Data-Driven Batch Process Monitoring for Continuous Annealing of Cold-Rolled Strip Steel
Abstract
:1. Introduction
2. Materials and Methods
2.1. DISSIM Improved via Kernel Trick
2.2. Clustering Based on Kmeans++
2.3. Batch Process Monitoring Procedure
2.3.1. Central Batch Selection
2.3.2. Boundary Batch Selection
- (1)
- The historical batch data XI×J×K are used as the input to the model, where I, J and K denote the number of the batch, variable and sample, respectively.
- (2)
- Normalize the XI×J×K according to Equation (1).
- (3)
- Calculate the distance between each batch and other batches to obtain the distance matrix , as in Equation (7).
- (4)
- Cluster with the Kmeans++ method, and then the silhouette coefficient calculated from Equations (8) and (9) is combined with the actual situation to choose the reference batches from the largest cluster.
- (5)
- Determine the central batch of reference batches using Equations (10)–(12).
- (6)
- Estimate the probability density function of the distance from the reference batch to the central batch with the kernel density estimation method using Equations (13)–(15). The 90% control limit kdlimit is determined by integration as threshold.
- (1)
- Obtain new batch data .
- (2)
- Normalize the as in Equation (1).
- (3)
- Calculate the between the new batch and the central batch using Equation (7).
- (4)
- Compare the with the control limit kdlimit. If it exceeds the control limit, the batch is considered as a batch with an unstable control level; otherwise, the batch is considered as a batch with a stable control level.
3. Results
3.1. Data Preparation for the CAP
3.2. Batch Monitoring Results
4. Discussion
5. Conclusions
- (1)
- A space–time transformation method based on velocity and time integration is proposed so as to solve the problem of aligning multivariate time series data caused by different annealing temperature measurement locations in the CAP.
- (2)
- The KDISSIM algorithm is proposed to extract the nonlinear features of multiple annealing temperatures and further measure the similarity between steel coils with different lengths.
- (3)
- The improved clustering model is employed to find batches with stable temperature control in historical data, and these batches are used as the training set to construct a reference space, monitoring the temperature control levels of different batches of steel coils in the CAP.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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No. | Parameter Name | Parameter Description |
---|---|---|
1 | PHT | Preheating temperature |
2 | HT | Heating temperature |
3 | ST | Soaking temperature |
4 | SCT | Slow cooling temperature |
5 | RCT | Rapid cooling temperature |
6 | OAT1 | Overaging temperature 1 |
7 | OAT2 | Overaging temperature 2 |
8 | FCT | Final cooling temperature |
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Zhou, Y.; He, F.; Zhang, Y.; Zhou, H. Data-Driven Batch Process Monitoring for Continuous Annealing of Cold-Rolled Strip Steel. Metals 2024, 14, 867. https://doi.org/10.3390/met14080867
Zhou Y, He F, Zhang Y, Zhou H. Data-Driven Batch Process Monitoring for Continuous Annealing of Cold-Rolled Strip Steel. Metals. 2024; 14(8):867. https://doi.org/10.3390/met14080867
Chicago/Turabian StyleZhou, Yujie, Fei He, Yutao Zhang, and Hang Zhou. 2024. "Data-Driven Batch Process Monitoring for Continuous Annealing of Cold-Rolled Strip Steel" Metals 14, no. 8: 867. https://doi.org/10.3390/met14080867