A bearing life prediction method based on spectral characteristics and improved particle filtering

Abstract

The present invention discloses a life prediction method based on bearing spectrum characteristics and improved particle filtering. The method includes: performing equally spaced sliding window processing on the full-life time series signal of the bearing, and using the amplitude spectrum obtained from the signal in each window to form a row vector; obtaining a two-dimensional matrix of correlation coefficients; obtaining an average correlation coefficient curve, establishing a normalized root mean square bearing health index, and finding the accurate starting fault point in the normalized root mean square bearing health index; constructing an exponential spatial state model and predicting the particle prior distribution at time k; improving the particle filtering algorithm to obtain an updated particle distribution; when there is no more observation input, estimating the subsequent bearing health index trend and obtaining an accurate remaining service life value. The present invention not only improves the accuracy of identifying the moment of early initial failure of the bearing, but also improves the accuracy of the remaining service life prediction of the bearing, and overcomes the adverse effects of local fluctuation observations on the prediction performance in the standard particle filtering algorithm.

Claims

1. A life prediction method based on bearing spectrum characteristics and improved particle filtering, characterized in that: The following steps are involved: S1. Perform equal-interval sliding window processing on the bearing life time series signal, and use the amplitude spectrum obtained from the signal in each window to form a row vector D; The time domain signal Y of the entire life cycle of the bearing is collected, and the time domain signal Y is divided into T window signals using a sliding window with a window length of T1 and a step size of T1, denoted as Y = [Y(1), Y(2), …, Y(k), …, Y(T)], and the amplitude spectrum P of the signal Y(k) in each window is calculated. k , k=1,2,…,T, row vector D=[P1,P2,…,P k ,…,P T ]; S2, perform Pearson correlation analysis on the pairwise amplitude spectra of the row vector D to obtain a two-dimensional matrix M of correlation coefficients; In order to evaluate the correlation between any two amplitude spectra, the Pearson correlation coefficient is used to construct a two-dimensional correlation coefficient matrix M, namely: The expression for calculating the pairwise amplitude spectrum of the Pearson correlation coefficient is: Where s,t=1,2,…,T; ρ st Represents the amplitude spectrum P of the signal in the sth window s and the amplitude spectrum P of the signal in the tth window t The correlation coefficient of N is the total number of sampling points of the signal in each window, and P s,n represents the value of the nth point in the sth amplitude spectrum, Represents the average value of all points of the signal amplitude spectrum in the sth window. Similarly, P t,n represents the value of the nth point in the tth amplitude spectrum, Represents the average value of all points of the signal amplitude spectrum in the tth window; S3, according to the correlation coefficient two-dimensional matrix M, obtain the average correlation coefficient curve ACC, establish the normalized root mean square bearing health index, and calculate the average correlation coefficient curve ACC according to the ACC curve and the lower limit threshold β. - Finding the exact initial fault point FPT in the normalized root mean square bearing health index includes the following steps: S3.

1. After obtaining the two-dimensional correlation coefficient matrix M, the average correlation coefficient curve ACC, which includes the short-term high similarity and long-term low similarity information of the spectral characteristics, is used to represent the correlation between the signal in the first window and the signals in T windows. The average correlation coefficient curve ACC includes T values ​​and is defined as: d i =(ρ 1,1 +r 1,i +r i,1 +r i,i ) / 4,i=1,2,…,T (3) Among them, d i is the i-th value in the average correlation coefficient curve ACC; S3.2, take a positive integer ξ in the interval [30%T-10%T, 50%T-10%T] and take the first ξ points ACC of the T values ​​in the average correlation coefficient curve ACC. normal =[d1,d2,…,d ξ ] to calculate the 3σ threshold criterion and obtain the lower threshold β - , the lower threshold β - The calculation formula is: b - =μ-3σ (4) Where, μ=(d1+d2+…+d ξ ) / ξ and Represents the mean and variance of the previous ξ points, r represents the rth value within the previous ξ points; combined with the average correlation coefficient curve ACC and the lower limit threshold β - , find the first time it falls below the lower threshold β - The corresponding time is the starting fault point FPT; S4. Construct an exponential spatial state model and predict the particle prior distribution P(Θ k |y k-1 ), specifically including the following steps: S4.

1. Determine the exponential space state model; The exponential model is used to represent the bearing degradation model, and the expression is as follows: x k =a k exp(b k k),k∈[1,T] (5) Where a k and b k Represents the two unknown parameters of the exponential model at time k; in order to facilitate the use of the particle filter algorithm based on Bayesian theory, formula (6) is a recursive form of the spatial state model, that is: Among them, Θ k =[a k ,b k ] Τ is the parameter vector of the spatial state model at time k; y k is the system observation value at time k, i.e. HI index, x k =a k exp(b k k) is the system state value at time k, u k and v k Represents k moment a respectively k and b k The uncertainty process error is denoted as ω k =[u k ,υ k ] T ; χ k Characterizes the observation error at time k; the errors are respectively subject to and Normal distribution, σ v , σ q and σ r u k 、v k and χ k variance; S4.

2. Set global experience parameters; S4.

3. Predicting particle prior distribution; S5. Using the loss function and the adaptive weight factor to improve the particle filter algorithm, obtain an updated particle distribution; S6. When no more observation values ​​are input, the subsequent bearing health indicator trends are estimated and an accurate remaining service life value is obtained.

2. The life prediction method based on bearing spectrum characteristics and improved particle filtering according to claim 1 is characterized in that: In step S4.2, the time domain signal Y of the bearing's entire life cycle is converted into a root mean square index as a series of observations reflecting the overall degradation trend of the bearing, recorded as (y1, y2, ..., y k ,...,y T ): Where, X N,k is the corresponding amplitude of the Nth point of the signal Y(k) in the window; The observation values ​​are fitted by the least squares method to obtain the global empirical model parameter vector, which is recorded as Θ0 = [a0, b0] Τ , which also serves as the initialization model parameters a0 and b0 for k=0; setting u k 、v k and χ k The standard deviation σ v , σ q and σ r .

3. The life prediction method based on bearing spectrum characteristics and improved particle filtering according to claim 2 is characterized in that: In step S4.3, the particle prior distribution P(Θ k |y k-1 ); the number of particles in a group is N p Particles Describe the prior distribution of the particle, j = 1 ~ N p , N p is a positive integer in the interval [100,1000]; then the model parameter prediction value of the jth particle is obtained for: in, and are the model parameter values ​​stored by the jth particle at time k-1; and are the process error and observation error values ​​stored by the j-th particle at time k, respectively.

4. The life prediction method based on bearing spectrum characteristics and improved particle filtering according to any one of claim 3, characterized in that: Step S5 specifically includes the following steps: S5.

1. Constructing the loss function: the loss function at time k There are two parts, one of which includes the estimated value of the j-th particle state and system observation y k The other part includes the parameter vector of the jth particle and the global empirical parameter vector Θ0=[a0,b0] Τ Difference information: Where λ k ∈[0,1] is a measure of the global empirical model parameter vector Θ0=[a0,b0] Τ Term and system observation y k The weight coefficient of the item, Indicates Respectively and Find partial differentials; S5.

2. Constructing an adaptive weight factor: weight coefficient λ k The details are as follows: Weight coefficient λ k Will be based on the system observation value y at time k k and the global empirical model value x 0,k =a0exp(b0k) is adaptively changed; c and δ are constant factors; S5.

3. Gradient descent to correct particle distribution: The final particle parameters are updated as follows: in, and η are and The gradient formula and learning rate, and respectively right and Find partial differentials; S5.

4. Update the weight of the gradient correction particle set and normalize it: Get the system observation value y at time k k , update the weight of each predicted particle value The details are as follows: The weight of the jth particle at time k Normalize it: S5.5, Particle resampling: If the number of effective particles Then a random resampling method is needed to generate a new set of weights.

5. The life prediction method based on bearing spectrum characteristics and improved particle filtering according to claim 4 is characterized in that: In step S6, the state estimation value x at time k is calculated based on the weight and state value of each particle. k , as follows: When the bearing index condition estimate x k When the set failure threshold γ is exceeded for the first time, the corresponding time is recorded as T, and the remaining service life prediction value is defined as the time difference RUL between time T and the last input observation time h h , as follows: RUL h ={(T-h)|x k-1 <γ,x k >γ} (15)。

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