Vibration data prediction method based on time sequence model parameters
Through the ARHMM model, the bearing vibration signals in the rotating mechanical system are randomly described and predicted, which solves the problem that the complex characteristics of the bearing vibration signals cannot be effectively portrayed in the prior art, and achieves more accurate fault identification and equipment maintenance support.
Patent Information
- Application Number
- CN202510444125.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-10
- Publication Date
- 2025-07-11
AI Technical Summary
The existing classic dynamic modeling methods and mechanism-based signal models have shortcomings in describing the randomness of bearing vibration signals in rotating mechanical systems, and cannot fully characterize complex characteristics, resulting in insufficient recognition of early signs of failure.
The autoregressive hidden Markov model (ARHMM) based on timing model parameters is used to establish a random model through short-time Fourier transform and autoregressive hidden Markov model to capture the cyclic stationary mode in the vibration signal and make accurate predictions.
It improves the ability to identify early signs of failure, provides more scientific equipment maintenance and reliability analysis support, describes and quantifies the randomness in the data through probabilistic statistics, and improves prediction accuracy.
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Figure CN120296358A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of rotating equipment status monitoring and intelligent operation and maintenance, and particularly relates to a vibration data prediction method based on time series model parameters. Background Art
[0002] As key components, rolling bearings are widely used in various rotating machinery systems, and at the same time they are also components prone to failure. Therefore, in order to avoid economic and time losses caused by bearing failures, analyzing bearing vibration signals to ensure their normal operation is an important research topic. In an industrial environment, bearing vibration signals are usually complex, and modeling such cyclostationary signals and determining transient impact patterns during rotation is a hot research direction. Classical dynamic modeling methods or mechanism-based signal models usually attempt to reveal the essential laws of vibration signals in order to better achieve effective analysis of vibration signals. However, most of these methods are based on deterministic models, and thus they have deficiencies in describing the inevitable randomness in vibration signals and cannot fully characterize the complex characteristics of actual signals. Therefore, when dealing with bearing vibration signals, introducing statistical or stochastic models that can handle signal randomness has become an important research trend. Based on this, the present invention proposes a vibration data prediction method based on time series model parameters. Summary of the Invention
[0003] The present invention provides a vibration data prediction method based on time series model parameters, which can describe the randomness in vibration signals through a time series stochastic model, capture the cyclostationary patterns in vibration signals, and perform effective randomness description and accurate prediction on complex time-domain vibration signals.
[0004] According to one aspect of the present disclosure, there is provided a data prediction method based on time series model parameters, the method comprising: Collecting vibration signals of a target bearing and performing a time-frequency spectrum on the collected vibration signals; Establishing a stochastic model based on the time-frequency spectrum of the signal; Estimating the autoregressive parameter matrix in the model; Predicting a new time-frequency spectrum and its time-domain signal through the model to obtain a predicted time-domain signal.
[0005] In a possible implementation manner, the collecting vibration signals of a target bearing and performing a time-frequency spectrum on the collected vibration signals includes: 1-1: Collecting vibration signals of a target bearing y t , t = 1, 2, 3,..., T, where T is the number of time points of a single signal sample, and the sampling frequency is ; 1-2: Select a window function ω(t) and perform a short-time Fourier transform (STFT) on the collected vibration signal y t The result obtained is a time-frequency matrix Y(n, f), where each column represents the spectrum within a window, and each column represents how a specific frequency changes over time. The short-time Fourier transform is expressed as Equation (1): (1) where Y(n, f) is the complex amplitude at time n and frequency f, and n = 1, 2, 3, …, N n ; f = 1, 2, 3, …, N f ; 1-3: According to the central limit theorem, it is known that the STFT coefficients converge in distribution to a Gaussian distribution of complex values. After centering processing, it can be further simplified to a circularly symmetric Gaussian distribution, as shown in Equation (2) below: (2) Centering processing means subtracting the mean value from Y n ; where represents the covariance matrix of the distribution, and in the formula represents the conjugate transpose.
[0006] In a possible implementation, a stochastic model is established based on the time-frequency spectrum of the signal, including: 2-1: Take the sequence Y n as the observation sequence of the stochastic model, where z n represents the hidden state, and n = 1, 2, 3, …, N n , and model the observed value Y n as a linear combination of the previous observed values ,..., . The mathematical expression of Y n is as shown in Equation (3) below: (3) where represents the autoregressive coefficient of the model, i = 1, 2, 3, …, M, and any coefficient is a diagonal matrix; 2-2: The above linear combination relationship is written in the form of a matrix expression as (4) where is a column vector , is a The autoregressive coefficient matrix, where each coefficient is affected by the hidden state Z n ; 2-3: Different from the hidden Markov model, the emission probability p(Y n ) of this model is not only affected by the hidden state , but also affected by the previous M-order ,..., . The calculation formula (5) of p(Y n ) of this model is as follows: (5) According to 1-3, since Y n follows a circularly symmetric Gaussian distribution, p(e n ) also follows a circularly symmetric Gaussian distribution and is only affected by the covariance matrix of Yn under the current state Z n ; 2-4: The joint probability distribution of the stochastic model is as follows: (6).
[0007] In a possible implementation, estimating the autoregressive parameter matrix in the model includes: 3-1: Using the forward-backward recursion formula to calculate the maximum likelihood value of the joint probability of the model, and calculating the forward probability α n (j) and the backward probability β n (j). The formulas are as follows: (7) (8) 3-2: Using α n (j) and β n (j) calculated in 3-1 to calculate the posterior probability n = i of the state Z in the time window n. The formula is as follows: (9) 3-3: Calculating the autoregressive coefficient matrix Φ in the model under the time window n . The calculation formula is as follows: (10) where represents taking the real part of the complex number; 3-4: Based on the autoregressive coefficient matrix Φ, calculating the corresponding error coefficient e n . The calculation formula is as follows: (11).
[0008] In a possible implementation, a predicted time-domain signal is obtained by predicting a new time-frequency spectrum and its time-domain signal through a model, including: 4-1: Based on the autoregressive coefficient matrix Φ and the error coefficient e n , a new time-frequency coefficient, Y, is obtained n+1 The calculation formula is as follows: (12) And so on, to obtain the sequence ; 4-2: The time-domain signal is obtained by performing an inverse short-time Fourier transform on the new sequence in step 4-1 y ( t ).
[0009] Compared with the prior art, the beneficial effects of the present invention are: The embodiments of the present disclosure propose a statistical stochastic model based on vibration signals. This method describes and quantifies the randomness in data through probability statistics. This model can not only effectively capture the complex random features in vibration signals, but also use these features to accurately predict the trends of data. At the same time, this method can identify and analyze the cyclostationary patterns in signals, thereby improving the ability to identify early signs of faults and providing more scientific data support for equipment maintenance and reliability analysis. The present invention uses the short-time Fourier transform (STFT) and the autoregressive hidden Markov model (ARHMM) to mathematically characterize the time-series random behavior contained in vibration signals. Through this model, the regularity of transient states can be extracted using the time-series parameters in the model for subsequent management. BRIEF DESCRIPTION OF THE DRAWINGS
[0010] Figure 1 Flowchart of data prediction based on the ARHMM random model.
[0011] Figure 2 Schematic diagram of the second-order autoregressive hidden Markov model ARHMM.
[0012] Figure 3 Effect diagram of verifying ARHMM signal prediction and analysis in Case 1.
[0013] Figure 4 Effect diagram of verifying ARHMM signal prediction and analysis in Case 2. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0014] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the drawings denote elements having the same or similar functions. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.
[0015] As used herein, the term "exemplary" means "serving as an example, instance, or illustration". Any embodiment described herein as "exemplary" is not necessarily to be construed as superior or better than other embodiments.
[0016] In addition, for a better illustration of the present disclosure, numerous specific details are given in the following detailed description. Those skilled in the art should understand that the present disclosure can be implemented without some of these specific details. In some instances, methods, means, elements, and circuits well known to those skilled in the art are not described in detail so as to highlight the gist of the present disclosure.
[0017] The present invention uses a stochastic model ARHMM to mathematically characterize the stochastic patterns in cyclostationary signals, and then uses the model parameters to predict new data. Figure 1 The specific implementation steps of the invention are shown. Figure 2 The schematic diagram of the second-order ARHMM model is shown, and each observation sequence is affected not only by the current hidden state but also by the previous two observations, which characterizes the strong correlation of adjacent windows in the time-frequency spectrum. Figure 3 and Figure 4 The effect comparison diagram with the linear fitting method is shown.
[0018] Perform a time-frequency spectrum on the collected signal. In this embodiment, the short-time Fourier transform (STFT) is used for illustration, and other video transforms are also applicable. The calculation formula is shown in Step 1. The window width and window shift R of STFT in the method need to be specifically selected according to the rotational speed sampling frequency of the vibration signal. In this embodiment, N w = 128, R = 8. After the short-time Fourier transform, the coefficients Y n , n = 1, 2, 3,..., N f are obtained for ARHMM modeling.
[0019] The model selects the order M = 8, that is, the current time-frequency coefficient Y n is a linear combination of Y n-1 to Y n-8 .
[0020] Through the forward-backward iteration algorithm, the state posterior probability sequence in the model is obtained. The specific formula is shown in Eq. 9. Using the posterior probability , the autoregressive coefficient matrix Φ and the error coefficient e n in the model are calculated, as shown in Equations (10) and (11).
[0021] Based on the model parameters, new time-frequency coefficients , as shown in Equation (12). By performing the inverse short-time Fourier transform on the newly fitted time-frequency spectrum, the predicted time-domain signal is obtained. The comparison effect with the classical linear regression method is shown in Figure 3 and Figure 4 .
[0022] It can be seen from the case verification that the autoregressive hidden Markov model (ARHMM) shows significant advantages over the classical linear regression method in describing the randomness of cyclostationary signals. ARHMM can not only capture the random fluctuations of the signal, but also reveal the potential structure and pattern of the time-series data through the probability characteristics of state transitions. Specifically, in the modeling process of ARHMM, not only the strong correlation between short-time Fourier transform windows is fully considered, so as to obtain a more accurate signal representation in the local time domain, but also the dynamic change process of the signal is predicted through the transfer and distribution law of hidden states. Based on the parameters analyzed by this model, a reliable prediction basis can be provided for complex time-series signals, making signal analysis no longer rely solely on the simple regression of past data, but introducing a reasonable estimate of the possibility of future states. This discovery can effectively improve the understanding and prediction accuracy of the random components in periodic signals, providing strong support for further optimizing signal processing methods.
[0023] According to one aspect of the present disclosure, a data prediction method based on time-series model parameters is provided, and the method includes: S01, collecting the vibration signal of the target bearing and performing a time-frequency spectrum on the collected vibration signal; S02, establishing a random model based on the time-frequency spectrum of the signal; S03, estimating the autoregressive parameter matrix in the model; S04, predicting a new time-frequency spectrum and its time-domain signal through the model to obtain the predicted time-domain signal.
[0024] In a possible implementation manner, the collecting the vibration signal of the target bearing and performing a time-frequency spectrum on the collected vibration signal includes: 1-1: Collecting the vibration signal of the target bearing y t， t = 1, 2, 3,..., T, where T is the number of time points of a single signal sample, and the sampling frequency is ; 1-2: Selecting a window function ω(t) and performing the short-time Fourier transform STFT on the collected vibration signal y t to obtain a result which is a time-frequency matrix Y(n, f), where each column represents the spectrum within a window, and each column represents how a specific frequency changes with time. The short-time Fourier transform is expressed as Equation (1): (1) Where Y(n, f) is the complex amplitude at time n and frequency f, where n = 1, 2, 3, …, N n ; f = 1, 2, 3, …, N f ; 1 - 3: According to the central limit theorem, it is known that the STFT coefficients converge in distribution to a Gaussian distribution of complex values. After centering, it can be further simplified to a circularly symmetric Gaussian distribution, as shown in Equation (2) below: (2) Centering means subtracting the mean of Y n ; where represents the covariance matrix of the distribution, and in the formula represents the conjugate transpose.
[0025] In a possible implementation, a stochastic model is established based on the time - frequency spectrum of the signal, including: 2 - 1: Taking the sequence Y n as the observation sequence of the stochastic model ARHMM, where z n represents the hidden state, n = 1, 2, 3, …, N n , in the STFT algorithm of step one, there is a high overlap between adjacent windows, which results in a strong correlation between each FFT coefficient. Therefore, we model the observed value Y n as a linear combination of the previous observed values ,..., , and the mathematical expression of Y n is as shown in Equation (3) below: (3) Where represents the autoregressive coefficient of the model, i = 1, 2, 3, …, M, and any coefficient is a diagonal matrix; The ARHMM autoregressive hidden Markov model is a hybrid model that combines the autoregressive model (AR) and the hidden Markov model (HMM), mainly used to process time - series data and can handle hidden states and observed data in the data.
[0026] 2 - 2: The above linear combination relationship is written in the form of a matrix expression, (4) Where is a column vector , is a The autoregressive coefficient matrix, where each coefficient is affected by the hidden state Z n ; 2-3: Different from the hidden Markov model, the emission probability p(Y n ) of this model is not only affected by the hidden state , but also affected by the previous M-order ,..., . The calculation formula (5) of p(Y n ) of this model is as follows: (5) According to 1-3, since Y n follows a circularly symmetric Gaussian distribution, p(e n ) also follows a circularly symmetric Gaussian distribution and is only affected by the covariance matrix of Yn under the current state Z n ; 2-4: The joint probability distribution of the stochastic model is as follows: (6).
[0027] In a possible implementation, estimating the autoregressive parameter matrix in the model includes: analyzing the parameters in the model through corresponding algorithms, including the following sub-steps: 3-1: Using the forward-backward recursion formula to calculate the maximum likelihood value of the joint probability of the model, calculating the forward probability α n (j) and the backward probability β n (j), and the formulas are as follows: (7) (8) 3-2: Using α n (j) and β n (j) calculated in 3-1 to calculate the posterior probability n = i of the state Z in the time window n, and the formula is as follows: (9) 3-3: Calculating the autoregressive coefficient matrix Φ in the model under the time window n , and the calculation formula is as follows: (10) where represents taking the real part of the complex number; 3-4: Based on the autoregressive coefficient matrix Φ, calculating the corresponding error coefficient e n , and the calculation formula is as follows: (11).
[0028] In a possible implementation, a predicted time-domain signal is obtained by predicting a new time-frequency spectrum and its time-domain signal through a model, including: 4-1: Based on the autoregressive coefficient matrix Φ and the error coefficient e n , a new time-frequency coefficient, Y, is obtained n+1 The calculation formula is as follows: (12) By analogy, a sequence ; 4-2: The time-domain signal is obtained by performing an inverse short-time Fourier transform on the new sequence in step 4-1 y ( t ).
[0029] The embodiments of the present disclosure have been described above. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art in the technical field without departing from the scope and spirit of the described embodiments. The selection of the terms used herein is intended to best explain the principles of the embodiments, practical applications, or improvements to the technology in the market, or to enable other ordinary skill in the art in the technical field to understand the disclosed embodiments.
Claims
1. A data prediction method based on the parameters of a time series model, characterized in that, The method includes: Collect the vibration signal of the target bearing and perform a time-frequency spectrum on the collected vibration signal; Establish a stochastic model based on the time-frequency spectrum of the signal; Estimate the autoregressive parameter matrix in the model; Predict a new time-frequency spectrum and its time-domain signal through the model to obtain the predicted time-domain signal.
2. The data prediction method based on the time series model parameters according to claim 1, wherein The step of collecting the vibration signal of the target bearing and performing a time-frequency spectrum on the collected vibration signal includes: 1-1: Collect the vibration signal of the target bearing y t， t = 1, 2, 3,..., T, where T is the number of time points of a single signal sample, and the sampling frequency is ; 1-2: Select a window function ω(t) and perform a short-time Fourier transform (STFT) on the collected vibration signal y t The result obtained is a time-frequency matrix Y(n, f), where each column represents the spectrum within a window, and each row represents how a specific frequency changes over time. The short-time Fourier transform is expressed as Equation (1): （1） where Y(n, f) is the complex amplitude at time n and frequency f, and n = 1, 2, 3, …, N n ; f = 1, 2, 3, …, N f ; 1-3: According to the central limit theorem, it is known that the STFT coefficients converge in distribution to a Gaussian distribution of complex values. After centering, it can be further simplified to a circularly symmetric Gaussian distribution, as shown in Equation (2) below: (2) Decentralized processing representation Y n Subtract its mean value; where Represents the covariance matrix of the distribution, where in the formula Represents the conjugate transpose.
3. A data prediction method based on the parameters of a time series model according to claim 1, characterized in that, The step of establishing a stochastic model based on the time-frequency spectrum of the signal includes: 2-1: Take sequence Y n as the observed sequence of the random model, where z n represents the hidden state, n = 1, 2, 3, …, N n , and model the observed value Y n as a linear combination of the previous observed values ,..., . The mathematical expression of Y n is as shown in Equation (3) below: （3） Among them, represents the autoregressive coefficient of the model, i = 1, 2, 3, …, M, and any one of the coefficients is a diagonal matrix; 2-2: The above linear combination relationship is written in the form of a matrix expression, （4） Among them, is a column vector of , is an autoregressive coefficient matrix, and each coefficient is affected by the hidden state Z n . 2-3: Different from the Hidden Markov Model, the emission probability p(Y n ) is not only affected by the hidden state , but also affected by the previous M-order ,..., . The calculation formula (5) of p(Y n ) of this model is as follows: （5） As can be seen from 1 - 3, since Y n obeys a circularly symmetric Gaussian distribution, p(e n ) also obeys a circularly symmetric Gaussian distribution and is only affected by the covariance matrix of Yn in the current state Z n ; 2-4: The joint probability distribution of the stochastic model is as follows: （6）。 4. A data prediction method based on the parameters of a time series model according to claim 1, characterized in that, The step of estimating the autoregressive parameter matrix in the model includes: 3-1: Calculate the maximum likelihood value of the model joint probability using the forward-backward recursion formula, and calculate the forward probability α n (j) and the backward probability β n (j), the formula is as follows: （7） （8） 3-2: Using α calculated in 3-1 n (j) and β n (j), calculate the posterior probability that the time window n is in state Z n = i as follows: The formula is as follows: （9） 3-3: Calculate the autoregressive coefficient matrix Φ in the model within the time window n as follows. The calculation formula is as follows: （10） wherein represents taking the real part of a complex number; 3-4: Calculate the corresponding error coefficient e based on the autoregressive coefficient matrix Φ n , and the calculation formula is as follows: （11） 。 5. A data prediction method based on the parameters of a time series model according to claim 1, characterized in that The step of predicting a new time-frequency spectrum and its time-domain signal through the model to obtain the predicted time-domain signal includes: 4-1: Based on the autoregressive coefficient matrix Φ and the error coefficient e n , a new time-frequency coefficient, Y, is obtained n+1 The calculation formula is as follows: （12） By analogy, the sequence ; 4-2: Obtain the time-domain signal by performing the inverse short-time Fourier transform on the new sequence in step 4-1 y ( t )。