CN108680302A - Error calibrating method for rocking measuring system - Google Patents
Error calibrating method for rocking measuring system Download PDFInfo
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- CN108680302A CN108680302A CN201810644159.5A CN201810644159A CN108680302A CN 108680302 A CN108680302 A CN 108680302A CN 201810644159 A CN201810644159 A CN 201810644159A CN 108680302 A CN108680302 A CN 108680302A
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L25/00—Testing or calibrating of apparatus for measuring force, torque, work, mechanical power, or mechanical efficiency
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Abstract
The invention discloses a kind of error calibrating methods for rocking measuring system, and this approach includes the following steps：Step S100：Apply known calibration power to the measuring system of rocking, v measured value is obtained by system parameter calibration method, v vibration characteristics systematic parameter is obtained according to the measured value and the known calibration power；Step S200：Mutually independent normal distribution random sequence is generated using monte carlo method, test data sampling is carried out to test result according to normal distribution random sequence, system parameter calibration error is obtained according to sampled result；Step S300：Carry out n times step S200, obtain n system parameter calibration error, using in n system parameter calibration error maximum value and minimum value as error burst；Step S400：Using the measurement for rocking measuring system progress thrust or momentum, the error of acquired results is in error burst.Accurately measuring system measuring result error is rocked in estimation to this method, improves calibration efficiency and accuracy rate.
Description
Technical field
The present invention relates to a kind of error calibrating methods for rocking measuring system, belong to spacecraft micromass culture field.
Background technology
Thrust and momentum are the important propulsive performance indexs of microthruster.In microthruster design, development and application stage
Thrust and the momentum performance to generating for thruster is both needed to assess.The assessment of usual thrust and momentum, which uses, rocks, hangs pendulum
Etc. measuring systems directly measured, the rotational angle for rocking equal rotatable parts measured under thrust or Impulse is scaled
Thrust or momentum.The Accurate Calibration of systematic parameter and the error analysis of calibration directly determine the standard of thrust and impulse measurement result
True degree.Usually in thrust and the calibration process of impulse measurement, the mark of systematic parameter is only obtained with certain test data
Definite value and error.But in actually measuring, the random error of the generations such as system noise error, constant force error can be to systematic parameter
It has an impact, to reduce existing measuring system to the accuracy for thruster thrustimpulse measurement result.It is especially existing
Method can not accurately obtain each measurement error and its calibrated error in measurement process.To analyzing and evaluating microthruster performance
It causes to hinder.
Therefore, the calibrated error rocked in thrust and impulse measurement how is effectively analyzed to be a technical problem to be solved urgently.
Invention content
According to the one side of the application, a kind of error calibrating method for rocking measuring system, this method are provided
It can accurately estimate to rock measuring system measuring result error, improving calibration efficiency and accuracy rate, errors section can use
The follow-up multiple measurement results of measuring device are rocked in same.
The error calibrating method for rocking measuring system includes the following steps：
Step S100：Apply known calibration power to the measuring system of rocking, the progress of primal system response curve will be obtained
Noise reduction obtains v measured value, according to the measured value according to the primal system response curve by system parameter calibration method
V vibration characteristics systematic parameter is obtained with the known calibration power；The vibration characteristics systematic parameter includes systematic parameter
Estimated value；
Step S200：It is that input is given birth to using monte carlo method with systematic parameter estimated value after setting emulation initializaing variable
At mutually independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to the normal distribution random sequence Δ θ (t)~N
(0,σ2) test data sampling is carried out to the v measured values, system parameter calibration error is obtained according to the sampled result；
Step S300：Step S200 described in n times is carried out, the n system parameter calibration errors are obtained, with the n systems
Maximum value and minimum value in parameter calibration error of uniting is as error burst；
Step S400：Using the measurement rocked measuring system and carry out thrust or momentum, the error of acquired results is in
In the error burst；
It is described to emulate standard deviation sigma and the measurement that initializaing variable includes the systematic parameter estimated value, system responds error of making an uproar
Force characteristic parameter.
Optionally, noise reduction process method described in the step S100 is the smooth noise-reduction method of orthogonal polynomial.
Optionally, the vibration characteristics includes with systematic parameter：Vibration frequency estimated value, coefficient of torsional rigidity estimated value,
Damping ratio estimated value, rotary inertia estimated value, coefficient of torsional rigidity；
The known calibration power and the measuring force include constant force or impulsive force.
Preferably, when the known calibration power is constant force, the step S100 includes the following steps：
Step S110：Apply known constant power to the measuring system of rocking, measuring system response production is rocked described in acquisition
Raw stable state torsion angle, system response extreme point correspond to the time and system responds extreme point and corresponds to torsion angle；
Step S120：Extreme point is responded according to the system and corresponds to the time, calculates vibration frequency, obtains vibration frequency estimation
Value responds extreme point according to the system and corresponds to torsion angle, calculate damping ratio, according to the stable state torsion angle, it is rigid to obtain torsion
Spend coefficient estimated value.
Preferably, when the known calibration power is impulsive force, the step S100 includes the following steps：
Step S110：Apply known impulsive force to the measuring system of rocking, measuring system response pole is rocked described in acquisition
Value point corresponding time, extreme point correspond to torsion angle calibration vibration frequency and damping ratio；
Step S120：Mass block is set in the crossbeam shaft for rocking measuring system；
Step S130：Measuring system is rocked described in measuring respectively to add before the mass block and after adding the mass block
Vibration frequency ωdAnd dampingratioζ, calculate separately accordingly before the additional mass block described rocks measuring system intrinsic vibration frequency
Rate and add after the mass block it is described rock measuring system eigentone, obtain described rocking measuring system accordingly
Rotary inertia obtains the coefficient of torsional rigidity k for rocking measuring system accordingly.
Optionally, the make an uproar standard deviation sigma of error of system response is calculated according to the following steps：Measurement is not rocked to described
Before system applies known calibration power, the system response measurement value of measuring system is rocked described in measurement, is calculated by formula (19)
The standard deviation sigma of system response noises error：
Wherein, Θ (t) responds for real system, Θ (t)=Δ θ (t), Δ θ (ti) it is system response noises error, n is
Sample number.
Preferably, when the measuring force is constant force, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal state point according to the standard deviation sigma of system response noises error
Cloth random sequence Δ θ (t)~N (0, σ2), ith measurement is carried out by the measuring system of rocking, obtains the response of ith system
Noise error Δ θi, according to system response noises error delta θi, generate real system response and its curve；
(2) it on the real system response curve, obtains system response extreme point and corresponds to time tMi, corresponding twist angle phi
(tMi), ith measure gained vibration frequency ωdiAnd dampingratioζi, after the system response that ith measures enters lower state,
Stable state torsion angle estimated value is obtained, coefficient of torsional rigidity estimated value is calculated according to the stable state torsion angle estimated value
(3) system ginseng when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter
Number estimated value, is calculated the system parameter calibration error
Optionally, the calibrated error of the systematic parameterIt is calculated as follows：
Wherein, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；K surveys for ith
Coefficient of torsional rigidity is measured,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；To shake
Dynamic characteristic coefficient of torsional rigidity estimated value.
Preferably, when the measuring force is impulsive force, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to
The distribution chooses 30 to 50 extreme points for calculating damping ratio and vibration frequency, in the vibration characteristics systematic parameter
Dampingratioζ and vibration frequency ωd, the rotary inertia J of measuring system, the rotary inertia J of the mass block are rocked described in setting1, turn
Dynamic inertia J1Error
(2) pass through the ith measurement rocked measuring system and measure momentum S, obtain ith system response noises
Error delta θi, according to system response noises error delta θi, generate before applying the mass block and apply the reality after the mass block
System responds and its curve；
(3) on the real system response curve, obtain before applying the mass block system response extreme point to it is corresponding when
Between and corresponding torsion angle [tMi,Θ(tMi)], calculate vibration frequency and damping ratioWith system after the application mass block
Response extreme point corresponds to time and corresponding torsion angle [tM1i,Θ1(tM1i)], calculate vibration frequency and damping ratioIt surveys
The rotary inertia estimated value of measuring system and its calibrated error of systematic parameter are rocked described in amount；
(4) system ginseng when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter
Number estimated value, is calculated the system parameter calibration error
Optionally, the rotary inertia J of the mass block1Meet J with the rotary inertia for rocking measuring system J1≤J/
3。
Optionally, it includes vibration frequency that ith, which measures the gained system parameter calibration error,Damping ratio εζi, rotation
Inertia εJiIt is calculated as follows：
In formula, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；J surveys for ith
The rotary inertia measured,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；
For vibration characteristics rotary inertia estimated value.
Beneficial effects of the present invention include but not limited to：
(1) error calibrating method provided by the present invention for rocking measuring system rocks systematic survey for using
During thrust and momentum, by ambient noise, systematic parameter constant force error and systematic parameter, additional mass error is demarcated
The error in measurement process is demarcated in the influence brought, to improve measurement accuracy, reduces all kinds of errors to measuring
As a result influence.Thrust produced by existing micro-thruster is only milli ox and milli ox hereinafter, minimum in micro- ox magnitude.In measurement result
Existing error causes larger fluctuation to measurement result, seriously affects the accuracy of measurement result.It is each in measurement process simultaneously
Item error can also be superimposed amplification, the accuracy of severe jamming microthruster measurement result.
(2) error calibrating method provided by the present invention for rocking measuring system, in the prior art, thrust and momentum
Calibration process in, the calibration value and error of systematic parameter are only obtained with certain test data.But in practice, system noise
The error that sound error, constant force error etc. randomly generate can generate systematic parameter and seriously affect, and then interference measurement results.This
Invent the method that proposes can accurately calibration system parameter, obtain systematic parameter error, and the confidence of error can be provided
Degree.To which influence of the systematic parameter error to result in measurement process is rocked in correction, the accuracy for rocking measurement result is improved.It should
Method can be used for demarcating thrust and momentum respectively.
(3) error calibrating method provided by the present invention for rocking measuring system can effectively be carried out and be based on rocking
The thrust and impulse measurement system parameter calibration of system；With preferable versatility, shake suitable for the similar second order for rocking system
The system response measurement of dynamic measuring system.
Description of the drawings
Fig. 1 is the error calibrating method schematic process flow diagram provided by the present invention for rocking measuring system；
Fig. 2 is system response curve schematic diagram under constant force effect in the preferred embodiment of the present invention；
Fig. 3 is system response curve schematic diagram under pulsed force function in the preferred embodiment of the present invention；
Fig. 4 is the close-up schematic view rocked in the preferred embodiment of the present invention after measuring system additional mass；
Fig. 5 is the vibration frequency error result under constant force effect in errors range in the preferred embodiment of the present invention 1
Schematic diagram；
Fig. 6 is the damping ratio error schematic diagram under constant force effect in errors range in the preferred embodiment of the present invention 1；
Fig. 7 is that coefficient of torsional rigidity error is shown in errors range under constant force effect in the preferred embodiment of the present invention 1
It is intended to；
Fig. 8 is vibration frequency error schematic diagram in errors range under pulsed force function in the preferred embodiment of the present invention 2；
Fig. 9 is to damp ratio error schematic diagram in the preferred embodiment of the present invention 2 under pulsed force function in errors range；
Figure 10 is that rotary inertia error is illustrated in errors range under pulsed force function in the preferred embodiment of the present invention 2
Figure.
Specific implementation mode
The present invention is described in detail with reference to embodiment, but the invention is not limited in these embodiments.
Include the following steps provided by the present invention for rocking the error calibrating method of measuring system referring to Fig. 1：
Step S100：Apply 1 known calibration power to the measuring system of rocking, obtains primal system response curve, root
V measured value is obtained by system parameter calibration method according to the primal system response curve, according to the measured value and described
Known calibration power obtains v vibration characteristics systematic parameter；
Vibration characteristics includes with systematic parameter：Vibration frequency estimated value, coefficient of torsional rigidity estimated value, damping compared estimate
Value, rotary inertia estimated value, coefficient of torsional rigidity；Vibration frequency estimated value therein, coefficient of torsional rigidity estimated value, damping ratio
Estimated value, rotary inertia estimated value are known as systematic parameter estimated value.
The calibration power and measuring force include constant force or impulsive force,
Step S200：It is that input is given birth to using monte carlo method with systematic parameter estimated value after setting emulation initializaing variable
At mutually independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to the normal distribution random sequence Δ θ (t)~N
(0,σ2) test data sampling is carried out to the v measured values, system parameter calibration error is obtained according to the sampled result；
In this step, gained systematic parameter estimated value is as the actual value inputted in the errors simulation analysis of Monte Carlo
Reference value uses.For example the vibration frequency estimated value obtained herein is 100, then in the errors simulation analysis of Monte Carlo, is
The actual value of system vibration frequency is exactly to select rational range in its vicinity, for example can select [90,110] with 100 for reference
Between take number of values according to a fixed step size after emulated.By obtaining random noise after Monte Carlo simulation (by formula (33)
Obtain) as emulate obtained real system response Δ θi~N (0, σ2)。
Step S300：Step S100~step S200 steps described in n times are carried out, the v system parameter calibrations is obtained and misses
Difference, using in n system parameter calibration errors maximum value and minimum value as error burst；
Step S400：Using the measurement rocked measuring system and carry out thrust or momentum, the error of acquired results is in
In the error burst.
It is described emulation initializaing variable include the vibration characteristics systematic parameter, system response make an uproar error standard deviation sigma and
Measuring force characterisitic parameter；
The measuring force characterisitic parameter includes that the rotary inertia error of additional mass isAnd constant force
Characteristic f0With constant force systematic error accounting R0S=f0S/f0It indicates.
The method provided by the present invention carries out multiple system parameter calibration error measure, acquired results shape using monte carlo method
At interval, can be used to instruct subsequently measure in acquired results error value.It can realize that quantitative correction is rocked substantially
Measuring system measures acquired results.This method can be used to rock thrust measurement and impulse measurement in measuring.Made with error burst
For the error range of acquired results in practical measure, the confidence level of error>99%.Illustrate this method errors range reliability
It is higher.It is used simultaneously using monte carlo method, improves the randomness of sampling, make errors section closer to true
Value.Using Monte Carlo method, the influence that residual noise corresponds to extreme point time, corresponding torsion angle, stable state torsion angle is obtained.
To according to system parameter calibration method, provide systematic parameter estimated value, error and confidence level.This method can be obtained accurately
Systematic parameter is rocked, and provides its error range.
This method errors section simultaneously, can be suitably used for one and rocks measuring system, is both needed to when avoiding measuring every time pair
It rocks measuring system to be demarcated, improves measurement efficiency.
System herein refers to rocking Micromass cell culture system.The system building rocks the normal of thrust-measuring device by existing
Rule method is built.
Preferably, when the known calibration power is constant force, the step S100 includes the following steps：
Step S110：Apply known constant power to the measuring system of rocking, measuring system response production is rocked described in acquisition
Raw stable state torsion angle, system response extreme point correspond to the time and system responds extreme point and corresponds to torsion angle；
Step S120：Extreme point is responded according to the system and corresponds to the time, calculates vibration frequency, obtains vibration frequency estimation
Value responds extreme point according to the system and corresponds to torsion angle, calculate damping ratio, according to the stable state torsion angle, it is rigid to obtain torsion
Spend coefficient estimated value；
The vibration characteristics systematic parameter corresponding at this time includes that vibration frequency and its estimated value, damping ratio and torsion are rigid
Spend coefficient estimated value.
The constant force scaling method of systematic parameter is to demarcate unknown system according to system response measurement value under constant force effect
Parameter.In the constant force scaling method of systematic parameter, needs constant force generating apparatus being mounted on and rock on crossbeam, when known mark
Determine power be constant force when, be applicable to rock measuring system greatly.
When this method is used for thrust measurement error calibration, by applying constant force, obtaining system oscillation process is accordingly
System parameter；When this method is used for momentum error calibration, after mainly using additional mass, obtaining system free oscillation is accordingly
System parameter.
Preferably, when the known calibration power is impulsive force, the step S100 includes the following steps：
Step S110：Apply known impulsive force to the measuring system of rocking, measuring system response pole is rocked described in acquisition
Value point corresponding time, extreme point correspond to torsion angle calibration vibration frequency and damping ratio；
Step S120：Mass block is set in the crossbeam shaft for rocking measuring system；
Step S130：Measuring system is rocked described in measuring respectively to add before the mass block and after adding the mass block
Vibration frequency ωdAnd dampingratioζ, calculate separately accordingly before the additional mass block described rocks measuring system intrinsic vibration frequency
Rate and add after the mass block it is described rock measuring system eigentone, obtain described rocking measuring system accordingly
Rotary inertia obtains the coefficient of torsional rigidity k for rocking measuring system accordingly.
The vibration characteristics systematic parameter includes dampingratioζ, vibration frequency ωdWith coefficient of torsional rigidity k.
The impulsive force scaling method of systematic parameter is to demarcate unknown system according to system response measurement value under pulsed force function
Parameter.In the impulsive force scaling method of systematic parameter, constant force generating apparatus is not needed, when known calibration power is impulsive force,
This method is applicable to small rock measuring system.
Preferably, noise reduction process method described in the step S100 is the smooth noise-reduction method of orthogonal polynomial.
The smooth noise-reduction method of orthogonal polynomial, includes the following steps：
Step S111：Experiment sampling curve is fitted using orthogonal polynomial least-square fitting approach；
Step S112：It is kept away with the local value characteristic of adequacy test data point using micro-slip data window approximating method
The error of whole data point fitting is exempted from；
Step S113：Using orthogonal polynomial, in conjunction with sliding data window method, using least-square fitting approach, according to
Test data point upper and lower fluctuating characteristic near mean place, searches out best mean place curve.Improve polynomial fitting
Coefficient computational accuracy.
Preferably, the make an uproar standard deviation sigma of error of system response is calculated according to the following steps：Measurement system is rocked to described
System applies known calibration power, and the system response measurement value of measuring system is rocked described in measurement, and system, which is calculated, by formula (19) rings
Answer the standard deviation sigma of noise error：
Wherein, Θ (t) responds for real system, and Θ (t)=Δ θ (t), n are sampling total number, Δ θ (ti) it is that system is rung
Noise error, i is answered to be sampled for ith.
Specifically, actual measurement system is constantly present system response noises error, if system response noises error is Δ θ
(t)~N (0, σ2), it is mutually independent normally distributed random variable, real system response is：
Θ (t)=θ (t)+Δ θ (t) (18)
When not applying known calibration power, there are θ (t)=0 and Θ (t)=Δ θ (t), there are Δ θ (t at this timei)=Θ (ti) (i=
1,2 ..., n), the standard deviation sigma of system response noises error is：
I.e. by not applying system response measurement value under the conditions of constant force or impulsive force, computing system response noises error
Standard deviation.
Preferably, the N is more than or equal to 300 times.The confidence level of errors range can reach at this time>99%.
Preferably, when the measuring force is constant force, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal state point according to the standard deviation sigma of system response noises error
Cloth random sequence Δ θ (t)~N (0, σ2), damping ratio, vibration frequency, the torsion stiffness system estimation value that S100 steps are obtained
It is referred to as actual value, damping ratio, vibration frequency when Select Error simulation analysis, coefficient of torsional rigidity parameter actual value, to
The system of rocking applies constant force, generates real system response and its curve；
Standard deviation reflection is before not applying calibration power, and measuring system is by measuring the random noise characteristic obtained.
(2) it on the real system response curve, obtains system response extreme point and corresponds to time tMi, corresponding twist angle phi
(tMi), ith measure gained vibration frequency ωdiAnd dampingratioζi, after the system response that ith measures enters lower state,
Stable state torsion angle estimated value is obtained, coefficient of torsional rigidity estimated value is calculated according to the stable state torsion angle estimated value
(3) system ginseng when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter
Number estimated value, is calculated the system parameter calibration error
The calibrated error of systematic parameter includes vibration frequency calibrated error, damping ratio calibrated error, rocks stiffness coefficient mark
Determine error.
Preferably, the calibrated error of the systematic parameterIt is calculated as follows：
Wherein, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；K surveys for ith
Coefficient of torsional rigidity is measured,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；To shake
Dynamic characteristic coefficient of torsional rigidity estimated value.
Preferably, the impulsive force refers to action time infinitesimal instantaneous force.
Preferably, when the measuring force is impulsive force, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to
The distribution chooses 30 to 50 extreme points for calculating damping ratio and vibration frequency, selectes in the vibration characteristics systematic parameter
Dampingratioζ and vibration frequency ωd, the rotary inertia J of measuring system, the rotary inertia J of the mass block are rocked described in setting1、
Rotary inertia J1Error
(2) pass through the ith measurement rocked measuring system and measure momentum S, obtain ith system response noises
Error delta θi, according to system response noises error delta θi, generate before applying the mass block and apply the reality after the mass block
System responds and its curve；
(3) on the real system response curve, obtain before applying the mass block system response extreme point to it is corresponding when
Between and corresponding torsion angle [tMi,Θ(tMi)], calculate vibration frequency and damping ratioWith system after the application mass block
Response extreme point corresponds to time and corresponding torsion angle [tM1i,Θ1(tM1i)], calculate vibration frequency and damping ratioIt surveys
The rotary inertia estimated value of measuring system and its calibrated error of systematic parameter are rocked described in amount；
(4) system ginseng when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter
Number estimated value, is calculated the system parameter calibration error
Preferably, the rotary inertia J of the mass block1Meet J with the rotary inertia for rocking measuring system J1≤J/3。
Preferably, it includes vibration frequency that ith, which measures the gained system parameter calibration error,Damping ratio εζi, turn
Dynamic inertia εJiIt is calculated as follows：
In formula, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；J surveys for ith
The rotary inertia measured,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；
For vibration characteristics rotary inertia estimated value.
The method provided by the present invention is described in detail below in conjunction with specific example：
The constant force scaling method of 1 systematic parameter
1.1 system response measurement principles
The constant force scaling method of systematic parameter is to demarcate unknown system according to system response measurement value under constant force effect
Parameter.In the constant force scaling method of systematic parameter, needs constant force generating apparatus being mounted on and rock on crossbeam, therefore, fit
For rocking measuring system greatly.
In constant force f (τ)=f0Under effect, system response is
Consideration system response noises error delta θ~N (0, σ2) (zero-mean normal distribution), real system, which responds, is
Θ (t)=θ (t)+Δ θ (2)
In formula, θ is to rock crossbeam torsion angle, LfFor the thrust arm of force, k is pivot torsional rigidity coefficient, and ζ is damping ratio, ωd
For vibration frequency.
As shown in Fig. 2, being responded for system under constant force effect, according under constant force effect, system responds extreme point and corresponds to
The calibration systems parameters such as time, corresponding torsion angle, stable state torsion angle.
Extreme point is responded according to system and corresponds to the time, can be calculated vibration frequency, is
Vibration frequency estimated value is
In formula, q is is taken extreme value to count out, ωdiFor the corresponding vibration frequency of i-th of extreme point, tMiFor i-th of extreme value
Point corresponding time, tM1For the 1st extreme point corresponding time；
Extreme point is responded according to system and corresponds to torsion angle, can be calculated damping ratio, is
Damping ratio estimated value is
In formula, q is is taken extreme value to count out, Θ (tMi) it is to rock system torsion under i-th of extreme point corresponding time
Angle, Θ (∞) are the torsion angle after system tends towards stability.
According to stable state torsion angle, coefficient of torsional rigidity estimated value is
The impulsive force scaling method of 2 systematic parameters
The impulsive force scaling method of systematic parameter is to demarcate unknown system according to system response measurement value under pulsed force function
Parameter.In the impulsive force scaling method of systematic parameter, constant force generating apparatus is not needed, therefore, measurement system is rocked suitable for small
System.
Impulsive force refers to action time infinitesimal instantaneous force, if the momentary action momentum of momentary action impulsive force is
S, impulsive force are represented by f (τ)=S δ (τ), by the system motion differential equation it is found that system response is
In formula, ωnFor the vibration frequency under system undamped, J is torsional pendulum moment of inertia.
Consideration system response noises error delta θ~N (0, σ2) (zero-mean normal distribution), real system, which responds, is
Θ (t)=θ (t)+Δ θ (9)
As shown in figure 3, being responded for system under pulsed force function, according under pulsed force function, system responds extreme point and corresponds to
Time, corresponding torsion angle etc. can demarcate vibration frequency and damping ratio, but cannot demarcate rotary inertia or coefficient of torsional rigidity.
In order to further demarcate rotary inertia or coefficient of torsional rigidity, the additional standard mass block on rocking crossbeam is needed,
As shown in figure 4, set torsional pendulum moment of inertia J to be unknown, the rotary inertia J of attached mass block1To be known (in order to not influence measurement
The sensibility and jamtosignal of system, generally require J1≤ J), due to the coefficient of torsional rigidity of measuring system before and after additional mass
It is constant, it is known that
In formula, subscript " 1 " rocks eigentone, ω after indicating additional massn1For rocking after additional mass
Eigentone.
Therefore, additional mass block method needs the vibration frequency of measurement twice and damping ratio before and after additional mass, so as to
Calculate the eigentone before and after additional mass.
Extreme point is responded according to system and corresponds to the time, can be constructed the calculation formula of vibration frequency, is
Vibration frequency estimated value is
In formula, q is is taken extreme value to count out.
Extreme point is responded according to system and corresponds to torsion angle, can be constructed the calculation formula of damping ratio, is
In formula, Θ (t should be metM1)≥Θ(tMi).Measuring system damping ratio very little and system response noises are rocked due to small
Error interference, if there are Θ (tM1) ＜ Θ (tMi), ζ should be enabledi=0.
Damping ratio estimated value is
In formula, q is is taken extreme value to count out.
In order to measure torsional pendulum moment of inertia, additional rotation inertia is J on crossbeam1Mass block, it is known that
In formula, subscript " 1 " rocks eigentone after indicating additional mass.And have
In formula, ω before additional massdAnd ζ after ζ and additional mass1And ωd1, being can amount measured directly.
Referring to Fig. 4, mass block is set on the torsional axis for rocking crossbeam, and crossbeam is rotated around torsional axis, and mass block is sheathed on torsional axis
And it rotates around the axis with crossbeam.
3 system response noises error analyses
Actual measurement system is constantly present system response noises error, if system response noises error be Δ θ (t)~N (0,
σ2), it is mutually independent normally distributed random variable, real system response is
Θ (t)=θ (t)+Δ θ (t) (18)
Under the conditions of not applying constant force or impulsive force, there are θ (t)=0 and Θ (t)=Δ θ (t), there are Δ θ (t at this timei)=Θ
(ti) (i=1,2 ..., n), the standard deviation estimate value of system response noises error is
I.e. by not applying system response measurement value under the conditions of constant force or impulsive force, computing system response noises error
Standard deviation.
The smooth noise-reduction method of 4 orthogonal polynomials
4.1 orthogonal polynomial method
There are when randomness noise jamming, in order to find the mean place curve of test data, most using orthogonal polynomial
Small two multiply approximating method.Known data point sampled value is (xi,yi) (i=0,1 ..., m), by the unrelated function of known linearConstruction multinomial P (x) is fitted, and is
But due to solving coefficient ajVery Ill-conditioned equation, which occurs, in (j=0,1 ..., n) causes the calculating error of solution larger,
Therefore, orthogonal polynomial is chosen to be fitted.
Common construction orthogonal polynomial pk(x) recurrence formula of (k=0,1 ..., n) is
Wherein
Finally, using least square method, it is using way of fitting curve
P (x)=a0p0(x)+a1p1(x)+…+anpn(x) (24)。
4.2 orthogonal polynomials slide the smooth noise reduction of data window
It interferes to cut down noise error Δ θ (t) in real system response Θ (t)=θ (t)+Δ θ (t), is smoothly dropped
It makes an uproar processing, specific method is：
(1) orthogonal polynomial method is used, prevents occurring Abnormal Linear equation set when solving fitting coefficient, is improved quasi-
Polynomial coefficient computational accuracy is closed, to improve fitting precision.
(2) micro-slip data window approximating method is used, with the local value characteristic of adequacy test data point, is avoided complete
The error of number of passes strong point fitting all has good fit ability to complicated system response sample value, thrust calculated value.
For test data point (xi,yi) in (i=0,1 ..., m), with match point xiCentered on, it takes
(xi-p,yi-p), (xi-p+1,yi-p+1) ..., (xi,yi) ..., (xi+p-1,yi+p-1), (xi+p,yi+p)
Equal 2p+1 points carry out orthogonal polynomial sliding data window fitting, and data window center is (xi,yi), left and right respectively takes p
Point, sliding data window length are 2p+1.
(3) orthogonal polynomial is utilized, in conjunction with sliding data window method, using least-square fitting approach, according to experiment number
Strong point upper and lower fluctuating characteristic near mean place, searches out best mean place curve, is
P (x)=a0p0(x)+a1p1(x)+…+anpn(x) (25)
When fitting function form is P (x)=a0+a1x+a2x2When, exactly slide data window parabolic fit method, parabolic
Line fitting has good local fit ability to various curves.
The calibrated error of 5 constant force scaling methods analyzes Monte Carlo method
Emulate initializaing variable selection：1) standard deviation sigma of system response noises error；2) vibration characteristics dampingratioζ, vibration
Frequencies omegadIt is indicated with coefficient of torsional rigidity k；3) constant force characteristic f0With constant force systematic error accounting R0S=f0S/f0It indicates.
Itd is proposed monte carlo simulation methodology, it is specific as follows：
(1) mutually independent normal distribution random sequence Δ θ (t)~N (0, σ is generated2)。
Using Random sampling method, (0,1) section random number r is generatedi(i=1,2 ...) is enabled
Then there is Δ θi~N (0, σ2)。
(2) ζ ∈ [0.1,0.3] within the scope of the common damping ratio of constant force scaling method, select dampingratioζ within this range；
Selection gives vibration frequency ωd, ωdSpecific value do not influence the discussion of problem, only influence time value range；Time T is selected
5~6 extreme points can be chosen by selecting enters stable state for foundation for calculating damping ratio and vibration frequency and system response.
(3) coefficient of torsional rigidity k and constant force f is selected0And constant force systematic error accounting R0S=f0S/f0, f0SFor perseverance
Determine power error.
(4) spare system response noises error generates real system response, is
Θi=θi+Δθ0S,i+Δθi (27)
In formula,
Δθ0S,i=R0Sθi, Δ θ0S,iFor constant force error, Δ θiFor noise error..
(5) it on real system response curve, obtains system response extreme point and corresponds to time tMi, corresponding twist angle phi
(tMi), calculate vibration frequency and damping ratio.
Vibration frequency is
Wherein, vibration frequency estimated value isQ is is taken extreme value to count out.
Damping ratio is
Wherein, damping ratio estimated value is
(6) sampled point serial number l of the system response into stable state1And l2, stable state torsion angle estimated value is
Coefficient of torsional rigidity estimated value is
(7) calibrated error of systematic parameter is
(8) continuous emulation is repeated the above process, standard deviation sigma, the constant force error for studying system response noises error are (constant
Force system error accounting R0S), to vibration frequency ωd, dampingratioζ, the calibrated errors such as coefficient of torsional rigidity k affecting laws.
(9) for giving measuring system, according to systematic parameter estimated value (ζ, the ω of measuring systemd, k), constant force f0And perseverance
Determine power error f0SCarry out above-mentioned emulation, it is desirable that simulation times >=300 time are determined with the envelope up and down of system parameter variations range
Error, such as determine 2 points of envelope up and down, the confidence level of error is 298/300>99%.
The calibrated error of 6 impulsive force scaling methods analyzes Monte Carlo method
Emulate initializaing variable selection：1) standard deviation sigma of system response noises error indicates；2) rotation of additional mass is used
Amount error is εJ1=Δ J1/J1；3) vibration characteristics dampingratioζ, vibration frequency ωdIt is indicated with coefficient of torsional rigidity k.It is proposed
Monte carlo simulation methodology, it is specific as follows：
(1) mutually independent normal distribution random sequence Δ θ (t)~N (0, σ is generated2)。
Using Random sampling method, (0,1) section random number r is generatedi(i=1,2 ...) is enabled
Then there is Δ θi~N (0, σ2)。
(2) ζ ∈ [0.01,0.1] within the scope of the common damping ratio of impulsive force scaling method, select dampingratioζ within this range；
Selection gives vibration frequency ωd, ωdSpecific value do not influence the discussion of problem, only influence time value range；Time T is selected
It selects and (can get more multiple extreme values since damping ratio is small so that 30~50 extreme points can be chosen for calculating damping ratio and vibration frequency
Point).
(3) the rotary inertia J of the rotary inertia J, additional mass of selective measuring system1, rotary inertia J1Error
In order not to significantly reducing signal-to-noise ratio, the rotary inertia J of additional mass after additional mass1≤J/3。
(4) momentum S is given, spare system response noises error generates real system response, is actually before additional mass
System responds
Θi=θi+Δθi (34)
Real system, which responds, after additional mass is
Θ1i=θ1i+Δθi (36)
Wherein：
(5) on real system response curve, time and corresponding torsion are corresponded to system response extreme point before additional mass
Corner [tMi,Θ(tMi)], calculate vibration frequency and damping ratioIt is corresponded to system response extreme point after additional mass
Time and corresponding torsion angle [tM1i,Θ1(tM1i)], calculate vibration frequency and damping ratio
Vibration calculating formula frequency is
Vibration frequency estimated value is
In formula, q is is taken extreme value to count out.
Damping ratio is
Damping ratio estimated value is
(6) estimated value for rocking the rotary inertia of system is
Wherein：
(7) calibrated error of systematic parameter is
(8) continuous emulation is repeated the above process, the standard deviation sigma of system response noises error, turn of additional mass are studied
Dynamic inertia errorTo vibration frequency ωd, dampingratioζ, the calibrated errors such as rotary inertia J affecting laws.
(9) for giving measuring system, according to systematic parameter estimated value (ζ, the ω of measuring systemd, J), additional mass
Rotary inertia error εJ1=Δ J1/J1Carry out above-mentioned emulation, it is desirable that simulation times >=300 time, with system parameter variations range
Envelope up and down determine error, such as determine 2 points of envelope up and down, the confidence level of error is 298/300>99%.
Error confidence level reflects its credibility, obtains the error confidence level of systematic parameter by analysis, can obtain
The credibility of error.(such as emulation 300 times obtains final error by being maximized and minimum value by the difference of the two, that
There are 298 results inevitable within error envelope, such confidence level is more than 99%, therefore has reason to firmly believe what we obtained
The credibility of systematic parameter error is more than 99%.), example explanation is added after this section.
Following example 1~2 are emulated by above-mentioned steps, and obtain calibrated error.
Illustrate method provided by the invention with reference to example 1, it is constant force that power is demarcated applied in example 1, it is assumed that is turned round
Put force measuring system relevant parameter：Its vibration frequency is ωd=1rad/s, damping ratio are ζ=0.2, coefficient of torsional rigidity k=
2.5Nm/rad, arm of force Lf=0.5m, constant force are f (t)=10-3N, the jamtosignal R of system response noises errorNS=
0.01 (constant force error is zero).
Step is provided according to the present invention and carries out above-mentioned simulation process, and simulation times are 300 times, determine error envelope up and down
With minimum and maximum 2 point tolerance values, therefore the probability that error falls into the enclosing interval is 300-2/300 ≈ 99%, i.e. assessment misses
The confidence level of difference is 99%.When dampingratioζ=0.2 and jamtosignal RNSUnder the conditions of=0.01, several extreme points is taken to demarcate and carry out
Smoothing and noise-reducing process.
In this example, simulation result is as shown in Fig. 5~7.Wherein, vibration frequency calibrated error simulation result as shown in figure 5,
Vibration frequency calibrated error numberical range -0.55~0.35% after emulation repeatedly as seen from the figure；Damping ratio calibrated error emulation knot
Fruit is as shown in fig. 6, damping ratio calibrated error numberical range is -0.25~0.55% after emulation repeatedly as seen from the figure；Torsion stiffness
Coefficient calibrated error simulation result as shown in fig. 7, emulate multiple retrotorsion stiffness coefficient calibrated error numberical range as seen from the figure
It is -0.025~0.03%.
Illustrate method provided by the invention with reference to example 2, it is impulsive force to demarcate power applied in example 2, if thrust
Measuring system relevant parameter：Vibration frequency is ωd=4rad/s, damping ratio are ζ=0.02, and rotary inertia is J=4 × 10- 4kg·m2, arm of force Lf=0.1m, the rotary inertia rocked after additional mass are J1=J/3, in order to which calibration system parameter is applied
It is S=5 × 10 to add momentary action momentum-6N·s。
Step is provided according to aforementioned present invention to be emulated, simulation times are 300 times, determine that error up and down use most by envelope
Big and minimum 2 point tolerance values, therefore the probability that error falls into the enclosing interval is 300-2/300 ≈ 99%, i.e. assessment errors
Confidence level is 99%.The jamtosignal R of system response noises errorNS=0.01 (the rotary inertia error of additional mass is zero).
When dampingratioζ=0.02 and jamtosignal RNSUnder the conditions of=0.01, takes several extreme points to demarcate and carry out smoothing and noise-reducing process.
In this example, simulation result is as shown in figs. 8-10.Vibration frequency calibrated error simulation result is as shown in figure 8, by scheming
It can be seen that after emulation repeatedly, vibration frequency calibrated error numberical range is 0.001~0.018%；Damping ratio calibrated error emulation knot
For fruit as shown in figure 9, as seen from the figure after emulation repeatedly, damping ratio calibrated error numberical range is -0.17~0.2%；Torsion stiffness
Coefficient calibrated error simulation result is as shown in Figure 10, as seen from the figure after emulation repeatedly, coefficient of torsional rigidity calibrated error numerical value model
Enclose is -0.6~-0.1%.
The above is only several embodiments of the present invention, not any type of limitation is done to the present invention, although this hair
It is bright to be disclosed as above with preferred embodiment, however not to limit the present invention, any person skilled in the art is not taking off
In the range of technical solution of the present invention, makes a little variation using the technology contents of the disclosure above or modification is equal to
Case study on implementation is imitated, is belonged in technical proposal scope.
Claims (10)
1. a kind of error calibrating method for rocking measuring system, which is characterized in that include the following steps：
Step S100：Apply known calibration power to the measuring system of rocking, obtains primal system response and carry out noise reduction, according to institute
It states primal system response curve and v measured value is obtained by system parameter calibration method, according to the measured value and described known
Calibration power obtains v vibration characteristics systematic parameter；The vibration characteristics systematic parameter includes systematic parameter estimated value；
Step S200：It is that input generates phase using monte carlo method with systematic parameter estimated value after setting emulation initializaing variable
Mutual independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to the normal distribution random sequence Δ θ (t)~N (0,
σ2) test data sampling is carried out to the v measured values, system parameter calibration error is obtained according to the sampled result；
Step S300：Step S200 described in n times is carried out, the n system parameter calibration errors are obtained, is joined with the n systems
Maximum value and minimum value in number calibrated error is as error burst；
Step S400：Using the measurement rocked measuring system and carry out thrust or momentum, the error of acquired results is in described
In error burst；
It is described to emulate standard deviation sigma and the measuring force spy that initializaing variable includes the systematic parameter estimated value, system responds error of making an uproar
Property parameter.
2. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that the step
Noise reduction process method described in S100 is the smooth noise-reduction method of orthogonal polynomial.
3. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that when described known
When calibration power is constant force, the step S100 includes the following steps：
Step S110：Apply known constant power to the measuring system of rocking, rocks what measuring system response generated described in acquisition
Stable state torsion angle, system response extreme point correspond to the time and system response extreme point corresponds to torsion angle；
Step S120：Extreme point is responded according to the system and corresponds to the time, is calculated vibration frequency, is obtained vibration frequency estimated value,
Extreme point is responded according to the system and corresponds to torsion angle, calculates damping ratio and torsion stiffness system is obtained according to the stable state torsion angle
Number estimated value.
4. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that when described known
When calibration power is impulsive force, the step S100 includes the following steps：
Step S110：Apply known impulsive force to the measuring system of rocking, measuring system response extreme point is rocked described in acquisition
Corresponding time, extreme point correspond to torsion angle calibration vibration frequency and damping ratio；
Step S120：Mass block is set in the crossbeam shaft for rocking measuring system；
Step S130：Measuring system is rocked described in measuring respectively adds before the mass block and add the vibration after the mass block
Frequencies omegadAnd dampingratioζ, calculate separately accordingly before the additional mass block it is described rock measuring system eigentone and
Measuring system eigentone is rocked described in after the additional mass block, obtains the rotation for rocking measuring system accordingly
Inertia obtains the coefficient of torsional rigidity k for rocking measuring system accordingly.
5. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that the system is rung
The standard deviation sigma for the error that should make an uproar is calculated according to the following steps：Not to it is described rock measuring system apply known calibration power when, measure
The system response measurement value for rocking measuring system, the standard deviation sigma of system response noises error is calculated by formula (19)：
Wherein, Θ (t) responds for real system, Θ (t)=Δ θ (t), Δ θ (ti) it is system response noises error, n is that sampling is total
Number.
6. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that the measuring force
For constant force when, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal state point according to the standard deviation sigma of the system response noises error
Cloth random sequence Δ θ (t)~N (0, σ2), ith measurement is carried out by the measuring system of rocking, obtains the response of ith system
Noise error Δ θi, according to system response noises error delta θi, generate real system response and its curve；
(2) it on the real system response curve, obtains system response extreme point and corresponds to time tMi, corresponding twist angle phi
(tMi), ith measure gained vibration frequency ωdiAnd dampingratioζi, after the system response that ith measures enters lower state,
Stable state torsion angle estimated value is obtained, coefficient of torsional rigidity estimated value is calculated according to the stable state torsion angle estimated value
(3) systematic parameter when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter is estimated
The system parameter calibration error is calculated in evaluation
7. the error calibrating method according to claim 6 for rocking measuring system, which is characterized in that the system ginseng
Several calibrated errorsIt is calculated as follows：
Wherein, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；K is that ith measures torsion
Turn stiffness coefficient,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；It is special for vibration
Property coefficient of torsional rigidity estimated value.
8. the error calibrating method according to claim 1 for rocking measuring system, which is characterized in that the measuring force
For impulsive force when, the step S200 includes the following steps：
(1) monte carlo method is used to generate mutually independent normal distribution random sequence Δ θ (t)~N (0, σ2), according to this point
Cloth chooses 30 to 50 extreme points for calculating damping ratio and vibration frequency, with the damping in the vibration characteristics systematic parameter
Than ζ and vibration frequency ωd, the rotary inertia J of measuring system, the rotary inertia J of the mass block are rocked described in setting1, rotation it is used
Measure J1Error
(2) pass through the ith measurement rocked measuring system and measure momentum S, obtain ith system response noises error
Δθi, according to system response noises error delta θi, generate before applying the mass block and apply the real system after the mass block
Response and its curve；
(3) on the real system response curve, obtain system response extreme point before applying the mass block corresponds to the time with
Corresponding torsion angle [tMi,Θ(tMi)], calculate vibration frequency and damping ratioIt is responded with system after the application mass block
Extreme point corresponds to time and corresponding torsion angle [tM1i,Θ1(tM1i)], calculate vibration frequency and damping ratioDescribed in measurement
Rock the rotary inertia estimated value of measuring system and its calibrated error of systematic parameter；
(4) systematic parameter when being measured according to ith in gained real system parameter and the vibration characteristics systematic parameter is estimated
The system parameter calibration error is calculated in evaluation
9. the error calibrating method according to claim 8 for rocking measuring system, which is characterized in that the mass block
Rotary inertia J1Meet J with the rotary inertia for rocking measuring system J1≤J/3。
10. the error calibrating method according to claim 8 for rocking measuring system, which is characterized in that ith measures
The gained system parameter calibration error includes vibration frequencyDamping ratio εζi, rotary inertia εJiIt is calculated as follows：
In formula, ωdThe vibration frequency obtained for ith measurement；ζ is the damping ratio that ith measurement obtains；J is that ith measures
The rotary inertia arrived,For vibration characteristics vibration frequency estimated value；For vibration characteristics damping ratio estimated value；For vibration
Characteristic rotary inertia estimated value.
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| CN111964573A (en) * | 2020-08-11 | 2020-11-20 | 桂林电子科技大学 | Device and method for calculating installation error of grating interferometer |
| CN112231890A (en) * | 2020-09-03 | 2021-01-15 | 兰州空间技术物理研究所 | Thrust evaluation method of high-stability electric thruster based on torsional pendulum measurement system |
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