CN111024214B - Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process - Google Patents

Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process Download PDF

Info

Publication number
CN111024214B
CN111024214B CN201911355502.5A CN201911355502A CN111024214B CN 111024214 B CN111024214 B CN 111024214B CN 201911355502 A CN201911355502 A CN 201911355502A CN 111024214 B CN111024214 B CN 111024214B
Authority
CN
China
Prior art keywords
acoustic resonance
model
resonance mixer
modal
real
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201911355502.5A
Other languages
Chinese (zh)
Other versions
CN111024214A (en
Inventor
詹小斌
姜乾坤
李必然
李锡文
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huazhong University of Science and Technology
Original Assignee
Huazhong University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huazhong University of Science and Technology filed Critical Huazhong University of Science and Technology
Priority to CN201911355502.5A priority Critical patent/CN111024214B/en
Publication of CN111024214A publication Critical patent/CN111024214A/en
Application granted granted Critical
Publication of CN111024214B publication Critical patent/CN111024214B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H13/00—Measuring resonant frequency

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Apparatuses For Generation Of Mechanical Vibrations (AREA)

Abstract

The invention belongs to the field of multiphase flow mixing characteristics, and particularly discloses a method for acquiring natural frequency of an acoustic resonance mixer in real time in the operation process. The method comprises the following steps: acquiring real-time acceleration signals of a mixing container part of the acoustic resonance mixer and the number of rotating pulses of a motor of the acoustic resonance mixer so as to obtain displacement signals and exciting force; extracting m modal parameters of the frequency response function model according to the displacement signal and the frequency response function model, and outputting a curve graph of the frequency response function model; and constructing a modal parameter fitting model, randomly selecting m-1 modal parameters, inputting the m-1 modal parameters into the modal parameter fitting model to obtain a modal parameter fitting curve, carrying out variance processing on the modal parameter fitting curve and a curve graph of the frequency response function model, and carrying out false modal parameter elimination according to m-1 modal parameters in the modal parameter fitting curve with the minimum variance value so as to obtain real modal parameters. The calculated result obtained by the invention can truly reflect the natural frequency of the acoustic resonance mixer.

Description

Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process
Technical Field
The invention belongs to the field of multiphase flow mixing characteristics, and particularly relates to a method for acquiring natural frequency of an acoustic resonance mixer in real time in the operation process.
Background
Compared with the traditional mixer, the acoustic resonance mixer has the advantages of short mixing time, high efficiency, high safety and the like, and has more obvious advantages for high-viscosity materials, high-molecular-weight materials, high-value powder materials and dangerous materials. The acoustic resonance mixer mainly utilizes the characteristics of low power consumption and high mixing intensity when equipment runs at a resonance point, so that the identification of the resonance point is particularly important for the acoustic resonance mixer.
The identification of the natural frequency of the system by the existing acoustic resonance mixer is mainly realized by adopting the following two methods: the first method is that the system is swept in the starting stage of the equipment, the natural frequency of the system is identified, and then the natural frequency of the system is considered to be approximately kept unchanged in the running process and is used as the control parameter of the system; in the second method, the system is swept during the start-up phase of the plant, but during subsequent operation, the system is continuously adjusted with the aim of characterizing the system at the resonance point. In fact, during the mixing process, the damping of the material in the mixing pan changes, as well as the splashing of the material, etc., which causes the natural frequency of the system to change slightly at any moment. Especially when the material that becomes a ball splashes, the change of system natural frequency can produce comparatively obvious influence to equipment operation to lead to equipment unstable condition to appear in the operation process, this kind of condition appears when mixing comparatively violently and can cause very big damage and threaten operating personnel's personal safety even to equipment.
Therefore, there is a need in the art to provide a method for acquiring the natural frequency of the acoustic resonance mixer in real time, so that the calculated result can truly reflect the natural frequency of the acoustic resonance mixer, and further, the acoustic resonance mixer can be effectively controlled to control the equipment to operate according to the obtained natural frequency, and the purpose of maintaining the equipment to stably operate at the resonance point all the time is achieved.
Disclosure of Invention
In view of the above defects or improvement needs of the prior art, the present invention provides a method for acquiring the natural frequency of an acoustic resonance mixer in real time during the operation process, wherein the characteristics of the acoustic resonance mixer in the operation process and the characteristics of the real-time calculation method of the natural frequency thereof are combined, and the unstable conditions of the acoustic resonance mixer during the operation process caused by the natural frequency of the acoustic resonance mixer, the damping change of the materials in a mixing container, and the like are separated, i.e., the real mode and the false mode of the acoustic resonance mixer during the operation process are extracted, the false mode is eliminated, and the natural frequency of the acoustic resonance mixer is constructed and acquired according to the real mode. The invention can truly reflect the natural frequency of the acoustic resonance mixer according to the calculated result, and further can effectively control the acoustic resonance mixer to control the equipment to operate according to the obtained natural frequency, thereby achieving the purpose of maintaining the equipment to stably operate at the resonance point all the time.
In order to achieve the purpose, the invention provides a method for acquiring the natural frequency of an acoustic resonance mixer in real time in the operation process, which comprises the following steps:
s1, collecting real-time acceleration signals of a mixing container part of the acoustic resonance mixer and the number of rotating pulses of a motor of the acoustic resonance mixer in the running process of the acoustic resonance mixer;
s2, filtering and integrating the real-time acceleration signal of the mixing container part to obtain a displacement signal, and calculating the exciting force of the acoustic resonance mixer according to the phase difference of the motor and the pulse number;
s3, constructing a frequency response function model of the displacement signal and the exciting force according to the displacement signal and the exciting force, extracting m modal parameters of the frequency response function model, and outputting a curve graph of the frequency response function model;
s4, constructing a modal parameter fitting model, randomly selecting m-1 modal parameters to be input into the modal parameter fitting model to obtain a modal parameter fitting curve, and carrying out variance processing on the modal parameter fitting curve and a curve graph of the acoustic function model to obtain a variance value of the modal parameter fitting curve and the curve graph of the acoustic function model;
s5 repeating the step S4 until m modal parameters are traversed, so that m variance values are obtained, and the modal parameters which are not selected in the modal parameter fitting curve with the minimum variance value are removed;
s6, if m is equal to m-1, repeating steps S4 and S5 if m is greater than N, where N is the number of degrees of freedom in the operation of the acoustic resonance mixer, and obtaining N real modal parameters in the operation of the acoustic resonance mixer; and if m is equal to N, ending the iterative calculation, acquiring N real modal parameters in the running process of the acoustic resonance mixer, and then determining the natural frequency in the running process of the acoustic resonance mixer from the N real modal parameters according to the required frequency band.
As a further preferred, the filtering and integrating process for the real-time acceleration signal of the mixing container part in step S2 specifically includes the following steps:
performing low-pass filtering processing on the real-time acceleration signal of the mixing container part by adopting a first-order RC low-pass filtering model; then, a first-order RC high-pass filtering model is adopted to carry out high-pass filtering processing on the real-time acceleration signal after the low-pass filtering processing; then, integrating the real-time acceleration signal after the high-pass filtering processing to obtain a speed signal; and finally, processing the speed signal to obtain a displacement signal.
As a further preferred, the first-order RC low-pass filtering model is:
Y(n)＝a·X(n)+(1-a)·Y(n-1)
the first-order RC high-pass filtering model is as follows:
Y’(n)＝a·[X(n)-X(n-1)]+a·Y(n-1)
wherein, X (n) is a real-time acceleration signal; y (n-1) is the filter output value of the (n-1) th time; a is a filter coefficient; y (n) is the nth filtered output value.
Preferably, the step S3 of constructing a frequency response function model of the displacement signal and the excitation force according to the displacement signal and the excitation force specifically includes the following steps:
s311, calculating the self-power spectrum of the exciting force:
Figure GDA0002649964900000031
wherein G isFFIs the self-power spectrum of the exciting force; p is the number of the acquired real-time acceleration signals; fiDiscrete Fourier transform for the ith real-time excitation force;
Figure GDA0002649964900000032
is FiConjugation of (1);
s312, calculating the cross-power spectrum of the displacement signal:
Figure GDA0002649964900000041
wherein G isXFThe cross power spectrum of the displacement signal and the exciting force is obtained; xiDiscrete fourier transform for the ith displacement signal;
s313, constructing a frequency response function model of the displacement signal and the exciting force:
Figure GDA0002649964900000042
wherein H1The frequency response function model of the displacement signal and the exciting force is obtained.
Preferably, the step S3 of extracting m modal parameters of the frequency response function model specifically includes the following steps:
s321, constructing a dynamic characteristic model in the running process of the acoustic resonance mixer:
Figure GDA0002649964900000043
wherein f (t) is the N-dimensional force vector of the acoustic resonance mixer;
Figure GDA0002649964900000044
x is the N-dimensional acceleration, speed and displacement vector of the acoustic resonance mixer respectively; m, C, K are the mass matrix of the acoustic resonance mixer, the damping matrix of the acoustic resonance mixer and the stiffness matrix of the acoustic resonance mixer,
Figure GDA0002649964900000045
Figure GDA0002649964900000046
y(t)＝Qx(t)，
Figure GDA0002649964900000047
h (t) denotes NxNiAn impulse response matrix of the acoustic resonance mixer, N being the degree of freedom of the acoustic resonance mixer, NiThe number of input pulse numbers; u (t) is a variable matrix; y (t) is a displacement signal matrix; a is a state transition matrix; b is an exciting force coefficient matrix; q is a displacement signal coefficient matrix;
s322, constructing a transfer function matrix model of the acoustic resonance mixer:
H(s)＝C[sI-A]-1B
wherein, the variable of the s transfer function matrix model, I is a unit matrix;
s323, constructing a relation model of the displacement signal and the transfer function matrix model:
[s2I+sM-1C+M-1K]H(s)＝2M-1
s324, constructing a relation model of the transfer function of the acceleration and the force:
[s2I+sM-1C+M-1K]Ha(s)＝s2M-1-sM-1CM-1-M-1KM-1
wherein Ha(s) is a transfer function of acceleration and exciting force;
s325 construction of overdetermined equation set
Figure GDA0002649964900000051
And then solving the characteristic values and the characteristic vectors of the over-determined equation set according to the four models constructed in the steps S321 to S324, wherein the characteristic values and the characteristic vectors of the over-determined equation set are the extreme points and the m modal parameters of the frequency response function model.
More preferably, step S4 specifically includes the following steps:
s41, constructing a modal parameter fitting model in the running process of the N-degree-of-freedom acoustic resonance mixer:
H2＝H1(ω)+…+Hm-1(ω)
wherein H (omega) is a modal parameter fitting model in the running process of the acoustic resonance mixer with a certain degree of freedom,
Figure GDA0002649964900000052
x is a displacement signal; f is an exciting force; omega is a natural frequency; h1(ω) is the modal parameter during operation of the 1 st acoustic resonance mixer, Hm-1(omega) is a modal parameter in the operation process of the m-1 st acoustic resonance mixer;
s42 sequentially selecting m-1 modal parameters from m modal parameters, inputting the m-1 modal parameters into a modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, then carrying out curve fitting on the modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, and then solving the variance delta of curves of the modal parameter fitting model and the acoustic function model in the operation process of the N-DOF acoustic resonance mixer after curve fitting.
Further preferably, the calculation model of the variance Δ is:
Figure GDA0002649964900000053
in the formula, H1iAnd H2iThe values of the modal parameter fitting model and the frequency response function model in the operation process of the N-degree-of-freedom acoustic resonance mixer after curve fitting are respectively the values of the corresponding ordinate at the abscissa point i, N is the number of the abscissa points of the curve, and N is an integer greater than 1.
More preferably, in step S2, the calculation model of the excitation force is:
Figure GDA0002649964900000061
wherein, FCombination of Chinese herbsF is the centrifugal force generated by a single eccentric block of the motor; m is the mass of a single eccentric block of the motor; omega is the rotating speed of the eccentric block of the motor; r is the distance from the center of gravity of the eccentric block of the motor to the rotation center; t is the rotation time of the motor, thetaDifference (D)Is the phase difference of the eccentric masses, thetaAndis the phase sum of the eccentric mass.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. according to the invention, the real mode and the false mode can be distinguished according to the current collected signal, and the false mode is eliminated, so that the calculated result can truly reflect the natural frequency of the acoustic resonance mixer, the acoustic resonance mixer can be effectively controlled to control the equipment to operate according to the obtained natural frequency, and the purpose of maintaining the equipment to stably operate at the resonance point all the time is achieved.
2. The invention adopts signal processing modes such as filtering, integration and the like, can carry out denoising processing on the acquired original acceleration signal and process the original acceleration signal into a displacement signal. The method can obtain a smoother displacement signal oscillogram according to the collected original acceleration signals, reflect the real-time displacement condition of the system load end, and prepare for subsequent frequency response function calculation of the displacement signals and the exciting force.
3. The method can construct a frequency response function model of the displacement signal and the exciting force according to the displacement signal and the exciting force, solve the frequency response function, and solve m modal parameters of the system according to the solved frequency response function. Modal parameters of the system under different working states can be calculated in real time according to the displacement signals and the exciting force after the previous processing.
4. The method can remove the false modes of all the identified system mode parameters, and only keeps each real mode of the system. Then, the required modal parameter of the first order can be selected from the real modes according to the required frequency band, and the required system resonance frequency can be obtained.
Drawings
FIG. 1 is a flow chart of a method for real-time acquisition of natural frequencies during operation of an acoustic resonance mixer according to an embodiment of the present invention;
FIG. 2 is a flow chart of the elimination of spurious modes referred to in FIG. 1, resulting in system natural frequencies;
FIG. 3 is a signal transmission flow diagram of an acoustic resonance mixer according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an acoustic resonance mixer according to an embodiment of the present invention;
fig. 5 is a schematic diagram of an eccentric structure of a motor of an acoustic resonance mixer according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, fig. 2, fig. 3, fig. 4 and fig. 5, the method for acquiring the natural frequency of the acoustic resonance mixer in real time comprises the following steps:
s1 collects real time acceleration signals of the mixing vessel portion of the acoustic resonance mixer and the number of pulses of rotation of the motor of the acoustic resonance mixer during operation of the acoustic resonance mixer.
S2, filtering and integrating the real-time acceleration signal of the mixing container part to obtain a displacement signal, and calculating the exciting force of the acoustic resonance mixer according to the phase difference of the motor and the pulse number.
The filtering and integrating process of the real-time acceleration signal of the mixing container part specifically comprises the following steps: performing low-pass filtering processing on the real-time acceleration signal of the mixing container part by adopting a first-order RC low-pass filtering model; then, a first-order RC high-pass filtering model is adopted to carry out high-pass filtering processing on the real-time acceleration signal after the low-pass filtering processing; then, integrating the real-time acceleration signal after the high-pass filtering processing to obtain a speed signal; and finally, processing the speed signal to obtain a displacement signal.
Further, the first-order RC low-pass filtering model is:
Y(n)＝a·X(n)+(1-a)·Y(n-1)
the first-order RC high-pass filtering model is as follows:
Y’(n)＝a·[X(n)-X(n-1)]+a·Y(n-1)
wherein, X (n) is a real-time acceleration signal; y (n-1) is the filter output value of the (n-1) th time; a is a filter coefficient; y (n) is the nth filtered output value.
The calculation model of the exciting force is as follows:
Figure GDA0002649964900000081
wherein, FCombination of Chinese herbsF is the centrifugal force generated by a single eccentric block of the motor; m is the mass of a single eccentric block of the motor; omega is the rotating speed of the eccentric block of the motor; r is the distance from the center of gravity of the eccentric block of the motor to the rotation center; t is the rotation time of the motor, thetaDifference (D)Is the phase difference of the eccentric masses, thetaAndis the phase sum of the eccentric mass.
S3, constructing a frequency response function model of the displacement signal and the exciting force according to the displacement signal and the exciting force, extracting m modal parameters of the frequency response function model, and outputting a curve graph of the frequency response function model.
In step S3, constructing a frequency response function model of the displacement signal and the excitation force according to the displacement signal and the excitation force specifically includes the following steps:
s311, calculating the self-power spectrum of the exciting force:
Figure GDA0002649964900000082
wherein G isFFIs the self-power spectrum of the exciting force; p is the number of the acquired real-time acceleration signals; fiDiscrete Fourier transform for the ith real-time excitation force;
Figure GDA0002649964900000083
is FiConjugation of (1);
s312, calculating the cross-power spectrum of the displacement signal:
Figure GDA0002649964900000084
wherein G isXFA cross-power spectrum of the displacement signal and the excitation force; xiDiscrete Fourier transform of the displacement signal of the ith measuring point;
s313, constructing a frequency response function model of the displacement signal and the exciting force:
Figure GDA0002649964900000091
wherein H1The frequency response function model of the displacement signal and the exciting force is obtained.
The method for extracting the m modal parameters of the frequency response function model specifically comprises the following steps:
s321, constructing a dynamic characteristic model in the running process of the acoustic resonance mixer:
Figure GDA0002649964900000092
wherein f (t) is the N-dimensional force vector of the acoustic resonance mixer;
Figure GDA0002649964900000093
x is the N-dimensional acceleration, speed and displacement vector of the acoustic resonance mixer respectively; m, C, K are the mass matrix of the acoustic resonance mixer, the damping matrix of the acoustic resonance mixer and the stiffness matrix of the acoustic resonance mixer,
Figure GDA0002649964900000094
Figure GDA0002649964900000095
y(t)＝Qx(t)，
Figure GDA0002649964900000096
h (t) denotes NxNiAn impulse response matrix of the acoustic resonance mixer, N being the degree of freedom of the acoustic resonance mixer, NiThe number of input pulse numbers; u (t) is a variable matrix; y (t) is a displacement signal matrix; a is a state transition matrix; b is an exciting force coefficient matrix; q is a displacement signal coefficient matrix;
s322, constructing a transfer function matrix model of the acoustic resonance mixer:
H(s)＝C[sI-A]-1B
wherein s is a variable of a transfer function matrix model and is generally expressed by s, and I is a unit matrix;
s323, constructing a relation model of the displacement signal and the transfer function matrix model:
[s2I+sM-1C+M-1K]H(s)＝2M-1
s324, constructing a relation model of the transfer function of the acceleration and the force:
[s2I+sM-1C+M-1K]Ha(s)＝s2M-1-sM-1CM-1-M-1KM-1
wherein Ha(s) is a transfer function of acceleration and exciting force;
s325 construction of overdetermined equation set
Figure GDA0002649964900000097
And then solving the characteristic values and the characteristic vectors of the over-determined equation set according to the four models constructed in the steps S321 to S324, wherein the characteristic values and the characteristic vectors of the over-determined equation set are the extreme points and the m modal parameters of the frequency response function model.
S4, a modal parameter fitting model is constructed, m-1 modal parameters are selected randomly and input into the modal parameter fitting model to obtain a modal parameter fitting curve, and variance processing is carried out on the modal parameter fitting curve and a curve graph of the acoustic function model to obtain a variance value of the modal parameter fitting curve and the curve graph of the acoustic function model.
Step S4 specifically includes the following steps:
s41, constructing a modal parameter fitting model in the running process of the N-degree-of-freedom acoustic resonance mixer:
H2＝H1(ω)+…+Hm-1(ω)
wherein H (omega) is a modal parameter fitting model in the running process of the acoustic resonance mixer with a certain degree of freedom,
Figure GDA0002649964900000101
x is a displacement signal; f is an exciting force; omega is a natural frequency; h1(ω) is the modal parameter during operation of the 1 st acoustic resonance mixer, Hm-1(omega) is a modal parameter in the operation process of the m-1 st acoustic resonance mixer;
s42 sequentially selecting m-1 modal parameters from m modal parameters, inputting the m-1 modal parameters into a modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, then carrying out curve fitting on the modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, and then solving the variance delta of curves of the modal parameter fitting model and the acoustic function model in the operation process of the N-DOF acoustic resonance mixer after curve fitting.
The calculation model of the variance Δ is:
Figure GDA0002649964900000102
in the formula, H1iAnd H2iThe values of the modal parameter fitting model and the frequency response function model in the operation process of the N-degree-of-freedom acoustic resonance mixer after curve fitting are respectively the values of the corresponding ordinate at the abscissa point i, N is the number of the abscissa points of the curve, and N is an integer greater than 1.
S5 repeating the step S4 until m modal parameters are traversed, so that m variance values are obtained, and the modal parameters which are not selected in the modal parameter fitting curve with the minimum variance value are removed;
s6, if m is equal to m-1, repeating steps S4 and S5 if m is greater than N, where N is the number of degrees of freedom in the operation of the acoustic resonance mixer, and obtaining N real modal parameters in the operation of the acoustic resonance mixer; and if m is equal to N, ending the iterative calculation, acquiring N real modal parameters in the running process of the acoustic resonance mixer, and then determining the natural frequency in the running process of the acoustic resonance mixer from the N real modal parameters according to the required frequency band.
Example 1
As shown in fig. 2 and 4, the acoustic resonance mixer according to the embodiment of the present invention includes: the device comprises a load end 1, an acceleration sensor 2, a motor 3, an encoder 4 and an industrial personal computer 5, wherein the industrial personal computer 5 is respectively connected with the acceleration sensor 2 and the encoder 4, the load end 1 is a part where a mixing container is located, and real-time acceleration at the part needs to be acquired; the acceleration sensor 2 is used for acquiring the acceleration of the load end and transmitting data to the industrial personal computer; the motor 3 is a power source of the whole acoustic resonance mixer, and the whole mixing process is controlled according to the rotating speed and the phase difference of the motor; the encoder 4 is used for acquiring the number of pulses of the rotation of the motor and transmitting data to the industrial personal computer 5; and the industrial personal computer 5 analyzes and processes the acceleration signal acquired by the acceleration sensor 2 and the pulse number acquired by the encoder 4, and finally calculates the natural frequency of the acoustic resonance mixer.
The method for calculating the natural frequency in the running process of the acoustic resonance mixer provided by the embodiment of the invention can calculate the natural frequency in the running process of the acoustic resonance mixer in real time according to the currently acquired real-time acceleration signal of the mixing container part of the acoustic resonance mixer and the rotating pulse number of the motor of the acoustic resonance mixer, and further control the acoustic resonance mixer to run according to the obtained natural frequency control equipment, thereby achieving the purpose of maintaining the stable running of the acoustic resonance mixer at the resonance point all the time. In the implementation, after the original data and the signals are collected, the subsequent analysis and processing are all completed in the industrial personal computer. In the implementation, the acceleration signal acquired by the acceleration sensor is an analog quantity, and can be processed continuously only by performing analog-to-digital conversion and converting the analog quantity into a digital quantity; the number of pulses collected by the encoder is itself a digital quantity and does not need to be converted.
The process of analyzing and processing the original data of the acoustic resonance mixer in the embodiment of the invention specifically comprises the following steps:
step 6, filtering and integrating the collected acceleration signals to obtain speed signals;
step 7, filtering and integrating the speed signal to obtain a displacement signal;
step 8, calculating an exciting force;
step 9, calculating a Frequency Response Function (FRF) of the displacement signal and the exciting force;
step 10, extracting modal parameters;
and 11, eliminating false modes to obtain the natural frequency of the system.
In step 6, the output of the acceleration sensor has a fixed zero drift, that is, when the acceleration is 0, the output of the sensor is not necessarily 0, and an accumulated error is generated by directly integrating the output of the acceleration sensor; and high-frequency noise may exist in the original acceleration signal collected by the acceleration sensor, so that the original acceleration signal needs to be filtered. To eliminate the effect of high frequency noise, a low pass filter may be added, with a cut-off frequency higher than the natural frequency of the system. Typically the operating frequency of an acoustic resonant mixer is 50-70Hz, while the frequency of high frequency noise is greater than a few thousand Hz.
The first order RC low pass filtering algorithm is as follows:
Y(n)＝a·X(n)+(1-a)·Y(n-1)
wherein, X (n) is the sampling value of the current signal; y (n-1) is the last filtering output value; a is a filter coefficient, which is typically much smaller than 1; y (n) is the output value of this filtering.
In order to eliminate the influence of zero drift, a high-pass filter can be added, and the cut-off frequency is set to be slightly larger than 0.
The first order RC high pass filter algorithm is as follows:
Y(n)＝a·(X(n)-X(n-1))+a·Y(n-1)
after the filtering of the original acceleration signal is finished, the original acceleration signal can be integrated to obtain a speed signal.
In step 7, it is necessary to perform the same filtering process as in step 6 on the velocity signal, and then integrate the velocity signal to obtain a displacement signal. This displacement signal is used as a response signal in the calculation of the frequency response function in step 9.
In step 8, the acoustic resonance mixer generates exciting force in various ways, such as an electromagnetic driving way and a motor driving way. The embodiment of the invention adopts a motor driving mode, and four servo driving motors are used for driving four eccentric blocks to generate exciting force. The method for calculating the exciting force comprises the following steps: the number of pulses related to the rotation of the motor is collected by the encoder, the phase difference of the motor is calculated, the phase difference is the phase difference of the eccentric block, and the exciting force is obtained according to the phase difference.
The method for calculating the exciting force specifically comprises the following steps: as shown in FIG. 5, a, b, c and d are eccentric masses connected with four servo driving motors, and the rotating speeds of the eccentric masses are all omega, wherein the rotating directions of a and d are opposite, and the rotating directions of b and c are opposite. Fa，Fb，Fc，FdCentrifugal forces, F, produced by eccentric masses a, b, c, d, respectivelyCombination of Chinese herbsThe resultant force of the four centrifugal forces is the exciting force generated by the acoustic resonance mixer. To calculate the excitation force, the phase of the eccentric mass is first determined. Wherein, the phase calculation formula of the eccentric block is as follows:
Figure GDA0002649964900000131
in the formula, theta is the actual phase of the eccentric block; theta0Calibrating the initial phase of the eccentric block before the equipment works; n ismThe total pulse number collected by the encoder for the motor connected with the eccentric block; n is0The number of pulses collected by the encoder is one circle of the motor rotation.
Let θDifference (D)The phase difference of the eccentric blocks a and c is also the phase difference of the eccentric blocks b and d; thetaAndis the phase sum of the eccentric masses a and c, and is also the phase sum of the eccentric masses b and d. ThetaDifference (D)And thetaAndthe calculation method comprises the following steps: (taking eccentric blocks a and c as examples)
θDifference (D)＝θa-θc
θAnd＝θa+θc
in the formula, thetaaIs the actual phase of the eccentric mass a; thetacIs the actual phase of the eccentric mass c.
FCombination of Chinese herbsThe calculation formula of (2) is as follows:
F＝mω2r
Figure GDA0002649964900000132
wherein F is the centrifugal force generated by a single eccentric block; m is the mass of a single eccentric block; omega is the rotating speed of the eccentric block; r is the distance from the gravity center of the eccentric block to the rotation center; fCombination of Chinese herbsIs an exciting force; t is the rotation time of the motor.
Of course, the calculation process is only the excitation force calculation method adopting the motor-eccentric block driving mode, and other different driving modes can also adopt different algorithms to calculate the excitation force. This excitation force is used as an input signal in the calculation of the frequency response function in step 9.
In step 9, the method for calculating the frequency response function of the input and output signals is specifically as follows: in the system, the output signal (namely, the displacement signal) is calculated by the original signal collected by the acceleration sensor, and the noise is large; the input signal (i.e. the excitation force signal) is calculated from the original signal collected by the encoder, and is less affected by noise, so the H1 estimation of the frequency response function is used here. The specific calculation process is as follows:
calculating the self-power spectrum of the input signal:
Figure GDA0002649964900000141
in the formula, GFFIs the self-power spectrum of the input signal; n is the number of the sampling signal measuring points; fiDiscrete Fourier transform of the input signal of the ith measuring point;
Figure GDA0002649964900000142
is FiConjugation of (1).
Calculating the cross-power spectrum of the input and the output:
Figure GDA0002649964900000143
in the formula, GXFInputting and outputting a cross-power spectrum; xiDiscrete Fourier transform of output signal of ith measuring point.
The calculation formula of the frequency response function FRF is:
Figure GDA0002649964900000144
in step 10, modal parameters are determined from the frequency response function, requiring the use of a modal parameter extraction algorithm. The modal parameter extraction algorithm includes various algorithms, such as frequency domain polynomial fitting method (FDPI), overall orthogonal polynomial fitting method (FPDI), and least squares complex exponential method (LSCE). The embodiment of the invention selects a frequency domain polynomial fitting method (FDPI) to identify the modal parameters of the system. FDPI is an identification method based on a low-order frequency response function model, and the method is suitable for estimating a large attenuation mode, and is particularly suitable for finding out the large attenuation mode in a narrow frequency band. The FDPI method is applied to identify the modal parameters of the system and comprises the following steps:
firstly, estimating a structural matrix;
calculating extreme points and modal parameters of the structure according to the system model;
and constructing a complete model of the system by using a reduced data technology.
The specific implementation process of the method is as follows:
the dynamic behavior of a structure can be generally expressed in the form of an N-th order matrix differential equation:
Figure GDA0002649964900000151
wherein f (t) is an N-dimensional force vector;
Figure GDA0002649964900000152
x is N-dimensional acceleration, speed and displacement vector respectively; m, C, K are the mass matrix, damping matrix and stiffness matrix of the system structure, respectively.
The following equation is used to derive equation (1):
Figure GDA0002649964900000153
y(t)＝Qx(t) (3)
in the above formula
Figure GDA0002649964900000154
h (t) denotes NxNiAn impulse response matrix, N being the system degree of freedom, NiThe number of input pulses; u (t) is an input variable matrix (from Di)A rake pulse matrix); y (t) is a defined output matrix; a is a state transition matrix; b is an input matrix; q is the output matrix.
The general equation for the transfer function matrix can then be found:
H(s)＝C[sI-A]-1B (4)
and according to the relation of the transfer function of the displacement and the force:
[s2I+sM-1C+M-1K]H(s)＝2M-1 (5)
the relationship of the acceleration to the transfer function of force is:
[s2I+sM-1C+M-1K]Ha(s)＝s2M-1-sM-1CM-1-M-1KM-1 (6)
in equations (5) and (6), all s are true, so that if the measurement data is sufficient, either of the two equations above can be constructed with respect to matrix M-1C、M-1K and M-1An overdetermined system of equations.
The essence of the state transition matrix a is:
Figure GDA0002649964900000155
and calculating the eigenvalue and the eigenvector of the matrix A to obtain the extreme point and the modal vector of the tested system.
In step 10, since the modal parameters of the acoustic resonance mixer generally have multiple stages, and all real modes of the system are generally subjected to the order expansion processing, a false mode is introduced, and the modal parameters of the stage which contributes most to the system resonance mixing are required in the invention, so that the extracted modal parameters need to be removed.
In step 11, the modal parameters extracted in step 10 need to be removed to obtain the required modal parameters, i.e. the natural frequency of the system.
Fig. 5 shows a specific implementation flow of step 11, which is specifically as follows:
step 12, identifying m modes including false modes;
step 13, removing one of the m identified modal parameters, wherein m is m-1;
step 14, judging whether m is equal to N (m is greater than N, N is the degree of freedom of the system and is the order of the real mode of the system), if not, returning to step 13, and if yes, jumping to step 15;
and step 15, obtaining the required natural frequency.
Step 13 is a key step of eliminating false modes, and iteration is needed for m-N times in total. In the step, frequency response function simulation calculation is carried out by utilizing the identified different modal parameters to obtain a simulation curve, and then the simulation curve is fitted with the frequency response function (H) obtained by the original data1) And comparing the curves, wherein the simulation result containing more real modes is closer to the frequency response function fitting curve of the original data than the simulation result containing more false modes. I.e. true modes contribute more to the fitting result of the simulation curve than spurious modes. The specific iteration strategy is as follows: each iteration rejects one spurious mode, the mode of the order that contributes least to the curve fit.
Step 13 is implemented specifically as follows: sequentially selecting m-1 modal parameters from the m identified modal parameters, namely sequentially removing one modal parameter, carrying out simulation calculation on a frequency response function, then subtracting an actually measured curve (a frequency response function curve of an input signal and a response signal), calculating the variance of the actually measured curve, and carrying out m times in total. And comparing the variances to extract the group with the minimum variance, namely rejecting the mode with the minimum contribution to the fitted curve. There are m-1 of the m identified modal parameters remaining at this time.
Step 13 may specifically be: and sequentially selecting m-1 modal parameters from the m identified modal parameters, and simulating and calculating a frequency response function by using the m-1 modal parameters. The frequency response function of the single-degree-of-freedom system (i.e. with only first-order modal parameters) has various expressions, and the following expressions are adopted here:
Figure GDA0002649964900000171
wherein X is a response signal (i.e., a displacement signal); f is the input signal (i.e., the excitation force signal); ω is the natural frequency.
And the frequency response function of the N-degree-of-freedom system (with N-order modal parameters) is linear superposition of frequency response functions of various orders of modes.
H2＝H1(ω)+…+Hm-1(ω) (8)
Can obtain the linear superposition H of m-1H (omega)2I.e. the frequency response function under the m-1 modal parameters, and then the function is subjected to curve fitting. Respectively discretizing frequency response function fitting curves under m-1 modal parameters and the frequency response function fitting curves of the original data.
The deviation degree of the frequency response function of m-1 modal parameters from the frequency response function of the original data is represented by delta.
Figure GDA0002649964900000172
In the formula, H1iAnd H2iAre respectively represented by H1And H2Discretizing the ith function value.
M-1 of the m identified modal parameters are selected in sequence, and m different combinations are total. The process is carried out m times to obtain delta1,Δ2，…，ΔmAnd comparing the m deltas, and selecting the minimum value, wherein the m-1 modal parameter corresponding to the delta is the modal parameter combination closest to the real mode.
In step 15, the real modal parameters of N (N is the degree of freedom of the acoustic resonance mixer) systems are obtained, and the required modal parameters can be obtained by selecting a first-order modal parameter according to the required frequency band, where the obtained modal parameters include a natural frequency and a damping ratio, and the natural frequency is the required natural frequency.
The real-time calculation method for the natural frequency in the operation process of the acoustic resonance mixer, provided by the embodiment of the application, can calculate the natural frequency of the system in real time according to the current collected signal, further control the system to control the equipment to operate according to the obtained natural frequency, and achieve the purpose of maintaining the equipment to operate stably at the resonance point all the time.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A method for acquiring natural frequency in the operation process of an acoustic resonance mixer in real time is characterized by comprising the following steps:
s1, collecting real-time acceleration signals of a mixing container part of the acoustic resonance mixer and the number of rotating pulses of a motor of the acoustic resonance mixer in the running process of the acoustic resonance mixer;
s2, filtering and integrating the real-time acceleration signal of the mixing container part to obtain a displacement signal, and calculating the exciting force of the acoustic resonance mixer according to the phase difference of the motor and the pulse number;
s3, constructing a frequency response function model of the displacement signal and the exciting force according to the displacement signal and the exciting force, extracting m modal parameters of the frequency response function model, and outputting a curve graph of the frequency response function model;
s4, constructing a modal parameter fitting model, randomly selecting m-1 modal parameters to be input into the modal parameter fitting model to obtain a modal parameter fitting curve, and carrying out variance processing on the modal parameter fitting curve and a curve graph of the acoustic function model to obtain a variance value of the modal parameter fitting curve and the curve graph of the acoustic function model;
s5 repeating the step S4 until m modal parameters are traversed, so that m variance values are obtained, and the modal parameters which are not selected in the modal parameter fitting curve with the minimum variance value are removed;
s6, if m is equal to m-1, repeating steps S4 and S5 if m is greater than N, where N is the number of degrees of freedom in the operation of the acoustic resonance mixer, and obtaining N real modal parameters in the operation of the acoustic resonance mixer; and if m is equal to N, ending the iterative calculation, acquiring N real modal parameters in the running process of the acoustic resonance mixer, and then determining the natural frequency in the running process of the acoustic resonance mixer from the N real modal parameters according to the required frequency band.
2. The method for acquiring the natural frequency of the acoustic resonance mixer in real time as claimed in claim 1, wherein the step S2 of filtering and integrating the real-time acceleration signal of the mixing container part specifically comprises the following steps:
performing low-pass filtering processing on the real-time acceleration signal of the mixing container part by adopting a first-order RC low-pass filtering model; then, a first-order RC high-pass filtering model is adopted to carry out high-pass filtering processing on the real-time acceleration signal after the low-pass filtering processing; then, integrating the real-time acceleration signal after the high-pass filtering processing to obtain a speed signal; and finally, processing the speed signal to obtain a displacement signal.
3. The method for acquiring the natural frequency of the acoustic resonance mixer in real time according to claim 2, wherein the first-order RC low-pass filtering model is as follows:
Y(n)＝a·X(n)+(1-a)·Y(n-1)
the first-order RC high-pass filtering model is as follows:
Y’(n)＝a·[X(n)-X(n-1)]+a·Y(n-1)
wherein, X (n) is a real-time acceleration signal; y (n-1) is the filter output value of the (n-1) th time; a is a filter coefficient; y (n) is the nth filtered output value.
4. The method for acquiring the natural frequency of the acoustic resonance mixer in the operation process in real time according to claim 1, wherein the step S3 of constructing the frequency response function model of the displacement signal and the exciting force according to the displacement signal and the exciting force specifically comprises the following steps:
s311, calculating the self-power spectrum of the exciting force:
Figure FDA0002680710220000021
wherein G isFFIs the self-power spectrum of the exciting force; p is the number of the acquired real-time acceleration signals; fiDiscrete Fourier transform for the ith real-time excitation force;
Figure FDA0002680710220000022
is FiConjugation of (1);
s312, calculating the cross-power spectrum of the displacement signal:
Figure FDA0002680710220000023
wherein G isXFThe cross power spectrum of the displacement signal and the exciting force is obtained; xiDiscrete fourier transform for the ith displacement signal;
s313, constructing a frequency response function model of the displacement signal and the exciting force:
Figure FDA0002680710220000031
wherein H1The frequency response function model of the displacement signal and the exciting force is obtained.
5. The method of claim 1, wherein the step S3 of extracting m modal parameters of the frequency response function model specifically includes the steps of:
s321, constructing a dynamic characteristic model in the running process of the acoustic resonance mixer:
Figure FDA0002680710220000032
wherein f (t) is the N-dimensional force vector of the acoustic resonance mixer;
Figure FDA0002680710220000033
x is the N-dimensional acceleration, speed and displacement vector of the acoustic resonance mixer respectively; m, C, K are the mass matrix of the acoustic resonance mixer, the damping matrix of the acoustic resonance mixer and the stiffness matrix of the acoustic resonance mixer,
Figure FDA0002680710220000034
Figure FDA0002680710220000035
y(t)＝Qx(t)，
Figure FDA0002680710220000036
h (t) denotes NxNiAn impulse response matrix of the acoustic resonance mixer, N being the degree of freedom of the acoustic resonance mixer, NiThe number of input pulse numbers; u (t) is a variable matrix; y (t) is a displacement signal matrix; a is a state transition matrix; b is an exciting force coefficient matrix; q is a displacement signal coefficient matrix;
s322, constructing a transfer function matrix model of the acoustic resonance mixer:
H(s)＝C[sI-A]-1B
wherein, the variable of the s transfer function matrix model, I is a unit matrix;
s323, constructing a relation model of the displacement signal and the transfer function matrix model:
[s2I+sM-1C+M-1K]H(s)＝2M-1
s324, constructing a relation model of the transfer function of the acceleration and the force:
[s2I+sM-1C+M-1K]Ha(s)＝s2M-1-sM-1CM-1-M-1KM-1
wherein Ha(s) is a transfer function of acceleration and exciting force;
s325 construction of overdetermined equation set
Figure FDA0002680710220000037
And then solving the characteristic values and the characteristic vectors of the over-determined equation set according to the four models constructed in the steps S321 to S324, wherein the characteristic values and the characteristic vectors of the over-determined equation set are the extreme points and the m modal parameters of the frequency response function model.
6. The method for acquiring the natural frequency of the acoustic resonance mixer in real time according to claim 1, wherein the step S4 specifically comprises the following steps:
s41, constructing a modal parameter fitting model in the running process of the N-degree-of-freedom acoustic resonance mixer:
H2＝H1(ω)+…+Hm-1(ω)
wherein H2As a frequency response function of an N degree-of-freedom system, H1(ω)、……、Hm-1(omega) is a frequency response function under each order of mode;
s42 sequentially selecting m-1 modal parameters from m modal parameters, inputting the m-1 modal parameters into a modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, then carrying out curve fitting on the modal parameter fitting model in the operation process of the N-DOF acoustic resonance mixer, and then solving the variance delta of curves of the modal parameter fitting model and the acoustic function model in the operation process of the N-DOF acoustic resonance mixer after curve fitting.
7. The method for acquiring the natural frequency of the acoustic resonance mixer in real time according to claim 6, wherein the calculation model of the variance Δ is as follows:
Figure FDA0002680710220000041
in the formula, H1iAnd H2iThe values of the modal parameter fitting model and the frequency response function model in the operation process of the N-degree-of-freedom acoustic resonance mixer after curve fitting are respectively the values of the corresponding ordinate at the abscissa point i, and N is the value of the abscissa point of the curveNumber, n is an integer greater than 1.
8. The method for acquiring the natural frequency of the acoustic resonance mixer in real time as claimed in claim 1, wherein in step S2, the calculation model of the exciting force is:
Figure FDA0002680710220000042
wherein, FCombination of Chinese herbsF is the centrifugal force generated by a single eccentric block of the motor; m is the mass of a single eccentric block of the motor; omega is the rotating speed of the eccentric block of the motor; r is the distance from the center of gravity of the eccentric block of the motor to the rotation center; t is the rotation time of the motor, thetaDifference (D)Is the phase difference of the eccentric masses, thetaAndis the phase sum of the eccentric mass.
CN201911355502.5A 2019-12-25 2019-12-25 Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process Active CN111024214B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911355502.5A CN111024214B (en) 2019-12-25 2019-12-25 Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911355502.5A CN111024214B (en) 2019-12-25 2019-12-25 Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process

Publications (2)

Publication Number Publication Date
CN111024214A CN111024214A (en) 2020-04-17
CN111024214B true CN111024214B (en) 2020-11-24

Family

ID=70214750

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911355502.5A Active CN111024214B (en) 2019-12-25 2019-12-25 Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process

Country Status (1)

Country Link
CN (1) CN111024214B (en)

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112729736B (en) * 2020-12-18 2022-11-08 中国工程物理研究院总体工程研究所 Double-station parallel-pushing synchronization real-time representation identification and protection method
CN113144997B (en) * 2021-03-23 2022-10-25 西安近代化学研究所 Method and system for determining critical fluctuation rate and judging mixing uniformity in resonant sound mixing
CN112862825A (en) * 2021-04-23 2021-05-28 中船重工（上海）新能源有限公司 Method for detecting natural frequency of gas column of compressor pipeline
CN113731279B (en) * 2021-08-31 2022-09-27 华中科技大学 Online evaluation method and equipment for mixing state in acoustic resonance mixing process

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103473468A (en) * 2013-09-23 2013-12-25 中国海洋大学 False identifying method for modal parameter of ocean structure
CN104133950A (en) * 2014-07-17 2014-11-05 浙江工业大学 Cantilever beam operational modal analysis experiment method and cantilever beam operational modal analysis experiment device
CN106441759A (en) * 2016-09-06 2017-02-22 东南大学 Bridge rapid test device and method based on microwave radar and mobile loading vehicle

Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2011250035A (en) * 2010-05-25 2011-12-08 Sony Corp Receiving apparatus, receiving method, program, and reception system
CN101949731B (en) * 2010-08-13 2011-12-14 株洲时代新材料科技股份有限公司 Method for testing high-order frequency of large wind-power blades
CN102222136B (en) * 2011-05-26 2013-05-22 西安交通大学 ARMA (Autoregressive Moving Average) model order determination method based on steady state graph
CN104239681B (en) * 2014-07-17 2018-04-20 浙江工业大学 Axis system operational modal analysis method based on pulse excitation response signal crosspower spectrum function
KR20180013631A (en) * 2016-07-29 2018-02-07 삼익키리우(주) Quality Inspection Method of Brake Disk Using Natural Frequency
CN106706285B (en) * 2016-11-24 2018-12-28 重庆工业职业技术学院 A kind of brake disc intrinsic frequency online test method
CN108416141A (en) * 2017-08-31 2018-08-17 北京理工大学 A kind of linear time-varying structural modal vibration shape discrimination method
CN107991080A (en) * 2017-12-05 2018-05-04 中国人民解放军总参谋部第六十研究所 A kind of high frequency Modal Analysis on Blade method based on non-contact vibration measuring and simulation calculation
CN108459631B (en) * 2018-04-13 2019-08-30 华中科技大学 A kind of acoustic resonance hybrid control system
CN109598027B (en) * 2018-11-08 2022-04-19 合肥工业大学 Method for correcting structural model parameters based on frequency response function

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103473468A (en) * 2013-09-23 2013-12-25 中国海洋大学 False identifying method for modal parameter of ocean structure
CN104133950A (en) * 2014-07-17 2014-11-05 浙江工业大学 Cantilever beam operational modal analysis experiment method and cantilever beam operational modal analysis experiment device
CN106441759A (en) * 2016-09-06 2017-02-22 东南大学 Bridge rapid test device and method based on microwave radar and mobile loading vehicle

Also Published As

Publication number Publication date
CN111024214A (en) 2020-04-17

Similar Documents

Publication Publication Date Title
CN111024214B (en) Method for acquiring natural frequency of acoustic resonance mixer in real time in operation process
Batel Operational modal analysis-another way of doing modal testing
JP4994448B2 (en) Modal parameter estimation method and apparatus
JP5480255B2 (en) Method and apparatus for frequency analysis of data
DK2085902T3 (en) Order tracking method and system
CN107167306B (en) Order extraction-based rotating machine rotor running state modal analysis method
CN112798280A (en) Rolling bearing fault diagnosis method and system
Dai et al. Fault diagnosis of rotating machinery based on deep reinforcement learning and reciprocal of smoothness index
Diao et al. Analysis and compensation of MEMS gyroscope drift
Henry et al. The Prism: efficient signal processing for the internet of things
CN110705041B (en) EASI-based linear structure working modal parameter identification method
Cao et al. A New Joint Denoising Algorithm for High‐G Calibration of MEMS Accelerometer Based on VMD‐PE‐Wavelet Threshold
CN111766574B (en) Middle section group target translation compensation method based on cubic phase function
CN107122724A (en) A kind of method of the online denoising of sensing data based on adaptive-filtering
CN111125613A (en) Method for improving noise-resistant capacity of Duffing chaotic oscillator for detecting weak resonant signal
CN110782041A (en) Structural modal parameter identification method based on machine learning
Persson Event based sampling with application to spectral estimation
CN116317781A (en) Unbalanced vibration control method and device for coaxial double-rotor system based on micro speed difference
CN114838924A (en) Structural damping ratio identification method based on wind-induced vibration non-stationary response
CN103134947A (en) Aero-engine body vibration gross speed effective value numerical computation method
RU2365981C1 (en) Method and device for spectral time analysis of non-stationary signals
Qian et al. On modeling of random drift of MEMS gyroscope and design of Kalman filter
JP2958568B2 (en) Signal analysis method using Walsh transform
Jan et al. Tracking Filter Design for Predictive Maintenance of Jet Engine–Different Approaches and their Comparison
CN110308300B (en) Rotating speed measuring method and device fusing multiple characteristic data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant