CN114608786B - Aircraft dynamic derivative test data processing method - Google Patents

Aircraft dynamic derivative test data processing method Download PDF

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CN114608786B
CN114608786B CN202210509556.8A CN202210509556A CN114608786B CN 114608786 B CN114608786 B CN 114608786B CN 202210509556 A CN202210509556 A CN 202210509556A CN 114608786 B CN114608786 B CN 114608786B
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陈鹏
陈立立
刘春华
吴双
苏欣
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Equipment Design and Testing Technology Research Institute of China Aerodynamics Research and Development Center
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Abstract

The invention discloses an aircraft dynamic derivative test data processing method, which is applied to the field of aircraft test data processing and comprises the following steps: obtaining a truncated signal; carrying out direct current component filtering processing on a first moment signal and a first angular displacement signal in the truncated signals to obtain a second moment signal and a second angular displacement signal; processing the second moment signal and the second angular displacement signal to obtain a first amplitude estimation value and a first initial phase estimation value of a 1 st harmonic component in the second moment signal, and a second amplitude estimation value and a second initial phase estimation value of the 1 st harmonic component in the second angular displacement signal; obtaining a phase difference based on the first initial phase estimation value and the second initial phase estimation value; calculating to obtain a pneumatic pitch damping moment derivative and a pneumatic pitch restoring moment derivative based on the phase difference, the first amplitude estimation value and the second amplitude estimation value; the method can effectively remove noise influence and improve the accuracy of the aerodynamic pitch damping moment derivative and the aerodynamic pitch restoring moment derivative.

Description

Aircraft dynamic derivative test data processing method
Technical Field
The invention belongs to the field of aircraft test data processing, and particularly relates to a method for processing aircraft dynamic derivative test data.
Background
The dynamic derivative is a characteristic parameter of the dynamic aerodynamic characteristics of the aircraft and is also an important parameter for aircraft control system design and aircraft quality analysis, the gain coefficient is usually determined by the control system design based on the dynamic derivative, the dynamic derivative directly determines the convergence and dispersion characteristics of the oscillation of the aircraft open-loop system when the aircraft open-loop system is disturbed, the stability of the aircraft closed-loop system not only depends on the aerodynamic stability, but also is mainly related to the control system, and the control system can change the stability of the system through the feedback of the attitude plane and the angular rate. The rapid and accurate prediction of the dynamic derivative is critical to the design and safety of the aircraft. The method for acquiring the dynamic derivative of the aircraft mainly comprises theoretical calculation, numerical simulation and wind tunnel test. The theoretical method is high in efficiency, but the application range is narrow, the precision is usually not high, the numerical simulation method is high in efficiency, but the dependence degree on the algorithm is high, and wind tunnel test data are usually needed to be verified. Therefore, the test simulation still has an important effect on the prediction of the aircraft dynamic derivative, the environmental interference is more received in the wind tunnel test process, and the data processing of the wind tunnel test is still the core technology for obtaining the accurate dynamic derivative. In the case of an aircraft with a small angle of attack and attached flow, the dynamic derivative of the aircraft can be obtained by an engineering calculation method, but with the expansion of the angle of attack range and the complication of the appearance of the aircraft, the dynamic derivative is dependent on the reasons of flow separation, vortex formation and fragmentation and the like to a certain extent. It is difficult to simulate the flow separation, vortex formation, and fragmentation in a dynamic state by numerical methods. The dynamic derivative wind tunnel test is usually carried out by a free vibration method and a forced vibration method. Forced vibration is the forcing of a model to vibrate at a fixed frequency in one or more degrees of freedom in simple harmonics (rotation or translation). Forced vibration methods typically work in a resonance region away from the model balance system, where frequency and amplitude can be separately adjusted to allow dynamic instability testing. During the test, the change of the attack angle and the sideslip angle is realized through the wind tunnel turntable rotation angle and the support rod rotation angle combined mechanism. Four directional degrees of freedom including rotation about the three body axes of the model and movement normal thereto may be achieved. The simple harmonic oscillation motion is driven by a direct current servo motor, the motor rotates and is transmitted to a crank through a speed reducer, and the crank rotates to drive a connecting rod to move up and down to change the angle between a swing rod and the vertical direction, so that the pitching oscillation of the airplane is realized.
When the model performs single-degree-of-freedom pitching forced vibration, the vibration differential equation is as follows:
Figure 100002_DEST_PATH_IMAGE001
(1)
in the formula (1), the reaction mixture is,
Figure 100002_DEST_PATH_IMAGE002
to rotate the inertia about the pitch axis through the center of mass,
Figure 100002_DEST_PATH_IMAGE003
in order to be the angular displacement of the model,
Figure 100002_DEST_PATH_IMAGE004
and
Figure 100002_DEST_PATH_IMAGE005
first and second derivatives of the angular displacement respectively,
Figure 100002_DEST_PATH_IMAGE006
and
Figure 100002_DEST_PATH_IMAGE007
known respectively for the mechanical damping and spring constant of the vibration system,
Figure 100002_DEST_PATH_IMAGE008
in order to know the frequency of the vibration,
Figure 100002_DEST_PATH_IMAGE009
as the time of the vibration, there is,
Figure 100002_DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 100002_DEST_PATH_IMAGE011
is the unit of an imaginary number,
Figure 100002_DEST_PATH_IMAGE012
in order to add a forced vibration moment value,
Figure 100002_DEST_PATH_IMAGE013
and
Figure 100002_DEST_PATH_IMAGE014
the derivative of the pneumatic pitching resistance moment and the derivative of the restoring moment are respectively values which are finally required to be acquired in the dynamic derivative test.
By solving the differential equation, it can be obtained
Figure 99819DEST_PATH_IMAGE013
And
Figure 751381DEST_PATH_IMAGE014
。
Figure 100002_DEST_PATH_IMAGE015
(2)
it can be seen that the key to the data processing of the forced vibration dynamic derivative test is to acquire the amplitude of the applied external moment
Figure 593435DEST_PATH_IMAGE012
Amplitude of angular displacement
Figure 100002_DEST_PATH_IMAGE016
And the initial phase difference between the two
Figure 100002_DEST_PATH_IMAGE017
。
By digital sampling, the torque signal can be sampled
Figure 100002_DEST_PATH_IMAGE018
And sampling the angular displacement signal
Figure 100002_DEST_PATH_IMAGE019
Respectively expressed as:
Figure 100002_DEST_PATH_IMAGE020
(3)
in the formula (3), the reaction mixture is,
Figure 100002_DEST_PATH_IMAGE021
、
Figure 411480DEST_PATH_IMAGE012
、
Figure 100002_DEST_PATH_IMAGE022
and
Figure 100002_DEST_PATH_IMAGE023
、
Figure 366798DEST_PATH_IMAGE016
and
Figure 100002_DEST_PATH_IMAGE024
respectively representing the amplitudes of the direct current component, the 1 st harmonic component and the mth harmonic component of the torque signal and the angular displacement signal;
Figure 100002_DEST_PATH_IMAGE025
and
Figure 100002_DEST_PATH_IMAGE026
respectively representing the initial phases of the 1 st harmonic component and the mth harmonic component of the torque signal,
Figure 100002_DEST_PATH_IMAGE027
、
Figure 100002_DEST_PATH_IMAGE028
and
Figure 100002_DEST_PATH_IMAGE029
respectively representing the initial phases of the 1 st harmonic component, the mth harmonic component and the frequency offset component of the angular displacement signal;
Figure 100002_DEST_PATH_IMAGE030
which represents the frequency offset component of the received signal,
Figure 100002_DEST_PATH_IMAGE031
for the magnitude of the frequency offset component,
Figure 100002_DEST_PATH_IMAGE032
is the frequency offset;
Figure 100002_DEST_PATH_IMAGE033
and
Figure 100002_DEST_PATH_IMAGE034
respectively representing the harmonic component orders of the torque signal and the angular displacement signal,
Figure 100002_DEST_PATH_IMAGE035
，
Figure 100002_DEST_PATH_IMAGE036
and
Figure 100002_DEST_PATH_IMAGE037
respectively representing a sampling time point and a sampling length;
Figure 100002_DEST_PATH_IMAGE038
and
Figure 100002_DEST_PATH_IMAGE039
respectively, mean value is 0 and variance is
Figure 100002_DEST_PATH_IMAGE040
The two are independent of each other.
According to the formula (2), the dynamic derivative value can be obtained only by calculating the amplitude and the phase difference of the 1 st harmonic of the torque signal and the angular displacement signal. Currently, there are several main processing methods for dynamic derivative test data:
the first type: and the Fourier transform method is used for directly carrying out Fourier transform on the torque signal and the angular displacement signal to obtain the amplitude and the initial phase of the torque signal and the angular displacement signal. The method has simple steps and is easy to realize, but is greatly influenced by noise and harmonic waves, and the precision needs to be improved.
The second type: the delay correlation method directly delays the signal according to the known vibration frequency to realize the 90-degree phase shift of the sampling signal. In practical use, due to the random step-out influence of the driving motor, the angular displacement signal is easy to find out frequency offset, the method does not have the capability of resisting the frequency offset, phase shift errors can be caused by direct use, and the calculation precision of the dynamic derivative is reduced.
In the third category: the method combining Hilbert and a related method comprises the steps of firstly inhibiting the influence of noise and harmonic waves through a band-pass filter, and then obtaining the amplitude and the initial phase of a main frequency component of a signal by using the Hilbert and the related method. Because the harmonic wave is not filtered thoroughly, the residual harmonic wave can generate frequency spectrum leakage, which affects the estimation precision of amplitude and initial phase, and the method is not suitable for the condition of small frequency offset. More importantly, the method does not consider the times of harmonic components, cannot accurately inhibit harmonic influence, and reduces the estimation precision of the amplitude and the initial phase, thereby influencing the data processing precision of the dynamic derivative test.
The traditional wind tunnel test data dynamic derivative processing method can analyze data to obtain a dynamic derivative, but still has the problems of low precision, complex processing process, low efficiency and the like.
Disclosure of Invention
Aiming at the problems, the invention provides a data processing method for the aircraft dynamic derivative test, which can effectively remove the noise influence, extract the main test parameters and improve the accuracy of the pneumatic pitching damping moment derivative and the pneumatic pitching restoring moment derivative.
In order to achieve the aim, the invention provides an aircraft dynamic derivative test data processing method, which comprises the following steps:
acquiring and obtaining sampling torque signal
Figure 100002_DEST_PATH_IMAGE041
And sampling the angular displacement signal
Figure 100002_DEST_PATH_IMAGE042
Truncating the sampled signal to obtain a first torque signal
Figure 100002_DEST_PATH_IMAGE043
And a first angular displacement signal
Figure 100002_DEST_PATH_IMAGE044
；
Carrying out direct current component filtering processing on the first moment signal and the first angular displacement signal to respectively obtain a second moment signal and a second angular displacement signal;
analyzing and processing the second moment signal to obtain a first amplitude estimation value and a first initial phase estimation value of a 1 st harmonic component in the second moment signal;
analyzing and processing the second angular displacement signal to obtain a second amplitude estimation value and a second initial phase estimation value of a 1 st harmonic component in the second angular displacement signal;
obtaining a phase difference based on the first initial phase estimate and the second initial phase estimate;
and respectively calculating and obtaining an aerodynamic pitch damping moment derivative and an aerodynamic pitch restoring moment derivative based on the phase difference, the first amplitude estimation value and the second amplitude estimation value.
In order to inhibit the influence of harmonic component and frequency offset component frequency spectrum leakage and improve the data processing precision of a dynamic derivative test, the invention provides the method, firstly, the sampling signal is truncated to obtain an approximate whole-period sampling signal, and the direct current component in the torque signal and the angular displacement signal is filtered; and secondly, estimating the harmonic times of the moment signal by utilizing a subtraction strategy and judging the energy ratio, and obtaining the accurate amplitude and initial phase of the 1 st harmonic component of the moment signal in the modes of the subtraction strategy, spectral analysis, iterative computation and the like. Then, the angular displacement signal is processed by using the same idea, and the accurate amplitude and initial phase of the 1 st harmonic component of the angular displacement signal are obtained. And finally, calculating a damping moment derivative and a restoring moment derivative according to the amplitudes of the main frequency components of the torque signal and the angular displacement signal and the initial phase difference between the two.
Preferably, the calculation modes of the aerodynamic pitch damping moment derivative and the aerodynamic pitch restoring moment derivative are respectively as follows:
Figure 831671DEST_PATH_IMAGE015
wherein,
Figure 567545DEST_PATH_IMAGE013
and
Figure 500866DEST_PATH_IMAGE014
respectively the derivative of the pneumatic pitch resistance torque and the derivative of the restoring torque,
Figure 28800DEST_PATH_IMAGE002
to rotate the inertia about the pitch axis through the center of mass,
Figure 756584DEST_PATH_IMAGE006
and
Figure 979755DEST_PATH_IMAGE007
known respectively as mechanical damping and spring constant for vibration systems,
Figure 60975DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 100002_DEST_PATH_IMAGE045
is an estimate of the first amplitude value,
Figure 100002_DEST_PATH_IMAGE046
is an estimate of the second amplitude value and,
Figure 646677DEST_PATH_IMAGE017
is the phase difference.
Preferably, the following method is adopted to perform truncation processing on the sampling signal to obtain a truncated signal, so as to perform truncation on the sampling signal to obtain the truncated signal, so that the truncated signal satisfies sampling of a whole period as much as possible. Shortened length
Figure 100002_DEST_PATH_IMAGE047
Expressed as:
Figure 100002_DEST_PATH_IMAGE048
wherein,
Figure 686308DEST_PATH_IMAGE047
less than the length of the sampled signal
Figure 100002_DEST_PATH_IMAGE049
，
Figure 100002_DEST_PATH_IMAGE050
Represents the closest approach
Figure 100002_DEST_PATH_IMAGE051
Is a positive integer of (a) to (b),
Figure 100002_DEST_PATH_IMAGE052
is a positive integer, and satisfy
Figure 100002_DEST_PATH_IMAGE053
，
Figure 100002_DEST_PATH_IMAGE054
Express get
Figure 100002_DEST_PATH_IMAGE055
The absolute value of (a) is,
Figure 100002_DEST_PATH_IMAGE056
a first threshold value is indicated which is,
Figure 11155DEST_PATH_IMAGE008
is the vibration frequency.
Preferably, the first moment signal and the first angular displacement signal in the truncated signals are subjected to dc component filtering processing in the following manner:
Figure 100002_DEST_PATH_IMAGE057
Figure 100002_DEST_PATH_IMAGE058
wherein,
Figure 100002_DEST_PATH_IMAGE059
in order to index the signal(s),
Figure 100002_DEST_PATH_IMAGE060
in order to shorten the length of the optical fiber,
Figure 630486DEST_PATH_IMAGE018
in order to be able to generate the first torque signal,
Figure 867433DEST_PATH_IMAGE019
in order to be the first angular displacement signal,
Figure 100002_DEST_PATH_IMAGE061
in order to be able to generate the second torque signal,
Figure 100002_DEST_PATH_IMAGE062
in the form of the second angular displacement signal,
Figure 218911DEST_PATH_IMAGE033
and
Figure 275729DEST_PATH_IMAGE034
representing the order of the harmonic components of the second moment signal and the second angular displacement signal respectively,
Figure 100002_DEST_PATH_IMAGE063
representing the magnitude of the mth harmonic component in the second moment signal,
Figure 100002_DEST_PATH_IMAGE064
representing the magnitude of the mth harmonic component in the second angular displacement signal,
Figure 167592DEST_PATH_IMAGE026
representing the mth harmonic component of the second moment signalAt the initial phase, the phase of the phase-locked loop,
Figure 259045DEST_PATH_IMAGE028
representing an initial phase of an mth harmonic component in the second angular displacement signal;
Figure 100002_DEST_PATH_IMAGE065
the magnitudes of the frequency offset components in the second angular displacement signal,
Figure 312583DEST_PATH_IMAGE032
in order to be the amount of frequency offset,
Figure 856697DEST_PATH_IMAGE029
representing the initial phase of the frequency offset component in the second angular displacement signal,
Figure 473623DEST_PATH_IMAGE038
and
Figure 560528DEST_PATH_IMAGE039
respectively mean value of 0 and variance of
Figure 237496DEST_PATH_IMAGE040
White additive gaussian noise.
Preferably, the analyzing and processing the second moment signal to obtain a first amplitude estimation value and a first initial phase estimation value of a 1 st harmonic component in the second moment signal specifically includes:
step 1: calculating and obtaining the harmonic times of the second moment signal and the complex amplitude of each harmonic component in the second moment signal;
step 2: constructing a first reference signal based on the calculation result of the step 1, obtaining a third moment signal based on the first reference signal and the second moment signal, and updating the complex amplitude of each harmonic component in the second moment signal based on the third moment signal;
and step 3: and (3) carrying out multiple iterative calculations on the step (2), and obtaining a first amplitude estimated value and a first initial phase estimated value of the 1 st harmonic component in the second moment signal based on the iterative calculation result.
Preferably, the step 1 is specifically according to
Figure 100002_DEST_PATH_IMAGE066
The second torque signal is processed in the following steps 1.1 to 1.6 in sequence:
step 1.1: is constructed by
Figure 100002_DEST_PATH_IMAGE067
A second reference signal for each harmonic component;
step 1.2: subtracting the second reference signal from the second torque signal to obtain a fourth torque signal;
step 1.3: based on the fourth moment signal and the vibration frequency, calculating to obtain the second moment signaliA complex amplitude of the sub-harmonic component;
step 1.4: based on the second one obtained in step 1.3iConstructing a third reference signal by the complex amplitude of the subharmonic component, and calculating to obtain a third reference signal based on the third reference signaliA first energy of the sub-harmonic component;
step 1.5: calculating a second energy for obtaining the second torque signal, calculating a second energy based on the first energy and the second energyiEnergy ratio of harmonic component based oniBefore obtaining the energy ratio of harmonic componentiThe sum of the energy ratios of the individual harmonic components;
step 1.6: before judgmentiWhether the sum of the energy ratios of the harmonic components is greater than or equal to a second threshold value, if so, theniIs taken as the harmonic order of the second torque signal
Figure 816377DEST_PATH_IMAGE033
。
Preferably, the second energy of the second torque signal is calculated by:
Figure 100002_DEST_PATH_IMAGE068
wherein,
Figure 100002_DEST_PATH_IMAGE069
is the second energy, and is,
Figure 100002_DEST_PATH_IMAGE070
in order to truncate the signal length of the signal,
Figure 190988DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 397979DEST_PATH_IMAGE061
is the second torque signal.
Preferably, the firstiThe complex amplitude of the subharmonic component is calculated in the following manner:
Figure 100002_DEST_PATH_IMAGE071
wherein,
Figure 100002_DEST_PATH_IMAGE072
is as followsiThe complex amplitude of the sub-harmonic components,
Figure 449111DEST_PATH_IMAGE070
in order to truncate the signal length of the signal,
Figure 452971DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 411699DEST_PATH_IMAGE061
in order to be able to generate the second torque signal,
Figure 66672DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 819864DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 100002_DEST_PATH_IMAGE073
is an imaginary unit.
Preferably, the third reference signal is:
Figure 100002_DEST_PATH_IMAGE074
wherein,
Figure 100002_DEST_PATH_IMAGE075
is the third reference signal and is the third reference signal,
Figure 100002_DEST_PATH_IMAGE076
is as followsiThe complex amplitude of the sub-harmonic components,
Figure 373336DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 870177DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 661546DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 585640DEST_PATH_IMAGE073
is the unit of an imaginary number,
Figure 100002_DEST_PATH_IMAGE077
to represent
Figure 954304DEST_PATH_IMAGE076
Complex conjugation of (a);
first, theiThe first energy of the subharmonic component is:
Figure 100002_DEST_PATH_IMAGE078
wherein,
Figure 100002_DEST_PATH_IMAGE079
is as followsThe energy is used for supplying energy to the power supply,
Figure 926939DEST_PATH_IMAGE070
the signal length for the truncated signal;
first, theiThe energy ratio of the harmonic component is
Figure 100002_DEST_PATH_IMAGE080
，
Figure 25346DEST_PATH_IMAGE080
The calculation method is as follows:
Figure 100002_DEST_PATH_IMAGE081
wherein,
Figure 198969DEST_PATH_IMAGE079
is the first energy, and is,
Figure 320509DEST_PATH_IMAGE069
is the second energy.
Preferably, the second reference signal
Figure 100002_DEST_PATH_IMAGE082
Expressed as:
Figure 100002_DEST_PATH_IMAGE083
wherein,
Figure 100002_DEST_PATH_IMAGE084
is as follows
Figure 100002_DEST_PATH_IMAGE085
The sub-harmonic component is referenced to the signal.
The fourth torque signal
Figure 100002_DEST_PATH_IMAGE086
Is shown as：
Figure 100002_DEST_PATH_IMAGE087
。
Wherein,
Figure 100002_DEST_PATH_IMAGE088
is the second torque signal is a function of the second torque signal,
Figure 124865DEST_PATH_IMAGE082
is the second reference signal.
Preferably, the step 2 specifically includes:
step 2.1: constructing a first reference signal based on the calculation result of step 1
Figure 100002_DEST_PATH_IMAGE089
，
Figure 235035DEST_PATH_IMAGE089
Expressed as:
Figure 100002_DEST_PATH_IMAGE090
wherein,
Figure 641877DEST_PATH_IMAGE077
is shown asiThe complex conjugate of the complex amplitude of the sub-harmonic component,
Figure 578609DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 96309DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 841411DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 137263DEST_PATH_IMAGE073
is the unit of an imaginary number,
Figure 702236DEST_PATH_IMAGE033
representing the order of the harmonic components of the second moment signal,
Figure 148261DEST_PATH_IMAGE084
is as follows
Figure 92078DEST_PATH_IMAGE085
A sub-harmonic component reference signal;
step 2.2: obtaining a third torque signal based on the first reference signal and the second torque signal
Figure 100002_DEST_PATH_IMAGE091
，
Figure 100002_DEST_PATH_IMAGE092
Expressed as:
Figure 100002_DEST_PATH_IMAGE093
wherein,
Figure 699777DEST_PATH_IMAGE088
is the second torque signal and is a second torque signal,
Figure 752046DEST_PATH_IMAGE089
is a first reference signal.
Step 2.3: based on the third torque signal
Figure 100002_DEST_PATH_IMAGE094
The complex amplitude of each harmonic component in the second moment signal is updated.
Preferably, the first amplitude estimation value and the first initial phase estimation value of the 1 st harmonic component in the second moment signal are calculated by:
Figure 100002_DEST_PATH_IMAGE095
wherein,
Figure 100002_DEST_PATH_IMAGE096
is an estimate of the first amplitude value,
Figure 100002_DEST_PATH_IMAGE097
is the first initial phase estimate value and is,
Figure 100002_DEST_PATH_IMAGE098
is the complex amplitude of the 1 st harmonic component in the second moment signal,
Figure 100002_DEST_PATH_IMAGE099
representation complex amplitude
Figure 159019DEST_PATH_IMAGE098
The value of the modulus of the (c) component,
Figure 100002_DEST_PATH_IMAGE100
representation complex amplitude
Figure 100002_DEST_PATH_IMAGE101
The angle of (c).
Preferably, the analyzing and processing the second angular displacement signal to obtain a second amplitude estimation value and a second initial phase estimation value of the 1 st harmonic component in the second angular displacement signal specifically includes:
step a: calculating to obtain the harmonic times of the second angular displacement signal, a second estimation value of the complex amplitude of each harmonic component in the second angular displacement signal and the complex amplitude of the frequency offset component in the second angular displacement signal;
step b: constructing a fourth reference signal based on the calculation result of the step a, obtaining a third angular displacement signal based on the fourth reference signal and the second angular displacement signal, and updating the complex amplitude of each harmonic component and the complex amplitude of the frequency offset component in the second angular displacement signal based on the third angular displacement signal; obtaining a frequency offset component positive frequency component in the second angular displacement signal based on the complex amplitude of each harmonic component in the second angular displacement signal and the complex amplitude of the frequency offset component; calculating and updating a frequency offset component complex amplitude value based on a frequency offset component positive frequency component in the second angular displacement signal; updating a frequency offset component reference signal based on the updated frequency offset component complex amplitude, and updating the third angular displacement signal based on the updated frequency offset component reference signal;
step c: and c, carrying out multiple iterative calculations on the step b, and obtaining a second amplitude estimated value and a second initial phase estimated value of the 1 st harmonic component in the second angular displacement signal based on the iterative calculation result.
Preferably, the step a specifically includes:
according to
Figure 100002_DEST_PATH_IMAGE102
The second angular displacement signal is analyzed, the construction includes
Figure 691763DEST_PATH_IMAGE067
Reference signal of harmonic component and frequency deviation component
Figure 100002_DEST_PATH_IMAGE103
；
Figure 100002_DEST_PATH_IMAGE104
Wherein,
Figure 100002_DEST_PATH_IMAGE105
is as followsiiThe sub-harmonic component is referenced to the signal,
Figure 100002_DEST_PATH_IMAGE106
for the frequency offset component reference signal(s),
Figure 939204DEST_PATH_IMAGE036
is a sampling time point;
based on the reference signal
Figure 744349DEST_PATH_IMAGE103
Processing the second angular displacement signal to obtain a processed second angular displacement signal
Figure 100002_DEST_PATH_IMAGE107
；
Based on
Figure 100002_DEST_PATH_IMAGE108
Calculate the firstiA complex amplitude of the sub-harmonic component;
the construction comprises the followingiReference signal of subharmonic component
Figure 100002_DEST_PATH_IMAGE109
Based on
Figure 407543DEST_PATH_IMAGE109
Calculate the firstiEnergy of subharmonic component
Figure 100002_DEST_PATH_IMAGE110
；
Calculating the energy of the second angular displacement signal
Figure 100002_DEST_PATH_IMAGE111
；
Based on the
Figure 653848DEST_PATH_IMAGE110
And said
Figure 603349DEST_PATH_IMAGE111
Is calculated to obtainiEnergy ratio of subharmonic component
Figure 100002_DEST_PATH_IMAGE112
；
Based on the index of the frequency offset component
Figure 100002_DEST_PATH_IMAGE113
And spectral offset estimation
Figure 100002_DEST_PATH_IMAGE114
Calculating the complex amplitude of the frequency offset component
Figure DEST_PATH_IMAGE115
；
Based on
Figure 36736DEST_PATH_IMAGE115
Constructing a frequency offset component reference signal
Figure 226322DEST_PATH_IMAGE106
；
Based on
Figure 123871DEST_PATH_IMAGE106
Calculating the energy of the obtained frequency deviation component
Figure DEST_PATH_IMAGE116
；
Based on the
Figure 103328DEST_PATH_IMAGE116
And said
Figure 883066DEST_PATH_IMAGE111
Calculating the energy ratio of the obtained frequency deviation component
Figure DEST_PATH_IMAGE117
；
Based on
Figure 356903DEST_PATH_IMAGE117
And
Figure 499172DEST_PATH_IMAGE112
before calculation is obtainediSum of energy ratios of harmonic component and frequency offset component
Figure DEST_PATH_IMAGE118
；
When in use
Figure 56055DEST_PATH_IMAGE118
Greater than or equal to a third threshold value at which timeiIs the harmonic order of the second angular displacement signal
Figure 57509DEST_PATH_IMAGE034
。
Preferably, the fourth reference signal is
Figure DEST_PATH_IMAGE119
；
Figure DEST_PATH_IMAGE120
Wherein,
Figure DEST_PATH_IMAGE121
is shown asiThe complex conjugate of the complex amplitude of the sub-harmonic component,
Figure 210404DEST_PATH_IMAGE034
being a harmonic order of the second angular displacement signal,
Figure 348124DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 934963DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 423714DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 239354DEST_PATH_IMAGE073
is the unit of an imaginary number,
Figure DEST_PATH_IMAGE122
is as follows
Figure 825056DEST_PATH_IMAGE085
The sub-harmonic component is referenced to the signal,
Figure DEST_PATH_IMAGE123
is a frequency offset component reference signal;
first, theiThe sub-harmonic component has a positive frequency component of
Figure DEST_PATH_IMAGE124
；
Figure DEST_PATH_IMAGE125
Wherein,
Figure DEST_PATH_IMAGE126
in order to be said second angular displacement signal,
Figure DEST_PATH_IMAGE127
is a fourth reference signal;
by using the said
Figure 474474DEST_PATH_IMAGE124
Calculate and updateiComplex amplitude of subharmonic component
Figure DEST_PATH_IMAGE128
；
Figure DEST_PATH_IMAGE129
Wherein,
Figure 981679DEST_PATH_IMAGE062
in order to be said second angular displacement signal,
Figure 866590DEST_PATH_IMAGE070
for the length of the second angular displacement signal,
Figure 978902DEST_PATH_IMAGE036
in order to sample the point in time,
Figure 923855DEST_PATH_IMAGE008
in order to be the frequency of the vibration,
Figure 246252DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 59488DEST_PATH_IMAGE073
in units of imaginary numbers.
Based on updated secondiComplex amplitude of subharmonic component
Figure 901673DEST_PATH_IMAGE128
According to
Figure DEST_PATH_IMAGE130
Calculating to obtain the complex amplitude of each harmonic component;
frequency offset component of positive frequency component
Figure 611003DEST_PATH_IMAGE124
；
Figure DEST_PATH_IMAGE131
Wherein,
Figure 155117DEST_PATH_IMAGE113
is an index to the frequency offset component,
Figure 772043DEST_PATH_IMAGE114
for the purpose of the spectral offset estimation,
Figure 468734DEST_PATH_IMAGE034
being a harmonic order of the second angular displacement signal,
Figure 880124DEST_PATH_IMAGE070
in order to truncate the signal length of the signal,
Figure 911534DEST_PATH_IMAGE036
in order to sample the point in time,
Figure DEST_PATH_IMAGE132
is the complex conjugate of the complex magnitude of the frequency offset component,
Figure DEST_PATH_IMAGE133
is as follows
Figure 614042DEST_PATH_IMAGE085
The sub-harmonic component is referenced to the signal,
Figure 680087DEST_PATH_IMAGE062
in order to be said second angular displacement signal,
Figure 996799DEST_PATH_IMAGE010
is a natural number with a base number of natural,
Figure 658DEST_PATH_IMAGE073
in units of imaginary numbers.
Preferably, the second amplitude estimation value of the 1 st harmonic component in the second angular displacement signal is
Figure DEST_PATH_IMAGE134
The second initial phase estimation value of the 1 st harmonic component in the second angular displacement signal is
Figure DEST_PATH_IMAGE135
：
Figure DEST_PATH_IMAGE136
Wherein,
Figure DEST_PATH_IMAGE137
being the complex amplitude of the 1 st harmonic component in the second angular displacement signal,
Figure DEST_PATH_IMAGE138
representation complex amplitude
Figure 975698DEST_PATH_IMAGE137
The value of the modulus of the (c) component,
Figure DEST_PATH_IMAGE139
representation complex amplitude
Figure 365092DEST_PATH_IMAGE137
The angle of (c).
One or more technical schemes provided by the invention at least have the following technical effects or advantages:
the invention can effectively remove the noise influence and improve the accuracy of the pneumatic pitching damping moment derivative and the pneumatic pitching restoring moment derivative.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a schematic flow chart of a method for processing data of a dynamic derivative test of an aircraft according to the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
Example one
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for processing aircraft dynamic derivative test data, and the method for processing aircraft dynamic derivative test data according to the present invention can be divided into four steps: signal preprocessing, moment signal analysis, angular displacement signal analysis and dynamic derivative calculation.
Signal preprocessing:
firstly, according to the known vibration frequency, a sampling signal is truncated to obtain a truncated signal, wherein the acquisition signal can be acquired through related equipment or a sensor.
Figure 383863DEST_PATH_IMAGE048
(4)
In formula (4):
Figure 406177DEST_PATH_IMAGE070
in order to shorten the length of the optical fiber,
Figure 637438DEST_PATH_IMAGE050
represents the closest approach
Figure 146917DEST_PATH_IMAGE051
The positive integer of (a) is,
Figure 336590DEST_PATH_IMAGE052
is a positive integer, and satisfy
Figure 970833DEST_PATH_IMAGE053
，
Figure DEST_PATH_IMAGE140
Express get
Figure 220767DEST_PATH_IMAGE055
The absolute value of (a) is,
Figure 991276DEST_PATH_IMAGE056
a first threshold value is indicated which is,
Figure 351851DEST_PATH_IMAGE008
is the vibration frequency.
Then, the dc component in the truncated signal is filtered out:
Figure DEST_PATH_IMAGE141
(5)
obtaining a preprocessed torque signal
Figure 817598DEST_PATH_IMAGE061
And angular displacement signal
Figure 797187DEST_PATH_IMAGE062
：
Figure 422203DEST_PATH_IMAGE058
(6)
Analyzing a torque signal:
when the moment signal is analyzed, three steps are divided. The first step is as follows: and calculating the harmonic frequency of the signal.
First, a preprocessed torque signal is calculated
Figure 812733DEST_PATH_IMAGE061
Energy of
Figure 155990DEST_PATH_IMAGE069
。
Figure 673690DEST_PATH_IMAGE068
(7)
Secondly, based on the preprocessed torque signal and vibration frequency, calculatingiThe complex amplitude of the sub-harmonic component.
Figure 418792DEST_PATH_IMAGE071
(8)
In the formula:
Figure 714644DEST_PATH_IMAGE072
as a parameter
Figure DEST_PATH_IMAGE142
Is determined by the estimated value of (c),
Figure DEST_PATH_IMAGE143
is as followsiThe complex amplitude of the sub-harmonic components,
Figure 92667DEST_PATH_IMAGE011
are complex symbols.
Then based on the secondiComplex amplitude of subharmonic component, the construction containing only the firstiReference signal of subharmonic component
Figure 132167DEST_PATH_IMAGE075
(ii) a And calculate the firstiEnergy of subharmonic component
Figure 731776DEST_PATH_IMAGE079
。
Figure 605054DEST_PATH_IMAGE074
(9)
Figure 532690DEST_PATH_IMAGE078
(10)
In formula (9):
Figure DEST_PATH_IMAGE144
to represent
Figure 110301DEST_PATH_IMAGE076
Complex conjugation of (a).
Then it is firstiThe energy ratio of the harmonic component is:
Figure 829996DEST_PATH_IMAGE081
(11)
therefore, frontiThe sum of the energy ratios of the harmonic components is:
Figure DEST_PATH_IMAGE145
(12)
finally, according to
Figure 687225DEST_PATH_IMAGE066
The sequence of (2) analyzing the torque signal, the structure containing the front
Figure 367736DEST_PATH_IMAGE067
Reference signal of harmonic component
Figure 280197DEST_PATH_IMAGE082
。
Figure 323239DEST_PATH_IMAGE083
(13)
And a subtraction strategy is adopted to subtract the middle front of the torque signal
Figure 413686DEST_PATH_IMAGE067
The harmonic components.
Figure 174969DEST_PATH_IMAGE087
(14)
Will be provided with
Figure DEST_PATH_IMAGE146
Substitution of formula (8), substitution
Figure 359962DEST_PATH_IMAGE061
Calculating the firstiComplex amplitudes of subharmonic components, calculated using equations (8) - (12)iEnergy ratio of individual harmonic components
Figure DEST_PATH_IMAGE147
. When in use
Figure DEST_PATH_IMAGE148
When the temperature of the water is higher than the set temperature,
Figure DEST_PATH_IMAGE149
is a threshold value of 2, at this timeiIs the harmonic order of the torque signal
Figure 929615DEST_PATH_IMAGE033
。
The second step is that: and calculating the more accurate complex amplitude of each harmonic component.
Firstly, according to the rough estimation value of the complex amplitude of each harmonic component in the first step, aiming at the second stepiA sub-harmonic component of structure containing
Figure DEST_PATH_IMAGE150
A harmonic component not to be estimated andireference signal with sub-harmonic component negative frequency component phase-superposed
Figure 863067DEST_PATH_IMAGE089
。
Figure 767438DEST_PATH_IMAGE090
(15)
Secondly, subtracting the reference signal in the moment signal by adopting a subtraction strategy
Figure 897068DEST_PATH_IMAGE089
To obtain the firstiPositive frequency component of subharmonic component
Figure 914703DEST_PATH_IMAGE092
。
Figure 878111DEST_PATH_IMAGE093
(16)
Then, will
Figure 754931DEST_PATH_IMAGE094
Substitution of formula (8), substitution
Figure 157094DEST_PATH_IMAGE061
Update the firstiThe complex amplitude of the sub-harmonic component.
Finally, according to
Figure 153868DEST_PATH_IMAGE066
The more accurate complex amplitude of each harmonic component is obtained through the loop calculation of the expressions (15) and (16).
The third step: the exact amplitude and initial phase of the 1 st harmonic component are calculated.
To the second step
Figure DEST_PATH_IMAGE151
Performing sub-iterative computation to obtain an accurate amplitude estimation value of the 1 st harmonic component of the torque signal
Figure 694702DEST_PATH_IMAGE045
And an initial phase estimate
Figure DEST_PATH_IMAGE152
。
Figure 511349DEST_PATH_IMAGE095
(17)
Wherein,
Figure 592568DEST_PATH_IMAGE098
is the complex amplitude of the 1 st harmonic component.
Angular displacement signal analysis
The method is consistent with the torque signal analysis idea, and the analysis process is also divided into three steps aiming at the angular displacement signal. The first step is as follows: the harmonic order of the signal is calculated.
First, the energy of the sampled signal is calculated
Figure 584795DEST_PATH_IMAGE069
。
Figure 608115DEST_PATH_IMAGE068
(18)
Secondly, according to the known vibration frequency, the solution ofiThe complex amplitude of the sub-harmonic component.
Figure 584161DEST_PATH_IMAGE129
(19)
In the formula (19), the compound represented by the formula (I),
Figure DEST_PATH_IMAGE153
is as followsiThe complex amplitude of the sub-harmonic component.
Then, the structure contains only the secondiReference signal of subharmonic component
Figure 937913DEST_PATH_IMAGE109
And calculate the firstiEnergy of subharmonic component
Figure 784646DEST_PATH_IMAGE110
。
Figure DEST_PATH_IMAGE154
(20)
Figure DEST_PATH_IMAGE155
(21)
In the formula (20), the reaction mixture is,
Figure DEST_PATH_IMAGE156
to represent
Figure 249039DEST_PATH_IMAGE128
Complex conjugation of (a).
Then it is firstiThe energy fraction of the subharmonic component is:
Figure DEST_PATH_IMAGE157
(22)
when in use
Figure DEST_PATH_IMAGE158
Then, the spectral index of the frequency offset component is calculated. Using a subtraction strategy to sum the angular displacement signal and a reference signal
Figure DEST_PATH_IMAGE159
Subtracting to obtain a signal containing a frequency offset component
Figure DEST_PATH_IMAGE160
。
Figure DEST_PATH_IMAGE161
(23)
And performing fast Fourier transform to obtain a signal
Figure 728693DEST_PATH_IMAGE160
Spectrum of
Figure DEST_PATH_IMAGE162
Extracting spectral index
Figure DEST_PATH_IMAGE163
。
Figure DEST_PATH_IMAGE164
(24)
Figure DEST_PATH_IMAGE165
(25)
In the formula (25), symbol
Figure DEST_PATH_IMAGE166
Indicating the index of the extracted spectral maximum.
In the index
Figure 541929DEST_PATH_IMAGE163
Interpolation is carried out on two sides, the interval is 0.5, and the frequency spectrum of the interpolation point on the left side is calculated
Figure DEST_PATH_IMAGE167
And right hand interpolated point spectrum
Figure DEST_PATH_IMAGE168
And calculating the spectral offset according to the interpolation point spectrum.
Figure DEST_PATH_IMAGE169
(26)
Figure DEST_PATH_IMAGE170
(27)
In the formula (27), the reaction mixture is,
Figure DEST_PATH_IMAGE171
represents taking a complex number
Figure DEST_PATH_IMAGE172
An imaginary part of (c).
Based on the index of the frequency offset component
Figure 197163DEST_PATH_IMAGE163
And spectral offset estimation
Figure 437652DEST_PATH_IMAGE114
And calculating the complex amplitude of the frequency deviation component.
Figure DEST_PATH_IMAGE173
(28)
In the formula (28), the reaction mixture is,
Figure DEST_PATH_IMAGE174
is the complex amplitude of the frequency offset component.
Then a frequency offset component reference signal may be constructed:
Figure DEST_PATH_IMAGE175
(29)
in the formula (29), the reaction mixture is,
Figure DEST_PATH_IMAGE176
is composed of
Figure 935760DEST_PATH_IMAGE115
And (4) complex conjugation.
The energy of the frequency offset component is:
Figure DEST_PATH_IMAGE177
(30)
the energy ratio of the frequency offset component is:
Figure DEST_PATH_IMAGE178
(31)
thus, frontiThe sum of the energy ratios of the harmonic and frequency-offset components is:
Figure DEST_PATH_IMAGE179
(32)
finally, according to
Figure DEST_PATH_IMAGE180
In a sequence of angular displacement signals, the structure including the first
Figure 959211DEST_PATH_IMAGE067
Reference signal of harmonic component and frequency deviation component
Figure 46116DEST_PATH_IMAGE103
。
Figure DEST_PATH_IMAGE181
(33)
And a subtraction strategy is adopted to subtract the middle front of the angular displacement signal
Figure 519822DEST_PATH_IMAGE067
Harmonic components and frequency offset components.
Figure DEST_PATH_IMAGE182
(34)
Will be provided with
Figure 770806DEST_PATH_IMAGE108
Substitution (19), substitution
Figure 50478DEST_PATH_IMAGE062
Calculating the firstiThe complex amplitude of the subharmonic component is calculated using the equations (20) - (22), (32) - (34)iEnergy ratio of harmonic component and frequency offset component
Figure 991889DEST_PATH_IMAGE118
. When in use
Figure DEST_PATH_IMAGE183
When the temperature of the water is higher than the set temperature,
Figure DEST_PATH_IMAGE184
is a threshold value of 3, at this timeiThe value of (A) is the harmonic frequency of the angular displacement signal
Figure 980705DEST_PATH_IMAGE034
。
The second step is that: the complex amplitude of each component is calculated.
First, rough estimation values of harmonic components and frequency offset components are calculated for the first stepiA sub-harmonic component of structure containing
Figure DEST_PATH_IMAGE185
Harmonic frequency components not to be estimated, secondiReference signal with sub-harmonic negative frequency component and frequency offset component superposed
Figure 718985DEST_PATH_IMAGE119
。
Figure DEST_PATH_IMAGE186
(35)
Secondly, adopting a subtraction strategy to combine the angular displacement signal and the reference signal
Figure 474451DEST_PATH_IMAGE119
Are subtracted to obtain the firstiSub-harmonic component positive frequency component
Figure 145735DEST_PATH_IMAGE124
。
Figure DEST_PATH_IMAGE187
(36)
Then, will
Figure 757982DEST_PATH_IMAGE124
Substitution (19), substitution
Figure 373771DEST_PATH_IMAGE062
Update the firstiComplex amplitude of the subharmonic component, and according to
Figure 745978DEST_PATH_IMAGE066
The more accurate complex amplitude of each harmonic component is obtained through the loop calculation of the expressions (35) and (36).
Finally, aiming at the frequency deviation component, according to the more accurate complex amplitude of each harmonic component, a subtraction strategy is adopted to subtract all harmonic components and the negative frequency components of the frequency deviation component in the angular displacement signal to obtain the positive frequency components of the frequency deviation component
Figure DEST_PATH_IMAGE188
。
Figure DEST_PATH_IMAGE189
(37)
Will be provided with
Figure 458719DEST_PATH_IMAGE124
Substitution of formulae (26) to (28)
Figure DEST_PATH_IMAGE190
Calculating the complex amplitude value and the spectral offset of the obtained frequency offset component, and constructing a frequency offset component reference signal by using the formula (29)
Figure DEST_PATH_IMAGE191
。
The third step: the exact amplitude and initial phase of the 1 st harmonic component are calculated.
To the second step
Figure DEST_PATH_IMAGE192
Performing sub-iterative computation to obtain an accurate amplitude estimation value of the 1 st harmonic component of the angular displacement signal
Figure 789337DEST_PATH_IMAGE046
And an initial phase estimate
Figure 298947DEST_PATH_IMAGE135
。
Figure 283301DEST_PATH_IMAGE136
(38)
Calculating a dynamic derivative:
and after the amplitude value and the initial phase of the 1 st harmonic component of the torque signal and the angular displacement signal are obtained, calculating the phase difference between the moment signal and the angular displacement signal.
Figure DEST_PATH_IMAGE193
(39)
And calculating the derivative of the aerodynamic pitch resistance moment by using the formula (2)
Figure 194756DEST_PATH_IMAGE013
And aerodynamic pitch recovery moment derivative
Figure 555330DEST_PATH_IMAGE014
。
Although the invention has given a specific dynamic derivative calculation process, aiming at the requirement of the dynamic derivative, the method can process the aerodynamic parameters of various aircrafts with the change of the motion state along with the time, and the obtained dynamic derivative can be directly used as the input parameter of the dynamic stability analysis of the aircrafts, thereby realizing the mode analysis of long period and short period of the aircrafts, further researching the longitudinal dynamic balance capability, control capability and the like of the aircrafts, analyzing the aircraft roll convergence, the Dutch roll and spiral mode and the like according to the horizontal heading mode, providing data support for the aircraft control strategy and control law design, and further guiding the improvement research of the overall layout of the aircrafts.
According to the content, the invention mainly provides a method for efficiently processing dynamic test data of a wind tunnel, obtains the concerned dynamic derivative parameters of the aircraft in different flight states, and provides parameter input for the aerodynamic layout design and flight control of the aircraft.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (11)

1. An aircraft dynamic derivative test data processing method is characterized by comprising the following steps:
when the aircraft performs a dynamic derivative experiment, a data acquisition unit is used for acquiring the torque and angular displacement change conditions of the aircraft to obtain sampling signals, wherein the sampling signals comprise torque signals
Figure DEST_PATH_IMAGE001
And angular displacement signal
Figure DEST_PATH_IMAGE002
Truncating the sampled signal to obtain a first torque signal
Figure DEST_PATH_IMAGE003
And a first angular displacement signal
Figure DEST_PATH_IMAGE004
；
Carrying out direct current component filtering processing on the first moment signal and the first angular displacement signal to respectively obtain a second moment signal and a second angular displacement signal;
analyzing and processing the second moment signal to obtain a first amplitude estimation value and a first initial phase estimation value of a 1 st harmonic component in the second moment signal;
analyzing and processing the second angular displacement signal to obtain a second amplitude estimation value and a second initial phase estimation value of a 1 st harmonic component in the second angular displacement signal;
obtaining a phase difference based on the first initial phase estimate and the second initial phase estimate;
respectively calculating and obtaining an aerodynamic pitch damping moment derivative and an aerodynamic pitch restoring moment derivative based on the phase difference, the first amplitude estimation value and the second amplitude estimation value;
the calculation modes of the aerodynamic pitch damping moment derivative and the aerodynamic pitch restoring moment derivative are respectively as follows:
Figure DEST_PATH_IMAGE005
wherein,
Figure DEST_PATH_IMAGE006
and
Figure DEST_PATH_IMAGE007
respectively the derivative of the pneumatic pitch resistance torque and the derivative of the restoring torque,
Figure DEST_PATH_IMAGE008
to rotate the inertia about the pitch axis through the center of mass,
Figure DEST_PATH_IMAGE009
and
Figure DEST_PATH_IMAGE010
known respectively for the mechanical damping and spring constant of the vibration system,
Figure DEST_PATH_IMAGE011
in order to be the frequency of the vibration,
Figure DEST_PATH_IMAGE012
is an estimate of the first amplitude value,
Figure DEST_PATH_IMAGE013
is the second amplitude estimate and is,
Figure DEST_PATH_IMAGE014
is the phase difference;
calculating to obtain the truncation length aiming at the sampling signal
Figure DEST_PATH_IMAGE015
Intercepting the mid-front of the sampled signal
Figure 406567DEST_PATH_IMAGE015
The point data realizes the truncation processing of the sampling signal to obtain the length of
Figure 402336DEST_PATH_IMAGE015
The truncated first moment signal and the first angular displacement signal of (a);
Figure 447652DEST_PATH_IMAGE015
the calculation method is as follows:
Figure DEST_PATH_IMAGE016
wherein,
Figure 921490DEST_PATH_IMAGE015
less than the length of the sampled signal
Figure DEST_PATH_IMAGE017
，
Figure DEST_PATH_IMAGE018
Represents the closest approach
Figure DEST_PATH_IMAGE019
Is a positive integer of (a) to (b),
Figure DEST_PATH_IMAGE020
is a positive integer, and satisfy
Figure DEST_PATH_IMAGE021
，
Figure DEST_PATH_IMAGE022
Express get
Figure DEST_PATH_IMAGE023
The absolute value of (a) is,
Figure DEST_PATH_IMAGE024
a first threshold value is indicated which is,
Figure DEST_PATH_IMAGE025
is the vibration frequency;
and performing direct-current component filtering processing on the first moment signal and the first angular displacement signal in the following way:
Figure DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE027
wherein,
Figure DEST_PATH_IMAGE028
in order to index the signal(s),
Figure DEST_PATH_IMAGE029
in order to be able to generate the second torque signal,
Figure DEST_PATH_IMAGE030
in the form of the second angular displacement signal,
Figure DEST_PATH_IMAGE031
and
Figure DEST_PATH_IMAGE032
representing the order of the harmonic components of the second moment signal and the second angular displacement signal respectively,
Figure DEST_PATH_IMAGE033
representing the magnitude of the mth harmonic component in the second moment signal,
Figure DEST_PATH_IMAGE034
representing the magnitude of the mth harmonic component in the second angular displacement signal,
Figure DEST_PATH_IMAGE035
representing the initial phase of the mth harmonic component in the second moment signal,
Figure DEST_PATH_IMAGE036
representing an initial phase of an mth harmonic component in the second angular displacement signal;
Figure DEST_PATH_IMAGE037
is the magnitude of the frequency offset component in the second angular displacement signal,
Figure DEST_PATH_IMAGE038
is the frequency offset，
Figure DEST_PATH_IMAGE039
Representing the initial phase of the frequency offset component in the second angular displacement signal,
Figure DEST_PATH_IMAGE040
and
Figure DEST_PATH_IMAGE041
respectively mean value of 0 and variance of
Figure DEST_PATH_IMAGE042
Additive white gaussian noise of (1);
the analyzing and processing the second moment signal to obtain a first amplitude estimation value and a first initial phase estimation value of a 1 st harmonic component in the second moment signal specifically includes:
step 1: calculating and obtaining the harmonic times of the second moment signal and the complex amplitude of each harmonic component in the second moment signal;
step 2: constructing a first reference signal based on the calculation result of the step 1, obtaining a third moment signal based on the first reference signal and the second moment signal, and updating the complex amplitude of each harmonic component in the second moment signal based on the third moment signal;
and step 3: performing iterative computation for multiple times on the step 2, and obtaining a first amplitude estimated value and a first initial phase estimated value of the 1 st harmonic component in the second moment signal based on the iterative computation result;
the analyzing and processing the second angular displacement signal to obtain a second amplitude estimation value and a second initial phase estimation value of a 1 st harmonic component in the second angular displacement signal specifically includes:
step a: calculating to obtain the harmonic times of the second angular displacement signal, a second estimation value of the complex amplitude of each harmonic component in the second angular displacement signal and the complex amplitude of the frequency offset component in the second angular displacement signal;
step b: constructing a fourth reference signal based on the calculation result of the step a, obtaining a third angular displacement signal based on the fourth reference signal and the second angular displacement signal, and updating the complex amplitude of each harmonic component and the complex amplitude of the frequency offset component in the second angular displacement signal based on the third angular displacement signal; obtaining a frequency offset component positive frequency component in the second angular displacement signal based on the complex amplitude of each harmonic component in the second angular displacement signal and the complex amplitude of the frequency offset component; calculating and updating a frequency offset component complex amplitude value based on a frequency offset component positive frequency component in the second angular displacement signal; updating a frequency offset component reference signal based on the updated frequency offset component complex amplitude, and updating the third angular displacement signal based on the updated frequency offset component reference signal;
step c: and c, carrying out multiple iterative calculations on the step b, and obtaining a second amplitude estimated value and a second initial phase estimated value of the 1 st harmonic component in the second angular displacement signal based on the iterative calculation result.
2. Method for processing data of aircraft dynamic derivative tests according to claim 1, characterized in that step 1 is carried out in particular according to
Figure DEST_PATH_IMAGE043
The second torque signal is processed in the following steps 1.1 to 1.6 in sequence:
step 1.1: is constructed by
Figure DEST_PATH_IMAGE044
A second reference signal for each harmonic component;
step 1.2: subtracting the second reference signal from the second torque signal to obtain a fourth torque signal;
step 1.3: based on the fourth moment signal and the vibration frequency, calculating to obtain the second moment signaliA complex amplitude of the sub-harmonic component;
step 1.4: based on the second one obtained in step 1.3iConstructing a third reference signal by the complex amplitude of the subharmonic component, and calculating to obtain a third reference signal based on the third reference signaliA first energy of the sub-harmonic component;
step 1.5: calculating a second energy for obtaining the second torque signal, calculating a second energy based on the first energy and the second energyiEnergy ratio of sub-harmonic component based oniBefore obtaining the energy ratio of the subharmonic componentiThe sum of the energy ratios of the individual harmonic components;
step 1.6: before judgmentiWhether the sum of the energy ratios of the harmonic components is greater than or equal to a second threshold value, if so, then the time isiIs taken as the harmonic order of the second torque signal
Figure 382865DEST_PATH_IMAGE031
。
3. The method for processing aircraft dynamic derivative test data according to claim 2, wherein the second energy of the second torque signal is calculated by:
Figure DEST_PATH_IMAGE045
wherein,
Figure DEST_PATH_IMAGE046
is the second energy, and is,
Figure 267645DEST_PATH_IMAGE015
in order to shorten the length of the optical fiber,
Figure 816569DEST_PATH_IMAGE028
in order to index the signal(s),
Figure 749890DEST_PATH_IMAGE029
is the second torque signal.
4. The aircraft dynamic derivative test data processing method of claim 2, wherein the first step isiThe complex amplitude of the subharmonic component is calculated in the following manner:
Figure DEST_PATH_IMAGE047
wherein,
Figure DEST_PATH_IMAGE048
is as followsiThe complex amplitude of the sub-harmonic components,
Figure 12244DEST_PATH_IMAGE015
in order to shorten the length of the optical fiber,
Figure 553078DEST_PATH_IMAGE028
in order to index the signal(s),
Figure 572986DEST_PATH_IMAGE029
in order to be able to generate the second torque signal,
Figure 841157DEST_PATH_IMAGE025
in order to be the frequency of the vibration,
Figure DEST_PATH_IMAGE049
is a natural number with a base number of natural,
Figure DEST_PATH_IMAGE050
is an imaginary unit.
5. The aircraft dynamic derivative test data processing method according to claim 2, wherein the third reference signal is:
Figure DEST_PATH_IMAGE051
wherein,
Figure DEST_PATH_IMAGE052
is the third reference signal and is the third reference signal,
Figure DEST_PATH_IMAGE053
is as followsiThe complex amplitude of the sub-harmonic components,
Figure 849695DEST_PATH_IMAGE028
in order to index the signal(s),
Figure 13960DEST_PATH_IMAGE025
in order to be the frequency of the vibration,
Figure 583482DEST_PATH_IMAGE049
is a natural number with a base number of natural,
Figure 593026DEST_PATH_IMAGE050
is the unit of an imaginary number,
Figure DEST_PATH_IMAGE054
to represent
Figure 315126DEST_PATH_IMAGE053
Complex conjugation of (a);
first, theiThe first energy of the subharmonic component is:
Figure DEST_PATH_IMAGE055
wherein,
Figure DEST_PATH_IMAGE056
is the first energy, and is,
Figure 447030DEST_PATH_IMAGE015
is a truncated length;
first, theiThe energy ratio of the harmonic component is
Figure DEST_PATH_IMAGE057
，
Figure 254580DEST_PATH_IMAGE057
The calculation method is as follows:
Figure DEST_PATH_IMAGE058
wherein,
Figure 598974DEST_PATH_IMAGE046
is the second energy.
6. The method for processing aircraft dynamic derivative test data according to claim 5, wherein the second reference signal
Figure DEST_PATH_IMAGE059
Expressed as:
Figure DEST_PATH_IMAGE060
wherein,
Figure DEST_PATH_IMAGE061
is a first
Figure DEST_PATH_IMAGE062
A sub-harmonic component reference signal;
the fourth torque signal
Figure DEST_PATH_IMAGE063
Expressed as:
Figure DEST_PATH_IMAGE064
；
wherein,
Figure DEST_PATH_IMAGE065
is the second torque signal.
7. The aircraft dynamic derivative test data processing method according to claim 1, wherein the step 2 specifically comprises:
step 2.1: constructing a first reference signal based on the calculation result of step 1
Figure DEST_PATH_IMAGE066
，
Figure 926312DEST_PATH_IMAGE066
Expressed as:
Figure DEST_PATH_IMAGE067
wherein,
Figure 963538DEST_PATH_IMAGE054
is shown asiThe complex conjugate of the complex amplitude of the sub-harmonic component,
Figure 445335DEST_PATH_IMAGE028
in order to index the signal(s),
Figure 858999DEST_PATH_IMAGE025
in order to be the frequency of the vibration,
Figure 758953DEST_PATH_IMAGE049
is a natural number with a base number of natural,
Figure DEST_PATH_IMAGE068
is the unit of an imaginary number,
Figure DEST_PATH_IMAGE069
representing the order of the harmonic components of the second moment signal,
Figure 498239DEST_PATH_IMAGE061
is as follows
Figure 467332DEST_PATH_IMAGE062
A sub-harmonic component reference signal;
step 2.2: obtaining a third torque signal based on the first reference signal and the second torque signal
Figure DEST_PATH_IMAGE070
，
Figure DEST_PATH_IMAGE071
Expressed as:
Figure DEST_PATH_IMAGE072
wherein,
Figure 28894DEST_PATH_IMAGE065
is the second torque signal is a function of the second torque signal,
Figure 235885DEST_PATH_IMAGE066
is a first reference signal;
step 2.3: based on the third torque signal
Figure 896804DEST_PATH_IMAGE070
The complex amplitude of each harmonic component in the second moment signal is updated.
8. The method for processing the data of the aircraft dynamic derivative test according to claim 1, wherein the first amplitude estimation value and the first initial phase estimation value of the 1 st harmonic component in the second moment signal are calculated by:
Figure DEST_PATH_IMAGE073
wherein,
Figure DEST_PATH_IMAGE074
is an estimate of the first amplitude value,
Figure DEST_PATH_IMAGE075
is the first initial phase estimate value and is,
Figure DEST_PATH_IMAGE076
is the complex amplitude of the 1 st harmonic component in the second moment signal,
Figure DEST_PATH_IMAGE077
representation complex amplitude
Figure DEST_PATH_IMAGE078
The value of the modulus of the (c) component,
Figure DEST_PATH_IMAGE079
representation complex amplitude
Figure 725432DEST_PATH_IMAGE076
The angle of (c).
9. The aircraft dynamic derivative test data processing method according to claim 1, wherein the step a specifically comprises:
according to
Figure DEST_PATH_IMAGE080
The second angular displacement signal is analyzed, the construction includes
Figure 559526DEST_PATH_IMAGE044
Reference signal of harmonic component and frequency deviation component
Figure DEST_PATH_IMAGE081
；
Figure DEST_PATH_IMAGE082
Wherein,
Figure DEST_PATH_IMAGE083
is as follows
Figure 27548DEST_PATH_IMAGE062
The sub-harmonic component is referenced to the signal,
Figure DEST_PATH_IMAGE084
for the frequency offset component reference signal(s),
Figure 577478DEST_PATH_IMAGE028
indexing the signal;
based on the reference signal
Figure 786743DEST_PATH_IMAGE081
Processing the second angular displacement signal to obtain a processed second angular displacement signal
Figure DEST_PATH_IMAGE085
；
Based on
Figure 893370DEST_PATH_IMAGE085
Calculate the first
Figure DEST_PATH_IMAGE086
A complex amplitude of the sub-harmonic component;
the construction comprises the followingiReference signal of subharmonic component
Figure DEST_PATH_IMAGE087
Based on
Figure 888002DEST_PATH_IMAGE087
Calculate the firstiEnergy of subharmonic component
Figure DEST_PATH_IMAGE088
；
Calculating the energy of the second angular displacement signal
Figure DEST_PATH_IMAGE089
；
Based on the
Figure 936729DEST_PATH_IMAGE088
And said
Figure 118443DEST_PATH_IMAGE089
Is calculated to obtainiEnergy ratio of subharmonic component
Figure DEST_PATH_IMAGE090
；
Based on the index of the frequency offset component
Figure DEST_PATH_IMAGE091
And spectral offset estimation
Figure DEST_PATH_IMAGE092
Calculating the complex amplitude of the frequency offset component
Figure DEST_PATH_IMAGE093
；
Based on
Figure 294341DEST_PATH_IMAGE093
Constructing a frequency offset component reference signal
Figure 923905DEST_PATH_IMAGE084
；
Based on
Figure 18900DEST_PATH_IMAGE084
Calculating the energy of the obtained frequency deviation component
Figure DEST_PATH_IMAGE094
；
Based on the
Figure 484648DEST_PATH_IMAGE094
And said
Figure 385607DEST_PATH_IMAGE089
Calculating the energy ratio of the obtained frequency deviation component
Figure DEST_PATH_IMAGE095
；
Based on
Figure 338520DEST_PATH_IMAGE095
And
Figure 869995DEST_PATH_IMAGE090
before calculation is obtainediSum of energy ratios of harmonic component and frequency offset component
Figure DEST_PATH_IMAGE096
；
When in use
Figure 619777DEST_PATH_IMAGE096
Greater than or equal to a third threshold value at which timeiIs the harmonic order of the second angular displacement signal
Figure DEST_PATH_IMAGE097
。
10. The method for processing aircraft dynamic derivative test data according to claim 1, wherein the fourth reference signal is
Figure DEST_PATH_IMAGE098
；
Figure DEST_PATH_IMAGE099
Wherein,
Figure DEST_PATH_IMAGE100
is shown asiThe complex conjugate of the complex amplitude of the sub-harmonic component,
Figure 403056DEST_PATH_IMAGE032
being a harmonic order of the second angular displacement signal,
Figure 961208DEST_PATH_IMAGE028
in order to index the signal(s),
Figure 460322DEST_PATH_IMAGE025
in order to be the frequency of the vibration,
Figure 822033DEST_PATH_IMAGE049
is a natural number with a base number of natural,
Figure 330375DEST_PATH_IMAGE050
is the unit of an imaginary number,
Figure 929984DEST_PATH_IMAGE083
is as follows
Figure 147469DEST_PATH_IMAGE062
The sub-harmonic component is referenced to the signal,
Figure 465318DEST_PATH_IMAGE084
is a frequency offset component reference signal;
first, the
Figure 246192DEST_PATH_IMAGE086
The sub-harmonic component has a positive frequency component of
Figure DEST_PATH_IMAGE101
；
Figure DEST_PATH_IMAGE102
Wherein,
Figure DEST_PATH_IMAGE103
is the second angular displacement signal;
by using the said
Figure 106832DEST_PATH_IMAGE101
Calculate and updateiComplex amplitude of subharmonic component
Figure DEST_PATH_IMAGE104
；
Figure DEST_PATH_IMAGE105
Wherein,
Figure 88695DEST_PATH_IMAGE015
is the second angular displacement signal length;
based on updated secondiComplex amplitude of subharmonic component
Figure 893840DEST_PATH_IMAGE104
According to
Figure DEST_PATH_IMAGE106
Calculating to obtain the complex amplitude of each harmonic component;
frequency offset component of positive frequency component
Figure 748577DEST_PATH_IMAGE101
；
Figure DEST_PATH_IMAGE107
Wherein,
Figure 916253DEST_PATH_IMAGE091
is an index to the frequency offset component,
Figure 131334DEST_PATH_IMAGE092
for the purpose of the spectral offset estimation,
Figure 705666DEST_PATH_IMAGE097
being a harmonic order of the second angular displacement signal,
Figure DEST_PATH_IMAGE108
is the complex conjugate of the complex magnitude of the frequency offset component,
Figure 890659DEST_PATH_IMAGE083
is as follows
Figure 116104DEST_PATH_IMAGE062
The sub-harmonic component is referenced to the signal.
11. The method for processing data of aircraft dynamic derivative tests according to claim 1, wherein the second amplitude estimation value of the 1 st harmonic component in the second angular displacement signal is
Figure DEST_PATH_IMAGE109
The second initial phase estimation value of the 1 st harmonic component in the second angular displacement signal is
Figure DEST_PATH_IMAGE110
：
Figure DEST_PATH_IMAGE111
Wherein,
Figure DEST_PATH_IMAGE112
being the complex amplitude of the 1 st harmonic component in the second angular displacement signal,
Figure DEST_PATH_IMAGE113
representation complex amplitude
Figure 377452DEST_PATH_IMAGE112
The value of the modulus of the (c) signal,
Figure DEST_PATH_IMAGE114
representation complex amplitude
Figure 235818DEST_PATH_IMAGE112
The angle of (c).
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