summary of the invention

In view of this, the object of this invention is to provide a kind of measuring method of the non-contacting vibration amplitude based on least square method, the backscatter signal of Vibration Targets is deployable is series of harmonic, utilize these harmonic wave inverting intended vibratory amplitudes based on least square method simultaneously, significant to the measuring accuracy improving intended vibratory amplitude.

Realize technical scheme of the present invention as follows:

Based on a measuring method for the non-contacting vibration amplitude of least square method, detailed process is:

The frequency spectrum of the complex base band echo of step one, Analysis of Radar, extracts the amplitude H of each harmonic wave ₁, H ₂, H ₃h _n, wherein N is the quantity of default observation harmonic wave;

Step 2, calculate the right ratio of different harmonic wave, obtain observation harmonic wave to vector wherein l > k, this harmonic wave is to there is N (N-1)/2 element in vector;

Step 3, hypothetical target amplitude at harmonic wave to vector what middle different harmonic wave was right can the common factor A of sensing range _b~ A _ein; According to the vibration measuring amplitude precision of expection, define an Oscillation Amplitude step value A ₀, according to described A ₀by A _b~ A _ediscretely turn to A ₁, A ₂, A ₃a _m, m=(A _e-A _b)/A ₀represent harmonic wave to the number of the harmonic wave existed in matrix to vector;

Step 4, successively by A ₁, A ₂, A ₃a _mas intended vibratory amplitude estimation value, under calculating each situation, harmonic wave is to vector, obtains harmonic wave to matrix J m;

$Jm=\left[\begin{array}{c}{\stackrel{\→}{x}}_1\\ {\stackrel{\→}{x}}_2\\ \mathrm{...}\\ {\stackrel{\→}{x}}_m\end{array}\right]=\left[\begin{array}{ccccc}{H}_{12}/H_{11}& \mathrm{...}& H_{1l}/H_{1k}& \mathrm{...}& H_{1N}/H_{1(N-1)}\\ H_{22}/H_{21}& \mathrm{..}& H_{2l}/H_{2k}& \mathrm{...}& H_{2N}/H_{2(N-1)}\\ & & \mathrm{...}& & \\ H_{m2}/H_{m1}& \mathrm{...}& H_{ml}/H_{mk}& \mathrm{...}& H_{mN}/H_{m(N-1)}\end{array}\right]$

Step 5, calculate Jm every a line and square error and, obtain

$J_i\left(A\right)=\underset{k=1}{\overset{N-1}{\Σ}}\underset{l=k+1}{\overset{N}{\Σ}}{(H_{il}/H_{ik}-H_l/H_k)}^2---\left(12\right)$

Wherein, i=1,2 ... m;

Then according to least-squares estimation, based on minimum J _i(A) estimated value of intended vibratory amplitude, is obtained

The present invention has following beneficial effect:

The measuring method of a kind of non-contacting vibration amplitude based on least square method of the present invention, utilizes multiple harmonic waves of radar base band echo simultaneously based on least square method, this algorithm is more direct, and obtain the precision of Oscillation Amplitude based on a pair harmonic ratio higher.Therefore, method of the present invention is significant to radar high-acruracy survey intended vibratory amplitude.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the measuring method of the non-contacting vibration amplitude that the present invention is based on least square method.

The harmonic constant of Fig. 2 radar base band echo than with target amplitude and the radar wavelength funtcional relationship than A/ λ.

The frequency spectrum of base band echo when Fig. 3 emulates.

Fig. 4 is the average of the target amplitude that each method utilizing Monte Carlo simulation to obtain is finally inversed by.

Fig. 5 is experimental observation target and experiment scene; Wherein Fig. 5 (a) is observed object vibration marking apparatus, and Fig. 5 (b) is experiment scene.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

Do not consider amplitude, the simple signal that continuous wave radar is launched can be expressed as:

s _T(t)＝cos(2πf _ct+φ(t))(1)

Wherein, f _cfor signal carrier frequency, φ (t) is for make an uproar mutually.If this signal is by distance d ₀near be the Vibration Targets reflection of x (t) do displacement, then from being transmitted into, to receive the distance of process be 2d (t)=2d to signal ₀+ 2x (t).Received signal strength can be expressed as:

$s_R\left(t\right)=cos\[2{\mathrm{\πf}}_c\left(t-\frac{2d(t-d\left(t\right)/c)}{c}\right)+\mathrm{\φ}\left(t-\frac{2d(t-d\left(t\right)/c)}{c}\right)\]---\left(2\right)$

Wherein, c is the light velocity.

Substitute d (t-d (t)/c)=d ₀+ x (t-d (t)/c):

$s_R\left(t\right)=cos\[2{\mathrm{\πf}}_{c}t-\frac{4{\mathrm{\πd}}_0}{\mathrm{\λ}}-\frac{4\mathrm{\π}x(t-d\left(t\right)/c)}{\mathrm{\λ}}+\mathrm{\φ}\left(t-\frac{2d_0}{c}-\frac{2x(t-d\left(t\right)/c)}{c}\right)\]---\left(4\right)$

Wherein, radar wavelength λ=c/f _c.

Consider the vibration period T > > d of target ₀/ c, then d (the t)/c in x (t-d (t)/c) can ignore, then

$s_R\left(t\right)\≈cos\[2{\mathrm{\πf}}_{c}t-\frac{4{\mathrm{\πd}}_0}{\mathrm{\λ}}-\frac{4\mathrm{\π}x\left(t\right)}{\mathrm{\λ}}+\mathrm{\φ}\left(t-\frac{2d_0}{c}-\frac{2x\left(t\right)}{c}\right)\]---\left(5\right)$

Again due to x (t) < < d ₀, and function of making an uproar mutually is slow change, then Received signal strength can be expressed as:

$s_R\left(t\right)\&ap;cos\&lsqb;2{\mathrm{\&pi;f}}_{c}t-\frac{4{\mathrm{\&pi;d}}_0}{\mathrm{\&lambda;}}-\frac{4\mathrm{\&pi;}x\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{\&phi;}\left(t-\frac{2d_0}{c}\right)\&rsqb;---\left(6\right)$

Utilize complex signal demodulation techniques, obtain baseband I/Q and export and can be expressed as:

$s_I\left(t\right)=cos\&lsqb;\mathrm{\&theta;}+\frac{4\mathrm{\&pi;}x\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{\&Delta;}\mathrm{\&phi;}\left(t\right)\&rsqb;---\left(7\right)$

$s_Q\left(t\right)=sin\&lsqb;\mathrm{\&theta;}+\frac{4\mathrm{\&pi;}x\left(t\right)}{\mathrm{\&lambda;}}+\mathrm{\&Delta;}\mathrm{\&phi;}\left(t\right)\&rsqb;---\left(8\right)$

Wherein, θ is d ₀reflect with target surface the phase place caused, and Δ φ (t) is total residual phase-noise.

For the target of single-frequency vibration, its displacement can be expressed as x (t)=Asin (2 π f _vt), export in conjunction with baseband I/Q road, obtain radar complex base band echoed signal and can be expressed as Fourier series:

$\begin{array}{c}{s}_B\left(t\right)=s_I\left(t\right)+j\&CenterDot;s_Q\left(t\right)\\ =\exp \left\{j\&lsqb;\frac{4\mathrm{\&pi;}A\sin \left(2{\mathrm{\&pi;f}}_{v}t\right)}{\mathrm{\&lambda;}}+\mathrm{\&phi;}+\mathrm{\&Delta;}\mathrm{\&phi;}\left(t\right)\&rsqb;\right\}\\ =\underset{n=-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Sigma;}}{J}_n\left(\frac{4\mathrm{\&pi;}A}{\mathrm{\&lambda;}}\right)\exp \left\{j\left(2{\mathrm{\&pi;nf}}_{v}t+\mathrm{\&phi;}\right)\right\}\end{array}---\left(9\right)$

Wherein, φ=θ+Δ φ (t) is total residual phase, J _nx () is n rank Bessel function of the first kind.Due to e ^{j φ}modulus value perseverance be 1, so can not signal amplitude be affected.Therefore, when carrier frequency is fixed, s _bt Bezier coefficient that the amplitude of each harmonic wave of () is only intended vibratory amplitude by variable determines.

Known by formula (8), the vibration frequency of target can directly obtain by obtaining the fundamental frequency of radar complex base band echoed signal.On the other hand, the Amplitude Ration of l and k order harmonics:

$\frac{H_l}{H_k}=\frac{\left|J_l\left(\frac{4\mathrm{\&pi;}A}{\mathrm{\&lambda;}}\right)e^{j\mathrm{\&phi;}}\right|}{\left|J_k\left(\frac{4\mathrm{\&pi;}A}{\mathrm{\&lambda;}}\right)e^{j\mathrm{\&phi;}}\right|}=\left|\frac{J_l(4\mathrm{\&pi;}A/\mathrm{\&lambda;})}{J_k(4\mathrm{\&pi;}A/\mathrm{\&lambda;})}\right|---\left(10\right)$

Make l=2, k=1, obtain harmonic amplitude ratio as shown in Figure 2.Due to non-linear, same harmonic ratio correspond to different Oscillation Amplitudes.In order to can A be solved, need, for each harmonic wave can sensing range to defining 1, to make harmonic amplitude than between 0.2-5.Be normalized relative to λ, list front several harmonic ratio can sensing range as shown in the table:

What the different harmonic wave of table 1 was right can sensing range

Harmonic wave pair	H 2/H 1	H 3/H 1	H 3/H 2
				Can sensing range lower limit	0.062	0.153	0.093
Can the sensing range upper limit	0.288	0.289	0.391

When intended vibratory amplitude a certain harmonic wave right can in sensing range time, although intended vibratory amplitude can be finally inversed by, but noise can cause the skew of harmonic amplitude, and the error of inversion result to harmonic amplitude is very sensitive, thus can cause there is the error of can not ignore in measurement result.Improving one's methods is based on least square method, utilizes multiple harmonic wave pair simultaneously, the impact of minimum noise, and as shown in Figure 1, concrete operations are described below:

The frequency spectrum of the complex base band echo of step one, Analysis of Radar, extracts the amplitude H of each harmonic wave ₁, H ₂, H ₃h _n, wherein N is the quantity of default observation harmonic wave.

Step 2, calculate the right ratio of different harmonic wave, obtain observation harmonic wave to vector to in vector, there is N (N-1)/2 element in this harmonic wave.

Step 3, hypothetical target amplitude at harmonic wave to vector what middle different harmonic wave was right can the common factor A of sensing range _b~ A _ein.According to the vibration measuring amplitude precision of expection, define an Oscillation Amplitude step value A ₀, can according to this value by A _b~ A _ediscretely turn to A ₁, A ₂, A ₃a _m, m=(A _e-A _b)/A ₀represent harmonic wave to the number of the harmonic wave existed in matrix to vector.

Step 4, successively by A ₁, A ₂, A ₃a _mas intended vibratory amplitude estimation value, under calculating each situation, harmonic wave is to vector, obtains harmonic wave to matrix J m;

$Jm=\left[\begin{array}{c}{\stackrel{\&RightArrow;}{x}}_1\\ {\stackrel{\&RightArrow;}{x}}_2\\ \mathrm{...}\\ {\stackrel{\&RightArrow;}{x}}_m\end{array}\right]=\left[\begin{array}{ccccc}{H}_{12}/H_{11}& \mathrm{...}& H_{1l}/H_{1k}& \mathrm{...}& H_{1N}/H_{1(N-1)}\\ H_{22}/H_{21}& \mathrm{..}& H_{2l}/H_{2k}& \mathrm{...}& H_{2N}/H_{2(N-1)}\\ & & \mathrm{...}& & \\ H_{m2}/H_{m1}& \mathrm{...}& H_{ml}/H_{mk}& \mathrm{...}& H_{mN}/H_{m(N-1)}\end{array}\right]---\left(11\right)$

Step 5, calculate Jm every a line and square error and, obtain

$J_i\left(A\right)=\underset{k=1}{\overset{N-1}{\&Sigma;}}\underset{l=k+1}{\overset{N}{\&Sigma;}}{(H_{il}/H_{ik}-H_l/H_k)}^2---\left(12\right)$

Wherein, i=1,2 ... m;

Then according to least-squares estimation, based on minimum J _i(A) estimated value of intended vibratory amplitude, is obtained

The harmonic wave observed in theory is more to quantity, and vibration measuring amplitude precision is higher.But, along with the increase of N, can sensing range can narrow.So N value should suitably be chosen.

Embody rule:

1., by monitoring human life signal (breathing and heartbeat), carry out human body health status.

2. non-contact monitoring physical construction and Complex engineering structure (floor, bridge etc.), thus realize fault detect.

3. for microwave Eavesdropping provides basis.

Embodiment:

In this example, the N value chosen is 3.Known by table 1, this time-harmonic wave subtend amount can sensing range be 0.153 λ ~ 0.288 λ.Because residual phase can not affect the amplitude of signal, so can φ=0 be made.Add multiple Gaussian noise, radar base band echo can be expressed as:

${\mathrm{sn}}_B\left(t\right)=\exp \left\{j\&lsqb;\frac{4\mathrm{\&pi;}Asin\left(2{\mathrm{\&pi;f}}_{v}t\right)}{\mathrm{\&lambda;}}\&rsqb;\right\}+w\left(t\right)---\left(12\right)$

Wherein, w (t) is multiple Gaussian noise.Because Gaussian noise is random, so be necessary to carry out Multi simulation running, analyze final statistics.Relevant simulation parameter is as follows:

Table 2 simulation parameter

Parameter	A/λ	f v(Hz)	SNR(dB)
				Value	0.23	10	-9

Wherein simulation result is once: sn _bt the frequency spectrum of () as shown in Figure 3, utilizes harmonic wave to H respectively ₂/ H ₁, H ₃/ H ₁and H ₃/ H ₂, the target amplitude be finally inversed by is with error is respectively 1.56%, 1.35% and 6.87%.The amplitude stepping of order is A ₀=0.0001 λ, then utilizes the method in the present invention, and the target amplitude be finally inversed by is very close to true value.

Carry out Monte Carlo simulation, as shown in Figure 4, wherein A21, A31 and A32 represent and utilize harmonic wave to H the normalized amplitude that each method of gained is finally inversed by respectively ₂/ H ₁, H ₃/ H ₁and H ₃/ H ₂the amplitude be finally inversed by, and A321 represents the amplitude of new method inverting.In figure, A321 is closest to true value.Visible, relative to directly utilizing a harmonic wave to the method being finally inversed by target amplitude, method of the present invention has higher precision.

In order to the result, the vibration survey experiment of being correlated with.Observed object is the angle anti-(Fig. 5 (a)) on vibration marking apparatus, and experiment scene is as shown in Fig. 5 (b).It is 663.5 μm as amplitude that vibration marking apparatus drives angle counter, and vibration frequency is the single-frequency vibration of 10Hz.Radar is placed on distance objective and is about 30m place, measurement result is as follows:

Utilize harmonic wave to H respectively ₂/ H ₁, H ₃/ H ₁and H ₃/ H ₂, the target amplitude be finally inversed by is with error is respectively 8.29%, 4.63% and 25.74%.Utilize new method, the amplitude stepping of setting is 0.1 μm, and the target amplitude be finally inversed by is error is 0.12%.Visible, new method can increase substantially the measuring accuracy of intended vibratory amplitude.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. based on a measuring method for the non-contacting vibration amplitude of least square method, it is characterized in that, detailed process is:

The frequency spectrum of the complex base band echo of step one, Analysis of Radar, extracts the amplitude H of each harmonic wave ₁, H ₂, H ₃h _n, wherein N is the quantity of default observation harmonic wave;

Step 2, calculate the right ratio of different harmonic wave, obtain observation harmonic wave to vector wherein l > k, this harmonic wave is to there is N (N-1)/2 element in vector;

Step 3, hypothetical target amplitude at harmonic wave to vector what middle different harmonic wave was right can the common factor A of sensing range _b~ A _ein; According to the vibration measuring amplitude precision of expection, define an Oscillation Amplitude step value A ₀, according to described A ₀by A _b~ A _ediscretely turn to A ₁, A ₂, A ₃a _m, m=(A _e-A _b)/A ₀represent harmonic wave to the number of the harmonic wave existed in matrix to vector;

Step 4, successively by A ₁, A ₂, A ₃a _mas intended vibratory amplitude estimation value, under calculating each situation, harmonic wave is to vector, obtains harmonic wave to matrix J m;

$Jm=\left[\begin{array}{c}{\stackrel{\&RightArrow;}{x}}_1\\ {\stackrel{\&RightArrow;}{x}}_2\\ ...\\ {\stackrel{\&RightArrow;}{x}}_m\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccccc}{H}_{12}/H_{11}& ...& H_{1l}/H_{1k}& ...& H_{1N}/H_{1\left(N-1\right)}\end{array}\\ \begin{array}{ccccc}{H}_{22}/H_{21}& ...& H_{2l}/H_{2k}& ...& H_{2N}/H_{2\left(N-1\right)}\end{array}\\ ...\\ \begin{array}{ccccc}{H}_{m2}/H_{m1}& ...& H_{ml}/H_{mk}& ...& H_{mN}/H_{m\left(N-1\right)}\end{array}\end{array}\right]$

Step 5, calculate Jm every a line and square error and, obtain

$J_i\left(A\right)=\underset{k=1}{\overset{N-1}{\&Sigma;}}\underset{l=k+1}{\overset{N}{\&Sigma;}}{(H_{il}/H_{ik}-H_l/H_k)}^2---\left(12\right)$

Wherein, i=1,2 ... m;

Then according to least-squares estimation, based on minimum J _i(A) the final estimated value of intended vibratory amplitude, is obtained