CN117606724A - A multi-resolution dynamic signal time domain and spectrum characteristic analysis method and device - Google Patents

Abstract

The invention discloses a multi-resolution dynamic signal time domain and frequency spectrum characteristic analysis method and a device, wherein the method comprises the steps of initializing modal decomposition quantity K, and carrying out variation modal decomposition based on a sampling signal to obtain an intrinsic mode function IMF; performing phase space reconstruction on the inherent mode function, sequencing the reconstructed signals, calculating the probability of occurrence of the sequenced signal sequences, calculating the combined weighted permutation entropy to determine the complexity of signal decomposition, and adjusting the mode decomposition quantity K; setting high, medium and low frequency bands, corresponding intermediate frequency bands and window width adjustment factors corresponding to each frequency band, and performing multi-resolution generalized S transformation on K IMF components aiming at a plurality of frequency bands to realize dynamic signal time domain and frequency domain feature extraction under multi-resolution. The invention aims to help diagnose the fan fault vibration signal by using multi-resolution analysis and realize the time domain and frequency domain feature extraction of the fan fault vibration signal.

Description

A multi-resolution dynamic signal time domain and spectrum characteristic analysis method and device

Technical field

The invention relates to the field of dynamic signal testing and analysis, and in particular to a multi-resolution dynamic signal time domain and spectrum characteristic analysis method and device.

Background technique

With the increasing demand for renewable energy in modern society, wind energy has become a widely adopted clean energy source. However, there are many challenges in the operation and maintenance of wind turbine systems, one of which is rapid and accurate diagnosis of potential faults. Fan failure not only results in reduced productivity, it can also result in equipment damage and expensive repair costs. In order to effectively perform wind turbine fault diagnosis, effective monitoring and analysis tools need to be developed. Among them, the analysis of time domain and spectrum characteristics of dynamic signals is a key part. This analysis can help engineers understand what is going on inside the wind turbine system, detect potential failures and take appropriate maintenance measures in advance.

In engineering practice, it is crucial to accurately analyze the time domain and frequency domain characteristics of signals. At this stage, a single time domain or frequency domain analysis method usually cannot capture information related to the local changing characteristics of non-stationary dynamic signals. Therefore, time-frequency analysis is usually used to analyze non-stationary signals. It maps the one-dimensional time domain signal to the two-dimensional time-frequency domain (this mapping is called time-frequency representation) and generates a time-frequency density distribution spectrogram to reflect various non-stationary signals in time and frequency. amplitude change characteristics. Traditional signal analysis methods can meet these needs to a certain extent, but they are often limited by resolution. In particular, in wind turbine systems, the spectral characteristics of signals often have multi-resolution characteristics. For example, a wind turbine may be affected by multiple frequency components simultaneously, representing different modes of mechanical motion or vibration. Therefore, in order to analyze these signals more accurately, a multi-resolution method needs to be developed that can consider both the time domain and spectral characteristics of the signal. Multi-resolution analysis refers to dividing the signal into components of different resolutions to narrow the scope of analysis, which is equivalent to decomposing the data for analysis on different frequency bands. However, many traditional signal time-frequency analysis methods have some limitations. On the one hand, some methods can only analyze at specific resolutions and are difficult to adapt to the diversity of signals in different application scenarios. On the other hand, other methods may be inefficient when dealing with large-scale data, or lack accuracy when dealing with non-stationary signals. Therefore, the accurate extraction and analysis of time-domain and frequency-domain features in multi-resolution dynamic signals is a key problem that needs to be solved urgently.

Contents of the invention

Technical problems to be solved by the present invention: In view of the above-mentioned problems of the prior art, a multi-resolution dynamic signal time domain and spectrum characteristic analysis method and device are provided. The present invention aims to use multi-resolution analysis to help diagnose fan fault vibrations. signal to achieve time domain and frequency domain feature extraction of wind turbine fault vibration signals.

In order to solve the above technical problems, the technical solution adopted by the present invention is:

A multi-resolution dynamic signal time domain and spectrum characteristic analysis method, including:

S101, initialize the number of decomposition layers K of variational mode decomposition VMD;

S102, perform variational mode decomposition VMD on the input original signal based on the decomposition layer number K;

S103. Calculate the permutation entropy of the K modal components IMF obtained by variational mode decomposition VMD;

S104, if the permutation entropy of the modal component IMF is greater than the set value, jump to step S105; otherwise, add 1 to the decomposition layer number K of the variational mode decomposition VMD, and jump to step S102;

S105, set multiple frequency bands as different resolutions, and perform multi-resolution generalized S transformation on the K modal components IMF for the multiple frequency bands, thereby obtaining multi-resolution signal time domain and frequency characteristics corresponding to the original signal.

Optionally, step S103 includes:

S20l, perform phase space reconstruction on the K modal components IMF, and introduce different time delays to each modal component IMF through phase space reconstruction to construct an m-dimensional phase space vector, where m is the phase space embedding dimension;

S202, sort the elements in the reconstructed modal component IMF of the phase space in ascending order, and calculate the probability of occurrence of the sorted signal sequence;

S203: Calculate the combined weighted permutation entropy according to the probability of occurrence of the sorted signal sequence, and standardize the combined weighted permutation entropy to obtain the final permutation entropy.

Optionally, the function expression for phase space reconstruction of any k-th modal component IMF in step S20l is:

X _k (1)={x _k (1), x _k (1+τ),..., x _k (1+(m-1)τ)}

X _k (2)={x _k (2), x _k (2+τ),..., x _k (2+(m-1)τ)}

…

X _k (i)={x _k (i), x _k (i+τ),..., x _k (i+(m-1)τ)}

…

X _k (N-(m-1)τ)={x _k (N-(m-1)τ),...,x _k (N)}

_In the above _{formula ,} , m is the phase space embedding dimension.

Optionally, in step S202, the functional expression for sorting the elements in the phase space reconstructed modal component IMF in ascending order is:

x _k (i+(j ₁ -1)τ)≤x _k (i+(j ₂ -1)τ)≤…≤x _k (i+(j _m -1)τ),

In the above formula, i+(j ₁ -1)τ is the index of the smallest element in X _k (i), the result of phase space reconstruction of x _k (i), and i+(j ₂ -1)τ is x _k ( i) The index of the second smallest element in X _k (i), the result of phase space reconstruction, i+(j _m -1)τ is x _k (i) The result of X _k (i), the result of phase space reconstruction The index of the largest element in i), j ₁ to j _m are respectively the index of the sorted signal sequence; calculating the probability of occurrence of the sorted signal sequence in step S202 includes:

S301, extract the signal sequence from the sorted signal sequence:

S(g)=[j ₁ , j ₂ ,..., j _m ],

In the above formula, S(g) is the extracted signal sequence, j ₁ ~ j _m are the indexes of the sorted signal sequence respectively;

S302, calculate the probability of occurrence of the sorted signal sequence according to the following formula:

P _i =l/k,

In the above formula, P _i is the probability of occurrence of the signal sequence corresponding to x _k (i), l is the frequency of occurrence of the extracted signal sequence S(g), and k is the number of decomposition layers.

Optionally, in step S203, the functional expression for calculating the combined weighted permutation entropy based on the probability of occurrence of the sorted signal sequence is:

In the above formula, H _p (m) is the combined weighted permutation entropy, γ and θ are the parameters of the combined weighted permutation entropy, P _i is the probability of the signal sequence corresponding to x _k (i), and k is the number of decomposition layers; The functional expression of the final permutation entropy obtained by standardizing the combined weighted permutation entropy is:

In the above formula, P _E is the final permutation entropy, m! represents the factorial of m, and m is the phase space embedding dimension.

Optionally, when performing multi-resolution generalized S transformation on the K modal components IMF for multiple frequency bands in step S105, the functional expression of the Gaussian window function used is:

In the above formula, ω(t-τ, f) represents the improved Gaussian window function, t is time, τ is time delay, f is frequency, σ(f) is window width, and there are:

In the above formula, μ is the window width adjustment factor corresponding to each frequency band, and p and q are constant parameters.

Optionally, multiple frequency bands are set in step S105, including five frequency bands of high frequency, medium high frequency, medium frequency, medium low frequency and low frequency that are continuously distributed in sequence, and the functional expression of the window width adjustment factor corresponding to each frequency band is:

In the above formula, μ _h is the window width adjustment factor corresponding to the high-frequency band, μ _m is the window width adjustment factor corresponding to the mid-frequency band, μ _l is the window width adjustment factor corresponding to the low-frequency band, and μ _hm is the window width adjustment factor corresponding to the mid-frequency band. Window width adjustment factor, μ _ml is the window width adjustment factor corresponding to the middle and low frequency bands.

Optionally, in step S105, performing multi-resolution generalized S transformation on the K modal components IMF for multiple frequency bands includes:

S401, perform Fourier transform and dimension expansion on each modal component in the K modal components IMF to obtain the translation spectrum;

S402, multiply the translation spectrum and the Gaussian window function and perform inverse Fourier transform to obtain a two-dimensional complex matrix composed of the inverse Fourier transform corresponding to the K modal components IMF;

S403: Modulo the two-dimensional complex matrix to obtain the S matrix, and output the obtained S matrix as the multi-resolution signal time domain and frequency characteristics corresponding to the original signal. The column vector in the S matrix describes the amplitude of the signal at a specific moment. Features, row vectors describe the time domain distribution of a signal at a specific frequency.

In addition, the present invention also provides a multi-resolution dynamic signal time domain and spectrum characteristic analysis device, including a microprocessor and a memory connected to each other, and the microprocessor is programmed or configured to execute the multi-resolution based Dynamic signal time domain and spectrum characteristic analysis method.

In addition, the present invention also provides a computer-readable storage medium in which a computer program is stored, and the computer program is used to be programmed or configured by a microprocessor to execute the multi-resolution based dynamic Signal time domain and spectrum characteristic analysis methods.

Compared with the existing technology, the present invention mainly has the following advantages: the present invention determines the signal decomposition correctness of VMD decomposition layer number k by combining weighted permutation entropy, and realizes the adaptive determination of the number of decomposition layers according to the complexity of the decomposed signal; Define high frequency, medium frequency, low frequency and corresponding intermediate frequency bands, and set corresponding window width adjustment factors according to the corresponding frequency bands, so that the window length of the Gaussian window can be adaptively adjusted according to the frequency domain where the signal components are located, which can effectively improve the original S transform algorithm. It is difficult to take into consideration different frequency domains and time-frequency resolutions to meet the requirements of multi-resolution signal analysis.

Description of drawings

Figure 1 is a flow chart of a multi-resolution dynamic signal time domain and spectrum characteristic analysis method according to an embodiment of the present invention.

Figure 2 is a waveform of an original signal in an embodiment of the present invention.

Figure 3 is a waveform diagram of the modal component IMF obtained after performing VMD of K=3 on the original signal of Figure 2.

Figure 4 is a spectrum diagram of the natural mode function obtained after S-transformation of the natural mode function in the embodiment of the present invention.

FIG. 5 is a waveform diagram of a test signal obtained by decomposing a test signal into layers ranging from 1 to 6 through discrete wavelet transform in an embodiment of the present invention.

Detailed ways

As shown in Figure 1, the multi-resolution dynamic signal time domain and spectrum characteristic analysis method in this embodiment includes:

S101, initialize the number of decomposition layers K of variational mode decomposition VMD;

S102, perform variational mode decomposition VMD on the input original signal based on the decomposition layer number K;

S103. Calculate the permutation entropy of the K modal components IMF obtained by variational mode decomposition VMD;

S104, if the permutation entropy of the modal component IMF is greater than the set value, jump to step S105; otherwise, add 1 to the decomposition layer number K of the variational mode decomposition VMD, and jump to step S102;

S105, set multiple frequency bands as different resolutions, and perform multi-resolution generalized S transformation on the K modal components IMF for the multiple frequency bands, thereby obtaining multi-resolution signal time domain and frequency characteristics corresponding to the original signal.

It can be understood that the multi-resolution dynamic signal time domain and spectrum characteristic analysis method of this embodiment determines the correctness of the signal decomposition of the VMD decomposition layer number K by combining the weighted permutation entropy, and realizes the adaptive determination of the decomposition according to the complexity of the decomposed signal. Number of layers; by setting multiple frequency bands as different resolutions and performing multi-resolution generalized S transformation on the modal component IMF for multiple frequency bands, the multi-resolution analysis requirements of dynamic signals are realized and the time analysis of dynamic signals can be improved. The ability to express frequency characteristics facilitates the diagnosis of wind turbine fault vibration signals through multi-resolution analysis, and enables the extraction of time and frequency domain features of wind turbine fault vibration signals. Among them, variational mode decomposition VMD is an existing well-known method. Performing variational mode decomposition VMD on the original signal includes: decomposing the original signal x(t) into K modal components x _k (t) with center frequency and limited bandwidth. ), k=1,...,K, the constraint is that the sum of all modal components obtained by decomposition is equal to the original signal x(t), and the modal component x _k (t) is subjected to Hilbert transformation to obtain its corresponding The single-sided spectrum of , and adding a center frequency ω _k to the analytical signal of modal component x _k (t), and modulating the spectrum to the corresponding fundamental frequency band, the demodulated signal can be obtained:

Among them, * represents the convolution operation; δ(t) is the impact function; solve the square of the L2 norm of the gradient of the above demodulated signal to obtain the bandwidth of the modal component x _k (t), and construct the variational mode decomposition VMD The variational constraint model is solved using Lagrangian multiplier factors, and K modal components IMF (Intrinsic Mode Function) are output in order from high frequency to low frequency.

Step S103 of this embodiment calculates the permutation entropy of the K modal components IMF obtained by variational mode decomposition VMD, including:

S201, perform phase space reconstruction on k modal components IMF, and introduce different time delays to each modal component IMF through phase space reconstruction to construct an m-dimensional phase space vector, where m is the phase space embedding dimension;

S202, sort the elements in the reconstructed modal component IMF of the phase space in ascending order, and calculate the probability of occurrence of the sorted signal sequence;

S203: Calculate the combined weighted permutation entropy according to the probability of occurrence of the sorted signal sequence, and standardize the combined weighted permutation entropy to obtain the final permutation entropy.

In this embodiment, step S103 includes:

S201, perform phase space reconstruction on the K modal components IMF, and introduce different time delays to each modal component IMF through phase space reconstruction to construct an m-dimensional phase space vector, where m is the phase space embedding dimension;

S202, sort the elements in the reconstructed modal component IMF of the phase space in ascending order, and calculate the probability of occurrence of the sorted signal sequence;

S203: Calculate the combined weighted permutation entropy according to the probability of occurrence of the sorted signal sequence, and standardize the combined weighted permutation entropy to obtain the final permutation entropy.

In this embodiment, the function expression for phase space reconstruction of any k-th modal component IMF in step S201 is:

X _k (1)={x _k (1), x _k (1+τ),..., x _k (1+(m-1)τ)}

X _k (2)={x _k (2), x _k (2+τ),..., x _k (2+(m-1)τ)}

…

X _k (i)={x _k (i), x _k (i+τ),..., x _k (i+(m-1)τ)}

…

X _k (N-(m-1)τ)={x _k (N-(m-1)τ),...,x _k (N)}

_In the above _{formula ,} , m is the phase space embedding dimension.

In this embodiment, the functional expression for sorting the elements in the phase space reconstructed modal component IMF in ascending order in step S202 is:

x _k (i+(j ₁ -1)τ)≤x _k (i+(j ₂ -1)τ)≤…≤x _k (i+(j _m -1)τ),

In the above formula, i+(j ₁ -1)τ is the index of the smallest element in X _k (i), the result of phase space reconstruction of x _k (i), and i+(j ₂ -1)τ is x _k ( i) The index of the second smallest element in X _k (i), the result of phase space reconstruction, i+(j _m -1)τ is x _k (i) The result of X _k (i), the result of phase space reconstruction The index of the largest element in i), j ₁ to j _m are respectively the index of the sorted signal sequence; calculating the probability of occurrence of the sorted signal sequence in step S202 includes:

S301, extract the signal sequence from the sorted signal sequence:

S(g)=[j ₁ , j ₂ ,..., j _m ],

In the above formula, S(g) is the extracted signal sequence, j ₁ ~ j _m are the indexes of the sorted signal sequence respectively;

S302, calculate the probability of occurrence of the sorted signal sequence according to the following formula:

P _i =l/k,

In the above formula, P _i is the probability of occurrence of the signal sequence corresponding to x _k (i), l is the frequency of occurrence of the extracted signal sequence S(g), and k is the number of decomposition layers.

In this embodiment, the functional expression for calculating the combined weighted permutation entropy according to the probability of occurrence of the sorted signal sequence in step S203 is:

In the above formula, H _p (m) is the combined weighted permutation entropy, γ and θ are the parameters of the combined weighted permutation entropy, P _i is the probability of the signal sequence corresponding to x _k (i), and k is the number of decomposition layers; The functional expression of the final permutation entropy obtained by standardizing the combined weighted permutation entropy is:

In the above formula, P _E is the final permutation entropy, m! represents the factorial of m, and m is the phase space embedding dimension.

It should be noted that the set value in step S104 can be set as needed. For example, as an optional implementation, the setting value in step S104 of this embodiment is 0.5. If the final permutation entropy is greater than 0.5, it means that the number of signal layers of the variational mode decomposition VMD is appropriate and the signal is stable; if If the final permutation entropy is less than or equal to 0.5, it means that the signal of variational mode decomposition VMD is too complex, and the number of decomposition layers K of variational mode decomposition VMD is not enough, so it is necessary to increase the number of decomposition layers K. It should be noted that the number of decomposition layers K of traditional variational mode decomposition VMD is determined artificially and is highly subjective. If the number of decomposition layers K is too small, the fault characteristic information contained in the modal component IMF will be incomplete, and important information will be discarded; if the number of decomposition layers K is too large, the center frequency will be too close, resulting in an over-decomposition state. This embodiment uses permutation entropy to calculate the correctness and stability of the signal decomposition of the current decomposition layer number K, thereby determining the optimal variational mode decomposition VMD decomposition layer number K, achieving adaptive determination based on the complexity of the decomposed signal. The decomposition layer number K can effectively solve the problem that variational mode decomposition VMD needs to artificially set the decomposition layer number K, which may cause improper setting of the decomposition layer number to affect the results of signal analysis. The decomposition can be adaptively determined according to the complexity of the signal itself. Number of layers K.

In this embodiment, when performing multi-resolution generalized S transformation on K modal components IMF for multiple frequency bands in step S105, the functional expression of the Gaussian window function used is:

In the above formula, ω(t-τ, f) represents the improved Gaussian window function, t is time, τ is time delay, f is frequency, σ(f) is window width, and there are:

In the above formula, μ is the window width adjustment factor corresponding to each frequency band, and p and q are constant parameters. Specifically, the values of p and q can be set to 0.4 and 0.5.

In this embodiment, the multiple frequency bands set in step S105 include five frequency bands of high frequency, medium high frequency, medium frequency, medium low frequency and low frequency that are continuously distributed in sequence, and the functional expression of the window width adjustment factor corresponding to each frequency band is: :

In the above formula, μ _h is the window width adjustment factor corresponding to the high-frequency band, μ _m is the window width adjustment factor corresponding to the mid-frequency band, μ _l is the window width adjustment factor corresponding to the low-frequency band, and μ _hm is the window width adjustment factor corresponding to the mid-frequency band. Window width adjustment factor, μ _ml is the window width adjustment factor corresponding to the middle and low frequency bands.

Specifically, according to the application requirements of the actual frequency band, as an optional implementation method, in this embodiment, the frequency band is divided into: high frequency is above 1001Hz, medium frequency is 401~800Hz, low frequency is 1~200Hz, and medium frequency is 800Hz ~1000Hz, mid-low frequency is 200Hz~400Hz. It can be understood that this embodiment defines high frequency, medium frequency, low frequency and corresponding intermediate frequency bands, and sets corresponding window width adjustment factors according to the corresponding frequency bands, so that the window length of the Gaussian window can be adaptively adjusted according to the frequency domain where the signal components are located. It can effectively improve the problem of difficulty in balancing different frequency domains and time-frequency resolutions of the original S transform algorithm, and meet the requirements of multi-resolution signal analysis.

In step S105 of this embodiment, performing multi-resolution generalized S transformation on k modal components IMF for multiple frequency bands includes:

S401, perform Fourier transform and dimension expansion on each modal component in the k modal components IMF to obtain the translation spectrum;

S402, multiply the translation spectrum and the Gaussian window function and perform inverse Fourier transform to obtain a two-dimensional complex matrix composed of the inverse Fourier transform corresponding to the k modal components IMF;

S403: Modulo the two-dimensional complex matrix to obtain the S matrix, and output the obtained S matrix as the multi-resolution signal time domain and frequency characteristics corresponding to the original signal. The column vector in the S matrix describes the amplitude of the signal at a specific moment. Features, row vectors describe the time domain distribution of a signal at a specific frequency.

Among them, the specific steps of performing multi-resolution generalized S transform on k modal components IMF are as follows:

B1 (corresponding to step S401): Fourier transform and dimension expansion are performed on each modal component to obtain the translation spectrum:

In the above formula, x _k [n], k = 1, 2, 3 are the discrete quantities of the modal components. Let the discrete time series be x _k [hT], k = 1, 2, 3, h is the discrete time point. , h=0, 1,..., N-1, T is the sampling time interval, N is the total number of samples; for each x _k [hT], perform fast Fourier transform (FFT) to obtain the translation spectrum:

B2 (corresponding to step S402): Calculate the local Gaussian window, that is, perform fast Fourier transform FFT on the Gaussian window function w _k (t, f) to obtain the local Gaussian window:

Then translate the translation spectrum to get:

Then multiply the local Gaussian window and the translated translation spectrum to get:

Then perform an inverse Fourier transform on it to obtain the signal in the time domain:

Its specific calculation function expression is as follows:

In the above formula, let the frequency f→n/NT and the time parameter τ→jT;

B3 (corresponding to step S403): for a single translation spectrum:

Loop through step B2 until all sampling frequency points obtain a corresponding two-dimensional negative matrix:

After taking the modulus of the matrix elements, the time domain and spectral characteristics of the dynamic signal output by the S matrix can be obtained.

It can be understood that the multi-resolution dynamic signal time domain and spectrum characteristic analysis method of this embodiment performs generalized S transformation based on the adaptive Gaussian window, in which the window width adjustment factor adaptively adjusts the window of the Gaussian window according to the frequency domain where the signal components are located. Long, it can effectively improve the original S transform algorithm's problem of difficulty in balancing time and frequency resolution in different frequency domains, and realize signal time domain and frequency domain feature analysis.

In this embodiment, in order to diagnose the fan fault vibration signal, simulate the time-frequency characteristics of the fan stator and rotor collision fault, and realize the time domain and frequency domain feature extraction of the fan fault vibration signal, this embodiment uses a signal generator based on the fan fault. Signal sample library, the generated original signal is shown in Figure 2. The receiving end uses the DSP platform model SM320C6457 for signal processing.

With the sampling rate f _s = 6.4kHz as the sampling frequency, the time domain signal x(t) is discretely sampled to obtain a sampling signal sequence x[n] with a length of N, n=1, 2,...,N, and the sampling time is 3 Second. Consider a test signal containing three frequency components, whose frequency components are 50Hz, 450.6Hz, and 949.2Hz respectively. The expression of the time domain signal x(t) is:

x(t)=cos(2π·50t)+0.2cos(2π·450.6t)+0.06cos(2π·945.2t)

Initialize the number of decomposition layers of variational mode decomposition VMD K = 2, perform variational mode decomposition VMD on the sampled signal x[n] to obtain 2 modal components x _k [n], k = 1, 2, each mode The state components can be expressed as:

x _k [n]＝A _k [n]cos(φ _k [n])

In the formula, A _k [n] is the amplitude of the finite mode component; φ _k [n] is the phase.

Perform phase space reconstruction on the two modal components respectively, sort the elements in the reconstructed modal component IMF in ascending order, and calculate the probability of occurrence of the sorted signal sequence, and finally obtain its permutation entropy, The combined weighted permutation entropy of 2 finite mode components x _k [n] is calculated as follows:

It can be seen from the calculation that when the number of decomposed modes is set to K = 2, the calculated combined weighted permutation entropy is 0.4637, which is less than 0.5, indicating that the decomposed signal is unstable, the original signal is relatively complex, and the current decomposition is insufficient, resulting in mode confusion. Stacking requires increasing the number of decomposition layers. Therefore, K=K+1=3, and return to the first step to re-execute VMD and calculate the combined weighted permutation entropy of the decomposed three finite mode components x _k [n]:

It can be seen from the calculation that when the number of decomposition modes K=3, the calculated combined weighted permutation entropy is 0.8995, which is greater than 0.5, indicating that the decomposed signal is stable, so the decomposition is stopped and 3 modal components x _k (t) are output, k=1, 2, 3. The waveforms of these three modal components are shown in Figure 3. In Figure 3, they are marked as: intrinsic mode function_0~intrinsic mode function_2.

Each modal component is set with different window width adjustment factors according to its frequency components. The window width adjustment factors for high frequency, medium frequency, low frequency, high-to-medium transition frequency band and medium-to-low transition frequency band are respectively:

and/>

Then the calculation method of Gaussian window function is:

Since the center frequencies of the three natural mode functions are in the low frequency, medium frequency and high medium frequency bands respectively, their corresponding window function calculation formulas are:

For three intrinsic mode functions x _k [n], k = 1, 2, 3, let the discrete time series be x _k [hT], k = 1, 2, 3, h is a discrete time point, h = 0 , 1,...,N-1, T is the sampling time interval, N is the total number of samples; finally, the three S matrices output in this embodiment are visualized as shown in Figure 4, where (a), ( b) and (c) are the time-frequency diagrams obtained after visualizing the S matrix corresponding to the intrinsic mode function_0~the intrinsic mode function_2 respectively. It can be seen that the multi-resolution signal time domain and frequency characteristics (S matrix) obtained based on the method of this embodiment can realize the extraction of dynamic signal time domain and frequency domain characteristics at multi-resolution, thereby helping different types of wind turbine fault vibration signals diagnosis. As an optional implementation, in this embodiment, the original multi-resolution signal time domain and frequency characteristics (S matrix) are input into a pre-trained machine learning classifier (for example, using a neural network support vector machine SVM, etc. ), you can get the corresponding equipment fault type, such as normal status and fault status.

In contrast, classic multi-resolution analysis methods such as wavelet transform have the problem that it is difficult to determine the number of wavelet decomposition layers. If there are too many decomposition layers and threshold processing is performed on the coefficients of all wavelet spaces at each layer, the signal will be The information loss is serious, and as the number of decomposition layers increases, the time domain characteristics weaken and the frequency domain characteristics increase. As shown in Figure 5, the analysis of the test signal x[n] by discrete wavelet transform is shown. Figure (a) corresponds to the approximate coefficient of decomposition layer 5, and Figures (b), (c), (d), (e) and (f) correspond to the detail coefficients when the number of decomposition layers is 5, 4, 3, 2, and 1 respectively. In wavelet analysis, the approximation coefficient represents the low-frequency part information of the signal wavelet decomposition and reconstruction, and the detail coefficient represents the high-frequency part information of the signal. It can be seen from the results that when there are too many decomposition layers, signal information is seriously lost and it is difficult to extract time domain and spectral features.

In summary, this embodiment is based on the multi-resolution dynamic signal time domain and spectrum characteristic analysis method, which can adaptively determine the mode number of the signal variational mode decomposition, effectively solving the problem that requires manual determination. At the same time, this embodiment The dynamic signal time domain and spectrum characteristic analysis method based on multi-resolution defines high, medium, low frequency bands and transition frequency bands, and introduces multi-band window width adjustment factors to solve the problem that the multi-resolution analysis of dynamic signals cannot be based on the timing of different frequencies of the signal. The problem of insufficient flexibility can be solved by adjusting the frequency characteristics, thereby improving the ability of the generalized S transform to express the time-frequency characteristics of dynamic signals.

In addition, this embodiment provides a multi-resolution dynamic signal time domain and spectrum characteristic analysis device, including a microprocessor and a memory connected to each other, and the microprocessor is programmed or configured to perform the multi-resolution based analysis described above. Frequency dynamic signal time domain and spectrum characteristic analysis method. This embodiment also provides a computer-readable storage medium, in which a computer program is stored, and the computer program is used to be programmed or configured by a microprocessor to perform the multi-resolution-based processing described above. Dynamic signal time domain and spectrum characteristic analysis method.

Those skilled in the art will understand that embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment that combines software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein. The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each process and/or block in the flowchart illustrations and/or block diagrams, and combinations of processes and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce a use A device for realizing the functions specified in one process or multiple processes of the flowchart and/or one block or multiple blocks of the block diagram. These computer program instructions may also be stored in a computer-readable memory that causes a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction means, the instructions The device implements the functions specified in a process or processes of the flowchart and/or a block or blocks of the block diagram. These computer program instructions may also be loaded onto a computer or other programmable data processing device, causing a series of operating steps to be performed on the computer or other programmable device to produce computer-implemented processing, thereby executing on the computer or other programmable device. Instructions provide steps for implementing the functions specified in a process or processes of a flowchart diagram and/or a block or blocks of a block diagram.

The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above-mentioned embodiments. All technical solutions that fall under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements and modifications may be made without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims (10)

1. A multi-resolution dynamic signal time domain and frequency spectrum feature analysis method, comprising:

s101, initializing a decomposition layer number K of a variation mode decomposition VMD;

s102, performing variable mode decomposition on VMD on an input original signal based on a decomposition layer number K;

s103, calculating the arrangement entropy of K modal components IMF obtained by decomposing the VMD in a variation mode;

s104, if the arrangement entropy of the modal component IMF is larger than a set value, jumping to the step S105; otherwise, adding 1 to the decomposition layer number K of the variant mode decomposition VMD, and jumping to the step S102;

s105, setting a plurality of frequency bands as different resolutions, and performing multi-resolution generalized S transformation on K modal components IMF according to the plurality of frequency bands, so as to obtain multi-resolution signal time domains and frequency characteristics corresponding to the original signals.

2. The multi-resolution dynamic signal time-domain and frequency-spectrum feature analysis method according to claim 1, wherein step S103 comprises:

s201, carrying out phase space reconstruction on K modal components IMF, and constructing an m-dimensional Xiang Kongjian vector by introducing different time delays into each modal component IMF through the phase space reconstruction, wherein m is a phase space embedding dimension;

s202, sorting elements in the modal component IMF after phase space reconstruction according to ascending order, and calculating the probability of occurrence of the sorted signal sequence;

s203, calculating combined weighted permutation entropy according to the probability of occurrence of the ordered signal sequence, and normalizing the combined weighted permutation entropy to obtain final permutation entropy.

3. The multi-resolution dynamic signal time domain and frequency spectrum feature analysis method according to claim 2, wherein the function expression for performing phase space reconstruction on any kth modal component IMF in step S201 is:

X _k (1)＝{x _k (1)，x _k (1+τ)，...，x _k (1+(m-1)τ)}

X _k (2)＝{x _k (2)，x _k (2+τ)，...，x _k (2+(m-1)τ)}

…

X _k (i)＝{x _k (i)，x _k (i+τ)，...，x _k (i+(m-1)τ)}

…

X _k (N-(m-1)τ)＝{x _k (N-(m-1)τ)，...，x _k (N)}

in the above, X _k (1)～X _k (N- (m-1) τ) is the component element obtained by phase space reconstruction, x _k (i) The i-th component element representing the kth modal component IMF, τ is the time delay, m is the phase space embedding dimension, and N is the total number of component elements.

4. The multi-resolution dynamic signal time domain and frequency spectrum feature analysis method according to claim 2, wherein in step S202, the function expression for sorting the elements in the phase space reconstructed modal component IMF in ascending order is:

x _k (i+(j ₂ -1)τ)≤x _k (i+(j ₂ -1)τ)≤…≤x _k (i+(j _m -1)τ)，

in the above formula, i+ (j) ₁ -1) τ is x _k (i) The result X obtained by phase space reconstruction _k (i) Cable of the smallest element in the seriesLeading, i+ (j) ₂ -1) τ is x _k (i) The result X obtained by phase space reconstruction _k (i) Index of the second small element, i+ (j) _m -1) τ is x _k (i) The result X obtained by phase space reconstruction _k (i) Index of the largest element, j ₁ ～j _m Respectively indexing the ordered signal sequences; the calculation of the probability of occurrence of the ordered signal sequence in step S202 includes:

s301, extracting a signal sequence from the ordered signal sequences:

S(g)＝[j ₁ ，j ₂ ，…，j _m ]，

in the above formula, S (g) is the extracted signal sequence, j ₁ ～j _m Respectively indexing the ordered signal sequences;

s302, calculating the probability of occurrence of the ordered signal sequence according to the following formula:

P _i ＝l/k，

in the above, P _i Is x _k (i) The probability of occurrence of the corresponding signal sequence, i is the frequency of occurrence of the extracted signal sequence S (g), and k is the number of decomposition layers.

5. The multi-resolution dynamic signal time domain and frequency spectrum feature analysis method according to claim 4, wherein in step S203, a function expression of the combined weighted permutation entropy is calculated according to the probability of occurrence of the ordered signal sequence, which is:

in the above, H _p (m) is the combined weighted permutation entropy, γ and θ are parameters of the combined weighted permutation entropy, P _i Is x _k (i) The probability of occurrence of the corresponding signal sequence, k being the number of decomposition layers; the function expression for normalizing the combined weighted permutation entropy to obtain the final permutation entropy is as follows:

in the above, P _E For the final permutation entropy, m-! Representing a factorization of m, which is the phase space embedding dimension.

6. The multi-resolution dynamic signal time domain and frequency spectrum feature analysis method according to claim 1, wherein in step S105, when multi-resolution generalized S transform is performed on K modal components IMFs for a plurality of frequency bands, a function expression of a gaussian window function is adopted as follows:

in the above formula, ω (t- τ, f) represents an improved gaussian window function, t is time, τ is time delay, f is frequency, σ (f) is window width, and there are:

in the above formula, μ is a window width adjustment factor corresponding to each frequency band, and p and q are constant parameters.

7. The method of claim 6, wherein the setting of the plurality of frequency bands in step S105 includes sequentially and continuously distributing five frequency bands, i.e., high frequency band, medium frequency band, low frequency band, and the window width adjustment factor corresponding to each frequency band has a functional expression:

in the above, mu _h For window width adjusting factor corresponding to high frequency band, mu _m Is the window width adjusting factor corresponding to the intermediate frequency band, mu _l Window width adjustment factor for low frequency band，μ _hm For the window width adjusting factor corresponding to the middle-high frequency band, mu _ml Is a window width adjusting factor corresponding to the middle-low frequency band.

8. The multi-resolution dynamic signal time domain and frequency spectrum feature analysis method according to claim 7, wherein the performing multi-resolution generalized S transformation on K modal components IMFs for a plurality of frequency bands in step S105 includes:

s401, carrying out Fourier transformation and dimension expansion on each modal component in the K modal components IMF to obtain a translation spectrum;

s402, multiplying the translation spectrum and the Gaussian window function and performing inverse Fourier transform to obtain a two-dimensional complex matrix formed by inverse Fourier transform corresponding to k modal components IMF;

s403, performing modulo on the two-dimensional complex matrix to obtain an S matrix, and outputting the obtained S matrix as multi-resolution signal time domain and frequency characteristic corresponding to the original signal, wherein a column vector in the S matrix is used for describing amplitude characteristic of a signal at a specific moment and time domain distribution of a line vector description signal at a specific frequency.

9. A multi-resolution dynamic signal time domain and spectral feature analysis apparatus comprising a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to perform the multi-resolution dynamic signal time domain and spectral feature analysis method of any one of claims 1 to 8.

10. A computer readable storage medium having a computer program stored therein, wherein the computer program is for being programmed or configured by a microprocessor to perform the multi-resolution dynamic signal time domain and spectral feature analysis method of any one of claims 1 to 8.