Method for predicting residual life of continuous casting mold vibration device

Abstract

The application provides a continuous casting crystallizer vibration device residual life prediction method, comprising the following steps: S1. obtaining the vibration deflection of the continuous casting crystallizer vibration device to be measured and taking the vibration deflection as degradation data; S2. constructing a continuous casting crystallizer vibration device degradation model; S3. determining a drift coefficient in the degradation model and a parameter vector of the drift coefficient based on a nonlinear function regression algorithm; S4. estimating the prior parameters of the continuous casting crystallizer vibration device degradation model based on an expectation maximization (EM) algorithm and determining optimal prior parameters θ; S5. constructing a residual life probability density model, substituting the prior parameters into the residual life probability density model to calculate residual life probability values, and taking the residual life corresponding to the maximum probability value as the final prediction value of the residual life of the continuous casting crystallizer vibration device; only the degradation data of the continuous casting crystallizer vibration device to be measured is needed to accurately predict the residual life of the vibration device.

Description

TECHNICAL FIELD

[0001] The present application relates to a life prediction method, in particular to a remaining life prediction method of a continuous casting crystallizer vibration device. BACKGROUND

[0002] The crystallizer is a copper pipe and auxiliary part that receives molten steel and solidifies into a casting blank according to a specified cross-sectional shape, and is an important part of the continuous casting machine. The function of the crystallizer vibration is to prevent the casting blank from sticking to the crystallizer copper wall during the solidification process, reduce the drawing resistance and improve the casting blank surface quality. The crystallizer is often vibrated by mechanical, hydraulic, electro-hydraulic and electric vibration devices. With the increase of working time, the crystallizer vibration quality will become worse due to device aging and other reasons, and the casting blank quality will be seriously affected.

[0003] If the vibration quality of the crystallizer vibration device can be predicted online, that is, the remaining service life of the crystallizer vibration device is predicted, the maintenance plan can be reasonably arranged to ensure the quality of the casting blank production.

[0004] For the continuous casting crystallizer vibration device, due to its own cost and high cost, it is difficult to obtain the degradation data of the same type of continuous casting crystallizer vibration device by using the existing algorithm (such as prediction based on big data), and it is also not suitable to use the traditional accelerated aging test to obtain the degradation data of the continuous casting crystallizer to predict the remaining life of the vibration device. Therefore, there is no effective technical means to accurately predict the remaining life of the continuous casting crystallizer vibration device in the prior art. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a continuous casting crystallizer vibration device remaining life prediction method, which can accurately predict the remaining life of the vibration device by only monitoring the degradation data of the continuous casting crystallizer vibration device to be tested, effectively ensure the accuracy of the final prediction, provide accurate data support for the formulation of a reasonable maintenance plan for the continuous casting crystallizer vibration device, and ensure the product quality of the final casting blank.

[0006] The present application provides a continuous casting crystallizer vibration device remaining life prediction method, comprising the following steps:

[0007] S1. Obtain the vibration deflection of the continuous casting crystallization vibration device to be tested and take the vibration deflection as the degradation data, wherein the degradation data sequence is represented as Y 0：n ={y0, y1,...yn}, t n is the nth monitoring time point of the degradation data, y n is the degradation data monitored at t n

[0008] S2. Construct a continuous casting crystallizer vibration device degradation model:​

[0009]

[0010] Y(t) = X(t) + ε(t)

[0011] wherein X(0) represents a degradation state of the vibrating device at time 0, is a drift coefficient reflecting a degradation trend, is a parameter vector, σ B is a diffusion coefficient reflecting a fluctuation degree of the degradation process, B(t) is a standard Brownian motion, Y(t) is the degradation data monitored at time t, and ε(t) is a measurement error;

[0012] and the degradation data sequence Y 0：n corresponding to the implicit degradation state sequence is represented as: X 0：n = {x0, x1,... x n};

[0013] S3. Determining the drift coefficient in the degradation model based on a nonlinear function regression algorithm and a parameter vector of the drift coefficient

[0014] S4. Estimating the prior parameters of the degradation model of the continuous casting mold vibrating device based on an expectation maximization (EM) algorithm and determining the optimal prior parameters θ, wherein the prior parameters θ are represented as:

[0015] μ0 and ∑0 are the expectation and variance of x0, respectively, and f is a shorthand for the expression of the drift coefficient, representing the variance of the measurement error;

[0016] S5. Constructing a residual life probability density model, substituting the prior parameters into the residual life probability density model to calculate the residual life probability value, and finding the residual life corresponding to the maximum probability value as the final prediction value of the residual life of the continuous casting mold vibrating device.

[0017] Further, step S3 specifically includes:

[0018] S31. Constructing a drift coefficient function model, including the following three types:

[0019] The first type: a parameter vector

[0020] The second type: a parameter vector

[0021] The third type: a parameter vector

[0022] S32. Given 0 = t0 < t1 < ... < t n Y is the independent variable. 0：n ={y0-y0, y1-y0, ... y n With `-y0}` as the dependent variable, a nonlinear regression algorithm is used to... Perform fitting to determine the parameter vector in each drift coefficient model.

[0023] S32. Calculate the correction determination coefficient.

[0024] in:

[0025] Where p is The number of parameters in Y′ 0：n The average value, For the regression function at t i The time interval can take values ​​i = 0, 1, 2, ..., n:

[0026] S32. Identify the correction determination coefficients in each drift coefficient function model. The drift coefficient parameter model corresponding to the maximum value is used as the final determined drift coefficient.

[0027] Furthermore, step S4 specifically includes:

[0028] E-step of the EM algorithm:

[0029] S41. Set the initial value of the prior parameter θ. (0) :

[0030] in, The value of y is 0;

[0031] S42. Construct the likelihood function with respect to the prior parameter θ:

[0032]

[0033] S42. Determine the prior parameter estimate θ for the j-th iteration in the EM algorithm. (j) Then, based on the prior parameter estimate θ (j) Calculate the latent variable X 0：n Conditional expectation Q(θ|θ) (j) ),in, The specific calculation formula is as follows:

[0034]

[0035] wherein: E() represents an expected value and E() is a short form of

[0036] M step of EM algorithm:

[0037] S43. based on the expectation Q (theta | theta 0：n ), find the prior parameter theta which makes the expectation Q (theta | theta (j) ) maximum as the optimal prior parameter; (j)

[0038] S44. repeat the E step and M step of EM algorithm until convergence, and the convergence condition is:

[0039]

[0040] Further, the optimal value of the prior parameter theta is determined by the following method:

[0041]

[0042] wherein, and Solved by fminsearch in Mat lab.

[0043] Further, the expected value E() in step S42 is processed by Kalman smoothing algorithm.

[0044] Further, in step S5, the probability density model of the remaining life is:

[0045] wherein, l n represents the remaining life of the vibration device from the monitoring time t n , is a random variable, omega is the failure threshold of the vibration device, and are the expectation and variance of the hidden variable x n respectively and are obtained by processing by Kalman filtering algorithm.

[0046] The beneficial effects of the present application: by the present application, only the degradation data of the vibration device of the continuous casting crystallizer to be measured is needed to accurately predict the remaining life of the vibration device, effectively ensure the accuracy of the final prediction, provide accurate data support for the formulation of the reasonable maintenance plan of the continuous casting crystallizer vibration device, and ensure the product quality of the final casting blank. BRIEF DESCRIPTION OF DRAWINGS

[0047] The present application will be further described below in combination with the drawings and examples:

[0048] Figure 1 is a flowchart of the present application. ​

[0049] Figure 2 Figure 1 is a diagram of the vibration performance degradation data of the crystallizer vibration device of the present application.

[0050] Figure 3 Figure 2 is a diagram of the regression results obtained by regression algorithm (including linear regression and nonlinear regression) for the degradation data in the present application.

[0051] Figure 4 Figure 3 is a diagram of the remaining life prediction results when the drift coefficient function form in the present application is .

[0052] Figure 5 Figure 4 is a diagram of the remaining life prediction results when the drift coefficient function form in the present application is .

[0053] Figure 6 Figure 5 is a diagram of the remaining life prediction results when the drift coefficient function form in the present application is . DETAILED DESCRIPTION

[0054] The present application is further described in detail below in conjunction with the accompanying drawings of the specification:

[0055] The present application provides a remaining life prediction method of a continuous casting crystallizer vibration device, comprising the following steps:

[0056] S1. Obtain the vibration runout of the continuous casting crystallizer vibration device to be measured and take the vibration runout as the degradation data, wherein the degradation data sequence is represented as Y(t) = {y0, y1,... yn}, t is the n th monitoring time point of the degradation data, y t is the degradation data monitored at time t; y0, y1, yn respectively represent the degradation data at the initial time, the 1st time and the n th time; wherein the vibration runout refers to the maximum displacement deviation perpendicular to the vibration direction. The vibration runout can be obtained by acquiring the crystallizer vibration original data through an acceleration sensor, a speed sensor, a displacement sensor, etc. and performing integral calculation, etc. 0：n n n n n n

[0057] S2. Construct a continuous casting crystallizer vibration device degradation model:

[0058]

[0059] Y(t) = X(t) + ε(t) (2)

[0060] wherein X(0) represents the degradation state of the vibration device at time 0, X(t) represents the degradation state of the vibration device at time t, ε(t) represents the random error of the vibration device at time t, and is the drift coefficient reflecting the degradation trend.​​​​​​ for The parameter vector, σ B ε(t) is the diffusion coefficient reflecting the degree of fluctuation in the degradation process, B(t) is the standard Brownian motion, Y(t) is the degradation data monitored at time t, and ε(t) is the measurement error; wherein, the degradation model is a degradation model based on the nonlinear Wiener process;

[0061] and degraded data sequence Y 0：n The corresponding implicit degenerate state sequence is represented as: X 0：n ={x0, x1, ... x n The degradation data of the vibration device is obtained through sensor monitoring, and therefore inevitably contains random measurement errors, failing to fully reflect the true degradation state (or implicit degradation state). The relationship between the monitored degradation data and the implicit degradation state can be described by the following model:

[0062] Y(t)=X(t)+ε(t) (3):

[0063] Y(t) represents the degradation data monitored at time t, X(t) represents the implicit degradation state at time t, and ε(t) is the measurement error. Generally, ε(t) can be considered to satisfy: independent and identically distributed at any time point t, and... ε(t) and B(t) are independent; equation (3) shows that for any degenerate data y i For each (i = 0, 1, ..., n), there exists a corresponding implicit degenerate state x. n , where x n As a random variable, therefore, the degraded data sequence Y 0：n The corresponding implicit degenerate state can be represented as X 0：n Because of the real data X 0：n Let X be a random variable. With each iteration of steps S3 and S4, the actual data X... 0：n It will get closer and closer to the true value;

[0064] S3. Determining the drift coefficient in the degradation model based on a nonlinear function regression algorithm. and the parameter vector of the drift coefficient

[0065] S4. Based on the expectation-maximization (EM) algorithm, the prior parameters of the degradation model of the continuous casting mold vibration device are estimated and the highest prior parameter θ is determined, where the prior parameter θ is expressed as:

[0066] μ0 and ∑0 are the expectation and variance of x0, respectively, and f is a simplified expression for the drift coefficient. The variance represents the measurement error;

[0067] S5. Constructing the remaining life probability density model, substituting the prior parameters into the remaining life probability density model to calculate the remaining life probability value, finding the corresponding remaining life when the probability value is maximum as the final prediction value of the remaining life of the continuous casting mold vibration device. Through the above method, only the degradation data of the continuous casting mold vibration device to be measured is needed to accurately predict the remaining life of the vibration device, effectively ensuring the accuracy of the final prediction, providing accurate data support for the formulation of a reasonable maintenance plan for the continuous casting mold vibration device, and ensuring the product quality of the final casting blank.

[0068] In this embodiment, when using the degradation model based on the Wiener process to predict the life, the selection of the model will greatly affect the accuracy of the life prediction, therefore, step S3 specifically includes:

[0069] S31. Constructing a drift coefficient function model, including the following three types:

[0070] The first type: Parameter vector

[0071] The second type: Parameter vector

[0072] The third type: Parameter vector a and b are the coefficients of the model;

[0073] Of course, in practice, the drift coefficient function model can be set to more types, that is, the model complexity is higher. Although the higher model complexity can improve the final accuracy, it will make the entire algorithm process too complex and there is overfitting, which will reduce the accuracy of the final result. Therefore, the above three models can ensure the accuracy of the final life prediction.

[0074] S32. Taking 0=t0<t1<…<t n as the independent variable, Y 0：n ={y0-y0, y1-y0,... y n -y0} as the dependent variable, and using a nonlinear regression algorithm to fit In this step, lsqcurvefit in matlab can be used to calculate to determine the parameter vector

[0075] S32. Calculate the correction determination coefficient

[0076] Where:

[0077] wherein p is the number of parameters in Y' is 0：n the average value of the value of the regression function at t i i = 0, 1, 2,..., n;

[0078] S32. Find the drift coefficient parameter model corresponding to the maximum correction coefficient of determination in each drift coefficient function model as the final drift coefficient parameter model. S33. Output the final drift coefficient parameter model. Through the above method, the speed of the remaining life prediction process can be improved, and the accuracy of the final result is guaranteed.

[0079] The regression results of the embodiments given in Figure 2 and Figure 3 using degradation data up to the 350th hour are easy to know The form of a should be abt b-1 , and the parameter vector is the corresponding regression calculation result:

[0080]

[0081] In this embodiment, step S4 specifically includes:

[0082] E step of EM algorithm:

[0083] S41. Set the initial value θ (0) of the prior parameter θ:

[0084] wherein the value of is y0, f and is determined in step S3, and the remaining parameters can be selected according to engineering experience;

[0085] S42. Construct the likelihood function of the prior parameter θ:

[0086]

[0087] S42. Determine the prior parameter estimation value θ (j) of the jth step iteration in the EM algorithm, and then calculate the conditional expectation Q(θ|θ (j) of the latent variable X 0：n based on the prior parameter estimation value θ (j) , wherein The specific calculation formula is:

[0088]

[0089] Where: E() represents the expected value and E() is The abbreviation; to ensure the accuracy of the final result, for the expected value E(x) t x t ), E(x) t x t-1 ), E(x) t (t = 1, ..., n) is estimated using the Kalman smoothing algorithm:

[0090] C1: Kalman forward recursion, or Kalman filtering:

[0091]

[0092] in, For x t Desired filter value For x t Expected forecast value For x t Filtered value of variance For x t The predicted value of variance, K t For the Kalman gain, the initial recursive value is:

[0093] C2: Kalman backward recursion, also known as Kalman smoothing:

[0094]

[0095] in, For x t Expected smoothing value, For x t The smoothed value of variance, J t As an intermediate variable, For x t With x t-1 Smoothed values ​​of the covariance; initial recursive values:

[0096] C3: E(x) is obtained based on Kalman smoothing results. t x t ), E(x) t x t-1 ), E(x) t (t = 1, ..., n)

[0097]

[0098] M-step of the EM algorithm:

[0099] S43. Based on the latent variable X 0：n Expected Q(θ|θ)(j) ), find the prior parameter θ that maximizes the expected Q(θ|θ (j) ) as the optimal prior parameter, i.e., the parameter θ (j+1) of the j+1th iteration.

[0100]

[0101] wherein, and are solved by fminsearch in Matlab, and other parameters are directly calculated by formula (11); wherein: the solving steps based on fminsearch are as follows:

[0102] D1: in formula (11), set to to obtain

[0103] D2: substitute back into Q(θ|θ (j) ), search for (j) that maximizes Q(θ|θ

[0104] D3: in formula (11), set to to obtain

[0105] D4:

[0106] S44. Repeat the E step and the M step of the EM algorithm until convergence, and the convergence condition is:

[0107]

[0108] In this embodiment, in step S5, the probability density model of the remaining life is:

[0109] wherein, l n represents the remaining life of the vibration device from the monitoring time t n , is a random variable, ω is the failure threshold of the vibration device, and are the expectation and variance of the hidden variable x n respectively and are obtained by processing through the Kalman filtering algorithm, by substituting the random variable l n into formula (13) through the above method, find the l n corresponding to the maximum value of formula (13) as the final predicted remaining life.

[0110] Still with Figure 2 and Figure 3 For example, the distance example given in the text:

[0111] in, Figure 4 yes The remaining life prediction results are correct. Figure 5 yes The remaining life prediction results at that time Figure 6 yes The remaining lifetime prediction results at that time. From Figures 4-6 It can be seen that the drift coefficient The choice of function form has a significant impact on the accuracy of remaining lifetime prediction. as well as The prediction accuracy of the results is generally good. And the results selected by S13... The overall accuracy of the remaining lifetime prediction is the best under these conditions, which fully demonstrates the effectiveness of the present invention.

[0112] Table 3 shows the results at the 350th hour. The preliminary calculation was performed using a nonlinear regression algorithm. Parameters and random selection The comparison shows that using the parameters obtained from regression as the initial values ​​for the EM algorithm to predict remaining lifetime significantly reduces the number of iterations and improves the computation speed.

[0113] Table 3

[0114]

[0115]

[0116] The results above show that the method proposed in this invention can reliably predict the remaining life of a device with only the degradation data of the vibration device to be predicted. At the same time, the drift coefficient function form selection and parameter calculation method based on nonlinear regression proposed in this invention can effectively improve the accuracy and calculation speed of the remaining life prediction.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the remaining life of a continuous casting mold vibration device, characterized by: The method comprises the following steps: S1. Obtain the vibration deviation of the continuous casting crystallization vibration device to be tested and take the vibration deviation as degradation data, wherein the degradation data sequence is represented as Y 0：n ={y0, y1,... y n}, t n is the nth monitoring time point of the degradation data, y n is the degradation data monitored at t n . S2. Constructing a degradation model of the continuous casting crystallizer vibration device: Y(t) = X(t) + ε(t) wherein X(0) represents the degradation state of the vibrating device at time 0, is a drift coefficient reflecting the degradation trend, is a parameter vector, σ B is a diffusion coefficient reflecting the fluctuation degree of the degradation process, B(t) is a standard Brownian motion, Y(t) is the monitored degradation data at time t, and ε(t) is a measurement error. and the degraded data sequence Y 0：n The corresponding implicit degraded state sequence is represented as: X 0：n = {x0, x1,... x n} S3. determining a drift coefficient in the degradation model based on a non-linear function regression algorithm and a parameter vector of the drift coefficient S4. Estimating the prior parameters of the degradation model of the continuous casting crystallizer vibration device based on an expectation maximization (EM) algorithm and determining optimal prior parameters θ, wherein the prior parameters θ are expressed as: μ0and Σ0are the mean and variance of x0, respectively, f is a shorthand for the drift coefficient expression, denotes the variance of the measurement error; S5. Constructing a residual life probability density model, substituting the prior parameters into the residual life probability density model to calculate residual life probability values, and finding a residual life corresponding to a maximum probability value as a final prediction value of the residual life of the continuous casting crystallizer vibration device; Step S3 specifically comprises: S31. Constructing a drift coefficient function model, including the following three kinds: Firstly: Parameter vector Secondly: Parameter vector Thirdly: Parameter vector S32. Take 0 = t0< t1<... < t n as independent variables, Y' = {y0- y0, y1- y0,... y 0：n - y0} as dependent variables, use nonlinear regression algorithm to fit n , determine the parameter vector in each drift coefficient model ​ S33. Calculate the correction decision coefficient wherein: where p is the number of parameters in Y′ 0：n is the average value of is the value of the regression function at t i i = 0, 1, 2, ···, n. S34. Find the drift coefficient parameter model that corresponds to the maximum value of the corrected determination coefficient in each drift coefficient function model the drift coefficient parameter model that corresponds to the maximum value of the corrected determination coefficient as the final drift coefficient Step S4 specifically comprises: E step of the EM algorithm: S41. Set the initial value of the prior parameter θ θ (0) : wherein, y0; S42. Constructing a likelihood function of the prior parameters θ: S43. Determine the prior parameter estimate value θ of the jth step iteration in the EM algorithm (j) Then, based on the prior parameter estimate value θ (j) Calculate the conditional expectation Q(θ|θ 0:n ) of the latent variable X (j) , wherein, The specific calculation formula is: wherein: E() denotes the expected value and E() is the abbreviation for M step of the EM algorithm: S44. Based on the latent variable X 0:n Expected Q(θ|θ) (j) Find the desired value Q(θ|θ). (j) The largest prior parameter θ is taken as the highest prior parameter; S45. Repeating the E step and the M step of the EM algorithm until convergence, and the convergence condition is: In step S5, the probability density model of the residual life is: wherein, l n represents the residual life of the vibrating device from the monitoring time t n , ω is the failure threshold of the vibrating device, and are the expectation and variance of the hidden variable x n , respectively, and are obtained by processing with the Kalman filtering algorithm.

2. The method of claim 1, wherein: The optimal value of the prior parameters θ is determined by the following method: wherein With Solved by fminsearch in Matlab.

3. The method of claim 1, wherein the method further comprises: determining a remaining life of the vibration device based on the comparison result. In step S42, the expected value E() is processed by using a Kalman smoothing algorithm.

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