Quality-Related Process Monitoring and Diagnosis of Hot-Rolled Strip Based on Weighted Statistical Feature KPLS

Rolling is the main process in steel production. There are some problems in the rolling process, such as insufficient ability of abnormal detection and evaluation, low accuracy of process monitoring, and fault diagnosis. To improve the accuracy of quality-related fault diagnosis, this paper proposes a quality-related process monitoring and diagnosis method for hot-rolled strip based on weighted statistical feature KPLS. Firstly, the process-monitoring and diagnosis model of strip thickness and quality based on the KPLS method is introduced. Then, considering that the KPLS diagnosis method ignores the contribution of process variables to quality, it is easy to misjudge the root cause of quality in the diagnosis process. Based on the rolling mechanism model, the influence weight of strip thickness is constructed. By weighing the statistical data features, a quality diagnosis framework of series structure data fusion is constructed. Finally, the method is applied to the 1580 mm hot-rolling process for industrial verification. The verification results show that the proposed method has higher diagnostic accuracy than PLS, KPLS, and other methods. The results show that the diagnostic model based on weighted statistical feature KPLS has a diagnostic accuracy of more than 96% for strip thickness and quality-related faults.


Introduction
Quality-related process monitoring and diagnosis are crucial for maintaining a high level of industrial development and product upgrading [1,2]. To ensure production safety and improve product quality, the comprehensive intelligent development of manufacturing industry puts forward new requirements for product quality inspection of process industry [3][4][5]. In the process of hot rolling, there are many process parameters related to the final product quality, such as width and thickness, and the relationship between quality factors and quality indicators is unclear. How to quickly monitor and diagnose the abnormal quality fluctuations in the rolling process, locate the causes of abnormalities, and improve the product quality has become an important problem in the production process of strip [6]. In recent years, to improve the production efficiency in industrial processes, industrial production equipment and processes have become more complex. Once the process abnormality or fault transfer occurs, it is very likely to cause a series of cascading failures leading to serious production accidents, and even cause serious economic losses and casualties. Therefore, how to carry out timely and accurate anomaly detection of the production processes to ensure its production safety and product quality has become an urgent problem to be solved in industry and academia [7,8].
For the monitoring and diagnosis of product quality in the production process, a lot of research work has been carried out. Based on multivariate statistical process control (MSPC), the quality-related process monitoring the multivariate production process is realized, including canonical correlation analysis (CCA), principal component analysis (PCA), characteristics improves the physical interpretation of process variables on strip quality. Considering the degree of influence of different variables on quality, the weight of mass variable influence is constructed based on rolling mechanism model. Improve the detection rate of quality-related failures by influencing weight reconstruction monitoring model input data. In addition, the data model is improved in the form of data weighting, which can solve the problem that the fault characteristics of industrial processes are not significant due to small amplitude or slow change. Finally, the industrial verification of the model is carried out by using the production data of the 1580 hot rolling production line. The results meet the requirements of the field quality detection and can effectively identify the abnormal fluctuation variables.
The remaining sections are arranged as follows: Section 2 introduced the monitoring and diagnosis model of the KPLS algorithm for strip quality. In Section 3, the weight of thickness quality influence was constructed based on the rolling process, and the data set was weighted and reconstructed by the weight. A series structure model of qualityrelated fault diagnosis based on mechanism data fusion was established. The verification experiment and summary are found in Sections 4 and 5, respectively.

Monitoring and Diagnosis of Quality-Related Faults of Hot-Rolled Strip Based on KPLS
A large amount of data generated in the production process of hot rolled strip have strong nonlinearity. Aiming at the nonlinearity of the plate and strip rolling process. Given input matrix X consisting of n samples with m process variables, and output matrix Y containing n observations with p quality variables, respectively, i.e., where x i ∈ R m and y i ∈ R p (i = 1, 2, · · · , n) are row vectors, respectively.
Using the nonlinear mapping function, it is a common way [20] to map the original input data to a high-dimensional feature space. To this aim, given a nonlinear projection function φ, has φ : x → φ(x) . The data mapping matrix of high dimensional space is obtained Φ.
The element K ij of the ith row and jth column of kernel matrix K is Due to the diversity of mapping functions, including polynomial, sigmoid, and other kernel functions, these kernel functions introduce multiple parameters. However, the Gaussian kernel function only has one parameter σ, which is beneficial for controlling model accuracy. Therefore, this article selects Gaussian kernel function to calculate the kernel matrix.
where K x i , x j is Gaussian kernel function and σ is constant, σ = 16, i = 1, 2, · · · , n, j = 1, 2, · · · , n, respectively. The following kernel matrix K is usually defined [30] to avoid the explicit using of Φ: Centralize the kernel matrix. K = K − 1 n I n K − 1 n KI n + 1 n 2 I n KI n (5) The kernel matrix of the sample to be monitored is constructed, and the new data in the kernel matrix of the feature space is centralized by using the training data.
The above formulas P and Q are the load matrix of K and Y respectively, T and U are the score matrix of K and Y, respectively.
Sample score matrix to be tested.
The covariance matrix of the training sample score is Λ = T T T n−1 . The T 2 statistic follows the F distribution, and the SPE statistic is based on the assumption of standard normal distribution. The control limits are calculated as follows.
where g = S 2µ , h = 2µ 2 S , µ is the average value of SPE statistics, S is the variance, α 0 is the significance level, A is the number of principal elements determined by cross validation, respectively.
The nonlinear contribution plot is used to calculate the contribution of the parameters in the sample points to the monitoring indicators, find out the fault variables that affect the quality, and realize the identification and diagnosis of abnormal causes in the production process. For the new test sample x new,l ∈ R 1×m (l = 1, 2, · · · , m) of the new input point, the partial derivatives of the nuclear matrix K new of the new input point for each parameter are as follows.
Calculate the SPE contribution value of each parameter.
where K new is the partial derivative vector K new,i , which forms the partial derivative kernel matrix. The monitoring and diagnosis of quality-related faults of hot-rolled strip based on KPLS is solved by Algorithm 1.

Algorithm 1:
The calculation algorithm of KPLS [19] Step 1 Set Select the first column of Y i as u i .
Step 5 Step 7 Repeat step 3 to step 6 until t i converges.
Set i = i + 1 and repeat step 2 to step 9 until i > r

KPLS Quality-Related Process Monitoring and Diagnosis Based on Data Weighting
In the above KPLS monitoring model, the monitoring and diagnosis of quality-related faults of hot rolled plates and strips can be realized, but there is a lack of reasonable physical explanation for each variable, resulting in a misjudgment of the cause of quality defects. Thus, a method for quality-related process monitoring and diagnosis of hot-rolled strips based on the weighted statistical feature KPLS (WKPLS) was proposed.

Introduction to the Hot Rolling Process
Hot rolling is a complex multi-process collaborative industrial production process [32]. It mainly includes heating, roughing mill, finishing mill, laminar cooling, coiling, and other processes, as shown in Figure 1. The finishing mill stage is usually composed of 5-7 stands. Each stand of finishing mill is mainly composed of frame, work roll, back-up roll, hydraulic screw down, bending roll device, corresponding hydraulic control system, feedback control, and signal data acquisition system. The strip is affected by rolling force and other related parameters. The metal produces elastic-plastic deformation between the roll gap, and the abnormal quality fluctuation of the strip is caused by the abnormal rolling parameters [33]. The thickness difference of strip is affected by the abnormal fluctuation of parameters such as inlet thickness  The strip is affected by rolling force and other related parameters. The metal produces elastic-plastic deformation between the roll gap, and the abnormal quality fluctuation of the strip is caused by the abnormal rolling parameters [33]. The thickness difference of strip is affected by the abnormal fluctuation of parameters such as inlet thickness change, temperature change, tension change, rolling speed change, and roll gap change. To improve quality-related process monitoring and diagnostic accuracy. In this paper, the influence coefficient of thickness in rolling process is analyzed by the thickness difference equation of the steady state rolling process. Based on the influence coefficient of thickness difference, the index weight of thickness influence coefficient is established. This improves the data model's ability to physically interpret process variables.

Strip Thickness Influence Weight
The rolling spring curve of strip steel is the basis of this study, and the thickness depends on the three main factors of no-load roll gap, rolling mill modulus, and rolling force [34]. According to the bounce curve, the outlet thickness h can be expressed by the following formula.
where S 0 is the actual roll gap, P and P 0 refer to the rolling force and preloading force, respectively. δ and δ 0 are the oil film thickness of liquid friction bearing and the oil film thickness at the artificial zero position, respectively. M is the longitudinal stiffness modulus of the rolling mill. Stiffness of rolling mill is the definite value of rolling mill. The gap position between the rollers remains unchanged, and the thickness of the strip outlet is affected by the change in the rolling force. According to the bouncing equation, the thickness increment takes the following form.
The expression of longitudinal thickness difference can be changed to the following formula. Note that ∆h is calculated in detail as shown in Appendix A.
Based on the thickness increment equation of the rolling process, the influence coefficients of the thickness difference ∆H, the back tension increment ∆T b , the front tension increment ∆T f , the friction coefficient ∆µ, the deformation resistance ∆K and other parameters on the thickness difference ∆h can be obtained. As shown below. In the multi-stand rolling process, each stand controls the longitudinal thickness differently. The equivalent longitudinal stiffness of the rolling mill can be obtained.
where, α is the compensation coefficient. F1 and F2 stands set a larger equivalent stiffness modulus so that α = 0.2. F3 stand is natural stiffness, taking α = 0. F4-F7 stand adopts a small compensation coefficient and obtains better flatness quality through soft characteristic control, in this paper α = −0.2.
Order ϕ = 1 M α +W , The influence coefficient of each variable on the thickness difference can be obtained, as shown in Table 1.
For the convenience of calculation, the secant method is used to calculate the partial score of the influence coefficient [34]. As shown in Figure 2, take the plastic deformation curve of the plate and strip during rolling as an example. In the rolling process, ∆h = 0.001h i is the thickness fluctuation; thus, the new rolling force P can be obtained. Therefore, the partial differential coefficient can be expressed by the following formula.

∂P ∂h
In the multi-stand rolling process, each stand controls the longitudinal thickness ferently. The equivalent longitudinal stiffness of the rolling mill can be obtained.
is the compensation coefficient. F1 and F2 stands set a larger equivalent stiffness modulus so that = 0.2. F3 s is natural stiffness, taking = 0. F4-F7 stand adopts a small compensation coefficient obtains better flatness quality through soft characteristic control, in this paper = − Order = , The influence coefficient of each variable on the thickness di ence can be obtained, as shown in Table 1. For the convenience of calculation, the secant method is used to calculate the pa score of the influence coefficient [34]. As shown in Figure 2, take the plastic deforma curve of the plate and strip during rolling as an example. In the rolling process, ∆ 0.001ℎ is the thickness fluctuation; thus, the new rolling force can be obtained. Th fore, the partial differential coefficient can be expressed by the following formula.  the influence coefficient of the thickness difference of the strip behaves differently in each stand, as shown in Figure 3b. In the influence coefficient of thickness difference, the ϕ value is positive in F1-F3 stands and negative in F4-F7 stands. At the same time, the plastic stiffness coefficient of the rolled piece increases with the increase in rolling passes, and the difficulty of metal deformation increases. The plastic stiffness coefficient and longitudinal stiffness modulus of the rolling mill of each stand is shown in Figure 3a. This paper selects the equivalent longitudinal stiffness coefficient of the rolling mill. Since the longitudinal stiffness modulus of the rolling mill and the plastic stiffness of the rolled parts are different in each stand, the parameter in the influence coefficient of the thickness difference of the strip behaves differently in each stand, as shown in Figure 3b. In the influence coefficient of thickness difference, the value is positive in F1-F3 stands and negative in F4-F7 stands. At the same time, the plastic stiffness coefficient of the rolled piece increases with the increase in rolling passes, and the difficulty of metal deformation increases.  Based on the incremental model of comprehensive static analysis, the influence coefficient of strip thickness difference in the steady rolling process can be calculated by the secant method. Based on the 1580 hot rolling historical data, the partial differential of each pass variable of 3.00 mm gauge strip with final rolling thickness was established. As shown in Table 2, partial differential values of rolling force, roll gap, and roll bending force need not be calculated. In this paper, the partial score of the thickness difference influence coefficient was calculated by the secant method to calculate the thickness difference influence coefficient of the strip. Based on the influence coefficient of thickness difference, the influence weight of thickness difference of the strip based on the rolling mechanism is constructed.
Based on the above static comprehensive analysis of the strip rolling process, the influence coefficients of each variable are calculated (The influence coefficient in Table 1 is expressed by , = 1,2, ⋯ , ). Thus, in the rolling process, the influence of various influence factors on the longitudinal thickness difference can be seen through the Based on the incremental model of comprehensive static analysis, the influence coefficient of strip thickness difference in the steady rolling process can be calculated by the secant method. Based on the 1580 hot rolling historical data, the partial differential of each pass variable of 3.00 mm gauge strip with final rolling thickness was established. As shown in Table 2, partial differential values of rolling force, roll gap, and roll bending force need not be calculated. Table 2. Partial scores of variables of 1580 mm hot rolling stands.

Stand
No. In this paper, the partial score of the thickness difference influence coefficient was calculated by the secant method to calculate the thickness difference influence coefficient of the strip. Based on the influence coefficient of thickness difference, the influence weight of thickness difference of the strip based on the rolling mechanism is constructed.
Based on the above static comprehensive analysis of the strip rolling process, the influence coefficients of each variable are calculated ξ i (The influence coefficient in Table 1 is expressed by ξ i , i = 1, 2, · · · , m). Thus, in the rolling process, the influence of various influence factors on the longitudinal thickness difference can be seen through the influence coefficient ξ i . Therefore, the influence coefficients of the above variables form the influence coefficient matrix ψ.
Mean value of each variable.
Take the diagonal element. It is the influence weight of each variable that affects the abnormal fluctuation of the thickness of the strip in the hot rolling finishing mills.
The normalized data set Noted that X is calculated in detail as shown in Appendix B. The data set is weighted and reconstructed. Reconstruct the data matrix as follows.

Monitoring and Diagnosis Model Based on Weighted Data Reconstruction
Through the analysis of the influence weight of thickness quality, the normalized data is weighted and reconstructed. The reconstructed data is used to monitor and diagnose quality-related faults. The monitoring and diagnosis method of hot rolled strip qualityrelated process based on WKPLS method is shown in Algorithm 2.

Algorithm 2: The WKPLS-based fault detection approach
Off-line training: Step 1 Collect process variable data X and quality variable data Y.

Step 2
Normalization of process data X by Equation (35).
Step 3 Quality influence weight by Equation (33) Step 4 Reconstruct the feature data set X w by Equation (34).
Step 5 Run Algorithm 1 to calculate T and U.
Step 6 Given confidence limit α, calculate thresholds T 2 ucl (α 0 ) and SPE 2 ucl (α 0 ) by Equation (15). On-line detecting: Step 1 Collect on-line samples x new . Additionally, the data reconstruction is carried out in Steps 2 to 4 of the offline training part.
Step 2 Calculate K new,i by Equation (17).
Step 3 Calculate statistics T 2 and SPE by Equation (14). Step 4 Calculate the contribution plot to identify the abnormal variables.
Based on the above quality-related fault-detection process, decisions can be made according to the following diagnosis logic.
, at this point, the quality is stable and there is no fault.
, at this point, the quality-related fault has occurred.
, at this point, the quality-unrelated fault has occurred.
The detailed steps of the fault detection method based on WKPLS are summarized as Algorithm 2. The model framework is shown in Figure 4.
T > T ucl SPE > SPE ucl or SPE < SPE ucl , at this point, the quality-related fault has occurred.
T < T ucl SPE > SPE ucl , at this point, the quality-unrelated fault has occurred.
The detailed steps of the fault detection method based on WKPLS are summarize as Algorithm 2. The model framework is shown in Figure 4.

Data Preprocessing
To verify the feasibility of the proposed methods for abnormal diagnosis and pat identification of quality-related variables, 1580 mm hot finishing production data wer collected from the process data acquisition (PDA) system, and the required data were rea by IBA analyzer. The hot rolling line mainly produces stainless steel, containers, high-en steel, and other products. Its product specification is steel plate and strips with a thicknes of 1.2 mm~12.7 mm and width of 800 mm~1400 mm. In the rolling process, the rollin speed can reach more than 20 m/s, so the sampling interval of the actual production pro cess data is 20-50 ms per point. Therefore, the data of strips with the same specification (same specification, same slab thickness, same target thickness) are selected from the his torical database to verify the model. In this paper, the production data of Q345B are use for industrial verification. The main variables include 43 process variables and 1 qualit variable (Thickness), as shown in Table 3. Table 3. Names of variables in the finishing rolling stage of hot-rolled strip.

Data Preprocessing
To verify the feasibility of the proposed methods for abnormal diagnosis and path identification of quality-related variables, 1580 mm hot finishing production data were collected from the process data acquisition (PDA) system, and the required data were read by IBA analyzer. The hot rolling line mainly produces stainless steel, containers, high-end steel, and other products. Its product specification is steel plate and strips with a thickness of 1.2 mm~12.7 mm and width of 800 mm~1400 mm. In the rolling process, the rolling speed can reach more than 20 m/s, so the sampling interval of the actual production process data is 20-50 ms per point. Therefore, the data of strips with the same specifications (same specification, same slab thickness, same target thickness) are selected from the historical database to verify the model. In this paper, the production data of Q345B are used for industrial verification. The main variables include 43 process variables and 1 quality variable (Thickness), as shown in Table 3. Table 3. Names of variables in the finishing rolling stage of hot-rolled strip.

Influence Weight of Each Stand Variable
To improve and optimize the data model, the model is verified by the above hot rolling process data. Table 4 shows each stand variable's influence coefficient on the strip's thickness. Due to the order of magnitude of each variable, it is difficult to directly use this influence coefficient for the optimization of the data model. Therefore, considering that the influence of dimensionality is eliminated after data standardization, this paper uses the mean value of each variable to optimize the influence coefficient. The average value of each stand variable is shown in Table 5. For the 1580 mm hot rolling process, the influence weight of each stand variable on the thickness is calculated. The weight of each variable's impact on quality is shown in Figure 5. Figure 5a shows the influence weight of rolling speed, in which the influence weight of the F3 stand is significantly higher than that of other stands. With the increase of rolling passes, the degree of metal deformation decreases, and the influence weight shows a downward trend in the rear stand. Figure 5b,c show the influence weight of the front, and rear tension, in which the F7 stand has no front tension and the F1 stand has no post-tension. It can be seen that the influence of each stand's front and rear tension on the thickness of the strip is different, and the influence weight of the front and rear tension of the F2 stand is the maximum. Figure 5d,f show the influence weights of the inlet thickness and the roll gap value, respectively. The inlet thickness causes the thickness deviation by affecting the rolling force and the roll gap value. The thickness difference of the strip is gradually corrected at each stand with the rolling passes, so the influence weight of the inlet thickness and the roll gap value shows a downward trend. Figure 5e,g show the influence weights of rolling force and bending force, respectively. From the analysis of the influence mechanism of strip thickness, it can be seen that the rolling force is the passive momentum, and the changes of various variables affect the rolling force, resulting in the thickness fluctuation of the strip, and the bending roll is an important control means of strip crown and shape in the rolling process. Therefore, the influence weight of rolling force and bending force on thickness shows a low value. Figure 5h shows the influence weights of the inlet and outlet temperatures of finishing rolling, and the outlet temperature of finishing rolling has a greater influence on the thickness.  Based on the above introduction, in the finishing rolling stage, the influence of each variable on the thickness is different. The first four passes greatly influence the thickness of the strip and play a leading role in the thickness control. The last three passes are mainly controlled by shape; thus, the influence on the thickness is reduced.

Thickness Monitoring Results Based on PLS and KPLS
In the feature space, Hotelling's T and SPE statistics are used to calculate the statistical monitoring indicators, and the statistical control limits of T and SPE are determined through the training data. The monitoring results of variables related to strip thickness and quality through PLS and KPLS monitoring methods are shown in Figure 6. Due to the nonlinearity between multivariate variables, as shown in Figure 6a-f, a large number of sample points exceeded the limit in the PLS monitoring process of F1-F3 stand, resulting in a large number of misjudgments. The monitoring statistics show a narrowing trend, showing more accurate monitoring results for the fluctuations of variables related to the quality of the production process. The thickness fluctuation of the head and tail of the strip is caused by the lack of complete tension control of the strip in the biting stage at the initial stage of rolling and the loss of tension at the tail of the strip at the end of rolling. From the statistical monitoring process in Figure 6g-n, it can be seen that the 0-100 sample points at the head and 650-680 sample points at the tail of the strip steel exceed the control limit. In the stable rolling state, the sample points are within the control limit, and the Based on the above introduction, in the finishing rolling stage, the influence of each variable on the thickness is different. The first four passes greatly influence the thickness of the strip and play a leading role in the thickness control. The last three passes are mainly controlled by shape; thus, the influence on the thickness is reduced.

Thickness Monitoring Results Based on PLS and KPLS
In the feature space, Hotelling's T 2 and SPE statistics are used to calculate the statistical monitoring indicators, and the statistical control limits of T 2 and SPE are determined through the training data. The monitoring results of variables related to strip thickness and quality through PLS and KPLS monitoring methods are shown in Figure 6. Due to the nonlinearity between multivariate variables, as shown in Figure 6a-f, a large number of sample points exceeded the limit in the PLS monitoring process of F1-F3 stand, resulting in a large number of misjudgments. The monitoring statistics show a narrowing trend, showing more accurate monitoring results for the fluctuations of variables related to the quality of the production process. The thickness fluctuation of the head and tail of the strip is caused by the lack of complete tension control of the strip in the biting stage at the initial stage of rolling and the loss of tension at the tail of the strip at the end of rolling. From the statistical monitoring process in Figure 6g-n, it can be seen that the 0-100 sample points at the head and 650-680 sample points at the tail of the strip steel exceed the control limit. In the stable rolling state, the sample points are within the control limit, and the product thickness quality is stable. However, in Figure 6g-n, the statistical monitoring process of SPE on the residual subspace showed significant fluctuations at 200-300 sample points but did not cause quality abnormalities. It shows that some process variables may fluctuate greatly in the rolling production process. The inlet and outlet temperatures of the strips extracted from the production data of this batch of strips are shown in Figure 7. Figure 7b shows that there is a temperature depression at the outlet temperature of 200-300 sample points in the rolling stage, which is consistent with the fluctuation stage of SPE statistical monitoring. The uneven distribution of outlet temperature is the main reason for the large thickness fluctuation in the strip rolling process. The T 2 statistic of each stand does not exceed the limit after 100 sample points, and the system operates normally and is in a controlled state.
Sensors 2023, 23, x FOR PEER REVIEW 13 of product thickness quality is stable. However, in Figure 6g-n, the statistical monitorin process of SPE on the residual subspace showed significant fluctuations at 200-300 samp points but did not cause quality abnormalities. It shows that some process variables m fluctuate greatly in the rolling production process. The inlet and outlet temperatures the strips extracted from the production data of this batch of strips are shown in Figure  Figure 7b shows that there is a temperature depression at the outlet temperature of 20 300 sample points in the rolling stage, which is consistent with the fluctuation stage of SP statistical monitoring. The uneven distribution of outlet temperature is the main reas for the large thickness fluctuation in the strip rolling process. The T statistic of ea stand does not exceed the limit after 100 sample points, and the system operates normal and is in a controlled state.

Thickness Monitoring Results Based on Mechanism Data Fusion
The above statistical process of quality-related process monitoring based on the da method shows the fluctuation of variables related to strip quality. To analyze the caus of abnormal fluctuation of strip quality, we build a contribution plot to identify variable

Thickness Monitoring Results Based on Mechanism Data Fusion
The above statistical process of quality-related process monitoring based on the da method shows the fluctuation of variables related to strip quality. To analyze the caus of abnormal fluctuation of strip quality, we build a contribution plot to identify variabl

Thickness Monitoring Results Based on Mechanism Data Fusion
The above statistical process of quality-related process monitoring based on the data method shows the fluctuation of variables related to strip quality. To analyze the causes of abnormal fluctuation of strip quality, we build a contribution plot to identify variables. When constructing the contribution plot based on the traditional monitoring method, it is difficult to realize the variable root cause diagnosis when multiple variables' contribution value is large because each stand's variables in the rolling process have different influences on the quality. Therefore, based on the mechanism model, the influence weight of qualityrelated variables is constructed, and the strip quality-related process monitoring and diagnosis model based on the integration of the mechanism and data model are established. The monitoring model can achieve higher fault detection accuracy through the mechanism model to explain the input variables of the data model. Figure 8 shows the monitoring statistics of abnormal plate thickness based on the fusion of the rolling mechanism and data algorithm. When constructing the contribution plot based on the traditional monitoring method, it difficult to realize the variable root cause diagnosis when multiple variables' contributio value is large because each stand's variables in the rolling process have different influ ences on the quality. Therefore, based on the mechanism model, the influence weight o quality-related variables is constructed, and the strip quality-related process monitorin and diagnosis model based on the integration of the mechanism and data model are es tablished. The monitoring model can achieve higher fault detection accuracy through th mechanism model to explain the input variables of the data model. Figure 8 shows th monitoring statistics of abnormal plate thickness based on the fusion of the rolling mech anism and data algorithm. Comparing the monitoring statistics in Figures 6 and 8, it can be seen that the stat tical monitoring process of the fusion mechanism is highly consistent with the monitori statistics based on the KPLS algorithm. It can be seen from the T statistical process th the coordinate value of the T statistic of the fusion mechanism is reduced because t monitoring process integrates the weight of the rolling mechanism and reconstructs a optimizes the strong correlation and weak correlation variables of quality. According the SPE monitoring statistics of F3 in Figures 6f and 8f, the fusion mechanism weight mo itoring process is more stable. In the process of monitoring 0-130 sample points of the stand, the mechanism data fusion monitoring shows a higher recognition rate, as show in Figures 6l and 8l. In Figures 6n and 8n, although SPE statistics can identify 190-3 sample points, the latter shows a more stable monitoring state. Therefore, the qualitylated fault monitoring model based on mechanism data fusion has better stability. Th method is more obvious for the expression of data features.

Cause Identification of Quality Abnormity Based on Contribution Plot
To identify the causes of quality defects, the contribution map of each variable quality-related anomalies is constructed using the contribution plot, as shown in Figure 9.   Comparing the monitoring statistics in Figures 6 and 8, it can be seen that the statistical monitoring process of the fusion mechanism is highly consistent with the monitoring statistics based on the KPLS algorithm. It can be seen from the T 2 statistical process that the coordinate value of the T 2 statistic of the fusion mechanism is reduced because the monitoring process integrates the weight of the rolling mechanism and reconstructs and optimizes the strong correlation and weak correlation variables of quality. According to the SPE monitoring statistics of F3 in Figures 6f and 8f, the fusion mechanism weight monitoring process is more stable. In the process of monitoring 0-130 sample points of the F6 stand, the mechanism data fusion monitoring shows a higher recognition rate, as shown in Figures 6l and 8l. In Figures 6n and 8n, although SPE statistics can identify 190-300 sample points, the latter shows a more stable monitoring state. Therefore, the quality-related fault monitoring model based on mechanism data fusion has better stability. This method is more obvious for the expression of data features.

Cause Identification of Quality Abnormity Based on Contribution Plot
To identify the causes of quality defects, the contribution map of each variable to quality-related anomalies is constructed using the contribution plot, as shown in Figure 9. Comparing the monitoring statistics in Figures 6 and 8, it can be seen that the s tical monitoring process of the fusion mechanism is highly consistent with the monito statistics based on the KPLS algorithm. It can be seen from the T statistical process the coordinate value of the T statistic of the fusion mechanism is reduced becaus monitoring process integrates the weight of the rolling mechanism and reconstructs optimizes the strong correlation and weak correlation variables of quality. Accordin the SPE monitoring statistics of F3 in Figures 6f and 8f, the fusion mechanism weight m itoring process is more stable. In the process of monitoring 0-130 sample points of th stand, the mechanism data fusion monitoring shows a higher recognition rate, as sh in Figures 6l and 8l. In Figures 6n and 8n, although SPE statistics can identify 190 sample points, the latter shows a more stable monitoring state. Therefore, the qualit lated fault monitoring model based on mechanism data fusion has better stability. method is more obvious for the expression of data features.

Cause Identification of Quality Abnormity Based on Contribution Plot
To identify the causes of quality defects, the contribution map of each variab quality-related anomalies is constructed using the contribution plot, as shown in Figure   90.  Combined with the statistical monitoring results, 1-100 sample points are out erance, and 190-300 sample points gradually fluctuate sharply in the SPE statistics F7 stands. This sample point exceeds the control limit in Figure 8n. From the contrib plot based on the KPLS algorithm in Figure 9, we can see the contribution value o stand variable to the strip quality. However, this method is difficult to effectively guish the main abnormal variable from the secondary fault variable when there are anomalies in multiple variables in the process of fault variable identification. As sho Figure 9b-d, the contribution value of unmerged mechanism weight and the contrib values of each variable are not different, which is easy to cause misjudgments an cause of abnormal quality in the diagnosis process. Therefore, this paper conside influence mechanism of strip thickness in the rolling process and establishes the infl weight of thickness based on the influence mechanism. The monitoring and dia model of strip quality-related faults is established based on mechanism data f Combined with the statistical monitoring results, 1-100 sample points are out of tolerance, and 190-300 sample points gradually fluctuate sharply in the SPE statistics of F3-F7 stands. This sample point exceeds the control limit in Figure 8n. From the contribution plot based on the KPLS algorithm in Figure 9, we can see the contribution value of each stand variable to the strip quality. However, this method is difficult to effectively distinguish the main abnormal variable from the secondary fault variable when there are large anomalies in multiple variables in the process of fault variable identification. As shown in Figure 9b-d, the contribution value of unmerged mechanism weight and the contribution values of each variable are not different, which is easy to cause misjudgments and the cause of abnormal quality in the diagnosis process. Therefore, this paper considers the influence mechanism of strip thickness in the rolling process and establishes the influence weight of thickness based on the influence mechanism. The monitoring and diagnosis model of strip quality-related faults is established based on mechanism data fusion. Effectively improve the recognition of the contribution value of variables related to the quality of the rolling process.
At the entrance of the finishing mill, the temperature of the strip head drops due to the use of high-pressure water for descaling, which makes the overall temperature of the slab uneven and causes the thickness deviation of the strip head. Through the diagnosis of the method in this paper, it can be determined that the inlet temperature of the F1 stand is the main reason for the head thickness deviation, which is consistent with the field test results, as shown in Figure 9a. At the same time, the contribution value of each variable of the F1 stand fluctuates to varying degrees. Because the head thickness is out of tolerance, the contribution value of F2 stand Var24 (Entry thickness) is the largest, which is the main reason for the monitoring statistics of this stand to exceed the limit. According to the analysis of the rolling mechanism, the change of inlet thickness causes the fluctuation of Var25 (Rolling force) and Var26 (Roll gap value), which become the secondary fault source of the diagnosis of the stand, as shown in Figure 9b. Due to the quality transfer characteristics between processes, the thickness difference of the strip head in the last pass will lead to fluctuations in the variable inlet thickness, rolling force, and roll gap values in the subsequent rolling process, as shown in Figure 9c-e. With the increase in rolling passes, F5-F7 stands are biased towards shape control, and the weight of each variable on strip thickness gradually decreases. Since the plate thickness and shape are coupled in the hot rolling process, Var63 (front tension) of the F6 stand and Var73 (post tension) of the F7 stand show the largest contribution to the longitudinal thickness difference of the strip, as shown in Figure 9f,g. Based on the influence mechanism of strip thickness in the rolling process, the change of tension affects the stress state of rolled pieces, which leads to the fluctuation of metal deformation resistance, and finally leads to the fluctuation of longitudinal thickness difference of strip. At the same time, the metal deformation resistance is affected by the change in rolling temperature. Extract the outlet temperature of the hot rolling 1580 production line. As shown in Figure 7b, there are temperature pits at 200-300 sample points, which makes the 200-300 sample points in the SPE monitoring statistical process in Figure 8n exceeds the limit. Therefore, the monitoring and diagnosis results of the variables related to the longitudinal thickness of the strip through the mechanism and data fusion are consistent with the actual production state. This paper establishes the thickness influence weight through the mechanism model. It integrates the data model, which can not only show the stability of the quality-related fault diagnosis process but also have a better detection rate in the monitoring and diagnosis of quality-related abnormal variables in complex industrial processes than in traditional algorithms, as shown in Table 6. Therefore, the quality-related process monitoring and diagnosis method of hot-rolled strips based on the weighted feature KPLS proposed in this paper can better realize the diagnosis of quality-related strip faults. The new method has a better detection rate than the traditional algorithm in the monitoring and diagnosis of quality-related abnormal variables in complex industrial processes, and the average accuracy rate can reach 96%.

Fault Detection Rate and False Alarm Rate of WKPLS Diagnosis Method
However, although the diagnostic rate of quality abnormality reached 96%, there is still about 5.58% false alarm rate, as shown in Table 7. It can be seen from the literature [25,35] that the quality diagnosis method proposed in this paper does not have a better reduction in the rate of misjudgment. However, the proposed method strengthens the interpretation of process variables to quality variables, and improves the clarity of the diagnosis of causes affecting quality defects.

Conclusions
We aimed to solve the problem of traditional data models neglecting the physical significance of variables and the contribution of each variable to quality in the process of quality-related fault diagnosis. The above issues caused incorrect identification of abnormal variables during the diagnostic process. Therefore, a method for quality-related process monitoring and diagnosis of hot-rolled strips based on the weighted statistical feature KPLS was proposed. Through the analysis of industrial test results of the 1580 production line, the following conclusions were drawn.
(1) In this paper, the Gaussian radial basis kernel function is introduced to transform the nonlinear relationship into a linear relationship in the high-dimensional feature space.
The ability of the model to process nonlinear data is improved. (2) Based on the rolling mechanism model, the thickness influence weight is constructed.
The input features of the data model are weighted by the influence weight, which improves the physical interpretation ability of the data model to each variable. (3) The contribution diagram is introduced to identify the causes of abnormal thickness quality and determine the relevant variables that cause quality abnormalities. (4) The industrial verification was carried out by using the measured data of 1580 production line. It can be seen that the monitoring and diagnosis model of strip thickness quality related fault combined with rolling mechanism has high detection accuracy, and the accuracy can reach 96%.