On-line diagnosis method for service state of roller of plate and strip rolling mill

Abstract

The invention discloses a strip mill roller service state online diagnosis method, and belongs to the technical field of metallurgical engineering.The method comprises the steps that a finite element model of a strip mill roller is constructed, simulation calculation is conducted on the rolling process under different working conditions, an Archard wear model is coupled, and roller state parameters under all the working conditions are output; constructing an agent model for calculating a roller state under given production parameters; forming a closed-loop interaction system by the agent model and the finite element model, and repeatedly training and optimizing the agent model to obtain an optimized agent model; and deploying the optimized agent model on a production line to realize online diagnosis of the service state of the roller of the plate and strip rolling mill. According to the method, through an iterative optimization mechanism, the problems that the prior art cannot adapt to complex and changeable working conditions and the prediction precision is attenuated along with time are solved, and an intelligent and self-evolution solution is provided for predictive maintenance and product quality control of the roller.

Description

Technical Field

[0001] This invention relates to the field of metallurgical engineering technology, and in particular to an online diagnostic method for the service status of rolls in strip mills. Background Technology

[0002] In sheet metal production, rolls (including work rolls, intermediate rolls, and support rolls) are key consumables that directly participate in metal deformation and determine the surface quality of the strip. Each stand is typically equipped with six rolls. Under harsh conditions of high speed and high pressure, rolls experience both uniform and uneven wear (such as localized spalling and cracking). Uneven wear is directly replicated on the strip surface, forming periodic defects that lead to product downgrading or scrapping. Currently, roll management and maintenance mainly rely on empirically-based periodic roll replacement based on fixed rolling tonnage or operating time, or on forced shutdowns for investigation when serious quality problems occur. This approach has significant drawbacks, such as inaccurate prediction: empirical cycles cannot accurately reflect the actual wear state of rolls under different specifications, steel grades, and process parameters, potentially leading to "over-maintenance" or "under-maintenance." Secondly, location is difficult: when defects appear on the strip surface, due to the interconnected operation of the five stands, it is difficult to quickly and accurately determine which roll on which stand the problem originates. Inspection must be carried out on each stand individually, which is time-consuming and labor-intensive, severely impacting production efficiency and costs.

[0003] In existing technologies, some studies predict roll wear using theoretical formulas or simplified models. For example, Chinese Patent CN117875137A discloses a data-driven method for predicting roll wear in the rolling process, establishing a roll wear value prediction model based on data mechanism fusion to predict roll wear values. Chinese Patent CN117772818A discloses an online roll wear calculation method based on fully free-process rolling, using historical data to classify different stands and rolls, using machine learning to quickly fit clusters, improving the accuracy of wear calculation value correction, and outputting the corrected wear results. Chinese Patent CN114492024A discloses a mathematical model-based method for predicting roll wear in bar rolling, establishing a mathematical model for online roll wear prediction, and calculating the roll wear value of the stand under test.

[0004] However, the aforementioned technologies all suffer from limited predictive accuracy and generally lack deep integration with online production data, failing to achieve true dynamic prediction and precise diagnosis. Therefore, developing a system capable of accurately predicting roll life and quickly locating the source of faults when quality problems occur is of urgent need and significant importance for achieving predictive maintenance, improving product quality, and reducing production costs. Summary of the Invention

[0005] This invention provides an online diagnostic method for the service status of rolls in strip mills, which solves the technical problems of limited prediction accuracy in existing technologies, lack of deep integration with online production data, inability to adapt to complex and variable working conditions, inability to achieve true dynamic prediction and accurate diagnosis, and the decay of prediction accuracy over time.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: On one hand, the present invention provides an online diagnostic method for the service status of rolls in a strip mill, comprising: A finite element model of the rolls of a strip mill is constructed. The rolling process under different working conditions is simulated and calculated using the finite element model. The Arcard wear model is coupled to output the roll state parameters under each working condition. Construct a proxy model; wherein the proxy model uses production process parameters as input feature vectors and roll state parameters as multi-objective output vectors; The proxy model and the finite element model are combined to form a closed-loop interactive system. The proxy model is repeatedly trained and optimized to obtain an optimized proxy model. The optimized proxy model is deployed on the production line to achieve online diagnosis of the service status of strip mill rolls.

[0007] Furthermore, a finite element model of the strip mill rolls is constructed. This finite element model is used to simulate the rolling process under different operating conditions, and the Arcard wear model is coupled to output the roll state parameters under each operating condition, including: Multi-source heterogeneous data covering the entire lifecycle of the rolls is collected from the production line. This multi-source heterogeneous data includes: production process parameters, roll body data, and strip quality data from historical production processes. The production process parameters include: real-time rolling force, bending force, rolling speed, inter-stand tension, rolling kilometers, and rolling tonnage for each stand. The roll body data includes: material chemical composition, microstructure, initial geometric dimensions, initial surface roughness, measured grinding amount after rolling, and surface morphology for the work rolls, intermediate rolls, and support rolls. The strip quality data includes: defect types corresponding to production batches, defect image grayscale distribution, defect location coordinates, and defect periodicity characteristics. The collected data is preprocessed to construct a relational time-series database with the coil number as the primary key and the roll ID as the foreign key. The preprocessing includes data cleaning, timestamp alignment, outlier handling, and normalization. Based on the pre-processed roll body data, a finite element model including the work roll, intermediate roll, and support roll is established using ABAQUS finite element analysis software. The finite element model is a dynamic explicit analysis model that considers the elastic deformation of the roll, used to simulate the transient processes of strip bite-in, stable rolling, and strip ejection. Multiple production conditions are applied as loads and boundary conditions to the finite element model for simulation calculation, and coupled with the Archard wear model to output the roll state parameters under each condition; wherein, the roll state parameters include: the contact stress distribution, strain energy density and theoretical wear data of the roll.

[0008] Furthermore, the formula for the Archard wear model is:

[0009] in, V Where is the wear volume; K is the wear coefficient; F N The normal load on the contact surface; L This is the sliding distance; H The value of K is the hardness of the roll material. The value of K is not a constant, but is calibrated by inverse calculation. That is, by comparing the actual grinding amount of the roll after it is removed from the mill with the wear amount predicted by simulation, the mapping relationship between the value of K and the working condition is established. The value of K is determined according to the real-time working condition, thereby realizing the online adaptive correction of the wear model.

[0010] Furthermore, the construction of the proxy model includes: The preprocessed production process parameters from the historical production process are used as input feature vectors, and the simulated roll state parameters are used as multi-objective output vectors to construct a training sample set. Based on the training sample set, a Gaussian process regression algorithm is used to establish an independent regression model for each target variable in the multi-objective output vector, thereby constructing a surrogate model.

[0011] Furthermore, the kernel function of the Gaussian process regression algorithm adopts a combination of radial basis function and white noise function.

[0012] Furthermore, the proxy model and the finite element model are combined to form a closed-loop interactive system. The proxy model is repeatedly trained and optimized to obtain an optimized proxy model, including: Step 1: Utilize the Gaussian process characteristics of the surrogate model to calculate the prediction variance under complex superimposed working conditions that are not fully covered in the new or historical database, and mark the regions where the prediction variance exceeds a set threshold as high uncertainty regions. Step 2: In the high uncertainty region, the most valuable combination of working points is selected according to the active learning strategy to maximize the expected prediction error, and submitted as a new simulation task to the finite element model for simulation. Step 3: Add the new data generated by the finite element model simulation to the training sample set to obtain a new training sample set. Use the new training sample set to perform incremental training or periodic retraining on the surrogate model, update the model parameters, and thus reduce the prediction error of the surrogate model in the high uncertainty region. Step 4: Repeat steps 1 to 3 until the average prediction uncertainty of the surrogate model is lower than the preset convergence threshold or the maximum number of iterations is reached, and output the optimized surrogate model.

[0013] Furthermore, the optimized proxy model is deployed on the production line to achieve online diagnosis of the service status of strip mill rolls, including: Deploy the optimized agent model on the production line; Real-time acquisition of production process parameters, input into the surrogate model, and dynamic prediction of roll state parameters using the surrogate model; Based on the predicted values ​​of roll condition parameters, the remaining service life or health index of the roll is calculated; among which, The calculation process for the remaining useful life is as follows: The total wear rate is obtained by integrating the instantaneous wear rate predicted by the surrogate model over time. Based on the total wear, the remaining service life is calculated using the following formula:

[0014] in, Remaining useful life; W max This represents the maximum permissible wear limit of the rolls; Total wear amount; The predicted average wear rate over a future period of time; The formula for calculating the health index is as follows:

[0015] in, HI As a health index; α,β,γ For preset weighting coefficients and α + β + γ =1; σ vonMises The maximum equivalent stress of the rolls predicted by the surrogate model; σ yield Surface_Quality_Index is the yield strength of the roll material; Surface_Quality_Index is a rating index obtained based on the surface quality data of strip steel produced recently using the current roll.

[0016] Furthermore, after deploying the optimized proxy model on the production line to achieve online diagnosis of the service status of strip mill rolls, the online diagnosis method for the service status of strip mill rolls also includes: When periodic defects appear on the strip surface, the specific stand and roll type that caused the quality problem are identified, and targeted roll replacement and maintenance recommendations are generated based on the identification results.

[0017] Furthermore, the specific frame and roll types that cause quality problems due to positioning include: The defect image is transformed in the frequency domain to extract its dominant spatial wavelength λ; The theoretical defect cycle is calculated by combining the real-time rotational speed of the rolls in each stand. Suspect stands are initially screened by wavelength matching to construct a set of suspect stands. The proxy model is invoked to inversely calculate the theoretical wear morphology of the rolls of the suspected stand under the current working conditions, and its periodic features are extracted. Modal matching or cross-correlation coefficient algorithms are used to calculate the similarity between theoretical wear morphology features and measured defect features. The frame and roll with the highest similarity are taken as the frame and roll that cause quality problems.

[0018] Furthermore, the preliminary screening of suspected racks through wavelength matching includes: Calculate the circumference of the work rolls or intermediate rolls of each frame. C i =π× D i ;in, D i Current roller diameter; Connect λ with C i / n Perform a comparison; if |λ— C i / n ∣< If so, the corresponding rack will be marked as a suspected rack; among which, n The harmonic order is 1 or 2; This is the preset allowable error threshold.

[0019] In another aspect, the present invention also provides an electronic device comprising a processor and a memory; wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described method.

[0020] In another aspect, the present invention also provides a computer-readable storage medium storing at least one instruction, which is loaded and executed by a processor to implement the above method.

[0021] The beneficial effects of the technical solution provided by this invention include at least the following: This invention is not a simple data fitting process, but rather uses high-fidelity finite element simulation incorporating the Archard wear model as a "digital laboratory of the physical world" to profoundly reveal the deep-seated mechanisms between process parameters and roll wear. By integrating massive amounts of real production data, the constructed surrogate model possesses both the accuracy of physical mechanisms and the adaptability of data-driven approaches, fundamentally solving the pain point of insufficient prediction accuracy in traditional empirical formulas or simple models. Traditional methods make troubleshooting surface defects in strip steel as difficult as finding a needle in a haystack. However, this invention, through surrogate model inversion calculation, accurately matches the defect features detected online with the theoretical wear morphology of each stand's rolls, establishing a rapid analysis channel from quality phenomena directly to the root cause of the fault. This reduces fault location from potentially several hours to minutes, greatly improving the continuity and efficiency of the production line.

[0022] By using dynamic remaining life prediction based on model integration, this invention transforms roll replacement decisions from a rigid "on-time" plan to a precise "on-demand" arrangement based on the real-time health status of the rolls. This not only avoids "over-maintenance" of rolls in good condition but also eliminates "under-maintenance" and batch quality accidents caused by potential roll problems, thereby significantly reducing spare parts consumption and quality losses and improving overall equipment efficiency (OEE).

[0023] Compared to "black box" models, this invention, based on an authoritative physical wear model and rigorous mathematical integration methods, ensures that every step of the prediction process has clear physical meaning and mathematical foundation. This interpretability enhances the credibility of the prediction results, providing a solid and reliable basis for field engineers to make maintenance decisions and powerfully promoting the practical application of intelligent systems in actual production. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of the online diagnostic method for the service status of strip mill rolls provided in this embodiment of the invention; Figure 2 This is a schematic diagram of a three-dimensional finite element model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the dynamic prediction curve of roll wear provided in an embodiment of the present invention; Figure 4This is a system block diagram of the electronic device provided in the embodiments of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0027] First, it should be noted that in the embodiments of the present invention, the words "exemplarily," "for example," etc., are used to indicate that they are examples, illustrations, or descriptions. Any embodiment or design scheme described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of the term "exemplarily" is intended to present the concept in a specific manner. Furthermore, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or it can be either one or the other.

[0028] First Embodiment This embodiment provides an online diagnostic method for the service status of rolls in a strip mill, applicable to four- or six-roll strip mills. The implementation process is as follows: Figure 1 As shown, this method addresses the challenges of existing technologies failing to adapt to complex and variable operating conditions and the decline in prediction accuracy over time, providing an intelligent and self-evolving solution for predictive maintenance of rolls and product quality control. This method can be implemented electronically, and its execution flow includes the following steps:

[0029] S1. Construct a finite element model of the strip mill rolls, use the finite element model to simulate the rolling process under different working conditions, and couple the Archard wear model to output the roll state parameters under each working condition. Specifically, in this embodiment, the implementation process of S1 is as follows: S11, Data Acquisition, details are as follows: S111 collects multi-source heterogeneous data covering the entire lifecycle of the rolls from the basic automation system, process control system, and manufacturing execution system of the cold rolling mill. The collected data includes: production process data, roll body data, and strip quality data. Production process data includes: real-time rolling force, bending roll force, rolling speed, inter-stand tension, rolling kilometers, and rolling tonnage for each stand; The data of the roll body includes: the chemical composition of the material of the work roll, intermediate roll, and support roll, the microstructure, the initial geometric dimensions, the initial surface roughness, the actual grinding amount after the roll is removed from the machine, and the surface morphology. The strip steel quality data includes: defect types, defect image grayscale distribution, defect location coordinates, and defect periodic characteristics recorded by the online strip steel surface inspection system that strictly corresponds to the production batch; S112 involves cleaning, timestamp alignment, outlier handling, and normalization preprocessing of the collected data to construct a relational time-series database with the coil number as the primary key and the roll ID as the foreign key.

[0030] S12, Finite Element Simulation, details are as follows: S121. Based on the roll parameters collected in S11, a refined finite element model including the work roll, intermediate roll, and support roll is established using ABAQUS finite element analysis software. The finite element model is a dynamic explicit analysis model that considers the elastic deformation of the rolls, and is used to accurately simulate the transient processes of strip biting, stable rolling, and strip ejection. S122, using the various typical production conditions collected in S11 as loads and boundary conditions, applies them to the finite element model for simulation calculation, and couples the Archard wear model to output the contact stress distribution, strain energy density, and theoretical wear data of the rolls under each condition. The basic formula of the Archard wear model is:

[0031] in, V This refers to the wear volume; K The wear coefficient; F N The normal load on the contact surface; L This is the sliding distance; H The hardness of the roll material is used; in the finite element simulation, the model is discretized into an incremental form. It is applied to each contact unit to calculate the local wear depth. Δ d, where, P To contact pressure, Δ s is the sliding distance within the increment step; It should be noted that the wear coefficient K is not a constant, but is calibrated by inverse method. That is, by comparing the actual amount of grinding of the roll after it comes off the mill with the wear amount predicted by simulation, the mapping relationship between the K value and the lubrication conditions (emulsion flow rate and concentration) is established, thereby realizing the online adaptive correction of the wear model.

[0032] S2, Construct a proxy model; where the proxy model uses production process parameters as input feature vectors and roll state parameters as multi-objective output vectors; Specifically, in this embodiment, the implementation process of S2 is as follows: S21, using the preprocessed production process parameters from S112 as the input feature vector X, and the simulated roll state parameters from S122 as the multi-objective output vector Y=[y1,y2,...,y m Construct a training sample set {X,Y}; S22 uses the Gaussian process regression algorithm for each target variable y in the output vector Y. k (k=1,2,...,m) Establish independent regression models. Here, a Gaussian process is a stochastic process defined on the function space. Its core idea is that the set of function values ​​f(X) at any finite number of input points follows a multivariate Gaussian distribution. For the k-th output target, its Gaussian process model is defined as:

[0033]

[0034]

[0035] in, m k (X) is the mean function, which is usually set to a constant or zero; K k (X,X') is the covariance function (kernel function) used to characterize the similarity between input points X and X'; It is observation noise that follows a Gaussian distribution.

[0036] S23, Selection and Design of Kernel Function; the kernel function adopts a combination of radial basis function and white noise function to simultaneously capture global trends and local noise, and its mathematical expression is as follows:

[0037] Where, σ f,k The variance of the signal controls the range of fluctuation of the function value. l k The length scale parameter determines the radius of influence of the input features; σ n,k σ(X,X') is the noise variance, used to model the uncertainty in the observed data; σ(X,X') is the Kronecker delta function (1 when X=X', 0 otherwise).

[0038] This combined kernel function can simultaneously capture the global trend (dominated by radial basis functions) and local noise (dominated by white noise functions) between process parameters and roll conditions.

[0039] S24, optimize the kernel function hyperparameters using maximum likelihood estimation; specifically, optimize the kernel function hyperparameters of the k-th model using maximum likelihood estimation. θ k ={σ f,k， l k， σ n,k Specifically, this is achieved by maximizing its logarithmic marginal likelihood function:

[0040] in, n The number of training samples. K k It is determined by the kernel function K k ( X,X′ The covariance matrix calculated over all training sample pairs, I It is an identity matrix.

[0041] The hyperparameters that maximize the likelihood function are solved using optimization algorithms such as the conjugate gradient method.

[0042] S25, Model Prediction and Uncertainty Quantification, specifically: For a new input point, the trained Gaussian process regression model... Its relationship with the k-th target variable Predicted value It follows a Gaussian distribution, and its predicted mean is... (i.e., the best estimate) and prediction variance (That is, the uncertainty measure) is given by the following formula:

[0043] in, It is a new input point With all training input points X The covariance vector between them; It is the covariance of the new input point itself. Prediction variance. It is directly used to quantify the uncertainty of model predictions, providing a basis for subsequent active learning and iterative optimization.

[0044] S26. The K-fold cross-validation method is used to evaluate the generalization ability of the constructed multi-objective Gaussian process surrogate model, ensuring that the model maintains high prediction accuracy even on unseen data. The final result is a high-precision surrogate model that can quickly and accurately map input process parameters to roll contact stress, strain, and wear; this surrogate model can rapidly calculate the roll state under given production parameters.

[0045] S3, the proxy model and the finite element model are combined into a closed-loop interactive system, and the proxy model is repeatedly trained and optimized to obtain the optimized proxy model; Specifically, in this embodiment, the implementation process of S3 is as follows: S31. Utilizing the Gaussian process characteristics of the surrogate model, calculate the prediction variance under complex superimposed working conditions that are not fully covered in the new or historical database, and mark the regions where the prediction variance exceeds a set threshold as high uncertainty regions. S32, In the region of high uncertainty, the most valuable combination of working points is selected according to the active learning strategy to maximize the expected prediction error, and submitted as a new simulation task to the finite element model for high-fidelity simulation. S33 adds the new data generated by finite element simulation to the training sample set, performs incremental training or periodic retraining on the surrogate model, updates the model parameters, and thus reduces the prediction error in the high uncertainty region. S34. Repeat S31 to S33 until the average prediction uncertainty of the surrogate model is lower than the preset convergence threshold or the maximum number of iterations is reached, and output the optimized high-precision and high-robust surrogate model.

[0046] S4 deploys the optimized proxy model on the production line to achieve online diagnosis of the service status of strip mill rolls; Specifically, in this embodiment, the implementation process of S4 is as follows: S41 integrates the trained surrogate model into the online monitoring system of the cold rolling production line; S42 collects real-time data on rolling force, bending force, and rolling speed for each stand, inputs this data into the surrogate model, and dynamically predicts and displays the remaining service life (RUL) or health index of the rolls for each stand; among which, Remaining useful life (RUL) prediction is achieved by integrating the instantaneous wear rate predicted by the surrogate model over time. The core formula for calculating the total wear is as follows:

[0047] in, The instantaneous wear rate predicted by the surrogate model; The remaining useful life is estimated using the following formula:

[0048] in, W max This represents the maximum permissible wear limit of the rolls; w This represents the predicted average wear rate over a future period.

[0049] The health index is a comprehensive evaluation indicator that integrates multiple factors, and its calculation formula is as follows:

[0050] in, HI Health index (between 0 and 1). α,β,γ The weighting coefficients and α + β + γ =1, σ vonMisesThe maximum equivalent stress of the rolls is predicted by the surrogate model. σ yield Surface_Quality_Index is the yield strength of the roll material, and it is a rating index based on the surface quality data of the strip steel produced by the roll in recent times. Its value is determined according to the actual production situation and is used to evaluate the recent production quality of the roll.

[0051] S5: When periodic defects appear on the surface of the strip, the specific stand and roll type that caused the quality problem are identified, and targeted roll replacement and maintenance suggestions are generated based on the identification results. Specifically, in this embodiment, the implementation process of S5 is as follows: When the strip surface inspection system detects a periodic defect, it automatically triggers a diagnostic process and executes the following steps: S51, Perform frequency domain transformation on the defect image to extract its dominant spatial wavelength λ; S52, combining the real-time rotational speed of each stand's rolls to calculate the theoretical defect cycle, and using wavelength matching to initially screen the set of suspected stands {Suspicious_Stand}; specifically, wavelength matching involves calculating the circumference of the work rolls or intermediate rolls of each stand. C i =π× D i ( D i (for the current roll diameter), the defect-dominant wavelength λ is compared with... C i / n (n is the harmonic order, usually taken as 1 or 2) A comparison is made, if the perimeter corresponding to frame i... C i Satisfy: |λ— C i / n ∣< ( If the allowable error threshold is used, then rack i will be included in the suspected rack set; S53, invoke the proxy model, invert and calculate the theoretical wear morphology of the suspected stand rolls under the current working conditions, and extract its periodic characteristics; S54 uses modal matching or cross-correlation coefficient algorithms to calculate the similarity between theoretical wear morphology features and measured defect features. It uses the highest similarity to identify the specific stand and roll type that causes quality problems and generates targeted roll replacement and maintenance suggestions.

[0052] In summary, this embodiment provides an online diagnostic method for the service status of rolls in strip mills. First, historical production data and roll parameters of the cold continuous rolling mill are collected. A high-fidelity roll simulation model is established using ABAQUS finite element software coupled with an Archard wear model. Stress, strain, and theoretical wear data of the rolls under various production conditions are obtained through multi-condition simulation. Subsequently, based on a Gaussian process multi-objective regression algorithm, a high-precision surrogate model is constructed, using key process parameters such as rolling force, bending force, and rolling speed as inputs, and roll contact stress and wear as outputs. Further, an interactive iterative mechanism between the surrogate model and the finite element model is established. The surrogate model is used to quickly filter out production parameter points with high prediction uncertainty or complex superposition of operating conditions, driving the finite element model to perform targeted simulations. New simulation data is fed back to the surrogate model for incremental training, achieving continuous self-optimization of the surrogate model. Finally, this high-precision surrogate model is linked with the online production system, and the remaining service life of the rolls on each stand is dynamically and accurately predicted through integral wear rate. When defects appear on the strip surface, the system can accurately locate the problematic roll on a specific stand by comparing real-time data with the wear characteristics output by the proxy model. This solves the problem that existing technologies cannot adapt to complex and variable working conditions and that prediction accuracy decays over time, providing an intelligent and self-evolving solution for predictive maintenance of rolls and product quality control.

[0053] Second Embodiment To verify the effectiveness of the method of the present invention, this embodiment uses a cold continuous rolling mill six-roll mill production line of a steel plant as an example to illustrate the implementation process and effectiveness of the method of the present invention. This embodiment uses two types of strip steel involving different strengths and widths, namely BR50W1000 silicon steel and ordinary carbon steel (SPCC), as examples, as follows:

[0054] S1, Data Acquisition Phase: Production data from the past year was collected from the basic automation system, process control system, and manufacturing execution system of the steel plant's cold rolling mill. This data covers the entire lifecycle of the rolls, spanning over 2000 rolling kilometers. After preprocessing, a training sample library containing over 100,000 valid data records was created. The collected data includes:

[0055] Production process data: real-time rolling force, bending roll force, rolling speed, inter-stand tension, rolling kilometers, and rolling tonnage for each stand; Roll body data: A total of 50 pairs of work rolls, intermediate rolls, and 20 pairs of support rolls were tracked and recorded, including the chemical composition, microstructure, initial geometric dimensions, initial surface roughness, measured grinding amount after loading and unloading the mill, and roll profile curves. Strip steel quality data: Defect types, defect image grayscale distribution, defect location coordinates, and defect periodic characteristics recorded by the online surface inspection system of strip steel that strictly corresponds to the production batch; By cleaning, aligning timestamps, handling outliers, and normalizing the collected data, a relational time-series database with coil number as the primary key and roll ID as the foreign key is constructed.

[0056] S2, Finite Element Simulation Stage: S2-1, Based on the roll parameters collected in S1, and considering the rolls of this production line (e.g., material is high-chromium steel Gr15, initial roll diameter...), Based on the actual parameters (520mm), a dynamic explicit analysis model considering elastic deformation was established in ABAQUS. The mesh was generated using C3D8R elements, with mesh refinement in the roll contact area. The element size was approximately 1mm. Some roll simulation models are shown below. Figure 2 As shown.

[0057] S2-2 uses various typical production conditions collected in S1 as loads and boundary conditions, applying them to the finite element model for simulation calculations. The Latin hypercube sampling method is employed, and 500 sets of typical working condition combinations are designed within the parameter range for simulation. Each simulation outputs the equivalent stress cloud map, contact pressure distribution, and wear depth data based on the Archard model for the rolls. By comparing the actual grinding amount of 10 pairs of work rolls after removal from the mill with the simulated predicted wear amount, the wear coefficient under the current lubrication conditions (emulsion concentration 3.5%, flow rate 1500 L / min) is calculated. The material hardness is H=650HB. The Arcard wear model is coupled to output the contact stress distribution, strain energy density, and theoretical wear data of the rolls under various working conditions.

[0058] The basic formula for the Archard wear model is as follows:

[0059] in, V This refers to the wear volume; K The wear coefficient; F N The normal load on the contact surface; L This is the sliding distance; H The hardness of the roll material; In finite element simulation, the model is discretized into incremental form. It is applied to each contact unit to calculate the local wear depth. Δ d, where, P For contact pressure; Δs represents the sliding distance within the increment step; it should be noted that the wear coefficient K is not a constant, but is calibrated by inverse calculation, that is, by comparing the actual grinding amount of the roll after it comes off the mill with the wear amount predicted by simulation, a mapping relationship between the K value and the lubrication conditions (emulsion flow rate, concentration) is established, thereby realizing the online adaptive correction of the wear model.

[0060] S3, Agent Model Construction Phase: S3-1: The production process parameters preprocessed in S1 are used as the input feature vector X, and the key state parameters of the roll obtained from the simulation in S2 are used as the multi-objective output vector Y to construct a training sample set. S3-2 employs a Gaussian process regression algorithm to establish an independent regression model for each target variable in the output vector Y. Its kernel function combines radial basis functions and white noise functions to simultaneously capture global trends and local noise. Maximum likelihood estimation is used to optimize the kernel function hyperparameters, and K-fold cross-validation is employed to evaluate the model's generalization ability. Ultimately, a high-precision surrogate model is obtained that can quickly map process parameters to roll contact stress, strain, and wear. This surrogate model can rapidly calculate the roll state under given production parameters. S4, Model Iteration and Optimization Stage: The proxy model constructed by S3 and the finite element simulation model constructed by S2 form a closed-loop interactive system; including: S4-1 utilizes the Gaussian process characteristics of the surrogate model to calculate the prediction variance under complex superimposed working conditions that are not fully covered in new or historical databases, and marks the regions where the prediction variance exceeds a set threshold as high uncertainty regions. S4-2, In the region of high uncertainty, the most valuable combination of working points is selected according to the active learning strategy to maximize the prediction error, and submitted as a new simulation task to the finite element model for high-fidelity simulation. S4-3 adds the new data generated by finite element simulation to the training sample set of S3, performs incremental training or periodic retraining on the surrogate model, updates the model parameters, and thus reduces the prediction error in the high uncertainty region. S4-4, Repeat S4-1 to S4-3 until the average prediction uncertainty of the surrogate model across the entire operating range is lower than the preset convergence threshold, or the maximum number of iterations is reached, and output the optimized high-precision, high-robust surrogate model; wherein, in this embodiment, the data changes of the model in the first three iterations are shown in the following table: Table 1. Data changes after model iteration

[0061] S5, Online Prediction and Diagnosis Phase: S5-1 integrates a well-trained surrogate model into the online monitoring system of the cold rolling production line; S5-2, real-time acquisition of rolling force, bending force, and rolling speed data for each stand, input into the surrogate model, dynamically predicting and displaying the remaining service life (RUL) or health index of the rolls for each stand; wherein, in this embodiment, the dynamic prediction curve of roll wear is as follows: Figure 3 As shown; The remaining useful life (RUL) prediction is achieved by integrating the instantaneous wear rate predicted by the surrogate model over time. The core formula for calculating the total wear is as follows:

[0062] in, w (t) represents the instantaneous wear rate predicted by the surrogate model; the remaining service life is estimated using the following formula:

[0063] in, W max This represents the maximum permissible wear limit of the rolls. w This represents the predicted average wear rate over a future period.

[0064] The health index is a comprehensive evaluation indicator that integrates multiple factors, and its calculation formula is as follows:

[0065] in, HI Health index (between 0 and 1); α,β,γ The weighting coefficients and α + β + γ =1; σ vonMises The maximum equivalent stress of the rolls predicted by the surrogate model; σ yield Surface_Quality_Index represents the yield strength of the roll material; Surface_Quality_Index is a rating index based on the surface quality data of strip steel produced recently by this roll.

[0066] S6, Abnormal Diagnosis and Localization Stage: S6-1, Perform frequency domain transformation on the defect image to extract its dominant spatial wavelength λ; S6-2, combined with the real-time rotational speed of the rolls in each stand, the theoretical defect cycle is calculated, and the suspected stand set {Suspicious_Stand} is initially screened by wavelength matching; Specifically, wavelength matching involves calculating the circumference of the work rolls or intermediate rolls of each frame. C i =π× D i ( Di (for the current roll diameter), the defect-dominant wavelength λ is compared with... C i / n ( n For harmonic orders, usually taken as 1 or 2, comparison is performed. If |λ— C i / n ∣< ( If the allowable error threshold is used, then rack i will be included in the suspected rack set.

[0067] S6-3, invoke the proxy model to invert and calculate the theoretical wear morphology of the suspected stand rolls under the current working conditions, and extract its periodic characteristics; S6-4 uses modal matching or cross-correlation coefficient algorithms to calculate the similarity between theoretical wear morphology features and measured defect features. It uses the highest similarity to identify the specific stand and roll type that causes quality problems and generates targeted roll replacement and maintenance suggestions.

[0068] Using the above solution, and after long-term verification, the surface inspection instrument successfully triggered an alarm during production. A scratch approximately 68 mm wide and 100 mm long was detected on the strip surface at a distance of 843.4 meters from the head, 923 mm from the drive side, 310 mm from the operating side, and 8.1 meters from the tail. The system calculated and locked onto the F3 stand. The proxy model calculated the theoretical wear of the work rolls based on the current process parameters of the F3 stand, which highly matched the measured defects. The system diagnostic interface concluded: "Uneven wear of the work rolls under the F3 stand is suspected; priority inspection and replacement are recommended," guiding maintenance personnel to perform precise operations. Through the implementation of this solution, the number of unplanned roll changes on this rolling line decreased by over 50%, and the quality degradation rate caused by roll problems decreased by 30%, achieving significant economic benefits.

[0069] As can be seen from the above examples, the method of the present invention can dynamically and accurately predict the remaining service life of each stand roll, and can quickly and accurately diagnose and locate the specific stand and roll causing the problem when surface quality problems occur in strip steel, thereby realizing the scientific and intelligent management of rolls.

[0070] Third Embodiment This embodiment provides an electronic device, such as... Figure 4 As shown, the electronic device includes a processor and a memory; wherein the processor and the memory can be connected via a communication bus; the memory stores at least one instruction, which is loaded and executed by the processor to implement the method of the first embodiment described above. Furthermore, the electronic device may also include a transceiver, the processor and the transceiver can be connected via a communication bus, and the transceiver is used to communicate with other devices.

[0071] Below, in conjunction with Figure 4 A detailed introduction to each component of this electronic device is provided below: The processor is the control center of the electronic device. The electronic device may include multiple processors, each of which can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). The term "processor" can refer to a single processor or a collective term for multiple processing elements. For example, a processor can be one or more central processing units (CPUs), other general-purpose processors, application-specific integrated circuits (ASICs), or one or more integrated circuits configured to implement embodiments of the present invention, such as one or more digital signal processors (DSPs), one or more field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor can perform various functions of the electronic device by running or executing software programs stored in memory and by calling data stored in memory.

[0072] In a specific implementation, as one example, the processor may include one or more CPUs, for example... Figure 4 CPU0 and CPU1 shown are, of course, merely illustrative examples.

[0073] The memory is used to store the software program that executes the solution of the present invention, and the processor controls its execution. For specific implementation methods, please refer to the above method embodiments, which will not be repeated here.

[0074] Optionally, the memory may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto. The memory may be integrated with the processor or exist independently, and may be accessed through the interface circuit of the electronic device ( Figure 4 (Not shown in the image) is coupled to the processor; however, this embodiment of the invention does not impose specific limitations on this.

[0075] The transceiver may include a receiver and a transmitter. Figure 4 (Not shown separately). The receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function. The transceiver can be integrated with the processor or exist independently, and can be connected through the interface circuit of the electronic device (…). Figure 4 (Not shown in the image) is coupled to the processor, and this embodiment of the invention does not specifically limit this.

[0076] In addition, it should be noted that, Figure 4 The structure of the electronic device shown is not intended to limit the device. Actual devices may include more or fewer components than shown, or combine certain components, or have different component arrangements. Furthermore, the technical effects achieved by this electronic device when performing the method of the first embodiment described above can be referenced to the technical effects described in the first embodiment; therefore, they will not be repeated here.

[0077] Fourth embodiment This embodiment provides a computer-readable storage medium storing at least one instruction, which is loaded and executed by a processor to implement the method of the first embodiment described above. The computer-readable storage medium may be a ROM, random access memory, CD-ROM, magnetic tape, floppy disk, or optical data storage device, etc. The instruction stored therein can be loaded and executed by a processor in a terminal.

[0078] Furthermore, it should be noted that the present invention can be provided as a method, apparatus, or computer program product. Therefore, embodiments of the present invention can take the form of a completely or partially hardware embodiment, a completely or partially software embodiment, or an embodiment combining software and hardware aspects. Moreover, when implemented in software, embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any usable medium accessible to a computer or a data storage device such as a server or data center containing one or more sets of usable media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive (SSD).

[0079] Embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0080] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0081] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element. Furthermore, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, and B alone, where A and B can be singular or plural. Additionally, the character " / " in this text generally indicates an "or" relationship between the preceding and following objects, but it can also indicate an "AND / OR" relationship. Please refer to the context for specific interpretations. "At least one" refers to one or more items, while "more than" refers to two or more items. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items. For example, at least one of a, b, or c can be represented as: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0082] Furthermore, it is understood that in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0083] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0084] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of functional modules / units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms. Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, i.e., they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs. Additionally, the functional units in the various embodiments of this invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0085] If the method is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0086] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments of the present invention have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make several improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A method for on-line diagnosis of the service condition of a rolling mill roll for strip, characterized in that, include: A finite element model of the rolls of a strip mill is constructed. The rolling process under different working conditions is simulated and calculated using the finite element model. The Arcard wear model is coupled to output the roll state parameters under each working condition. Construct a proxy model; wherein the proxy model uses production process parameters as input feature vectors and roll state parameters as multi-objective output vectors; The proxy model and the finite element model are combined to form a closed-loop interactive system. The proxy model is repeatedly trained and optimized to obtain an optimized proxy model. The optimized proxy model is deployed on the production line to achieve online diagnosis of the service status of strip mill rolls.

2. The strip mill roll service condition on-line diagnostic method of claim 1, characterized in that, A finite element model of the strip mill rolls is constructed. This model is then used to simulate the rolling process under different operating conditions. The model is coupled with an Archard wear model to output the roll state parameters for each operating condition, including: Multi-source heterogeneous data covering the entire lifecycle of the rolls is collected from the production line. This multi-source heterogeneous data includes: production process parameters, roll body data, and strip quality data from historical production processes. The production process parameters include: real-time rolling force, bending force, rolling speed, inter-stand tension, rolling kilometers, and rolling tonnage for each stand. The roll body data includes: material chemical composition, microstructure, initial geometric dimensions, initial surface roughness, measured grinding amount after rolling, and surface morphology for the work rolls, intermediate rolls, and support rolls. The strip quality data includes: defect types corresponding to production batches, defect image grayscale distribution, defect location coordinates, and defect periodicity characteristics. The collected data is preprocessed to construct a relational time-series database with the coil number as the primary key and the roll ID as the foreign key. The preprocessing includes data cleaning, timestamp alignment, outlier handling, and normalization. Based on the pre-processed roll body data, a finite element model including the work roll, intermediate roll, and support roll is established using ABAQUS finite element analysis software. The finite element model is a dynamic explicit analysis model that considers the elastic deformation of the roll, used to simulate the transient processes of strip bite-in, stable rolling, and strip ejection. Multiple production conditions are applied as loads and boundary conditions to the finite element model for simulation calculation, and coupled with the Archard wear model to output the roll state parameters under each condition; wherein, the roll state parameters include: the contact stress distribution, strain energy density and theoretical wear data of the roll.

3. The strip mill roll service condition on-line diagnostic method of claim 1, wherein, The formula for the Archard wear model is: ； wherein, V is the wear volume; K is the wear coefficient; F N is the normal load on the contact surface; L is the sliding distance; H is the hardness of the roll material; the value of K is not a constant, but is calibrated by a reverse method, that is, by comparing the actual grinding amount of the roll after the machine with the simulated predicted wear amount, a mapping relationship between the value of K and the working condition is established, the value of K is determined according to the real-time working condition, so as to realize the online self-adaptive correction of the wear model.

4. The strip mill roll service condition on-line diagnostic method of claim 2, wherein The construction of the proxy model includes: The preprocessed production process parameters from the historical production process are used as input feature vectors, and the simulated roll state parameters are used as multi-objective output vectors to construct a training sample set. Based on the training sample set, a Gaussian process regression algorithm is used to establish an independent regression model for each target variable in the multi-objective output vector, thereby constructing a surrogate model.

5. The strip mill roll service condition on-line diagnostic method of claim 4, characterized in that, The kernel function of the Gaussian process regression algorithm adopts a combination of radial basis function and white noise function.

6. The strip mill roll service condition on-line diagnostic method of claim 4, wherein The proxy model and the finite element model constitute a closed-loop interactive system, the proxy model is repeatedly trained and optimized to obtain an optimized proxy model, including: Step 1, using the Gaussian process characteristics of the proxy model, calculating the prediction variance of the complex rolling condition not fully covered in the new or historical database, and marking the area with a prediction variance exceeding a set threshold as a high uncertainty area; Step 2, in the high uncertainty area, according to the active learning strategy, the most valuable combination of working condition points is selected as the new simulation task to be submitted to the finite element model for simulation; Step 3, adding the new data generated by the finite element model simulation to the training sample set to obtain a new training sample set, using the new training sample set to incrementally train or periodically retrain the proxy model, updating the model parameters, thereby reducing the prediction error of the proxy model in the high uncertainty area; Step 4, repeating steps 1 to 3 until the average prediction uncertainty of the proxy model in the full working condition range is lower than the preset convergence threshold, or the maximum number of iterations is reached, and outputting the optimized proxy model.

7. The strip mill roll service state online diagnostic method of claim 1, wherein, Deploying the optimized proxy model on the production line to realize online diagnosis of the service state of the plate and strip rolling mill roll, including: Deploying the optimized proxy model on the production line; Real-time acquisition of production process parameters, inputting the proxy model, and dynamically predicting the roll state parameters using the proxy model; Based on the predicted value of the roll state parameters, the remaining service life or health index of the roll is calculated; wherein, The calculation process of the remaining service life is: Time integration of the instantaneous wear rate predicted by the proxy model to obtain the total wear amount; Based on the total wear amount, the remaining service life is calculated by the following formula: ； wherein, is the remaining useful life; W max is the maximum wear limit allowed for the roll; is the total wear amount; is the predicted average wear rate over a future period of time; The calculation formula of the health index is: ； wherein, HI is a health index; α,β,γ is a preset weight coefficient and α + β + γ = 1; σ vonMises is a maximum equivalent stress of the roll predicted by the surrogate model; σ yield is a yield strength of the roll material; and Surface_Quality_Index is a score index obtained based on strip surface quality data of recent production of the current roll.

8. The strip mill roll service state online diagnostic method of claim 1, wherein, After deploying the optimized proxy model on the production line to realize online diagnosis of the service state of the plate and strip rolling mill roll, the online diagnosis method of the plate and strip rolling mill roll service state further includes: When periodic defects appear on the surface of the strip steel, the specific stand and roll type causing the quality problem is located, and targeted roll replacement maintenance suggestions are generated according to the positioning results.

9. The strip mill roll service condition online diagnostic method of claim 8, wherein, The specific stand and roll type causing the quality problem includes: Performing frequency domain transformation on the defect image to extract its dominant spatial wavelength λ; Combined with the real-time speed of each stand roll, the theoretical defect period is calculated, the suspected stand is preliminarily screened through wavelength matching, and a suspected stand set is constructed; Calling the proxy model, the theoretical wear morphology characteristics of the roll of the suspected stand under the current working condition are calculated by inversion, and the periodic characteristics are extracted; Using modal matching or cross-correlation coefficient algorithm, the similarity between the theoretical wear morphology characteristics and the measured defect characteristics is calculated, and the stand and roll corresponding to the highest similarity are taken as the stand and roll causing the quality problem.

10. The strip mill roll service condition online diagnostic method of claim 9, wherein, The suspected stand is preliminarily screened through wavelength matching, including: calculating the circumference of each stand work roll or intermediate roll C i = π x D i ; wherein, D i is the current roll diameter; λ is compared with C i / n If |λ— C i / n | , the corresponding rack is marked as a suspected rack; wherein, n is a harmonic number, which is 1 or 2; is a preset allowable error threshold.

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