Method for extracting vibration characteristics of underwater rotating machinery based on time-frequency energy analysis

Abstract

This invention discloses a method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis. The method includes: preprocessing the original mechanical vibration signal of the underwater rotating machinery to obtain a filtered vibration signal; constructing a time-frequency distribution matrix after performing a Fourier synchronous compression transform; establishing an optimal path model including smoothing constraints to obtain the instantaneous frequency trajectory and thus estimate the optimal time-varying rotational speed; mapping the filtered vibration signal to the time domain and angle domain to construct an angle domain vibration signal, and then constructing a time-order distribution matrix; determining the dominant order component of the vibration and the optimal operating conditions from both the order domain and time domain dimensions. This invention can extract vibration signal features of underwater rotating machinery under varying operating conditions with high accuracy, and estimate the rotational speed-time mapping relationship without a rotational speed sensor. Through order and rotational speed energy distribution features, it can extract excitation characteristics and vibration intensity, which has significant engineering application value in vibration monitoring and optimization design.

Description

Technical Field

[0001] This invention relates to a method for extracting mechanical vibration features, specifically to a method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis. Background Technology

[0002] With the rapid development of marine resource development and underwater equipment technology, vibration characteristic analysis of underwater rotating machinery (such as propulsion motors, pumps, and turbines) has become crucial for ensuring stable equipment operation and optimizing design. Traditional vibration monitoring methods for underwater rotating machinery mostly rely on time-domain or frequency-domain analysis, but these methods have significant limitations: Firstly, they require the equipment to operate at a constant speed, which is inconsistent with the wide speed range and variable operating conditions commonly found in complex underwater environments, resulting in limited dimensions of vibration signal information obtained by traditional methods. Secondly, because underwater machinery generally has compact structures, strong sealing, and lightweight design characteristics, and most adopt open-loop control strategies without speed sensors, this further increases the difficulty of extracting and analyzing vibration signal features related to operating conditions, making it difficult to accurately and comprehensively assess the vibration state of the equipment during operation.

[0003] Therefore, developing advanced vibration monitoring technology for underwater rotating machinery to analyze the vibration characteristics of underwater machinery under varying operating conditions without speed sensors has significant engineering application value. However, to achieve effective analysis of the vibration characteristics of underwater rotating machinery under varying operating conditions, the following three key issues still need to be addressed:

[0004] 1) Low accuracy in analyzing non-stationary vibration signals under varying operating conditions: Due to the significant non-stationary characteristics of vibration signals from rotating machinery under varying operating conditions, their statistical features evolve dynamically over time. Although traditional time-frequency analysis methods (such as short-time Fourier transform) can characterize the time-frequency characteristics of the signal to some extent, they have inherent limitations in terms of resolution and accuracy. Especially under the influence of factors such as spectral aliasing and noise interference, severe frequency ambiguity will occur, making it difficult to accurately capture the dynamic changes of non-stationary vibration signals.

[0005] 2) Difficulty in estimating rotational speed solely from vibration signals: As a key parameter characterizing the performance of rotating machinery, accurate estimation of rotational speed is crucial. Most existing rotational speed estimation methods are based on steady-state assumptions. When the rotational speed changes dynamically, due to the dispersion of time-frequency energy distribution, traditional threshold segmentation or peak tracking algorithms struggle to continuously extract the instantaneous frequency trajectory, resulting in insufficient accuracy of the obtained rotational speed-time mapping relationship, which in turn affects the reliability of vibration characteristic analysis results.

[0006] 3) Vibration characteristic analysis under variable speed conditions is complex: During dynamic changes in speed, the working state of the mechanical system continuously evolves, causing the frequency and amplitude characteristics of the vibration signal to exhibit time-varying features, significantly increasing the complexity of signal analysis. Furthermore, speed changes may cause coupling between the system's excitation frequency and natural frequency, inducing resonance. These factors result in significant nonlinear characteristics in the system's vibration characteristics, making traditional vibration characteristic analysis methods difficult to apply effectively. Summary of the Invention

[0007] To address the problems existing in the background technology, the present invention provides a method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis.

[0008] The technical solution adopted in this invention is:

[0009] The present invention provides a method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis, comprising:

[0010] Step a: Obtain the raw mechanical vibration signal of the underwater rotating machinery during underwater operation, and obtain the filtered vibration signal after preprocessing the raw mechanical vibration signal.

[0011] Step b: Perform a Fourier synchronous compression transform on the filtered vibration signal. Improve the time-frequency resolution through the compression operator, thereby constructing the time-frequency distribution matrix of the filtered vibration signal and accurately capturing the instantaneous characteristics of the vibration signal.

[0012] Step c: Based on the time-frequency distribution matrix of the filtered vibration signal, establish an optimal path model containing a smoothing constraint term, thereby extracting the optimal time-frequency path distribution with concentrated energy and smooth waveform in the filtered vibration signal. Obtain the instantaneous frequency trajectory of the filtered vibration signal as the rotational speed changes from the optimal time-frequency path distribution, thereby obtaining the estimated optimal time-varying rotational speed, i.e., the rotational speed-time mapping relationship.

[0013] Step d: Based on the estimated optimal time-varying rotational speed, perform time-domain to angle-domain mapping on the filtered vibration signal from step a to construct the angle-domain vibration signal. Then, use the same Fourier synchronous compression transform as in step b to construct the time-order distribution matrix, thereby extracting the order features of underwater rotating machinery vibration related to rotational speed.

[0014] Step e: Perform order slicing on the time-order distribution matrix to obtain the order energy spectrum of the angular domain vibration signal, i.e., the energy distribution along the entire order axis, thereby determining the dominant order component causing vibration in the original mechanical vibration signal, i.e., extracting the excitation characteristics based on the order energy distribution characteristics; at the same time, perform time slicing on the time-order distribution matrix to obtain the rotational speed energy spectrum of the angular domain vibration signal, i.e., the energy distribution within the entire rotational speed range, extracting the vibration intensity based on the rotational speed energy distribution characteristics, thereby obtaining the optimal rotational speed, and controlling the rotational speed of the underwater rotating machinery to operate under optimal operating conditions.

[0015] In step a, the original mechanical vibration signal is preprocessed based on the fractional resampling method, specifically by performing upsampling and zero-placing processing, bidirectional anti-aliasing filtering based on Butterworth filter, and downsampling and decimation processing in sequence.

[0016] In step b, the Fourier synchronous compression transform employs a synchronous compression transform based on the short-time Fourier transform.

[0017] In step c, the optimal path model including the smoothing constraint term is as follows:

[0018]

[0019] Wherein, U(t,f c,t ) and U(t-1,f c,t-1 The values ​​f represent the optimal time-frequency path distributions of the filtered vibration signals at time t and t-1, respectively, used to search for time-frequency paths in the vibration signal that vary with rotational speed; c,t and f c,t-1 F(t,f) represents the frequency of the filtered vibration signal at time t and time t-1, respectively. c ) is the time-frequency distribution matrix; Δ is the maximum allowable frequency change step size, realizing frequency variation constraint; λ is the trade-off parameter, λ>0, which controls the smoothing intensity.

[0020] Based on the frequency f of the filtered vibration signal at each time t c,t Obtain the instantaneous frequency trajectory f of the filtered vibration signal at each time t as the rotational speed changes. c (t), thus obtaining the estimated optimal time-varying speed data as follows:

[0021] ω(t)=60·f c (t)

[0022] Where ω(t) is the estimated optimal time-varying rotational speed.

[0023] In step d, the filtered vibration signal from step a is mapped from the estimated optimal time-varying rotational speed to the angle domain. Specifically, the estimated optimal time-varying rotational speed ω(t) is first integrated to obtain the cumulative rotation angle θ(t); then, a linear interpolation method is used to map the filtered vibration signal y[n] to the angle domain, thereby constructing the angle domain vibration signal y[θ]. k ],as follows:

[0024]

[0025] θ k =kΔθ

[0026] θ n ≤θ k ≤θ n+1

[0027] Where, θ k Let θ be the angle at the k-th sampling point, where k = 0, 1, 2, ... n and θ n+1 y[n] and y[n+1] are the angles at the nth and (n+1)th sampling points, respectively; y[n] and y[n+1] are the filtered vibration signals at the nth and (n+1)th sampling points, respectively; Δθ is the preset angle domain sampling interval, which is determined by the cumulative rotation angle θ(t) and the number of samples k.

[0028] In step e, the time-order distribution matrix is ​​processed by order slicing, as follows:

[0029] e11) First, divide the order range and determine the upper limit value O of the target order range. max as follows:

[0030]

[0031] Where P and Q are the interpolation factor and the extraction factor, respectively; f s f0 is the sampling rate of the original mechanical vibration signal; f0 is the maximum fundamental frequency of the filtered vibration signal.

[0032] Then, the upper limit of the range from 0 to the target order is O. max The orders between them are divided into several equally spaced order slices according to a preset order resolution ΔO, thereby generating the order sequence {O}. i |i = 1, 2, ..., N}, O i Let N be the i-th order slice, and N be the total number of order slices.

[0033] e12) Based on each order slice, the order domain integration interval is set over its entire time range as follows:

[0034]

[0035] Among them, Ω i For the i-th order slice O i The order of the domain integration interval.

[0036] Based on the order domain integration interval, the cumulative energy of each order slice is obtained as follows:

[0037]

[0038] Among them, E(O) i ) represents the i-th order slice O i The cumulative energy; F(O,t) is the time-order distribution matrix of the order slice O at time t.

[0039] e13) After obtaining the cumulative energy of each order slice, it is represented as an order energy distribution sequence {(O1, E(O1)), (O2, E(O2)), ..., (O1, E(O1))}. N ,E(O N The cumulative energy of each order slice is summed and normalized to obtain the order energy spectrum of the angular domain vibration signal, i.e., the relative order energy distribution is as follows:

[0040]

[0041] in, This indicates the order of the energy spectrum.

[0042] In step e, the time-order distribution matrix is ​​processed by time slicing to obtain the rotational speed energy spectrum of the original mechanical vibration signal, as follows:

[0043] Step e21: Based on the optimal time-varying speed estimated in step c, determine the speed range ω0~ω max ω max ω and ω0 are the estimated maximum and minimum values ​​of the optimal time-varying speed, respectively; then, the speed range is divided into several equally spaced speed slices according to the preset speed resolution Δω, thereby generating the speed sequence {ω j |j=1,2,…,M},ω j Let M be the j-th rotational speed slice, and M be the total number of rotational speed slices; then determine the time sequence {T} based on the time corresponding to the rotational speed sequence. j |j=1,2,…,M},T j This represents the time corresponding to the j-th rotational speed slice.

[0044] Step e22: Set the time-domain integration interval according to the time series as follows:

[0045]

[0046] Where, Φ jFor the j-th rotational speed slice ω j The time-domain integration interval is defined; ΔT is the time-domain resolution; P and Q are the interpolation factor and decimation factor, respectively; f s The sampling rate of the original mechanical vibration signal is denoted as ; T is the sampling duration of the original mechanical vibration signal, in seconds.

[0047] Based on the time-domain integration interval, the cumulative energy of each rotational speed slice is obtained as follows:

[0048]

[0049] Where, E(ω) j ) represents the j-th rotational speed slice ω j The cumulative energy; F(O,t) is the time-order distribution matrix of the order slice O at time t.

[0050] Step e23: Based on the correspondence between the time domain and the rotational speed domain, the cumulative energy of each rotational speed slice is reordered in ascending order of rotational speed; then, the maximum value of the cumulative energy of each reordered rotational speed slice is normalized to obtain the rotational speed energy spectrum of the angular domain vibration signal, i.e., the relative rotational speed energy distribution is as follows:

[0051]

[0052] in, For the j-th rotational speed slice ω j The rotational energy spectrum.

[0053] In step e, based on the rotational speed energy spectrum, the trend of vibration energy variation with rotational speed is obtained. Within a preset rotational speed range, the rotational speed at which the vibration energy is lowest is taken as the optimal rotational speed. This controls the vibration intensity of the underwater rotating machinery, thereby achieving optimized configuration of the system's operating conditions.

[0054] The electronic device of the present invention includes: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor invokes the program data to execute the method described above.

[0055] The present invention provides a computer-readable storage medium having program data stored thereon, which, when executed by a processor, implements the method described above.

[0056] This invention utilizes a fractional resampling signal preprocessing method and an improved time-frequency analysis method to achieve high-precision extraction of time-varying vibration signal characteristics of underwater rotating machinery under varying operating conditions. It establishes a rotational speed estimation model based on vibration signals, breaking through the traditional reliance on rotational speed sensors. Furthermore, it proposes a vibration feature extraction method based on angle and order energy distribution characteristics, obtaining vibration feature parameters with clear physical meaning and engineering interpretability, thus providing a new technical approach for the vibration characteristic analysis and monitoring of underwater rotating machinery.

[0057] The beneficial effects of this invention are:

[0058] This invention provides a method capable of extracting vibration signal characteristics of underwater rotating machinery under varying operating conditions with high precision. Furthermore, it estimates the rotational speed-time mapping relationship of the rotating machinery without a rotational speed sensor, and extracts the excitation characteristics and vibration intensity under varying operating conditions through order and rotational speed energy distribution features. This method has significant engineering application value in the vibration monitoring and optimization design of underwater rotating machinery. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 This is a time-frequency characteristic diagram of the vibration signal according to an embodiment of the present invention;

[0061] Figure 3 This is a diagram showing the rotational speed-time mapping relationship according to an embodiment of the present invention;

[0062] Figure 4 This is a vibration signal order feature diagram according to an embodiment of the present invention;

[0063] Figure 5 This is a diagram showing the order energy distribution of an embodiment of the present invention;

[0064] Figure 6 This is a rotational speed energy distribution diagram according to an embodiment of the present invention. Detailed Implementation

[0065] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. However, these embodiments and the accompanying drawings do not limit the scope of protection of the present invention. Obviously, the described embodiments are merely one embodiment of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

[0066] like Figure 1 As shown, the underwater rotating machinery vibration feature extraction method based on time-frequency energy analysis of the present invention is as follows:

[0067] Step a: Obtain the raw mechanical vibration signal of the underwater rotating machinery during underwater operation by installing a vibration signal sensor on the equipment shell of the underwater rotating machinery. The raw mechanical vibration signal is then preprocessed to obtain a filtered vibration signal. Specifically, the sensor arrangement of this invention is as follows: a piezoelectric accelerometer (sensitivity: 10 mV / m·s) is installed at a radial position on the shell of the deep-sea plunger pump of the underwater electro-hydraulic actuator. 2 Measurement range: ±50g; Frequency response: 0.5~7000Hz; Resolution: 0.0005g), used to collect vibration signals from the pump surface. Signal acquisition system: Employs a 24-bit high-precision data acquisition card, set to a sampling frequency of 50kHz, continuously acquiring vibration signals of the pump under variable speed conditions (under an external pressure of 40MPa, the speed increases approximately from 1000RPM to 2000RPM).

[0068] The original mechanical vibration signal is preprocessed using a fractional resampling method, specifically by performing upsampling and zero-placing, bidirectional anti-aliasing filtering based on a Butterworth filter, and downsampling. In practice, the target sampling rate of the vibration signal after fractional resampling is set to 10kHz, and the anti-aliasing filter is a 10-7kHz bandpass filter.

[0069] The fractional resampling method is as follows:

[0070] a1) Upsampling and zero-interpolation: The original mechanical vibration signal x[m] is upsampled by P times interpolation to generate an intermediate signal x. l [n], the upsampling and zero-interpolation function is as follows:

[0071]

[0072] Where n and m are the sampling points of the vibration signal after zero insertion and the original mechanical vibration signal, respectively; x l [n] represents the original mechanical vibration signal after upsampling and zero-placing; x[m] represents the original mechanical vibration signal currently being processed; in specific implementation, P = 1.

[0073] a2) Two-way anti-aliasing filtering: A third-order Butterworth filter is used to filter the upsampled, zero-placed vibration signal x. l [n] Perform forward and reverse filtering at 10–7 kHz to maintain signal phase and suppress spectral aliasing, resulting in a bidirectional filtered signal x. f [n], the bidirectional filtering function is as follows:

[0074]

[0075] Where h[n] is the Butterworth filter response function, and h[-n] is the response function of h[n] after time reversal.

[0076] By applying a bidirectional anti-aliasing filtering method using a Butterworth filter, the original mechanical vibration signal is filtered to eliminate spectral aliasing while preserving the signal's phase characteristics.

[0077] a3) Downsampling and decimation: For the bidirectional filtered signal x f [n] The output signal is generated by downsampling with Q as the decimation factor. The downsampling function is as follows:

[0078] y[n]=x f [Qn]

[0079] Where y[n] is the filtered vibration signal; P and Q are the interpolation factor and decimation factor, respectively, and Q is an integer greater than 1 that satisfies that P / Q constitutes an irreducible fraction. In specific implementation, Q = 5.

[0080] The sampling rate f of the original mechanical vibration signal s Convert to target sampling rate P·f s / Q is used to obtain vibration signals within a specific frequency range and compress the signal to reduce the signal sampling frequency, thereby improving the post-processing speed.

[0081] The above method converts the original signal sampling rate from 50kHz to the target sampling rate of 10kHz, obtains vibration signals in the frequency range of 10 to 7kHz, and compresses the number of sampling points of the original vibration signal to 1 / 5 of the original, thereby reducing the signal sampling frequency and improving the post-processing speed.

[0082] Step b: Perform a synchronous Fourier transform on the filtered vibration signal. The compression operator improves the time-frequency resolution, thereby constructing the time-frequency distribution matrix of the filtered vibration signal and accurately capturing its instantaneous characteristics. The synchronous Fourier transform is based on the short-time Fourier transform. The time-frequency analysis method of the synchronous Fourier transform is as follows:

[0083] F(t,f c )=∫F(t,f)δ(ω(t,f)-f c )df

[0084]

[0085] Where F(t,f) c Let f be the time-frequency distribution matrix, where t is time, and f is the frequency distribution matrix. cδ(t,f) represents the compressed frequency variable; F(t,f) is the short-time Fourier transform result, representing the time-frequency representation of the signal, where f is the original frequency variable; δ(·) is the Dirac function, which concentrates energy at the instantaneous frequency; ω(t,f) is the phase transform function, which redistributes the frequency variable and frequency point in the time-frequency domain according to the mapping relationship (t,f)→(t,ω(t,f)); y(τ) is the continuous-time representation of the filtered vibration signal, where τ is the time variable; g(τ-t) is the window function of the Fourier transform, specifically using a Kaiser window with a window shape coefficient of 5, a window length of 2000, and a frequency domain resolution of 2000; i is the imaginary unit.

[0086] The phase transformation function ω(t,f) is as follows:

[0087]

[0088] The preprocessed vibration signal is subjected to Fourier synchronous compression transform to construct the time-frequency distribution matrix. The resulting time-frequency feature map is shown below. Figure 2 As shown, the concentrated area of ​​time-frequency energy clearly reflects the instantaneous frequency change of the vibration signal.

[0089] Step c: Based on the time-frequency distribution matrix of the filtered vibration signal, establish an optimal path model including a smoothing constraint term. This extracts the optimal time-frequency path distribution with concentrated energy and smooth waveform in the filtered vibration signal. From this optimal time-frequency path distribution, obtain the instantaneous frequency trajectory of the filtered vibration signal as a function of rotational speed, thus obtaining the estimated optimal time-varying rotational speed, i.e., the rotational speed-time mapping relationship. The optimal path model including the smoothing constraint term is as follows:

[0090]

[0091] Wherein, U(t,f c,t ) and U(t-1,f c,t-1 The values ​​f represent the optimal time-frequency path distributions of the filtered vibration signals at time t and t-1, respectively, used to search for time-frequency paths in the vibration signal that vary with rotational speed; c,t and f c,t-1 F(t,f) represents the frequency of the filtered vibration signal at time t and time t-1, respectively. c ) is the time-frequency distribution matrix; Δ is the maximum allowable frequency change step size to achieve frequency variation constraint, and is selected as Δ = 2; λ is the trade-off parameter, λ > 0, to control the smoothing intensity, and is selected as λ = 0.2.

[0092] Based on the frequency f of the filtered vibration signal at each time t c,t Obtain the instantaneous frequency trajectory f of the filtered vibration signal at each time t as the rotational speed changes. c(t), thus obtaining the estimated optimal time-varying speed data as follows:

[0093] ω(t)=60·f c (t)

[0094] Where ω(t) is the estimated optimal time-varying rotational speed.

[0095] In the optimal path model, the first term is the magnitude term, ensuring the optimal U(t,f) is achieved. c,t Approximates the original F(t,f) c,t The second term constrains the frequency range and smoothness, i.e., the smoothness constraint term, to ensure the extraction of a continuous and energy-concentrated instantaneous frequency trajectory.

[0096] The estimated speed-time mapping is shown in the figure below. Figure 3 As shown in the figure, the rotational speed of the underwater rotating machinery exhibits a non-linear characteristic. Within 10 seconds, the rotational speed increases from 1024 RPM to 1964 RPM, and its trend is similar to... Figure 2 The time-frequency characteristic maps in the data are highly consistent, further verifying the accuracy of the estimated rotational speed.

[0097] Step d: Based on the estimated optimal time-varying rotational speed, perform time-domain to angle-domain mapping on the filtered vibration signal from step a to construct the angle-domain vibration signal. Then, using the same Fourier synchronous compression transform as in step b, construct the time-order distribution matrix to extract the order features of the underwater rotating machinery vibration related to the rotational speed. Specifically, the time-domain to angle-domain mapping of the filtered vibration signal from step a is performed by first integrating the estimated optimal time-varying rotational speed ω(t) to obtain the cumulative rotational angle θ(t). Then, a linear interpolation method is used to map the filtered vibration signal y[n] to the angle domain, thereby constructing the angle domain vibration signal y[θ]. k ],as follows:

[0098]

[0099] θ k =kΔθ

[0100] θ n ≤θ k ≤θ n+1

[0101] Where, θ k Let θ be the angle at the k-th sampling point, where k = 0, 1, 2, ... n and θ n+1y[n] and y[n+1] are the angles at the nth and (n+1)th sampling points, respectively; y[n] and y[n+1] are the filtered vibration signals at the nth and (n+1)th sampling points, respectively; Δθ is the preset angle domain sampling interval, determined by the cumulative rotation angle θ(t) and the number of samples k, and is set to Δθ = 0.00236 to generate the angle sequence θ. k =kΔθ(k=0,1,2,...,10) 5 ).

[0102] The vibration signal order characteristic map obtained by constructing the time-order distribution matrix is ​​shown below. Figure 4 As shown, it can be clearly seen that the order feature map exhibits obvious energy concentration characteristics on the order axis, reflecting the characteristic that the order of the vibration signal does not change with the rotational speed, and can accurately capture the key frequency components in the vibration signal.

[0103] Step e: Perform order slicing on the time-order distribution matrix to obtain the order energy spectrum of the angular domain vibration signal, i.e., the energy distribution along the entire order axis, thereby determining the dominant order component causing vibration in the original mechanical vibration signal, i.e., extracting the excitation characteristics based on the order energy distribution characteristics; at the same time, perform time slicing on the time-order distribution matrix to obtain the rotational speed energy spectrum of the angular domain vibration signal, i.e., the energy distribution within the entire rotational speed range, extracting the vibration intensity based on the rotational speed energy distribution characteristics, thereby obtaining the optimal rotational speed, and controlling the rotational speed of the underwater rotating machinery to operate under optimal operating conditions.

[0104] The time-order distribution matrix is ​​sliced ​​according to its order, as follows:

[0105] e11) First, divide the order range and determine the upper limit value O of the target order range. max as follows:

[0106]

[0107] Where P and Q are the interpolation factor and the extraction factor, respectively; f s f0 represents the sampling rate of the original mechanical vibration signal; f0 represents the maximum fundamental frequency of the filtered vibration signal. In specific implementation, the upper limit of the target order range is determined. max =150.

[0108] Then, the upper limit of the range from 0 to the target order is O. max The orders between them are divided into several equally spaced order slices according to a preset order resolution ΔO, thereby generating the order sequence {O}. i |i = 1, 2, ..., N}, O iLet N be the number of order slices, where N is the total number of order slices. In practical applications, since the energy proportion of higher orders is very low, the target order range is set to 0-100. Next, the order axis from 0 to 100 is divided into several equally spaced order slices according to a preset order resolution ΔO = 1, generating the order sequence {O}. i |i=1,2,…,100}.

[0109] e12) Based on each order slice, the order domain integration interval is set over its entire time range as follows:

[0110]

[0111] Among them, Ω i For the i-th order slice O i The order of the domain integration interval.

[0112] Based on the order domain integration interval, the cumulative energy of each order slice is obtained as follows:

[0113]

[0114] Among them, E(O) i ) represents the i-th order slice O i The cumulative energy; F(O,t) is the time-order distribution matrix of the order slice O at time t.

[0115] e13) After obtaining the cumulative energy of each order slice, it is represented as an order energy distribution sequence {(O1, E(O1)), (O2, E(O2)), ..., (O1, E(O1))}. N ,E(O N The cumulative energy of each order slice is summed and normalized to obtain the order energy spectrum of the angular domain vibration signal, i.e., the relative order energy distribution is as follows:

[0116]

[0117] in, This indicates the order of the energy spectrum.

[0118] For each order O i Calculate the total cumulative energy over the entire time span, and define the order-domain integration interval:

[0119]

[0120] Obtain the order energy map, analyze the contribution ratio of each order to the total vibration, and identify the dominant order. The obtained order energy map is as follows: Figure 5As shown, the vibration order of this underwater rotating machinery is mainly concentrated in multiples of 7, which is consistent with the vibration characteristics of a piston pump with a seven-plunger structure. Meanwhile, the dominant order is 35, and the vibration energy generated by the dominant order accounts for more than 17% of the total vibration energy.

[0121] The contribution of each order to the overall vibration can be intuitively obtained through the relative order energy spectrum. By setting a preset energy threshold, the dominant order component causing the vibration can be identified, thereby effectively evaluating the vibration source and providing a basis for the optimized design of mechanical structures.

[0122] The time-order distribution matrix is ​​processed by time slicing to obtain the rotational speed energy spectrum of the original mechanical vibration signal, as follows:

[0123] Step e21: Based on the optimal time-varying speed estimated in step c, determine the speed range ω0~ω max ω max ω and ω0 are the estimated maximum and minimum values ​​of the optimal time-varying speed, respectively; then, the speed range is divided into several equally spaced speed slices according to the preset speed resolution Δω, thereby generating the speed sequence {ω j |j=1,2,…,M},ω j Let M be the j-th rotational speed slice, and M be the total number of rotational speed slices; then determine the time sequence {T} based on the time corresponding to the rotational speed sequence. j |j=1,2,…,M},T j Let ω be the time corresponding to the j-th speed slice. In practice, based on the estimated speed range, the speed analysis range is determined to be 1000–2000 RPM, and this range is divided into several equally spaced speed slices according to a preset speed resolution Δω = 2 RPM, generating the speed sequence {ω}. j |j=1,2,…,100}; determine the corresponding time-domain resolution ΔT=1000 according to the rotational speed sequence; similarly, generate the time sequence {T j |j=1,2,…,100}.

[0124] Step e22: Set the time-domain integration interval according to the time series as follows:

[0125]

[0126]

[0127] Where, Φ j For the j-th rotational speed slice ω j The time-domain integration interval is defined; ΔT is the time-domain resolution; P and Q are the interpolation factor and decimation factor, respectively; f s The sampling rate of the original mechanical vibration signal is denoted as ; T is the sampling duration of the original mechanical vibration signal, in seconds.

[0128] Based on the time-domain integration interval, the cumulative energy of each rotational speed slice is obtained as follows:

[0129]

[0130] Where, E(ω) j ) represents the j-th rotational speed slice ω j The cumulative energy; F(O,t) is the time-order distribution matrix under the order slice O at time t, which is plotted on the order graph according to t∈Φ. j In the specific implementation of time-slice analysis, the cumulative energy summation across the entire order is calculated at time-domain resolution, and the time-domain integration interval Φ is defined. j =[T j -500,T j +500].

[0131] Step e23: Based on the correspondence between the time domain and the speed domain, reorder the cumulative energy of each speed slice in ascending order of speed, resulting in a speed energy distribution sequence {(ω1, E(ω1)), (ω2, E(ω2)), ..., (ω... M ,E(ω M Then, the cumulative energy of each reordered rotational speed slice is normalized to obtain the rotational speed energy spectrum of the angular domain vibration signal, i.e., the relative rotational speed energy distribution is as follows:

[0132]

[0133] in, For the j-th rotational speed slice ω j The rotational energy spectrum.

[0134] Based on the rotational speed energy spectrum, the trend of vibration energy variation with rotational speed is obtained. Within a preset rotational speed range, the rotational speed at which the vibration energy is lowest is taken as the optimal rotational speed. The vibration intensity of the underwater rotating machinery is controlled, thereby optimizing the system's operating conditions. A rotational speed energy distribution diagram is obtained, and the trend of vibration intensity variation with rotational speed is analyzed to select the optimal operating conditions for the system. The obtained rotational speed energy diagram is shown below. Figure 6 As shown, the underwater rotating machinery exhibits relatively low and stable vibration energy within the speed range of 1350–1750 RPM, and this speed range can meet general operational requirements. Therefore, the optimal operating conditions for this system can be determined.

[0135] Based on the time-order distribution matrix, the excitation characteristics and vibration intensity of the system are comprehensively evaluated from both the order domain and the time domain. First, through order slice analysis, the energy distribution characteristics along the entire order axis are obtained to determine the dominant order components causing vibration. Second, time slice analysis is performed, and the data on the time axis are rearranged in order of speed from low to high to obtain the energy distribution characteristics within the entire speed range, revealing the trend of system vibration intensity with speed, thereby determining the optimal operating conditions of the system.

[0136] This embodiment verifies the effectiveness of the method of the present invention in analyzing the vibration characteristics of underwater rotating machinery under variable speed conditions, as shown in the following specific examples:

[0137] 1) Without a speed sensor, the speed estimation error is small and can meet the analysis requirements.

[0138] 2) Through order energy analysis, the main vibration order components of underwater machinery under variable speed conditions were identified.

[0139] 3) Through speed energy analysis, the optimal operating conditions of the system in different speed ranges were obtained.

[0140] The method of this invention can be widely applied to vibration monitoring and design optimization of rotating machinery such as underwater thrusters, underwater motors, and pumps.

[0141] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis, characterized in that, include: Step a: Obtain the raw mechanical vibration signal of the underwater rotating machinery during underwater operation, and obtain the filtered vibration signal after preprocessing the raw mechanical vibration signal; Step b: Perform a Fourier synchronous compression transform on the filtered vibration signal to construct the time-frequency distribution matrix of the filtered vibration signal; Step c: Based on the time-frequency distribution matrix of the filtered vibration signal, establish an optimal path model containing a smoothing constraint term, thereby extracting the optimal time-frequency path distribution of the filtered vibration signal. In the optimal time-frequency path distribution, obtain the instantaneous frequency trajectory of the filtered vibration signal as the rotational speed changes, thereby obtaining the estimated optimal time-varying rotational speed. Step d: Based on the estimated optimal time-varying rotational speed, perform time-domain to angle-domain mapping on the filtered vibration signal in step a to construct the angle-domain vibration signal, and then use the same Fourier synchronous compression transform as in step b to construct the time-order distribution matrix. Step e: Perform order slicing on the time-order distribution matrix to obtain the order energy spectrum of the angular domain vibration signal, thereby determining the dominant order component causing vibration in the original mechanical vibration signal; at the same time, perform time slicing on the time-order distribution matrix to obtain the rotational speed energy spectrum of the angular domain vibration signal, thereby obtaining the optimal rotational speed and controlling the rotational speed of the underwater rotating machinery to operate under optimal operating conditions.

2. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step a, the original mechanical vibration signal is preprocessed based on the fractional resampling method, specifically by performing upsampling and zero-placing processing, bidirectional anti-aliasing filtering based on Butterworth filter, and downsampling and decimation processing in sequence.

3. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step b, the Fourier synchronous compression transform employs a synchronous compression transform based on the short-time Fourier transform.

4. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step c, the optimal path model including the smoothing constraint term is as follows: where U(t, f c,t ) and U(t-1, f c,t-1 ) are the optimal time-frequency path distribution of the filtered vibration signal at time t and t-1, respectively, f c,t and f c,t-1 are the frequency of the filtered vibration signal at time t and t-1, respectively; F(t, f c ) is the time-frequency distribution matrix; Δ is the maximum frequency change step; and λ is the weighting parameter. Based on the frequency f of the filtered vibration signal at each time t c,t Obtain the instantaneous frequency trajectory f of the filtered vibration signal at each time t as the rotational speed changes. c (t), thus obtaining the estimated optimal time-varying speed data as follows: ω(t)=60·f c (t) Where ω(t) is the estimated optimal time-varying rotational speed.

5. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step d, the filtered vibration signal from step a is mapped from the estimated optimal time-varying rotational speed to the angle domain. Specifically, the estimated optimal time-varying rotational speed ω(t) is first integrated to obtain the cumulative rotation angle θ(t); then, a linear interpolation method is used to map the filtered vibration signal y[n] to the angle domain, thereby constructing the angle domain vibration signal y[θ]. k ],as follows: i k =kΔθ i n ≤θ k ≤θ n+1 Where, θ k Let θ be the angle at the k-th sampling point, where k = 0, 1, 2, ... n and θ n+1 y[n] and y[n+1] are the angles at the nth and (n+1)th sampling points, respectively; y[n] and y[n+1] are the filtered vibration signals at the nth and (n+1)th sampling points, respectively; Δθ is the preset angle domain sampling interval.

6. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step e, the time-order distribution matrix is ​​processed by order slicing, as follows: e11) First, divide the order range and determine the upper limit value O of the target order range. max as follows: Where P and Q are the interpolation factor and the extraction factor, respectively; f s f0 is the sampling rate of the original mechanical vibration signal; f0 is the maximum fundamental frequency of the filtered vibration signal. Then, the upper limit of the range from 0 to the target order is O. max The orders between them are divided into several equally spaced order slices according to a preset order resolution ΔO, thereby generating the order sequence {O}. i |i = 1, 2, ..., N}, O i Let N be the i-th order slice, and N be the total number of order slices. e12) The order domain integration intervals are set according to each order slice as follows: Among them, Ω i For the i-th order slice O i The order of the domain integration interval; Based on the order domain integration interval, the cumulative energy of each order slice is obtained as follows: Among them, E(O) i ) represents the i-th order slice O i The cumulative energy; F(O,t) is the time-order distribution matrix of the order slice O at time t; e13) After obtaining the cumulative energy of each order slice, the cumulative energy of each order slice is summed and normalized to obtain the order energy spectrum of the angular domain vibration signal as follows: in, This indicates the order of the energy spectrum.

7. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 1, characterized in that: In step e, the time-order distribution matrix is ​​processed by time slicing to obtain the rotational speed energy spectrum of the original mechanical vibration signal, as follows: Step e21: Based on the optimal time-varying speed estimated in step c, determine the speed range ω0~ω max ω max ω and ω0 are the estimated maximum and minimum values ​​of the optimal time-varying rotational speed, respectively; Then, the speed range is divided into several equally spaced speed slices according to a preset speed resolution Δω, thereby generating a speed sequence {ω}. j |j=1,2,…,M},ω j Let M be the j-th rotational speed slice, and M be the total number of rotational speed slices; then determine the time sequence {T} based on the time corresponding to the rotational speed sequence. j |j=1,2,…,M},T j The time corresponding to the j-th rotational speed slice; Step e22: Set the time-domain integration interval according to the time series as follows: Where, Φ j For the j-th rotational speed slice ω j The time-domain integration interval is defined; ΔT is the time-domain resolution; P and Q are the interpolation factor and decimation factor, respectively; f s The sampling rate of the original mechanical vibration signal is denoted as ; T is the sampling duration of the original mechanical vibration signal. Based on the time-domain integration interval, the cumulative energy of each rotational speed slice is obtained as follows: Where, E(ω) j ) represents the j-th rotational speed slice ω j The cumulative energy; F(O,t) is the time-order distribution matrix of the order slice O at time t; Step e23: Based on the correspondence between the time domain and the rotational speed domain, the cumulative energy of each rotational speed slice is reordered in ascending order of rotational speed; then, the maximum value of the cumulative energy of each reordered rotational speed slice is normalized to obtain the rotational speed energy spectrum of the angular domain vibration signal as follows: in, For the j-th rotational speed slice ω j The rotational energy spectrum.

8. The method for extracting vibration features of underwater rotating machinery based on time-frequency energy analysis according to claim 7, characterized in that: In step e, the trend of vibration energy variation with rotational speed is obtained based on the rotational speed energy spectrum. Within a preset rotational speed range, the rotational speed at which the vibration energy is lowest is obtained as the optimal rotational speed.

9. An electronic device, characterized in that, include: A memory and a processor are coupled to each other, wherein the memory stores program data, and the processor invokes the program data to perform the method as described in any one of claims 1-8.

10. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements the method as described in any one of claims 1-8.

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