A method for estimating coordinates of temperature measurement points of an isar furnace outer wall temperature field

Abstract

The application discloses a kind of for isasa furnace outer wall temperature field temperature measurement point coordinate estimation method, belong to industrial process measurement and control technical field.It includes the following steps: S1, collection isasa furnace relevant data;S2, collection outer wall temperature measurement point measured temperature time series and temperature measurement point prior installation information;S3, establish three-dimensional transient temperature field mathematical model;S4, obtain temperature distribution on the surface of furnace wall;S5, generate a finite number of spatial coordinate positions for each temperature measurement point to be calibrated;S6, extract simulation temperature time series;S7, establish joint calibration objective function and solve;S8, output the coordinate confidence of each temperature measurement point;S9, establish parameter correction objective function and solve to generate corrected outer wall temperature field.The application takes temperature measurement point coordinates as the object to be identified, realizes temperature measurement point position reverse calibration through candidate coordinate library and temperature time series matching, and can solve the data space corresponding problem under the condition of drawing loss, temperature measurement point migration and temperature measurement point account incompleteness.

Description

Technical Field

[0001] This invention relates to the field of industrial process measurement and control technology, specifically to a method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace. Background Technology

[0002] The Isa furnace is a key thermal equipment in the continuous smelting process of non-ferrous metals such as copper. The furnace interior is constantly subjected to complex thermal effects, including high temperatures in the molten pool, flue gas scouring, radiative heat transfer, exothermic chemical reactions, material disturbance, and reaction zone migration. The furnace wall temperature field exhibits significant non-uniformity and dynamic variation in both time and space. Temperature measurement data from external wall points are crucial for assessing the furnace lining heat load, localized overheating, lining erosion, and operational safety.

[0003] In actual industrial settings, ISA furnaces typically have several infrared thermometers, thermoelectric thermometers, or online temperature measuring devices installed on their outer walls to collect the temperature of the furnace surface. However, due to the long operating cycles of ISA furnaces, which involve multiple maintenance, replacements, modifications, and relocations of thermometers, problems often arise such as lost historical drawings, incomplete installation records of thermometers, and unclear correspondence between thermometer numbers and their actual spatial locations. In such cases, only the thermometer numbers and their corresponding temperature time series can be obtained on-site, but the accurate circumferential angular position and axial height position of each thermometer on the furnace outer wall cannot be determined.

[0004] The lack of temperature measurement point coordinates directly affects the reliability of temperature field modeling and parameter correction. If the actual coordinates of the temperature measurement points are unknown, and the simulated temperature is still extracted from the temperature field model based on empirical, nominal, or manually estimated positions, the model sampling location and the actual measurement location may be inconsistent. This means that the error between the measured and simulated temperatures will no longer only originate from heat transfer parameter errors but also include temperature measurement point coordinate errors. In this case, directly identifying boundary heat flux, furnace wall heat absorption coefficient, thermal conductivity parameters, or reaction heat distribution parameters can easily lead to the coordinate errors being incorrectly attributed to model parameter errors, resulting in miscalibrated model parameters and reduced physical reliability of the temperature field model.

[0005] For the Isa furnace, the furnace wall generally has a cylindrical shell structure, and the temperature measuring points on the outer wall are usually distributed on several observation sides or at different heights. The furnace wall, along its thickness, comprises a three-layer structure: a refractory working layer, an insulation layer, and a steel shell layer. The thermal effects within the furnace are also influenced by factors such as the molten pool zone, the flue gas zone, the moving hotspots in the reaction zone, fluctuations in oxygen supply, fuel fluctuations, and changes in materials. Therefore, relying solely on the average temperature of a single measuring point, the similarity of a single temperature curve, or estimation based on manual experience is insufficient to reliably determine the actual spatial coordinates of the measuring points.

[0006] Therefore, it is necessary to propose a method for estimating the coordinates of temperature measuring points on the outer wall of the Isa furnace when the coordinates of these points are missing. Summary of the Invention

[0007] To address the problems existing in the prior art, the present invention provides a method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: A method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace is provided, comprising the following steps: S1. Collect relevant data of the Isa furnace, including geometric structure data, furnace wall material parameter data and industrial operating condition data, and calculate the equivalent heat of reaction; S2. Collect the time series of measured temperatures at the external wall temperature measurement points and the prior installation information of the temperature measurement points; S3. Establish a three-dimensional transient temperature field mathematical model of the three-layer furnace wall, including the heat conduction control equation, interlayer interface conditions, inner wall mixing heat flow boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary. S4. Input the geometric structure, furnace wall material parameters and equivalent reactive heat obtained in S1 into S3. Use the numerical discretization method to mesh the spatial domain and step through the time domain to solve for the temperature distribution on the outer surface of the furnace wall. S5. Based on the prior installation information of the collected temperature measurement points, generate a finite number of possible spatial coordinate positions for each temperature measurement point to be calibrated. S6. From the temperature distribution on the outer surface of the furnace wall obtained in S4, extract the corresponding simulation temperature time series for each candidate coordinate constructed in S5, and establish the mapping relationship between the candidate coordinates and the simulation temperature series. S7. Using measured temperature time series and candidate coordinates to simulate temperature series, a joint calibration objective function is established through three levels: single-point matching, multi-temperature point related structural constraints, and template layout prior constraints. The optimal spatial coordinates of each temperature point are solved through discrete optimization. S8. Construct a model parameter perturbation group to perturb the parameters in the temperature field mathematical model of S3. Repeat S4 to S7 to evaluate the stability of the calibration coordinates of each temperature measurement point under different model parameter conditions, and output the coordinate confidence of each temperature measurement point. S9. Fix the coordinates of temperature measurement points with a confidence level higher than the preset threshold as reliable observation positions, establish a parameter correction objective function, solve the objective function and substitute it into the temperature field mathematical model to generate the corrected outer wall temperature field, and complete the estimation of the coordinates of the temperature measurement points on the outer wall of the Isa furnace.

[0009] Furthermore, the specific content of the collected data in S1 includes: S1.1 Geometric Structure Data Acquisition The outer wall of the Isa furnace is approximately a cylindrical shell structure, and the radius of the outer wall is assumed to be... Circumferential angle is axial height is Then any position on the outer wall is represented as: S1.2, Data Acquisition of Material Parameters for Three-Layer Furnace Wall The Isa furnace wall comprises three material domains along its thickness: a refractory working layer, an insulation layer, and a steel shell layer. Physical property parameters of each of these layers were collected. For the first... l Layer material ( l =1,2,3), collect the corresponding density. (Unit: kg / m³), specific heat capacity (Unit: J / (kg·K)) and thermal conductivity (Unit: W / (m·K)).

[0010] S1.3 Industrial Operating Condition Data Acquisition Industrial operation data is collected for each shift cycle, including: oxygen input, air input, total sulfur, coal input, oil input, and mineral composition ratio. The cumulative output for each shift is converted into an average flow rate for that shift. Based on stoichiometry, the lower heating value of the fuel, and the furnace wall heat absorption ratio, the equivalent heat of reaction acting on the furnace wall is calculated. The specific conversion method is based on the principle of metallurgical thermochemical equilibrium, which is obtained by multiplying the input amount of each reactant by its respective enthalpy change and deducting heat loss.

[0011] Furthermore, the specific process of S2 is as follows: S2.1 Acquiring the measured temperature time series Installed on the outer wall of the Isa furnace N Each temperature measurement point (which can be an infrared temperature measurement point, a thermocouple temperature measurement point, or an online temperature measurement device) collects data. N Each temperature measurement point within the time interval t ∈[ t 0, t The measured temperature data within [1]. The measured temperature sequence of all temperature measurement points is arranged into a measured temperature matrix as follows: In the formula, i For temperature measurement point indexing, For the first i The measured temperature time series (column vector) at each temperature measurement point has a length equal to the number of time sampling points. Considering gain error, emissivity error, field-of-view averaging effect, and noise during the measurement process, the measured temperature... Represented as: in, This represents the correction factor related to the gain or emissivity of the temperature measurement point; This indicates that the temperature measurement point is offset; This represents measurement noise and unmodeled disturbances; This indicates the surface temperature of the outer wall of the temperature measuring point.

[0012] S2.2, Collect preliminary installation information of temperature measurement points (1) Observe the side: determine the first i To which observation plane does each temperature measuring point belong (e.g., relative to the northeast, southeast, or northwest side of the temperature measuring point), and to define the circumferential angular range of that temperature measuring point. .

[0013] (2) Height level range: Determine the height level based on the installation level of the temperature measuring point or on-site records. i Possible height range of each temperature measuring point This limits the range of candidate axial heights.

[0014] (3) Temperature measurement point numbering sequence and installation template: If there are design drawings or original installation plan (i.e. installation template), record the design relative position and spacing range between each temperature measurement point. If there is no complete template, use the temperature measurement point numbering sequence to determine the height arrangement order of the temperature measurement points on the same side.

[0015] The order of temperature measurement point numbers and the range of height levels are used to constrain the relative order of temperature measurement points on the same observation side when constructing candidate coordinates later.

[0016] This information does not include precise spatial coordinates, but it provides the possible spatial distribution range and relative positional relationship of each temperature measurement point.

[0017] It should be noted that the temperature measurement points of the Isa furnace are usually numbered according to specific spatial logic during the equipment design or installation phase. For example, the temperature measurement points on the same observation side are numbered consecutively, and the numbering order has a monotonic correspondence with the height position. Therefore, even if the precise spatial coordinate records are lost, the temperature measurement point numbers themselves still carry valuable relative spatial position information, which can be used as a priori constraints for subsequent coordinate calibration.

[0018] Furthermore, the specific process of S3 is as follows: A three-dimensional transient temperature field mathematical model of the three-layer furnace wall was established, including the governing equations, interlayer interface conditions, inner wall mixing heat flux boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary. S3.1 Establish the heat conduction control equations within each material layer domain. set up Indicates the temperature field of the furnace wall. r Radial coordinates, r ∈[ R in , R ], R in Let be the inner wall radius.R Let be the outer wall radius, for the The actual but unknown spatial location of each external wall temperature measuring point is represented as follows: in, For the first The circumferential angular position of each temperature measuring point For the first The axial height position of each temperature measuring point. The object to be estimated in this invention is the equivalent coordinate of each temperature measuring point. .

[0019] In the The three-dimensional transient heat conduction governing equations within the layered material domain are as follows: in, Represents the volumetric heat source term; For gradient operators; Let be the divergence form of the thermal conductivity term; for the refractory working layer, a volumetric heat source term is set according to the equivalent transformation of the heat source effect in the furnace; for the insulation layer and the steel shell layer, we can set: S3.2 Establish interlayer interface conditions At the interface between different material layers, since there is no energy accumulation and no additional heat source at the interface, the interlayer interface conditions must be satisfied, namely, temperature continuity and normal heat flow continuity, which can be expressed as: In the formula, T 1 and T 2 represents the temperatures on both sides of the interface. and The thermal conductivity of the materials on both sides of the interface; and These represent the temperature gradients along the normal direction on both sides of the interface; this condition ensures the physical continuity of heat flow transfer between the two layers of material.

[0020] S3.3 Establish the inner wall mixing heat flux boundary On the inner surface of the furnace wall, considering the convective heat transfer in the molten pool zone, the convective heat transfer in the flue gas zone, the high-temperature radiative heat transfer, and the exothermic effect of chemical reactions during the actual operation of the ISA furnace, the boundary of the mixed heat flow on the inner wall is uniformly represented as: in, Indicates the position of the inner surface of the furnace wall The total heat flux density experienced at time t; This refers to the convective heat flux density on the molten pool or flue gas side. This refers to the radiative heat flux density of the high-temperature medium inside the furnace to the furnace wall. The heat flux of chemical reactions that occur and act on the furnace wall during processes such as feeding, oxygen supply, and oxidation-reduction. This represents a constrained dynamic compensation term used to describe reaction zone migration, oxygen supply deviation, fuel fluctuations, and unmodeled local thermal disturbances. The dynamic compensation term can be in the form of temperature-based PID feedback correction or use Kalman filtering to perform state estimation compensation for unmodeled thermal disturbances.

[0021] S3.4 Calculation of the spatial distribution of heat of chemical reaction The equivalent heat of reaction obtained from S1 is distributed to the inner surface of the furnace wall using a spatially normalized distribution function. The spatial distribution formula for the heat of chemical reaction is: in, Of the heat released by the metallurgical chemical reaction, the amount actually transferred to the inner surface of the furnace wall is at location [missing information]. and the heat flux density at time t; The furnace wall heat absorption coefficient; It is a spatial distribution function. Gaussian distribution, multi-hotspot seasonal distribution, or moving hotspot distribution that varies with operating conditions can be adopted, and the area normalization condition must be met. For effective heat-receiving area.

[0022] Chemical reaction thermal boundary term It is the boundary of mixed heat flow on the inner wall. One of the dominant factors directly reflects the spatial distribution characteristics of the heat source on the furnace wall during the Isa furnace smelting process.

[0023] S3.5 Establish the outer wall heat dissipation boundary The outer surface of the outer wall adopts a boundary for heat dissipation through natural convection and radiation with respect to the environment, as shown in the formula: in, The thermal conductivity of the outermost material; The external wall convective heat transfer coefficient; Emissivity of the outer wall; The Stefan-Boltzmann constant; The outer wall surface temperature, The ambient temperature.

[0024] S3.6 Establishing a complete boundary value problem for the temperature field By simultaneously solving the heat conduction control equations, interlayer interface conditions, inner wall mixing heat flux boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary, the temperature distribution throughout the entire furnace wall region is preferably obtained using the finite element method (or finite volume method / finite difference method) for numerical discretization and iteration. Take the outer wall surface. r = R The temperature value at that location is used as the continuous temperature field of the outer wall. The simulated temperature field used for subsequent temperature measurement point coordinate extraction is represented as follows: The specific process of S4 is as follows: The geometric dimensions acquired by S1 are... R、 Material parameters of each layer In steps S3.1-S3.5, the equivalent reaction zone is introduced, and the spatial domain is meshed using numerical discretization methods (such as the finite element method or the finite volume method). The time domain is then progressively advanced, and the outer wall surface is solved. r = R Temperature distribution at [location] .

[0025] Furthermore, the specific process of S5 is as follows: Based on the prior installation information of the collected temperature measurement points, a finite number of possible spatial coordinate positions are generated for each temperature measurement point to be calibrated, transforming the infinite search problem in continuous space into a discrete optimization problem on a finite number of candidate points.

[0026] For the i Temperature measurement points ( i =1,2,…, N Based on the observed side, determine the candidate circumferential angle range on the cylindrical surface of the furnace exterior. Based on the temperature measurement point number, installation level, nominal template, or on-site record obtained from S2, determine the candidate height range. Within the circumferential angle range According to the set resolution Discrete, in the height range According to the set resolution Discrete, Generate Candidate coordinate points: Construct a set of candidate coordinates for each temperature measurement point: in, For the first A set of candidate coordinates for each temperature measurement point; For the first Number of candidate coordinates for each temperature measurement point M The total number of candidate coordinates for each temperature measurement point; For the first The first temperature measurement point One candidate coordinate; The index of the candidate coordinates.

[0027] After generating candidate points, candidate points that do not meet the constraints of furnace structure, on-site installation conditions, or relative order of temperature measurement points on the same side are removed (for example, temperature measurement points on the same observation side should be arranged in order of number along the height, and the height of the later temperature measurement point should not be lower than that of the earlier temperature measurement point), thus obtaining the final set of candidate coordinates for each temperature measurement point.

[0028] Furthermore, the specific process of S6 is as follows: From the temperature distribution (continuous temperature field) on the outer surface of the furnace wall obtained from S4, the corresponding simulation temperature time series is extracted for each candidate coordinate constructed in S5, and a mapping relationship between "candidate coordinates and simulation temperature series" is established.

[0029] No. The first temperature measurement point The candidate coordinates are represented as follows: in, Located within the candidate angle range of the observation side of the temperature measurement point; It is located within the possible height range of the temperature measurement point.

[0030] For each candidate coordinate The continuous temperature field of the outer wall of the three-dimensional transient temperature field mathematical model of the three-layer furnace wall obtained from S4. Extract the corresponding simulation temperature sequence using the following formula: in, For the first i Each temperature measurement point is located at the candidate coordinates The simulated temperature time series at point S2 has the same time sampling points as the measured temperature series in S2. The time sampling points are kept consistent to ensure that the error calculation in S7 is comparable point by point.

[0031] For each temperature measurement point i All candidate coordinates m =1, 2, ..., Repeat the simulation temperature sequence extraction operation to obtain the set of simulation temperature sequences corresponding to all candidate coordinates. .

[0032] Furthermore, the specific process of S7 is as follows: After the model is established, coordinate estimation is performed. The estimation method of this invention includes candidate coordinate library construction, single-point temperature time series matching, consistency constraint of multi-temperature measurement point correlation matrix structure, template layout prior constraint, joint coordinate optimization, parameter perturbation robustness verification, and temperature field parameter correction after coordinate fixing.

[0033] Using the measured temperature time series of S2 and the simulated temperature series of candidate coordinates of S6, a joint calibration objective function is established through three levels: single-point matching, multi-temperature-point related structural constraints, and template layout prior constraints. The optimal spatial coordinates of each temperature-point are then solved by discrete optimization.

[0034] S7.1 Calculate the single-point candidate matching error Extracted simulation temperature sequence With measured temperature series Single-point matching is performed, and the single-point matching error includes temperature amplitude error, normalized shape error, time difference error, and time lag error.

[0035] S7.1.1 Temperature Amplitude Error The formula for directly comparing the difference in amplitude between simulated and measured temperatures is as follows: In the formula, Let L2 be the norm of the vector; For the first i The temperature measurement point is at the first m Temperature amplitude error at each candidate coordinate is used to measure the degree of similarity between two temperature curves in absolute amplitude.

[0036] S7.1.2, Normalized shape error To eliminate the influence of absolute temperature bias on matching, the two temperature series are first normalized for mean and standard deviation, and then their shape similarity is compared. The normalized shape error is expressed as: in, For the first i The temperature measurement point is at the first m Normalized shape error at each candidate coordinate; This indicates the mean and standard deviation normalization operation, used to reduce the impact of absolute temperature bias on the matching results.

[0037] S7.1.3, Time Difference Dynamic Error By comparing the rate of change (i.e., heating and cooling trends) of the simulated temperature series and the measured temperature series over time, the consistency of the dynamic change trend is constrained. The time difference error can be expressed as: in, For the first i The temperature measurement point is at the first m Time difference dynamic error at each candidate coordinate; This represents the time difference operator; this term is used to constrain the consistency of heating, cooling, and dynamic change trends.

[0038] S7.1.4, Time Lag Error When there is a certain lag in the thermal inertia or operating condition response of the furnace wall, a dynamic matching error within a finite time offset range is introduced, as shown in the formula: In the formula, For the first i The temperature measurement point is at the first m Time lag error at each candidate coordinate; This is the time offset. This is the preset maximum allowable hysteresis time. This error term compensates for the effects of thermal inertia and response delay by searching for the optimal hysteresis amount within the allowable range, thus avoiding incorrect judgment of coordinates due to phase difference.

[0039] S7.1.5, Comprehensive Single-Point Matching Error The formula for the single-point candidate matching error is as follows: in, For the first i The temperature measurement point is at the first m The combined single-point matching error at each candidate coordinate; These are preset weighting coefficients that control the contribution ratios of temperature amplitude error, normalized shape error, time difference dynamic error, and time lag error to the total single-point matching error. Each weighting coefficient can be adjusted based on factors such as the signal-to-noise ratio, temperature fluctuation amplitude, and sampling frequency of the field data, typically ensuring that the magnitudes of the various errors are roughly equivalent.

[0040] The smaller the single-point matching error value, the higher the degree of single-point matching between the simulated temperature sequence and the measured temperature sequence at that candidate coordinate, which is a fundamental term for subsequent joint optimization. Through single-point matching, several candidate coordinates with smaller matching errors are selected for each temperature measurement point. Since the temperature field on the outer wall of the ISA furnace may have locally similar regions, and different spatial locations may produce similar temperature change curves, relying solely on single-point matching can easily lead to error calibration. Therefore, this invention proposes to introduce a consistency constraint on the structure of the correlation matrix of multiple temperature measurement points in one step.

[0041] S7.2 Calculate the correlation structural error of multiple temperature measurement points The measured temperature matrix obtained for S2 is: Calculate the correlation coefficient matrix between the measured temperature points. C Y : Among them, corr( The ) indicates the operation of calculating the correlation coefficient matrix.

[0042] For a set of candidate coordinate combinations The corresponding simulated temperature matrix is ​​extracted from the temperature field. The formula is: in, Indicates the first i The simulated temperature sequence corresponding to the selected candidate coordinates of each temperature measurement point. The superscript here... i Indicates from the first i The index of the selected candidate coordinates from the candidate set of temperature measurement points.

[0043] Calculate the correlation matrix between temperature measurement points in the simulated temperature matrix. The formula is: Multi-temperature measurement point related structural error Defined as: in, This represents the Frobenius norm.

[0044] If multiple temperature measurement points are spatially close or affected by the same reaction zone or heat flow region, their temperature changes should have a strong correlation. If multiple temperature measurement points are located on different sides or at different heights, their temperature correlation should differ. Therefore, a correct coordinate combination should not only match the temperature curves of each temperature measurement point, but also ensure that the temperature correlation structure between multiple temperature measurement points is consistent with the measured data.

[0045] S7.3 Calculate the prior constraint error of the template layout This invention introduces prior constraints on template layout. For multiple temperature measurement points on the same observation side, constraints can be established based on the temperature measurement point numbering order, installation level, adjacent spacing, or nominal template. For example, the height of temperature measurement points on the same side should meet the requirements of the numbering order, the height difference and angle difference between adjacent temperature measurement points should be within a reasonable range, and different temperature measurement points should not fall into the same unreasonable area.

[0046] Template layout error Defined as: in, and The first i The and the first j The spatial position vector of each temperature measurement point in the current candidate coordinate combination; and Indicates the first reference position in the layout The and the first The relative positions of the temperature measuring points are referenced from the original design drawings, installation plans, or historical records of the ISA furnace, including the theoretical design coordinates of the temperature measuring points or the relative positional relationships between them. For scenarios without coordinates in the reference position layout, the order, lateral affiliation, or spacing range between the temperature measuring points can be used as prior constraints.

[0047] S7.4 Establish and solve the joint calibration objective function. Taking into account single-point matching error, multi-temperature measurement point related structural error, and template layout prior constraints, the joint calibration objective function is established as follows: in, Candidate coordinate combinations P The joint calibration objective function value is obtained under the following conditions; This indicates a coordinate smoothing constraint, used to prevent unreasonable jumps in the coordinates of temperature measurement points; , and The regularization weights control the contribution of the multi-temperature measurement point related structural error, template layout prior constraint, and coordinate smoothing constraint to the overall objective function.

[0048] Candidate coordinate set for each temperature measurement point In the middle, select an optimal set of coordinates as: The coordinate combination must satisfy the following conditions: the corresponding simulated temperature sequence not only matches the measured temperature sequence of each temperature measurement point at a single point, but also the correlation structure between multiple temperature measurement points is consistent with the measured data.

[0049] The optimal coordinate combination is obtained by solving the following discrete optimization formula: Solving the discrete optimization formula yields the equivalent spatial coordinates of each temperature measurement point. : In the formula, For the first i The circumferential angle obtained by calibrating each temperature measurement point (optimal solution); For the first i The axial height (optimal solution) is obtained by calibrating a number of temperature measurement points. The solution to this optimization problem is performed in a discrete combinatorial space and can be achieved using discrete optimization methods such as exhaustive search (when the total number of candidate coordinates is small), dynamic programming, genetic algorithms, or graph cut.

[0050] Furthermore, the specific process of S8 is as follows: Because parameters such as thermal conductivity, outer wall heat transfer coefficient, furnace wall heat absorption coefficient, reaction heat distribution width, and hot spot center location in the temperature field model may have uncertainties, coordinate calibration based on only a single parameter combination may misjudge model parameter errors as coordinate deviations. To further improve the reliability of coordinate estimation results, this invention introduces parameter perturbation robustness verification.

[0051] By perturbing the key parameters in the S3 temperature field mathematical model, the calibration process from S4 to S7 is repeated to evaluate the stability of the calibration coordinates of each temperature measurement point under different model parameter conditions, and the coordinate confidence of each temperature measurement point is output to identify reliable temperature measurement points and low-confidence temperature measurement points.

[0052] S8.1 Constructing a model parameter perturbation group The key uncertain parameters in the S3 temperature field mathematical model are summarized into a model parameter vector. for: in, These represent the thermal conductivity of the three furnace wall materials, respectively. Indicates the heat transfer coefficient of the outer wall; Indicates the furnace wall heat absorption coefficient; and These represent the circumferential width and vertical width of the hotspot spatial distribution, respectively. and These represent the circumferential and elevation positions of the hotspot center, respectively. The circumferential position of the hotspot center... and the height position of the hotspot center These represent the center coordinates of the concentrated areas of reaction heat in the circumferential and axial directions of the furnace wall, respectively.

[0053] In parameter nominal value (Referring to the initial estimates or default values ​​of the model parameters before correction), construct S groups of different perturbation parameter combinations according to a preset perturbation amplitude (e.g., ±10%-±30%): In the formula; These are the disturbance parameters; s Index for perturbation parameter combinations; For the set of parameter perturbations; S8.2 Repeatedly perform coordinate calibration for each set of disturbance parameters. For each set of disturbance parameters ,Will Substituting the temperature field mathematical model of S3, the continuous temperature field of the outer wall is recalculated, and the temperature measurement point coordinate calibration is repeated to obtain the corresponding calibration coordinates: , i =1,2,……N , i =1,2,…… S In the formula, In the first s Group of disturbance parameters i The calibration coordinates of each temperature measurement point.

[0054] S8.3 Calculate coordinate stability index For the Calculate the calibration coordinates of each temperature measurement point. S The spatial dispersion (standard deviation) under the set of perturbation parameters, used as an index of coordinate stability, is calculated using the following formula: In the formula, For the first i The coordinate stability index of each temperature measurement point; std(·) represents the standard deviation of all elements in the set; The circumferential angle is usually calculated separately. θ and axial height z The standard deviation in direction is then combined to form the standard deviation of spatial distance. Preferably, the circumferential angle is used. θ and axial height z The standard deviations in each direction are then weighted and dimensionless. The smaller the value, the more stable the calibration coordinates of the temperature measurement point are under different model parameter disturbances, and the less sensitive it is to model parameter uncertainties.

[0055] S8.4 Calculate the frequency of repetition For the i A candidate coordinate of a temperature measurement point P exist S Frequency of repeatedly becoming the optimal coordinates under group parameter perturbation Represented as: In the formula, count(·) represents a counting operation, which counts the number of items that satisfy the following conditions: The number of disturbance groups; This reflects the probability that the candidate coordinate is repeatedly selected under model parameter perturbation; the higher the frequency, the more robust the coordinate is.

[0056] S8.5 Calculate the confidence level of the coordinates of the temperature measurement point. Based on the comprehensive coordinate stability index and the frequency of recurrence, the first... i Confidence of coordinates of temperature measurement points i for: in, The scale parameter controls the sensitivity of the spatial dispersion to the confidence level, and is typically taken as several times the spatial resolution of the candidate coordinates of the temperature measurement points; Conf i The larger the confidence level, the more stable the calibration coordinates of the temperature measurement point are under different model parameter perturbations, and the higher the reliability. For temperature measurement points with a confidence level below the preset threshold, they can be marked as low-confidence temperature measurement points, prompting manual review or recalibration after expanding the candidate coordinate range.

[0057] Furthermore, the specific process of S9 is as follows: S9.1, Fix the coordinates of the temperature measurement point that meet the confidence level requirements. Conf based on the coordinates of each temperature measurement point calculated in S8 i Filter out those with a confidence level higher than a preset threshold. th The temperature measurement points were calibrated and their coordinates were determined. Fixed as a reliable observation location. Temperature measurement points with a confidence level below the threshold are marked as low-confidence temperature measurement points, temporarily excluded from parameter correction, and prompted for manual review.

[0058] S9.2 Establish the objective function for parameter correction Let the parameter vector of the continuous temperature field model to be corrected be... This includes the furnace wall heat absorption coefficient, outer wall heat transfer coefficient, boundary heat flux correction coefficient, reaction heat distribution parameters, hot spot center location, hot spot diffusion width, and observation gain at temperature measurement points. The objective function for parameter correction is established as follows: in, The objective function value is used to correct the parameters (the smaller the value, the more accurate the model prediction). For the first i Time series of measured temperatures at several temperature measurement points; The magnitude of the disturbance; parameter Below the calibrated coordinates The simulated temperature sequence extracted from the sample; Indicates parameters The correlation matrix of the simulated temperature measurement points is as follows. and For regularization weights.

[0059] The objective function for parameter correction includes a temperature fitting term. This allows the simulated temperature at the calibrated coordinates to approximate the measured temperature; parameter regularization term To prevent parameters from deviating excessively from their physical reasonable range; relevant constraint terms. To maintain consistency between the correlation structure and actual measurements among multiple temperature measurement points.

[0060] S9.3 Solving the parameter correction optimization problem The parameters of the corrected temperature field mathematical model are obtained by solving the objective function for parameter correction using the following formula: In the formula, To obtain the optimal model parameters, so that the objective function... The parameter vector that achieves the minimum value, i.e., the corrected optimal parameter combination; The parameter vector of the model to be corrected contains all the parameters that need to be identified and corrected, such as the furnace wall heat absorption coefficient, the outer wall heat transfer coefficient, the hot spot center position, the hot spot diffusion width, the observation gain and bias of each temperature measurement point; the optimization is carried out in a continuous parameter space and can be solved by numerical optimization methods such as gradient descent, Levenberg-Marquardt algorithm, Bayesian optimization or genetic algorithm.

[0061] S9.4, Generate the corrected temperature field Will Substituting the three-dimensional transient continuous temperature field model of S3, the corrected continuous temperature field of the outer wall is generated: In the formula, To obtain the corrected continuous temperature field of the outer wall, the optimal parameters are... After substituting into the temperature field model, the continuous temperature distribution on the outer wall surface is recalculated. The "*" in the upper right corner indicates that the temperature field is the result after parameter correction and optimization. For The outer wall temperature field function is defined by parameters. This indicates that when the model parameters are fixed... At that time, the outer wall surface calculated by the S3 temperature field model ( r = R ) location ( θ , z )time t Temperature value.

[0062] S9.5 Convergence Verification The simulated temperature extracted from the calibrated temperature measurement point after correction is compared with the industrial measured temperature. If the temperature reaches the preset threshold in terms of single-point temperature error, dynamic change trend, and multi-temperature measurement point related structure, the temperature measurement point coordinate estimation and temperature field parameter correction are completed. If the preset threshold is not reached, the process returns to the candidate coordinate library construction in S5 or the model parameter perturbation step in S8 to expand the search range or adjust the parameter range before recalculation.

[0063] This invention provides a method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace, which has the following advantages: (1) This invention treats the measured temperature time series as a sampled response of the continuous temperature field on the outer wall at an unknown location, realizing automatic estimation of the equivalent spatial coordinates of the temperature measurement points without relying on the actual coordinate records of the temperature measurement points. By using the coordinates of the temperature measurement points as the objects to be identified, the reverse calibration of the temperature measurement point positions is achieved through candidate coordinate library and temperature time series matching, which can solve the problem of data spatial correspondence under the conditions of lost drawings, migration of temperature measurement points, and incomplete temperature measurement point ledgers. At the same time, the candidate coordinate library is constructed using the cylindrical outer wall structure of the Isa furnace, the observation side, the numbering order of the temperature measurement points, and the installation template information, so that the temperature measurement point coordinate search process is constrained by the furnace geometry and on-site installation logic, which improves the physical rationality of the calibration results.

[0064] (2) This invention evaluates the stability of temperature measurement point coordinates under different model parameter conditions through repeated coordinate calibration under temperature field model parameter perturbation, and outputs coordinate confidence, thereby reducing the impact of heat transfer parameter uncertainty on coordinate estimation results. First, temperature measurement point coordinates are calibrated, and then temperature field parameters are corrected after the reliable coordinates are fixed. This weakens the coupling between coordinate errors and model parameter errors, avoiding miscalibration problems caused by directly correcting model parameters when the coordinates are unknown. A closed-loop process of "temperature measurement point coordinate calibration—coordinate robustness verification—temperature field parameter correction—temperature field update" is formed, providing a reliable data foundation for ISA furnace wall temperature field verification, furnace lining thermal state monitoring, abnormal hot spot location, and safety early warning.

[0065] (3) This invention utilizes temperature amplitude, normalized shape, time difference dynamic features and time lag features simultaneously to improve the robustness of temperature sequence matching at a single temperature measurement point. At the same time, it introduces consistency constraints on the correlation matrix structure of multiple temperature measurement points, and uses the temperature correlation between multiple temperature measurement points as the basis for judging the overall spatial layout, which can reduce the risk of single-point mismatch caused by similar temperature curves at different spatial locations.

[0066] (4) This invention is applicable to complex industrial scenarios such as missing drawings, replacement of temperature measurement points, relocation of temperature measurement points, on-site modification and incomplete historical data, and has strong engineering practicality and promotion value. Attached Figure Description

[0067] Figure 1 This is a flowchart of a method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to the present invention.

[0068] Figure 2 This is a diagram showing the calibration results of the furnace wall temperature measurement points with a circumferential angle of 0°-120° in Embodiment 1 of the present invention.

[0069] Figure 3 This is a diagram showing the calibration results of the furnace wall temperature measurement points with a circumferential angle of 120°-240° in Embodiment 1 of the present invention.

[0070] Figure 4 This is a diagram showing the calibration results of the furnace wall temperature measurement points with a circumferential angle of 240°-360° in Embodiment 1 of the present invention. Detailed Implementation

[0071] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings, but the scope of protection of the present invention is not limited to the content described.

[0072] This invention addresses the problems of unknown coordinates of temperature measurement points on the outer wall of the Isa furnace, strong subjectivity of manual calibration, difficulty in corresponding the sampling position of the temperature field model with the actual temperature measurement point position, and the coupling between coordinate error and model parameter error. It proposes a method for estimating the coordinates of temperature measurement points on the outer wall of the Isa furnace.

[0073] The method of this invention, when the true coordinates of the temperature measurement points are unknown, first establishes a three-dimensional transient temperature field model based on the geometry of the ISA furnace body, the structure of the three-layer furnace wall materials, and industrial operating conditions to obtain the continuous temperature field of the outer wall. Then, according to the cylindrical structure of the ISA furnace outer wall, the observation side to which the temperature measurement point belongs, the order of the temperature measurement point number, or the installation template information, a set of candidate coordinates is constructed for each temperature measurement point to be calibrated. Furthermore, the simulated temperature sequence at each candidate coordinate is matched with the actual temperature time sequence of the temperature measurement point. At the same time, the consistency constraints of the correlation matrix structure of multiple temperature measurement points and the prior constraints of the template layout are introduced to avoid mismatches caused by the similarity of single-point temperature curves. Then, the coordinate stability is evaluated by the repeated calibration results under the perturbation of the temperature field model parameters, and the reliable temperature measurement point coordinates are selected and the coordinate confidence is output. Finally, based on the fixed reliable temperature measurement point coordinates, the temperature field model parameters are identified and corrected, forming a closed-loop process of "temperature measurement point coordinate calibration - coordinate robustness verification - temperature field parameter correction - temperature field update".

[0074] The process of the method for estimating the coordinates of temperature measurement points on the outer wall of the Isa furnace according to the present invention is as follows: Figure 1 As shown, it includes the following steps: S1. Collect relevant data of the Isa furnace, including geometric structure data, furnace wall material parameter data and industrial operating condition data, and calculate the equivalent heat of reaction; S2. Collect the time series of measured temperatures at the external wall temperature measurement points and the prior installation information of the temperature measurement points; S3. Establish a three-dimensional transient temperature field mathematical model of the three-layer furnace wall, including the heat conduction control equation, interlayer interface conditions, inner wall mixing heat flow boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary. S4. Input the geometric structure, furnace wall material parameters and equivalent reactive heat obtained in S1 into S3. Use the numerical discretization method to mesh the spatial domain and step through the time domain to solve for the temperature distribution on the outer surface of the furnace wall. S5. Based on the prior installation information of the collected temperature measurement points, generate a finite number of possible spatial coordinate positions for each temperature measurement point to be calibrated. S6. From the temperature distribution on the outer surface of the furnace wall obtained in S4, extract the corresponding simulation temperature time series for each candidate coordinate constructed in S5, and establish the mapping relationship between the candidate coordinates and the simulation temperature series. S7. Using measured temperature time series and candidate coordinates to simulate temperature series, a joint calibration objective function is established through three levels: single-point matching, multi-temperature point related structural constraints, and template layout prior constraints. The optimal spatial coordinates of each temperature point are solved through discrete optimization. S8. Construct a model parameter perturbation group to perturb the parameters in the temperature field mathematical model of S3. Repeat S4 to S7 to evaluate the stability of the calibration coordinates of each temperature measurement point under different model parameter conditions, and output the coordinate confidence of each temperature measurement point. S9. Fix the coordinates of temperature measurement points with a confidence level higher than the preset threshold as reliable observation positions, establish a parameter correction objective function, solve the objective function and substitute it into the temperature field mathematical model to generate the corrected outer wall temperature field, and complete the estimation of the coordinates of the temperature measurement points on the outer wall of the Isa furnace.

[0075] Through the above method, the present invention realizes the joint coordinate calibration of multiple temperature measurement points based on the three-dimensional temperature field model of the Isa furnace and the industrial measured temperature sequence under the condition that the true coordinates of the temperature measurement points are unknown, and further realizes the closed-loop correction of the temperature field model.

[0076] This invention addresses the problem of reverse calibration of unknown sampling locations under conditions where the spatial coordinates of temperature measurement points are missing. Unlike general temperature inversion methods, this invention does not simply infer a parameter from the temperature error, but instead treats the coordinates of the temperature measurement points as the object to be identified and improves the reliability of the coordinate estimation results by utilizing the consistency of the temperature time series structure of multiple temperature measurement points and the robustness of parameter perturbation verification.

[0077] This invention treats the measured temperature time series as a sampled response of the continuous outer wall temperature field at an unknown spatial location. The three-dimensional transient temperature field model of the Isa furnace, candidate coordinate library, single-point temperature time series matching, consistency constraints of the correlation matrix structure of multiple temperature measurement points, and robustness verification of parameter perturbation are used to reversely determine the equivalent spatial coordinates of each temperature measurement point. Furthermore, temperature field parameters are corrected based on the calibrated coordinates, thereby providing a reliable observation location basis for the modeling of the Isa furnace wall temperature field, monitoring of the furnace lining thermal state, and location of abnormal hot spots.

[0078] Without departing from the basic idea of ​​this invention, the candidate coordinate matching stage can also use methods such as dynamic time warping, kernel correlation analysis, graph matching, optimal transport or deep representation learning to replace part of the matrix similarity calculation; the parameter identification stage can also use methods such as Bayesian optimization, genetic algorithm, ensemble Kalman filter, particle filter or neural operator-assisted inversion.

[0079] For different furnace types, the coordinate system of the cylindrical shell can be replaced with the coordinate system of the irregular curved surface, or the three sides can be expanded into a multi-sided point arrangement around the entire circumference; the reaction heat model can also adopt a superposition of multiple hot spots, a time-varying trajectory hot spot, or a heat flow model driven by process variables. All of the above alternatives should be considered as optional embodiments of the present invention.

[0080] Based on the above method, the present invention will be further illustrated by the following embodiments: Example 1 This embodiment uses a certain oxygen-enriched top-blown Isa furnace as an example. The outer wall of this Isa furnace is approximately cylindrical, and the furnace body height is... Circumferential angle range of the outer wall for The outer wall of the furnace is divided into three sides, each side corresponding to... Circumferential range, i.e.: Arrangement on each side There are 27 temperature measurement points in total. Due to issues such as lost drawings, unclear point numbers, point replacements, or installation misalignments, the actual spatial coordinates of the measurement points are unknown; only the point numbers and their temperature time series are available. Therefore, this embodiment utilizes the three-dimensional external wall temperature field and the temperature series of the measurement points to perform reverse calibration of the point coordinates.

[0081] 1. Establish a three-dimensional furnace wall temperature field model. Let the temperature field of the Isa furnace wall be: in, Radial coordinates, Circumferential angle, This refers to the height of the furnace body. For time.

[0082] The furnace wall consists of a refractory layer, an insulation layer, and a steel shell layer. For the first... The transient heat transfer equation for the furnace wall material is as follows: in, , , The first The density, specific heat capacity, and thermal conductivity of the layer material.

[0083] Adjacent material layers must satisfy the conditions of temperature continuity and heat flow continuity: The above formula is equivalent to S3.2 in this invention. .

[0084] The inner wall heat flux boundary is calculated from process parameters and is expressed as: The outer wall heat dissipation boundary is: in, The outer wall surface temperature, For ambient temperature, The external wall convective heat transfer coefficient is... For the outer wall emissivity, is the Stefan-Boltzmann constant.

[0085] Solving the above three-dimensional transient heat transfer model yields the outer wall temperature field: 2. Construct candidate coordinate regions for temperature measurement points For each side, its circumferential and height ranges are divided into... Candidate regions. (Based on the first face) For example, it can be divided into: Several candidate coordinate points are set within each region. The set of candidate coordinates for a temperature measurement point is denoted as: in: Indicates the first The first temperature measurement point 1 candidate coordinate.

[0086] For example, for 9 temperature measurement points on a certain side, it can be done as follows: Layout constraints: The left column, from bottom to top, consists of... The middle column is from bottom to top. The right column from bottom to top is This arrangement serves only as a spatial constraint to prevent cross-regional mismatch of temperature measurement points during the inversion process.

[0087] 3. Extract the simulated temperature sequence at candidate coordinates. For the The first temperature measurement point From the candidate coordinates, the corresponding simulated temperature sequence is extracted from the three-dimensional outer wall temperature field: Right now: The on-site measured temperature sequence is recorded as follows: Because factors such as infrared temperature measurement, thermocouple installation, external wall emissivity, and local obstruction can introduce measurement deviations, an observation model with gain and bias is used to differentiate between the measured and simulated temperatures. in, This is the gain correction factor for the temperature measurement point. To offset the temperature measurement point, This represents measurement error.

[0088] 4. Calculate the single-point temperature timing matching error. For each candidate coordinate, calculate the matching error between the measured temperature sequence and the simulated temperature sequence.

[0089] The amplitude error is: The normalized shape error is: The time difference error is: in: The comprehensive single-point matching error is defined as: in, These are the weighting coefficients.

[0090] 5. Introduce structural constraints related to multiple temperature measurement points. Relying solely on temperature curve matching at a single temperature measurement point can easily lead to local mismatches. Therefore, this embodiment further introduces multi-temperature-point related structural constraints.

[0091] Suppose a certain side has a total of The measured temperature matrix for each temperature measurement point is as follows: Corresponding candidate coordinate combinations The simulation temperature matrix is ​​as follows: The measured temperature correlation matrix is ​​as follows: The simulated temperature correlation matrix is ​​as follows: The relevant structural error is defined as: This constraint is used to ensure that the inversion results not only satisfy the similarity of single-point temperature curves, but also the consistency of the overall temperature response relationship among multiple temperature measurement points.

[0092] 6. Add spatial layout constraints To maintain the spatial rationality of the temperature measurement point array, a reference layout constraint is introduced. Let the... The and the first The positions of the temperature measurement points in the current candidate coordinate combination are as follows: and The relative position in the reference layout is and The layout error is: If only the vertical or horizontal order of the temperature measurement points is known, order constraints can also be used. For example, for the same column of temperature measurement points, if the temperature measurement points... It should be located at the temperature measurement point Below, the following conditions are met: If the distance between adjacent temperature measuring points is within a reasonable range, then the following conditions must be met: and These are the minimum and maximum allowable distances between adjacent measuring points; 7. Establish the objective function for joint coordinate calibration. By combining single-point temperature matching error, multi-temperature measurement point related structural error, and spatial layout error, a joint objective function is established: in, Indicates the first The candidate coordinate numbers selected for each temperature measurement point. and These are the weighting coefficients.

[0093] The optimal combination of temperature measurement point coordinates is: The final result is: in, That is, the first The reverse calibration coordinates of each temperature measurement point.

[0094] In this way, the deviation temperature measurement point is still retained in the system, but it will not have a significant impact on coordinate calibration and temperature field correction.

[0095] 8. Output the reverse calibration results of the coordinates of the temperature measurement points on the three sides. After completing the above calculations, the coordinate calibration results of the three sides were obtained respectively.

[0096] For page 1: Output the estimated coordinates of the 9 temperature measurement points: For page 2: Output: For page 3: Output: The temperature fields of the outer walls on the three sides are displayed separately as follows: Figure 2-4 As shown. The background color represents the temperature distribution on the outer wall, the black hollow circle represents the reference true coordinates, and the red cross represents the inverse estimated coordinates. If the red cross is close to the black hollow circle, it indicates that the coordinate calibration accuracy of the temperature measurement point is relatively high.

[0097] Figure 2 The first side view of the outer wall of a certain layer of the Isa furnace is shown, namely the circumferential angle. The temperature field distribution on the outer wall within the range and the results of reverse calibration of the coordinates of the temperature measuring points. The horizontal axis in the figure represents the circumferential angle. The vertical axis represents the axial height of the furnace body. The background color represents the temperature distribution of the outer wall on this side, the black hollow circle represents the hidden true coordinates, and the red cross represents the inversely estimated coordinates. The temperature field distribution shows that the temperature on this side exhibits significant spatial non-uniformity, with the high-temperature area mainly concentrated in the lower right to middle right region. , The low-temperature zone is mainly located in the upper left area. The inversion results of the temperature measurement point coordinates show that most of the estimated red points are close to their corresponding true black points, maintaining overall consistency. The spatial relationship of the temperature measurement point array demonstrates that the spatial gradient of the temperature field on this side provides an effective constraint for the reverse calibration of the temperature measurement point coordinates. The estimated positions of temperature measurement points 1, 2, 3, 4, 6, 7, 8, and 9 are relatively close to their actual locations, while temperature measurement point 5 shows a certain offset, possibly related to its location in an area with a significant temperature gradient change. Overall, the reverse calibration effect on the first side is better, indicating that this method can recover the approximate spatial location of the temperature measurement points in an outer wall temperature field with significant differences in heat and cold distribution.

[0098] Figure 3 The second side of the outer wall of a certain layer of the Isa furnace is shown, namely the circumferential angle. The temperature field of the outer wall and the coordinates of the temperature measuring points within the range are obtained through reverse calibration. The temperature distribution on this side differs significantly from that on the first side, with the high-temperature zone mainly concentrated in the lower-middle area on the left side. , The temperature is relatively low in the lower right area, indicating a significant circumferential temperature non-uniformity on the furnace outer wall. From the coordinate inversion results, the estimated red coordinates of temperature measurement points 10–18 generally match the actual black coordinates well, with most points remaining within their respective local regions without significant cross-regional mismatches. The estimated positions of temperature measurement points 10, 11, 12, 13, 14, 15, 17, and 18 are relatively accurate, while temperature measurement point 16 shows a slight offset, but this does not disrupt the overall temperature distribution. Array structure. The results show that, in the second surface, although there is a clear high-low temperature transition region in the temperature field, the reverse calibration method can still stably identify the spatial location of the temperature measurement points, indicating that the constraints of the multi-temperature measurement point region and the spatial distribution information of the temperature field have a good constraining effect on coordinate inversion.

[0099] Figure 4 The third side of the outer wall of a certain layer of the Isa furnace is shown, namely the circumferential angle. The temperature field of the outer wall and the coordinates of the temperature measuring points within the range are determined by reverse calibration. Compared with the previous two sides, the temperature field of this side exhibits a more pronounced low-temperature region in the middle and lower parts, with the low-temperature area mainly concentrated in... , The temperature is relatively high in the vicinity of the upper left and right edge regions, indicating a significant difference in heat load distribution on this side compared to the previous two sides. The coordinate inversion results of the temperature measurement points show that the estimated coordinates of temperature measurement points 19–27 generally maintain a good correspondence with the actual coordinates. The inverted positions of temperature measurement points 19, 20, 21, 22, 23, 25, and 27 are relatively close to their actual positions, indicating that this method still has a certain coordinate recovery capability in temperature fields with local cold zones. However, temperature measurement points 24 and 26 show a certain degree of circumferential or height shift, possibly related to their location at the edge of a low-temperature zone or rapid changes in the local temperature gradient. Overall, the coordinate inversion results for the third side maintain good array structure consistency, but the deviation of local temperature measurement points is relatively more significant, indicating that complex cold and heat distribution boundaries can have a certain impact on the accuracy of the coordinate inversion of temperature measurement points.

[0100] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace, characterized in that: Includes the following steps: S1. Collect relevant data of the Isa furnace, including geometric structure data, furnace wall material parameter data and industrial operating condition data, and calculate the equivalent heat of reaction; S2. Collect the time series of measured temperatures at the external wall temperature measurement points and the prior installation information of the temperature measurement points; S3. Establish a three-dimensional transient temperature field mathematical model of the three-layer furnace wall, including the heat conduction control equation, interlayer interface conditions, inner wall mixing heat flow boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary. S4. Input the geometric structure, furnace wall material parameters and equivalent reactive heat obtained in S1 into S3. Use the numerical discretization method to mesh the spatial domain and step through the time domain to solve for the temperature distribution on the outer surface of the furnace wall. S5. Based on the prior installation information of the collected temperature measurement points, generate a finite number of possible spatial coordinate positions for each temperature measurement point to be calibrated. S6. From the temperature distribution on the outer surface of the furnace wall obtained in S4, extract the corresponding simulation temperature time series for each candidate coordinate constructed in S5, and establish the mapping relationship between the candidate coordinates and the simulation temperature series. S7. Using measured temperature time series and candidate coordinates to simulate temperature series, a joint calibration objective function is established through three levels: single-point matching, multi-temperature point related structural constraints, and template layout prior constraints. The optimal spatial coordinates of each temperature point are solved through discrete optimization. S8. Construct a model parameter perturbation group to perturb the parameters in the temperature field mathematical model of S3. Repeat S4 to S7 to evaluate the stability of the calibration coordinates of each temperature measurement point under different model parameter conditions, and output the coordinate confidence of each temperature measurement point. S9. Fix the coordinates of temperature measurement points with a confidence level higher than the preset threshold as reliable observation positions, establish a parameter correction objective function, solve the objective function and substitute it into the temperature field mathematical model to generate the corrected outer wall temperature field, and complete the estimation of the coordinates of the temperature measurement points on the outer wall of the Isa furnace.

2. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 1, characterized in that: The specific content of the collected data in S1 includes: S1.1 Geometric Structure Data Acquisition The outer wall of the Isa furnace is approximately a cylindrical shell structure, and the radius of the outer wall is assumed to be... Circumferential angle is axial height is Then any position on the outer wall is represented as: S1.2, Data Acquisition of Material Parameters for Three-Layer Furnace Wall The Isa furnace wall comprises three material layers along its thickness: a refractory working layer, an insulation layer, and a steel shell layer. For the first... l Layer material, collect the corresponding density Specific heat capacity and thermal conductivity ; S1.3 Industrial Operating Condition Data Acquisition Collect industrial operation data for each shift cycle, including: oxygen input, air input, total sulfur, coal input, oil input, and ore composition ratio; convert the cumulative output for each shift into the average flow rate for that shift, and calculate the equivalent heat of reaction that can act on the furnace wall. .

3. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 2, characterized in that: The specific process of S2 is as follows: S2.1 Acquiring the measured temperature time series Installed on the outer wall of the Isa furnace N Temperature measurement points, collecting data N Each temperature measurement point within the time interval t ∈[ t 0, t The measured temperature data within [1] are arranged into a measured temperature matrix by arranging the measured temperature sequences of all temperature measurement points: In the formula, i For temperature measurement point indexing, For the first i The measured temperature time series at each temperature measurement point has a length equal to the number of time sampling points; measured temperature Represented as: in, This represents the correction factor related to the gain or emissivity of the temperature measurement point; This indicates that the temperature measurement point is offset; This represents measurement noise and unmodeled disturbances; This indicates the surface temperature of the outer wall of the measuring point; S2.2, Collect preliminary installation information of temperature measurement points Collect the observation side, height level range, temperature measurement point number sequence, and installation template of each temperature measurement point.

4. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 3, characterized in that: The specific process of S3 is as follows: S3.1 Establish the heat conduction control equations within each material layer domain. set up Indicates the temperature field of the furnace wall. r Radial coordinates, r ∈[ R in , R ], R in Let be the inner wall radius. R Let be the outer wall radius, for the The spatial locations of the external wall temperature measurement points are represented as follows: in, For the first The circumferential angular position of each temperature measuring point For the first Axial height position of each temperature measuring point; In the The three-dimensional transient heat conduction governing equations within the layered material domain are as follows: in, Represents the volumetric heat source term; For gradient operators; This is the divergence form of the thermal conductivity term; S3.2 Establish interlayer interface conditions At the interface between different material layers, since there is no energy accumulation and no additional heat source at the interface, the interlayer interface conditions must be satisfied: temperature continuity and normal heat flow continuity, expressed as: In the formula, T 1 and T 2 represents the temperatures on both sides of the interface. and The thermal conductivity of the materials on both sides of the interface; and These are the temperature gradients along the normal direction on both sides of the interface; S3.3 Establish the inner wall mixing heat flux boundary On the inner surface of the furnace wall, the boundary of the mixed heat flow is uniformly represented as: in, Indicates the position of the inner surface of the furnace wall and time t The total heat flux density experienced by the location; This refers to the convective heat flux density on the molten pool or flue gas side. This refers to the radiative heat flux density of the high-temperature medium inside the furnace to the furnace wall. The heat flux of chemical reactions that occur and act on the furnace wall during processes including feeding, oxygen supply, and oxidation-reduction. This represents the constrained dynamic compensation term that describes reaction zone migration, oxygen supply deviation, fuel fluctuations, and unmodeled local thermal disturbances. S3.4 Calculation of the spatial distribution of heat of chemical reaction The equivalent heat of reaction obtained from S1 is distributed to the inner surface of the furnace wall using a spatially normalized distribution function. The spatial distribution formula for the heat of chemical reaction is: in, Of the heat released by the metallurgical chemical reaction, the amount actually transferred to the inner surface of the furnace wall is at location [missing information]. and time t Heat flux density at that location; The furnace wall heat absorption coefficient; It is a spatial distribution function. Gaussian distribution, multi-hotspot seasonal distribution, or moving hotspot distribution that varies with operating conditions can be used; For effective heat-receiving area; S3.5 Establish the outer wall heat dissipation boundary The outer surface of the outer wall adopts a boundary for heat dissipation through natural convection and radiation with respect to the environment, as shown in the formula: in, The thermal conductivity of the outermost material; The external wall convective heat transfer coefficient; Emissivity of the outer wall; The Stefan-Boltzmann constant; The outer wall surface temperature, Ambient temperature; S3.6 Establishing a complete boundary value problem for the temperature field The temperature distribution throughout the entire furnace wall region is obtained by simultaneously solving the heat conduction control equations, interlayer interface conditions, inner wall mixing heat flux boundary, spatial distribution of chemical reaction heat, and outer wall heat dissipation boundary. Take the outer wall surface r = R The temperature value at that location is used as the continuous temperature field of the outer wall. The simulated temperature field used for subsequent temperature measurement point coordinate extraction is represented as follows: 。 5. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 4, characterized in that: The specific process of S5 is as follows: For the i For each temperature measuring point, a candidate circumferential angle range is determined on the cylindrical surface of the outer wall of the furnace, based on the observed side. Determine the candidate height range Within the circumferential angle range According to the set resolution Discrete, in the height range According to the set resolution Discrete, Generate Candidate coordinate points: Construct a set of candidate coordinates for each temperature measurement point: in, For the first A set of candidate coordinates for each temperature measurement point; For the first Number of candidate coordinates for each temperature measurement point M The total number of candidate coordinates for each temperature measurement point; For the first The first temperature measurement point One candidate coordinate; The index of the candidate coordinates; After generating candidate points, candidate points that do not meet the constraints of furnace structure, on-site installation conditions, or relative order constraints of temperature measurement points on the same side are removed, resulting in the final set of candidate coordinates for each temperature measurement point; among them, the relative order constraints of temperature measurement points on the same side are the order of temperature measurement point numbers and the range of height levels.

6. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 5, characterized in that: The specific process of S6 is as follows: No. The first temperature measurement point The candidate coordinates are represented as follows: in, Located within the candidate angle range of the observation side of the temperature measurement point; Located within the possible height range of the temperature measurement point; For each candidate coordinate Temperature distribution obtained from S4 Extract the corresponding simulation temperature sequence using the following formula: in, For the first i Each temperature measurement point is located at the candidate coordinates The simulated temperature time series at point S2, and the time sampling points compared with the measured temperature series in S2. The time sampling points remain consistent; For each temperature measurement point i For all candidate coordinates, repeat the simulation temperature sequence extraction operation to obtain the set of simulation temperature sequences corresponding to all candidate coordinates. .

7. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 6, characterized in that: The specific process of S7 is as follows: S7.1 Calculate the single-point candidate matching error Extracted simulation temperature sequence With measured temperature series Perform single-point matching; S7.1.1 Temperature Amplitude Error The formula for comparing the difference in amplitude between simulated and measured temperatures is as follows: In the formula, Let L2 be the norm of the vector; For the first i The temperature measurement point is at the first m Temperature amplitude error at each candidate coordinate; S7.1.2, Normalized shape error The simulated and measured temperature sequences are normalized by their mean and standard deviation, and then their shape similarity is compared. The normalized shape error is expressed as: in, For the first i The temperature measurement point is at the first m Normalized shape error at each candidate coordinate; This indicates the normalization operation for mean and standard deviation; S7.1.3, Time Difference Dynamic Error Comparing the rates of change of the simulated temperature series and the measured temperature series over time, the time difference error is expressed as: in, For the first i The temperature measurement point is at the first m Time difference dynamic error at each candidate coordinate; Represents the time difference operator; S7.1.4, Time Lag Error When there is a lag in the thermal inertia or operating condition response of the furnace wall, a dynamic matching error within a finite time offset range is introduced, as shown in the formula: In the formula, For the first i The temperature measurement point is at the first m Time lag error at each candidate coordinate; This is the time offset. This is the preset maximum allowable delay time; S7.1.5, Comprehensive Single-Point Matching Error The combined single-point candidate matching error is obtained The method is: to , , and The weighted calculation is performed to obtain the result. S7.2 Calculate the correlation structural error of multiple temperature measurement points Multi-temperature measurement point related structural error Defined as: in, Represents the Frobenius norm; CY is the correlation coefficient matrix between measured temperature points; This is the correlation matrix between temperature measurement points in the simulated temperature matrix; S7.3 Calculate the prior constraint error of the template layout Introducing prior constraints on template layout, for multiple temperature measurement points on the same observation side, the template layout error... Defined as: in, and The first i The and the first j The spatial position vector of each temperature measurement point in the current candidate coordinate combination; and Indicates the first reference position in the layout The and the first The relative positions of the temperature measuring points are referenced from the original design drawings of the Isa furnace, the temperature measuring point installation plan, or historical records, including the theoretical design coordinates of the temperature measuring points or the relative positional relationships between the temperature measuring points; for scenarios without coordinates in the reference position layout, only the order, side affiliation, or spacing range between the temperature measuring points are used as prior constraints. S7.4 Establish and solve the joint calibration objective function. Taking into account single-point matching error, multi-temperature measurement point related structural error, and template layout prior constraints, the joint calibration objective function is established as follows: in, Candidate coordinate combinations P The joint calibration objective function value is obtained under the following conditions; Indicates coordinate smoothing constraints; , and These are the regularization weight coefficients; Candidate coordinate set for each temperature measurement point In the middle, select an optimal set of coordinates as: The optimal coordinate combination must satisfy the following conditions: the corresponding simulated temperature sequence not only matches the measured temperature sequence at each temperature measurement point individually, but also the correlation structure between multiple temperature measurement points is consistent with the measured data. The optimal coordinate combination is obtained by solving the following discrete optimization formula: Solving the discrete optimization formula yields the equivalent spatial coordinates of each temperature measurement point. : In the formula, For the first i The circumferential angle obtained by calibrating each temperature measuring point; For the first i The axial height is obtained by calibrating each temperature measuring point.

8. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 7, characterized in that: The specific process of S8 is as follows: S8.1 Constructing a model parameter perturbation group The key uncertain parameters in the S3 temperature field mathematical model are summarized into a model parameter vector. , is represented as: in, These represent the thermal conductivity of the three furnace wall materials, respectively. Indicates the heat transfer coefficient of the outer wall; Indicates the furnace wall heat absorption coefficient; and These represent the circumferential width and vertical width of the hotspot spatial distribution, respectively. and These represent the circumferential and vertical positions of the hotspot center, respectively. Based on parameter nominal value S sets of different perturbation parameter combinations are constructed according to the preset perturbation amplitude, and the formula is as follows: In the formula; These are the disturbance parameters; s Index for perturbation parameter combinations; For the set of parameter perturbations; S8.2 Repeatedly perform coordinate calibration for each set of disturbance parameters. For each set of disturbance parameters ,Will Substituting the temperature field mathematical model of S3, the continuous temperature field of the outer wall is recalculated, and the temperature measurement point coordinate calibration is repeated to obtain the corresponding calibration coordinates: ， i =1,2,…… N ， s =1,2,…… S In the formula, In the first s Group of disturbance parameters i Calibration coordinates of each temperature measurement point; S8.3 Calculate coordinate stability index For the Calculate the calibration coordinates of each temperature measurement point. S The standard deviation of the group of disturbance parameters is given by the formula: In the formula, For the first i The coordinate stability index of each temperature measurement point; std(·) represents the standard deviation of all elements in the set; To calculate the circumferential angle separately θ and axial height z The standard deviation in direction is then combined with the standard deviation in spatial distance. Preferably, the circumferential angle is considered. θ and axial height z The standard deviation in each direction is then weighted and aggregated using a dimensionless method. S8.4 Calculate the frequency of repetition For the i A candidate coordinate of a temperature measurement point P exist S Frequency of repeatedly becoming the optimal coordinates under group parameter perturbation Represented as: In the formula, count(·) represents a counting operation, which counts the number of items that satisfy the following conditions: The number of disturbance groups; This reflects the probability that the candidate coordinates are repeatedly selected under model parameter perturbations; S8.5 Calculate the confidence level of the coordinates of the temperature measurement point. Based on coordinate stability index and repetition frequency, the first... i Confidence of coordinates of temperature measurement points i for: in, This is the scale parameter.

9. The method for estimating the coordinates of temperature measurement points on the outer wall of an Isa furnace according to claim 8, characterized in that: The specific process of S9 is as follows: S9.1, Fix the coordinates of the temperature measurement point that meet the confidence level requirements. Conf based on the coordinates of each temperature measurement point calculated in S8 i Filter out those with a confidence level higher than a preset threshold. th The temperature measurement points were calibrated and their coordinates were determined. Fixed as a reliable observation location; for temperature measurement points with a confidence level below the threshold, they are marked as low-confidence temperature measurement points, temporarily excluded from parameter correction, and prompted for manual review; S9.2 Establish the objective function for parameter correction Let the parameter vector of the mathematical model of the continuous temperature field to be corrected be... The parameters include the furnace wall heat absorption coefficient, outer wall heat transfer coefficient, boundary heat flux correction coefficient, reaction heat distribution parameters, hot spot center location, hot spot diffusion width, and observation gain at the temperature measurement point. The objective function for parameter correction is established as follows: in, The objective function value is used to correct the parameters (the smaller the value, the more accurate the model prediction). For the first i Time series of measured temperatures at several temperature measurement points; The magnitude of the disturbance; parameter Below the calibrated coordinates The simulated temperature sequence extracted from the sample; Indicates parameters The correlation matrix of the simulated temperature measurement points is as follows. and For regularization weights; S9.3 Solving the parameter correction optimization problem The parameters of the corrected temperature field mathematical model are obtained by solving the objective function for parameter correction using the following formula: In the formula, To obtain the optimal model parameters, so that the objective function... The parameter vector that yields the minimum value is the corrected optimal parameter combination; This is the vector of model parameters to be corrected; S9.4, Generate the corrected temperature field Will Substituting the three-dimensional transient continuous temperature field model of S3, the corrected continuous temperature field of the outer wall is generated: In the formula, This is the corrected continuous temperature field of the outer wall; For The outer wall temperature field function is a parameter, representing the condition where the model parameters are fixed. At that time, the location of the outer wall surface at r=R, calculated by the S3 temperature field mathematical model ( θ , z (moment) t Temperature value; S9.5 Convergence Verification The simulated temperature extracted from the calibrated temperature measurement point after correction is compared with the industrial measured temperature. If the temperature reaches the preset threshold in terms of single-point temperature error, dynamic change trend, and multi-temperature measurement point related structure, the temperature measurement point coordinate estimation and temperature field parameter correction are completed. If the preset threshold is not reached, the process returns to the candidate coordinate library construction in S5 or the model parameter perturbation step in S8 to expand the search range or adjust the parameter range before recalculation.

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