CN102878989A - Triaxial angular vibration measuring method through adopting satellite-borne linear accelerometers - Google Patents

Abstract

A triaxial angular vibration measuring method through adopting satellite-borne linear accelerometers includes the following steps: firstly, selecting a mounting plane representing the angular vibration characteristic of a to-be-measured object on the to-be-measured object; secondly, selecting a rectangle region on the mounting plane and mounting the four linear accelerometers; thirdly, collecting time-domain data of the four linear accelerometers, amplifying and filtering the data on the satellite, and downloading the data to the ground; fourthly, calculating the vibration angular acceleration of the to-be-measured object in the directions of x-axis, y-axis and z-axis; and fifthly, calculating the root-mean-square value of the vibration angular acceleration, the root-mean-square value of the vibration angular velocity and the root-mean-square value of the vibration angular displacement, so as to complete the triaxial angular vibration measurement. Through the adoption of the method provided by the invention, requirements of the sensor for the mounting plane of the satellite as well as the resource occupation of the satellite are reduced, the mounting accuracy of the sensor can be guaranteed more easily, and the realization manner is simpler.

Description

A kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys

Technical field

The present invention relates to a kind of high precision angular oscillation method of AEROSPACE APPLICATION, particularly a kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys.

Background technology

It is to realize that the satellite high-precision attitude is pointed to and the prerequisite of remote optical sensing load high-resolution imaging and basis that angular oscillation is measured with control.May bring obvious impact to camera modulation transfer function (MTF), image resolution ratio, image geometry distortion and the geographic position mensuration etc. of Optical remote satellite when the angular oscillation amplitude is excessive.

The common method that can be used at present direct measured angular vibration is to utilize gyro, star sensor and angular-rate sensor, at present the measuring accuracy of optical fibre gyro can reach 0.05 "/s; the star sensor difference is estimated the angular velocity of spacecraft, and measuring accuracy can reach 0.01 °/s.The two main measurement frequency band is low-frequency range at present, generally is lower than 10Hz.Although in recent years, laser gyro and optical fibre gyro have been obtained faster development, measure frequency band and can reach 500Hz, and the degree of ripeness of product not enough.

Angular velocity or displacement transducer are based on the angular-rate sensor of magnetic fluid (magneto_hydro_dynamic, the MHD) kinetic theory of plasma characteristics, and its research starts from the seventies in last century six.The product of successful Application mainly contains the ARS series of U.S. ATA company in the world.Sensor output signal can be treated to angular acceleration, angular velocity or angular displacement data by circuit or software.Wherein ARS-12 type sensor is the sensitiveest inertia angular oscillation sensor, and noise equivalent angle is better than 35nrad (0.007arcsec), bandwidth 1～1000Hz.Japan has adopted angular displacement sensor (ADS) to carry out angle displacement measurement at its ALOS (ALOS).Its ADS sensor has adopted the wideband angular rate sensor (Angular Rate Sensor, ARS) based on the magnetohydrodynamics principle.It uses three ARS-12G angular rate sensors and optional power supply/signal condition and temperature measuring circuit to consist of Dynapak12 or Dynapak14 sensor bag.Can measure the variation in angular displacement in 2Hz～500Hz, it is said that its measuring accuracy at the 500Hz place has reached 0.01arcsec (rms).But because ARS is based on the sensor of angular rate measurement principle, therefore, can only by to the angular speed of time domain collection uniformly-spaced discrete data make in real time the numerical value integration and obtain angular displacement.

At home, at present mainly by the parameters such as attitude angular velocity of traditional attitude sensor instrumented satellite at rail, also do not experience the matured product of the wide-band measured angular vibration of flight validation.And attitude sensor is limit by its principle, can only carry out low-frequency range measure (＜10Hz), can't satisfy the measurement requirement.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys is provided.

Technical solution of the present invention is:

A kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys, step is as follows:

(1) at the selected mounting plane of measurand and definite coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis all are positioned at this mounting plane, measurand axis of rolling direction is X-axis, the pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or the star;

(2) select the rectangular area at mounting plane, at four drift angles of rectangle four linear accelerometers are installed respectively, wherein the First Line accelerometer is three axis accelerometer meters; The second and the 3rd linear acceleration is counted two-axis accelerometer, and two of the second linear accelerometer are axially pointed to respectively Y-direction and Z-direction, and two of the 3rd linear accelerometer are axially pointed to respectively X-direction and Z-direction; The 4th linear acceleration is counted single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;

(3) time domain data of 4 linear accelerometers of collection, after star is through amplification and filtering processing, the lower ground of passing to;

(4) pass through formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}=\frac{c_z-a_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1y}=\frac{b_z-a_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1z}=\frac{c_x-a_x}{\mathrm{La}}\end{array}\right\}$ With $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}=\frac{d_z-b_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2y}=\frac{d_z-c_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2z}=\frac{b_y-a_y}{\mathrm{La}}\end{array}\right\}$ Calculate two groups of measurands around X axle, Y-axis, three axial angle of throw acceleration of Z axis With Pass through again afterwards formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_x=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_y=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1y}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2y}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_z=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1z}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2z}}{2}\end{array}\right\}$ Ask its mean value to obtain With

In the formula: a _x, a _y, a _zBe respectively X-direction, Y-direction, the Z-direction acceleration of First Line accelerometer, b _y, b _zBe respectively Y-direction, the Z-direction acceleration of the second linear accelerometer, c _x, c _zBe respectively X-direction, the Z-direction acceleration of the 3rd linear accelerometer, d _zIt is the Z-direction acceleration of the 4th linear accelerometer; La, Lb are respectively the rectangle of four linear accelerometers compositions along the length of side of Y-axis and X-axis;

(5) according to obtaining in the step (4) With Calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely finished the measurement of three shaft angles vibrations.

Basis in the described step (5) With Calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, carry out in accordance with the following steps:

(5.1) pass through formula $\left.\begin{array}{c}{B}_X\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{X}\left(\mathrm{i\Δf}\right)\·X\left(\mathrm{i\Δf}\right)}\\ B_Y\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Y}\left(\mathrm{i\Δf}\right)\·Y\left(\mathrm{i\Δf}\right)}\\ B_Z\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Z}\left(\mathrm{i\Δf}\right)\·Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}$ I=0,1,2 ..., N/2 calculates measurand around X-axis, Y-axis, three axial angle of throw acceleration power spectral density of Z axis,

Wherein, i is the sequence number of power spectral density value, and N is the sampling sum;

Δ f is frequency interval,

B _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular acceleration power spectral density value at f=i Δ f place,

X (i Δ f), Y (i Δ f) and Z (i Δ f) are measurand around X-axis, Y-axis, three axial frequencies of the Z axis FFT function at f=i Δ f place;

With Be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);

(5.2) according to the measurand that calculates in the step (5.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_X\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Y\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw acceleration root-mean-square value at f=i Δ f place ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angle of throw acceleration root-mean-square value;

(5.3) according to the measurand that calculates in the step (5.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^{2\left(\mathrm{i\Δf}\right)}}{{\left(\mathrm{i\Δf}\right)}^2}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular velocity of vibration root-mean-square value at f=i Δ f place ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angular velocity of vibration root-mean-square value;

(5.4) according to the measurand that calculates in the step (5.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw displacement root-mean-square value at f=i Δ f place ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] angle of throw displacement root-mean-square value.

The present invention's advantage compared with prior art is:

(1) relatively adopts the direct measurement means of angular oscillation such as gyro, star sensor and angular-rate sensor, the linear accelerometer technology is more simple, ripe, and in the industrial circle widespread use, only need that measurement data is carried out a series of data processing and can obtain the angular oscillation data;

(2) the used linear accelerometer of the present invention adopts coplanar layout, and all accelerometers are arranged on the plane, and the range accuracy of installation and the depth of parallelism can guarantee by plane machining, require lower to satellite;

(3) the present invention only needs four linear accelerometers acceleration information of totally 8 passages, can obtain two groups of angular oscillation data, obtain the angular oscillation data by the mode of averaging, improve the accuracy that angular oscillation is measured, and data volume is less, and it is less to take satellite resource when transmitting over the ground.

(4) the present invention obtains the impact that mode that the angular acceleration time domain data adopts difference can be eliminated neighbourhood noise, obtain the angular acceleration frequency domain data follow-up by the FFT conversion, successively obtain angular velocity of vibration data and angular displacement data by twice integration, spectral leakage is few.

Description of drawings

Fig. 1 is the coplanar mounting arrangement figure of accelerometer of the present invention.

Fig. 2 is that the present invention adopts the coplanar installation of accelerometer to carry out system's composition diagram that angular oscillation is measured.

Fig. 3 is the inventive method process flow diagram.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing.

The invention provides a kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys, spaceborne linear accelerometer be exactly have space environment adaptive, carry out the sensor linear oscillator acceleration analysis, that have certain measuring accuracy.The method of three shaft angle vibration surveys has comprised that space layout implementation method and the employing linear accelerometer of accelerometer on satellite or useful load carries out the implementation method that angular oscillation calculates, the present invention utilizes spaceborne linear accelerometer to carry out the method for three shaft angle vibration surveys, stipulate the configuration layout implementation of sensor on star, solved the inconvenience of sensor complex configuration layout implementation.Adopt this method, both reduced sensor to the requirement of satellite mounting plane with to the taking of satellite resource, again so that the installation of sensors precision be more prone to guarantee that implementation is more simple.

As shown in Figure 3, step is as follows:

(1) at the selected mounting plane of measurand and definite coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis all are positioned at this mounting plane, measurand axis of rolling direction is X-axis, the pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or the star;

(2) select the rectangular area at mounting plane, at four drift angles of rectangle four linear accelerometers are installed respectively, as shown in Figure 1, wherein the First Line accelerometer is three axis accelerometer meters; The second and the 3rd linear acceleration is counted two-axis accelerometer, and two of the second linear accelerometer are axially pointed to respectively Y-direction and Z-direction, and two of the 3rd linear accelerometer are axially pointed to respectively X-direction and Z-direction; The 4th linear acceleration is counted single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;

(3) as shown in Figure 2, gather the time domain data of 4 linear accelerometers, after star is through amplification and filtering processing, the lower ground of passing to;

(4) pass through formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}=\frac{c_z-a_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1y}=\frac{b_z-a_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1z}=\frac{c_x-a_x}{\mathrm{La}}\end{array}\right\}$ With $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}=\frac{d_z-b_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2y}=\frac{d_z-c_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2z}=\frac{b_y-a_y}{\mathrm{La}}\end{array}\right\}$ Calculate two groups of measurands around X-axis, Y-axis, three axial angle of throw acceleration of Z axis With Pass through again afterwards formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_x+\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_y=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1y}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2y}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_z=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1z}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2z}}{2}\end{array}\right\}$ Ask its mean value to obtain With

In the formula: a _x, a _y, a _zBe respectively X-direction, Y-direction, the Z-direction acceleration of First Line accelerometer, b _y, b _zBe respectively Y-direction, the Z-direction acceleration of the second linear accelerometer, c _x, c _zBe respectively X-direction, the Z-direction acceleration of the 3rd linear accelerometer, d _zIt is the Z-direction acceleration of the 4th linear accelerometer; La, Lb are respectively the rectangle of four linear accelerometers compositions along the length of side of Y-axis and X-axis;

(5) according to obtaining in the step (4) With Calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely finished the measurement of three shaft angles vibrations.

Specifically carry out in accordance with the following steps:

(a) pass through formula $\left.\begin{array}{c}{B}_X\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{X}\left(\mathrm{i\Δf}\right)\·\left(\mathrm{i\Δf}\right)}\\ B_Y\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Y}\left(\mathrm{i\Δf}\right)\·Y\left(\mathrm{i\Δf}\right)}\\ B_Z\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Z}\left(\mathrm{i\Δf}\right)\·Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}$ I=0,1,2 ..., N/2 calculates measurand around X-axis, Y-axis, three axial angle of throw acceleration power spectral density of Z axis,

Wherein, i is the sequence number of power spectral density value, and N is the sampling sum;

Δ f is frequency interval,

B _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular acceleration power spectral density value at f=i Δ f place,

X (i Δ f), Y (i Δ f) and Z (i Δ f) are measurand around X-axis, Y-axis, three axial frequencies of the Z axis FFT function at f=i Δ f place;

With Be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);

(b) according to the measurand that calculates in the step (a) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density BX of Z axis (i Δ f), BY (i Δ f) and BZ (i Δ f), by formula

$\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_X\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Y\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw acceleration root-mean-square value at f=i Δ f place ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angle of throw acceleration root-mean-square value;

(c) according to the measurand that calculates in the step (a) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular velocity of vibration root-mean-square value at f=i Δ f place ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angular velocity of vibration root-mean-square value;

(d) according to the measurand that calculates in the step (a) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw displacement root-mean-square value at f=i Δ f place ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}{,\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}{,\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] angle of throw displacement root-mean-square value.

Claims (2)

1. method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys is characterized in that step is as follows:

(1) at the selected mounting plane of measurand and definite coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis all are positioned at this mounting plane, measurand axis of rolling direction is X-axis, the pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or the star;

(2) select the rectangular area at mounting plane, at four drift angles of rectangle four linear accelerometers are installed respectively, wherein the First Line accelerometer is three axis accelerometer meters; The second and the 3rd linear acceleration is counted two-axis accelerometer, and two of the second linear accelerometer are axially pointed to respectively Y-direction and Z-direction, and two of the 3rd linear accelerometer are axially pointed to respectively X-direction and Z-direction; The 4th linear acceleration is counted single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;

(3) time domain data of 4 linear accelerometers of collection, after star is through amplification and filtering processing, the lower ground of passing to;

(4) pass through formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}=\frac{c_z-a_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1y}=\frac{b_z-a_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{1z}=\frac{c_x-a_x}{\mathrm{La}}\end{array}\right\}$ With $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}=\frac{d_z-a_z}{\mathrm{La}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2y}=\frac{d_z-a_z}{\mathrm{Lb}}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{2z}=\frac{b_y-a_y}{\mathrm{La}}\end{array}\right\}$ Calculate two groups of measurands around X-axis, Y-axis, three axial angle of throw acceleration of Z axis With Pass through again afterwards formula $\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_x=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1x}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2x}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_y=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1y}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2y}}{2}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_z=\frac{{\stackrel{\·\·}{\mathrm{\θ}}}_{1z}+{\stackrel{\·\·}{\mathrm{\θ}}}_{2z}}{2}\end{array}\right\}$ Ask its mean value to obtain With

In the formula: a _x, a _y, a _zBe respectively X-direction, Y-direction, the Z-direction acceleration of First Line accelerometer, b _y, b _zBe respectively Y-direction, the Z-direction acceleration of the second linear accelerometer, c _x, c _zBe respectively X-direction, the Z-direction acceleration of the 3rd linear accelerometer, d _zIt is the Z-direction acceleration of the 4th linear accelerometer; La, Lb are respectively the rectangle of four linear accelerometers compositions along the length of side of Y-axis and X-axis;

(5) according to obtaining in the step (4) With Calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely finished the measurement of three shaft angles vibrations.

2. a kind of method of utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys according to claim 1 is characterized in that: basis in the described step (5) With Calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, carry out in accordance with the following steps:

(2.1) pass through formula $\left.\begin{array}{c}{B}_X\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{X}\left(\mathrm{i\Δf}\right)\·X\left(\mathrm{i\Δf}\right)}\\ B_Y\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Y}\left(\mathrm{i\Δf}\right)\·Y\left(\mathrm{i\Δf}\right)}\\ B_Z\left(\mathrm{i\Δf}\right)=\sqrt{\frac{2h}{N}\stackrel{\‾}{Z}\left(\mathrm{i\Δf}\right)\·Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}$ I=0,1,2 ..., N/2 calculates measurand around X-axis, Y-axis, three axial angle of throw acceleration power spectral density of Z axis,

Wherein, i is the sequence number of power spectral density value, and N is the sampling sum;

Δ f is frequency interval,

B _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular acceleration power spectral density value at f=i Δ f place,

X (i Δ f), Y (i Δ f) and Z (i Δ f) are measurand around X-axis, Y-axis, three axial frequencies of the Z axis FFT function at f=i Δ f place;

With Be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);

(2.2) according to the measurand that calculates in the step (2.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_X\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Y\left(\mathrm{i\Δf}\right)}\\ {\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}{B}_Z\left(\mathrm{i\Δf}\right)}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw acceleration root-mean-square value at f=i Δ f place ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angle of throw acceleration root-mean-square value;

(2.3) according to the measurand that calculates in the step (2.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\\ {\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{2\mathrm{\π}}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^2}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angular velocity of vibration root-mean-square value at f=i Δ f place ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\stackrel{\·}{\mathrm{\θ}}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\stackrel{\·}{\mathrm{\θ}}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\stackrel{\·}{\mathrm{\θ}}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] the angular velocity of vibration root-mean-square value;

(2.4) according to the measurand that calculates in the step (2.1) around X-axis, Y-axis, three axial angle of throw acceleration power spectral density B of Z axis _X(i Δ f), B _Y(i Δ f) and B _Z(i Δ f) is by formula

$\left.\begin{array}{c}{\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_X}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Y}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\\ {\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}=\frac{1}{{4\mathrm{\π}}^2}\sqrt{\mathrm{\Δf}\underset{i=f_1/\mathrm{\Δf}}{\overset{f_2/\mathrm{\Δf}}{\mathrm{\Σ}}}\frac{{B_Z}^2\left(\mathrm{i\Δf}\right)}{{\left(\mathrm{i\Δf}\right)}^4}}\end{array}\right\}i=\mathrm{0,1,2},\·\·\·,N/2$

Calculate measurand around X-axis, Y-axis, three axial frequencies of the Z axis angle of throw displacement root-mean-square value at f=i Δ f place ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}\·$

Wherein: ${\mathrm{\θ}}_{X\_\mathrm{RMS}}{|}_{[f_1,f_2]},{\mathrm{\θ}}_{Y\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ With ${\mathrm{\θ}}_{Z\_\mathrm{RMS}}{|}_{[f_1,f_2]}$ Be followed successively by measurand around X-axis, Y-axis, the interval [f of being of three axial frequency of Z axis ₁, f ₂] angle of throw displacement root-mean-square value.