Method and device for data processing for automatically adjusting parameters in a mathematical model

Abstract

The present invention describes a method and a device for data processing for automatically adjusting parameters in a mathematical model. The technical problem consists in improving a computer-implemented method for automatically adjusting parameters in a mathematical model for the monitoring and / or open-loop / closed-loop control of a production process for steelmaking, said improvement being achieved by optimizing parameters. Input variables comprising at least one measured value are fed into the mathematical model, and the mathematical model outputs output variables that are used for the monitoring and / or open-loop / closed-loop control of the production processes. The technical problem is solved in that the input variables and the parameters are recorded at least in part, wherein operands comprise at least one process variable, for which measurands are also available. A cost function of differences is determined which evaluates the deviation between said measurands and the corresponding operands, with a sensitivity vector being determined from the cost function of differences and from the parameters. By means of an optimization method, parameters are determined progressively such that the cost function of differences is minimized.

Description

[0001] Description

[0002] Title of the invention

[0003] Method and device for data processing for the automatic adaptation of parameters of a mathematical model

[0004] field of technology

[0005] The described invention is in the field of computer-implemented mathematical models for monitoring and / or controlling steel production processes.

[0006] Input variables, including measured variables, are fed into the computer-implemented mathematical model. After performing calculation steps, output variables are output, which are used to monitor, control, and / or regulate the manufacturing processes.

[0007] Furthermore, the invention comprises a data processing system, a computer program product and a computer-readable storage medium.

[0008] State of the art

[0009] Electric arc furnaces (EAF), blown oxygen converters (BOF) or argon-oxygen decarburization (AOD) are often used in metallurgical manufacturing processes in the steel industry.

[0010] For example, to optimize the supply of electrical power to an EAF during operation or to monitor and / or control various process variables, a so-called process optimization system is used.

[0011] The process optimization system can include monitoring / controlling / regulating the temperature, the chemical composition of the melt, power consumption, and the introduction of materials. Both sensors and mathematical models are used to capture the process status. Mathematical models are particularly useful when measurement technology is unable to capture process parameters with the required quality.

[0012] Based on the collected process data, the metallurgical manufacturing process is controlled / regulated in real time. This can, among other things, improve production efficiency and the quality of the final product, reduce energy consumption and emissions, and increase production yield.

[0013] The mathematical models used in process optimization systems use parameters. These parameters can be used to adjust a model to maximize prediction accuracy and ensure the model reflects reality as accurately as possible. Therefore, it is particularly important that these parameters are adjusted or optimized accordingly.

[0014] RICHARD DM MACROSTY ET AL: "Dynamic Modeling of an Industrial Electric Arc Furnace," INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol. 44, No. 21, October 1, 2005 (2005-10-01), pages 8067-8083, describes a mathematical model of an electric arc furnace. Parameter estimation is performed based on measured data.

[0015] TAKANO YUI ET AL: "Iterative Feedback Tuning for Regulatory Control Systems Using Identified Sensitivity Functions via Predictive Error Method", 2022 61 ST ANNUAL CONFERENCE OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS (SICE), THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS - SICE, 6 September 2022 (2022-09-06), pages 46-51 proposes an iterative principle for tuning parameters of a control system aiming to optimize a cost function.

[0016] ZHANG ZHUOLUN ET AL: "Deep learning-based prediction framework of temperature control time for wide-thick slab hot rolling production", EXPERT SYSTEMS WITH APPLICATIONS, ELSEVIER, AMSTERDAM, NL, Vol. 227, April 19, 2023 (2023-04-19) describes a deep learning-based prediction framework for the temperature control time of hot rolling processes.

[0017] Starting from standard values, the parameters used can be adjusted using techniques such as trial and error.

[0018] Typically, this adjustment takes place during plant commissioning during a so-called "tuning phase".

[0019] The goal of the tuning phase is to find the best parameter set to minimize the deviation between the model predictions and the actual plant condition and thus improve the prediction accuracy of the mathematical model.

[0020] However, the tuning phase is time-consuming, expensive, and can only be performed on the system itself. Summary of the invention

[0021] Metallurgical manufacturing processes utilize process optimization systems that incorporate mathematical models that simulate real physical and chemical processes. These models contain specific parameters whose adjustment or optimization is intended to replicate reality as accurately as possible. These parameters are partially plant-dependent and therefore must be determined anew for each plant.

[0022] The object of the invention is to provide a computer-implemented method which automatically adapts the mathematical model to the existing conditions and processes.

[0023] At least one, preferably at least five input variables are fed to the computer-implemented method, where at least one, preferably at least three input variables is / are a measured variable of a process variable. Then, calculations are carried out using calculated variables, and finally, the mathematical model outputs output variables. The parameters influence the calculations and thus the calculated variables and output variables. Examples of parameters are material-specific correction values ​​for specific enthalpies of input materials. In this case, these are differences between the values ​​of specific enthalpies that are actually used for the calculations and their theoretical values. After optimization of the parameters, the calculated results of the mathematical model lead to the smallest possible deviations between the existing measured values ​​of process variables and the corresponding calculated variables.One such process variable is, for example, the temperature of a melt. "Accordingly" means that measured values ​​and calculated values ​​are available for a specific process variable, which can be compared or subtracted.

[0024] The problem is solved by at least partially recording the input variables and the parameters, whereby the calculated variables include at least one process variable for which measured variables are also available.

[0025] Furthermore, at least one cost function of differences is determined, which evaluates the deviation between these measured variables and the corresponding calculated variables.

[0026] A sensitivity vector is determined from the cost function of differences and the parameters, which indicates how the parameters influence the cost function of differences. New values ​​for the parameters of the mathematical model are then determined using an optimization procedure that utilizes the sensitivity vector in such a way that the cost function of differences is minimized. The basis for automatic parameter adjustment is recorded process data. This data is available in the form of measured variables as a function of time, such as electrical energy input, process gas consumption, etc., or as values ​​from individual measurements or input values, such as measured temperatures or scrap basket load.

[0027] In order to obtain a quantitative statement about the influence of certain parameters on the calculated values ​​of the mathematical model, the calculation of a sensitivity vector can be carried out.

[0028] The starting point for the optimization procedure is a cost function of differences, which is formed, for example, from the difference between measured variables and calculated variables of process variables.

[0029] For example, if a temperature model is considered, the cost function J of differences can be calculated as

[0030] J = (T(p) - T meas ) 2 (Equation 1)

[0031] Here, T(p) describes a calculated value of a temperature as a mathematical function of a parameter vector p and T meas a measured value of this temperature.

[0032] This temperature for a next journal can be represented as a mathematical function f of the temperature of the current time step and the parameter vector p with

[0033] T k+ i(p) = f(T k (p),p) (Equation 2)

[0034] Thus, the sensitivity of this calculated temperature can be expressed as a mathematical function of the parameter vector p with respect to the parameter for the next journal can be calculated as (equation 3)

[0035] At the time of measurement, the sensitivity of the cost function of differences is given by (Equation 4)

[0036] If further parameters are considered, further sensitivities follow, which are represented in a sensitivity vector.

[0037] Analogously, other computational variables or their corresponding measured variables can be incorporated into the calculation of the cost function of differences. Instead of scalar variables, vectors of computational variables and measured variables are used, and a vector norm is calculated before applying the square.

[0038] Furthermore, multiple cost functions of differences can be calculated, with each of these cost functions of differences depending on its own set of parameters. The described calculation method is performed sequentially for all cost functions of differences. Further calculation variables and cost functions of differences can be defined, for example, in connection with modeling the concentration of elements such as carbon or phosphorus in steel.

[0039] For example, using a gradient method, the parameters can be adjusted step by step to minimize the cost function of differences. One possible parameter adjustment is the steepest descent method with (Equation 5) where Ap represents a stepwise change in the respective parameters and p represents a step size. Such an optimization step can be performed in any journal, preferably when a new measured value is available. p is also referred to as the learning rate below.

[0040] The learning rate indicates how quickly a model parameter is adapted to the respective process situation. If the learning rate is set too high, the calculation method can become unstable. It is also called the sensitivity vector and indicates how strongly a change in certain parameters affects the change in the cost function of differences. This approach allows for multidimensional evaluation. For example, if several parameters influence the result, this is taken into account. Parameters with a smaller influence on the result are given less weight by the sensitivity vector.

[0041] In an advantageous embodiment, the mathematical model simulates real physical and chemical processes and comprises equations, wherein the sensitivity vector is preferably determined repeatedly, wherein the determination comprises an evaluation of equations analytically derived from the mathematical model.

[0042] Again and again means that the investigation is carried out at least on certain journals.

[0043] In an advantageous embodiment, the parameters of the mathematical model are at least partially loaded from a data storage device and / or are at least partially stored in a data storage device after application of the optimization method. This makes it possible to utilize both individual parameters and sets of parameters that have already been optimized in the past and use them for the manufacturing process. These parameters or sets of parameters can also be used for future applications of the manufacturing process or further optimized.

[0044] In a further advantageous embodiment, the computer-implemented method can be carried out online and / or offline.

[0045] If the computer-implemented method is used online, i.e. during the manufacturing process to monitor / control / regulate the same, a continuous step-by-step optimization of the parameters of the mathematical model can be carried out.

[0046] If the computer-implemented method is executed offline and immediately after completion of a melt, the measurement data belonging to a melt can first be analyzed and checked for plausibility, completeness and erroneousness.

[0047] For example, if two measurements taken in quick succession differ significantly from each other, the measurement data from that melt would not be used to calculate the parameters, especially if they would have a significant impact on the parameters. This also allows for continuous, step-by-step optimization of the parameters of the mathematical model.

[0048] Furthermore, the computer-implemented process can also be executed offline, independent of the manufacturing process. The parameters determined in this way can be stored in the data storage and thus made available for online execution of the mathematical model.

[0049] In a further advantageous embodiment, the method for optimizing the parameters of the mathematical model is carried out by minimizing the cost function of differences using a gradient method.

[0050] In a further advantageous embodiment, the method for optimizing the parameters of the mathematical model is carried out by minimizing the cost function of differences using the steepest descent method according to equation 5.

[0051] In a further advantageous embodiment, the change in the parameters per optimization step can be amplified or attenuated according to equation 5 via a so-called learning rate in the sense of a step size.

[0052] In a further advantageous embodiment, the production process for liquid steel production involves the operation of an electric arc furnace or a converter for steel production. In a further advantageous embodiment, the mathematical model is a model that models the temperature in a melt and / or the carbon concentration in a melt and / or the phosphorus concentration in a melt as process variables.

[0053] In a further advantageous embodiment, the parameters of the mathematical model for calculating the carbon concentration in the melt comprise one or more correction factors that describe the allocation ratio of oxygen introduced into the steelmaking process to carbon present in the steel bath for calculating an oxidation reaction.

[0054] These correction factors can be defined globally, i.e. the same for the entire range of possible carbon concentrations in the steel, or differently for specific ranges of carbon concentrations in the steel.

[0055] In a further advantageous embodiment, the parameters of the mathematical model for calculating the temperature in the melt include material-related additive correction values ​​for specific enthalpies of the substances used.

[0056] In a further advantageous embodiment, the parameters of the mathematical model for calculating the temperature in the melt include correction factors for heat losses and / or energy input. The correction factors can be defined globally, i.e., the same for the entire duration of the production process in the electric arc furnace, or differently for specific time periods of the production process.

[0057] In a further advantageous embodiment, the process variables of the mathematical model include heat losses due to thermal radiation from a melt to a furnace lid and / or an irradiated area of ​​a furnace wall.

[0058] A further object of the invention is to provide a data processing device / system comprising means for automatically adapting parameters of a mathematical model for monitoring and / or controlling / regulating a steelmaking process according to claims 1-12.

[0059] The object of the invention is also achieved by a computer program product which

[0060] Includes instructions which, when the program is executed by a computer, cause the computer to carry out the method / steps of the method according to claims 1-12.

[0061] Furthermore, the object is achieved by a computer-readable storage medium which comprises instructions which, when executed by a computer, cause the computer to carry out the method / steps of the method according to claims 1-12.

[0062] Short description of the drawings

[0063] The above-described properties, features, and advantages of this invention, as well as the manner in which they are achieved, will become clearer and more readily understood in connection with the following description of an embodiment, which is explained in more detail in conjunction with the drawings.

[0064] Fig 1 is a block diagram of a computer-implemented method for automatically adjusting parameters of a mathematical model 4 for monitoring and / or controlling a steelmaking process.

[0065] Description of the embodiments

[0066] Fig. 1 shows an embodiment of a computer-implemented method 1 for automatically adapting parameters 10 of a mathematical model 4 for monitoring and / or controlling / regulating 9 a steel production process.

[0067] At least one input variable 3 is fed to the mathematical model 4, wherein at least one input variable is a measured variable 2 of a process variable, and it outputs output variables 8. Typical input variables 3 can, for example, include time-varying measured values ​​of an electrical energy input or of the consumption of process gases. Other input variables can also be measured values ​​from specific individual temperature measurements or describe a scrap basket load. The input variables 3 can also contain further information such as setpoints for specific process variables. The schematic representation in Fig. 1 shows that the input variables are split into measured variables 2 and other input variables. The other input variables are fed to the mathematical model 4. The measured variables 2 refer to process variables for which calculated variables 5 of the mathematical model are also available. The measured variables 2 in Fig.1 therefore only form a subset of the input variables 3. The measured variables 2 subsequently play an important role, since they are compared with calculated variables 5 of the mathematical model 4.

[0068] Furthermore, the mathematical model includes 4 parameters, 10 which are understood as setting values. With their help, the mathematical model can be used, for example, to adjust the extent to which the addition of certain substances causes a temperature change in the liquid metal.

[0069] The input variables 3 and the parameters 10 are at least partially recorded in the data memory 11. This makes it possible for parameters determined after parameter optimization to be stored there and available for future applications of the manufacturing process.

[0070] The mathematical model 4 performs calculations that are used to monitor and control / regulate the steel production process. To describe the chemical and physical processes of the production process, process variables are used that are expressed in the mathematical model 4 by calculated variables 5. An example of such a calculation is equation 6. For those process variables for which calculated variables 5 are calculated and measured variables 2 are available from the input variables 3, calculated and measured values ​​can be compared. The calculated variables 5 therefore include at least one process variable for which measured variables 2 are also available. This is used to determine a cost function of differences 6 according to equation 1, which evaluates the deviation between these measured variables 2 and the corresponding calculated variables 5.From the cost function of differences 6 and the current values ​​of parameters 10, it is determined how parameters 10 influence the cost function of differences 6. Equations 2-4 describe this calculation using a temperature model as an example. This calculation is performed in each optimization step as part of parameter optimization 7, with new values ​​for parameters 10 of mathematical model 4 being determined in such a way that the cost function of differences 6 is minimized.

[0071] Mathematical Model 4 comprises equations and formulas and describes five process variables using calculation parameters. One possible process variable is, for example, heat loss through thermal radiation to a furnace lid in the form of a heat quantity. An example of the part of mathematical model 4 used for this purpose follows:

[0072] Square° = A (Equation

[0073] Q™ describes 7a heat loss through thermal radiation to a furnace lid, A Eff,roof an effective portion of a furnace roof area, A stl a calculated surface area of ​​a melt, corr a correction factor, LossFactor a factor for heat losses as a parameter, e an emission factor of a slag, a the Stefan-Boltzmann constant, conv a conversion factor from joules to kilocalories, T Calc a calculated value of a temperature in a melt, T Effiroof a temperature of a furnace lid and At a time step size.

[0074] During parameter optimization 7, the LossFactor parameter and other parameters 10 of the mathematical model 4 are optimized. In doing so, a cost function of differences 6 is minimized. The calculation of the cost function of differences 6 includes calculated variables 5 and measured variables 2 of a process variable related to the heat loss through thermal radiation to the furnace lid Q™. 7In this way, parameters 10 of the mathematical model 4 can be found that best match the measured and calculated values ​​of the process variables with respect to the cost function of differences 6.

[0075] Although the invention has been illustrated and described in detail by the preferred embodiments, the invention is not limited by the disclosed examples and other variations can be derived therefrom by those skilled in the art without departing from the scope of the invention.

[0076] List of reference symbols

[0077] 1 Computer-implemented procedure

[0078] 2 measured variables

[0079] 3 input variables

[0080] 4 Mathematical model

[0081] 5 calculation values

[0082] 6 Cost function of differences

[0083] 7 Parameter optimization

[0084] 8 output variables

[0085] 9 Monitoring, control, regulation

[0086] 10 parameters

[0087] 11 Data storage

Claims

Claims 1. A computer-implemented method (1) for automatically adapting parameters (10) of a mathematical model (4) for monitoring and / or controlling / regulating (9) a steel production process, wherein dynamic processes of the production process are described in the mathematical model (4) using process variables, characterized in that at least one, preferably at least five input variables (3) is / are supplied to the computer-implemented method (1), wherein at least one input variable, preferably at least three input variables, is / are a measured variable (2) of a process variable, and the mathematical model (4) comprises calculation variables (5) for calculating further process variables, and the mathematical model (4) outputs output variables (8), wherein the parameters are setting values ​​that influence the mathematical model, wherein the input variables (3) and the parameters (10) are at least partially recorded,wherein computational variables (5) comprise at least one process variable for which measured variables (2) are also available, wherein at least one cost function of differences (6) is determined which evaluates a deviation between these measured variables (2) and the corresponding computational variables (5), wherein at least one sensitivity vector is determined from the cost function of differences (6) and the parameters (10), which indicates how the parameters (10) influence the cost function of differences (6), and new values ​​for the parameters (10) of the mathematical model (4) are determined with the aid of an optimization method (7) using the sensitivity vector in such a way that the cost function of differences (6) is minimized.

2. The method according to claim 1, wherein the mathematical model simulates real physical and chemical processes and comprises equations, wherein the sensitivity vector is preferably determined repeatedly, wherein the determination comprises an evaluation of equations derived analytically from the mathematical model.

3. Method according to claim 1 or 2, wherein the parameters of the mathematical model are at least partially loaded from a data memory (11) and / or are at least partially stored in the data memory (11) after application of the optimization method.

4. Method according to claims 1 - 3, wherein the computer-implemented method (1) can be carried out online or offline.

5. Method according to claims 1 -4, wherein the parameter optimization (7) is carried out by minimizing the cost function of differences (6) by means of a gradient method.

6. Method according to claims 1-4, wherein the parameter optimization (7) is carried out by minimizing the cost function of differences (6) by means of the method of steepest descent, wherein the change in the parameters (10) is preferably amplified or attenuated for each optimization step by selecting a step size, wherein this step size defines a learning rate.

7. A process according to claims 1-6, wherein the production process is a liquid steel production process, particularly preferably a process for operating an electric arc furnace, preferably a process for operating a converter for steel production.

8. Method according to claims 1 - 7, wherein the mathematical model (4) is a model that models the temperature in a melt and / or the carbon concentration in a melt and / or the phosphorus concentration in a melt.

9. The method according to claim 8, wherein the parameters (10) of the mathematical model (4) for calculating the carbon concentration in the melt comprise one or more correction factors which are the same for the entire range of possible carbon concentrations in the steel or different for specific ranges of carbon concentrations in the steel, which describe the allocation ratio of an oxygen introduced into the steelmaking process to a carbon present in the steel bath for the calculation of an oxidation reaction.

10. Method according to claims 1 - 9, wherein the parameters (10) of the mathematical model (4) for calculating the temperature in the melt comprise material-related additive correction values ​​for specific enthalpies of substances used.

11. Method according to claims 1-10, wherein the parameters (10) of the mathematical model (4) for calculating the temperature in the melt comprise correction factors for heat losses and / or energy input that are the same for the entire duration of the production process or different for certain time periods of the production process.

12. Method according to claims 1 - 11, wherein the process variables of the mathematical model (4) comprise heat losses due to thermal radiation from a melt to a furnace lid and / or an irradiated area of ​​a furnace wall.

13. Device / system for data processing, comprising means for automatically adapting parameters (10) of a mathematical model (4) for monitoring and / or controlling / regulating (9) a steel production process according to claims 1 - 12 14. A computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the method / steps of the method according to claims 1-12.

15. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the method / steps of the method according to claims 1-12.

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