A blast furnace degradation model calibration and residual life prediction method in a noisy environment

Abstract

The present application belongs to the field of blast furnace system health management and prediction, and specifically discloses a blast furnace degradation model calibration and residual life prediction method under a noise environment. The method is based on a fractional Brownian motion with historical dependence, constructs an initial degradation model of the blast furnace system, estimates the model parameters by the maximum likelihood estimation method, and determines the optimal model structure of the blast furnace system temperature change by the Akaike information criterion. In addition, the present application also designs a model calibration trigger mechanism; when the mechanism is not triggered, the Bayesian fusion particle filter is used to estimate the potential degradation state of the system and update the model parameters; when the mechanism is triggered, a prediction error model is constructed and the degradation model structure is calibrated to adapt to complex working conditions. Finally, the probability distribution function of the residual life of the blast furnace system is derived, and the residual life prediction of the blast furnace system is carried out according to the calibrated degradation model.

Description

Technical Field

[0001] This invention belongs to the field of blast furnace system health management and prediction, specifically involving a method for calibrating a blast furnace degradation model and predicting its remaining life under noise conditions. Background Technology

[0002] In recent years, predictive health management (PHM) technology has gradually become an important means to ensure the safe and efficient operation of blast furnaces. It has been proven to effectively prevent sudden failures, optimize maintenance plans, reduce costs, and ensure system stability. Among them, residual life (RUL) prediction, as a key component of PHM, has been widely used in blast furnaces and other industrial equipment.

[0003] Currently, RUL prediction methods mainly rely on assumed or simplified degradation models, which have certain limitations in modeling the complex and dynamic degradation characteristics of blast furnaces. They struggle to accurately characterize the nonlinear degradation patterns during operating condition fluctuations or degradation mechanism evolution under complex noise influences. In practical case studies, the degradation process of the blast furnace wall is influenced by multiple factors, including erosion by high-temperature molten metal, slag adhesion and spalling, accumulation of thermal stress, and fluctuations in operating conditions. In the initial stage, the wall degradation is relatively slow, mainly manifested as slight wear of the surface material and gradual changes in thermal conductivity. However, as the blast furnace smelting process continues, the hearth and walls are subjected to long-term erosion by molten iron and slag, gradually forming a bonding layer that affects the thermophysical properties of the furnace wall. Under the combined effects of high temperature, high pressure, and complex chemical reactions, the bonding layer undergoes structural changes or even spalling, leading to significant changes in the thermal resistance characteristics of the furnace wall. This change may result in inappropriate equipment maintenance timing, accelerated performance degradation, increased failure risk, and even major safety hazards.

[0004] Furthermore, existing RUL prediction methods primarily focus on predicting the remaining life of products within the same batch, without fully considering the individual differences of individual sensors. This can lead to discrepancies between the assumptions of the degradation model and actual operating conditions, thus affecting the accuracy and reliability of the predictions. If the degradation model is not calibrated in a timely manner, the accuracy of RUL predictions may decrease significantly, adversely impacting production, maintenance, and safety. Summary of the Invention

[0005] The purpose of this invention is to propose a method for calibrating a blast furnace degradation model and predicting its remaining life under noisy conditions. This method enhances the model's ability to characterize complex and non-stationary degradation modes by dynamically adjusting the key parameters and structural form of the degradation model during online updates, thereby improving the matching degree between the degradation model and online monitoring data and effectively improving the accuracy of blast furnace system remaining life prediction.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for calibrating a blast furnace degradation model and predicting its remaining life under noisy conditions includes the following steps: Step 1. Acquire temperature data collected by thermocouples at different locations in the blast furnace system and perform preprocessing; Step 2. Based on the collected temperature data, construct an initial degradation model of the blast furnace wall; The initial degradation model incorporates a measurement error term, while the evolution of the furnace wall degradation thickness is indirectly characterized by a drift term, and the diffusion term is used to describe the inherent randomness and uncertainty of the system. The parameters of the initial degradation model were identified based on the maximum likelihood estimation (MLE) method, and the optimal model structure for the temperature change of the blast furnace system was determined by using the Akaike Information Criterion (AIC). Step 3. When new measurement data is detected online, compare the new measurement data with the predicted value of the current degradation model and calculate the prediction error of the model; at the same time, determine whether the predicted time of the blast furnace system's remaining life (RUL) has been reached. When the predicted time is reached, the RUL prediction of the blast furnace system is performed based on the current degradation model; Step 4. Based on the model prediction error value, construct a threshold-based model calibration trigger mechanism to determine the calibration method for the degraded model; if the mechanism is not triggered, proceed to step 5; if the mechanism is triggered, proceed to step 6. Step 5. Use a particle filter to estimate the potential degradation state of the blast furnace system, and use the Bayesian method to update the degradation model parameters. Then return to step 3 until the predicted time of RUL is reached. Step 6. Construct a prediction error model and calibrate the degradation model to compensate for the impact of changes in operating conditions or the evolution of degradation mechanisms during blast furnace operation. Then return to step 3 until the predicted time of RUL is reached. Step 7. Derive the analytical expression for the RUL probability density and update the parameters of the calibrated degradation model in real time based on the new measurements; Step 8. When the predicted time of the RUL of the blast furnace system is reached, predict the RUL of the blast furnace system according to the calibrated degradation model.

[0007] The present invention has the following advantages: This invention proposes a method for calibrating a blast furnace degradation model and predicting its remaining life under noisy conditions. This method introduces a stochastic process with a memory effect during the degradation modeling stage, providing a unified model for the random disturbances and long-term memory effects commonly present in the blast furnace wall temperature degradation process. This effectively overcomes the limitations of traditional Wiener processes or Markov models in characterizing degradation behavior under complex thermal conditions, improving the model's physical consistency and expressive ability towards the real degradation mechanism. Simultaneously, this invention uses the MLE method combined with AIC to jointly identify and optimize the degradation model parameters and structure, enabling the model structure to adaptively adjust with the blast furnace temperature evolution characteristics. This avoids model mismatch problems caused by artificially setting a fixed degradation structure, thereby improving the stability and generalization ability of the degradation model. This invention constructs a threshold-based triggering mechanism by real-time monitoring of the prediction error of the blast furnace system degradation model. This mechanism can quickly sense changes in blast furnace operating conditions or the evolution of degradation mechanisms. When model adaptability decreases, it can promptly trigger the model calibration process, effectively suppressing the accumulation of prediction errors and improving the robustness of online modeling and prediction. This invention achieves continuous estimation of potential degradation states and model parameters using particle filtering and Bayesian updates when the calibration mechanism is not triggered. When the calibration mechanism is triggered, it compensates for the impact of sudden changes in operating conditions and degradation mechanisms on model performance by reconstructing or adjusting the model structure or key parameters, thereby achieving adaptive modeling of non-stationary, multi-stage degradation processes. Based on the degradation model, this invention derives an analytical expression for the RUL probability density function, which can be updated in real time with online observation data. It can not only output point estimation results but also quantify the uncertainty of RUL prediction, providing more reliable probabilistic information support for the operation and maintenance decisions of blast furnace systems. Furthermore, this invention is implemented based on online temperature monitoring data of the blast furnace system, without relying on additional sensors or complex prior information. It has the advantages of low implementation cost, strong linearity, and good scalability, and is suitable for long-term health monitoring and life prediction of complex industrial equipment such as blast furnaces under noise interference and operating condition fluctuations, possessing good engineering practical value. Attached Figure Description

[0008] Figure 1 This is a flowchart of the method for calibrating the blast furnace degradation model and predicting its remaining life under noisy conditions in an embodiment of the present invention; Figure 2 This is a schematic diagram of blast furnace wall temperature data recorded over time by thermocouples at different locations in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the deviation between the temperature data predicted by the initial degradation model and the actual temperature data in an embodiment of the present invention. Figure 4 This is a schematic diagram of the calibration time for model prediction error and triggering mechanism in an embodiment of the present invention; Figure 5This is a schematic diagram showing the blast furnace wall degradation model and the RUL prediction results at 110 days using the MC method in this embodiment of the invention. Figure 6 This is a schematic diagram of the RUL probability density function of the blast furnace wall degradation model from 110 days to 137 days in an embodiment of the present invention. Detailed Implementation

[0009] Considering that the degradation process of the blast furnace system is affected by noise, memory effect and complex operating conditions during operation, this invention models and optimizes the noise environment and the memory effect of measurement data, and proposes a method for calibrating the blast furnace degradation model and predicting the remaining life under noise conditions. In the modeling process, an adaptive calibration mechanism oriented towards noise environment and long-range correlation is introduced, which is suitable for the research on the prediction of the remaining life of the blast furnace system under multiple operating conditions.

[0010] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 like Figure 1 As shown in Example 1, this method describes a blast furnace degradation model calibration and remaining life prediction method under noisy conditions, including the following steps: Step 1. Obtain temperature data collected by thermocouples at different locations in the Liugang blast furnace system and perform preprocessing.

[0011] The historical temperature data of the blast furnace was divided into training data and test data.

[0012] like Figure 2 As shown, the four sets of gray thermocouple temperature data on the furnace wall are used for model training; the blue test data are used to verify the theory. The failure threshold is defined as a critical level of temperature increment measured by thermocouples in the blast furnace system; when the observed temperature increment reaches this failure threshold, it is determined that the blast furnace system has failed and timely repair or maintenance is required.

[0013] Step 2. Based on the memory effect of the collected temperature data, that is, the influence of the current temperature state on the evolution of historical temperature, construct an initial degradation model of the blast furnace wall; Blast furnace temperature data, as a direct observation, is inevitably affected by measurement errors caused by factors such as sensor accuracy limitations, environmental interference, and the data acquisition process. Based on this, the established state-space model explicitly introduces a measurement error term into the observation equation. Since the furnace wall thickness is difficult to measure directly, the temperature increment is used as an indirect representation of its degradation state. The evolution process of the equivalent degradation level of the furnace wall thickness is indirectly characterized by the drift term in the state equation, and the diffusion term is used to describe the inherent randomness and uncertainty of the system caused by factors such as raw material fluctuations, changes in operating conditions, and complex thermochemical reactions. The parameters of the initial degradation model are identified based on the maximum likelihood estimation (MLE) method, and the optimal model structure for temperature changes in the blast furnace system is determined using the Akaike Information Criterion (AIC).

[0014] Step 2.1. Construct an initial degradation model of the blast furnace wall.

[0015] The initial degradation model based on fractional Brownian motion is constructed as follows: (1) in This represents the potential degradation state of the blast furnace system, which is affected by fractional Brownian motion. Driven by; This is a drift term that controls temperature changes; The diffusion term characterizes the uncertainty of temperature changes; The proportional parameter representing the rate of temperature change is the drift term coefficient of the initial degradation model; This is an unknown parameter vector used to describe the time-varying characteristics of blast furnace temperature; This represents the drift term function that indirectly reflects the level of furnace wall degradation. This represents the time integration factor, used to describe the cumulative effect mechanism of the degradation process over time; for ease of analysis, an initial degradation level is assumed throughout the process. .

[0016] set up Represents the vector of unknown parameters in the initial degradation model, where , , Unknown parameters for controlling the degradation level of blast furnace walls.

[0017] The potential degradation state of a blast furnace system is often difficult to measure directly. Without model calibration, the measured temperature values ​​of the blast furnace system are often incompatible with... Potential degenerative state at any moment The relationship between them is as follows: (2) in This represents the temperature measurement value of the blast furnace system. , This indicates the measurement error caused by sensor noise and external interference.

[0018] Step 2.2. Identify the initial degradation model parameters based on the MLE method.

[0019] for In the given thermocouples Temperature data The log-likelihood function under the given conditions is The calculation formula is as follows: (3) in This indicates the number of thermocouple sensors in the blast furnace. This indicates the number of days for which data is needed to determine the model parameters; , It is an identity matrix of order h. Representing fractional Brownian motion The covariance matrix, Indicates measurement error The variance; Represents the drift term coefficient Uncertainty Represents the drift term coefficient The mean; Indicates the current thermocouple, Indicates the current number Thermocouple order is Temperature increment measurement value; This is a function of temperature change.

[0020] make ,but , , Indicates the first At any given moment; among them The mean is variance is The Gaussian distribution.

[0021] Calculation formula (3) about and The first partial derivatives, and setting the first partial derivatives to zero, yield: (4) in , They are respectively , The maximum likelihood estimate, for The estimated value; The covariance matrix representing the standard fraction Brownian motion is expressed as follows: ; in The covariance operator is represented. Represents the Hearst exponent in the fractional Brownian motion covariance matrix; and They represent and Fractional Brownian motion at time points.

[0022] Substituting formula (4) into the log-likelihood function in formula (3), we get: (5) in for The maximum likelihood estimate, This indicates that the parameter vector is obtained. The maximum likelihood estimate is the value of the log-likelihood function.

[0023] definition , They are respectively , The estimated value; , , and The MLE is obtained through a multidimensional search method.

[0024] The solution , , and Substituting into formula (4), we get and The value of .

[0025] Step 2.3. Use AIC to determine the optimal model structure for temperature changes in the blast furnace system.

[0026] According to the definition of AIC, the most suitable error model can be determined by balancing the accuracy, complexity, and goodness of fit of the error model. AIC takes into account the complexity of the model and tends to choose a simplified model that performs well in interpreting the data to avoid overfitting.

[0027] The error model is determined based on the minimum AIC value. The formula for calculating the AIC value is as follows: (6) in This indicates the number of model parameters.

[0028] Based on this, the model's goodness of fit and complexity are comprehensively weighed by calculating the AIC value corresponding to different candidate model structures.

[0029] Specifically, for different drift term function forms and Parameters are estimated separately, and the corresponding AIC values ​​are calculated. The model with the smallest AIC value is selected as the optimal model structure.

[0030] This optimal model ensures good fitting performance while avoiding overfitting caused by excessive model complexity.

[0031] Step 3. When new measurement data is detected online, compare the new measurement data with the predicted value of the current degradation model and calculate the prediction error of the model; Simultaneously, it is determined whether the predicted time of the blast furnace system RUL has been reached; when the blast furnace temperature increment reaches 90% of the preset blast furnace failure threshold, this time is determined as the prediction time; when the prediction time is reached, the blast furnace system RUL is predicted according to the current degradation model.

[0032] The prediction error calculation process is as follows: The prediction error of the blast furnace system degradation model, i.e., the deviation between the predicted value of the blast furnace system degradation model and the actual temperature data, is calculated using the following formula: (7) in Indicates the first Temperature measurements of the blast furnace system after the second calibration. Indicates the first The predicted values ​​of the degradation model after subcalibration are defined. ,but Indicates the first Secondary prediction error data This indicates the mean operation; Indicates the first At that moment, Indicates completion The time of the next calibration.

[0033] No. Prediction error model during sub-calibration The expression is: (8) in Indicates triggering the first Next model calibration time Indicates the first The coefficients of the drift term in the prediction error model of the second calibration. Indicates the first The drift term function of the prediction error model after secondary calibration Indicates the first The unknown parameter vector of the drift term function in the prediction error model of the second calibration. Indicates the first The diffusion term coefficients of the prediction error model after secondary calibration. Represents standard Brownian motion. .

[0034] Figure 3The figure shows the deviation between the temperature data predicted by the initial degradation model and the actual measured temperature data, i.e., the online temperature data. As can be seen from the figure, the deviation between the predicted data and the actual temperature data is large. Therefore, the degradation model needs to be calibrated to avoid inaccurate RUL prediction results.

[0035] Step 4. Based on the value of the model prediction error, construct a threshold-based model calibration trigger mechanism to determine the calibration method for the degraded model; if the mechanism is not triggered, proceed to step 5; if the mechanism is triggered, proceed to step 6.

[0036] The threshold in the model calibration triggering mechanism is defined as follows: For online blast furnace systems, the blast furnace wall degradation model has been... After the first calibration, the parameters are: The actual temperature measurement data of the blast furnace wall is as follows: ;in , Representing the initial degradation model and the first degradation model respectively. The unknown parameter vector in the degraded model after secondary calibration. Model prediction data at time intervals. Within the prediction error and This is unrelated to the previous events.

[0037] definition Time-based blast furnace system degradation model structure calibration threshold as follows: (9) in Indicates the adjustment coefficient; This indicates the uncertainty inherent in the measured blast furnace temperature. This indicates the uncertainty of the blast furnace wall degradation model; , , The kernel function representing fractional Brownian motion. Indicates the total number of fractions; This indicates the uncertainty of the prediction error model. Indicates the first The coefficients of the diffusion term in the prediction error model after the second calibration.

[0038] Normally, it is determined This allows us to determine the threshold for model calibration, and also allows us to... An exhaustive approach is used to obtain the optimized threshold.

[0039] Random processes are often accompanied by a certain degree of uncertainty. In order to reduce the interference of random fluctuations in individual temperature measurements on the final decision, this embodiment sets a judgment criterion: the model calibration mechanism is only triggered when three consecutive detection results exceed the preset threshold, thereby improving the reliability and sensitivity of the model calibration mechanism in terms of system stability judgment and perception of real changes. Figure 4 This demonstrates the model calibration trigger point, which is the moment when the prediction error continuously exceeds the calibration threshold. The specific model calibration trigger mechanism is as follows: Step 4.1. Enter the first... Prediction error data after the second calibration.

[0040] Step 4.2. Set the number of model calibration triggers. Initialize to zero.

[0041] Step 4.3. Determine the range of prediction error. traversal prediction error , ; in Indicates triggering the first Next model calibration time This indicates the time required to identify the prediction error model.

[0042] Step 4.4. If Out of range ,but: , ; Then return to step 4.3; otherwise, return to step 4.2 and initialize. To prevent a single outlier from falsely triggering calibration; when At that time, the degradation model of the blast furnace wall was recorded. Next trigger calibration time And calibrate the blast furnace wall degradation model until the predicted time of remaining life is reached; if Not outside the range The blast furnace wall degradation model does not require calibration.

[0043] Step 4.5. Output trigger Secondary model calibration time Or the model does not require functional calibration at this moment.

[0044] Step 5. If the mechanism is not triggered, use a particle filter to estimate the potential degradation state of the blast furnace system with measurement uncertainty, update the degradation model parameters using a Bayesian method, and then return to step 3 until the predicted time of RUL is reached.

[0045] Step 5.1. To estimate the potential degradation state of the blast furnace system, the state-space model is constructed as follows: (10) in Indicates the number of times the degraded model structure has been calibrated; express The potential degradation status of the blast furnace system at all times; Represents the initial degradation model The drift term coefficient at time step, Indicates the first The coefficients of the drift term in the prediction error model of the second calibration. Indicates the first Temperature measurements of the blast furnace system after the second calibration. for exist The realization of a moment.

[0046] Step 5.2. Use a particle filter to estimate the potential degradation state of the blast furnace system.

[0047] Step 5.2.1. Initialize the potential degradation state of the blast furnace temperature.

[0048] Since the potential degradation state, i.e. the actual temperature of the blast furnace, cannot be directly observed, the probability density of the initial temperature of the blast furnace system is obtained according to the state transition equation in formula (10). ,right Sample generation of particles And according to the weights corresponding to the particles Weighting is performed; where , , Indicates the number of particles. Indicates particle-based The posterior probability density, This indicates the current thermocouple measurement value. Indicates the current potential degradation state. The first potential degradation state generated by the current state. One particle.

[0049] This step uses a set of discrete particles to approximate the probability distribution of the initial temperature of the blast furnace system. .

[0050] Step 5.2.2. Update the potential degradation state of the blast furnace system according to the state transition equation.

[0051] According to the state transition equation of the blast furnace system in formula (10), new particles are generated. ; in express The potential state of degradation at any given moment. , They represent the first Individual particles and The value at any given moment.

[0052] This step corresponds to the prior prediction process in Bayesian filtering. Its function is to advance the state from the previous moment to the current moment based on the degradation mechanism of the blast furnace system.

[0053] Step 5.2.3. Update particle weights.

[0054] When a new temperature measurement is obtained, the weights corresponding to the particles are calculated. ;in , , They represent and Time of the first The weight of each particle.

[0055] Then, weight normalization is performed: ; in This represents the normalized weights.

[0056] This step corrected the predicted particles using actual observation data.

[0057] Step 5.2.4. Resampling.

[0058] If the effective number of particles is lower than the threshold ,Right now Then the particle weights need to be initialized: ; in This indicates the percentage of effective particles. Indicates the number of resampling steps. The value of each particle.

[0059] This step eliminates low-weight particles, improves sample diversity, and avoids filter failure caused by particle degradation.

[0060] Step 5.2.5. Estimate the potential degradation state of the blast furnace system based on the current particle and its corresponding weight. for: .

[0061] This step transforms the probability distribution represented by discrete particles into a single true temperature estimate, which is used for subsequent degradation modeling and RUL prediction.

[0062] Step 5.3. Update the parameters of the degenerate model using the Bayesian method.

[0063] Based on the potential degradation state of the blast furnace system, update the drift term coefficients of the degradation model. .

[0064] In the time interval Above, observed increment satisfy: ; in, The drift term function represents the initial degradation model. ; The drift term function represents the prediction error model. ; express The implementation of noise in the current degradation model at any given time.

[0065] Therefore, conditional probability ; in , .

[0066] Overall likelihood ; in This represents a set of historical temperature measurements.

[0067] According to Bayes' theorem: (11) in express The prior probability.

[0068] Taking the logarithm of formula (11) and expanding it, the result is as follows: The quadratic form is rearranged to obtain: ; Where C represents the irrelevant term of the drift term coefficient in the initial degradation model. This indicates the actual temperature of the blast furnace at... arrive Increment in time.

[0069] Since the standard form of the Gaussian distribution is known, the posterior distribution is also a Gaussian distribution. Therefore, the parameter update results are as follows: ; .

[0070] in The mean is variance is The Gaussian distribution.

[0071] Step 5.4. When the blast furnace system degradation model triggers a new calibration or reaches the RUL prediction time, stop the estimation of potential degradation states and the updating of model parameters; otherwise... Then return to step 5.2.2.

[0072] Step 6. When the mechanism is triggered, construct the prediction error model and calibrate the degradation model structure to compensate for the impact of changes in operating conditions or the evolution of degradation mechanisms during blast furnace operation. Then return to step 3 until the prediction time of RUL is reached.

[0073] The prediction error model for the blast furnace system during the I-th calibration is: Its likelihood function is: (12) in , ; , ; ; ; ; express No. Line number Column elements; Indicates the use of the first Time series of prediction error model parameter identification; A collection of prediction error data; , This indicates the time when the covariance is calculated.

[0074] Based on formula (12), the MLE method is used to obtain the first... The unknown parameter vector of a prediction error model .

[0075] Assuming the degradation model is at the current time Calibrated Next, then the first Degenerate model after secondary calibration Represented as: (13) in It is an indicator function, when hour, The value is 1, otherwise It is 0.

[0076] Step 7. Derive the analytical expression for the RUL probability density and update the parameters of the calibrated degradation model in real time based on the new temperature measurements.

[0077] No. Degenerate model after secondary calibration Including fractional Brownian motion and Brownian motion, assuming its drift term is in If it is continuous in time, then it is continuous in time. Given the known temperature measurements of the blast furnace system and a set of estimated parameters, RUL is defined as: ; in Thermocouple measuring components The moment when the corresponding potential degradation state first exceeds the threshold, Indicates in The remaining lifespan at that location, This represents a predefined fault threshold. This indicates the predicted potential degradation state. It represents the infimum of a set.

[0078] RUL probability density function (PDF) Represented as: ; in, ; express The diffusion coefficient approximated by the initial degradation model at time . Indicates the first Coefficients of the diffusion term in the prediction error model; Represents a set of known parameters. express The set of all temperature measurements after the first calibration.

[0079] ; ; This represents the differential form of the drift term function of the initial degenerate model.

[0080] ; This represents the differential form of the drift term function in the prediction error model.

[0081] .

[0082] If calibration times If the initial degradation model is accurate, the degradation model can be transformed into a continuous degradation process model without the need for model calibration.

[0083] If calibration times If the value is a positive integer, then the initial degradation model is inaccurate, and the degradation model is converted into a calibration model. The model continuously degrades over time, and the parameters of the calibrated degradation model are updated in real time based on new temperature measurements.

[0084] Therefore, the model proposed in this invention is general and can include the two common degradation process models mentioned above. The PDF of remaining lifetime can be updated once new temperature measurements are available. Figure 5 The simulation curves of the residual lifetime (RUL) using the method of this invention at 110 days are shown, as well as the RUL simulation results using the Monte Carlo (MC) method. The predicted mean refers to the conditional expectation of the residual lifetime random variable, i.e., the mathematical expectation of its probability distribution, given the current degradation state or historical observation data. The results show that the method of this invention has high prediction accuracy. Figure 6 The results demonstrate the PDF, RUL prediction, and RUL actual value curves of the remaining lifetime prediction as new online temperature data are continuously acquired, further validating the accuracy of the method proposed in this invention.

[0085] Step 8. When the predicted time of the RUL of the blast furnace system is reached, predict the RUL of the blast furnace system according to the calibrated degradation model.

[0086] In step 2 of this invention, in response to the random disturbances and long-term memory characteristics commonly found in the temperature signals of the blast furnace system, a stochastic process with memory effect is used to model the furnace wall degradation. The degradation trend is characterized by the drift term, while the random uncertainties and memory effects caused by the complex thermal environment of the blast furnace, material fluctuations, and measurement disturbances are uniformly described by the diffusion term. At the same time, the maximum likelihood estimation method is used to identify the model parameters, and the optimal model structure is adaptively selected by combining the Akaike information criterion, thereby explicitly introducing noise and memory effects in the modeling stage. In steps 3–6, when new temperature measurement data is detected online, the prediction error between the measured value and the model prediction value is compared to assess the adaptability of the current degradation model to the actual degradation process in real time, and a calibration triggering mechanism based on the prediction error is constructed accordingly. When the prediction error is within a preset threshold range, particle filtering is used to estimate the potential degradation state online, and the model parameters are continuously corrected through a Bayesian update strategy, thereby achieving smooth tracking of degradation state and parameters in a noisy environment, demonstrating the model's robustness to random disturbances. When the prediction error exceeds the threshold and triggers the calibration mechanism, it is determined that the blast furnace operating conditions or degradation mechanism have changed significantly. By calibrating the model structure or key parameters, the modeling deviation caused by sudden changes in operating conditions, thermal field evolution, or degradation mechanism changes is compensated, thereby achieving adaptive modeling of non-stationary, strongly coupled degradation processes. Through the above online calibration and parameter update mechanism, in steps 7–8, the probability distribution of remaining life can be derived and updated in real time based on the latest degradation model, achieving a fine characterization of the complex degradation behavior of the blast furnace system, thereby significantly improving the accuracy and reliability of remaining life prediction.

[0087] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for calibrating a blast furnace degradation model and predicting its remaining life under noise conditions, characterized in that, Includes the following steps: Step 1. Acquire temperature data collected by thermocouples at different locations in the blast furnace system and perform preprocessing; Step 2. Based on the collected temperature data, construct an initial degradation model of the blast furnace wall; The initial degradation model incorporates a measurement error term, while the evolution of the furnace wall degradation thickness is indirectly characterized by a drift term, and the diffusion term is used to describe the inherent randomness and uncertainty of the system. The parameters of the initial degradation model were identified based on the maximum likelihood estimation (MLE) method, and the optimal model structure for the temperature change of the blast furnace system was determined by using the Akaike Information Criterion (AIC). Step 3. When new measurement data is detected online, compare the new measurement data with the predicted value of the current degradation model and calculate the prediction error of the model; at the same time, determine whether the predicted time of the blast furnace system's remaining life (RUL) has been reached. When the predicted time is reached, the RUL prediction of the blast furnace system is performed based on the current degradation model; Step 4. Based on the model prediction error value, construct a threshold-based model calibration trigger mechanism to determine the calibration method for the degraded model; if the mechanism is not triggered, proceed to step 5; if the mechanism is triggered, proceed to step 6. Step 5. Use a particle filter to estimate the potential degradation state of the blast furnace system, and use the Bayesian method to update the degradation model parameters. Then return to step 3 until the predicted time of RUL is reached. Step 6. Construct a prediction error model and calibrate the degradation model to compensate for the impact of changes in operating conditions or the evolution of degradation mechanisms during blast furnace operation. Then return to step 3 until the predicted time of RUL is reached. Step 7. Derive the analytical expression for the RUL probability density and update the parameters of the calibrated degradation model in real time based on the new measurements; Step 8. When the predicted time of the RUL of the blast furnace system is reached, predict the RUL of the blast furnace system according to the calibrated degradation model.

2. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 1, characterized in that, Step 2 specifically involves: Step 2.

1. Construct an initial degradation model for the blast furnace wall; An initial degradation model based on fractional Brownian motion is constructed, as shown in the following formula: (1) in This represents the potential degradation state of the blast furnace system, which is affected by fractional Brownian motion. Driven by; A drift term with temperature control; initial degradation level. ; The diffusion term characterizes the uncertainty of temperature changes; The proportional parameter representing the rate of temperature change is the drift term coefficient of the initial degradation model; This is an unknown parameter vector used to describe the time-varying characteristics of blast furnace temperature; This represents the drift term function that indirectly reflects the level of furnace wall degradation. Indicates the time integral factor; set up This represents the vector of unknown parameters in the initial degradation model; in , , Unknown parameters for controlling the degradation level of blast furnace walls; Without model calibration, the measured temperature values ​​of the blast furnace system are... Potential degenerative state at any moment The relationship between them is as follows: (2) in This represents the temperature measurement value of the blast furnace system. , This indicates the measurement error caused by sensor noise and external interference. Step 2.

2. Identify the initial degradation model parameters based on the MLE method; for In the given thermocouples Temperature data for the day The log-likelihood function under the given conditions is The calculation formula is as follows: (3) in This indicates the number of thermocouple sensors in the blast furnace. This indicates the number of days for which data is needed to determine the model parameters; , Is the order of The identity matrix, Representing fractional Brownian motion The covariance matrix, Indicates measurement error The variance; Represents the drift term coefficient Uncertainty Represents the drift term coefficient The mean; Indicates the current thermocouple, This indicates that the current thermocouple order is Temperature increment measurement value; It is a function of temperature change; make ,but , , Indicates the first At any given moment; among them The mean is variance is Gaussian distribution; Calculation formula (3) about and The first partial derivatives, and setting the first partial derivatives to zero, yield: (4) in , They are respectively , The maximum likelihood estimate, for The estimated value; The covariance matrix representing the standard fraction Brownian motion is expressed as follows: ； in The covariance operator is represented. Represents the Hearst exponent in the fractional Brownian motion covariance matrix; and They represent and Fractional Brownian motion at time step; Substituting formula (4) into the log-likelihood function in formula (3), we get: (5) in for The maximum likelihood estimate, This indicates that the parameter vector is obtained. The maximum likelihood estimate is the value of the log-likelihood function; definition , They are respectively , The estimated value; , , and The MLE is obtained through a multidimensional search method; The solution , , and Substituting into formula (4), we get and The value of ; Step 2.

3. Use AIC to determine the optimal model structure for temperature changes in the blast furnace system; The error model is determined based on the minimum AIC value. The formula for calculating the AIC value is as follows: (6) in Indicates the number of model parameters; Based on this, the model's goodness of fit and complexity are comprehensively weighed by calculating the AIC value corresponding to different candidate model structures. Specifically, for different drift term function forms and Parameters are estimated separately, and the corresponding AIC values ​​are calculated. The model with the smallest AIC value is selected as the optimal model structure.

3. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 2, characterized in that, In step 3, the prediction error of the model, i.e. the deviation between the predicted value and the actual temperature data, is calculated using the following formula: (7) in Indicates the first Temperature measurements of the blast furnace system after the second calibration. Indicates the first The predicted values ​​of the degradation model after subcalibration are defined. ,but Indicates the first Secondary prediction error data This indicates the mean operation; Indicates the first At that moment, Indicates completion The time of the next calibration; No. Prediction error model during sub-calibration The expression is: (8) in Indicates triggering the first Next model calibration time Indicates the first The coefficients of the drift term in the prediction error model of the second calibration. Indicates the first The drift term function of the prediction error model for the second calibration; Indicates the first The unknown parameter vector of the drift term function in the prediction error model of the second calibration. Indicates the first The diffusion term coefficients of the prediction error model after secondary calibration. Represents standard Brownian motion. .

4. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 3, characterized in that, In step 4, the threshold in the model calibration triggering mechanism is defined as follows: Blast furnace wall degradation model after After the first calibration, the parameters are: ,in , Representing the initial degradation model and the first degradation model respectively. The unknown parameter vector in the degraded model after secondary calibration; Define the actual temperature measurement data of the blast furnace wall as ; Model predicts data at time intervals Within the prediction error and This is unrelated to the previous events; definition Time-based blast furnace system degradation model structure calibration threshold as follows: (9) in Indicates the adjustment coefficient; This indicates the uncertainty inherent in the measured blast furnace temperature. This indicates the uncertainty of the blast furnace wall degradation model; , , The kernel function representing fractional Brownian motion. Indicates the total number of fractions; This indicates the uncertainty of the prediction error model. Indicates the first The coefficients of the diffusion term in the prediction error model after the second calibration.

5. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 4, characterized in that, In step 4, the model calibration triggering mechanism is specifically as follows: Step 4.

1. Enter the first... Prediction error data after the second calibration; Step 4.

2. Set the number of model calibration triggers. Initialize to zero; Step 4.

3. Determine the range of prediction error. traversal prediction error , ; in Indicates triggering the first -1 model calibration time, This indicates the necessary time length for identifying the prediction error model; Step 4.

4. If Out of range ,but: ， ； And return to step 4.3; Otherwise, return to step 4.2 and initialize. To prevent a single outlier from falsely triggering calibration; when At that time, the degradation model of the blast furnace wall was recorded. Next trigger calibration time And calibrate the blast furnace wall degradation model until the predicted time of remaining life is reached; if Not outside the range The blast furnace wall degradation model does not require calibration; Step 4.

5. Output trigger Secondary model calibration time Or the model does not require functional calibration at this moment.

6. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 5, characterized in that, Step 5 specifically involves: Step 5.

1. To estimate the potential degradation state of the blast furnace system, the state-space model is constructed as follows: (10) in Indicates the number of times the degraded model structure has been calibrated; express The potential degradation status of the blast furnace system at all times; Represents the initial degradation model The drift term coefficient at time step, Indicates the first The coefficients of the drift term in the prediction error model of the second calibration. Indicates the first Temperature measurements of the blast furnace system after the second calibration. for exist The realization of a moment; Step 5.

2. Use a particle filter to estimate the potential degradation state of the blast furnace system; Step 5.

3. Update the parameters of the degenerate model using the Bayesian method; Step 5.

4. When the blast furnace system degradation model triggers a new calibration or reaches the RUL prediction time, stop the estimation of potential degradation state and the updating of model parameters.

7. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 6, characterized in that, Step 5.2 specifically involves: Step 5.2.

1. Initialize the potential degradation state of the blast furnace temperature; The initial temperature probability density of the blast furnace system is obtained according to formula (10). ,right Sample generation of particles And according to the weights corresponding to the particles Weighting; in , , Indicates the number of particles. Indicates particle-based The posterior probability density, This indicates the current temperature measurement value of the thermocouple; Indicates the current potential degradation state. The first potential degradation state generated by the current state. One particle; Step 5.2.

2. Update the potential degradation state of the blast furnace system according to the state transition equation; According to the state transition equation of the blast furnace system in formula (10), new particles are generated: ； in express The potential state of degradation at any given moment. , They represent the first Individual particles and The value at time; Step 5.2.

3. Update particle weights; When a new temperature measurement is obtained, the weights corresponding to the particles are calculated. ;in , , They represent and Time of the first The weight of each particle; Then, weight normalization is performed: ; in This represents the normalized weights; Step 5.2.

4. Resampling; If the effective number of particles is lower than the threshold ,Right now Then the particle weights need to be initialized: ; in This indicates the percentage of effective particles. Indicates the number of resampling steps. The value of each particle; Step 5.2.

5. Estimate the potential degradation state of the blast furnace system based on the current particle and its corresponding weight. for: 。 8. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 7, characterized in that, Step 5.3 specifically involves: In the time interval Above, observed increment satisfy: ； in, These are the drift term coefficients of the current degradation model; The drift term function represents the initial degradation model. ; The drift term function represents the current prediction error model; ; express The implementation of noise in the current degradation model at any given moment; Therefore, conditional probability ; in ; ; Overall likelihood ;in This represents a set of historical temperature measurements. According to Bayes' theorem: (11) in express The prior probability; Taking the logarithm of formula (11) and expanding it, the result is as follows: The quadratic form is rearranged to obtain: ； Where C represents the irrelevant term of the drift term coefficient in the initial degradation model. This indicates the actual temperature of the blast furnace at... arrive Increment of time; As can be seen from the standard form of the Gaussian distribution, the posterior distribution is still a Gaussian distribution. Based on the potential degradation state of the blast furnace system, the drift term coefficients of the degradation model are updated. Its expression is as follows: ； ； in The mean is variance is The Gaussian distribution.

9. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 1, characterized in that, Step 6 specifically involves: The blast furnace system in the The prediction error model during the next calibration period is as follows: Its likelihood function is: (12) in , ; , ; ; ； ； express No. Line number Column elements; Indicates the use of the first Time series of prediction error model parameter identification; A collection of prediction error data; , Indicates the time when the covariance is calculated; Based on formula (12), the MLE method is used to obtain the first... The unknown parameter vector of a prediction error model ; Assuming the degradation model is at the current time Calibrated Next, then the first Degenerate model after secondary calibration Represented as: (13) in It is an indicator function, when hour, The value is 1, otherwise It is 0.

10. The method for calibrating the blast furnace degradation model and predicting its remaining life under noise conditions according to claim 1, characterized in that, Step 7 specifically involves: No. Degenerate model after secondary calibration Including fractional Brownian motion and Brownian motion, assuming its drift term is in If it is continuous in time, then it is continuous in time. Given the known temperature measurements of the blast furnace system and a set of estimated parameters, RUL is defined as: ； in Thermocouple measuring components The moment when the corresponding potential degradation state first exceeds the threshold, Indicates in The remaining lifespan at that location, This represents a predefined fault threshold. Indicates the predicted potential degradation state; Denotes the infimum of a set; RUL probability density function Represented as: ； in, ; express The diffusion coefficient approximated by the initial degradation model at time . Indicates the first Coefficients of the diffusion term in the prediction error model; Represents a set of known parameters. express The set of all temperature measurements after the first calibration; ； ； Represents the differential form of the drift term function in the initial degradation model; ； in This represents the differential form of the drift term function in the prediction error model; ； If calibration times If the initial degradation model is accurate, the degradation model can be transformed into a continuous degradation process model without the need for model calibration. If calibration times If the value is a positive integer, then the initial degradation model is inaccurate, and the degradation model is converted into a calibration model. The model continuously degrades over time, and the parameters of the calibrated degradation model are updated in real time based on new temperature measurements.

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