CN112816937A - Helicopter scale estimation method and device based on fundamental frequency line spectrum azimuth angle change rate - Google Patents
Helicopter scale estimation method and device based on fundamental frequency line spectrum azimuth angle change rate Download PDFInfo
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Abstract
The invention provides a helicopter scale estimation method and device based on a fundamental frequency line spectrum azimuth angle change rate, wherein the method comprises the steps of extracting fundamental frequencies of a helicopter rotor and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor and the tail rotor; calculating the angle change slope and the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal, and calculating the angle change slope and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; estimating extreme values of direction angle change rates of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and a moment corresponding to the maximum value of the extreme values; estimating the navigational speed of the helicopter; the wheelbase of the helicopter rotor and the tail rotor is estimated. According to the scheme of the invention, the wheel base of the main rotor and the tail rotor of the helicopter flying in a straight line and passing right above can be estimated.
Description
Technical Field
The invention relates to the field, in particular to a helicopter scale estimation method and device based on a fundamental frequency line spectrum azimuth angle change rate.
Background
With the rapid development and application of the UUV, the application field of the UUV is gradually expanded, and the underwater value is kept time, so that targets such as ships, UUVs, airplanes and the like may pass nearby, and if the helicopter is a specific detection and monitoring object, the scale of the helicopter needs to be estimated and calculated.
Disclosure of Invention
In order to solve the technical problems, the invention provides a helicopter scale estimation method and device based on the azimuth angle change rate of a fundamental frequency line spectrum, and the method and device are used for solving the problem of inaccurate helicopter scale estimation.
According to a first aspect of the present invention, there is provided a method for helicopter scale estimation based on the rate of change of the azimuth angle of a fundamental frequency spectrum, the method comprising the steps of:
step S101: the vector hydrophone acquires the sound pressure and particle vibration velocity signals of the target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
step S102: calculating the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
step S103: estimating the navigational speed of the helicopter based on the fundamental frequency extracted from the frequency domain and the estimated direction angle of the fundamental frequency signal;
step S104: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
According to a second aspect of the present invention, there is provided a helicopter dimension estimation apparatus based on the rate of change of the azimuth angle of a fundamental frequency spectrum, the apparatus comprising:
an azimuth angle estimation module: the method comprises the steps that a vector hydrophone is configured to obtain sound pressure and particle vibration velocity signals of a target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
an extreme value calculation module: the method comprises the steps of calculating the slope of the angle change slope of the direction angle of a helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
the navigation speed estimation module: estimating the navigational speed of the helicopter based on the fundamental frequency extracted in the frequency domain and the estimated direction angle of the fundamental frequency signal;
a scale estimation module: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
According to a third aspect of the present invention, there is provided a helicopter scale estimation system based on the azimuth angle change rate of a fundamental frequency spectrum, comprising:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the instructions are for being stored by the memory and loaded and executed by the processor to perform the helicopter dimension estimation method based on the fundamental frequency spectrum azimuth angle change rate as described above.
According to a fourth aspect of the present invention, there is provided a computer readable storage medium having a plurality of instructions stored therein; the instructions are used for loading and executing the helicopter scale estimation method based on the azimuth angle change rate of the fundamental frequency line spectrum by the processor.
According to the scheme, the estimation results of the fundamental frequency line spectrum direction angles of the main rotor and the tail rotor are used as input, slope and extreme value estimation is firstly carried out on the fundamental frequency line spectrum direction angles of the main rotor and the tail rotor, then the radial projection speed of the helicopter is estimated according to the change rule and the extreme value time of the fundamental frequency line spectrum direction angle slopes of the main rotor and the tail rotor, and finally the axial distance between the main rotor and the tail rotor of the helicopter is estimated by combining the extreme value time difference of the fundamental frequency line spectrum direction angle slopes of the main rotor and the tail rotor. The method has the technical effect of estimating the wheelbase of the main rotor and the tail rotor of the helicopter flying in a straight line and passing right above, and can also be used for estimating the size of the helicopter in other fields.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to implement them in accordance with the contents of the description, the following detailed description is given with reference to the preferred embodiments of the present invention and the accompanying drawings.
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The accompanying drawings, which 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. In the drawings:
FIG. 1 is a flowchart of a helicopter scale estimation method based on the rate of change of the azimuth angle of a fundamental frequency spectrum according to an embodiment of the present invention;
FIG. 2 is a schematic view of a space model of a helicopter according to an embodiment of the present invention in a flying state;
FIG. 3 is a schematic representation of a three-dimensional vector hydrophone in a Cartesian coordinate system in accordance with an embodiment of the present invention;
FIG. 4 is a line spectrum block diagram of a helicopter in accordance with an embodiment of the present invention;
FIG. 5 is a diagram illustrating the estimation of the fundamental frequency line spectral direction angles of the rotor and the tail rotor in a helicopter flight state according to an embodiment of the present invention;
fig. 6 is a structural block diagram of a helicopter scale estimation device based on the change rate of the azimuth angle of the fundamental frequency spectrum according to an embodiment of the present invention.
Detailed Description
First, a flow of a helicopter scale estimation method based on a fundamental frequency spectrum azimuth angle change rate according to an embodiment of the present invention will be described with reference to fig. 1. As shown in fig. 1, the method comprises the steps of:
step S101: the vector hydrophone acquires the sound pressure and particle vibration velocity signals of the target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
step S102: calculating the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
step S103: estimating the navigational speed of the helicopter based on the fundamental frequency extracted from the frequency domain and the estimated direction angle of the fundamental frequency signal;
step S104: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
The step S101: the vector hydrophone acquires the sound pressure and particle vibration velocity signals of the target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor and a tail rotor on a frequency domain, and estimating the direction angle of fundamental frequency signals of the helicopter rotor and the tail rotor, wherein:
the target helicopter has a sound field, and sound field information of the target sound field is obtained by a three-dimensional vector hydrophone;
in this embodiment, cartesian coordinates are established with the test system as the origin of coordinates, and when viewed from above and below, the helicopter flies from above the test system at a navigational speed with a horizontal projection velocity V starting from coordinates (x (0), y (0)), and the spatial model is shown in fig. 2. The method is characterized in that a certain traveling helicopter is taken as a target, the helicopter flies linearly at a constant speed at a putting height of less than 100m on water, a test system records data at a sampling speed of 50kHz by adopting a three-dimensional vector hydrophone, and sound pressure and particle vibration speed components transmitted by a cross medium of the helicopter in a low-altitude low-speed flying state are obtained.
As shown in FIG. 3, the vector hydrophone is placed at the origin of a Cartesian coordinate system, the output sound pressure of the three-dimensional vector hydrophone is recorded as p, and the particle vibration velocity v (v) is recorded as vx,vy,vz) Wherein v isxIs the component of the particle velocity in the x-axis direction of the coordinate system, vyIs the component of the particle velocity in the x-axis direction of the coordinate system, vzThe component of the particle vibration velocity in the z-axis direction of the coordinate system; v. ofx,vy,vzAre respectively parallel to the x, y and z axes of the Cartesian coordinates, and the acoustic center of the vector hydrophone coincides with the origin of the Cartesian coordinate system. The xoy plane here is the same as the xoy plane in fig. 2.
Note tiThe variation of sound pressure value at the moment is p (t)i) Vector three-dimensional orthogonal component is vx(ti)、vy(ti)、vz(ti)。
Recording the sampling rate as fsAt time tsSelecting sound pressure p (t) from discrete signals-N+1)、……、p(ts-1)、p(ts) The discrete signals of (a) are used to form samples, denoted as p (1), … …, p (N-1), p (N); wherein i is a natural number greater than 1, s is a sampling time, and N is a sample size.
Selecting x-axis component of particle velocity from discrete signal at time tsIs v isx(ts-N+1)、……、vx(ts-1)、vx(ts) Are used to form the samples, denoted v respectivelyx(1)、……、vy(N-1)、vx(N); wherein i is a natural number greater than 1, s is a sampling time, and N is a sample size.
At time tsSelecting a particle vibration velocity y-axis component from the discrete signal as vy(ts-N+1)、……、vy(ts-1)、vy(ts) Are used to form the samples, denoted v respectivelyy(1)、……、vy(N-1)、vy(N); wherein i is a natural number greater than 1, s is a sampling time, and N is a sample size.
Then tsSample sequence P (t) of sound pressure and particle vibration velocity at times)、Vx(ts)、Vy(ts)、Vz(ts) Respectively expressed as:
P(ts)＝[p(1),……,p(N-1),p(N)]……(1)
Vx(ts)＝[vx(1),……,vx(N-1),vx(N)]……(2)
Vy(ts)＝[vy(1),……,vy(N-1),vy(N)]……(3)
Vz(ts)＝[vz(1),……,vz(N-1),vz(N)]……(4)
for tsSample sequence P (t) of sound pressure and particle vibration velocity at times)、Vx(ts)、Vy(ts)、Vz(ts) Performing FFT to obtain N complex sequences in frequency domain, and respectively recording the obtained results as P (t)s,f)、Vx(ts，f)、Vy(ts，f)、Vz(ts，f)；P(ts,f)、Vx(ts，f)、Vy(ts，f)、Vz(tsThe k-th sequence of f) is denoted as p (f)k)、vx(fk)、vx(fk)、vz(fk) Then there is
P(ts,f)＝[p(fk)]……(5)
Vx(ts,f)＝[vx(fk)]……(6)
Vy(ts,f)＝[vy(fk)]……(7)
Vz(ts,f)＝[vz(fk)]……(8)
Wherein k is more than or equal to 1 and less than or equal to N;
by P (t)s,f)、Vz(tsF) calculating the cross-power spectrum of the z-axis component of the sequence, and modeling the obtained cross-power spectrum sequence and recording as Iz(ts,f)，
Wherein the content of the first and second substances,
represents Vz(tsAnd f) a conjugate sequence.
The helicopter has a fixed fundamental frequency of a rotor wing in a flying state, the fundamental frequency of a tail rotor is also in a certain range, and the fundamental frequency of the rotor wing and the fundamental frequency of the tail rotor can be extracted by a preset rule;
to Iz(tsExtracting the fundamental frequency of a rotor wing and the fundamental frequency of a tail rotor from the sequence of f);
in this embodiment, the time interval for obtaining the line spectrum is Δ t, at tsExtracting rotor fundamental frequency f from time to time1(m) and fundamental frequency f of tail rotor2(m), m is a positive integer, m ═ ts/Δt，f1(m)＝N×(mk1-1)/fs，f2(m)＝N×(mk2-1)/fs
Wherein, mk1、mk2Fundamental frequency f of rotor wing extracted at m moments respectively1(m) and fundamental tail rotor frequency f2(m) corresponding line spectrum serial numbers.
Preferably, it is done according to the phase line spectral energyThe interpolation process may be such that1(m)、f2The estimated value of (m) is more accurate.
Selecting P (t)s,f)、Vx(ts，f)、Vy(tsF) the mk th in the sequence1A plurality of complex quantities vx(f1(m))、vy(f1(m)), and the mk th2A plurality of complex quantities vx(f2(m))、vx(f2(m)), estimating the direction angle alpha of the fundamental frequency signal of the helicopter rotor1(m) and the direction angle alpha of the fundamental signal of the tail rotor2(m)：
Further, in the calculation process, the values of N and delta t are directly related to the frequency estimation precision and the helicopter rotor and tail rotor wheelbase estimation precision.
The frequency estimation error brought by the value is calculated according to the following formula:
Δf'＝fs/2/N……(12)
the estimation error of the shaft distance between the helicopter rotor and the tail rotor brought by the value is recorded as delta d, and the estimation error is calculated according to the following formula:
Δd＝Δt×C/2……(13)
wherein C is the sound velocity in air;
in this embodiment, the data sampling rate f is obtainedsThe rotor frequency of a helicopter used for the test is about 14Hz, and the tail rotor frequency is 136 Hz.
Selecting the forward and backward data of the straight line of the air route, extracting the fundamental frequency line spectrums of the rotor and the tail rotor in two narrow bands of 12Hz-15Hz and 130Hz-125Hz, and estimating the direction angles of the fundamental frequency line spectrums of the rotor and the tail rotor, wherein the line spectrums of the helicopter are shown in figure 4, and the estimation result of the direction angles of the fundamental frequency line spectrums of the rotor and the tail rotor in the flight state of the helicopter is shown in figure 5.
The step S102: calculating the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values, wherein the moment corresponding to the extreme values comprises the following steps:
recording the angle change Slope of the direction angle of the helicopter rotor fundamental frequency signal as Slope1(m) the Slope of the change in the direction angle of the fundamental frequency signal of the tail rotor is Slope2(m) which is calculated as follows:
wherein alpha is1(m-1) is the direction angle alpha of the fundamental frequency signal of the helicopter rotor at the moment m-12And (m-1) is the direction angle of the fundamental frequency signal of the tail rotor at the moment m-1.
Recording the Slope of the angle change Slope of the direction angle of the fundamental frequency signal of the helicopter rotor as D _ Slope1(m), the Slope of the change of the angle of the direction angle of the fundamental frequency signal of the tail rotor is D _ Slope2(m) which is calculated as follows:
wherein the Slope1(m-1) is the angle change Slope of the direction angle of the fundamental frequency signal of the helicopter rotor at the moment of m-1, Slope2And (m-1) is the angle change slope of the direction angle of the tail rotor fundamental frequency signal at the moment of m-1.
For D _ Slope1(m) and D _ Slope2(m) performing real-time mean smoothing, wherein the formula is as follows:
wherein M is an empirical value, and in this embodiment, M takes the value of 4.
The maximum value of the angle change Slope of the direction angle of the helicopter rotor fundamental frequency signal is recorded as Max _ Slope1And the corresponding time is recorded as mf1Max, extreme value judging the Slope variable of the middle process as Jz _ Slope1(m) real-time change of extremum moment mf1Jz (m); maximum value Max _ Slope of angle change Slope of direction angle of tail rotor base frequency signal2And the corresponding time is recorded as mf2Max, extreme value judging the Slope variable of the middle process as Jz _ Slope2(m) real-time change of extremum moment mf2Jz (m); and (3) carrying out extreme value judgment and recording the occurrence time of the extreme value on the time axis according to the following formula:
according to D1_ Slope1(m)、D1_Slope2(m) proceeding to the maximum value of the change rate of the direction angle slope at the corresponding time mf1_max、mf2Max estimate. The formula is as follows:
in this example, the mf was estimated using experimental data1Max and mf2The resulting values for _ max are 377 and 391.
The step S103: estimating the navigational speed of the helicopter based on the fundamental frequency extracted on the frequency domain and the estimated direction angle of the fundamental frequency signal, wherein:
and selecting the fundamental frequency extracted by the rotor or the tail rotor on the frequency domain and the direction angle of the estimated fundamental frequency signal in real time, and estimating the navigational speed of the helicopter.
In this embodiment, the tail rotor fundamental frequency f is selected2(m) and the estimated azimuth angle alpha of the fundamental frequency signal of the tail rotor2(m) as input to estimate the speed of the helicopter.
Let us note the state transition matrix from the state at time m to the state at time m +1 as phi, which is mathematically expressed as follows:
note HmIs an observation matrix of m time instants, will be alpha2(m) is denoted as amA 1 is to f2(m) is denoted by fmAnd the speed of sound in water is denoted as cmThe observation matrix at time m is represented as follows:
when the receiving system is on a moving platform cmPossibly varying with time, the example being applied as a stationary platform, cmThe constant is taken empirically, here the value is 1485 m/s.
Taking P (m) as a Kalman estimation error covariance matrix at the moment m, and taking P (m-1) as a Kalman estimation error covariance matrix at the moment m-1;
p (m/m-1) is recorded as a covariance matrix of prediction errors at the m moment, and K (m) is recorded as a gain matrix at the m moment; then the calculation formula of P (m/m-1), K (m), P (m) is:
P(m/m-1)＝φP(m-1)φT……(28)
P(m)＝[I-K(m)Hm]P(m/m-1)[I-K(m)Hm]T+K(m)R(m)KT(m)
……(30)
wherein the content of the first and second substances,
the direction angle and the variance of the frequency measurement error of the fundamental frequency signal of the tail rotor at the time m are obtained by calculating the direction angle of the fundamental frequency signal of the tail rotor obtained at the time m and the extracted linear spectrum frequency according to a mean square error formula, and I is an identity matrix; taking in the calculation:
definition of
Wherein
xmFor the position component of the helicopter in the x-axis direction at time m, ymFor the position component of the helicopter m time in the y-axis direction, VxmThe velocity component of the helicopter m moment in the x-axis direction is obtained; vymIs the velocity component of the helicopter m at the moment in the y-axis direction.
Taking X (0) ═ 1000100020-101/300]Noting the process variable from time m-1 to time m as
It is calculated according to the following formula:
in the formula
Is an estimate of time X (m-1) at time m-1,
estimating X (m) based on the state predicted value K (m) of m time calculated by using a gain matrix formula (29), and recording the estimated value as
The estimation formula is as follows:
in the formula
Here, the
Actually a sequence, the resulting sequences corresponding to xm、ym、Vxm、VymEstimated value of (2) using
And
respectively represent VxmAnd VymThe estimation result of the speed v (m) of the helicopter at the time m is:
the step S104: based on the appearance moment difference of the direction angle change rate maximum value of the helicopter rotor fundamental frequency signal and the direction angle change rate maximum value of the tail rotor fundamental frequency signal, and the helicopter navigational speed, the wheelbase of the helicopter rotor and the tail rotor is estimated, comprising:
d (m) is the wheelbase of the helicopter rotor and tail rotor, when mf2_max＞mf1Max will then satisfy the estimation requirement.
Preferably, a value other than 0 is obtained on condition that formula (34) is satisfied, and mf is2_max、mf1Max obtains the nearby time, VxmAnd VymIs relatively accurate and is therefore usually given in mf when applied2The moment when max gets a value other than 0 is the exact value.
In this embodiment, mf obtained by data simulation2The value of V (m) estimated for the time corresponding to max is 5.36m/s, and the value of d (m) estimated is: 5.36 ═ 391-.
The helicopter of the present embodiment is a helicopter having a single rotor and a tail rotor, and is not the object of the present embodiment for a long-distance or hovering helicopter.
The embodiment of the invention further provides a helicopter scale estimation device based on the fundamental frequency line spectrum azimuth angle change rate, as shown in fig. 6, the device comprises:
an azimuth angle estimation module: the method comprises the steps that a vector hydrophone is configured to obtain sound pressure and particle vibration velocity signals of a target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
an extreme value calculation module: the method comprises the steps of calculating the slope of the angle change slope of the direction angle of a helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
the navigation speed estimation module: estimating the navigational speed of the helicopter based on the fundamental frequency extracted in the frequency domain and the estimated direction angle of the fundamental frequency signal;
a scale estimation module: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
The embodiment of the invention further provides a helicopter scale estimation system based on the fundamental frequency line spectrum azimuth angle change rate, which comprises the following steps:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the instructions are for being stored by the memory and loaded and executed by the processor to perform the helicopter dimension estimation method based on the fundamental frequency spectrum azimuth angle change rate as described above.
The embodiment of the invention further provides a computer readable storage medium, wherein a plurality of instructions are stored in the storage medium; the instructions are used for loading and executing the helicopter scale estimation method based on the azimuth angle change rate of the fundamental frequency line spectrum by the processor.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In the embodiments provided in the present invention, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions in actual implementation, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.
The integrated unit implemented in the form of a software functional unit may be stored in a computer readable storage medium. The software functional unit is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a physical machine Server, or a network cloud Server, etc., and needs to install a Windows or Windows Server operating system) to perform some steps of the method according to various embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are still within the scope of the technical solution of the present invention.
Claims (10)
1. A helicopter scale estimation method based on a fundamental frequency line spectrum azimuth angle change rate is characterized by comprising the following steps:
step S101: the vector hydrophone acquires the sound pressure and particle vibration velocity signals of the target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
step S102: calculating the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
step S103: estimating the navigational speed of the helicopter based on the fundamental frequency extracted from the frequency domain and the estimated direction angle of the fundamental frequency signal;
step S104: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
2. The method for estimating helicopter dimensions based on the fundamental frequency line spectrum azimuthal angle rate of change of claim 1 wherein the vector hydrophone obtains the acoustic pressure and particle velocity signals of the target helicopter; sampling sound pressure and particle vibration velocity of a helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence, wherein the FFT comprises the following steps:
the vector hydrophone is arranged at the origin of a Cartesian coordinate system, the output sound pressure of the three-dimensional vector hydrophone is recorded as p, and the particle vibration velocity v (v) is recorded asx,vy,vz) Wherein v isxIs the component of the particle velocity in the x-axis direction of the coordinate system, vyIs the component of the particle velocity in the x-axis direction of the coordinate system, vzThe component of the particle vibration velocity in the z-axis direction of the coordinate system; v. ofx,vy,vzThe acoustic center of the vector hydrophone is coincided with the origin of a Cartesian coordinate system;
note tiThe variation of sound pressure value at the moment is p (t)i) Vector three-dimensional orthogonal component is vx(ti)、vy(ti)、vz(ti)；
Recording the sampling rate as fsAt time tsSelecting sound pressure p (t) from discrete signals-N+1)、……、p(ts-1)、p(ts) The x-axis component of the particle vibration velocity is vx(ts-N+1)、……、vx(ts-1)、vx(ts) The y-axis component of particle vibration velocity is vy(ts-N+1)、……、vy(ts-1)、vy(ts) The discrete signals of (a) are used to compose a sample, and the sound pressure of the sample is respectively denoted as p (1), … …, p (N-1), p (N); the x-axis component of the particle vibration velocity of the sampleIs denoted by vx(1)、……、vy(N-1)、vx(N); the y-axis component of the particle velocity of the sample is denoted as vy(1)、……、vy(N-1)、vy(N)；
Wherein i is a natural number greater than 1, s is a sampling moment, and N is a sample size;
then tsSample sequence P (t) of sound pressure and particle vibration velocity at times)、Vx(ts)、Vy(ts)、Vz(ts) Respectively expressed as:
P(ts)＝[p(1),……,p(N-1),p(N)]……(1)
Vx(ts)＝[vx(1),……,vx(N-1),vx(N)]……(2)
Vy(ts)＝[vy(1),……,vy(N-1),vy(N)]……(3)
Vz(ts)＝[vz(1),……,vz(N-1),vz(N)]……(4)
for tsSample sequence P (t) of sound pressure and particle vibration velocity at times)、Vx(ts)、Vy(ts)、Vz(ts) Performing FFT to obtain N complex sequences in frequency domain, and respectively recording the obtained results as P (t)s,f)、Vx(ts，f)、Vy(ts，f)、Vz(ts，f)；P(ts,f)、Vx(ts，f)、Vy(ts，f)、Vz(tsThe k-th sequence of f) is denoted as p (f)k)、vx(fk)、vx(fk)、vz(fk) Then there is
P(ts,f)＝[p(fk)]……(5)
Vx(ts,f)＝[vx(fk)]……(6)
Vy(ts,f)＝[vy(fk)]……(7)
Vz(ts,f)＝[vz(fk)]……(8)
Wherein k is more than or equal to 1 and less than or equal to N;
by P (t)s,f)、Vz(tsF) calculating the cross-power spectrum of the z-axis component of the sequence, and modeling the obtained cross-power spectrum sequence and recording as Iz(ts,f)，
Wherein the content of the first and second substances,
represents Vz(tsAnd f) a conjugate sequence.
3. The method according to claim 2, wherein the step of estimating the azimuth angle of the helicopter rotor and the tail rotor based on the fundamental frequency of the helicopter rotor and the tail rotor in the frequency domain comprises:
extracting the fundamental frequency of a rotor wing and the fundamental frequency of a tail rotor by using a preset rule;
to Iz(tsExtracting the fundamental frequency of a rotor wing and the fundamental frequency of a tail rotor from the sequence of f);
the time interval for obtaining the line spectrum is delta t, at tsExtracting rotor fundamental frequency f from time to time1(m) and fundamental frequency f of tail rotor2(m), m is a positive integer, m ═ ts/Δt，f1(m)＝N×(mk1-1)/fs，f2(m)＝N×(mk2-1)/fs
Wherein, mk1、mk2Fundamental frequency f of rotor wing extracted at m moments respectively1(m) and fundamental tail rotor frequency f2(m) corresponding line spectrum serial numbers;
selecting P (t)s,f)、Vx(ts，f)、Vy(tsF) the mk th in the sequence1A plurality of complex quantities vx(f1(m))、vy(f1(m)), and the mk th2A plurality ofQuantity vx(f2(m))、vx(f2(m)), estimating the direction angle alpha of the fundamental frequency signal of the helicopter rotor1(m) and the direction angle alpha of the fundamental signal of the tail rotor2(m)：
4. A helicopter scale estimation method according to claim 3 based on the rate of change of the azimuth angle of the fundamental frequency spectrum, characterized in that said step S102: calculating the slope of the angle change slope of the direction angle of the helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values, wherein the moment corresponding to the extreme values comprises the following steps:
recording the angle change Slope of the direction angle of the helicopter rotor fundamental frequency signal as Slope1(m) the Slope of the change in the direction angle of the fundamental frequency signal of the tail rotor is Slope2(m) which is calculated as follows:
wherein alpha is1(m-1) is the direction angle alpha of the fundamental frequency signal of the helicopter rotor at the moment m-12(m-1) is the direction angle of the fundamental frequency signal of the tail rotor at the moment m-1;
recording the Slope of the angle change Slope of the direction angle of the fundamental frequency signal of the helicopter rotor as D _ Slope1(m), the Slope of the change of the angle of the direction angle of the fundamental frequency signal of the tail rotor is D _ Slope2(m) which is calculated as follows:
wherein the Slope1(m-1) is the angle change Slope of the direction angle of the fundamental frequency signal of the helicopter rotor at the moment of m-1, Slope2(m-1) is the angle change slope of the direction angle of the tail rotor fundamental frequency signal at the m-1 moment;
for D _ Slope1(m) and D _ Slope2(m) performing real-time mean smoothing, wherein the formula is as follows:
wherein M is an empirical value;
the maximum value of the angle change Slope of the direction angle of the helicopter rotor fundamental frequency signal is recorded as Max _ Slope1And the corresponding time is recorded as mf1Max, extreme value judging the Slope variable of the middle process as Jz _ Slope1(m) real-time change of extremum moment mf1Jz (m); maximum value Max _ Slope of angle change Slope of direction angle of tail rotor base frequency signal2And the corresponding time is recorded as mf2Max, extreme value judging the Slope variable of the middle process as Jz _ Slope2(m) real-time change of extremum moment mf2Jz (m); and (3) carrying out extreme value judgment and recording the occurrence time of the extreme value on the time axis according to the following formula:
according to D1_ Slope1(m)、D1_Slope2(m) proceeding to the time mf corresponding to the maximum value of the angle change slope of the azimuth1_max、mf2Max estimate, the formula is as follows:
5. the method for helicopter dimension estimation based on fundamental frequency line spectral azimuth angle rate of change according to claim 4, wherein said step S103: estimating the navigational speed of the helicopter based on the fundamental frequency extracted on the frequency domain and the estimated direction angle of the fundamental frequency signal, wherein:
and selecting the fundamental frequency extracted by the rotor or the tail rotor on the frequency domain and the direction angle of the estimated fundamental frequency signal in real time, and estimating the navigational speed of the helicopter.
6. The method of claim 5, wherein the tail rotor fundamental frequency f is selected2(m) and the estimated azimuth angle alpha of the fundamental frequency signal of the tail rotor2(m) as an input for estimating the speed of the helicopter,
let us note the state transition matrix from the state at time m to the state at time m +1 as phi, which is mathematically expressed as follows:
note HmIs an observation matrix of m time instants, will be alpha2(m) is denoted as amA 1 is to f2(m) is denoted by fmAnd the speed of sound in water is denoted as cmThe observation matrix at time m is represented as follows:
cmtaking a constant according to experience;
taking P (m) as a Kalman estimation error covariance matrix at the moment m, and taking P (m-1) as a Kalman estimation error covariance matrix at the moment m-1;
p (m/m-1) is recorded as a covariance matrix of prediction errors at the m moment, and K (m) is recorded as a gain matrix at the m moment; then the calculation formula of P (m/m-1), K (m), P (m) is:
P(m/m-1)＝φP(m-1)φT ……(28)
P(m)＝[I-K(m)Hm]P(m/m-1)[I-K(m)Hm]T+K(m)R(m)KT(m) ……(30)
wherein the content of the first and second substances,
the direction angle and the variance of the frequency measurement error of the fundamental frequency signal of the tail rotor at the time m are obtained by calculating the direction angle of the fundamental frequency signal of the tail rotor obtained at the time m and the extracted linear spectrum frequency according to a mean square error formula, and I is an identity matrix; taking in the calculation:
definition of
Wherein
xmFor the position component of the helicopter in the x-axis direction at time m, ymFor the position component of the helicopter m time in the y-axis direction, VxmThe velocity component of the helicopter m moment in the x-axis direction is obtained; vymThe velocity component of the helicopter m moment in the y-axis direction is obtained;
obtaining the value of X (0), and recording the process variable from m-1 time to m time as
It is calculated according to the following formula:
in the formula
Is an estimate of time X (m-1) at time m-1,
estimating X (m) based on the state predicted value K (m) of m time calculated by using a gain matrix formula (29), and recording the estimated value as
The estimation formula is as follows:
in the formula
Here, the
Actually a sequence, the resulting sequences corresponding to xm、ym、Vxm、VymEstimated value of (2) using
And
respectively represent VxmAnd VymEstimated value of (c), then helicopter is at m hoursThe velocity at this moment, v (m), is estimated as:
7. the method for helicopter scale estimation based on the fundamental frequency line spectral azimuth angle rate of change of claim 6, said step S104: based on the appearance moment difference of the direction angle change rate maximum value of the helicopter rotor fundamental frequency signal and the direction angle change rate maximum value of the tail rotor fundamental frequency signal, and the helicopter navigational speed, the wheelbase of the helicopter rotor and the tail rotor is estimated, comprising:
d (m) is the wheelbase of the helicopter rotor and tail rotor, when mf2_max＞mf1Max will then satisfy the estimation requirement.
8. A helicopter dimension estimation apparatus based on the rate of change of the fundamental frequency line spectral azimuth angle, said apparatus comprising:
an azimuth angle estimation module: the method comprises the steps that a vector hydrophone is configured to obtain sound pressure and particle vibration velocity signals of a target helicopter; sampling sound pressure and particle vibration velocity of the helicopter to obtain a sound pressure and particle vibration velocity discrete signal sequence, and performing FFT (fast Fourier transform) on the sound pressure and particle vibration velocity discrete signal sequence; extracting fundamental frequencies of a helicopter rotor wing and a tail rotor on a frequency domain, and estimating direction angles of fundamental frequency signals of the helicopter rotor wing and the tail rotor;
an extreme value calculation module: the method comprises the steps of calculating the slope of the angle change slope of the direction angle of a helicopter rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the rotor fundamental frequency signal; calculating the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal and the slope of the angle change slope of the direction angle of the tail rotor fundamental frequency signal; respectively estimating extreme values of angle change slopes of direction angles of a helicopter rotor fundamental frequency signal and a tail rotor fundamental frequency signal and moments corresponding to the maximum values of the extreme values;
the navigation speed estimation module: estimating the navigational speed of the helicopter based on the fundamental frequency extracted in the frequency domain and the estimated direction angle of the fundamental frequency signal;
a scale estimation module: and estimating the wheelbase of the helicopter rotor and the tail rotor based on the occurrence time difference of the maximum value of the direction angle change rate of the fundamental frequency signal of the helicopter rotor and the maximum value of the direction angle change rate of the fundamental frequency signal of the tail rotor and the navigational speed of the helicopter.
9. A helicopter scale estimation system based on the change rate of the azimuth angle of a fundamental frequency line spectrum is characterized by comprising the following components:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the instructions are for storage by the memory and for loading and executing by the processor the method for helicopter dimension estimation based on the rate of change of the fundamental frequency spectral azimuth angle of any of claims 1-7.
10. A computer-readable storage medium having stored therein a plurality of instructions; the plurality of instructions for loading and executing by a processor the helicopter dimension estimation method based on the rate of change of the azimuth angle of the fundamental frequency spectrum according to any one of claims 1 to 7.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5231609A (en) * | 1992-09-28 | 1993-07-27 | The United States Of America As Represented By The Secretary Of The Navy | Multiplatform sonar system and method for underwater surveillance |
| JPH0882663A (en) * | 1994-09-13 | 1996-03-26 | Tech Res & Dev Inst Of Japan Def Agency | Analytical method of target motion |
| US5816533A (en) * | 1995-07-27 | 1998-10-06 | Eurocopter | Method and device for reducing the vibration generated on the structure of a helicopter |
| CN108051659A (en) * | 2017-12-01 | 2018-05-18 | 中国直升机设计研究所 | A kind of method of separation and Extraction rotor noise |
| CN110196407A (en) * | 2019-05-06 | 2019-09-03 | 东南大学 | A kind of single vector hydrophone signal arrival bearing's estimation method based on frequency estimation |
-
2020
- 2020-12-23 CN CN202011541454.1A patent/CN112816937B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5231609A (en) * | 1992-09-28 | 1993-07-27 | The United States Of America As Represented By The Secretary Of The Navy | Multiplatform sonar system and method for underwater surveillance |
| JPH0882663A (en) * | 1994-09-13 | 1996-03-26 | Tech Res & Dev Inst Of Japan Def Agency | Analytical method of target motion |
| US5816533A (en) * | 1995-07-27 | 1998-10-06 | Eurocopter | Method and device for reducing the vibration generated on the structure of a helicopter |
| CN108051659A (en) * | 2017-12-01 | 2018-05-18 | 中国直升机设计研究所 | A kind of method of separation and Extraction rotor noise |
| CN110196407A (en) * | 2019-05-06 | 2019-09-03 | 东南大学 | A kind of single vector hydrophone signal arrival bearing's estimation method based on frequency estimation |
Non-Patent Citations (3)
| Title |
|---|
| 李世智 等: "基于基频检测和谐波识别的直升机探测技术", 《水雷战与舰船防护》 * |
| 王阳等: "基于二维频谱方法的直升机噪声源的分辨与提取", 《空气动力学学报》 * |
| 耿高营: "单矢量水听器多目标自主探测方法研究及GPU软件实现", 《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅱ辑》 * |
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