Rotating machinery fault detection method based on multi-component sparse time domain synchronous average

Abstract

Disclosed is a rotating machinery fault detection method based on multi-component sparse time domain synchronous average, in which a sensor collects vibration signals and rotation frequency or rotation frequency pulse signals of the rotating machinery, and performs digital-to-analog conversion to obtain rotation information and rotation speed information; based on the known structure and component quantity information of the rotating machinery, time domain synchronous average vectors ω1 and ω2 corresponding to target components and rotation frequency independent components are calculated according to the rotation frequency information, multi-component sparse time domain synchronous average models F1 and F2 are constructed, the models are solved by using an iterative optimization solving algorithm to obtain sparse frequency domain information and reconstructed time domain information, corresponding components are analyzed according to the component type selection, fault diagnosis is performed through an index CI sTsA , and the signals are compressed and stored according to the analysis result.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery fault diagnosis technology, and in particular, it is a rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging. Background Technology

[0002] Large rotating machinery, such as high-speed trains, aircraft engines, and wind power equipment, is highly susceptible to major accidents if faults are not detected in a timely manner. The sparse time-domain synchronous averaging method, which combines time-domain synchronous averaging with sparse representation, has proven to perform well under complex rotating machinery fault conditions. This method is clear and easy to understand, and its computational speed is improved through a fast iterative algorithm. However, in practical engineering applications, the frequency components of gears, rotors, and bearings in actual rotating shafts are relatively complex. When the corresponding characteristic frequency components are close in magnitude, the sparse time-domain synchronous averaging method often results in component coupling and frequency interference, preventing the complete removal of necessary information. Therefore, improvements and enhancements to existing algorithms are needed, along with the design of corresponding signal compression and storage methods to meet the fault feature extraction requirements in practical engineering.

[0003] The information disclosed in the background section is only intended to enhance the understanding of the background of the present invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, which can solve the problem of spectral interference and can be used for fault diagnosis of various rotating machinery in mechanical systems.

[0005] The objective of this invention is achieved through the following technical solution: a method for detecting rotating machinery faults based on multi-component sparse time-domain synchronous averaging includes:

[0006] S100: Collect vibration signals and rotational speed information of rotating machinery;

[0007] S200. Construct time-domain synchronous average vectors ω1 and ω2 corresponding to frequency-dependent components and frequency-independent components based on the rotational speed information;

[0008] S300. Construct a multi-component sparse time-domain synchronous average model F1 and a sparse time-domain synchronous average model F2 containing an unrelated dictionary by using the time-domain synchronous average vectors ω1 and ω2 corresponding to the frequency-related and frequency-independent components as weighting terms.

[0009] S400. The optimization solution algorithm is used to iteratively solve the multi-component sparse time-domain synchronous average model F1 and the sparse time-domain synchronous average model F2 containing an unrelated dictionary.

[0010] S500. For different fault diagnosis objects such as gears, bearings, and rotors in rotating machinery, select the sparse representation coefficients of the corresponding components, obtain the time-domain signal of the corresponding components through inverse Fourier transform, and then use the index CI. STSA Perform fault diagnosis;

[0011] S600: Based on the diagnostic results, compress and store the signal.

[0012] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, S200 includes,

[0013] S201. Perform a Fourier transform on the rotational speed signal of the rotating machinery to obtain the rotational frequency from the spectrum.

[0014] S202. The components in the signal are divided into three categories: frequency-dependent components, frequency-independent components, and noise. Among them, frequency-dependent components contain frequency-related information, and their spectrum mainly contains the rotational frequency of the rotor components and its harmonics; frequency-independent components contain fault information other than rotational frequency information, and their spectrum mainly contains other effective frequency components other than the rotational frequency of the rotor components and its harmonics; noise components do not contain equipment status information and appear as messy small-amplitude frequency components in the spectrum, which are included in the subsequent model for denoising.

[0015] S203. Construct time-domain synchronization average vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components based on the frequency conversion, where...

[0016]

[0017] ω2=I-ω1

[0018] Where ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively, r is a pre-set small value, δ is the bandwidth of the frequency fluctuation, fz is the frequency, n is a positive integer, and N is the length of the time-domain synchronization average vector.

[0019] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, the time-domain synchronous averaging vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components of the frequency-constructed structure are updated.

[0020] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, S300 includes,

[0021] S301, the F1 score of the multi-component sparse time-domain synchronous averaging model is:

[0022]

[0023] In the formula, y is the noisy signal to be analyzed; A is the linear transform operator; x1 and x2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components, respectively; is the vector dot product operator; λ is the regularization parameter; ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively;

[0024] S302, the sparse time-domain synchronous averaging model F2 containing an unrelated dictionary is:

[0025]

[0026] In the formula, y is the noisy signal to be analyzed, A1A2 are the linear transformation operators corresponding to the frequency-dependent and frequency-independent components, respectively. Different components in the signal are sparsely represented under their respective dictionaries, while sparse representation cannot be achieved under other dictionaries; α1 and α2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components, respectively. The vector dot product operator; λ is the regularization parameter;

[0027] S303. When the dictionary A used in the multi-component sparse time-domain synchronous averaging model F1 is a Fourier transform dictionary, and the dictionary A1A2 used in the sparse time-domain synchronous averaging model F2 containing an uncorrelated dictionary is a weighted Fourier dictionary embedding frequency conversion information, the two models are equivalent. The weighted Fourier transform matrix A1A2 is constructed based on the time-domain synchronous averaging vectors ω1 and ω2 corresponding to the frequency conversion-related and frequency conversion-independent components.

[0028] A i =AW i -1 (i = 1, 2),

[0029] Where A is the Fourier transform dictionary, W i =diag(ω i ), (i=1,2) is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors;

[0030] S304. The sparse representation coefficients of the corresponding components of the sparse time-domain synchronous averaging model F2 with an uncorrelated dictionary are the spectral components of the corresponding components of the multi-component sparse time-domain synchronous averaging model F1 after embedding frequency conversion information. The sparse representation coefficients of the corresponding components of the multi-component sparse time-domain synchronous averaging model F1 and the sparse time-domain synchronous averaging model F2 with an uncorrelated dictionary have the following relationship:

[0031]

[0032] Where α i ω represents the sparse representation coefficient corresponding to the i-th component in model F2. iLet x be the class-time domain synchronous average vector corresponding to the i-th component. i These are the sparse representation coefficients corresponding to the i-th component in model F1. This is the vector dot product operator.

[0033] The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging includes iteratively solving the multi-component sparse time-domain synchronous averaging model F1 using an optimization algorithm.

[0034] S401. Initialize two parameters μ > 0, x and m set to 1, and set the number of iterations Nit, and a loop exit parameter ε. This parameter ensures that during optimization iteration, if the cost function of two iterations differs from the set ε value, the loop will exit directly; otherwise, the set number of iterations Nit will be completed until the loop stops.

[0035] S402. Use the soft threshold function (soft) for operation:

[0036]

[0037] The soft threshold function, soft, is expressed as follows:

[0038]

[0039] A is a linear transformation operator; and ω1 and ω2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively; μ is the iteration step size parameter; λ is the regularization parameter;

[0040] S403. Increment the loop variable i by 1. If the multi-component sparse time-domain synchronous averaging model F1 satisfies k > Nit or Then let Exit the loop; otherwise, return to step S402.

[0041] The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging includes iteratively solving the sparse time-domain synchronous averaging model F2 containing an uncorrelated dictionary using an optimization algorithm.

[0042] S403. For the soft threshold function of the model:

[0043]

[0044] The equivalent solution is obtained using the following formula:

[0045]

[0046] In the formula, and Let A and B be the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; A is the linear transformation operator, A T W is the corresponding inverse matrix; i is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors; μ is the iteration step size parameter and λ is the regularization parameter;

[0047] S404. After the solution iteration is completed, the spectrum α with embedded frequency conversion information is converted into the regular spectrum x.

[0048] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, in S500,

[0049] For gears, the sparse representation coefficients corresponding to the frequency-related components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators:

[0050] Root Mean Square (RMS) STSA :

[0051]

[0052] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components.

[0053] Peak Factor (PF) STSA :

[0054]

[0055] In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA The root mean square value,

[0056] KurV (Kullification Index) STSA :

[0057]

[0058] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components. The average value of the time-domain signal of the frequency-dependent component.

[0059] Envelope kurtosis index KU STSA :

[0060]

[0061] In the formula, is the length of the signal, is the envelope signal of the reconstructed time-domain signal corresponding to the sparse representation coefficients of the obtained frequency-correlation component, and is the average value of the envelope signal of the frequency-correlation component.

[0062] Meshing frequency amplitude OMX STSA :

[0063] OMX STSA,i,j =A ij

[0064] In the formula A ij Let x represent the amplitude of the j-th order fault characteristic frequency of the i-th gear in the sparse representation coefficients x1.

[0065] Characteristic frequency amplitude FQ STSA :

[0066]

[0067] In the formula A ij The value of CI represents the amplitude of the j-th order fault characteristic frequency of the i-th gear in the envelope spectrum, where each term CI... STSA The index is an estimated frequency conversion energy; the index for a normal signal is lower than that for a fault signal.

[0068] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, in S500,

[0069] For the rotor, the sparse representation coefficients corresponding to the frequency-dependent components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators:

[0070] Frequency conversion amplitude AR STSA :

[0071] AR STSA =AR ij

[0072] AR in the formula ij This represents the amplitude of the j-th harmonic of the i-th rotor in the sparse representation coefficients x1;

[0073] Root Mean Square (RMS) STSA ,

[0074]

[0075] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent components;

[0076] Average Amplitude (MA) STSA :

[0077]

[0078] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components.

[0079] Root amplitude RA STSA :

[0080]

[0081] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent components.

[0082] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, in S500,

[0083] For bearings, the sparse representation coefficients corresponding to the frequency-independent components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators:

[0084] Characteristic frequency amplitude FQ STSA :

[0085]

[0086] In the formula A ij This represents the amplitude of the j-th order frequency, which is the characteristic frequency of the i-th bearing fault in the envelope spectrum.

[0087] Peak Factor (PF) STSA :

[0088]

[0089] In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA The root mean square value,

[0090] KurV (Kullification Index) STSA ,

[0091]

[0092] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the obtained frequency-correlation component. This represents the average value of the time-domain signal of the frequency-dependent component.

[0093] In the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging, the compression and storage of the signal according to the diagnostic results includes:

[0094] S601. If the signal is considered to indicate the existence of a fault, the original signal is stored; if the signal is considered not to indicate the existence of a fault, that is, the target component is considered to be in a normal state, the compressed sensing method is used to compress and store the data.

[0095] S602. For a normal state signal, the frequency domain sparse representation coefficients x1 and x2 obtained by solving the multi-component sparse time-domain averaging model are compressed based on the sparsity of the two coefficients themselves. The threshold parameter ν is used to store the amplitude and corresponding frequency values ​​of the frequency components in x1 and x2 whose amplitudes are greater than the threshold.

[0096] S603. During storage, count the number n of frequency components greater than the threshold ν between the two coefficients. Then, predefine a table of size 2×n, select the frequency components greater than the threshold ν and store them in the table. The first row of the table stores the frequency values, and the second row stores the frequency amplitudes.

[0097] S604. The reconstruction process is achieved through the inverse Fourier transform, i.e. in To reconstruct the signal, A T is the inverse of the Fourier transform matrix, and x1 and x2 are the sparse representation coefficients of the two types of components in the frequency domain.

[0098] Compared with the prior art, the present invention has the following advantages: The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging described in the present invention overcomes the influence of characteristic frequency coupling between different components, extracts the required fault feature information, and reduces the interference of other irrelevant components. Attached Figure Description

[0099] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0100] In the attached diagram:

[0101] Figure 1 This is a flowchart of a rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging proposed in this invention;

[0102] Figure 2 To obtain the actual rotational frequency information from the spectrum of the gearbox speed signal;

[0103] Figure 3 It is a time-domain synchronization average vector for both frequency-dependent and non-frequency-dependent components;

[0104] Figure 4 The time-domain vibration waveforms are shown under two states of gearbox health and fault.

[0105] Figure 5 The time-domain waveforms of the two components of the gear fault signal after multi-component sparse time-domain synchronous averaging processing are shown.

[0106] Figure 6 The spectrum of the two components of the gear fault signal after multi-component sparse time-domain synchronous averaging processing;

[0107] Figure 7 The envelope spectrum of the two components of the gear fault signal after multi-component sparse time-domain synchronous averaging processing is given.

[0108] Figure 8 A comparison of the time-domain waveforms of the gear vibration signal under normal conditions and the reconstructed signal after compression;

[0109] Figure 9 The time-domain waveform of the bearing fault vibration signal;

[0110] Figure 10 To obtain actual rotational frequency information from the spectrum of the bearing tachometer;

[0111] Figure 11 The time-domain waveforms of the two components of the bearing fault signal after multi-component sparse time-domain synchronous averaging processing are shown.

[0112] Figure 12 The spectrum of the two components of the bearing fault signal after multi-component sparse time-domain synchronous averaging processing;

[0113] Figure 13 The envelope spectrum of the bearing fault signal after multi-component sparse time-domain synchronous averaging is the two components.

[0114] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0115] The following will refer to the appendix. Figures 1 to 13 Specific embodiments of the invention will be described in more detail below. While specific embodiments of the invention are shown in the accompanying drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0116] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0117] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0118] like Figures 1 to 13 As shown, the rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging includes:

[0119] Step 1: Collect vibration signals and rotational speed information of the transmission components using sensors and data acquisition devices;

[0120] Step 2: Construct time-domain synchronous average vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components based on the rotational speed information of the rotating machinery;

[0121] Step 3: Construct a sparse time-domain synchronous average model F1 based on the multi-component idea and a sparse time-domain synchronous average model F2 containing an unrelated dictionary by using the time-domain synchronous average vectors ω1 and ω2 corresponding to different components as weighting terms.

[0122] Step 4: Iteratively solve models F1 and F2 using appropriate optimization algorithms;

[0123] Step 5: For different fault diagnosis objects such as gears, bearings, and rotors, select the sparse representation coefficients of the corresponding components, obtain the time-domain signals of the corresponding components through inverse Fourier transform, and then use the index CI. STSA Perform fault diagnosis.

[0124] Step 6: Based on the diagnostic results, compress and store the signal appropriately.

[0125] Step 1: Collect vibration signals and rotational speed information of the transmission components using sensors and a data acquisition device. Vibration signals can be measured by installing various vibration sensors, including photoelectric and eddy current sensors, near the components of interest or on the outer casing, to measure displacement, velocity, acceleration, and other information. Rotational speed information can be measured by installing various sensors on any shaft throughout the transmission system. Sensor types include photoelectric encoders, Hall effect sensors, centrifugal sensors, tachogenerators, etc. The rotational speed pulse signals obtained from these sensors, or the correspondence between recorded time and rotational speed, constitute the rotational speed information.

[0126] The obtained vibration and rotational speed signals are converted from analog to digital for easier subsequent processing. In some other cases, the vibration or rotational speed signals undergo preprocessing such as low-pass, high-pass, or band-pass filtering; in these cases, the signals still conform to the vibration and rotational speed information required by this document. Additionally, in some situations, such as when the transmission relationship of the equipment is known, the corresponding rotational speed information can be obtained through a series of derivations; all of these fall under the category of obtaining rotational speed information discussed above.

[0127] Step 2: Construct time-domain synchronous average vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components based on the rotational speed information of the rotating machinery. Specific steps include:

[0128] Based on the fault mechanism, the components in the signal are divided into three categories: frequency-dependent components, frequency-independent components, and noise. Among them, frequency-dependent components contain frequency-related information, and their spectrum mainly contains the rotational frequency of the rotor components and its harmonics; frequency-independent components contain fault information other than rotational frequency information, and their spectrum mainly contains other effective frequency components other than the rotational frequency of the rotor components and its harmonics; noise components do not contain equipment status information and appear as messy small-amplitude frequency components in the spectrum, which are included in the subsequent model for noise reduction.

[0129] Based on the obtained rotational speed information, a Fourier transform is performed to obtain its frequency domain information, and the rotational frequency f is obtained from the frequency spectrum. z Meanwhile, based on the shape of the frequency shift in the spectrum, the bandwidth δ of the frequency shift fluctuation is estimated.

[0130] Based on the extracted frequency f z Construct time-domain synchronization average vectors ω1 and ω2:

[0131]

[0132] ω2=I-ω1

[0133] Where ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively, r is a pre-set small value, and δ is the bandwidth of the frequency fluctuation.

[0134] Furthermore, the weight vector is updated. This makes the weight vector, similar to that of a comb-shaped notch filter, symmetric about the Fs / 2 axis, thus conforming to the symmetry property of the spectrum in the Fourier transform. This yields the final two time-domain synchronous average vectors ω1 and ω2.

[0135] Step 3: Based on the obtained time-domain synchronous average vectors ω1 and ω2 corresponding to different components, construct the sparse time-domain synchronous average model F1 with the multi-component idea and the sparse time-domain synchronous average model F2 with unrelated dictionaries as weighting terms.

[0136] The expression for the F1 model of multi-component sparse time-domain synchronous averaging with vector weighting similar to time-domain synchronous averaging is as follows:

[0137]

[0138] In the formula, y is the noisy signal to be analyzed; A is a linear transformation operator, representing operations such as Fourier transform, short-time Fourier transform, wavelet transform, etc.; x1 and x2 are the sparse representation coefficients of frequency-dependent and frequency-independent components, respectively. is the vector dot product operator; λ is the regularization parameter; ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively;

[0139] The expression for the multi-component sparse time-domain synchronous averaging model F2 containing an uncorrelated dictionary is:

[0140]

[0141] In the formula, y is the noisy signal to be analyzed, A1A2 are the linear transformation operators corresponding to the frequency-dependent and frequency-independent components. Different components in the signal can be sparsely represented under their respective dictionaries, while they cannot be sparsely represented under other dictionaries; α1 and α2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components, respectively. λ is the vector dot product operator; λ is the regularization parameter.

[0142] It should be noted that the two models can be converted into each other under certain conditions, namely:

[0143] Condition 1: When model F1 uses a Fourier transform dictionary A, and model F2 uses a weighted Fourier dictionary A1A2 embedded with frequency conversion information, the two models are equivalent. Based on the time-domain synchronization average vectors ω1 and ω2, the weighted Fourier transform matrix A1A2 can be constructed, expressed as:

[0144] A i =AW i -1 (i = 1, 2)

[0145] Where A is the Fourier transform dictionary, W i =diag(ω i ), (i = 1, 2) is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors.

[0146] Condition 2: The sparse representation coefficients α of the corresponding components of model F2 i The spectrum x of the corresponding component of model F1 i The spectral components weighted by embedded frequency conversion information, i.e., the sparse representation coefficients of the corresponding components of model F1 and model F2, have the following relationship:

[0147]

[0148] Where α i ω represents the sparse representation coefficient corresponding to the i-th component in model F2. i Let x be the class-time domain synchronous average vector corresponding to the i-th component. i These are the sparse representation coefficients corresponding to the i-th component in model F1. This is the vector dot product operator.

[0149] Therefore, based on the time-domain synchronous average vector obtained in step 2, the two multi-component models can be constructed.

[0150] In model F1, the role of the time-domain synchronous average vectors ω1 and ω2 is to give the target frequency components smaller weights in the frequency domain, while other frequency components have relatively larger weights. This is ultimately reflected in the sparse representation of the result. In the sparse representation, the coefficients corresponding to the target frequency are preserved, while noise interference components and other irrelevant components are removed or weakened. Furthermore, it enables the extraction of features of specific frequencies such as frequency switching. λ is a regularization parameter that can be adjusted according to the actual situation. That is, when the signal noise to be processed is large, the value of λ should be increased, and conversely, λ should be set to a smaller value.

[0151] In model F2, the role of the time-domain synchronous average vectors ω1 and ω2 is reflected in the weighted Fourier transform matrix A1A2. Their function is to give the target frequency a smaller weight and other frequencies a larger weight. Ultimately, this is reflected in the sparse representation of the result. In the sparse representation, the coefficients corresponding to the target frequency are preserved, while noise interference and other irrelevant components are removed or weakened. Furthermore, it enables the extraction of features for specific frequencies such as frequency switching. λ is a regularization parameter that can be adjusted according to the actual situation. That is, when the noise of the signal to be processed is large, the value of λ should be increased, and conversely, λ should be set to a smaller value.

[0152] Step 4: Iteratively solve models F1 and F2 using appropriate optimization algorithms;

[0153] Since models F1 and F2 are common convex optimization BPD problems, this invention uses the iterative shrinkage / thresholding algorithm (ISTA), which guarantees a reduction in the cost function in each iteration of the algorithm. The following sections will elaborate on solving the two models:

[0154] For model F1:

[0155] Initialize parameters μ > 0, x1, x2, and set the number of iterations Nit, as well as a loop exit parameter ε. This parameter ensures that during optimization iterations, if the cost function of two iterations differs from the set ε value, the loop exits directly; otherwise, the loop continues for the set number of iterations Nit until the loop stops.

[0156] The following iterations are then repeated:

[0157]

[0158]

[0159] In the formula, the soft threshold function is expressed as:

[0160]

[0161] A is a linear transformation operator; and ω1 and ω2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively; μ is the iteration step size parameter; λ is the regularization parameter;

[0162] If k > Nit or Then let Exit the loop; otherwise, continue the loop with k = k + 1.

[0163] For model F2:

[0164] First, we need to initialize two parameters μ > 0, α1, α2. Here, μ is generally set to 1. We also need to set the number of loops Nit and a loop exit parameter ε.

[0165] For the iterative formula for solving F2 in ISTA:

[0166]

[0167]

[0168] Because the computational cost of the weighted Fourier matrix is ​​too high, severely limiting the processing time and signal length of this method, the following equivalent iterative expression can be calculated:

[0169]

[0170] In the formula, and Let A and B be the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; A is the linear transformation operator, A T W is the corresponding inverse matrix; i is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors; μ is the iteration step size parameter and λ is the regularization parameter;

[0171] If k > Nit or Then let Exit the loop; otherwise, continue the loop with k = k + 1.

[0172] After exiting the loop, according to Remove the frequency shift information embedded in the α spectrum and calculate the regular spectrum x.

[0173] Step 5 requires selecting different sparse representation coefficients based on whether the object is a gear or a bearing for analysis:

[0174] For gear and rotor components, sparse representation coefficients corresponding to frequency-related components are selected for subsequent calculations;

[0175] For bearing components, sparse representation coefficients corresponding to frequency-independent components are selected for subsequent calculations.

[0176] After selecting the sparse representation coefficients of the corresponding components, the time-domain signal of the corresponding components is obtained through inverse Fourier transform.

[0177] Step 5a: For gear faults, the sparse representation coefficients x1 corresponding to the frequency-related components are directly reconstructed into a time-domain signal, and then envelope demodulation is performed by performing envelope spectrum. By comparing the difference between the envelope spectrum and the envelope spectrum of the normal signal, the presence of a gear fault in the accessory transmission system is evaluated.

[0178] Typical gear failures, as seen in the spectrum, exhibit modulation of the rotational and meshing frequencies by the fault characteristic frequencies, resulting in sidebands around these frequencies. Envelope demodulation, corresponding to the frequency domain, allows the extraction of the modulated signal, i.e., the sideband components, from the envelope spectrum of a signal. Unlike bearing failures, gear failures manifest as sidebands around the rotational and meshing frequencies. While normal signals also exhibit sidebands, they are subject to other interferences. Furthermore, because each rotation of the faulty component is equivalent to applying an additional pulse, the amplitudes of the rotational frequency and its harmonics are significantly higher than those of normal signals. Therefore, when evaluating the presence of a gear failure, it is necessary to compare it with the gear signal under normal conditions and simultaneously calculate the signal's CI. STSA Value, compared to the CI of a normal signal STSA Comparing values, CI STSA The indicator consists of the following:

[0179] Root Mean Square (RMS) STSA :

[0180]

[0181] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent component obtained in step 4.

[0182] Peak Factor (PF) STSA :

[0183]

[0184] In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA The root mean square value,

[0185] KurV (Kullification Index) STSA :

[0186]

[0187] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency conversion correlation component obtained in step 4. This represents the average value of the time-domain signal of the frequency-dependent component.

[0188] Kurtosis indices are sensitive to impact-pulse faults, especially when the fault occurs in its early stages, where they increase significantly. However, once the index value increases to a certain level, it decreases with further fault progression, showing sensitivity to early faults but poor stability. RMS does not change significantly in early faults of gears or bearings, while the crazing factor is the ratio of the signal peak value to the root mean square value. An increase in the signal peak value will cause the crazing factor value to increase. The crazing factor is usually used to detect changes in signal patterns caused by impact vibration sources (such as gear breakage or bearing outer ring).

[0189] Envelope kurtosis index KU STSA :

[0190]

[0191] In the formula, N is the length of the signal, h i The envelope signal of the time-domain signal is reconstructed from the sparse representation coefficients x1 corresponding to the obtained frequency-dependent components. This represents the average value of the envelope signal of the frequency-dependent components.

[0192] Meshing frequency amplitude OMX STSA :

[0193] OMX STSA,i,j =A ij

[0194] In the formula A ij It represents the amplitude of the j-th order fault characteristic frequency of the i-th gear in the sparse representation coefficient x1.

[0195] In gear signals, the meshing frequency amplitude often dominates, and it also increases significantly when a fault occurs. The characteristic frequency amplitude and envelope kurtosis index obtained through the envelope spectrum more directly reflect the magnitude of the modulation component generated by the fault impact.

[0196] Characteristic frequency amplitude FQ STSA :

[0197]

[0198] In the formula A ij The value of CI represents the amplitude of the j-th order fault characteristic frequency of the i-th gear in the envelope spectrum, where each term CI... STSA The index is an estimated frequency conversion energy; the index for a normal signal is lower than that for a fault signal.

[0199] Among them, each CI STSA The index is used to estimate the energy of information such as frequency conversion, so the index of a normal signal should be lower than that of a fault signal.

[0200] Step 5b: For rotor faults, after reconstructing the sparse representation coefficients x1 of the obtained frequency-dependent components into a time-domain signal, envelope demodulation is performed using the envelope spectrum. By comparing the difference between the envelope spectrum and the envelope spectrum of the normal signal, the presence of a fault in the rotor can be evaluated.

[0201] Similar to gear faults, typical rotor faults manifest in the frequency spectrum as modulation of the rotational and meshing frequencies by the fault characteristic frequencies, resulting in sidebands around these frequencies. Furthermore, since each rotation of the faulty component is equivalent to applying an additional pulse, the amplitudes of the rotational frequency and its harmonics are significantly higher than normal signals. Therefore, when evaluating the presence of a rotor fault, it is necessary to compare the signal with that of a rotor under normal conditions and calculate the signal's CI. STSA Value, compared to the CI of a normal signal STSA Comparing values, CI STSA The indicator consists of the following:

[0202] Frequency conversion amplitude AR STSA :

[0203]

[0204] In the formula This represents the amplitude of the j-th harmonic of the i-th rotor in the sparse representation coefficients x1;

[0205] Root Mean Square (RMS) STSA The formula has the same form as the index with the same name in step 5a;

[0206] Average Amplitude (MA) STSA :

[0207]

[0208] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components.

[0209] Root amplitude RA STSA :

[0210]

[0211] In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent components.

[0212] Step 5c: For bearing faults, the sparse representation coefficients x2 corresponding to the obtained frequency-independent components are reconstructed into a time-domain signal. Finally, the envelope spectrum is used for envelope demodulation, and the presence of bearing faults in the accessory transmission system is evaluated by comparing the matching degree between the information in the envelope spectrum and the fault characteristic frequencies.

[0213] When a bearing fails, its fault characteristic frequencies often modulate with frequency-independent components in the signal, typically appearing as sidebands of these frequency-independent components in the spectrum, rather than directly in the spectrum image. To visualize this, envelope spectrum analysis of the obtained residual signal is necessary. By comparing the degree of matching between the information in the envelope spectrum and the bearing fault characteristic frequencies, and simultaneously calculating the signal's CI... STSA Value, compared to the CI of a normal signal STSA The values ​​are compared to evaluate whether there is a bearing failure in the accessory's transmission system. CI STSA The indicator consists of the following:

[0214] Characteristic frequency amplitude FQ STSA :

[0215]

[0216] In the formula A ij This represents the amplitude of the j-th order frequency, which is the characteristic frequency of the i-th bearing fault in the envelope spectrum.

[0217] Peak Factor (PF) STSA :

[0218]

[0219] In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA The root mean square value,

[0220] KurV (Kullification Index) STSA The formula has the same form as the index with the same name in step 5a;

[0221] Step 6: Based on the diagnostic results, compress and store the signal appropriately.

[0222] First, based on the diagnostic results, determine whether to compress and store the data.

[0223] If the signal is believed to indicate the presence of a fault, the original signal is stored without compression to protect the fault information in the signal as much as possible.

[0224] If the signal is deemed not to indicate a fault, meaning the target component is considered to be in a normal state, and to meet the requirement of a lightweight storage system, then based on the sparsity of the multi-component frequency domain representation coefficients x1 and x2 obtained in step 4, data compression and storage are performed. The process is as follows:

[0225] Set a threshold parameter ν and store the amplitude and corresponding frequency values ​​of the frequency components in x1 and x2 whose amplitudes are greater than the threshold.

[0226] The threshold parameter ν is used to limit the sparsity of the stored signal. If it is too large, it will easily lead to signal distortion. If it is too small, it will lead to the storage of a large number of small values, and compression will not be possible.

[0227] The stored procedure first counts the number n of frequency components greater than the threshold ν between the two coefficients, and then stores them in a table of size 2×n.

[0228] Select frequency components greater than the threshold ν and store them in a table. The first row of the table stores the frequency values, and the second row stores the frequency amplitudes.

[0229] The reconstruction process is achieved through the inverse Fourier transform, i.e. in To reconstruct the signal, A T is the inverse of the Fourier transform matrix, and x1 and x2 are the sparse representation coefficients of the two types of components in the frequency domain.

[0230] Example 1: A Gear Fault Detection Method

[0231] Example 1 involves the diagnosis of bearing faults in a gear transmission system, with the core algorithm implemented in MATLAB. The experimental subject is the SQI gear fault simulation test bench. This test bench consists of a drive motor, planetary gearbox, magnetic brake, parallel shaft gearbox, data acquisition system, computer with acquisition software, and sensors. During the experiment, the faulty or normal parts to be verified are replaced in the planetary gearbox. Its input shaft is connected to the left sun gear, passes through two stages of planetary reducers to the right parallel gear reducer, and then passes through two more parallel gear reductions to reach the right output shaft. The test bench also includes a bearing load and a programmable magnetic brake. During the experiment, different normal and faulty parts are replaced to conduct simulation experiments, while the test bench's built-in motor speed encoder outputs pulse signals. The motor speed is set to 18Hz, and the sampling frequency is 12800Hz. Signals under normal conditions and signals under a missing tooth fault on the first-stage sun gear are acquired. The acquired signals come from the horizontal and vertical directions of the planetary gearbox, as well as the speed signals.

[0232] When processing the two sets of signals below, the number of data points extracted under steady-state operating conditions is N=2. 19 The signal is processed. The sparse representation coefficient length is set to M = 2N = 2. 20 Its time-domain waveform is visible Figure 4 .

[0233] First, based on the obtained rotational speed information from step 2, a Fourier transform is performed to obtain its frequency domain information, which is shown below. Figure 2 Obtain the switching frequency f from the spectrum z =16.934Hz, and based on the shape of the frequency shift in the spectrum, the bandwidth of the frequency shift fluctuation is estimated to be δ = 5Δf.

[0234] Based on the extracted frequency f z =29.9316Hz and bandwidth δ=25Δf construct class-time domain synchronization average vectors ω1 and ω2:

[0235]

[0236] ω2=I-ω1

[0237] Where ω1 and ω2 are the time-domain synchronous average vectors corresponding to the frequency-dependent and frequency-independent components, respectively, r is a pre-set small value, δ is the bandwidth of the frequency fluctuation, fz is the frequency, and n is a positive integer.

[0238] Furthermore, the weight vector is updated. This makes the weight vector, similar to that of a comb-shaped notch filter, symmetric about the Fs / 2 axis, thus conforming to the symmetry property of the spectrum in the Fourier transform. This yields the final two time-domain synchronous average vectors ω1 and ω2, which are... Figure 3 .

[0239] Based on step 3, using the obtained time-domain synchronous average vectors ω1 and ω2 corresponding to different components as weighting terms, a sparse time-domain synchronous average model F1 based on the multi-component concept is constructed, expressed as:

[0240]

[0241] Here, the Fourier transform is used as the linear transform operator A. The maximum number of iterations Nit is set to 50, and the loop termination constant ε is set to 10. -5 Then run the iteration according to step 5.

[0242] Based on step 5, select the sparse representation coefficients in the frequency domain corresponding to the frequency-dependent components. and time-domain waveform Perform subsequent calculations.

[0243] Please refer to the comparison of the time domain, spectrum, and envelope spectrum of the frequency-dependent and frequency-independent components of the faulty gear after multi-component time-domain synchronous averaging. It can be found that the periodic impact in the time domain is more obvious after the algorithm of this invention, and its period corresponds to the fault characteristic frequency. The sidebands reflecting the fault are very obvious in the spectrum, and the interference between the two components has been eliminated. The fault characteristic frequency is very obvious in the envelope spectrum.

[0244] Referring to Table 1, which shows the comparison results of CI indices for the two sets of gear signals, it can be seen that all indices of the fault signal are significantly higher than those of the normal gear signal. This demonstrates the rationality of the CI index and the effectiveness of the sparse time-domain synchronous averaging diagnostic method proposed in this paper in gear fault diagnosis.

[0245] Table 1

[0246] Indicator Name Faulty gear normal gears <![CDATA[RMS STSA ]]> 0.3117 0.1080 <![CDATA[PF STSA ]]> 6.5101 4.8393 <![CDATA[KurV STSA ]]> 5.3286 3.4503 <![CDATA[KU STSA ]]> 6.8447 4.0940 <![CDATA[OMX STSA ]]> 0.07162 0.00577 <![CDATA[FQ STSA ]]> 0.01786 0.0217

[0247] Here, based on the diagnostic results, the signal of the normal gear is compressed using the sparse representation coefficients of the multi-component sparse time-domain averaging method.

[0248] Set the threshold parameter ν = 0.003 and store the amplitude and corresponding frequency values ​​of the frequency components in x1 and x2 whose amplitudes are greater than the threshold.

[0249] The threshold parameter ν is used to limit the sparsity of the stored signal. If it is too large, it will easily lead to signal distortion. If it is too small, it will lead to the storage of a large number of small values, and compression will not be possible.

[0250] The stored procedure first counts the number of frequency components greater than the threshold ν in the two coefficients, n = 1213, which is much smaller than the original signal length 2. 19 Then it is scheduled in a table of size 2×1213.

[0251] Select frequency components greater than the threshold ν and store them in a table. The first row of the table stores the frequency values, and the second row stores the frequency amplitudes.

[0252] The reconstruction process is achieved through the inverse Fourier transform, i.e. A comparison between the reconstructed signal and the original signal is shown in [link to original signal]. Figure 8 The prominent impulse and frequency-independent components in the original signal are effectively preserved, with a root mean square error of 1.6102, achieving efficient compression of the normal state signal.

[0253] Example 2: A bearing fault detection method

[0254] Example 2 involves the diagnosis of a bearing failure in the accessory drive system of an aero-engine, with the core algorithm implemented in MATLAB. The experimental object is a bearing in the accessory drive system of a certain type of aero-engine. The data are vibration and rotational speed signals obtained during ground testing on a civil aircraft engine with two damaged bearings. The accessory gearbox is connected to the high-pressure shaft HP via radial and horizontal drive shafts, and energy is transferred from the high-pressure shaft to each output shaft. A tachometer is mounted on L4, with a sampling frequency of 50,000 Hz and a resolution of 44 pulses per revolution. An accelerometer is located on the flange of the accessory gearbox near shaft L5, also with a sampling frequency of 50,000 Hz and a duration of 200 s; the signal is recorded during the slow acceleration from idle to full power. The fault is damage to the roller bearing on shaft L5, specifically a large area of ​​spalling on the outer race, within a 32° sector area, with a depth of approximately 0.1 mm.

[0255] A specific engine bearing fault analysis was conducted using the proposed adaptive bandwidth sparse time-domain synchronous averaging method. Based on known information, the speed fluctuation was relatively small in the first and last fifths of the signal; therefore, this data segment was selected for analysis. To improve the accuracy of the speed fluctuation range, the tachometer signal processing time was set to 5 seconds, and the sampling frequency was set to 50,000 Hz.

[0256] First, according to step 2, its frequency spectrum is plotted as shown in the figure, yielding a rotational speed of 9013.4 Hz. Since the tachometer resolution is 44 pulses per revolution, the actual rotational speed f is... z The frequency is 204.85 Hz.

[0257] Based on the transmission relationship:

[0258]

[0259] In the formula, f4 is the rotational frequency of the L4 shaft; f5 is the rotational frequency of the L5 shaft; Z4 is the number of teeth on the gear on the L4 shaft, which is 62 in this case; and Z5 is the number of teeth on the gear on the L5 shaft, which is 61 in this case.

[0260] The rotational frequency of the L5 axis was found to be 208.2082 Hz.

[0261] Next, we estimate the bandwidth of the speed fluctuation δ = 25Δf

[0262] Based on the extracted frequency f z =29.9316Hz and bandwidth δ=25Δf construct class-time domain synchronization average vectors ω1 and ω2:

[0263]

[0264] ω2=I-ω1

[0265] Where ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively, r is a pre-set small value, and δ is the bandwidth of the frequency fluctuation.

[0266] Furthermore, the weight vector is updated. This makes the weight vector, similar to that of a comb-shaped notch filter, symmetric about the Fs / 2 axis, thus conforming to the symmetry property of the spectrum in the Fourier transform. This yields the final two time-domain synchronous average vectors ω1 and ω2.

[0267] Based on step 3, using the obtained time-domain synchronous average vectors ω1 and ω2 corresponding to different components as weighting terms, a sparse time-domain synchronous average model F1 based on the multi-component concept is constructed, expressed as:

[0268]

[0269] Here, the Fourier transform is used as the linear transform operator A. The maximum number of iterations Nit is set to 50, and the loop termination constant ε is set to 10. -5 Then run the iteration according to step 5.

[0270] Please refer to the time-domain waveforms, spectra, and envelope spectra of both components for comparison. Especially in the envelope spectrum of the speed-independent component, the characteristic frequency of the outer ring fault and its various harmonics are very obvious, indicating that an outer ring fault has occurred in the bearing. This is consistent with the known large-area spalling area on the outer race of the roller bearing on shaft L5. Therefore, this demonstrates that the proposed method is correct and can still effectively complete the monitoring task.

[0271] The reconstructed time-domain signals are obtained by processing the normal and fault signals using the method proposed in this paper. The CI (Compatibility Index) for the bearing was calculated, and the results are shown in the table below. It can be seen that all indicators of the fault signal are significantly higher than those of the normal signal, thus demonstrating the rationality of the CI index and the effectiveness of the sparse time-domain synchronous averaging diagnostic method proposed in this paper in bearing fault diagnosis.

[0272] Table 3

[0273] Indicator Name STSA_CI indicator Original signal CI <![CDATA[FQ STSA ]]> 0.008936 0.001205 <![CDATA[PF STSA ]]> 4.5028 3.3544 <![CDATA[KurV STSA ]]> 3.2576 2.1816

[0274] Based on the analysis results, the original time-domain vibration data of the signal is stored to preserve the fault information in the original signal to the greatest extent possible, which will facilitate subsequent research.

[0275] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for detecting faults in rotating machinery based on multi-component sparse time-domain synchronous averaging, characterized in that, It includes the following steps, S100: Collect vibration signals and rotational speed information of rotating machinery; S200. Construct time-domain synchronous average vectors ω1 and ω2 corresponding to frequency-dependent components and frequency-independent components based on the rotational speed information; S300. Construct a multi-component sparse time-domain synchronous average model F1 and a sparse time-domain synchronous average model F2 containing an unrelated dictionary by using the time-domain synchronous average vectors ω1 and ω2 corresponding to the frequency-related and frequency-independent components as weighting terms. S400. The optimization solution algorithm is used to iteratively solve the multi-component sparse time-domain synchronous average model F1 and the sparse time-domain synchronous average model F2 containing an unrelated dictionary. S500. For different fault diagnosis objects such as gears, bearings, and rotors in rotating machinery, select the sparse representation coefficients of the corresponding components, obtain the time-domain signal of the corresponding components through inverse Fourier transform, and then use the index CI. STSA Perform fault diagnosis; S600: Based on the diagnostic results, compress and store the signal.

2. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, Preferably, S200 includes, S201. Perform a Fourier transform on the rotational speed signal of the rotating machinery to obtain the rotational frequency from the spectrum; S202. The components in the signal are divided into three categories: frequency-dependent components, frequency-independent components, and noise. Among them, frequency-dependent components contain frequency-related information, and their spectrum includes the rotational frequency of the rotor components and its harmonics; frequency-independent components contain fault information other than rotational frequency information, and their spectrum includes other effective frequency components other than the rotational frequency of the rotor components and its harmonics; noise components do not contain equipment status information. S203. Construct time-domain synchronization average vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components based on the frequency conversion, where... ω2=I-ω1 Where ω1 and ω2 are the time-domain quasi-synchronous average vectors corresponding to the frequency-dependent and frequency-independent components, respectively, r is a pre-set small value, δ is the bandwidth of the frequency fluctuation, fz is the frequency, n is a positive integer, and N is the length of the time-domain quasi-synchronous average vector.

3. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 2, characterized in that, The time-domain synchronization average vectors ω1 and ω2 corresponding to the frequency-dependent and frequency-independent components of the frequency conversion structure are updated. Where N is the length of the time-domain synchronization average vector.

4. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, The S300 includes, S301, the F1 score of the multi-component sparse time-domain synchronous averaging model is: In the formula, y is the noisy signal to be analyzed; A is the linear transform operator; x1 and x2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components, respectively; is the vector dot product operator; λ is the regularization parameter; ω1 and ω2 are the time-domain synchronous average vectors corresponding to the frequency-dependent and frequency-independent components, respectively; S302, the sparse time-domain synchronous averaging model F2 containing an unrelated dictionary is: In the formula, y is the noisy signal to be analyzed, A1A2 are the linear transformation operators corresponding to the frequency-dependent and frequency-independent components, respectively. Different components in the signal are sparsely represented under their respective dictionaries, while sparse representation cannot be achieved under other dictionaries; α1 and α2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components, respectively. The vector dot product operator; λ is the regularization parameter; S303. When the dictionary A used in the multi-component sparse time-domain synchronous averaging model F1 is a Fourier transform dictionary, and the dictionary A1A2 used in the sparse time-domain synchronous averaging model F2 containing uncorrelated dictionaries is a weighted Fourier dictionary with embedded frequency conversion information, the two models are equivalent. The weighted Fourier transform matrix A1A2 is constructed based on the time-domain synchronous averaging vectors ω1 and ω2 corresponding to the frequency conversion related components and the frequency conversion unrelated components. Where A is the Fourier transform dictionary, W i =diag(ω i ), (i=1,2) is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors; S304. The sparse representation coefficients of the corresponding components of the sparse time-domain synchronous averaging model F2 with an uncorrelated dictionary are the spectral components of the corresponding components of the multi-component sparse time-domain synchronous averaging model F1 after embedding frequency conversion information. The sparse representation coefficients of the corresponding components of the multi-component sparse time-domain synchronous averaging model F1 and the sparse time-domain synchronous averaging model F2 with an uncorrelated dictionary have the following relationship: Where α i ω represents the sparse representation coefficient corresponding to the i-th component in model F2. i Let x1 be the time-domain synchronous average vector corresponding to the i-th component, and let x1 be the sparse representation coefficients corresponding to the i-th component in model F1. This is the vector dot product operator.

5. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, The iterative solution of the multi-component sparse time-domain synchronous average model F1 using optimization algorithms includes: S401. Initialize two parameters μ>0, x, set μ to 1, and set the number of iterations Nit, as well as a loop exit parameter ε. This parameter ensures that during optimization iteration, if the cost function of two iterations differs from the set ε value, the loop exits directly; otherwise, the set number of iterations Nit is completed until the loop stops. S402. Use the soft threshold function (soft) for operation: The soft threshold function, soft, is expressed as follows: A is a linear transformation operator; and ω1 and ω2 are the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; ω1 and ω2 are the time-domain synchronization average vectors corresponding to the frequency-dependent and frequency-independent components, respectively; μ is the step size parameter of the iteration. λ is the regularization parameter; S403. Increment the loop variable i by 1. If the multi-component sparse time-domain synchronous averaging model F1 satisfies k>Nit or Then let Exit the loop; otherwise, return to step S402.

6. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, The iterative solution of the sparse time-domain synchronous averaging model F2 containing an uncorrelated dictionary is performed using an optimization algorithm, including: S403. For the soft threshold function of the model: The equivalent solution is obtained using the following formula: In the formula, and Let A and B be the sparse representation coefficients of the frequency-dependent and frequency-independent components in the k-th iteration, respectively; A is the linear transformation operator, A T W is the corresponding inverse matrix; i is a diagonal matrix whose diagonal elements are similar to time-domain synchronous average vectors; μ is the iteration step size parameter and λ is the regularization parameter; S404. After the solution iteration is completed, the spectrum α with embedded frequency conversion information is converted into the regular spectrum x.

7. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, In S500, For gears, the sparse representation coefficients corresponding to the frequency-related components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators: Root Mean Square (RMS) STSA : In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components. Peak Factor (PF) STSA : In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA It is the root mean square value; KurV (Kullification Index) STSA : In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components. This represents the average value of the time-domain signal of the frequency-dependent components. Envelope kurtosis index KU STSA : In the formula, N is the length of the signal, h i The envelope signal of the time-domain signal is reconstructed from the sparse representation coefficients x1 corresponding to the obtained frequency-dependent components. This represents the average value of the envelope signal of the frequency-dependent components; Meshing frequency amplitude OMX STSA : OMX STSA,i,j =A ij In the formula A ij This represents the amplitude of the j-th order fault characteristic frequency of the i-th gear in the sparse representation coefficients x1; Characteristic frequency amplitude FQ STSA : In the formula A ij The value of CI represents the amplitude of the j-th order fault characteristic frequency of the i-th gear in the envelope spectrum, where each term CI... STSA The index is an estimated frequency conversion energy; the index for a normal signal is lower than that for a fault signal.

8. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, In S500, For the rotor, the sparse representation coefficients corresponding to the frequency-dependent components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators: Frequency conversion amplitude AR STSA : In the formula This represents the amplitude of the j-th harmonic of the i-th rotor in the sparse representation coefficients x1; Root Mean Square (RMS) STSA : In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent components; Average Amplitude (MA) STSA : In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficients x corresponding to the frequency-dependent components. Root amplitude RA STSA : In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the frequency-dependent components.

9. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, In S500, For bearings, the sparse representation coefficients corresponding to the frequency-independent components are selected for subsequent calculations. The time-domain signal of the corresponding components is obtained through inverse Fourier transform. The STSA_CI index is composed of the following indicators: Characteristic frequency amplitude FQ STSA : In the formula A ij The amplitude of the j-th order frequency, representing the i-th bearing fault characteristic frequency in the envelope spectrum; Peak Factor (PF) STSA : In the formula RMS is the peak value of the time-domain signal of the frequency-dependent component. STSA It is the root mean square value; KurV (Kullification Index) STSA ; In the formula, N is the length of the signal. The reconstructed time-domain signal is the sparse representation coefficient x corresponding to the obtained frequency-correlation component. This represents the average value of the time-domain signal of the frequency-dependent component.

10. The rotating machinery fault detection method based on multi-component sparse time-domain synchronous averaging according to claim 1, characterized in that, Based on the diagnostic results, the signal is compressed and stored, including... S601. If the signal is considered to indicate the existence of a fault, the original signal is stored; if the signal is considered not to indicate the existence of a fault, that is, the target component is considered to be in a normal state, the compressed sensing method is used to compress and store the data. S602. For a normal state signal, the frequency domain sparse representation coefficients x1 and x2 obtained by solving the multi-component sparse time-domain averaging model are compressed based on the sparsity of the two coefficients themselves. The threshold parameter v is used to store the amplitude and corresponding frequency value of the frequency components in x1 and x2 whose amplitude is greater than the threshold. S603. During storage, count the number n of frequency components greater than the threshold v among the two coefficients. Then, predefine a table of size 2×n, select the frequency components greater than the threshold v and store them in the table. The first row of the table is used to store the frequency value and the second row is used to store the frequency amplitude. S604. The reconstruction process is achieved through the inverse Fourier transform, i.e. in To reconstruct the signal, A T is the inverse of the Fourier transform matrix, and x1 and x2 are the sparse representation coefficients of the two types of components in the frequency domain.

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