Low-frequency vibration frequency adaptive identification method and system, medium and equipment

Abstract

The invention discloses a low-frequency vibration frequency adaptive identification method, system, medium and equipment, and the method comprises the steps: analyzing a naval vessel vibration signal, and building a naval vessel vibration signal model; through setting of an excess order, zero-filling FFT transformation, relaxation iteration and adaptive penalty likelihood model order estimation, high-precision estimation of the multi-frequency component of the naval vessel vibration signal is realized. The method comprises the steps of manually setting a maximum order, preliminarily estimating a signal, iteratively executing signal decomposition, relaxation iteration updating, residual error calculation and parameter updating until a residual error meets a convergence condition. And analyzing the residual error based on self-adaptive penalty likelihood, determining the real order of the model, and further obtaining the frequency component of a real signal. The method is suitable for a low-signal-to-noise-ratio scene, and the estimation precision and stability are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of low-frequency vibration monitoring, and particularly to a method, system, medium, and device for adaptively identifying low-frequency vibration frequencies. Background Art

[0002] The line spectrum distribution of ship vibrations is one of the "acoustic fingerprint" characteristics of ships. Mechanical equipment, propulsion systems, combustion processes, etc. will all generate vibrations with specific frequencies and amplitudes. These vibrations are transmitted to the hull structure through different transmission paths, thereby causing the hull structure to vibrate and inducing underwater low-frequency radiated noise. It has unique spectral characteristics and can therefore be used to identify ships. Line spectrum vibration refers to the frequency components that mainly exist in the form of discrete components in vibrations, usually appearing in the low-frequency band and remaining stable and clear for a long time during underwater propagation. This makes the low-frequency line spectrum vibration noise an important basis for underwater detection.

[0003] Low-frequency vibration frequencies have several key characteristics. First, the energy of such vibrations is concentrated in a relatively low frequency range, which is often the dominant frequency band for underwater acoustic propagation, with a long propagation distance and a slow attenuation rate. Therefore, low-frequency vibrations can be propagated over long distances and become an ideal signal for long-distance detection. Compared with high-frequency vibrations, low-frequency vibrations have less propagation loss and are suitable for long-distance marine environment monitoring and target detection. Second, the low-frequency vibration frequencies of ships are less affected by environmental factors during underwater propagation and can penetrate through longer water areas, and can be received by detection systems even in complex marine environments. Therefore, using the low-frequency vibrations generated by ships for underwater target detection, especially in underwater confrontation, can effectively improve the detection ability of enemy ships and identify the movement trajectories and positions of enemy ships in advance. In military confrontation, the distribution of the vibration line spectrum of ships becomes an important reference for underwater confrontation between hostile forces. For example, underwater sensors (such as active sonar, passive sonar, etc.) can classify and identify different types of ships by capturing the line spectrum characteristics of specific frequency bands. By performing spectral analysis on these noise signals, we can infer information such as the type, speed, and heading of the ship, thereby providing a basis for tactical decision-making. The vibrations of ships will also affect the lifespan of the hull itself, other precision equipment, and the comfort of the crew on board. Therefore, researching the estimation of low-frequency vibration frequencies through an adaptive identification method of low-frequency vibration frequencies has great practical application potential.

[0004] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present invention and may therefore include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The present invention provides a method, system, medium and device for adaptively identifying low-frequency vibration frequencies. By adaptively identifying low-frequency vibration frequencies, the vibration signals of a ship are identified, and high-precision identification is carried out under the condition of low signal-to-noise ratio, providing useful information for technologies such as active control.

[0006] A method for adaptively identifying low-frequency vibration frequencies includes:

[0007] The first step is to obtain the vibration time-domain acceleration signal of the vibration point and establish a complex sine signal model.

[0008] The second step is to manually set the over-order number based on the complex sine signal model and perform a preliminary estimation of the signal frequency through zero-padded FFT.

[0009] The third step is to perform relaxation iteration to obtain the frequencies, amplitudes, and residual variance values of the complex sine signals at different orders.

[0010] The fourth step is to analyze the residual variance value results based on the adaptive penalty likelihood model order estimation method to estimate the frequency order, that is, the number of complex sines.

[0011] The fifth step is to finally determine the frequencies and amplitudes of the complex sines.

[0012] In the above-mentioned method for adaptively identifying low-frequency vibration frequencies, in the first step, the vibration time-domain acceleration signal of the vibration point is obtained and a complex sine signal model is established.

[0013]

[0014] where y n is the vibration time-domain acceleration signal of the vibration point; K is the model order, that is, the number of complex sines, k = 1, 2,..., K, representing the k-th complex sine component; α k represents the amplitude of the k-th complex sine component, f k represents the frequency of the k-th complex sine component, n = 0, 1,..., N - 1, representing the number of samples, N represents the total number of samples, and e represents the natural constant, e n represents Gaussian white noise.

[0015] In the above-mentioned method for adaptively identifying low-frequency vibration frequencies, in the second step, the maximum order K max and the convergence coefficient η are set, where K max exceeds the model order K.

[0016] The third step is to define the vibration time-domain acceleration signal vector as:

[0017] y = [y0 y1 … y N-1 H ​

[0018] Where y represents the vibration time domain acceleration signal vector,

[0019] Let k = 1, that is, assume that the order of the current model is 1, and define the estimated target complex sinusoidal signal as the kth target complex sine waves, where k target =1,2,…,k,

[0020] Perform zero-fill FFT on the vibration time domain acceleration signal y to obtain the frequency value f1 of the largest complex sinusoidal component. The amplitude α1 corresponding to the complex sinusoid of frequency f1 is calculated by the following formula:

[0021]

[0022] in (·) H represents the complex conjugate transpose;

[0023] The residual variance value at this time is obtained by the following formula

[0024]

[0025] Among them, ||·|| 2 represents the Euclidean norm,

[0026] So far, the relevant parameters of the first sinusoidal component are obtained, which are recorded as as well as

[0027] Let k = 2. It is known that the relevant parameters of the first complex sine wave are Next, the target complex sine wave is the second complex sine wave, which is obtained by removing the first complex sine signal through the following formula:

[0028]

[0029] where y target It represents the vibration time domain acceleration signal y after removing all complex sine wave signals except the target complex sine wave.

[0030] At this time k target =2, that is Calculate y2, perform zero-padded FFT on y2, and obtain the frequency value f2 of the largest complex sine component. The amplitude α2 corresponding to the second complex sine component is calculated, and we get By formula Calculated Recorded as Then, let k targetRepeatedly equal to 1 or 2, that is, the target estimates the relevant parameters of one of the two complex sine waves. The parameters of all complex sine waves except the target sine wave are known, and the formula Recalculate the frequency and amplitude of the target complex sine to obtain an updated Based on the updated And the formula Get the new residual variance value, recorded as Calculate to Where η represents the convergence coefficient, so far we get the complex sine correlation parameters when k = 2 And the last iterative update

[0031] Update to current k=K max , that is, there is K max A complex sinusoidal signal, based on the known K max -Related parameters of a complex sinusoidal signal By formula get That is, the calculation formula for Perform zero-padded FFT to obtain the frequency value of the largest complex sine component By formula Calculate the Kth max The amplitude corresponding to the complex sine component So far, we have By formula Calculated Recorded as Based on known Let k target Continue to iterate from 1 to K max , constantly calculating, that is Known, recalculate and new Until convergence, we finally get And the last iteration update

[0032] In the method for adaptively identifying low-frequency vibration, the fourth step is to collect As input, combined with the adaptive penalized likelihood model order estimation method, where The formula is:

[0033]

[0034] where p(y n ,θ k ) represents the observed sample y n About the quantity to be estimated θ kThe likelihood function obtain Take the minimum value among them, and the corresponding k is the estimated model order, that is, the number of complex sine signals.

[0035] In the described method for adaptively identifying low-frequency vibration frequencies, in the fifth step, as k = 0, 1, 2,..., K max generate residual variance values, where when k = 0 The adaptive penalty likelihood model order estimation method selects a small penalty factor when approaching the true order and a large penalty factor when far from the true order.

[0036] In the described method for adaptively identifying low-frequency vibration frequencies, the low-frequency vibration is a vibration less than 80 Hz.

[0037] In the described method for adaptively identifying low-frequency vibration frequencies, the vibration point is on the submarine.

[0038] An identification system for implementing the described method includes:

[0039] An acquisition module, which is used to acquire the vibration time-domain acceleration signal of the vibration point to establish a complex sine signal model;

[0040] An amplitude calculation module, which is used to obtain the amplitude corresponding to the complex sine and the relevant parameters of the sine component;

[0041] An adaptive penalty likelihood model order estimation module, which is used to calculate the number of complex sine signals.

[0042] A computer storage medium, the storage medium includes computer instructions, when it runs on a computer, it causes the computer to execute the described method.

[0043] An electronic device, the electronic device includes:

[0044] A memory, a processor, and a computer program stored on the memory and executable on the processor, where

[0045] When the processor executes the program, it implements the described method.

[0046] Compared with the prior art, the present invention has the following advantages: The present invention analyzes the residual based on adaptive penalty likelihood to determine the true model order, and then obtains the frequency components of the true signal. This method is applicable to low signal-to-noise ratio scenarios and significantly improves the estimation accuracy and stability. Description of the Drawings

[0047] Upon reading the detailed description in the following preferred specific embodiments, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The accompanying drawings of the specification are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Obviously, the following-described drawings are only some embodiments of the present invention, and for those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings. Moreover, throughout the drawings, the same reference numerals are used to represent the same components.

[0048] In the drawings:

[0049] Figure 1 is a schematic diagram of the steps of a low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention;

[0050] Figure 2 is an estimated diagram and an error diagram of the simulation results of the low-frequency vibration frequency adaptive identification method under single-frequency different working conditions according to an embodiment of the present invention;

[0051] Figure 3 is the accuracy rate of the simulation results of 1000 Monte Carlo order estimations of the low-frequency vibration frequency adaptive identification method under multi-frequency different working conditions and different signal-to-noise ratios according to an embodiment of the present invention;

[0052] Figure 4 is an estimated diagram and an error diagram of the simulation results of the low-frequency vibration frequency adaptive identification method under multi-frequency different working conditions according to an embodiment of the present invention;

[0053] Figure 5 is a schematic diagram of a cabin section scaled test bench of the low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention;

[0054] Figure 6 is a partial layout diagram of the cabin section scaled test bench of the low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention;

[0055] Figure 7 is a schematic diagram of the principle of the cabin section scaled test bench of the low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention;

[0056] Figure 8 is a data analysis diagram of the cabin section scaled test bench of the low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention.

[0057] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments. Specific Embodiments

[0058] Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be completely conveyed to those skilled in the art.

[0059] It should be noted that in the description of the specification and claims, certain terms are used to refer to specific components. Those skilled in the art should understand that technicians may use different terms to refer to the same component. The specification and claims do not use the difference in terms as a way to distinguish components, but use the difference in the functions of components as the criterion for distinction. As mentioned throughout the specification and claims, "comprising" or "including" is an open-ended term and should be interpreted as "including but not limited to". The subsequent description of the specification is for the purpose of implementing the preferred embodiments of the present invention, but the description is based on the general principles of the specification and is not used to limit the scope of the present invention. The protection scope of the present invention shall be determined by the scope defined by the appended claims.

[0060] To facilitate the understanding of the embodiments of the present invention, the following will further explain with specific embodiments as examples in conjunction with the accompanying drawings, and each accompanying drawing does not constitute a limitation on the embodiments of the present invention.

[0061] As Figures 1 to 8 shown, the low-frequency vibration frequency adaptive identification method includes the following steps:

[0062] The first step S1 is to obtain the vibration time-domain acceleration signal of the vibration point and establish a complex sinusoidal signal model, where y n is the vibration time-domain acceleration signal of the vibration point; K is the model order, that is, the number of complex sinusoids, k = 1, 2,..., K, representing the kth complex sinusoidal component; α k represents the amplitude of the kth complex sinusoidal component, f k represents the frequency of the kth complex sinusoidal component, n = 0, 1,..., N - 1, representing the number of samples, N represents the total number of samples, e represents the natural constant, e n represents Gaussian white noise;

[0063] The second step S2 is to set the maximum order K max and the convergence coefficient η, where K max exceeds the model order K;

[0064] The third step S3 is to define the vibration time-domain acceleration signal vector as:

[0065] y = [y0 y1 … y N-1 H ​

[0066] where \(y\) represents the vibration time-domain acceleration signal vector.

[0067] Let \(k = 1\). That is, assume the order of the current model is 1. At the same time, define the estimated target complex sinusoidal signal as the \(k\)th target complex sinusoidal wave, where \(k\) target = 1, 2, …, \(k\).

[0068] Perform zero-padding FFT on the vibration time-domain acceleration signal \(y\) to obtain the frequency value \(f_1\) of the largest complex sinusoidal component among them, and calculate the amplitude \(\alpha_1\) corresponding to the complex sinusoid of frequency \(f_1\) through the following formula

[0069]

[0070] where (·) H represents the complex conjugate transpose;

[0071] Obtain the residual variance value at this time through the following formula

[0072]

[0073] where \(\|\cdot\|\) 2 represents the Euclidean norm,

[0074] Thus, the relevant parameters of the first sinusoidal component are obtained, denoted as and

[0075] Let \(k = 2\). Given that the relevant parameters of the first complex sinusoidal wave are Next, the target complex sinusoid is the second complex sinusoidal wave. Remove the first complex sinusoidal signal through the following formula:

[0076]

[0077] where \(y\) target represents the signal after removing all complex sinusoidal signals other than the target complex sinusoidal wave from the vibration time-domain acceleration signal \(y\).

[0078] At this time, \(k\) target = 2, that is Calculate \(y_2\). Perform zero-padding FFT on \(y_2\) to obtain the frequency value \(f_2\) of the largest complex sinusoidal component among them, and calculate the amplitude \(\alpha_2\) corresponding to the second complex sinusoidal component through the formula Thus, Obtain through the formula Calculate to obtain Denoted as After that, let \(k\) targetRepeatedly equal to 1 or 2, that is, the target estimates the relevant parameters of one of the two complex sine waves. Given the parameters of all complex sine waves except the target sine wave, through the formula recalculate the frequency and amplitude of the target complex sine wave to obtain the updated Based on the updated and the formula obtain a new residual variance value, denoted as Calculate until where η represents the convergence coefficient, and thus obtain the relevant parameters of the complex sine wave when k = 2 and the

[0079] updated to the current k = K max , that is, there are K max complex sine signals at present. Based on the known relevant parameters of K max -1 complex sine signals through the formula obtain that is, calculate the expression For perform zero-padding FFT to obtain the frequency value of the largest complex sine component among them Through the formula calculate the amplitude corresponding to the K max th complex sine component Thus obtain Through the formula calculate to obtain Denoted as Based on the known Let k target continuously iterate from 1 to K max , continuously calculate, that is Known, recalculate and the new until convergence, and finally obtain and the

[0080] Fourth step S4. Combining the previous steps, we can obtain the set as the input, combined with the adaptive penalty likelihood model order estimation method, where The formula is:

[0081]

[0082] where p(y n ,θ k ) represents the likelihood function of the observed sample y n with respect to the quantity θ k to be estimated, Obtain Take the minimum value among them, and the corresponding k is the estimated model order, that is, the number of complex sine signals.

[0083] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, in the first step (S1), an acceleration sensor is installed at the vibration point to collect the vibration time-domain acceleration signal, and the vibration point is on a ship with rotating mechanical equipment.

[0084] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, in the fourth step (S4), k = 2, that is, there are currently 2 complex sine signals. First, the first complex sine signal is removed through the orthogonal projection of the null space. Through the formula α = (Ω H Ω) -1 Ω H y, where Ω = [ω(f1) ω(f2) … ω(f K )], and then zero-padding FFT is performed to estimate the frequency of the complex sine signal with the maximum energy component in the signal from which one has been removed. Under the condition of knowing the relevant parameters of one complex sine signal, the other is estimated, which is the relaxation iteration until the convergence condition is reached.

[0085] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, in the fifth step (S5), k = K max , assuming that there are currently K max complex sine signals. First, K max - 1 complex sine signals are removed through the orthogonal projection of the null space, and then zero-padding FFT is performed to estimate the frequency of the complex sine signal with the maximum energy component in the signal from which some have been removed. Under the condition of knowing the relevant parameters of K max - 1 complex sine signals, the relevant parameters of the remaining one complex sine signal are estimated, and the iteration is carried out until the convergence condition is reached.

[0086] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, in the sixth step (S6), as k = 0, 1, 2, …, K max residual variance values are generated, where when k = 0, The adaptive penalty likelihood model order estimation method selects a small penalty factor when approaching the true order and a large penalty factor when far from the true order.

[0087] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, the low-frequency vibration is a vibration less than 80 Hz.

[0088] In the preferred implementation of the described method for adaptively identifying low-frequency vibration frequencies, the vibration point is on a submarine.

[0089] An identification system for implementing the described method includes:

[0090] An acquisition module, which is used to acquire the vibration time-domain acceleration signal of the vibration point to establish a complex sine signal model;

[0091] An amplitude calculation module, which is used to obtain the amplitude corresponding to the complex sine and the relevant parameters of the sine component;

[0092] An adaptive penalty likelihood model order estimation module, which is used to calculate the number of complex sine signals.

[0093] A computer storage medium, the storage medium includes computer instructions, when it runs on a computer, it causes the computer to execute the described method.

[0094] An electronic device, the electronic device includes:

[0095] A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein,

[0096] When the processor executes the program, it implements the described method.

[0097] In one embodiment, as Figure 1 shown, the low-frequency vibration frequency adaptive identification method includes the following steps:

[0098] In the first step S1, a complex sine signal model is established for the vibration time-domain acceleration signal of the vibration point to obtain the model where y n is the vibration point acceleration signal; K is the model order, that is, the number of complex sines; k = 1, 2,..., K, representing the kth complex sine component; α k represents the amplitude of the kth complex sine component. f k represents the frequency of the kth complex sine component; n = 0, 1,..., N - 1, representing the number of samples, and N represents the total number of samples; e represents the natural constant; e n represents Gaussian white noise;

[0099] In the second step S2, the maximum order K max and the convergence coefficient η are manually set, where K max is much larger than the true order K;

[0100] In the third step S3, the vibration time-domain acceleration signal vector is defined as:

[0101] y = [y0 y1 … y N-1 H

[0102] where y represents the vibration time-domain acceleration signal vector.

[0103] Let \(k = 1\). That is, assume that the order of the current model is 1. At the same time, define the estimated target complex sine signal as the \(k\)th target complex sine wave, where \(k\) target = 1, 2, …, \(k\).

[0104] Perform zero-padding FFT on the vibration time-domain acceleration signal \(y\) to obtain the frequency value \(f_1\) of the largest complex sine component therein, and calculate the amplitude \(\alpha_1\) corresponding to the complex sine of frequency \(f_1\) through the following formula

[0105]

[0106] where (·) H denotes the complex conjugate transpose;

[0107] Obtain the residual variance value at this time through the following formula

[0108]

[0109] where \(\|\cdot\|\) 2 denotes the Euclidean norm,

[0110] Thus, the relevant parameters of the first sine component are obtained, denoted as and

[0111] Let \(k = 2\). Given that the relevant parameters of the first complex sine wave are Next, the target complex sine is the second complex sine wave. Remove the first complex sine signal through the following formula:

[0112]

[0113] where \(y\) target denotes the signal after removing all complex sine wave signals other than the target complex sine wave from the vibration time-domain acceleration signal \(y\).

[0114] At this time, \(k\) target = 2, that is Calculate \(y_2\). Perform zero-padding FFT on \(y_2\) to obtain the frequency value \(f_2\) of the largest complex sine component therein, and obtain the amplitude \(\alpha_2\) corresponding to the second complex sine component through the formula Calculate. Thus, Through the formula Calculate to obtain Denoted as After that, let \(k\) target Keep repeating equal to 1 or 2, that is, aim to estimate the relevant parameters of one of the two complex sine waves. Given the parameters of all complex sine waves other than the target sine wave, through the formula Recalculate the frequency and amplitude of the target complex sine to obtain the updated Based on the updated and the formula obtain the new residual variance value, denoted as Calculate until where η represents the convergence coefficient, and thus obtain the complex sine related parameters at k = 2 and those obtained from the last iterative update

[0115] Update to the current k = K max , that is, there are K max complex sine signals at present. Based on the known K max -1 complex sine signal related parameters Through the formula obtain That is, calculate the expression For perform zero-padding FFT to obtain the frequency value of the largest complex sine component among them Through the formula calculate to obtain the amplitude corresponding to the Kth max complex sine component Thus obtain Through the formula calculate to obtain Denoted as Based on the known Let k target continuously iterate from 1 to K max , continuously calculate, that is Known, recalculate and the new until convergence, and finally obtain and those obtained from the last iterative update

[0116] Step 4 S4. Combining the previous steps, we can obtain the set As the input, combined with the adaptive penalty likelihood model order estimation method, where The formula is:

[0117]

[0118] where p(y n , θ k ) represents the likelihood function of the observed sample y n with respect to the quantity to be estimated θ k , and here Obtain Take the minimum value among them, and the corresponding k is the estimated model order, that is, the number of complex sinusoidal signals. The corresponding amplitude and frequency are the estimation results of this method.

[0119] To further illustrate the method of the present invention, Figure 1 is a schematic diagram of the steps of the frequency vibration frequency adaptive identification method of the present invention. First, a vibration model based on complex sinusoidal signals is established for the vibration point acceleration time-domain signal; the over-order is manually set, and the signal frequency is initially estimated by zero-padding FFT. Next, relaxation iteration is performed to obtain the frequencies, amplitudes, and residual variance values of the complex sinusoidal signals at different orders; based on the adaptive penalty likelihood model order estimation method, the residual variance value results are analyzed to estimate the frequency order, that is, the number of complex sinusoids; finally, the frequencies and amplitudes of the complex sinusoids are determined.

[0120] Figure 2 is an estimation diagram and an error diagram of the simulation results of the low-frequency vibration frequency adaptive identification method according to an embodiment of the present invention under different single-frequency working conditions.

[0121] The settings of the four single-frequency working conditions are as follows:

[0122] Working condition 1: Frequency mutation. The frequency in the first three seconds is 20 hz. At the third second, it suddenly changes to 28 hz and remains for three seconds. At the sixth second, it suddenly changes to 22 hz and remains for three seconds.

[0123] Working condition 2: Linear frequency change. The frequency is 18 hz in the first three seconds, and then starts to change linearly at the third second and becomes 28 hz at the sixth second and remains for three seconds.

[0124] Working condition 3: Nonlinear frequency change. The frequency is 18 hz in the first three seconds. At the third second, the frequency starts to change nonlinearly, specifically in a quadratic form, and becomes 28 hz at the sixth second and remains for three seconds.

[0125] Working condition 4: Both the frequency and amplitude change linearly. The amplitude linearly changes from 1 to 3 in the first three seconds, and the frequency remains unchanged at 18 hz. At the third second, the frequency linearly changes from 18 hz to 38 hz, and the amplitude remains unchanged. At the sixth second, the frequency linearly changes from 38 hz to 28 hz, and the amplitude linearly changes from 3 to 6.

[0126] From Figure 2 we can see that this method can perform good estimations, and the error values are maintained within a small range, ensuring sufficient accuracy and timeliness.

[0127] Figure 3It is the accuracy rate of the simulation results of the 1000 - time Monte Carlo order estimation under different working conditions and different signal - to - noise ratios of the low - frequency vibration frequency adaptive recognition method according to an embodiment of the present invention. The adaptive penalty likelihood model order estimation has good accuracy under different signal - to - noise ratios. This indicates that the adaptive penalty likelihood model order estimation is superior and provides accurate information for subsequent frequency estimation.

[0128] Figure 4 It is the estimation graph and error graph of the simulation results of the low - frequency vibration frequency adaptive recognition method according to an embodiment of the present invention under different multi - frequency working conditions.

[0129] The settings of the four multi - frequency working conditions are as follows:

[0130] Working condition 1: The change of frequency is instantaneous. In the 0 - 3s stage, frequencies 1 and 2 are 28Hz and 33Hz respectively. In the 3 - 6s stage, the frequencies are 25Hz and 38Hz respectively. In the 6 - 9s stage, the frequencies are 25Hz and 38Hz respectively.

[0131] Working condition 2: In the 0 - 3s stage, frequencies 1 and 2 are 18Hz and 32Hz respectively. The frequencies in the 3 - 6s stage change linearly. Frequency 1 changes from 18Hz to 28Hz, and frequency 2 changes from 32Hz to 43Hz. In the 9s stage, they remain 28Hz and 43Hz.

[0132] Working condition 3: In the 0 - 3s stage, frequencies 1 and 2 are 18Hz and 32Hz respectively. The frequencies in the 3 - 6s stage change non - linearly. Frequency 1 changes from 18Hz to 28Hz, and frequency 2 changes from 32Hz to 43Hz. In the 6 - 9s stage, they remain 28Hz and 43Hz.

[0133] Working condition 4: In the 0 - 3s stage, frequencies 1 and 2 are 18Hz and 40Hz respectively, and the amplitude changes from 1 to 3. In the 3 - 6s stage, the amplitude remains unchanged. Frequency 1 changes from 18Hz to 38Hz, and frequency 2 changes linearly from 40Hz to 60Hz. In the 6 - 9s stage, the amplitude changes linearly from 3 to 6, frequency 1 changes linearly from 38Hz to 28Hz, and frequency 2 changes linearly from 60Hz to 50Hz.

[0134] From Figure 4 It can be seen that this method has good estimation performance for multi - frequency mutation, linear, non - linear, and signals with both linear changes in frequency and amplitude. From the error graph, it can be seen that the steady - state estimation error of this method is controllable.

[0135] Figure 5 It is a schematic diagram of the cabin - section scaled - down test bench of the low - frequency vibration frequency adaptive recognition method according to an embodiment of the present invention; In this paper, a multi - section cylindrical shell vibration isolation test bench is used to further verify the effectiveness of this method. The test bench is as Figure 5 shown.

[0136] Figure 6 is a partial layout diagram of the cabin section scaled test bench for the low-frequency vibration frequency adaptive recognition method according to an embodiment of the present invention; the positions of the exciters and actuators are as Figure 6 shown.

[0137] Figure 7 is a schematic diagram of the cabin section scaled test bench for the low-frequency vibration frequency adaptive recognition method according to an embodiment of the present invention; the basic process of the experiment is as Figure 7 shown. The host computer sends instructions to the controller to make the controller generate a specific signal, which is amplified by the power amplifier and then input into the exciter to generate a specific vibration. The acceleration sensor collects the vibration signal, inputs it into the controller, and then sends it to the host computer. At the same time, considering that the signals in the ship are all multi-frequency signals, for the sake of convenience, only two frequencies are considered here.

[0138] Figure 8 is a data analysis diagram of the cabin section scaled test bench for the low-frequency vibration frequency adaptive recognition method according to an embodiment of the present invention;

[0139] The settings of the four multi-frequency working conditions are as follows:

[0140] Working condition 1: The frequency changes suddenly and the amplitude remains unchanged. The signal duration is 9 s. In the 0-2 s stage, frequency 1 is 50 Hz and frequency 2 is 20 Hz. In the 2-5 s stage, frequency 1 is 55 Hz and frequency 2 is 46 Hz. In the 5-9 s stage, frequency 1 is 52 Hz and frequency 2 is 22 Hz. The amplitude in the 0-9 interval is 1.

[0141] Working condition 2: The frequency changes linearly and the amplitude remains unchanged. The signal duration is 6 s. Frequency 1 changes linearly from 54 Hz to 60 Hz, and frequency 2 changes linearly from 24 Hz to 30 Hz. The amplitude in the 0-6 interval is 1.

[0142] Working condition 3: The frequency changes non-linearly, specifically quadratic, and the amplitude remains unchanged. The signal duration is 5 s. Frequency 1 changes linearly from 50 Hz to 52.5 Hz, and frequency 2 changes linearly from 20 Hz to 22.5 Hz.

[0143] Working condition 4: The frequency changes linearly and the amplitude changes linearly. The signal duration is 6 s. Frequency 1 changes linearly from 50 Hz to 55 Hz, and frequency 2 changes linearly from 20 Hz to 25 Hz. The amplitude of frequency 2 changes linearly from 0.3 to 1.5 in the 0-5 s.

[0144] From Figure 8 we can see the frequency estimation results of this method for the cabin section scaled test bench, and it can be seen that this method still maintains high accuracy and real-time performance.

[0145] In one embodiment, the method includes

[0146] establishing a ship vibration signal model; realizing high-precision estimation of multi-frequency components of the ship vibration signal through setting the over-order, zero-padding FFT transform, relaxation iteration, and model order estimation of adaptive penalty likelihood. The method includes: manually setting the maximum order, preliminary estimation of the signal, iteratively performing signal decomposition, relaxation iteration update, residual calculation, and parameter update until the residual satisfies the convergence condition. Analyzing the residual based on adaptive penalty likelihood to determine the true order of the model, and then obtaining the frequency components of the true signal. This method is applicable to low signal-to-noise ratio scenarios and significantly improves the estimation accuracy and stability.

[0147] In one embodiment, the method includes

[0148] In the first step, set an appropriate sampling frequency f samp . Attach an appropriate acceleration sensor to the measurement point. Use a data acquisition instrument to collect the signal. Establish a complex sine signal model for the vibration time-domain acceleration signal of the vibration point to obtain the model where y n is the acceleration signal of the vibration point; K is the model order, that is, the number of complex sines; k = 1, 2,..., K, representing the k-th complex sine component; α k represents the amplitude of the k-th complex sine component. f k represents the frequency of the k-th complex sine component; n = 0, 1,..., N - 1, representing the number of samples, and N represents the total number of samples; e represents the natural constant; e n represents Gaussian white noise.

[0149] In the second step, manually set the maximum order K max and the convergence coefficient η, where K max is much larger than the true order K. The vibration sources in ship vibrations are diverse, but the main part of its energy is still rotating mechanical components such as diesel engines, and the number of rotation frequencies is relatively fixed, which provides certain prior information for the result of frequency estimation.

[0150] In the third step, according to the established complex sine signal model, we can obtain:

[0151]

[0152] Regarding the probability density function of can be expressed as:

[0153]

[0154] where σ represents the variance of the noise.

[0155] Therefore, the joint likelihood function for N samples can be expressed as:

[0156]

[0157] Substituting the probability density of a single sample into:

[0158]

[0159] The negative log-likelihood function can be expressed as:

[0160] NLL({α k ,f k},σ 2 )=-ln L({α k ,f k},σ 2 )

[0161] Right now:

[0162]

[0163] make: but

[0164]

[0165] Among them, the first term Nln(πσ 2 ) is the variance σ of the noise, and the second term is the sum of squared errors between the model predictions and the observed values. Let:

[0166]

[0167] The derivative of the above formula is:

[0168]

[0169] Substituting into C1 we have:

[0170]

[0171] With the goal of minimizing the above formula, based on the least squares method, we can get:

[0172]

[0173] Among them, ||·|| 2 represents the Euclidean norm

[0174] Next, we estimate the noise with the goal of minimizing C2:

[0175]

[0176] Therefore, the above formula is used as the loss function to calculate the frequency and amplitude of the complex sinusoidal signal.

[0177] Let:

[0178] α = [α1 α2 … α K T

[0179] Ω = [ω(f1) ω(f2) … ω(f K )]

[0180] We have:

[0181]

[0182] Where: represents the estimated values of frequency and amplitude

[0183] Minimize the following objective function for frequency estimation:

[0184]

[0185] Where, represents the orthogonal projection of Ω H onto the null space

[0186]

[0187] For Taking the derivative of the right side and finding the zero point can obtain the amplitude:

[0188]

[0189] Based on the above analysis process, the solution formulas for the frequency and amplitude of the complex sinusoidal signal can be obtained as:

[0190]

[0191] The above is the process of relaxation iteration. However, before the relaxation iteration, we need to first obtain the initial estimated value of the frequency.

[0192] Let k = 1. For y n Perform zero-padding FFT to obtain the frequency value of the largest complex sinusoidal component among them Zero-padding FFT can well compensate for the defect of low frequency accuracy caused by short sampling time, and ensure both timeliness and accuracy. Calculate the frequency of the corresponding amplitude of the complex sinusoid

[0193] y = [y0 y1 … y N-1 H ​​

[0194]

[0195] Among them (·) H denotes the complex conjugate transpose; where y k | k＝1 = y

[0196] The residual variance value at this time is obtained through the following formula

[0197]

[0198] Among them, ||·|| 2 denotes the Euclidean norm.

[0199] So far, the relevant parameters of the first sine component are obtained and denoted as and

[0200] Let k = 2, and remove the first complex sine signal through the following formula:

[0201]

[0202] y2 is calculated. Zero-padding FFT is performed on y2 to obtain the frequency value of the largest complex sine component among them Through the formula The amplitude corresponding to the second complex sine component is calculated So far, Through the formula It is calculated to obtain Denoted as Under the assumption that only the frequency, amplitude of one complex sine and the formula Recalculate the frequency and amplitude of the other complex sine to obtain the updated Based on the updated and the formula A new residual variance value is obtained and denoted as Relaxation iteration is calculated until where η represents the convergence coefficient. So far, the complex sine related parameters when k = 2 are obtained and

[0203] Update to the current k = K max , that is, there are K max complex sine signals at present. Based on the known and the formula Get For Perform zero-padding FFT to obtain the frequency value of the largest complex sine component among them Through the formula Calculated up to Kth max The amplitude corresponding to the complex sine component So far, we have By formula Calculated Recorded as Based on known Assume that the parameters of the Mth complex sinusoidal signal are unknown, M = 1, 2, ... K max ,Right now Known, recalculate Until convergence. Finally, we get as well as

[0204] gather As input, it is combined with the adaptive penalized likelihood model order estimation method, where The specific formula is:

[0205]

[0206] where p(y n ,θ k ) represents the observed sample y n About the quantity to be estimated θ k Likelihood function, where get Take the minimum value, and the corresponding k is the estimated model order, that is, the number of complex sinusoidal signals.

[0207] Install accelerometers at the vibration points to collect signals. The vibration in ships mainly comes from rotating mechanical equipment, etc. Its frequency is relatively fixed but has a small offset, which requires a high-precision estimation method. Manually set the maximum order K max , which is much higher than the actual order, which ensures that our method can estimate the order quickly and effectively. A suitable convergence coefficient is for example 1×10 -3 .

[0208] In one embodiment, assuming k=1, that is, assuming there is currently one complex sinusoidal signal, the frequency of the complex sinusoidal signal with the maximum energy component is estimated through zero-padded FFT. Zero-padded FFT can effectively improve the accuracy of the initial frequency estimate and prepare for subsequent relaxation iterations.

[0209] Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields. The above-mentioned specific embodiments are merely illustrative and instructive, and are not restrictive. A person skilled in the art, guided by this specification and without departing from the scope of protection of the claims of the present invention, may also devise various forms, all of which fall within the scope of protection of the present invention.

Claims

1. A method for adaptively identifying low-frequency vibration frequencies, characterized in that, It includes the following steps: The first step (S1), obtaining the vibration time-domain acceleration signal of the vibration point and establishing a complex sine signal model; The second step (S2), based on the complex sine signal model, manually setting the overdetermined order, and performing a preliminary estimation of the signal frequency through zero-padded FFT; The third step (S3), performing relaxation iteration to obtain the frequencies, amplitudes, and residual variance values of the complex sine signals at different orders; The fourth step (S4), analyzing the result of the residual variance value based on the adaptive penalty likelihood model order estimation method to estimate the frequency order, that is, the number of complex sines; The fifth step (S5), finally determining the frequencies and amplitudes of the complex sines.

2. The low-frequency vibration frequency adaptive recognition method according to claim 1, characterized in that Preferably, in the first step (S1), the vibration time-domain acceleration signal of the vibration point is obtained and a complex sine signal model is established; where y n is the vibration time-domain acceleration signal of the vibration point; K is the model order, that is, the number of complex sinusoids, k = 1, 2, …, K, representing the k-th complex sinusoidal component; α k represents the amplitude of the k-th complex sinusoidal component, f k represents the frequency of the k-th complex sinusoidal component, n = 0, 1, …, N - 1, representing the number of samples, N represents the total number of samples, e represents the natural constant, e n represents Gaussian white noise.

3. The low-frequency vibration frequency adaptive recognition method according to claim 1, characterized in that Second step (S2), set the maximum order K max and the convergence coefficient η, where K max exceeds the model order K; The third step (S3), defining the vibration time-domain acceleration signal vector as: y = [y0 y1 … y N-1 H ​ where y represents the vibration time-domain acceleration signal vector; Let \(k = 1\), that is, assume that the order of the current model is 1, and at the same time define the estimated target complex sinusoidal signal as the \(k\)th target complex sinusoidal wave, where \(k\) target \(= 1, 2, \ldots, k\). Performing zero-padding FFT on the vibration time-domain acceleration signal y to obtain the frequency value f1 of the largest complex sine component therein, and calculating the amplitude α1 corresponding to the complex sine of the frequency f1 through the following formula; wherein (·) H denotes complex conjugate transpose; Obtaining the residual variance value at this time through the following formula; where ||·|| 2 denotes the Euclidean norm, Thus, the relevant parameters of the first sine component are obtained and denoted as and Let k = 2. The relevant parameters of the first complex sine wave are known as Next, the target complex sine is the second complex sine wave minus the first complex sine signal through the following formula: where y target represents the signal after removing all complex sine wave signals other than the target complex sine wave from the vibration time-domain acceleration signal y. At this time, k target = 2, that is Calculate y2. Perform zero-padding FFT on y2 to obtain the frequency value f2 of the largest complex sine component among them. Through the formula Calculate the amplitude α2 corresponding to the second complex sine component. Thus, obtain Through the formula Calculate to obtain Denote it as After that, let k target Repeatedly equal to 1 or 2. That is, the goal is to estimate the relevant parameters of one of the two complex sine waves. Given the parameters of all complex sine waves except the target sine wave, through the formula Recalculate the frequency and amplitude of the target complex sine to obtain the updated Based on the updated And the formula Obtain the new residual variance value, denoted as Calculate until Where η represents the convergence coefficient. Thus, obtain the complex sine related parameters when k = 2 And the one obtained from the last iterative update Update to the current k = K max , that is, there are K max complex sinusoidal signals at present. Based on the known max correlation parameters of K - 1 complex sinusoidal signals obtain through the formula , that is, calculate the expression Perform zero - padding FFT on For to obtain the frequency value of the largest complex sinusoidal component among them Calculate through the formula to obtain the amplitude corresponding to the K max th complex sinusoidal component Up to this point, obtain Calculate through the formula to obtain Denote it as Based on the known Let k target continuously iterate from 1 to K max , and continuously calculate, that is Known, recalculate and the new until convergence, and finally obtain and the updated in the last iteration 4. A low-frequency vibration frequency adaptive recognition method according to claim 1, characterized in that Fourth step (S4), aggregate as input, combined with the adaptive penalty likelihood model order estimation method, where The formula is: where p(y n , θ k ) represents the likelihood function of the observed sample y n with respect to the quantity θ k to be estimated, obtain take the minimum value among them, and the corresponding k is the estimated model order, that is, the number of complex sinusoidal signals.

5. The low-frequency vibration frequency adaptive recognition method according to claim 1, characterized in that In the fifth step (S5), as k = 0, 1, 2, …, K max a residual variance value is generated, where when k = 0 For the adaptive penalty likelihood model order estimation method, a small penalty factor is selected when approaching the true order, and a large penalty factor is selected when far from the true order.

6. The low-frequency vibration frequency adaptive recognition method according to claim 1, characterized in that The low-frequency vibration is a vibration less than 80 Hz.

7. A method for adaptively identifying low-frequency vibration frequencies according to claim 1, characterized in that, The vibration point is on the submarine.

8. An identification system for implementing the method according to any one of claims 1-7, characterized in that, It includes: An acquisition module, which is used to acquire the vibration time-domain acceleration signal of the vibration point to establish a complex sine signal model; An amplitude calculation module, which is used to obtain the amplitude corresponding to the complex sine and the relevant parameters of the sine component; An adaptive penalty likelihood model order estimation module, which is used to calculate the number of complex sine signals.

9. A computer storage medium, characterized in that, The storage medium includes computer instructions, which when running on a computer, cause the computer to execute the method according to any one of claims 1-7.

10. An electronic device, characterized in that, The electronic device includes: A memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, it implements the method according to any one of claims 1-7.

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