A bearing residual life prediction method of time-varying neural wiener process

Abstract

The application discloses a bearing residual life prediction method of time-varying neural Wiener process, comprising the following steps: 1) obtaining bearing original vibration signal data by using a sensor, pre-processing time domain signals into frequency domain signals, and extracting signal amplitude spectrum features; 2) establishing a Seq2seq neural network model based on a time-varying Wiener process; 3) obtaining a drift function and a diffusion function about time and vibration amplitude data according to a martingale estimation function, training the Seq2seq model, and obtaining a degradation trend function and a fluctuation function; 4) using the degradation trend function and the fluctuation function as a degradation trend function based on the Wiener process to calculate a probability density function of residual service life in a closed form. The application uses monitored vibration signals in a bearing degradation failure process, extracts amplitude spectra of the vibration signals, realizes bearing residual life prediction, improves the adaptability of parameter estimation of a degradation model based on the Wiener process, and realizes accurate RUL prediction.

Description

Technical Field

[0001] This invention relates to the field of bearing condition assessment, specifically a method for predicting bearing remaining life based on a time-varying neural Wiener process. Background Technology

[0002] As a key technology in predictive maintenance, Remaining Useful Life (RUL) prediction has received increasing attention in recent years. It can avoid unnecessary maintenance activities and improve the safety, reliability, and availability of systems. However, RUL prediction performance is highly dependent on the ability to construct a system degradation process model based on available resources, making RUL prediction extremely difficult. Therefore, constructing an accurate degradation process model to achieve accurate RUL prediction has become a challenging task. Degradation models and remaining useful life estimation methods based on the Wiener process still have many shortcomings. In practice, the system degradation process is subject to complex interactions between the internal degradation of materials and the external operating environment or load. Therefore, the problem of estimating unknown model parameters using Wiener process-based degradation models still lacks adaptive capabilities. Furthermore, in existing methods, the estimated RUL distribution depends only on current degradation observations, affecting the accuracy of model predictions. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the remaining life of bearings based on time-varying neural Wiener processes, comprising the following steps:

[0004] 1) Use sensors to acquire raw bearing vibration signal data, preprocess the raw bearing vibration signal data in the time domain, convert it to obtain a frequency domain signal, and extract the signal amplitude spectrum features;

[0005] 2) Establish a Seq2seq neural network model based on the time-varying Wiener process;

[0006] 3) Obtain the drift function μ and diffusion function σ for time and vibration amplitude data based on the martingale estimation function, train the Seq2seq neural network model, and obtain the degradation trend function f(μ) and fluctuation function f(σ);

[0007] 4) Based on the first hit time, the degradation trend function f(μ) and the fluctuation function f(σ) are used as the degradation trend function based on the Wiener process, and the probability density function of the remaining lifetime is calculated in closed form.

[0008] Furthermore, the Wiener process-based Seq2seq model includes an input layer, an encoding layer, a decoding layer, and an output layer;

[0009] The input layer of the Seq2seq model stores estimation functions for the drift coefficient and the diffusion coefficient;

[0010] The coding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the coding layer is the drift coefficient and the diffusion coefficient, and the output is the coding vector.

[0011] The decoding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the decoding layer is the encoding vector, and the output is the decoding vector.

[0012] The input to the output layer is the decoding vector, and the output is the degradation trend function f(μ) and the fluctuation function f(σ).

[0013] Furthermore, the steps for establishing the estimation functions for the drift coefficient and diffusion coefficient are as follows:

[0014] a) Establish the Wiener process function, i.e.:

[0015] dX t =μ(t,X) t )dt+σ(t,X t )dW t (1)

[0016] In the formula, W t Represents the parameters that satisfy standard Brownian motion; μ(t,X) t ) is the drift coefficient; σ(t,X) t ) is the diffusion coefficient; the solution X of the Wiener process function t This represents the vibration amplitude data at time t;

[0017] Solution X of Wiener process function t Satisfy the following formula:

[0018]

[0019] In the formula, X(0) represents the observations at discrete time points that determine the degradation process; X(0) represents the initial observations.

[0020] b) For the two-dimensional parameter θ=(μ,σ 2 Considering the estimators based on the martingale estimator, we obtain the optimal linear estimator (3) and the optimal quadratic martingale estimator (4) for θ, namely:

[0021]

[0022]

[0023] In the formula, the time difference Δ = t i -t i-1 G1(θ) is the optimal linear estimation function; G2(θ) is the optimal quadratic martingale estimation function; n is the number of discrete time points;

[0024] Among them, parameters parameter They are shown below:

[0025]

[0026] In the formula, F(·) and φ(·) both represent martingale estimation functions; E θ V represents the expected value of the martingale; V represents the variance; x i-1 Indicates the vibration amplitude;

[0027] c) Let the function G1(θ) = 0, and we get:

[0028]

[0029] In the formula, β represents the linear coefficient;

[0030] d) Order get:

[0031]

[0032] e) Establish the estimation function (8) for the drift coefficient and the estimation function (9) for the diffusion coefficient, i.e.:

[0033]

[0034]

[0035] In the formula, X iΔ This is vibration amplitude data; These are the estimation functions for the drift coefficient and the diffusion coefficient.

[0036] Furthermore, the encoding layer output C of the Seq2seq model f As shown below:

[0037]

[0038]

[0039]

[0040] In the formula, V a W, U are the parameters to be learned; h f-1 s f-1 This represents the vector representation of the previous encoding layer and the neuron state; The weights of the coding layer output vector at time f; the coding layer vector h f-1 =b(h) f-2 ,x f-1 b is the activation function; column vector K is the length; h is an intermediate parameter. i is the vector representation of the coding layer; F represents the time step.

[0041] Furthermore, the output y of the output layer m As shown below:

[0042] y m =g(y m-1 ,s m C f (13)

[0043] In the formula s m =f(s) m-1 ,y m-1 C f ); g and f are activation functions; y m-1 This is the output at time m-1.

[0044] Furthermore, the first hit time is the time when the bearing degradation process first reaches the fault threshold w.

[0045] Furthermore, the steps for calculating the probability density function of the remaining useful life include:

[0046] I) Establish the mathematical expression for the bearing life T, namely:

[0047] T=inf{t:X(t)>w∣X(0)<w} (14)

[0048] In the formula, w is the fault threshold;

[0049] II) Establish the probability density function f of the remaining bearing life T. T (t), that is:

[0050]

[0051] In the formula, σ B Characterizing the wave function f σ ;

[0052] Under the concept of FHT, we can obtain the PDF of lifetime T.

[0053] Wherein, parameter S B (t) is shown below:

[0054]

[0055] III) Update the solution X of the Wiener process function t ,get:

[0056] X(t)=X(t k )+(ym (t)-y m (t k ))+f σ W(tt k (17)

[0057] IV) Calculation time t k The remaining service life of the bearing is l k ,Right now:

[0058] l k =tt k (18)

[0059] In the formula, t is the time to first hit;

[0060] V) in t k The remaining service life of the bearing at that moment is equivalent to the first time it reaches the failure threshold during the degradation process. k =wX(t) k According to (15), calculate time t. k The probability density function f of the remaining service life of the bearing Lk (L k ),Right now:

[0061]

[0062] In the formula, y μ Indicates output; f μ This represents a degradation trend function.

[0063] The technical effect of this invention is undeniable. This invention utilizes the vibration signals monitored during the bearing degradation failure process, extracts the amplitude spectrum of the vibration signals, realizes the prediction of the remaining life of the bearing, improves the adaptability of the parameter estimation of the degradation model based on the Wiener process, and achieves accurate RUL prediction.

[0064] Based on the analysis of bearing vibration signals, this patent uses the Wiener process and the martingale estimation function method to derive the drift and diffusion functions with respect to time and observed degradation values. It then trains a Seq2seq sequence-to-sequence model, which is used as the degradation rate function and fluctuation degree function of a degradation model based on the time-varying Wiener process. Finally, using the concept of first-hit time, it derives the analytical expression of the probability density function of the RUL in a closed loop. This not only solves the problem of estimating unknown model parameters in existing methods but also makes the model specification of the stochastic degradation process continuous, dependent on complete degradation observations, thus improving the adaptive capability of the model parameters. Attached Figure Description

[0065] Figure 1 The overall technical process for bearing condition assessment;

[0066] Figure 2 This is a seq2seq model based on an attention mechanism. Detailed Implementation

[0067] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0068] Example 1:

[0069] See Figures 1 to 2 A method for predicting the remaining life of bearings based on time-varying neural Wiener processes includes the following steps:

[0070] 1) Use sensors to acquire raw bearing vibration signal data, preprocess the raw bearing vibration signal data in the time domain, convert it to obtain a frequency domain signal, and extract the signal amplitude spectrum features;

[0071] 2) Establish a Seq2seq neural network model based on the time-varying Wiener process;

[0072] 3) Obtain the drift function μ and diffusion function σ for time and vibration amplitude data based on the martingale estimation function, train the Seq2seq neural network model, and obtain the degradation trend function f(μ) and fluctuation function f(σ);

[0073] 4) Based on the first hit time, the degradation trend function f(μ) and the fluctuation function f(σ) are used as the degradation trend function based on the Wiener process, and the probability density function of the remaining lifetime is calculated in closed form.

[0074] The Wiener process-based Seq2seq model includes an input layer, an encoding layer, a decoding layer, and an output layer.

[0075] The input layer of the Seq2seq model stores estimation functions for the drift coefficient and the diffusion coefficient;

[0076] The coding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the coding layer is the drift coefficient and the diffusion coefficient, and the output is the coding vector.

[0077] The decoding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the decoding layer is the encoding vector, and the output is the decoding vector.

[0078] The input to the output layer is the decoding vector, and the output is the degradation trend function f(μ) and the fluctuation function f(σ).

[0079] The steps for establishing the estimation functions for the drift coefficient and diffusion coefficient are as follows:

[0080] a) Establish the Wiener process function, i.e.:

[0081] dX t =μ(t,X) t )dt+σ(t,X t )dW t (1)

[0082] In the formula, W t Represents the parameters that satisfy standard Brownian motion; μ(t,X) t ) is the drift coefficient; σ(t,X) t ) is the diffusion coefficient; the solution X of the Wiener process function t This represents the vibration amplitude data at time t;

[0083] Solution X of Wiener process function t Satisfy the following formula:

[0084]

[0085] In the formula, X(0) represents the observations at discrete time points that determine the degradation process; X(0) represents the initial observations.

[0086] b) For the two-dimensional parameter θ=(μ,σ 2 Considering the estimators based on the martingale estimator, we obtain the optimal linear estimator (3) and the optimal quadratic martingale estimator (4) for θ, namely:

[0087]

[0088]

[0089] In the formula, the time difference Δ = t i -t i-1 G1(θ) is the optimal linear estimation function; G2(θ) is the optimal quadratic martingale estimation function; n is the number of discrete time points;

[0090] Among them, parameters parameter They are shown below:

[0091]

[0092] In the formula, F(·) and φ(·) both represent martingale estimation functions; E θ V represents the expected value of the martingale; V represents the variance; x i-1 Indicates the vibration amplitude;

[0093] c) Let the function G1(θ) = 0, and we get:

[0094]

[0095] In the formula, β represents the linear coefficient;

[0096] d) Order get:

[0097]

[0098] e) Establish the estimation function (8) for the drift coefficient and the estimation function (9) for the diffusion coefficient, i.e.:

[0099]

[0100]

[0101] In the formula, X iΔ This is vibration amplitude data; These are the estimation functions for the drift coefficient and the diffusion coefficient.

[0102] The encoding layer output C of the Seq2seq model f As shown below:

[0103]

[0104]

[0105]

[0106] In the formula, V a W, U are the parameters to be learned; h f-1 s f-1 This represents the vector representation of the previous encoding layer and the neuron state; The weights of the coding layer output vector at time f; the coding layer vector h f-1 =b(h) f-2 ,x f-1 b is the activation function; column vector K is the length; h is an intermediate parameter. i is the vector representation of the coding layer; F represents the time step.

[0107] Output y of the output layer m As shown below:

[0108] y m =g(y m-1 ,s m C f (13)

[0109] In the formula s m =f(s) m-1 ,y m-1 C f ); g and f are activation functions; y m-1 This is the output at time m-1.

[0110] The first hit time is the time when the bearing degradation process first reaches the fault threshold w.

[0111] The steps for calculating the probability density function of the remaining useful life include:

[0112] I) Establish the mathematical expression for the bearing life T, namely:

[0113] T=inf{t:X(t)>w∣X(0)<w} (14)

[0114] In the formula, w is the fault threshold;

[0115] II) Establish the probability density function f of the remaining bearing life T. T (t), that is:

[0116]

[0117] In the formula, σ B Characterizing the wave function f σ ;

[0118] Under the concept of FHT, we can obtain the PDF of lifetime T.

[0119] Wherein, parameter S B (t) is shown below:

[0120]

[0121] III) Update the solution X of the Wiener process function t ,get:

[0122] X(t)=X(t k )+(y m (t)-y m (t k ))+f σ W(tt k (17)

[0123] IV) Calculation time t k The remaining service life of the bearing is l k ,Right now:

[0124] l k =tt k (18)

[0125] In the formula, t is the time to first hit;

[0126] V) in t k The remaining service life of the bearing at that moment is equivalent to the first time it reaches the failure threshold during the degradation process. k =wX(t) k According to (15), calculate time t. k The probability density function of the remaining service life of the bearing Right now:

[0127]

[0128] In the formula, y μ Indicates output; f μ This represents a degradation trend function.

[0129] Example 2:

[0130] A method for predicting bearing remaining life based on time-varying neural Wiener processes includes the following steps:

[0131] 1) Use sensors to acquire raw bearing vibration signal data, preprocess the raw bearing vibration signal data in the time domain, convert it to obtain a frequency domain signal, and extract the signal amplitude spectrum features;

[0132] 2) Establish a Seq2seq neural network model based on the time-varying Wiener process;

[0133] 3) Obtain the drift function μ and diffusion function σ for time and vibration amplitude data based on the martingale estimation function, train the Seq2seq neural network model, and obtain the degradation trend function f(μ) and fluctuation function f(σ);

[0134] 4) Based on the first hit time, the degradation trend function f(μ) and the fluctuation function f(σ) are used as the degradation trend function based on the Wiener process, and the probability density function of the remaining lifetime is calculated in closed form.

[0135] Example 3:

[0136] A bearing remaining life prediction method based on a time-varying neural Wiener process, the main contents of which are described in Example 2, wherein the Wiener process-based Seq2seq model includes an input layer, an encoding layer, a decoding layer and an output layer;

[0137] The input layer of the Seq2seq model stores estimation functions for the drift coefficient and the diffusion coefficient;

[0138] The coding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the coding layer is the drift coefficient and the diffusion coefficient, and the output is the coding vector.

[0139] The decoding layer stores several layers of RNNs, each layer including several LSTM neural units; the input of the decoding layer is the encoding vector, and the output is the decoding vector.

[0140] The input to the output layer is the decoding vector, and the output is the degradation trend function f(μ) and the fluctuation function f(σ).

[0141] Example 4:

[0142] A method for predicting the remaining life of bearings based on time-varying neural Wiener processes is described in Example 2. The steps for establishing the estimation functions of the drift coefficient and diffusion coefficient are as follows:

[0143] a) Establish the Wiener process function, i.e.:

[0144] dX t =μ(t,X) t )dt+σ(t,X t )dW t (1)

[0145] In the formula, W t Represents the parameters that satisfy standard Brownian motion; μ(t,X) t ) is the drift coefficient; σ(t,X) t ) is the diffusion coefficient; the solution X of the Wiener process function t This represents the vibration amplitude data at time t;

[0146] Solution X of Wiener process function t Satisfy the following formula:

[0147]

[0148] In the formula, X(0) represents the observations at discrete time points that determine the degradation process; X(0) represents the initial observations.

[0149] b) For the two-dimensional parameter θ=(μ,σ 2 Considering the estimators based on the martingale estimator, we obtain the optimal linear estimator (3) and the optimal quadratic martingale estimator (4) for θ, namely:

[0150]

[0151]

[0152] In the formula, the time difference Δ = t i -t i-1 G1(θ) is the optimal linear estimation function; G2(θ) is the optimal quadratic martingale estimation function; n is the number of discrete time points;

[0153] Among them, parameters parameter They are shown below:

[0154]

[0155] In the formula, F(·) and φ(·) both represent martingale estimation functions; E θ V represents the expected value of the martingale; V represents the variance; x i-1 Indicates the vibration amplitude;

[0156] c) Let the function G1(θ) = 0, and we get:

[0157]

[0158] In the formula, β represents the linear coefficient;

[0159] d) Order get:

[0160]

[0161] e) Establish the estimation function (8) for the drift coefficient and the estimation function (9) for the diffusion coefficient, i.e.:

[0162]

[0163]

[0164] In the formula, X iΔ This is vibration amplitude data; These are the estimation functions for the drift coefficient and the diffusion coefficient.

[0165] Example 5:

[0166] A method for predicting bearing remaining life based on time-varying neural Wiener processes, the main contents of which are described in Example 2, wherein the encoding layer output C of the Seq2seq model... f As shown below:

[0167]

[0168]

[0169]

[0170] In the formula, V a W, U are the parameters to be learned; h f-1 s f-1 This represents the vector representation of the previous encoding layer and the neuron state; The weights of the coding layer output vector at time f; the coding layer vector h f-1 =b(h) f-2 ,xf-1 b is the activation function; column vector K is the length; h is an intermediate parameter. i is the vector representation of the coding layer; F represents the time step.

[0171] Example 6:

[0172] A method for predicting bearing remaining life based on a time-varying neural Wiener process, the main contents of which are described in Example 2, wherein the output y of the output layer... m As shown below:

[0173] y m =g(y m-1 ,s m C f (13)

[0174] In the formula s m =f(s) m-1 ,y m-1 C f ); g and f are activation functions; y m-1 This is the output at time m-1.

[0175] Example 7:

[0176] A method for predicting the remaining life of a bearing based on a time-varying neural Wiener process is described in Example 2. The first hit time is the time when the bearing degradation process first reaches the fault threshold w.

[0177] Example 8:

[0178] A method for predicting the remaining life of bearings based on time-varying neural Wiener processes, the main contents of which are described in Example 2, wherein the steps for calculating the probability density function of the remaining life include:

[0179] I) Establish the mathematical expression for the bearing life T, namely:

[0180] T=inf{t:X(t)>w∣X(0)<w} (14)

[0181] In the formula, w is the fault threshold;

[0182] II) Establish the probability density function f of the remaining bearing life T. T (t), that is:

[0183]

[0184] In the formula, σ B Characterizing the wave function f σ ;

[0185] Under the concept of FHT, we can obtain the PDF of lifetime T.

[0186] Wherein, parameter S B (t) is shown below:

[0187]

[0188] III) Update the solution X of the Wiener process function t ,get:

[0189] X(t)=X(t k )+(y m (t)-y m (t k ))+f σ W(tt k (17)

[0190] IV) Calculation time t k The remaining service life of the bearing is l k ,Right now:

[0191] l k =tt k (18)

[0192] In the formula, t is the time to first hit;

[0193] V) in t k The remaining service life of the bearing at that moment is equivalent to the first time it reaches the failure threshold during the degradation process. k =wX(t) k According to (15), calculate time t. k The probability density function of the remaining service life of the bearing Right now:

[0194]

[0195] In the formula, y μ Indicates output; f μ This represents a degradation trend function.

[0196] Example 9:

[0197] A method for predicting bearing remaining life based on time-varying neural Wiener processes includes the following steps:

[0198] 1. Data preprocessing. 2. Construction of a Seq2seq model based on the time-varying Wiener process to complete the function mapping of degradation trend. 3. RUL prediction.

[0199] 1) Manually extracting vibration signal features can lead to information loss, while the frequency domain amplitude spectrum of the signal has a more stable probability distribution in Euclidean space. To reduce the size of the original signal data and avoid information loss, the vibration signal in the time domain is converted into a frequency domain signal X(t). This paper uses the vibration signal amplitude spectrum as the observation data.

[0200] 2) Parameter estimation based on martingale estimation function

[0201] For a Wiener process that satisfies the following equation:

[0202] dX t =μ(t,X) t )dt+σ(t,X t )dW t (1)

[0203] Among them W t Represents standard Brownian motion, μ(t,X) t ) is the drift coefficient, reflecting the degradation rate of the system, σ(t,X) t ) is the diffusion coefficient, which describes the degree of random fluctuation. Its solution is:

[0204]

[0205] The diffusion process occurs at n discrete time points: 0 < t1 < ... < t2. n In this article, Δ = t i -t i-1 For its two-dimensional parameters θ=(μ,σ 2 Considering the estimator based on the martingale estimator, we obtain the optimal linear estimator function for θ:

[0206]

[0207] in

[0208]

[0209] Let G1(θ) = 0, then...

[0210]

[0211] Therefore, the optimal linear estimation function can yield an estimate of the drift coefficient.

[0212]

[0213] The optimal quadratic martingale estimation function with respect to θ is obtained:

[0214]

[0215] And because We can then obtain:

[0216]

[0217]

[0218] After deriving the above formula, it is easy to see that both the drift coefficient and the diffusion coefficient are time-varying functions and not constant values. Therefore, it is necessary to consider the parameter estimation of time-varying states.

[0219] 3) Seq2seq model based on time-varying Wiener process.

[0220] The parameters θ = (μ, σ) related to time t are given above. 2 The input layer is the Wiener process, and the output layer is the degradation trend function f(μ) and the fluctuation function f(σ).

[0221] A time-varying Wiener model is constructed using an attention-based seq2seq framework, such as... Figure 2 :

[0222] Input layer: N vibration amplitude data after preprocessing, P is the selected data length. Substituting into equations (6) and (9), the input layer dimension is P×2.

[0223] Encoding layer: The data from the input layer is fed into the encoding layer. The encoding layer uses a two-layer RNN (Recurrent Neural Network) based on the attention mechanism, with 128 LSTM (long short-term memory) neural units in each layer.

[0224] Given an input sequence x = (x1, x2, ... x... f ,…x F ), where x f (f∈{1,2,…,F}) is a column vector of length K. The encoding formula for the input to the hidden layer is: h f =b(h) f-1 ,x f ), where b is the activation function of LSTM, h f Let f be the vector representation of the hidden layer. The RNN reads all sequences sequentially and then performs a weighted summation of the hidden layer vectors based on an attention mechanism to obtain vector C. f Vector C f The specific calculation method is as follows:

[0225]

[0226]

[0227]

[0228] Among them, V a W and U are the parameters to be learned, h f-1 s f-1 These are the hidden layer states and neuron states from the previous step. The weights of the encoder output vector at time f are given.

[0229] Decoding layer: The vector C output by the final encoder layer. f As input to the decoding layer, the decoding layer uses two RNN layers, with 128 LSTM neural units in each layer.

[0230] Output layer: The final output state of the decoding layer is used as the output layer.

[0231] y m =g(y m-1 ,s m C f )#(13)

[0232] Where s m =f(s) m-1 ,y m-1 C f ), g,f is an activation function of LSTM,y m-1 This is the output of the previous time step m-1. The final output is the output y of the previous time step m-1. m-1 At time m, the hidden state neuron s m And the vector C calculated by the attention mechanism f Three factors determine this. The output layer dimension is M×P, where M is the number of all data types at all measurement points, and P is the length of the selected data.

[0233] 4) RUL Prediction

[0234] Lifetime T can be determined by the concept of First Hit Time (FHT), where FHT represents the time when the degradation process first reaches the failure threshold w. Lifetime T is defined as the length of time from the initial time to the failure time, and its mathematical expression is as follows:

[0235] T=inf{t:X(t)>w∣X(0)<w} (14)

[0236] Under the concept of FHT, we can obtain the PDF of lifetime T.

[0237]

[0238]

[0239] Where w is a predefined fault threshold, and the function f(t)-f(t-1) shown in the equation can be used as ym The approximate value of the first derivative; σ B It can be replaced by the fluctuation function f of a trained Seq2seq model. σ Assume X(t) k ) is at time t k Given the observed degradation values, equation (2) can be written as:

[0240] X(t)=X(t k )+(y m (t)-y m (t k ))+f σ W(tt k (17)

[0241] Define t as the FHT of X(t); then, time t k RUL l at the location k It can be defined as:

[0242] l k =tt k (18)

[0243] Time t k The PDF of the RUL can be described by the following formula:

[0244]

Claims

1. A method for bearing residual life prediction of time-varying neural Wiener process, characterized in that, The method comprises the following steps: 1) obtaining bearing original vibration signal data by using a sensor, preprocessing the bearing original vibration signal data in time domain, converting to obtain frequency domain signal, and extracting signal amplitude spectrum characteristics; 2) establishing a Seq2seq neural network model based on time-varying Wiener process; 3) obtaining a drift function μ and a diffusion function σ about time and vibration amplitude data according to a martingale estimation function, training the Seq2seq neural network model, and obtaining a degradation trend function f(μ) and a fluctuation function f(σ); 4) taking the degradation trend function f(μ) and the fluctuation function f(σ) as a degradation trend function based on Wiener process, and calculating a probability density function of the remaining useful life in a closed form according to the first hitting time; The Seq2seq model based on Wiener process comprises an input layer, an encoding layer, a decoding layer and an output layer; The input layer of the Seq2seq model stores an estimation function of drift coefficients and diffusion coefficients; The encoding layer stores a plurality of layers of RNN, each layer comprising a plurality of LSTM neural units; the input of the encoding layer is the drift coefficients and the diffusion coefficients, and the output is an encoding vector; The decoding layer stores a plurality of layers of RNN, each layer comprising a plurality of LSTM neural units; the input of the decoding layer is the encoding vector, and the output is a decoding vector; The input of the output layer is the decoding vector, and the output is the degradation trend function f(μ) and the fluctuation function f(σ); The steps of establishing the estimation function of the drift coefficients and the diffusion coefficients are as follows: s1) establishing a Wiener process function, namely: dX t = μ(t, X t )dt + σ(t, X t )dW t (1) wherein W t denotes parameters satisfying the standard Brownian motion; μ(t, X t ) is the drift coefficient; σ(t, X t ) is the diffusion coefficient; Solution X of the Wiener process function t represents the vibration amplitude data at time t; The solution X of the Wiener process function t satisfies the following equation: wherein is the observation of the degradation process at discrete time points; X(0) is the initial observation; s2) For the two-dimensional parameter θ = (μ, σ 2 Considering the estimators based on the martingale estimating functions, we obtain the optimal linear estimating function (3) and the optimal quadratic martingale estimating function (4) for θ, i.e., where the time difference Δ = t i -t i-1 ; G1(θ) is the optimal linear estimation function; G2(θ) is the optimal quadratic martingale estimation function; n is the number of discrete time points; wherein the parameters parameters are as follows, respectively: In the formula, F(·), φ(·) represent martingale estimation functions; E θ represents the expectation of a martingale; V represents variance; x i-1 represents the vibration amplitude; s3) setting the function G1(θ)=0, and obtaining: In the formula, β represents a linear coefficient; s4) let resulting in: s5) establishing the estimation function (8) of the drift coefficients and the estimation function (9) of the diffusion coefficients, namely: In the formula, X iΔ is the amplitude of vibration data; is the estimated function of drift coefficient, the estimated function of diffusion coefficient; The steps of calculating the probability density function of the remaining useful life comprise: 4.1) establishing a mathematical expression of bearing life T, namely: T=inf{t:X(t)>w∣X(0)<w} (14) In the formula, w is a failure threshold; 4.2) Establishing the probability density function f of the bearing residual lifetime T T (t), i.e.: In the formula, σ B characterizing the wave function f σ ; wherein the parameter S B (t) is as follows: 4.3) Update the solution X of the Wiener process function t gives: X(t) = X(t k )+(y m (t)-y m (t k ))+f σ W(t-t k ) (17) 4.4) Calculate the time t k The remaining useful life of the bearing l k That is: l k = t - t k (18) In the formula, t is the first hitting time; 4.5) At the time t k the bearing residual useful life corresponds to the first time the failure threshold w k = w - X(t k ) is reached during the degradation process, the probability density function of the bearing residual useful life at the time t k is calculated according to (15) i.e.: where y μ represents the output; f μ represents the degradation trend function.

2. The bearing residual life prediction method of a time-varying Wiener process according to claim 1, characterized in that, The encoding layer output C of the Seq2seq model f As shown below: where V a , W, U are parameters to be learned; h f-1 , s f-1 is the vector representation of the previous encoding layer and the neuron state; is the weight of the encoding layer output vector at time f; the encoding layer vector h f-1 = b(h f-2 , x f-1 ); b is the activation function; the column vector K is the length; is the intermediate parameter; h i is the vector representation of the encoding layer; F represents the number of times.

3. The bearing residual life prediction method of time-varying Wiener process according to claim 1, characterized in that, Output of the output layer y m As shown below: y m = g(y m-1, s m ,C f ) (13) where s m = f(s m-1 ,y m-1 ,C f ); g, f are activation functions; y m-1 is the output at time m-1.

4. The method of claim 1, wherein, The first hitting time is the time when the bearing degradation process first reaches the failure threshold w.

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