CN106971706B - Noise active control method based on generalized Lorentz-like system - Google Patents
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Abstract
The invention provides a noise active control method based on a generalized Lorentz-like system, which aims at the problem of the inhibition of sound wave energy of ship radiation noise, adopts a classical Lorentz system, adds a time lag feedback control quantity and external excitation to the system, and obtains the control effect on noise by using a chaotic dynamics judgment method. For the deformed generalized Lorentz-like system, Matlab programming is utilized to observe the output dynamic characteristics of the generalized Lorentz-like system, the dynamic characteristics comprise a phase locus diagram, a bifurcation diagram and a Lyapunov exponent diagram, an external excitation amplitude parameter, a frequency parameter and a corresponding parameter range of the system output in a periodic motion state, a quasi-periodic motion state or a chaotic motion state are given, a noise source energy value and an energy change value under the fixed frequency before and after the active sound source is applied are given by utilizing a frequency spectrum curve, and the noise suppression effect under the action of different sound sources is determined.
Description
Technical Field
The invention relates to a noise processing technology, in particular to a noise active control method based on a generalized Lorentz-like system.
Background
Ship sound stealth is always the most concerned problem in the field of marine military, and ship radiation noise is the main observation means for enemy detection targets, and the noise mainly comes from mechanical noise, propulsion system noise, hydrodynamic noise and the like. The radiation noise of ships is mainly low-frequency noise, the wavelength of the low-frequency noise is longer, the vibration and noise reduction is carried out by passive control methods such as floating rafts, flexible hoses, silencers, pump jet propulsion, electric propulsion, air curtain noise reduction, noise reduction tiles and the like at first, the passive noise control method for the low-frequency noise has obvious defects, and the active noise control method for the 20 th century and the 30 th century solves the problem. A great deal of research begins to apply the active noise control method to the sound stealth of ships, and various active vibration absorption technologies and vibration isolation technologies are developed. Ship radiated noise is a typical nonlinear non-stationary random signal, so many conventional analysis methods are greatly limited in processing such signals. With the development of chaotic dynamics, researchers find that ship radiation noise has a chaotic phenomenon, so that people begin to research the problem of ship radiation noise by using a chaotic analysis method. At present, a chaotic dynamics method is used for analyzing the problem of ship noise, for example, a chaotic oscillator theory is adopted to detect a ship signal with a low signal-to-noise ratio; phase space reconstruction is carried out on the basis of nonlinear local projection filtering, and target identification can be realized through natural measure and correlation dimension verification; the ship target identification is realized by extracting the chaotic characteristic of the correlation dimension.
However, the existing acoustic energy suppression technology for ship radiation noise signals is not mature, and the suppression effect of the prior art is poor.
Disclosure of Invention
The following presents a simplified summary of the invention in order to provide a basic understanding of some aspects of the invention. It should be understood that this summary is not an exhaustive overview of the invention. It is not intended to determine the key or critical elements of the present invention, nor is it intended to limit the scope of the present invention. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later.
In view of this, the invention provides a noise active control method based on a generalized lorentz-like system, so as to at least solve the problems that the existing acoustic energy suppression technology for ship radiation noise signals is not mature and the suppression effect is poor.
According to an aspect of the present invention, there is provided a noise active control method based on a generalized lorentz-like system, the noise active control method based on the generalized lorentz-like system including: the method comprises the following steps of firstly, giving expansion and non-compressibility conditions of a speed field and a temperature field by using a first equation set, wherein the first equation set comprises the following steps:
where u-u (x, y, z) represents the fluid velocity field, x represents the velocity mode, y represents the temperature mode, z represents the temperature gradient mode, and the temperature field is represented by T-T (x, y, z); epsilon is thermal expansion coefficient, g is gravity acceleration, rho is fluid density, P is fluid pressure field, nu is fluid viscosity coefficient, and k is heat conduction coefficient of fluid;
step two, a second equation set is obtained by introducing a scalar equation psi (x, z, T) and converting the temperature field T of the fluid to theta (x, z, T), wherein the gradient of psi (x, z, T) is a fluid velocity field; wherein the second system of equations is:
step three, expressing Fourier expansion forms of psi (x, z, t) and theta (x, z, t) as a formula I and a formula II respectively to obtain a third equation set, wherein the formula I is
The second formula is
X (t), Y (t) and Z (t) are functions of time t, C1、C2、a1And a2Is a Fourier integration constant, a1＝π/L，a2pi/H, L is the width in the x-direction, H is the height in the z-direction; the third program group is:
step four, adopting boundary conditions cos (2 a)2z) cos (pi) 1, and
ν(a1 2+a2 2)＝σ，
k(a1 2+a2 2)＝1，C1a1a2＝1，4ka2 2b to obtain a fourth set of equations; wherein, the fourth equation set is a first order ordinary differential equation set, and the expression is:
wherein, sigma is a prandtl number, r is a rayleigh number, and b is a parameter related to the size and shape of the container;
fifthly, expressing the underwater chaotic system by adopting the fourth process group;
step six, a trigonometric function noise signal with the amplitude of A and the frequency of f is added into the fourth equation set to obtain a fifth equation set so as to represent the noisy chaotic system; wherein the fifth system of equations is:
step seven, setting sigma to 10, b to 8/3, and r to 25, and initializing x, y and z, wherein the time step is 0.5;
and step eight, realizing chaotic control on the noisy chaotic system by adopting a phase space reconstruction, bifurcation and Lyapunov exponent method.
Further, the active noise control method further includes: adding a time delay feedback module in the noisy chaotic system to obtain the chaotic system with increased time delay feedback; wherein, the expression of the time delay feedback module is f (t) ═ -K [ u (t- τ) -u (t) ], τ >0 represents time lag, and K is an adjustable feedback gain vector; the chaotic system after the time lag feedback is added is as follows:
further, the active noise control method further includes: adding amplitude A to the chaotic system after time lag feedback is added1Frequency, frequencyA rate of f1The first preset external excitation is carried out to obtain time-lag feedback and a single external excitation chaotic system; the time-lag feedback and single external excitation chaotic system comprises the following steps:
further, the active noise control method further includes: adding a first preset external excitation and a second preset external excitation in the chaotic system with the added time-lag feedback to obtain the time-lag feedback and multi-external-excitation chaotic system, wherein the amplitude of the first preset external excitation is A1Frequency of f1And the amplitude of the second preset external excitation is A2Frequency of f2(ii) a The time-lag feedback and multi-external excitation chaotic system comprises the following steps:
the invention discloses a noise active control method based on a generalized Lorentz-like system, which mainly aims at the sound energy suppression of ship radiation noise signals, is an active noise control form based on delay added by the Lorentz system, and gives rules and change curves of different parameters of sound waves after passing through a chaotic system by adopting a phase diagram, a bifurcation diagram and a Lyapunov exponent diagram. The chaotic characteristic change rule of the system under different external excitation conditions is discussed, and the energy change is mainly analyzed through a spectrogram, so that the control of the sound wave energy is realized, the noise control is realized, and a new theoretical support and a new technical reference are provided for ship invisibility.
In the noise active control method, aiming at the problem of the inhibition of the sound wave energy of the radiation noise of the ship, a classical Lorentz system is adopted, a time lag feedback control quantity and an external excitation (sound source) are added to the system, and the noise control effect is researched by using a chaotic dynamics judgment method. For the deformed generalized Lorentz-like system, Matlab programming is utilized to observe the output dynamic characteristics of the generalized Lorentz-like system, the dynamic characteristics comprise a phase locus diagram, a bifurcation diagram and a Lyapunov exponent diagram, an external excitation amplitude parameter, a frequency parameter and a corresponding parameter range of the system output in a periodic motion state, a quasi-periodic motion state or a chaotic motion state are given, a noise source energy value and an energy change value under the fixed frequency before and after the active sound source is applied are given by utilizing a frequency spectrum curve, and the noise suppression effect under the action of different sound sources is determined. The research shows that: the noise suppression effect is best when the low-frequency-band external excitation is added, the value of the noise reduction is maximum when the external excitation with the amplitude of 3 and the frequency of 400Hz and the external excitation with the amplitude of 10 and the frequency of 350Hz is added, the spectrum shifting of noise can be realized by radiating a plurality of external signals with different frequencies for a ship and a feedback control module together, and the noise suppression effect is achieved.
Therefore, the active noise control method based on the generalized Lorentz-like system can better control low-frequency noise by using the active noise control method, ship radiation noise has a chaos phenomenon, and the chaos dynamics method has research significance in analyzing the ship noise problem.
These and other advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings.
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The invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like reference numerals are used throughout the figures to indicate like or similar parts. The accompanying drawings, which are incorporated in and form a part of this specification, illustrate preferred embodiments of the present invention and, together with the detailed description, serve to further explain the principles and advantages of the invention. In the drawings:
FIG. 1 is a flow chart that schematically illustrates one exemplary process of the noise active control method of the present invention based on a generalized Lorentzian-like system;
FIG. 2 is a bifurcation diagram of a noisy Lorentz system at different amplitudes A;
3A-3H are a plot of the phase trajectory and Lyapunov exponent of the system output;
FIG. 4 is a bifurcation diagram of the skew system at different time delays τ;
FIGS. 5A-5H are a phase trajectory diagram and a Lyapunov exponent diagram for a generalized Lorentzian-like system;
FIGS. 6A-6D are spectral diagrams of different f1 time-lag systems; and
fig. 7A-7D are spectral diagrams of different a1 time-lag systems.
Skilled artisans appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help improve the understanding of the embodiments of the present invention.
Detailed Description
Exemplary embodiments of the present invention will be described hereinafter with reference to the accompanying drawings. In the interest of clarity and conciseness, not all features of an actual implementation are described in the specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the device structures and/or processing steps closely related to the solution according to the present invention are shown in the drawings, and other details not so relevant to the present invention are omitted.
Fig. 1 shows an example of the noise active control method based on the generalized lorentz-like system according to the present invention. As shown in fig. 1, after the method starts, step one is first performed.
In step one, the expansion and non-compressibility conditions of the velocity field and the temperature field are given by using a first equation set, wherein the first equation set is as follows:
where u-u (x, y, z) represents the fluid velocity field, x represents the velocity mode, y represents the temperature mode, z represents the temperature gradient mode, and the temperature field is represented by T-T (x, y, z); epsilon is thermal expansion coefficient, g is gravity acceleration, rho is fluid density, P is fluid pressure field, nu is fluid viscosity coefficient, and k is heat conduction coefficient of fluid. Then, step two is executed.
In step two, a second system of equations is obtained by introducing a scalar equation ψ (x, z, T) whose gradient is the fluid velocity field and converting the temperature field T of the fluid T ═ T (x, y, z) to θ (x, z, T); wherein the second equation set is:
then, in step three, the fourier-expanded forms of ψ (x, z, t) and θ (x, z, t) are expressed as formula one and formula two, respectively, to obtain a third equation set, wherein formula one is formula one
The second formula is
X (t), Y (t) and Z (t) are functions of time t, C1、C2、a1And a2Is a Fourier integration constant, a1＝π/L，a2pi/H, L is the width in the x-direction, H is the height in the z-direction; the third program group is:
then, in step four, the boundary condition cos (2 a) is adopted2z) cos (pi) 1, and
ν(a1 2+a2 2)＝σ，
k(a1 2+a2 2)＝1，C1a1a2＝1，4ka2 2b to obtain a fourth set of equations; wherein, the fourth equation set is a first-order ordinary differential equation set, and the expression is:
where σ is a prandtl number, r is a rayleigh number, and b is a parameter relating to the size and shape of the container.
And then, in a fifth step, a fourth equation group is adopted to represent the underwater self chaotic system.
Thus, in the sixth step, a fifth equation set is obtained by adding a trigonometric function noise signal with the amplitude of A and the frequency of f in the fourth equation set to represent the noisy chaotic system; wherein the fifth equation set is:
then, in step seven, σ is set to 10, b to 8/3, and r to 25, and x, y, and z are initialized with a time step of 0.5.
In the eighth step, phase space reconstruction is realized by adding feedback control and external excitation, chaotic control is realized for the noisy chaotic system, and qualitative and quantitative analysis is performed by utilizing a bifurcation and Lyapunov exponent method.
The phase space reconstruction is the basis of nonlinear time series analysis and processing, and generally, the measured time series are scalar time series and cannot present the multidimensional phase space of the power system. It is therefore necessary to unfold this multi-dimensional structure to construct an auxiliary phase space equivalent to the prime mover system, and this method is a phase space reconstruction. The Takens embedding theorem indicates that a hyperplane with any m dimension can be differentiated, homomorphically and smoothly embedded into an equivalent corresponding dimension space, only one component is considered in a reconstruction system phase space, and a new vector sequence is found through an observed value on certain fixed delay points. The method for reconstructing the phase space corresponding to the Takens embedding theorem is a time-delay embedding reconstruction method, and the key point is to find out a proper tau, form a vector in an embedding space after time-delay on a scalar measurement value, and reconstruct to form a new space.
Bifurcation is a typical phenomenon of a non-linear system, and a change in the number of system parameters results in a change in some system performance qualities, such as the number of equilibrium points and stability. Instability is a physical premise of bifurcation occurrence, and the essence of instability is that the hyperbolic property of a system jacobian matrix eigenvalue is destroyed due to parameter change, so that the structural stability of the system is changed. The multiple period bifurcation, the quasi-period bifurcation and the paroxysmal leading to the chaos are three main modes of leading the system to the chaos, so that the bifurcation characteristic can be used for judging the motion state of the system.
In addition, the lyapunov exponent diagram can quantitatively indicate the motion state of the system, and the lyapunov exponent is used for describing the divergence situation of adjacent tracks of the system under the condition that small disturbance or small difference of initial value conditions exists. When the Lyapunov exponent is positive, namely lambda is greater than 0, adjacent tracks are gradually separated, and the system is unstable, so that the system is in a chaotic state; when the lyapunov exponent is negative, i.e. λ <0, indicating that the orbit is locally contracted, the system is stable, corresponding to periodic motion; when the Lyapunov exponent is 0, the system motion is in a critical state of period and chaotic motion.
According to one implementation, the noise active control method may further include: adding a time delay feedback module in the noisy chaotic system to obtain the chaotic system with increased time delay feedback; the expression of the time delay feedback module is f (t) ═ -K [ u (t- τ) -u (t) ], τ >0 represents time lag, and K is an adjustable feedback gain vector; the chaotic system after time lag feedback is added is as follows:
according to one of the embodiments, the first and second,the noise active control method may further include: adding amplitude A to the chaotic system after time lag feedback is added1Frequency of f1The first preset external excitation is carried out to obtain time-lag feedback and a single external excitation chaotic system; the time-lag feedback and single external excitation chaotic system comprises the following steps:
according to one implementation, the noise active control method may further include: adding a first preset external excitation and a second preset external excitation in the chaotic system after the time-lag feedback is added to obtain the time-lag feedback and multi-external-excitation chaotic system, wherein the amplitude of the first preset external excitation is A1Frequency of f1And the amplitude of the second predetermined external excitation is A2Frequency of f2(ii) a The time-lag feedback and multi-external excitation chaotic system comprises the following steps:
PREFERRED EMBODIMENTS
Dynamic characteristic research under line spectrum effect
The fourth way group is taken as a chaotic system of the underwater self in the embodiment. The frequency spectrum of the submarine radiation noise sound source level is a mixed spectrum formed by superposing a broadband continuous spectrum and a single-frequency line spectrum, the continuous spectrum reflects the capability distribution of a random noise part in a noise signal, a large number of measurement and analysis show that the continuous spectrum has a peak value, the upper limit of the frequency of the peak of the spectrum is different according to the type of ships and warships, but the peak frequency is between 200Hz and 400Hz, the peak frequency occupies most energy of radiation noise, and when the upper limit of the frequency is exceeded, the peak frequency is in an attenuation trend, and the attenuation of each octave is about 6d B. The single frequency line spectrum reflects the periodic components in the noise signal, is concentrated in the frequency band below 1k Hz, and is mainly generated by the mechanical noise of repeated motion, the propeller blade resonance line spectrum and the blade speed line spectrum, and the resonance caused by hydrodynamic force. When the submarine sails at low speed, mechanical noise is the main noise source, and when the submarine sails at high speed, propeller noise is the main noise source, and propeller cavitation noiseThe radiation noise is often the main component of the high frequency band of the submarine noise, and in conclusion, the frequency range of the submarine radiation noise is about 100Hz to 1k Hz, and depends on the navigation speed, the submergence depth and the type of the submarine[15]. This embodiment adds a trigonometric function as the noise signal for the study. The form of the system after adding the trigonometric noise with the amplitude of A and the frequency of f is shown as a fifth equation set.
The trend and the range of the system motion can be roughly known through the bifurcation diagram, the bifurcation diagram of the system after noise is added is shown in fig. 2, basic parameters are respectively set to be 10, b and 8/3, r is 25, the initial condition is set to be y0 and (0.01,0.01 and 0.01) (namely, the initial values of x, y and z are all 0.01), and the time step is 0.5. In FIG. 2, the abscissa is A and the ordinate is XmaxDenotes the X maximum value.
It can be known from the bifurcation diagram 2 that the system is in the process of continuously alternating from cycle to chaos to cycle, the system is in a cycle state when the parameter a is near 250, and then enters the chaos state, the system starts to have obvious bifurcation when the amplitude is about 300, the system starts to change into periodic motion again, and the bifurcation again appears when the parameter a is near 320.
In order to more intuitively study the motion state of the system, the embodiment provides a phase trajectory diagram and a lyapunov exponent diagram at four specific amplitudes. When the amplitude of the radiated noise is selected to be 250, 298, 320 and 332 respectively in the simulation process, the corresponding phase trajectory diagram and the maximum lyapunov exponent diagram are shown in fig. 3A-3H.
3A-3H, it is apparent from FIG. 3A that the system is in a periodic state when the amplitude is 250, and the maximum Lyapunov exponent is less than zero in FIG. 3B also indicates that the system is in a periodic state; FIG. 3C shows that the system is in a periodic state or a quasi-periodic state when the amplitude is 298, and the system is in a critical state of periodic and chaotic motion as the maximum Lyapunov exponent in FIG. 3D is equal to zero; it is apparent from FIG. 3E that the system is in a three-cycle state at an amplitude of 320, and that a maximum Lyapunov exponent of FIG. 3F that is less than zero also indicates that the system is in a cycle state; it is obvious from fig. 3G that the system is in a chaotic state when the amplitude is 332, and that the maximum lyapunov exponent in fig. 3H is greater than zero also indicates that the system is in a chaotic state. The phase diagram and the Lyapunov exponent diagram verify that the state change of the system conforms to the bifurcation diagram.
System output dynamics analysis under delay action
The method adopts an active noise control method to control noise, firstly adds a time delay feedback module in a noisy chaotic system, and adopts system state time delay feedback to change the dynamic characteristics of the system, so that the system generates complex nonlinear dynamic behaviors including periodic motion, quasi-periodic motion, chaotic motion and the like. The time-lag feedback can be used for controlling the chaotic system to move to a period, and can also be used for reversely controlling the system to generate more complex chaotic motion. The paper selects to add a negative feedback, and the expression is as follows: f (t) ═ K [ u (t- τ) -u (t) ].
Wherein τ >0 represents time lag, K is an adjustable feedback gain vector, and the new system after adding time lag feedback is:
the change of the system motion state after adding the time lag feedback is observed through a bifurcation diagram, basic parameters are set to be 10, b is 8/3 and r is 25 respectively when the bifurcation diagram is made, initial conditions are set to be y0 (0.01,0.01,0.01 and 0.01), the time step is 0.5, a fixed parameter k is 5, and the bifurcation diagram obtained by changing the time lag τ is shown in fig. 4.
As can be seen from the bifurcation diagram of fig. 4, the bifurcation of the system is more obvious after the control is added, and the chaotic state is controlled to a certain extent.
System output dynamics under external excitation
In order to achieve a better chaotic control effect, proper external excitation is added on the basis of a feedback module to further realize chaotic control. Adding amplitude of A1Frequency of f1The new system obtained after external excitation is:
and chaotic control is realized through time-lag feedback and external excitation together, and phase space reconstruction is carried out. The underwater self-chaotic system, the system after being influenced by the noise with the amplitude of 330 and the frequency of 1kHz, the time delay feedback with the time delay of 0.13, the system after the external excitation with the amplitude of 1.35 and the frequency of 100Hz, and the phase locus diagram and the Lyapunov exponent of the system when the external excitation frequency is converted into 400Hz are respectively given below. The results of the experiment are shown in FIGS. 5A-5H.
FIGS. 5A-5H are phase trajectory diagrams and Lyapunov exponent diagrams for generalized Lorentz-like systems.
From the lyapunov exponent curves of fig. 5B, 5D, 5F, and 5H, it can be seen that the maximum lyapunov exponent in each graph is greater than zero, and that there is a guest who judges that the four states are all in a chaotic state. FIG. 5A is a chaotic attractor under noiseless and controlled conditions; fig. 5C shows that the chaotic state of the system obviously changes under the influence of noise, and the noise is selected as a cosine signal with an amplitude of 330 and a frequency of 1 kHz; fig. 5E shows that when feedback control is added and an external excitation control signal with an amplitude of 1.35 and a frequency of 100Hz is radiated to the ship, the chaotic state of the system is controlled to be close to the original chaotic state of the water body; fig. 5G increases the frequency of the control signal to 400Hz, which shows that the chaotic state is closer to the original state, and it can be roughly seen that the chaotic control is substantially consistent with the change shown in the branch diagrams of fig. 2 to fig. 4.
Control effect of different frequency external excitation noise
In order to verify the denoising effect, the embodiment mainly provides a spectrogram, and quantitatively verifies the denoising effect of different external excitation forms by observing the change of the sound wave energy at 1 Hz. Fig. 6A to 6D respectively show spectrograms of a reference system, a system after noise addition, an external excitation with an addition delay and amplitude of 1, a frequency of 800 and a frequency of 400, a sampling frequency of 100Hz, and a delay parameter of 0.13 as verified by experiments. To investigate the relationship between the noise control effect and the external excitation frequency, table 1 shows a plurality of sets of data of the sound wave energy reduction amount at different frequencies.
As can be seen from fig. 6A-6D, the acoustic energy at 1Hz is 49, 53.5, 35 and 30dB, respectively, and the results clearly indicate that the acoustic energy is increased after the noise is added, and the acoustic energy is significantly decreased after the delay and the external excitation control amount are added. The external excitation frequency is changed to be respectively in a low frequency band and a high frequency band, and the reduction of the acoustic wave energy of the system compared with the noise-containing system without control is respectively given in tables 1 and 2.
TABLE 1 variation of acoustic energy at different f1 frequencies in the low band
| f1(Hz) | 800 | 600 | 400 | 200 | 100 | 10 | 1 |
| △E(dB) | 18.5 | 22.5 | 23.5 | 19.5 | 18.5 | 11 | 10 |
TABLE 2 high band different f1 acoustic energy variance
| f1(Hz) | 3k | 6.5k | 8k | 8.5k | 10k | 80k | 800k |
| △E(dB) | 11 | 10.5 | 13.5 | 10.5 | 10 | 13.5 | 11.5 |
The data comparison in table 1 and table 2 obviously shows that the external excitation in the low frequency band has a large sound wave energy reduction value compared with the high frequency band, which indicates that the control frequency should be selected in the low frequency band range, and the noise reduction effect is better. As can be seen from the energy reduction amounts at the frequencies of 10Hz and 1Hz in table 1, the noise suppression effect is significantly deteriorated when the frequency is too low, and the noise suppression effect is the best when the external excitation frequency is 400Hz in this embodiment.
Control effect of different amplitude external excitation noise
The external excitation frequency is fixed at 400Hz, the other system parameters are unchanged, the sampling frequency is 100Hz, the delay parameter is selected to be 0.13, the spectrograms of the reference system and the system after noise is added are given in fig. 7A-7B, and two representative spectrograms with amplitudes of 1 and 2 are given in fig. 7C-7D. Data for the amount of reduction in acoustic energy for various magnitudes is given in table 3.
From fig. 7A-7D, it can be seen that the acoustic energy at 1Hz is 49, 53.5, 40 and 26.6dB, respectively, and the results indicate that the noise suppression effect is reduced when the amplitude is increased to 2, but when the amplitude is 3, the acoustic energy is reduced by 26.9dB, and the noise reduction effect is better.
TABLE 3 variation of A1 sonic energy
| A1 | 0.5 | 1 | 1.5 | 2 | 3 | 3.1 | 4 |
| △P | 12.5 | 23.5 | 16 | 13.5 | 26.9 | 18.5 | 23.5 |
As can be seen from table 3, the reduction of the acoustic energy is sensitive to the external excitation amplitude, and the small change of the amplitude has a great influence on the noise suppression effect, and it can be seen from the data in table 3 that the reduction of the acoustic energy is the largest when the amplitude is 3, and the noise suppression effect is the best at this time.
Multiple external excitation noise control effects
Adding two external excitations with different amplitude and frequency, and establishing a new equation as follows:
the amplitude and frequency of the external excitation of the newly added trigonometric function are changed to obtain the sound wave energy reduction, and specific data are given in tables 4 and 5.
TABLE 4 variation of acoustic wave energy for different f2
| f2 | 800 | 600 | 350 | 300 | 200 | 100 | 1 |
| △P | 13.5 | 22.5 | 29.5 | 25.5 | 26 | 19.5 | 15.5 |
TABLE 5 variation of A2 sonic energy
| A1 | 1.5 | 2 | 2.5 | 3 | 4 | 5 | 10 |
| △P | 17.5 | 19.5 | 9.5 | 19.5 | 23 | 26.5 | 39.5 |
As can be seen from tables 3 and 4, when the external excitation with the frequency of 350Hz and the amplitude of 10 is added on the basis of the external excitation with the frequency of 400Hz and the amplitude of 3, the maximum amount of the sound wave energy reduction is 39.5dB, and is more than 26.9dB, which indicates that the two trigonometric functions can achieve better effect under the combined action. In order to achieve the noise suppression effect, an external excitation with the frequency lower than the noise frequency is selected, and when two trigonometric functions are added as the external excitation, the frequency of the second trigonometric function is close to and lower than the first term frequency.
Through analyzing the phase locus diagram, the bifurcation diagram and the maximum Lyapunov exponent diagram, different external excitation parameter thresholds can be selected to control the system in a periodic state, a quasi-periodic state and a chaotic state; the chaotic state of the system affected by the noise can be controlled to be a familiar chaotic state through the common control of external excitation and time-lag feedback in a proper form; the quantitative analysis of the spectrogram also finds that the addition of time-lag feedback and the radiation of low-frequency-band external excitation signals on the ships can shift the frequency spectrum of noise signals, thereby achieving the effect of noise suppression. Adding two external excitations of different frequencies, e.g. A1＝3,f1＝400,A2＝10,f2Compared with the method of adding single external excitation noise, the method has better suppression effect on 350 mm noise, and has important theoretical and engineering significance for developing the solution of the ship radiation noise denoising problem.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. Furthermore, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
Claims (4)
1. The noise active control method based on the generalized Lorentz-like system is characterized by comprising the following steps of:
the method comprises the following steps of firstly, giving expansion and non-compressibility conditions of a speed field and a temperature field by using a first equation set, wherein the first equation set comprises the following steps:
where u-u (x, y, z) represents the fluid velocity field, x represents the velocity mode, y represents the temperature mode, z represents the temperature gradient mode, and the temperature field is represented by T-T (x, y, z); epsilon is thermal expansion coefficient, g is gravity acceleration, rho is fluid density, P is fluid pressure field, nu is fluid viscosity coefficient, and k is heat conduction coefficient of fluid;
step two, a second equation set is obtained by introducing a scalar equation psi (x, z, T) and converting the temperature field T of the fluid to theta (x, z, T), wherein the gradient of psi (x, z, T) is a fluid velocity field; wherein the second system of equations is:
step three, expressing Fourier expansion forms of psi (x, z, t) and theta (x, z, t) as a formula I and a formula II respectively to obtain a third equation set, wherein the formula I is
The second formula is
X (t), Y (t) and Z (t) are functions of time t, C1、C2、a1And a2Is a Fourier integral constantNumber a1＝π/L，a2pi/H, L is the width in the x-direction, H is the height in the z-direction; the third program group is:
step four, adopting boundary conditions cos (2 a)2z) cos (pi) 1, and
ν(a1 2+a2 2)＝σ，
k(a1 2+a2 2)＝1，C1a1a2＝1，4ka2 2b to obtain a fourth set of equations; wherein, the fourth equation set is a first order ordinary differential equation set, and the expression is:
wherein, sigma is a prandtl number, r is a rayleigh number, and b is a parameter related to the size and shape of the container;
fifthly, expressing the underwater chaotic system by adopting the fourth process group;
step six, a trigonometric function noise signal with the amplitude of A and the frequency of f is added into the fourth equation set to obtain a fifth equation set so as to represent the noisy chaotic system; wherein the fifth system of equations is:
step seven, setting sigma to 10, b to 8/3, and r to 25, and initializing x, y and z, wherein the time step is 0.5;
and step eight, realizing chaotic control on the noisy chaotic system by adopting a phase space reconstruction, bifurcation and Lyapunov exponent method.
2. The active noise control method according to claim 1, further comprising:
adding a time delay feedback module in the noisy chaotic system to obtain the chaotic system with increased time delay feedback;
wherein, the expression of the time delay feedback module is f (t) ═ -K [ u (t- τ) -u (t) ], τ >0 represents time lag, and K is an adjustable feedback gain vector;
the chaotic system after the time lag feedback is added is as follows:
3. the active noise control method according to claim 2, further comprising:
adding amplitude A to the chaotic system after time lag feedback is added1Frequency of f1The first preset external excitation is carried out to obtain time-lag feedback and a single external excitation chaotic system;
the time-lag feedback and single external excitation chaotic system comprises the following steps:
4. the active noise control method according to claim 2, further comprising:
adding a first preset external excitation and a second preset external excitation in the chaotic system with the added time-lag feedback to obtain a time-lag feedback and multi-external-excitation chaotic system, wherein the amplitude of the first preset external excitation isA1Frequency of f1And the amplitude of the second preset external excitation is A2Frequency of f2；
The time-lag feedback and multi-external excitation chaotic system comprises the following steps:
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