Blast furnace system remaining life prediction method based on self-adaptive calibration model

Abstract

The invention belongs to the technical field of blast furnace system prediction and health management, and particularly discloses a blast furnace system residual life prediction method based on an adaptive calibration model. The method comprises the following steps: firstly, establishing an initial degradation model by utilizing partial observable blast furnace wall temperature data; estimating hyper-parameters in the degradation model based on maximum likelihood estimation, and designing a trigger mechanism based on a dynamic threshold to judge whether to perform adaptive calibration on parameters or structures of the degradation model; when the model is not triggered, updating the model parameters by adopting a Kalman filter; when the triggering condition is met, the model structure is calibrated based on the prediction error, parameters of the prediction error model are identified through a strong tracking filter and an expectation maximization algorithm, and the optimal structure of the prediction error model is determined through an akaike information criterion. According to the method, the parameters and the structure of the degradation model can be adaptively calibrated based on online data, the prediction precision of the residual life of the blast furnace system can be improved, and the online adaptability is high.

Description

Technical Field

[0001] The invention belongs to the technical field of blast furnace system prediction and health management, and in particular relates to a method for predicting the remaining life of a blast furnace system based on an adaptive calibration model. Background Art

[0002] As the core equipment of steel production, the stable operation of blast furnace is not only related to the continuity of production, but also directly affects the quality and economic benefits of products. However, due to the long-term high temperature, high pressure and complex chemical reaction environment of blast furnace, it is very easy to be damaged and fail, resulting in unplanned shutdown and even major safety accidents. In recent years, Prognostics Health Management (PHM) technology has attracted widespread attention from researchers and engineers as an effective preventive measure. As one of the core issues of PHM, Remaining Useful Life (RUL) prediction has been widely used in various industrial equipment and products to prevent unexpected failures, reduce maintenance costs, and ensure the safe and stable operation of the system.

[0003] However, traditional RUL prediction techniques usually rely on assumptions or simplifications of degradation models, which makes it difficult to fully capture the complex and dynamic degradation process of blast furnaces. For example, the blast furnace wall shows a relatively slow degradation trend in the early stages. As the blast furnace smelting process proceeds, iron ore melts at high temperatures to produce slag and molten iron. These molten materials corrode the surface of the furnace wall, forming a bonding layer, which in turn affects the thermal conductivity and thermal resistance of the furnace wall. However, with the scouring effect of molten iron, the bonding layer gradually peels off, resulting in changes in the degradation rate of the furnace wall. This change may lead to premature maintenance, failure or performance degradation of the equipment, and even cause serious safety problems. In addition, due to the differences in the installation positions of thermocouples on the blast furnace wall and changes in operating conditions, its degradation process gradually deviates from the actual situation, which may cause the assumptions of the degradation model to fail and the prediction error to increase over time. If the degradation model is not calibrated in time, the accuracy of RUL prediction may be greatly reduced, which will have an adverse impact on production, maintenance and safety. Summary of the invention

[0004] The purpose of the present invention is to propose a method for predicting the remaining useful life of a blast furnace system based on an adaptive calibration model. The method adaptively adjusts the relevant parameters and structure of the degradation model based on the temperature data of the blast furnace system, thereby achieving a potential enhancement in the matching degree between the model and the monitoring data, so as to ultimately improve the accuracy of RUL prediction.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme:

[0006] The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model comprises the following steps:

[0007] Step 1. Obtain temperature data collected by thermocouples at different locations of the blast furnace system, and construct training sets and test sets;

[0008] Step 2. construct an initial degradation model of the blast furnace wall based on the acquired temperature data of the blast furnace system;

[0009] The trend of temperature change is characterized by the drift term, and the uncertainty of temperature change and environment is described by the diffusion term. In addition, the degradation model parameters are identified based on the maximum likelihood estimation (MLE) method according to the data of the training set.

[0010] Step 3. When the test set is supplemented with new measurement data, prediction is performed based on the current degradation model and the predicted value is obtained. The predicted value is then compared with the measurement data to obtain the prediction error of the model.

[0011] Step 4. Design a model calibration trigger mechanism based on a dynamic threshold according to the value of the model prediction error to determine the calibration form of the degradation model, that is, to adaptively calibrate the parameters or structure of the degradation model;

[0012] Step 5. When the mechanism is not triggered, the Kalman filter KF is used to update the parameters of the degradation model and return to step 3 until the prediction time t k ;

[0013] Step 6. When the mechanism is triggered, a prediction error model is constructed based on the value of the prediction error in step 3, and the structure of the degradation model is calibrated to compensate for the impact of changes in operating conditions or degradation mechanisms during blast furnace operation;

[0014] Step 7. Identify the parameters of the prediction error model through the strong tracking filter STF and the expectation maximization algorithm EM, and determine the optimal model structure through the Akaike information criterion AIC, and return to step 3 until the prediction time t k ;

[0015] Step 8. At the prediction time t k , blast furnace RUL prediction is performed based on the adaptively calibrated degradation model.

[0016] The present invention has the following advantages:

[0017] As described above, the present invention relates to a method for predicting the remaining life of a blast furnace system based on an adaptive calibration model. The method aims at the problem that the degradation model does not match the actual degradation process of the blast furnace system. First, the initial degradation model is established using partially observable blast furnace wall temperature data, and the model hyperparameters are estimated by the maximum likelihood estimation method. Subsequently, a model calibration trigger mechanism based on a dynamic threshold is designed to determine whether the parameters or structure of the degradation model need adaptive calibration. In the case of no triggering, the model parameters are updated using a Kalman filter; when the triggering condition is met, the model structure is calibrated based on the prediction error. The parameters of the prediction error model are identified by a strong tracking filter and an expectation maximization algorithm, and the optimal model structure is determined using the Akaike information criterion. In the prediction process, the present invention takes into account the differences in temperature data measured by thermocouples at different positions on the blast furnace wall, and derives the RUL distribution under the first hit time (First Hitting Time, FHT) of the adaptive degradation model. The method of the present invention can adaptively calibrate the parameters and structure of the degradation model based on online data, showing higher prediction accuracy and stronger online adaptability, and improving the prediction accuracy of the RUL of the blast furnace system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Flow chart of a method for predicting the remaining life of a blast furnace system based on an adaptive calibration model in an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of blast furnace wall temperature data recorded over time by thermocouples at different positions in an embodiment of the present invention;

[0020] Figure 3 Schematic diagram of the actual degradation trajectory and the predicted degradation trajectory under different initial degradation model assumptions in the embodiment of the present invention; wherein Figure 3 (a) in the figure represents the initial degradation model 1 corresponding to the drift function μ(τ,θ)=bτ (b-1) , Figure 3 (b) in the figure indicates the drift function μ(τ,θ)=bexp(τb) corresponding to the initial degradation model 2;

[0021] Figure 4 Schematic diagram of predicted trajectory after model calibration under different initial degradation model assumptions in an embodiment of the present invention; Figure 4 (a) in the figure represents the initial degradation model 1. Figure 4 (b) in the figure represents the initial degradation model 2;

[0022] Figure 5 Schematic diagram of RUL prediction results of blast furnace adaptive calibration model in an embodiment of the present invention; Figure 5 (a) in the figure represents the initial degradation model 1. Figure 5(b) in the figure represents the initial degradation model 2;

[0023] Figure 6 Schematic diagram of the α-λ effect of the blast furnace adaptive calibration model RUL in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0025] like Figure 1 As shown, this embodiment describes a method for predicting the remaining life of a blast furnace system based on an adaptive calibration model, which aims to solve the problem that the degradation model does not match the actual degradation process of the blast furnace system. When modeling the degradation process, it is necessary to consider the adaptive calibration model. In this case, adjusting the relevant parameters and structure of the degradation model based on the degradation data of the blast furnace can enhance the matching degree between the model and the monitoring data, thereby improving the accuracy of the RUL prediction of the blast furnace system.

[0026] The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model in this embodiment includes the following steps:

[0027] Step 1. Obtain the temperature data collected by thermocouples at different locations in the blast furnace system and construct training and test sets.

[0028] Take the blast furnace temperature data of a company as an example: Assume that the historical degradation data of N sensors in the blast furnace are preprocessed, denoted as X = [X1,…,X N ], for any n∈[1,N], there is X n =[x n,1 ,…,x n,M ] T .

[0029] Among them, X1,…,X N Respectively represent the temperature data sequence measured by N sensors, x n,1 ,…,x n,M They respectively represent the temperature data sequence measured by the nth sensor, and M represents the length of the temperature data sequence.

[0030] like Figure 2 In the present study, four groups of thermocouple temperature data of the furnace wall were used for parameter identification, and one group was used for verification.

[0031] Step 2. Based on the acquired temperature data of the blast furnace system, an initial degradation model of the blast furnace wall is constructed.

[0032] The trend of temperature change is characterized by the drift term, and the uncertainty of temperature change and environment is described by the diffusion term. Construct the initial nonlinear Wiener process model {x(t)}, that is, the initial degradation model:

[0033]

[0034] Where x(t) represents the furnace wall temperature, which is driven by the standard Brownian motion B(t), t≥0, represents the drift term that controls temperature changes, σ B The diffusion parameter that characterizes the uncertainty of temperature change, λ represents the drift term coefficient that controls the temperature change rate, which follows the mean μ λ , the variance is The normal distribution of indicates the heterogeneity between different products. μ(τ,θ) represents a linear or nonlinear function that changes with time t, with an unknown parameter vector θ, which can be used to describe the time-varying characteristics of the blast furnace temperature.

[0035] Since the temperature data collected from the blast furnace was insufficient, it was difficult to determine the specific function form of μ(t,θ). The present invention proposes two assumptions: power law and exponential. Let θ0 = [μ λ ,σ λ ,σ B ,θ] represents the unknown parameters in the initial degradation model.

[0036] For the convenience of analysis, the present invention assumes that x(0)=0 in the whole process, that is, the relationship between temperature increment and degradation is considered.

[0037] In addition, the degradation model parameters are identified based on the maximum likelihood estimation (MLE) method according to the data of the training set.

[0038] For Θ0, the log-likelihood function under the given N sets of blast furnace temperature data X is Right now:

[0039]

[0040] Where ψ=[ψ1,ψ2,…,ψ M ] T .

[0041] For any m∈[1,M], we have t m Represents the mth time node.

[0042] According to formula (1) and the independence assumption of Brownian motion, for any n, X n Follows a multivariate Gaussian distribution with mean μ λ ψ, variance is Σ=Ω+σ λ 2 ψψ T .in:

[0043]

[0044] In formula (2), About μ λ and σ λ Taking the first-order differential, we get:

[0045]

[0046] By substituting the analytical expressions of formulas (4) and (5) into the log-likelihood function of formula (2), we obtain:

[0047]

[0048] Therefore, by maximizing formula (6) for maximum likelihood estimation, we can get σ B Then, Ω and ψ are calculated based on the estimated values ​​and substituted into formulas (4) and (5), and we get and

[0049] Step 3. When the test set is supplemented with new measurement data, prediction is performed based on the current degradation model and the predicted value is obtained. The predicted value is then compared with the measurement data to obtain the prediction error of the model.

[0050] The prediction error refers to the prediction error data between the measured value and the model predicted value.

[0051] The degradation trajectory is predicted based on the initial degradation model, and the prediction error between the predicted degradation trajectory and the actual temperature curve of the blast furnace is calculated. Figure 3 As shown, under two initial model assumptions:

[0052] Figure 3 (a) in the figure represents the drift function μ(τ; θ) = bτ corresponding to the initial degradation model 1 (i.e., the power law model). (b-1) , Figure 3 (b) in FIG. 2 represents the initial degradation model 2 (ie, the exponential model) corresponding to the drift function μ(τ,θ)=bexp(τb).

[0053] The calculation method for the prediction error between the red prediction curve and the actual temperature curve of the blast furnace is as follows:

[0054]

[0055] in, represents the prediction error between the model prediction result after i-1 calibration and the actual observation, represents the i-th prediction error model data, represents the i-th model calibration moment, x actual (t) represents the actual degradation trajectory, represents the predicted trajectory of the model after the i-1th calibration, Represents the external noise to the forecast error model.

[0056] Specifically, it is assumed that the degradation model has been calibrated I times at the current time t, expressed as:

[0057]

[0058] Among them, x(t) represents the initial degradation model, x I (t) represents the degradation model after I adaptive calibration, is the indicator function, when hour The value is 1, otherwise is 0.

[0059] Step 4. According to the value of the prediction error, a model calibration trigger mechanism based on a dynamic threshold is designed to determine the calibration form of the degradation model, that is, to adaptively calibrate the parameters or structure of the degradation model.

[0060] Define the degradation model of the blast furnace system after i-1 calibrations, with parameters Θ = [Θ0, ..., Θ i-1 ], the actual temperature data is x actual ; where Θ0,…,Θ i-1 Respectively represent the parameter vectors to be identified in the initial degradation model and the previous i-1 prediction error model; the model predicts data in the time interval The prediction error within The previous events are irrelevant. It indicates the time when the blast furnace degradation model is predicted after i-1 model calibrations. represents the i-th model calibration moment, and h represents the time span of the data collected within the preset time window used to identify the parameters in the prediction error model.

[0061] Define dynamic threshold ζ i (t r )as follows:

[0062]

[0063] in, represents the adjustment coefficient; represents the uncertainty of the drift coefficient of the degradation model, and t r ,t r-1represents the time after i-1 calibrations; ε represents the standard deviation of the drift coefficient; μ(t,θ) represents a linear or nonlinear function that changes with time t, with an unknown parameter vector θ, which is used to describe the time-varying characteristics of the blast furnace temperature; τ represents a small increment of time, and B(·) represents the standard Brownian motion; represents the inherent uncertainty of the random process itself, j = 1,…,i-1; σ B Diffusion parameters that characterize the uncertainty of temperature changes, represents the uncertainty diffusion characteristics caused by the jth operating condition change. Usually, once it is determined The threshold of model calibration can be determined, and An exhaustive method is performed to obtain the optimized threshold value.

[0064] The method to determine the model structure calibration moment is as follows:

[0065] Step 4.1. Input the prediction error after the i-1th model calibration and determine the range of the prediction error [-ζ i (t r ),ζ i (t r )];

[0066] Step 4.2. Initialize the trigger count e_count of the model calibration trigger mechanism to zero;

[0067] Step 4.3. Iterate over each prediction error

[0068] in, represents the time of the i-1th model calibration, t h Represents the length of time necessary to identify the prediction error model;

[0069] If Er i (t r )Continuously exceeds the range [-ζ i (t r ),ζ i (t r )],but:

[0070] e_count=e_count+1, r=r+1;

[0071] If e_count ≥ 3, the model calibration time is recorded as And calibrate the blast furnace degradation model structure; otherwise, return to step 4.2 until the prediction time t is reached k ;

[0072] At the prediction time t k , output model calibration time or the model does not require functional form calibration.

[0073] It is worth noting that the blast furnace degradation process usually involves a certain degree of uncertainty.

[0074] In order to mitigate the impact of individual observation randomness on the final conclusion, three consecutive occurrences of exceeding a predefined threshold are required, thereby increasing the sensitivity of the model calibration trigger mechanism to system stability and real changes.

[0075] Step 5. When the mechanism is not triggered (i.e., the parameter calibration of the model function form calibration mechanism is not triggered), the Kalman filter (KF) is used to update the model parameters and return to step 3 until the prediction time t is reached. k .

[0076] In this case, assuming that the drift coefficient follows a Gaussian distribution, the degradation model of formula (1) is rewritten as follows:

[0077]

[0078] in, Indicates t j The drift coefficient of the initial model at time , Indicates t j-1 The drift coefficient of the initial model at time x(t j ) indicates t j The temperature value at the moment, x(t j-1 ) indicates t j-1 The temperature value at the moment, B(t j -t j-1 ) indicates the temperature value at t j-1 to j The uncertainty of the moment.

[0079] Considering that the model may be calibrated in functional form, formula (10) can be rewritten as the following more general model structure:

[0080]

[0081] Among them, λ i represents the drift coefficient of the ith calibration, Represents the indicative function. The drift coefficient can be iteratively estimated by KF, and the parameter update process based on the KF method is as follows:

[0082] Step 5.1. Initialization.

[0083] At the initial time t0, the mean and variance of the initial drift coefficient are:

[0084] Var0|0 =ε 2 ;

[0085] Among them, E 0|0 represents the initial mean value of the drift coefficient, Var 0|0 Represents the initial variance of the drift coefficient.

[0086] Step 5.2: Prediction.

[0087] At time t j The mean and variance of the predicted drift coefficient are as follows:

[0088] E j|j-1 =E j-1|j-1 ;

[0089] Var j|j-1 =Var j-1|j-1 +ε 2 ;

[0090] Among them, E j|j-1 Indicates t j The predicted value of the time mean, E j-1|j-1 Indicates t j-1 Updated value of the time mean, Var j|j-1 Indicates t j The predicted value of the moment variance, Var j-1|j-1 Indicates t j-1 Updated value of the moment variance.

[0091] Step 5.3: Update.

[0092] When the new observation x(t j ) when available:

[0093] Kalman Gain for:

[0094]

[0095] Mean E j|j Updated to:

[0096]

[0097] Variance Var j|j Updated to:

[0098]

[0099] Step 5.4: Iterate.

[0100] If j is less than the maximum number of iterations k, set j=j+1 and return to step 5.2; end when j reaches the maximum number of iterations k.

[0101] Step 6. When the mechanism is triggered (i.e., parameter identification of the adaptive calibration of the blast furnace degradation model is triggered), a prediction error model is constructed based on the value of the prediction error in step 3, and the structure of the degradation model is calibrated to compensate for the impact of changes in operating conditions or degradation mechanisms during blast furnace operation.

[0102] The following three conditions need to be met to construct a prediction error model: the number of prediction error modeling is limited; the prediction error follows the dynamic characteristics of the nonlinear Wiener process; the time interval between two model calibrations should be greater than t h to ensure the calibration effect.

[0103] Among them, t h Represents the length of time necessary to identify the prediction error model.

[0104] Based on the above conditions, the prediction error model of the blast furnace system during the i-th calibration period is It is expressed as:

[0105]

[0106] Among them, λ i represents the prediction error model drift term caused by changes in operating conditions, represents the time of calibrating the prediction error model for the i-th time, μ i (τ,θ i ) represents the drift term of the i-th calibration prediction error model, θ i represents the unknown parameter in the drift term of the i-th calibration prediction error model, represents the uncertainty of the prediction error model for the i-th calibration, Represents the diffusion coefficient affected by the i-th operating condition change.

[0107] The parameter vector to be identified is expressed as:

[0108] Θ i =(λ i ,θ i ,σ Bi ), i = 1,…,I, where I represents the upper limit of the number of model calibration times.

[0109] After (i-1) model calibrations are performed, the calibration threshold is at time In the case of three consecutive triggers, assuming that the error sequence is known to be Based on this information, the i-th model calibration can be performed.

[0110] according to The maximum likelihood estimation method can be used to estimate the parameters of the prediction error model.

[0111] Step 7. Identify the parameters of the prediction error model through the strong track filter (STF) and the expectation-maximization algorithm (EM), determine the optimal model structure through the Akaike information criterion (AIC), and return to step 3.

[0112] The present invention combines the EM algorithm and the STF algorithm to solve the parameter estimation problem of the model with hidden state.

[0113] Step 7.1. First, to estimate the hidden state, construct the following state space model:

[0114]

[0115] Among them, e i (·) represents the prediction error model, t r ,t r-1 represents the forecast error model time series, Δt r Represents the time interval, which is expressed as Δt r =t r -t r-1 , represents the prediction error between the model prediction result after i-1 calibration and the actual observation, represents the forecast error model noise.

[0116] Step 7.2. Then initialize the parameters Θ of the prediction error model i,0 . Where Θ i,0 The subscript i in the equation represents the number of initial degradation model calibrations, Θ i,0 The subscript 0 in indicates that the number of initial parameter iterations is 0.

[0117] When the EM algorithm iterates s steps, the expectation of the likelihood function is:

[0118]

[0119] S represents the number of steps required for the EM algorithm to converge, s∈[1,S]; Express expectations, represents the likelihood function, express The prediction error between the model prediction results and the actual observations, represents the hidden state; h represents the time length for determining the model parameters, σ Bi,s-1 represents the diffusion coefficient of the prediction error model for the s-1th iteration; e i,s [·] represents the prediction error model after the sth iteration, λi,s-1 Represents the drift coefficient of the prediction error model after the sth iteration, μ i (τ,θ i,s-1 ) represents the drift term of the prediction error model after the sth iteration, θ i,s-1 represents the unknown parameter of the drift term of the prediction error model after the s-1th iteration of the i-th calibration, Θ i,s-1 represents the unknown parameters of the prediction error model after the s-1th iteration; Er i [r] represents the prediction error between the prediction result of the rth model and the actual observation; represents the expectation of the prediction error after the sth iteration.

[0120] In the maximization step, at the sth iteration, Θ i Value Calculated as:

[0121]

[0122] Among them, STF is used to estimate the hidden state

[0123] The process of parameter estimation based on the EM algorithm and STF is as follows:

[0124] Step 7.2.1. Initialize parameter Θ i,0 , and P i,0 [0|0]; where and P i,0 [0|0] refers to the initial assumptions of the mean and covariance of the prediction errors respectively; according to the following steps 7.2.2 to 7.2.4, s is traversed from 1 to S in sequence, and for each value of s, r is traversed from 1 to h.

[0125] Step 7.2.2. First, apply STF to calculate the mean and covariance of the prediction error at time r.

[0126]

[0127] P i,s [r|r-1]=P i,s [r-1|r-1]+Q s [r-1];

[0128] in, represents the estimated value of the prediction error of the ith calibration and the sth iteration at time r, represents the updated value of the prediction error at the time r-1 of the ith calibration and the sth iteration, P i,s [r|r-1] represents the variance of the ith calibration and the sth iteration at time r, Pi,s [r-1|r-1] represents the variance at time r-1, Q s [r-1] represents Gaussian noise.

[0129] Step 7.2.3. When a new BF temperature measurement is obtained, apply STF to calculate the error ν i,s [r], error covariance ρ i,s [r], Kalman gain and the attenuation factor β i,s [r], the formulas are as follows:

[0130]

[0131] Then, the mean of the prediction error at time r after applying STF update is and covariance P i,s [r|r], the formula is as follows:

[0132]

[0133]

[0134] Run the M step of the EM algorithm: maximize the likelihood function to estimate the parameters of the prediction error model.

[0135] Step 7.2.4. Check Convergence of parameters.

[0136] If the convergence criterion is not met Return to step 7.2.2;

[0137] Otherwise, get and σ r|r =P i,S The estimated value of [r|r].

[0138] In addition, the selection of the prediction error model is still difficult. Therefore, the present invention determines the most appropriate prediction error model by balancing the accuracy, complexity and fit of the error model according to the definition of AIC. AIC takes into account the complexity of the model and tends to select a simplified model that performs well in explaining the data to avoid overfitting.

[0139] According to the minimum AIC value, the appropriate prediction error model can be determined. AIC is calculated as follows:

[0140]

[0141] in represents the number of model parameters, represents the parameters that maximize the expectation of the likelihood function, Represents the expectation of the likelihood function. Once the model structure of the prediction error model is determined, the prediction error model with a small AIC value is further selected to compensate the system to obtain more accurate prediction and analysis.

[0142] The AIC is used to select the structure of the prediction error model because the structure of the prediction error model is also unknown.

[0143] After calibration, the prediction results of the model calibration under different initial model assumptions are as follows Figure 4 As shown. Figure 4 (a) in the figure represents the initial degradation model 1 corresponding to the drift function μ(τ,θ)=bτ (b-1) , Figure 4 (b) in the figure represents the drift function μ(τ,θ)=bexp(τb) corresponding to the initial degradation model 2. It can be seen that when the amount of data is insufficient, the adaptive calibration of the model can significantly improve the prediction accuracy and reduce the prediction error between the prediction result and the actual value. At the same time, this method has strong robustness in the selection of the degradation model and can maintain relatively stable prediction performance under different initial model assumptions.

[0144] Step 8. When the adaptively calibrated degradation model tends to be stable, the blast furnace RUL prediction is performed according to the current degradation model.

[0145] To derive the RUL of the blast furnace system according to the definition shown in equation (8), it is assumed that the degradation process x I (t) follows the Wiener process and assumes that its drift term is [t k ,∞), then the probability density function (Probability Density Function, PDF) of RUL is formally expressed as:

[0146]

[0147] Where λ represents the drift coefficient, which is assumed to be a constant; S B (l k ) represents the threshold of Brownian motion, and its expression is as follows:

[0148]

[0149] where t k represents the prediction time, l k Indicates that at t k The RUL,D at represents a predefined blast furnace failure threshold, which is defined by industry standards and expert experience.

[0150] For the calibration iteration number I, if I = 0, the initial degradation model is accurate, and the degradation model is converted into a continuous degradation process model without model calibration; if I is a constant, the initial degradation model is inaccurate, and the degradation model is converted into a continuous degradation process model calibrated I times.

[0151] Therefore, the model proposed in the present invention is universal and can include the above two common degradation process models.

[0152] With drift coefficient λ as the condition, RUL at time t k The PDF of is given by:

[0153]

[0154] in:

[0155]

[0156] Among them, x k Indicates t k Observed value of blast furnace temperature at time.

[0157] It is worth noting that equation (17) assumes that the drift coefficient λ is a constant.

[0158] However, different products show their own differences. In order to characterize the variability between units, considering that the random parameter λ follows a Gaussian distribution, based on the total probability formula, the PDF of RUL can be expressed as:

[0159]

[0160] Among them, μ λ and is the mean and variance of the drift term coefficient; considering the drift coefficient μ λ and σ λ Updated over time, they are at time t k where μ λ,k and σ λ,k , while the other unknown parameters are fixed.

[0161] In order to ensure the robustness of the initial degradation model selection, two initial degradation models are first introduced, which are defined as initial degradation model 1 and initial degradation model 2. For initial degradation model 1 (i.e., model_1) and initial degradation model 2 (i.e., model_2), they correspond to different forms of drift functions μ(τ,θ)=bτ (b-1) And μ(τ,θ)=bexp(τb).

[0162] Wherein, b represents the parameter controlling the temperature change of the blast furnace.

[0163] Then, at time t k , given x k and threshold D, the probability density functions of RUL of model_1 and model_2 are expressed as:

[0164]

[0165] in:

[0166] Ω3=(t k +l k ) b -(t k ) b ;

[0167] Ω4=exp((t k +l k )b)-exp(t k b);

[0168] Ω5=l k b(t k +l k ) (b-1) ;

[0169] Ω6=l k bexp((t k +l k )(b).

[0170] According to the results in (21) and (22), the initial degradation model 1 and the initial degradation model 2 respectively obtained the corresponding RUL probability density functions after calibration. It should be emphasized that the two models correspond to independent RUL probability density functions, and the final RUL is not determined by the combination of the two. This result shows that this method has strong robustness to the initial degradation model. No matter which initial degradation model is selected, it can generate a reasonable RUL prediction after calibration, thereby obtaining the remaining life distribution result of the blast furnace system. This result not only takes into account the multiple calibrations of the system, but also reflects the dynamic changes of the degradation process under complex operating conditions, thereby providing a more accurate basis for the life assessment of the blast furnace system.

[0171] The present invention takes into account the differences in temperature data measured by thermocouples at different positions on the blast furnace wall, and based on this, derives the remaining life RUL distribution under the first arrival time FHT concept of the adaptive degradation model.

[0172] like Figure 5 In this paper, under different initial model assumptions, this method can accurately predict the RUL of the equipment, where Figure 5 (a) in the figure represents model_1. Figure 5(b) in the figure represents model_2. By observing the prediction curves under the two models, it can be found that the method shows high prediction accuracy, whether under the assumption that the initial model is a power law model or an exponential model, and can effectively capture the degradation trend of the equipment, thereby providing a reliable RUL estimation. This further verifies the robustness and adaptability of the method of the present invention under a variety of working conditions and assumptions.

[0173] Figure 6 The α-λ diagram for remaining life prediction is given, where M1 (1) Represents model_1, M1 (2) Represents model_2. Figure 6 It can be seen that the method of the present invention can control the RUL prediction accuracy within 20%. This shows that the method of the present invention still has strong adaptability and robustness when dealing with challenges such as complex working conditions and limited data, and provides strong support for the remaining life prediction of industrial blast furnaces.

[0174] The RUL distribution predicted by the method of the present invention is highly consistent with the actual degradation trend, indicating that the method of the present invention can accurately evaluate the remaining life of the blast furnace system under complex operating conditions, and thus has high practicality and robustness.

[0175] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A method for predicting the remaining life of a blast furnace system based on an adaptive calibration model, characterized in that: The steps include: Step 1. Obtain temperature data collected by thermocouples at different locations of the blast furnace system, and construct training sets and test sets; Step 2. construct an initial degradation model of the blast furnace wall based on the acquired temperature data of the blast furnace system; The trend of temperature change is characterized by the drift term, and the uncertainty of temperature change and environment is described by the diffusion term. In addition, the degradation model parameters are identified based on the maximum likelihood estimation (MLE) method according to the data of the training set. Step 3. When the test set is supplemented with new measurement data, prediction is performed based on the current degradation model and the predicted value is obtained. The predicted value is then compared with the measurement data to obtain the prediction error of the model. Step 4. Design a model calibration trigger mechanism based on a dynamic threshold according to the value of the model prediction error to determine the calibration form of the degradation model, that is, to adaptively calibrate the parameters or structure of the degradation model; Step 5. When the mechanism is not triggered, the Kalman filter KF is used to update the parameters of the degradation model and return to step 3 until the prediction time t k ; Step 6. When the mechanism is triggered, a prediction error model is constructed based on the value of the prediction error in step 3, and the structure of the degradation model is calibrated to compensate for the impact of changes in operating conditions or degradation mechanisms during blast furnace operation; Step 7. Identify the parameters of the prediction error model through the strong tracking filter STF and the expectation maximization algorithm EM, and determine the optimal model structure through the Akaike information criterion AIC, and return to step 3 until the prediction time t k ; Step 8. At the prediction time t k , blast furnace RUL prediction is performed based on the adaptively calibrated degradation model.

2. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 1, characterized in that: In step 4, the definition of the dynamic threshold in the model calibration trigger mechanism is as follows: Define the degradation model of the blast furnace system after i-1 calibrations, with parameter Θ 0:i-1 =[Θ0,...,Θ i-1 ]; where Θ0, ..., Θ i-1 Respectively represent the parameter vectors to be identified in the initial degradation model and the previous i-1 prediction error model; the model predicts data in the time interval The prediction error within The previous events are irrelevant; It indicates the time when the blast furnace degradation model is predicted after i-1 model calibrations. represents the i-th model calibration moment, h represents the amount of data collected within the preset time window, and is used to identify the time span of the parameters in the prediction error model; Define dynamic threshold ζ i (t r )as follows: in, represents the adjustment coefficient; represents the uncertainty of the drift coefficient of the degradation model, and t r ,t r-1 represents the time after i-1 calibrations; ε represents the standard deviation of the drift coefficient; μ(t,θ) represents a linear or nonlinear function that changes with time t, with an unknown parameter vector θ, which is used to describe the time-varying characteristics of the blast furnace temperature; τ represents a small increment of time, and B(·) represents the standard Brownian motion; represents the inherent uncertainty of the random process itself, j = 1,…,i-1; σ B Diffusion parameters that characterize the uncertainty of temperature changes, Represents the uncertainty diffusion characteristics caused by the j-th operating condition change.

3. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 2, characterized in that: In step 4, the specific process of the model calibration trigger mechanism is as follows: Step 4.

1. Input the prediction error after the i-1th model calibration and determine the range of the prediction error [-ζ i (t r ),ζ i (t r )]; Step 4.

2. Initialize the trigger count e_count of the model calibration trigger mechanism to zero; Step 4.

3. Iterate over each prediction error Er i (t), in, represents the i-1th model calibration time, t h Represents the length of time necessary to identify the prediction error model; If the prediction error Er i (t r )Continuously exceeds the range [-ζ i (t r ),ζ i (t r )],but: e_count=e_count+1, r=r+1; If e_count ≥ 3, the model calibration time is recorded as And calibrate the blast furnace degradation model structure; otherwise, return to step 4.2 until the prediction time t is reached k ; At the prediction time t k , output model calibration time or the model does not require functional form calibration.

4. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 1, characterized in that: In step 6, the prediction error model satisfies the following three conditions: the number of prediction error modeling is finite; the prediction error follows the dynamic characteristics of the nonlinear Wiener process; the time interval between two model calibrations should be greater than t h ; Among them, t h Represents the length of time necessary to identify the prediction error model; Based on the above conditions, the prediction error model of the blast furnace system during the i-th calibration period is It is expressed as: Among them, λ i represents the prediction error model drift term caused by changes in operating conditions, represents the time of calibrating the prediction error model for the i-th time, μ i (τ,θ i ) represents the drift term of the i-th calibration prediction error model, θ i represents the unknown parameter in the drift term of the i-th calibration prediction error model, represents the uncertainty of the prediction error model for the i-th calibration, represents the i-th model calibration moment, represents the diffusion coefficient affected by the change of the i-th operating condition; The parameter vector Θ to be identified i It is expressed as: I i =(λ i ,i i ,s Bi ); Where i = 1, ..., I, I represents the upper limit of the number of model calibration times; Assume that the degradation model has been calibrated I times at the current time t, expressed as: Among them, x I (t) represents the degradation model after I times of adaptive calibration, x(t) represents the initial degradation model, is the indicator function, when hour The value is 1, otherwise is 0.

5. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 1, characterized in that: The step 7 is specifically as follows: Step 7.

1. First, to estimate the hidden state, construct the following state space model: Among them, e i (·) represents the prediction error model, t r ,t r-1 represents the forecast error model time series, Δt r Represents the time interval, which is expressed as Δt r =t r -t r-1 , It represents the prediction error between the model prediction result after i-1 calibration and the actual observation; represents the external noise of the forecast error model; represents the i-th model calibration moment; represents the diffusion coefficient affected by the change of the i-th operating condition; B(·) represents the standard Brownian motion; represents the diffusion coefficient affected by the jth operating condition change; Step 7.

2. Then initialize the parameters Θ of the prediction error model i,0 ; where Θ i,0 The subscript i in the equation represents the number of initial degradation model calibrations, Θ i,0 The subscript 0 in indicates that the number of initial parameter iterations is 0; When the EM algorithm iterates s steps, the expectation of the likelihood function for: in, Express expectations, represents the likelihood function, express The prediction error between the model prediction results and the actual observations, represents the hidden state; h represents the amount of data collected within the preset time window, σ Bi,s-1 represents the diffusion coefficient of the prediction error model for the s-1th iteration; e i,s [·] represents the prediction error model after the sth iteration, λ i,s-1 Represents the drift coefficient of the prediction error model after the sth iteration, μ i (τ,θ i,s-1 ) represents the drift term of the prediction error model after the sth iteration, θ i,s-1 represents the unknown parameter of the drift term of the prediction error model after the s-1th iteration of the i-th calibration, Θ i,s-1 represents the unknown parameters of the prediction error model after the s-1th iteration; Er i [r] represents the prediction error between the prediction result of the rth model and the actual observation; represents the expectation of the prediction error after the sth iteration; S represents the number of steps required for the EM algorithm to converge, s∈[1,S]; Δt r =t r -t r-1 ; In the maximization step, at the sth iteration, Θ i Value Calculated as: Using strong tracking filter STF to estimate hidden state 6. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 5, characterized in that: In step 7.2, the process of parameter estimation based on the EM algorithm and STF is as follows: Step 7.2.

1. Initialize parameter Θ i,0 , and P i,0 [0|0]; where and P i,0 [0|0] refers to the initial assumptions of the forecast error mean and covariance, respectively; According to the following steps 7.2.2 to 7.2.4, s is traversed from 1 to S in turn, and for each value of s, r is traversed from 1 to h; Step 7.2.

2. First, apply STF to calculate the mean and covariance of the prediction error at time r; P i,s [r|r-1]=P i,s [r-1|r-1]+Q s [r-1]; in, represents the estimated value of the prediction error of the ith calibration and the sth iteration at time r, represents the updated value of the prediction error at the time r-1 of the ith calibration and the sth iteration, P i,s [r|r-1] represents the variance of the ith calibration and the sth iteration at time r, P i,s [r-1|r-1] represents the variance at time r-1, Q s [r-1] represents Gaussian noise; Step 7.2.

3. When a new BF temperature measurement is obtained, apply STF to calculate the error ν i,s [r], error covariance ρ i,s [r], Kalman gain and the attenuation factor β i,s [r], the formulas are as follows: Then, the mean of the prediction error at time r after applying STF update is and covariance P i,s [r|r], the formula is as follows: Run the M step in the EM algorithm: maximize the likelihood function to estimate the parameters of the prediction error model; Step 7.2.

4. Check Convergence of parameters; If the convergence criterion is not met Return to step 7.2.2; Otherwise, get and σ r|r =P i,S The estimated value of [r|r].

7. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 1, characterized in that: The step 8 is specifically as follows: Assume that the degradation model x after I adaptive calibration I (t) follows the Wiener process, and its drift term is [t k ,∞), then the probability density function of RUL is The formal expression is: Among them, λ represents the drift coefficient, which is a constant; S B (l k ) represents the threshold of Brownian motion, and its expression is as follows: where t k represents the prediction time, l k Indicates that at t k RUL at, D represents the predefined blast furnace failure threshold, σ B Diffusion parameter that characterizes the uncertainty of temperature change; for the number of calibration iterations I, if I = 0, the initial degradation model is accurate, and the degradation model is converted into a continuous degradation process model without model calibration; if I is a constant, the initial degradation model is inaccurate, and the degradation model is converted into a continuous degradation process model calibrated I times; With drift coefficient λ as the condition, RUL at time t k The probability density function of Given by: in: Among them, x k Denotes the prediction time t k Observed values ​​of blast furnace temperature; represents the uncertainty diffusion coefficient caused by the change of the i-th operating condition, λ i represents the prediction error model drift term caused by operating condition changes, μ i (τ,θ i ) represents the drift term of the i-th calibration prediction error model, θ i represents the unknown parameter in the drift term of the i-th calibration prediction error model, represents the i-th model calibration moment; considering that λ follows a Gaussian distribution, based on the total probability law, the probability density function of RUL is expressed as: Among them, μ λ and is the mean and variance of the drift term coefficient; considering the drift coefficient μ λ and σ λ Updated over time, they are at time t k where μ λ,k and σ λ,k .

8. The method for predicting the remaining life of a blast furnace system based on an adaptive calibration model according to claim 7, characterized in that: In step 8, in order to ensure the robustness of the initial degradation model selection, two initial degradation models are first introduced, which are defined as initial degradation model 1 and initial degradation model 2 respectively; The two initial degradation models correspond to different forms of drift functions μ(τ,θ)=bτ (b-1) and μ(τ,θ)=bexp(τb); Among them, b represents the parameter that controls the temperature change of the blast furnace; Then, at the prediction time t k , given the observed value x of the blast furnace temperature k and blast furnace fault threshold D, the probability density functions of RUL of initial degradation model 1 and initial degradation model 2 are expressed as: in: Ω3=(t k +l k ) b -(t k ) b ; Ω4=exp((t k +l k )b)-exp(t k b); Ω5=l k b(t k +l k ) (b-1) ; Ω6=l k bexp((t k +l k )(b); After calibration, the initial degradation model 1 and the initial degradation model 2 obtained the corresponding RUL probability density functions, and then the remaining life distribution results of the blast furnace system were obtained.

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