A rotating machinery characteristic frequency enhancement extraction method based on optimal weighted envelope spectrum

Abstract

The application discloses a rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum, and comprises the following steps: (1) collecting vibration or noise data of the rotating machinery as a monitoring signal and calculating a spectrum correlation function; (2) normalizing the spectrum correlation function and constructing an enhanced envelope spectrum; (3) determining a basic modulation frequency; (4) performing slice processing on the spectrum correlation function and estimating a carrier-to-noise ratio; (5) constructing a cyclic stationary measure function of the basic modulation frequency and harmonic components thereof; (6) taking the carrier-to-noise ratio as an initial weighting function and searching for an optimal weighting function by using a cuckoo optimization algorithm; (7) performing weighted processing on the spectrum correlation function by using the optimal weighting function to obtain an optimal weighted spectrum correlation; and (8) integrating the optimal weighted spectrum correlation along a spectrum frequency axis to obtain an optimal weighted envelope spectrum. The application can effectively extract the modulation frequency components in the rotating machinery vibration noise signal under complex and strong noise interference.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, and in particular relates to a method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum. Background Technology

[0002] Rotating machinery is widely used in industrial production, water conservancy and hydropower, and military applications. Extracting its characteristic frequencies helps in the condition monitoring and fault diagnosis of critical rotating machinery equipment. Characteristic frequency extraction methods mainly include spectrum analysis and demodulation analysis.

[0003] The main approach to spectrum analysis is Fourier transform, which can depict the amplitude and phase of signal components at different frequencies. For example, Chinese patent document CN112633098A discloses a method for diagnosing faults in rotating machinery, which uses short-time Fourier transform to perform spectrum analysis on the vibration signal of the rotating machinery under test, which is acquired in real time, to obtain the spectrum of the vibration signal.

[0004] Spectrum analysis can depict the frequency distribution of deterministic signals relatively completely, but it is not suitable for the analysis of random signals. In reality, the vibration noise signals of rotating machinery are basically random signals, which limits the general applicability of spectrum analysis.

[0005] Demodulation analysis is another effective approach for extracting characteristic frequencies of rotating machinery, including signal processing methods such as narrowband envelope demodulation and cyclostationary analysis. For example, Chinese patent document CN104596756A discloses a multi-band envelope spectral array for rotating machinery fault diagnosis.

[0006] Narrowband envelope demodulation first identifies the optimal filtering frequency band containing the modulated signal, performs filtering on this band to obtain the filtered signal, constructs the envelope of the filtered signal using Hilbert transform, and finally performs Fourier transform on the envelope to obtain the envelope spectrum. This method is suitable for local defect detection and weak fault diagnosis in rotating machinery. Its drawback is that narrowband envelope demodulation only selects a specific narrow band for analysis, resulting in poor algorithm robustness, especially prone to failure under low signal-to-noise ratio conditions containing multiple types of noise, thus limiting its effectiveness.

[0007] Cyclostationary analysis can make full use of the cyclostationary components in the monitoring signals of rotating machinery to effectively extract the modulation frequency components. However, this method is also limited in the application of characteristic frequency extraction of rotating machinery. This is mainly because, in addition to the characteristic modulation frequencies caused by fault phenomena and key components, the monitoring signals usually also contain cyclostationary noise interference from other mechanical, electrical, and communication equipment. Traditional cyclostationary analysis cannot remove these noise interferences, which will affect the identification and extraction of characteristic frequencies of rotating machinery. Summary of the Invention

[0008] This invention provides a method for enhancing and extracting characteristic frequencies of rotating machinery based on optimal weighted envelope spectrum. It can effectively extract the modulation frequency components in the vibration noise signal of rotating machinery under complex and strong noise interference, and can be applied to the fields of condition monitoring and fault diagnosis of rotating machinery.

[0009] A method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum includes the following steps:

[0010] (1) Collect vibration or noise data of rotating machinery as monitoring signals and calculate the spectral correlation function of the monitoring signals;

[0011] (2) Normalize the spectral correlation function to obtain the spectral coherence function, and construct the enhanced envelope spectrum;

[0012] (3) Determine the fundamental modulation frequency based on the prior information of the rotating machinery, the diagnostic task, and the characteristic information of the enhanced envelope spectrum;

[0013] (4) Slice the spectral correlation function at the zero modulation frequency and the fundamental modulation frequency, and estimate the carrier-to-noise ratio based on the slicing results;

[0014] (5) Give the definition of the weighted spectrum correlation function, construct the cyclostationary metric function of the fundamental modulation frequency and its harmonic components from it, and regard it as the objective function;

[0015] (6) Using the carrier-to-noise ratio as the initial weighting function, set the search space for the optimal weighting function, and use the Cuckoo optimization algorithm to search for the optimal weighting function that maximizes the objective function;

[0016] (7) The spectral correlation function is weighted using the optimal weighting function to calculate the optimal weighted spectral correlation.

[0017] (8) Integrate the optimal weighted spectral correlation along the spectral frequency axis to obtain the optimal weighted envelope spectrum.

[0018] The method of the present invention can overcome the shortcomings of existing spectrum analysis and demodulation methods, which cannot accurately and effectively extract the modulation frequency of rotating machinery or contain too much noise interference in the extraction results. The method has high noise resistance and strong robustness, and can effectively achieve enhanced extraction of the characteristic frequency of rotating machinery under low signal-to-noise ratio conditions and complex noise interference conditions.

[0019] In step (1), the specific process of calculating the spectral correlation function of the monitoring signal is as follows:

[0020] (1-1) Calculate the two narrowband filtered signals x(t) of the monitoring signal x(t). Δf (t;f1) and x Δf The correlation coefficient corr between (t; f2) isx (f1, f2), the calculation formula is as follows:

[0021]

[0022] In the formula, t represents time, f represents frequency, f1≥f2, e is the natural constant, j is the imaginary number, * is the conjugate sign, -T / 2 and T / 2 are the lower and upper time limits, Δf represents the filtering range of the narrowband filtered signal, and x Δf (t;f1) and x Δf (t;f2) represent narrowband filtered time-domain signals with passband ranges of (f1-Δf / 2,f1+Δf / 2) and (f2-Δf / 2,f2+Δf / 2), respectively.

[0023] (1-2) Assuming f = (f1 + f2) / 2 and α = f1 - f2, the spectral correlation function of the monitoring signal can be obtained, and its calculation formula is as follows:

[0024]

[0025] In the formula, S x (α,f) is the spectral correlation function, where α is the modulation frequency and f is the carrier frequency.

[0026] The specific process of step (2) is as follows:

[0027] (2-1) Normalize the spectral correlation function of the monitoring signal to obtain the spectral coherence function γ of the monitoring signal. x (α,f), the calculation formula is as follows:

[0028]

[0029] In the formula, The result when the modulation frequency of the representative spectral correlation function is zero, i.e., we have

[0030] (2-2) Integrate the spectral coherence function along the carrier frequency axis to calculate the enhanced envelope spectrum (EES) of the monitoring signal. x (α), the calculation formula is as follows:

[0031]

[0032] In the formula, f1 and f2 are the lower and upper limits of the carrier frequency integral, respectively, and their default values ​​are 0 and F. s / 2, F s The sampling frequency for the monitoring signal.

[0033] The specific process of step (3) is as follows:

[0034] (3-1) Based on prior information, determine the faulty component of the rotating machinery to be diagnosed, and then determine the theoretical fundamental modulation frequency α based on the corresponding fault mechanism. B-T ;

[0035] (3-2) Because the values ​​of the modulation frequencies in the enhanced envelope spectrum are all integer multiples of the modulation frequency resolution Δα, therefore, from the enhanced envelope spectrum EES x (α) is used to obtain the theoretical fundamental modulation frequency α of the rotating machinery. B-T The closest modulation frequency value α opt =MΔα, where M is a positive integer;

[0036] (3-3) Modulation frequency range [α opt -NΔα,α opt The range of candidate fundamental modulation frequencies is defined as α[+NΔα], where N is a positive integer. The modulation frequency corresponding to the maximum amplitude of the enhanced envelope spectrum is selected from the candidate range and determined as the fundamental modulation frequency α. B .

[0037] The specific process of step (4) is as follows:

[0038] (4-1) gives the definition of carrier-to-noise ratio, which is the ratio of the carrier power spectral density of the second-order cyclic stationary component to the stationary noise power spectral density:

[0039]

[0040] In the formula, CNR(f) represents the carrier-to-noise ratio, and P v (f) represents the power spectral density of the carrier signal v(t), which contains the second-order cyclic stationary component of the monitoring signal. n represents the stationary noise contained in the monitoring signal s Power spectral density of (t);

[0041] (4-2) For signals containing second-order cyclostationary components and stationary noise:

[0042]

[0043] In the formula, Let v(t) represent the modulated signal of the second-order cyclostationary component, and n represent the carrier signal of the second-order cyclostationary component. s (t) represents stationary noise; its theoretical spectral correlation value is:

[0044]

[0045] In the formula, δ(·) represents the Kronecker function, which satisfies:

[0046]

[0047] Spectral correlation at α=0 and α=α B The value at which the station is used is used to estimate the power spectral density of stationary noise:

[0048]

[0049] (4-3) gives the definition of second-order cyclic stationary signal-to-noise ratio, which is the ratio of the absolute value of the spectral correlation of the monitoring signal to the power spectral density of the stationary noise:

[0050]

[0051] In the formula, SNR CS2 (α,f) represents the second-order cyclic stationary signal-to-noise ratio;

[0052] (4-4) The signal-to-noise ratio is stable at α = α through a second-order cyclic method. B The value at that location is used to estimate the carrier-to-noise ratio:

[0053]

[0054] As can be seen from the above formula, SNR CS2 (α B f) is approximately equal to the carrier-to-noise ratio after several weighted frequency shifts. The sum of the superpositions has a weighting factor of . Frequency shift amount is The frequency shift is significantly smaller than the carrier frequency range and will not have a significant impact on the carrier distribution estimation. Therefore, the second-order cyclostationary signal-to-noise ratio is within α = α B The value at that point can depict the carrier-to-noise ratio distribution.

[0055] The specific process of step (5) is as follows:

[0056] (5-1) The definition of weighted envelope spectrum is given:

[0057]

[0058] In the formula, represents the weighted envelope spectrum, and w(f) represents the weighting function;

[0059] (5-2) The candidate range of the fundamental modulation frequency and the corresponding cyclic frequencies of its harmonic components is determined as follows:

[0060] FB k =[kα B -mΔα,kα B +mΔα]

[0061] In the formula, FB k The range of cyclic frequencies corresponding to the kth harmonic of the fundamental modulation frequency is represented by mΔα, which represents the single-sided selection limit.

[0062] (5-3) Obtain the corresponding characteristic modulation frequency peaks from the weighted envelope spectrum. The calculation formula is as follows:

[0063]

[0064]

[0065] In the formula, m k The amplitude of the kth harmonic of the basic modulation frequency Indicates on FB k Take the maximum value from the middle.

[0066] (5-4) Assume the range of the cycle frequency under consideration is (0, α) max Within this range, the order of the highest harmonic of the fundamental modulation frequency is k. max The maximum index of the cycle frequency is n. max Based on this, the objective function used to measure the magnitude of cyclic stationarity is defined as:

[0067]

[0068] The specific process of step (6) is as follows:

[0069] (6-1) The process of obtaining the optimal weighting function is regarded as an optimization problem. Let the carrier-to-noise ratio be the initial weighting function:

[0070]

[0071] In the formula, w b ∈R 1×d The weighting function represents a vector form;

[0072] (6-2) Set the search range for the optimal weighting function:

[0073]

[0074] In the formula, w L and w U Let X and X represent the lower-bound weighted function and the upper-bound weighted function, respectively, and X% represent the percentage of one-sided fluctuation of the weighted function. Therefore:

[0075]

[0076] (6-3) Using the Cuckoo Optimization Algorithm, the optimal weighted function that maximizes the objective function is obtained.

[0077] In step (7), the formula for calculating the optimal weighted spectral correlation is as follows:

[0078]

[0079] In the formula, w opt (f) is the optimal weighting function. This represents the correlation of the optimal weighted spectrum.

[0080] In step (8), the formula for obtaining the optimal weighted envelope spectrum is:

[0081]

[0082] In the formula, This is the optimal weighted envelope spectrum.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] 1. This invention proposes a method for estimating the carrier-to-noise ratio of a monitoring signal using a spectral correlation function, which can roughly capture the carrier frequency range corresponding to the modulated signal components.

[0085] 2. This invention treats the acquisition of the optimal weighting function as an optimization problem and uses the Cuckoo Optimization Algorithm for optimization. This method can effectively obtain the optimal weighting function.

[0086] 3. The method proposed in this invention is based on cyclostationary analysis and spectral correlation weighting processing for signal demodulation, which can accurately and effectively extract the characteristic modulation frequency components of rotating machinery. The relevant information can be used for condition monitoring and fault diagnosis of rotating machinery. Attached Figure Description

[0087] Figure 1 This is a schematic flowchart of a rotating machinery feature frequency enhancement extraction method based on optimal weighted envelope spectrum according to the present invention.

[0088] Figure 2 This is a time-domain diagram of a simulated signal containing Gaussian noise, impulse noise, and cyclic stationary noise in an embodiment of the present invention.

[0089] Figure 3 This is the narrowband demodulation result of the kurtosis spectrum of the simulated signal in this embodiment of the invention;

[0090] Figure 4 This is the cyclostationary analysis and demodulation result of the simulated signal in the embodiment of the present invention;

[0091] Figure 5 This is the optimal weighted spectral correlation result of the simulated signal in the embodiments of the present invention;

[0092] Figure 6 This represents the optimal weighted envelope spectrum demodulation result of the simulated signal in this embodiment of the invention.

[0093] Figure 7This is the narrowband demodulation result of the kurtosis spectrum of the acoustic signal of the rolling bearing in this embodiment of the invention;

[0094] Figure 8 This is the result of cyclic stationarity analysis and demodulation of the acoustic signal of the rolling bearing in this embodiment of the invention;

[0095] Figure 9 This is the optimal weighted envelope spectrum demodulation result of the rolling bearing acoustic signal in this embodiment of the invention;

[0096] Figure 10 This is the narrowband demodulation result of the kurtosis spectrum of the centrifugal pump vibration signal in this embodiment of the invention;

[0097] Figure 11 This is the result of cyclic stationarity analysis and demodulation of the centrifugal pump vibration signal in this embodiment of the invention;

[0098] Figure 12 This is the optimal weighted envelope spectrum demodulation result of the centrifugal pump vibration signal in this embodiment of the invention. Detailed Implementation

[0099] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not constitute any limitation thereof.

[0100] like Figure 1 As shown, a method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum includes the following steps:

[0101] S01: Collect vibration or noise data of rotating machinery as monitoring signals and calculate the spectral correlation function of the monitoring signals.

[0102] (1-1) Calculate the two narrowband filtered signals x(t) of the monitoring signal x(t). Δf (t;f1) and x Δf The correlation coefficient corr between (t; f2) (where f1≥f2 is specified here) is x (f1, f2), the calculation formula is as follows:

[0103]

[0104] In the formula, t represents time, f represents frequency, e is the natural constant, j is the imaginary number, * is the conjugate sign, -T / 2 and T / 2 are the lower and upper time limits, Δf represents the filtering range of the narrowband filtered signal, and x Δf (t;f1) and x Δf (t;f2) represent narrowband filtered time-domain signals with passband ranges of (f1-Δf / 2,f1+Δf / 2) and (f2-Δf / 2,f2+Δf / 2), respectively.

[0105] (1-2) Assuming f = (f1 + f2) / 2 and α = f1 - f2, the spectral correlation function of the monitoring signal can be obtained, and its calculation formula is as follows:

[0106]

[0107] In the formula, S x (α,f) is the spectral correlation function, where α is the cycle frequency (also known as the modulation frequency) and f is the spectral frequency (also known as the carrier frequency, or simply the frequency).

[0108] S02, normalize the spectral correlation function to obtain the spectral coherence function, and construct the enhanced envelope spectrum.

[0109] (2-1) Normalize the spectral correlation function of the monitoring signal to obtain the spectral coherence function γ of the monitoring signal. x (α,f), the calculation formula is as follows:

[0110]

[0111] In the formula, The result when the modulation frequency of the representative spectral correlation function is zero, i.e., we have

[0112] (2-2) Integrate the spectral coherence function along the carrier frequency axis to calculate the enhanced envelope spectrum (EES) of the monitoring signal. x (α), the calculation formula is as follows:

[0113]

[0114] In the formula, f1 and f2 are the lower and upper limits of the carrier frequency integral, respectively, and their default values ​​are generally 0 and F. s / 2, F s The sampling frequency for the monitoring signal.

[0115] S03. Determine the fundamental modulation frequency based on prior information about the rotating machinery, the diagnostic task, and the characteristic information of the enhanced envelope spectrum.

[0116] (3-1) Based on prior information, determine the faulty component of the rotating machinery to be diagnosed, and then determine the theoretical fundamental modulation frequency α based on the corresponding fault mechanism. B-T ;

[0117] (3-2) Because the values ​​of the modulation frequencies in the enhanced envelope spectrum are all integer multiples of the modulation frequency resolution Δα, therefore, from the enhanced envelope spectrum EES x (α) is used to obtain the theoretical fundamental modulation frequency α of the rotating machinery. B-T The closest modulation frequency value α opt =MΔα (M is a positive integer);

[0118] (3-3) Modulation frequency range [α opt -NΔα,α opt The range of candidate fundamental modulation frequencies is determined by the sum of α and NΔα (where N is a positive integer). The modulation frequency corresponding to the maximum amplitude of the enhanced envelope spectrum is then selected from this range and determined as the fundamental modulation frequency α. B .

[0119] S04, slices the spectral correlation function at the zero modulation frequency and the fundamental modulation frequency, and estimates the carrier-to-noise ratio based on the slicing results.

[0120] (4-1) gives the definition of carrier-to-noise ratio, which is the ratio of the carrier power spectral density of the second-order cyclic stationary component to the stationary noise power spectral density:

[0121]

[0122] In the formula, CNR(f) represents the carrier-to-noise ratio, and P v (f) represents the power spectral density of the carrier signal v(t), which contains the second-order cyclic stationary component of the monitoring signal. The stationary noise n contained in the monitoring signal s The power spectral density of (t).

[0123] (4-2) For signals containing second-order cyclostationary components and stationary noise:

[0124]

[0125] In the formula, Let v(t) represent the modulated signal of the second-order cyclostationary component, and n represent the carrier signal of the second-order cyclostationary component. s (t) represents stationary noise. Its theoretical spectral correlation value is:

[0126]

[0127] In the formula, δ(·) represents the Kronecker function, which satisfies:

[0128]

[0129] Spectral correlation at α=0 and α=α B The value at a given location can be used to roughly estimate the power spectral density of stationary noise:

[0130]

[0131] (4-3) gives the definition of second-order cyclic stationary signal-to-noise ratio, which is the ratio of the absolute value of the spectral correlation of the monitoring signal to the power spectral density of the stationary noise:

[0132]

[0133] In the formula, SNR CS2 (α,f) represents the second-order cyclic stationary signal-to-noise ratio.

[0134] (4-4) The signal-to-noise ratio is stable at α = α through a second-order cyclic method. B The value at this point is used to roughly estimate the carrier-to-noise ratio:

[0135]

[0136] As can be seen from the above formula, SNR CS2 (α B f) is approximately equal to the carrier-to-noise ratio after several weighted frequency shifts. The sum of the superpositions has a weighting factor of . Frequency shift amount is (Generally, the frequency shift is significantly smaller than the carrier frequency range and will not have a significant impact on carrier distribution estimation). Therefore, it can be seen that the second-order cyclostationary signal-to-noise ratio is within α = α... B The value at that point can depict the carrier-to-noise ratio distribution.

[0137] S05 gives the definition of the weighted spectral correlation function, from which a cyclostationary metric function for the fundamental modulation frequency and its harmonic components is constructed, and this function is regarded as the objective function.

[0138] (5-1) The definition of weighted envelope spectrum is given:

[0139]

[0140] In the formula, represents the weighted envelope spectrum, and w(f) represents the weighting function.

[0141] (5-2) The candidate range of the fundamental modulation frequency and the corresponding cyclic frequencies of its harmonic components is determined as follows:

[0142] FB k =[kα B -mΔα,kα B +mΔα]

[0143] In the formula, FB k The range of candidate cyclic frequencies corresponding to the kth harmonic of the fundamental modulation frequency is represented by mΔα, which represents the single-sided candidate limit.

[0144] (5-3) Obtain the corresponding characteristic modulation frequency peaks from the weighted envelope spectrum. The calculation formula is as follows:

[0145]

[0146]

[0147] In the formula, m k The amplitude of the kth harmonic of the basic modulation frequency Indicates on FB k Take the maximum value from the middle.

[0148] (5-4) Assume the range of the cycle frequency under consideration is (0, α) max Within this range, the order of the highest harmonic of the fundamental modulation frequency is k. max The maximum index of the cycle frequency is n. max Based on this, the objective function used to measure the magnitude of cyclic stationarity is defined as:

[0149]

[0150] S06. Using the carrier-to-noise ratio as the initial weighting function, the search space for the optimal weighting function is set, and the optimal weighting function that maximizes the objective function is obtained by using the Cuckoo Optimization Algorithm.

[0151] (6-1) Consider the process of obtaining the optimal weighting function as an optimization problem, and let the carrier-to-noise ratio be the initial value of the weighting function:

[0152]

[0153] In the formula, w b ∈R 1×d This represents a weighted function in vector form.

[0154] (6-2) Set the search range for the optimal weighting function:

[0155]

[0156] In the formula, w L and w U Let X and X represent the lower-bound weighted function and the upper-bound weighted function, respectively, and X% represent the percentage of one-sided fluctuation of the weighted function. Therefore:

[0157]

[0158] (6-3) The optimal weighting function is obtained by using the Cuckoo Optimization Algorithm. The Cuckoo Optimization Algorithm includes large-span exploratory walking and small-span random walking.

[0159] Large-scale exploratory walking is achieved through Levy flight:

[0160]

[0161]

[0162]

[0163] In the formula, α and s represent the values ​​of the i-th solution of the Cuckoo algorithm after the t-th and t+1-th iterations, respectively. α > 0 represents the step size scaling factor, s represents the iteration step size, and Γ(λ) represents the gamma function.

[0164] Small-span random walks are achieved using the following formula:

[0165]

[0166] In the formula, Represents scalar multiplication. and H(·) represents two distinct solutions to this optimization problem, H(·) represents the Heaviside function, and ε represents the two distinct solutions to this optimization problem. i Representative solution The percentage of all solutions ranked in the t-th iteration (according to the solution) The ranking is based on the corresponding objective function; the larger the objective function, the higher the ε. i The smaller).

[0167] The process of using the Cuckoo Optimization Algorithm to search for the optimal weighting function is summarized as follows:

[0168]

[0169] S07, the spectral correlation function is weighted using the optimal weighting function to calculate the optimal weighted spectral correlation.

[0170] The calculation process for obtaining the optimal weighted spectrum is as follows:

[0171]

[0172] In the formula, w opt (f) is the optimal weighting function. This represents the correlation of the optimal weighted spectrum.

[0173] S08, integrate the optimal weighted spectral correlation along the spectral frequency axis to obtain the optimal weighted envelope spectrum.

[0174] The calculation process for obtaining the optimal weighted envelope spectrum is as follows:

[0175]

[0176] In the formula, This is the optimal weighted envelope spectrum.

[0177] To verify the effectiveness of this invention, simulation signals containing Gaussian noise, impulse noise, and cyclic stationary noise were analyzed, as follows:

[0178] The above methods are used to analyze the simulated signal x(t) containing Gaussian noise and impulse noise:

[0179]

[0180] In the formula, n p (t) and n s (t) represent impulse noise and Gaussian white noise, respectively. The parameter settings for the simulation signal are shown below:

[0181]

[0182]

[0183] Simulated signals such as Figure 2 As shown, the modulated signal is completely submerged by background noise. The kurtosis spectrum narrowband demodulation results and cyclostationary analysis demodulation results of the simulated signal are shown below. Figure 3 and Figure 4 As shown. It can be seen that although the fundamental modulation frequency α B Its harmonics were extracted, but the demodulation results still contained a large amount of Gaussian white noise and obvious cyclic stationary noise interference.

[0184] The optimal weighted spectral correlation and optimal weighted envelope spectrum corresponding to the simulated signal are as follows: Figure 5 and Figure 6 As shown, in the optimal weighted spectral correlation, the two carrier frequencies located at 2500-7500Hz and 12500-17500Hz are effectively captured. In the optimal weighted envelope spectrum, the fundamental modulation frequency α... B The clear and prominent harmonics, along with the near absence of other noise, indicate that the modulation frequency has been effectively extracted. These results demonstrate that, under the combined interference of complex and intense noises such as Gaussian noise, impulse noise, and cyclostationary noise, the optimal weighted envelope spectrum proposed in this invention can effectively and accurately extract and characterize the modulation frequency components.

[0185] The above methods were used to analyze the acoustic signal of a rolling bearing (outer ring pitting fault). The results of traditional kurtosis spectrum demodulation, cyclostationary analysis demodulation, and the optimal weighted envelope spectrum proposed in this invention are as follows: Figure 7-9As shown in the figure. Due to the diverse excitation sources, high interference noise, and complex transmission paths of rolling bearing noise signals, their signal-to-noise ratio is low. The modulation frequency of outer ring pitting is difficult to extract using traditional methods such as kurtosis spectrum analysis, which only extracts interference components such as the motor shaft frequency and its harmonics. While cyclostationary analysis can extract the outer ring pitting fault frequency, it also contains a large number of interference components such as the motor shaft frequency and its harmonics. However, in the optimal weighted envelope spectrum, although a small amount of interference components such as the motor shaft frequency and its harmonics are still present, the modulation frequency of outer ring pitting is effectively extracted and clearly distinguishable. These results demonstrate that when processing rolling bearing noise signals containing strong and complex noise, the optimal weighted envelope spectrum proposed in this invention can effectively and accurately extract and characterize characteristic frequency components.

[0186] The vibration signal of a centrifugal pump (in cavitation state) was analyzed using the above methods. The results of traditional kurtosis spectrum demodulation, cyclic stationarity analysis demodulation, and the optimal weighted envelope spectrum proposed in this invention are as follows: Figure 10-12 As shown, the vibration signal of a centrifugal pump has diverse excitation sources, high interference noise, and complex transmission paths, resulting in an extremely low signal-to-noise ratio. Characteristic frequency components such as rotor frequency and blade passage frequency are difficult to extract using kurtosis spectrum analysis, and the analysis results essentially only contain background interference. While cyclostationary analysis can effectively extract characteristic frequency components such as rotor frequency and blade passage frequency, it also contains a large amount of background interference. However, in the optimal weighted envelope spectrum, characteristic frequency components such as rotor frequency and blade passage frequency are effectively extracted and clearly distinguishable, and background noise is suppressed to a low level. These results demonstrate that when processing centrifugal pump vibration signals containing strong and complex noise, the optimal weighted envelope spectrum proposed in this invention can effectively and accurately extract and characterize characteristic frequency components.

[0187] The embodiments described above provide a detailed explanation of the technical solutions 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, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for enhancing and extracting the characteristic frequencies of rotating machinery based on optimal weighted envelope spectrum, characterized in that, Includes the following steps: (1) Collect vibration or noise data of rotating machinery as monitoring signals and calculate the spectral correlation function of the monitoring signals; (2) Normalize the spectral correlation function to obtain the spectral coherence function, and construct the enhanced envelope spectrum; (3) Determine the fundamental modulation frequency based on the prior information of the rotating machinery, the diagnostic task, and the characteristic information of the enhanced envelope spectrum; (4) Slice the spectral correlation function at the zero modulation frequency and the fundamental modulation frequency, and estimate the carrier-to-noise ratio based on the slicing results; the specific process is as follows: (4-1) gives the definition of carrier-to-noise ratio, which is the ratio of the carrier power spectral density of the second-order cyclic stationary component to the stationary noise power spectral density: In the formula, CNR(f) represents the carrier-to-noise ratio, and P v (f) represents the power spectral density of the carrier signal v(t), which contains the second-order cyclic stationary component of the monitoring signal. n represents the stationary noise contained in the monitoring signal s Power spectral density of (t); (4-2) For signals containing second-order cyclostationary components and stationary noise: In the formula, Let v(t) represent the modulated signal of the second-order cyclostationary component, and n represent the carrier signal of the second-order cyclostationary component. s (t) represents stationary noise; its theoretical spectral correlation value is: In the formula, δ(·) represents the Kronecker function, which satisfies: Spectral correlation at α=0 and α=α B The value at which the station is used is used to estimate the power spectral density of stationary noise: (4-3) gives the definition of second-order cyclic stationary signal-to-noise ratio, which is the ratio of the absolute value of the spectral correlation of the monitoring signal to the power spectral density of the stationary noise: In the formula, SNR CS2 (α,f) represents the second-order cyclic stationary signal-to-noise ratio; (4-4) The signal-to-noise ratio is stable at α = α through a second-order cyclic method. B The value at that location is used to estimate the carrier-to-noise ratio: As can be seen from the above formula, SNR CS2 (α B f) is approximately equal to the carrier-to-noise ratio after several weighted frequency shifts. The sum of the superpositions has a weighting factor of . Frequency shift amount is The frequency shift is significantly smaller than the carrier frequency range and will not have a significant impact on the carrier distribution estimation. Therefore, the second-order cyclostationary signal-to-noise ratio is within α = α B The value at that location can depict the carrier-to-noise ratio distribution; (5) Give the definition of the weighted spectrum correlation function, construct the cyclostationary metric function of the fundamental modulation frequency and its harmonic components from it, and regard it as the objective function; (6) Using the carrier-to-noise ratio as the initial weighting function, set the search space for the optimal weighting function, and use the Cuckoo optimization algorithm to search for the optimal weighting function that maximizes the objective function; (7) The spectral correlation function is weighted using the optimal weighting function to calculate the optimal weighted spectral correlation. (8) Integrate the optimal weighted spectral correlation along the spectral frequency axis to obtain the optimal weighted envelope spectrum.

2. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 1, characterized in that, In step (1), the specific process of calculating the spectral correlation function of the monitoring signal is as follows: (1-1) Calculate the two narrowband filtered signals x(t) of the monitoring signal x(t). Δf (t;f1) and x Δf The correlation coefficient corr between (t; f2) is x (f1, f2), the calculation formula is as follows: In the formula, t represents time, f represents frequency, f1≥f2, e is the natural constant, j is the imaginary number, * is the conjugate sign, -T / 2 and T / 2 are the lower and upper time limits, Δf represents the filtering range of the narrowband filtered signal, and x Δf (t;f1) and x Δf (t;f2) represent narrowband filtered time-domain signals with passband ranges of (f1-Δf / 2,f1+Δf / 2) and (f2-Δf / 2,f2+Δf / 2), respectively. (1-2) Assuming f = (f1 + f2) / 2 and α = f1 - f2, the spectral correlation function of the monitoring signal can be obtained, and its calculation formula is as follows: In the formula, S x (α,f) is the spectral correlation function, where α is the modulation frequency and f is the carrier frequency.

3. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 2, characterized in that, The specific process of step (2) is as follows: (2-1) Normalize the spectral correlation function of the monitoring signal to obtain the spectral coherence function γ of the monitoring signal. x (α,f), the calculation formula is as follows: In the formula, The result when the modulation frequency of the representative spectral correlation function is zero, i.e., we have (2-2) Integrate the spectral coherence function along the carrier frequency axis to calculate the enhanced envelope spectrum (EES) of the monitoring signal. x (α), the calculation formula is as follows: In the formula, f1 and f2 are the lower and upper limits of the carrier frequency integral, respectively, and their default values ​​are 0 and F. s / 2, F s The sampling frequency for the monitoring signal.

4. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 3, characterized in that, The specific process of step (3) is as follows: (3-1) Based on prior information, determine the faulty component of the rotating machinery to be diagnosed, and then determine the theoretical fundamental modulation frequency α based on the corresponding fault mechanism. B-T ; (3-2) Because the values ​​of the modulation frequencies in the enhanced envelope spectrum are all integer multiples of the modulation frequency resolution Δα, therefore, from the enhanced envelope spectrum EES x (α) is used to obtain the theoretical fundamental modulation frequency α of the rotating machinery. B-T The closest modulation frequency value α opt =MΔα, where M is a positive integer; (3-3) Modulation frequency range [α opt -NΔα,α opt The range of candidate fundamental modulation frequencies is defined as α[+NΔα], where N is a positive integer. The modulation frequency corresponding to the maximum amplitude of the enhanced envelope spectrum is selected from the candidate range and determined as the fundamental modulation frequency α. B .

5. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 4, characterized in that, The specific process of step (5) is as follows: (5-1) The definition of weighted envelope spectrum is given: In the formula, represents the weighted envelope spectrum, and w(f) represents the weighting function; (5-2) The candidate range of the fundamental modulation frequency and the corresponding cyclic frequencies of its harmonic components is determined as follows: Facebook k =[ka B -mDa,ka B +mΔa] In the formula, FB k The range of cyclic frequencies corresponding to the kth harmonic of the fundamental modulation frequency is represented by mΔα, which represents the single-sided selection limit. (5-3) Obtain the corresponding characteristic modulation frequency peak from the weighted envelope spectrum. The calculation formula is as follows: In the formula, m k The amplitude of the kth harmonic of the basic modulation frequency Indicates on FB k Take the maximum value from the middle. (5-4) Assume the range of the cycle frequency under consideration is (0, α) max Within this range, the order of the highest harmonic of the fundamental modulation frequency is k. max The maximum index of the cycle frequency is n. max Based on this, the objective function used to measure the magnitude of cyclic stationarity is defined as:

6. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 5, characterized in that, The specific process of step (6) is as follows: (6-1) The process of obtaining the optimal weighting function is regarded as an optimization problem. Let the carrier-to-noise ratio be the initial weighting function: In the formula, w b ∈R 1×d The weighting function represents a vector form; (6-2) Set the search range for the optimal weighting function: In the formula, w L and w U Let X and X represent the lower-bound weighted function and the upper-bound weighted function, respectively, and X% represent the percentage of one-sided fluctuation of the weighted function. Therefore: (6-3) Using the Cuckoo Optimization Algorithm, the optimal weighted function that maximizes the objective function is obtained.

7. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 6, characterized in that, In step (7), the formula for calculating the optimal weighted spectral correlation is as follows: In the formula, w opt (f) is the optimal weighting function. This represents the optimal weighted spectrum correlation.

8. The method for enhancing and extracting the characteristic frequencies of rotating machinery based on the optimal weighted envelope spectrum according to claim 7, characterized in that, In step (8), the formula for obtaining the optimal weighted envelope spectrum is: In the formula, This is the optimal weighted envelope spectrum.

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