Application of Time Series Data Anomaly Detection Based on Deep Learning in Continuous Casting Process

Abstract

The inclusion is a crucial factor affecting the quality of cord steel. The formation of inclusions is closely related to the abnormal production process in continuous casting process. Automatic anomaly detection algorithms are proposed to replace manual visual screening according to the smart manufacturing paradigm, and then the relationship between abnormal production process and product quality is mined through data-driven methods in this paper. Convolutional neural networks and autoencoder models are employed to detect various types of anomalies in time-dependent process parameters. A new idea of detecting abnormal intervals from time series is implemented instead of the conventional process monitoring based on the univariate control limit in process specifications. The abnormal intervals including starting time, duration and type are detected. Furthermore, the proposed scheme progresses from univariate detection to multi-variable process monitoring, which considers the nonlinear coupling of the process. Finally, various anomaly detection results are fused to analyze whether inclusions exist in the cast slab. The proposed scheme is applied to the continuous casting process of cord steel. The automatic anomaly detection scheme is verified to be effective via plenty of actual production data, with the recall rate of 93.06%. It is of prominent significance for product quality improvement of the cord steel.

1. Introduction

The continuous casting process plays a vital role in steel production. More than 95% of the steel in the world is produced by continuous casting every year.¹⁾ It has prominent advantages such as high efficiency, energy saving, and product quality improvement. However, the cast billet inevitably has various defects, including inclusions, segregations and cracks. It is vital to decrease the defects of the cast billet so as to guarantee the quality of the finished product. The defects formed in the continuous casting process will have a genetic effect on the product quality of the downstream processes such as hot rolling and cold rolling.^2,3) Cord steel is a typical representative of high-end wire. It needs to have the characteristics of high cleanliness, high strength, and high toughness under harsh processing and service conditions. However, the inclusions significantly reduce the mechanical strength and processability of the cord steel, resulting in deterioration of the fatigue performance, subsequent wire breaking and delamination.⁴⁾

The inclusions need to be detected and analyzed to promote the product quality. The morphology, size, content and composition of inclusions are detected by different methods, such as 2D automated SEM and 3D X-ray computed tomography,⁵⁾ ICP-AES,⁶⁾ optical microscope, and ultrasonic test.⁷⁾ However, these laboratory test methods lack real-time performance, which are hard to trace back to the production process that caused the inclusion. The mechanism model is currently widely used to trace the causes because of strong interpretability. The model of inclusions formation is developed based on the test results and thermodynamics to predict types and compositions of inclusions.⁸⁾ The formation, removal and control of inclusions involve steel-making, refining and continuous casting processes.⁹⁾ The continuous casting parameters are the primary factors affecting inclusions when the steel-making and refining process are relatively stable.¹⁰⁾ For example, the continuous casting speed has an impact on the distribution of non-metallic inclusions.¹¹⁾ Additionally, the effect of the turbulent fluctuation velocity on the removal of inclusions is studied in the continuous casting process.¹²⁾

Data-driven quality control is a promising trend with the vigorous progress of industrial big data.¹³⁾ There is a close relationship between product quality and process data, especially time-dependent variables. Therefore, the data-driven method can be applied to detect the abnormal patterns that cause inclusions in continuous casting process. Machine learning algorithms such as logistic regression, support vector machines, and random forests have been used to predict inclusions in cord steel.¹⁴⁾ However, traditional methods based on statistical values of time series variables are no longer applicable with the increasing demand for uniformity and stability of product quality.¹⁾ The modeling strategies based on time series have received widespread attention. The implicit feature in the time series has been extracted for process monitoring and fault diagnosis of strip rolling, so as to improve the quality of hot rolled strip.¹⁵⁾ During the continuous casting process, the mold oscillation is monitored via the time series data from the acceleration sensor, and the dynamic characteristics of the system is discussed.¹⁶⁾ A large number of studies have shown that the data-driven model has obvious advantages in analyzing the relationship between production process and product quality.

In this paper, the data-driven model is applied to the anomaly detection related to the inclusions in cord steel. The unsteady state in the continuous casting process is a crucial source of inclusions, which always exhibits a specific abnormal pattern in the process data. Traditional anomaly detection methods based on the control limits in process specifications and statistical values of time series data no longer provide the satisfactory results. Thus, deep learning is introduced to detect different types of anomalies in time series data, and univariate and multivariate detection results are jointly judged to achieve inclusion analysis. Finally, the effectiveness of the proposed method is verified via the laboratory results. This paper has made some contributions to the analysis of inclusions in cord steel. First, a data-driven anomaly detection scheme is proposed to monitor the key variables of the continuous casting process. Next, the analysis object is transformed from the statistical value of the variable to the real-time data, retaining more time-dependent information. Then, multi-scale and strongly coupled data features are extracted via the deep learning network. Finally, different abnormal intervals are defined, identified and classified, and then the manual visual inspection is improved to automatic computer detection, which is a vital application of artificial intelligence in quality promotion.

The rest of the paper is organized as follows: The formation of inclusions in the continuous casting process is introduced, then process and quality data collected from a factory are detailed in Section 2. A comprehensive anomaly detection scheme based on deep learning is proposed in Section 3. The experimental results of anomaly detection and the relationship analysis of inclusions are reported in Section 4. Finally, conclusions are drawn in Section 5.

2. Description of Inclusion Problems and Actual Production Data

In the cord steel of LX82AD produced by a steel plant, about 60% of the quality problems are caused by inclusions. The element and process control of this steel grade in the ironmaking and steelmaking processes are stable via historical data. Therefore, it can be inferred that inclusions are primarily formed in the continuous casting stage. Additively, continuous casting process parameters have time-dependent characteristics. It is essential to identity abnormal patterns in time series for inclusion analysis. The formation of inclusions in continuous casting is presented in this section, and the actual process and quality data from the foundry are introduced.

2.1. Formation of Inclusions in Continuous Casting

The continuous casting machine of a steel plant was put into operation in 2010, with an annual production capacity of 200000 tons. The detailed parameters are shown in Table 1. It principally produces blooms with a size of 390 * 390 mm. The main equipment and technological process are shown in Fig. 1. The molten steel from the refining process is transferred to the ladle on the turret. After the turret reaches the casting position, the molten steel flows into the tundish, and then into the mold controlled by the stopper rod. The molten steel solidifies in the mold and forms a blank shell of a certain thickness, which is pulled out via the dummy bar. The cast billet further solidifies in the secondary cooling section, and is finally straightened and cut to the required length.

Table 1. The continuous casting machine parameters.

Item	Description
Machine type	Vertical bending
Number of strands	5
Interval of Strands (m)	1.6
Machine radius (m)	90
Slab width (mm)	390
Slab thickness (mm)	390

Fig. 1.

Continuous casting machine equipment diagram.

The inclusions in the continuous casting process are inevitable, but most of them can be removed by rapidly floating. In general, inclusions are formed due to the following reasons: (1) The insufficient floating time results in formation of inclusions. (2) The mold powder is entangled to the steel due to the influence of molten steel flow. (3) The floating inclusions are re-entangled before completely entering the mold powder. The formation of inclusions is always related to actual operation.¹⁷⁾ The key process variables include the casting speed, the mold level, the submerged entry nozzle (SEN) insertion depth, and the tundish temperature. Among them, the casting speed and the mold level have a significant coupling relationship. The general trend of mold level fluctuations increases with the increasing casting speed.¹⁸⁾ When the mold width is constant, the increasing casting speed will augment the flow rate of molten steel, which flow out from the side hole of the nozzle. Then, the impact force on the narrow edge of the mold is enhanced, and the increase of the upward sub-velocity of molten steel aggravates the fluctuation of the mold level.

It is well known that the cleanliness of cast billet is influenced by unstable casting conditions, such as the mold level and casting speed fluctuations. The production efficiency and heat transfer will be influenced by the casting speed. The excessive fluctuation of casting speed can cause instantaneous disturbance, making the flow field in the nozzle and the mold change rapidly. It may make the inclusions have no sufficient time to float, and cause slag entrapment. Therefore, reasonable casting speed control is of great significance to the improvement of molten steel cleanliness.¹⁹⁾

The slag entrapment caused by the mold level fluctuation has become a critical factor to deteriorate the slab quality. The mold level fluctuation is closely related to the casting speed and the SEN depth. Mold powder is easily embroiled in molten steel due to excessive mold level fluctuations. The entangled slag droplets may re-float to the surface, or may be captured by the solidified shell to form inclusions. The mold level without any fluctuations will prevent the mold powder from being absorbed and lubricated. This leads to freezing of the molten steel meniscus, aggravating the formation of meniscus hooks, and eventually forming inclusions. Therefore, mold level must be controlled within a certain range. To sum up, the inclusions are closely related to multiple coupled process variables. It is reasonable to use data-driven models for anomaly detection and quality diagnosis.

2.2. Process Data

The production process data are gathered from the continuous casting machine of a steel plant, so as to explore the relationship between the production process and inclusions. The continuous casting machine is a complex device involving many types of process data, and most of the them are time-dependent. The first strand of data is used because the variables of the five strands are exactly the same. The primary process variables are listed in Table 2, and they have different effects on the inclusions. For example, the flow and pressure of the cooling water in the second cooling section have little influence because no more inclusions will be introduced in the second cooling section. In addition, the vibration frequency and amplitude of the mold do not need to be analyzed because they are constant during the existing data set.

Table 2. Variable table of the first casting strand.

No.	Variable	Description
1	ACTPULL	Actual continuous casting speed
2	MOLD_ACTLEVEL	Actual mold level
3	MOLD_CWTEMP	Mold cooling water temperature difference
4	MOLD_ACTSWG	Mold vibration amplitude
5	MOLD_ACTFRQ	Mold vibration frequency
6	FSTIR_ELE	Front-end stirring current
7	FSTIR_FRQ	Front-end stirring frequency
8	MOLD_CWFLOW	Mold cooling water flow rate
9	SEN_DEPTH	Submerged entry nozzle insertion depth
10	TUNDISH_STEELTEMP	Temperature of molten steel in tundish
11	TUNDISH_ARFLOW	Argon flow rate in tundish
12	TUNDISH_WEIGHT	Net weight of tundish
13	MOLD_CWTEMP	Mold cooling water inlet temperature
14	MOLD_CWPRESS	Mold cooling water pressure
15	FLOW1_PRESS	Cooling water pressure of stream 1#
16	FLOW1_FLOW	Cooling water flow rate of stream 1#

The time-dependent variables including the casting speed, mold level, submerged entry nozzle insertion depth, and tundish temperature are selected for anomaly detection, whose control limits specified in the process specifications are shown in Table 3. The process data are collected from the real-time database with 1 second temporal resolution. The molten steel of these ladles has similar and appropriate chemical element additions in the refining process, in order to ensure that the relationship between the continuous casting process and the inclusions is not interfered by the refining process. The time series curves and distribution charts of one ladle are shown in Figs. 2 and 3. It can be seen that the normal process variables fluctuate slightly, and remain stable overall. Abnormal process variables show different types of abnormalities, such as abnormal points of casting speed, abnormal interval of SEN depth and tundish temperature. The distribution charts in Fig. 3 show that the variables are coupled, so the machine learning models need to be employed to explore the potential features in the data.

Table 3. The key control variables and process specifications of continuous casting.

Control item	Control target	Upper control limit	Lower control limit
Casting speed (m/min)	0.59	0.61	0.57
Mold level (%)	85	88	82
SEN depth (mm)	120	130	110
Tundish temperature (°C)	1488	1496	1481

Fig. 2.

Time series curve of four variables in one ladle. (Online version in color.)

Fig. 3.

Probability distribution charts of four variables in one ladle. (Online version in color.)

2.3. Quality Test Results of Inclusions

The quality of cord steel is evaluated using Bekaert standards. Each ladle gets a score denoting the severity of inclusions. A ladle of molten steel could produce more than 25 blooms, where 12 blooms are sampled for inclusion test. The types of inclusions include non-deformable inclusions, macroscopic inclusions in cross section, and inclusions in longitudinal section. Test indicators for each type of inclusion include morphology and size. The quality evaluation index related to inclusions is the inclusion score S_inclu, which is the sum of penalty scores S_un, S_long, and S_cro for the three types of inclusions. A larger score represents more serious inclusions. For example, the penalty score S_un for non-deformable inclusions is calculated by the penalty rule shown in Table 4, where the different morphologies of inclusions are denoted by TW, N, TV, and V.

Table 4. The penalty rule of non-deformable inclusions.

Size Morphology	≤5 μm	≤10 μm	≤15 μm	≤20 μm	≤25 μm	>25 μm
TW	0.6	1.0	1.5	2.0	3.0	4.0
N	1.0	1.5	2.0	3.0	4.0	6.0
TV	1.5	2.0	3.0	4.0	6.0	8.0
V	2.0	3.0	4.0	6.0	8.0	12.0

The laboratory test report of the ladle No. LX2031007911 is shown in Table 5. The final inclusion score is 155.83 calculated by the Bekaert scoring standard. A total of 268 ladles of quality data are collected, and the distribution chart of the inclusion score is shown in Fig. 4. The highest score is 284.6, and the average score is 70.8. The slight inclusion will not seriously affect product quality. Therefore, the foundry stipulates that the ladles with the inclusion score less than 50 are normal.

Table 5. Laboratory report of casting slab inclusions of one ladle.

SAM_LOT_NO	SAM_NO	INCLU_THICK	INCLU_LEVEL	INCLCROS_SIZE	INCLLONG_SIZE
LX2031007911	1002	/	/	/	/
LX2031007911	1011	/	/	/	/
LX2031007911	1004	/	/	/	/
LX2031007911	1009	/	/	16	/
LX2031007911	1008	/	/	18	/
LX2031007911	1005	10	N	/	/
LX2031007911	1006	6	N	19	/
LX2031007911	1012	/	/	/	/
LX2031007911	1001	/	/	18	/
LX2031007911	1010	22	TW	/	/
LX2031007911	1003	17	TW	19	/
LX2031007911	1007	30	TW	10	/

Note: SAM_LOT_NO and SAM_NO represent the number of the sampled ladle and the slab in the test, respectively. INCLU_THICK and INCLU_LEVEL denote the thickness and morphology level of non-deformable inclusions, respectively. INCLCROS_SIZE and INCLLONG_SIZE indicate the size of the macroscopic inclusions in the cross section and the inclusions in the longitudinal section, respectively. The above size is the largest size in the microscope field of view, which contains the most inclusions in the cross section.

Fig. 4.

The distribution chart of inclusion scores. (Online version in color.)

3. Anomaly Detection Scheme for Continuous Casting Process

A comprehensive anomaly detection scheme shown in Fig. 5 is proposed, which consists of univariate abnormal interval detection and multivariable process monitoring. The multi-scale CNN-LSTM network is proposed as the univariate abnormal interval detection method, which can identify abnormal patterns in time series. Multivariable process monitoring supplements the univariate anomaly detection, which considers the coupling influence of multiple process variables on the overall quality. The autoencoder model is used for multivariable process monitoring.

Fig. 5.

The overall framework of anomaly detection scheme.

3.1. Abnormal Interval Detection Based on Multi-scale CNN-LSTM

An abnormal interval detection method based on multi-scale CNN-LSTM network is proposed, which is more effective compared with the univariate process monitoring based on process specification. The process specification is the main process standards that guides product production and worker operations. However, it only provides the theoretical control range, which is usually relatively large. It aims at reducing the difficulty of control, balancing costs and benefits. Therefore, it is not sufficient to detect abnormal patterns in the time series only through process specification. In the casting speed curve shown in Fig. 6, the green and yellow areas respectively indicate the normal area and the over-limit area divided by the control limit. The process monitoring based on the process specification can only detect the outliers marked by the red dashed line, but cannot detect the abnormal interval marked by the black dashed line. These abnormal intervals characterized by diverse scales and types²⁰⁾ are hard to be recognized via traditional algorithms. At present, expert experience is relied on to identify abnormal intervals, which immensely restricts the inclusion analysis.

Fig. 6.

The casting speed curve with marked abnormal interval. (Online version in color.)

The multi-scale CNN-LSTM model is an end-to-end deep learning network. The abnormal intervals of different scales and types in time series can be detected and classified. The model consists of a scale conversion layer, a convolution layer with regularization, and a fully connected layer. The network structure is shown in Fig. 7. In the scale conversion layer, the input sequence is sampled at multiple scales and filtered by low pass, so that the mutative features of abnormal intervals under different receptive fields can be extracted. In the convolutional layer with regularization, the stacked one-dimensional convolution is employed for feature extraction to mine the shallow local features and deep global features of the input samples. The long and short-term memory (LSTM) network is introduced as a regularization item, making the network maintain a long-term response to anomalies.²¹⁾ In the fully connected layer, the feature maps of different branches are concatenated together, and the classification results are acquired through the softmax function to form a complete end-to-end network. In addition, structures such as batch normalization²²⁾ and dropout²³⁾ are added to the network to accelerate convergence and prevent overfitting.

Fig. 7.

The proposed multi-scale CNN-LSTM network structure. (Online version in color.)

Offline training and online testing are performed as shown in Fig. 8. Data preprocessing includes training set and testing set generation, sample labeling and standardization. Sample labeling refers to marking the type and location of abnormal intervals in the training set based on expert experience. The proposed model is trained via the artificially labeled training set to learn the features and mapping relationships of abnormal intervals. The trained model is used to detect abnormal intervals in the time series. The model outputs the category label of the testing sample, including normal, impulse type anomaly, step type anomaly, and slow-varying type anomaly. The sequence composed of all category labels represents the anomaly detection result of the testing set.

Fig. 8.

Flow chart of univariate abnormal interval detection. (Online version in color.)

3.2. Multi-variable Process Monitoring Based on Autoencoder

The autoencoder²⁴⁾ is introduced for multi-variable process monitoring. The variables in the continuous casting process have complex nonlinear relationships. Univariate anomaly detection has limited effect on anomaly analysis, because product quality is influenced by all process variables. When one univariate abnormality is detected, the other variables can be adjusted to stabilize the overall process. For instance, when the temperature of the molten steel in the mold is too high, it will retard the solidification of the molten steel.²⁵⁾ The cooling water flow of the mold can be increased, so that the molten steel can maintain normal superheat and avoid quality problems.²⁶⁾ Therefore, it is indispensable to conduct a coupled analysis on the key variables related to inclusions.

Data dimensionality reduction²⁷⁾ is the major approach to deal with multivariate coupling relationship. It is employed to remove redundant and irrelevant information which will reduce the accuracy of the monitoring results, and retain the major features of the data. Principal component analysis (PCA)²⁸⁾ is a typical dimensionality reduction method, but it is incapable to find the nonlinear structure embedded in the data. The autoencoder is introduced to perform non-linear dimensionality reduction, while the reconstruction error is used for process monitoring. The autoencoder is a kind of neural network aiming at reconstructing the input variables via fewer hidden nodes than input nodes. The network needs to encode as much information as possible into the hidden nodes, so the autoencoder is divided into an encoder g₁ and a decoder g₂. The encoder compresses the high-dimensional original data x onto a low-dimensional nested structure. The decoder can be regarded as the inverse process of the encoder. It generates an expression x′ that is as close to its original input as possible from the reduced dimensionality code h. The encoding and decoding process are shown in Eqs. (1) and (2).   

$$h=g_1(x)=\sigma (W_{1}x+b_1),$$(1)

  

$$x^{\prime }=g_2(h)=\sigma (W_{2}h+b_2),$$(2)

where, the symbols W₁, W₂ and b₁, b₂ denote the weights and biases of the encoder and decoder, respectively. σ(·) is the nonlinear activation function.

Multivariable process monitoring based on autoencoder is divided into offline training and online monitoring, as shown in Fig. 9. The training set is the process data during normal production. And the autoencoder is trained according to the principle of minimizing the error between the original data and the reconstructed data. The reconstruction error is calculated as in Eq. (3).   

$$erro{r}_i={\sum }_j{(x_{ij}-x_{ij}^{\prime })}^2,$$(3)

where, the symbols i and j represent the i-th time point in the variable and the j-th variable in the ladle, respectively. All reconstruction errors in the training set are fitted to the probability distribution through kernel density estimation. And the threshold of reconstruction error is obtained with a confidence level of 0.95. Then, the testing data is input to the network and the reconstruction error is obtained. The abnormal production state will be reflected in the process data, and its reconstruction error will be significantly larger than the threshold. The process monitoring chart based on reconstruction errors is employed to detect abnormal production processes with multivariate coupling relationship.

Fig. 9.

Flow chart of multi-variable process monitoring. (Online version in color.)

The error contribution rate is introduced to find the abnormal variable. The error contribution rate calculated by Eq. (4) expresses the contribution of each variable to the reconstruction error.   

$$cont{r}_{ij}=\frac{{(x_{ij}-x_{ij}^{\prime })}^2}{{{\displaystyle \sum }}_j{(x_{ij}-x_{ij}^{\prime })}^2},$$(4)

where, the symbols i and j represent the i-th time point in the batch and the j-th variable in the sample, respectively. A large contribution rate indicates that the variable is abnormal. In summary, the autoencoder, reconstruction error and error contribution rate are presented in this section to monitor the continuous casting process. The potential relationship between the production process and inclusions is further explored.

3.3. Anomaly Detection Fusion Strategy

Multiple univariate abnormal interval detection results and the multivariate process monitoring results are obtained through Section 3.1 and Section 3.2. And the fusion strategy of anomaly detection results is proposed in this section. In the theory of multivariate statistical process control, time points within the single-variable control limit cannot guarantee that the multi-variable monitoring is normal, as shown in point A in Fig. 10. On the contrary, time points beyond the single-variable control limit cannot guarantee that the multi-variable monitoring is abnormal, as shown in point B in Fig. 10. Thus, it is unreliable to use multiple univariate joint monitoring to replace the overall monitoring of a complex process.

Fig. 10.

Comparison of single-variable and multi-variable control charts (The X-axis and Y-axis represent the control targets of the variables X₁ and X₂, respectively, and the dashed line represents the single variable control lower limit LCL and the control upper limit UCL. The blue ellipse indicates the multivariable control limit. The time point falls within the control limit, indicating that the process is normal.). (Online version in color.)

The univariate abnormal interval reflects the specific pattern of the production status, which has clear meaning. The univariate score S_j is calculated in consideration of the type and number of abnormal intervals detected, as shown in Eq. (5). The multivariate monitoring score S_mul is calculated according to the proportion of the outliers in the population, as shown in Eq. (6). The final anomaly score S_ladle of one ladle consists of univariate scores and multivariate monitoring scores, as shown in Eq. (7), and coefficients β_j are used to distinguish the impact of different variables on the overall system.   

$$S_j={\sum }_i{\alpha }_i\times N_i,$$(5)

  

$$S_{mul}= \frac{L\_outlier}{L}\times 100,$$(6)

  

$$S_{ladle}=S_{mul}+{\sum }_j{\beta }_j\times S_j,$$(7)

where, the symbol α_i ∈ [1.0, 5.0, 3.0] indicates the weights of the three abnormal intervals (impulse type anomaly, step type anomaly, and slow-varying type anomaly). The symbol N_i represents the quantity of the i-th type of abnormal intervals in one ladle. The symbols L_outlier and L indicate the number of time points beyond the control limit and the total number of time points in one ladle. The symbol β_j ∈ [1.0, 1.2, 0.8, 0.5] represents the influence degree of four variables (casting speed, model level, SEN depth, and tundish temperature) on the overall production process. Both α_i and β_j are hyperparameters determined by expert experience.

Each continuous casting ladle obtains the label by comparing the anomaly score S_ladle and the threshold S_threshold = 5. If the anomaly score is less than the threshold, the label is 0, indicating the normal production process. Instead, the label 1 means that the production process is abnormal. The accuracy, precision, and recall are used to evaluate the performance of anomaly detection schemes.   

$$Accuracy=\frac{TP+TN}{TP+FP+FN+TN}\times 100\%,$$(8)

  

$$Precision=\frac{TN}{FN+TN}\times 100\%,$$(9)

  

$$Recall=\frac{TN}{FP+TN}\times 100\%,$$(10)

where, TP denotes True Positives, which means that no abnormalities have been detected during the production process, and there are indeed no inclusions. Besides, FN, FP, and TN represent False Negatives, False Positives, and True Negatives, respectively. Further, the error contribution chart in Section 3.2 is employed to diagnose the abnormal variable. Then the type and duration of the abnormal interval are obtained through the multi-scale CNN-LSTM network in Section 3.1. In the end, anomalies in the production process are accurately identified and classified.

4. Results and Discussion

The experimental results of the proposed anomaly detection scheme are collectively displayed in this section. First, the comprehensive detection results are elaborated according to the fusion strategy. Then, typical abnormal ladles are further analyzed combined with the formation mechanism of inclusions.

The testing set contains 268 ladles, of which 193 ladles are detected as abnormal ladles. The confusion matrix of detection results and inclusions is shown in Table 6. The accuracy, precision and recall of the anomaly detection scheme are 83.58%, 83.42%, and 93.06%, respectively. It can be concluded that the overall performance of the proposed scheme is outstanding and can basically meet the actual needs of the industry. In particular, the recall over 93% shows that ladles with inclusions are hardly ignored, which is of great significance to improving product quality. The anomaly detection accuracy obtained using univariate anomaly interval detection or multivariate process monitoring are listed in Table 7. The proposed anomaly detection scheme has higher accuracy, indicating that the fusion strategy in Section 3.3 combines the advantages of anomaly interval detection and variable coupling analysis.

Table 6. Anomaly detection confusion matrix.

	Normal	Abnormal	Total
Non-inclusion	TP: 63	FN: 32	95
Inclusion	FP: 12	TN: 161	173
Total	75	193	268

Table 7. Comparison of accuracy of different methods.

Method	Accuracy
Proposed anomaly detection scheme	83.58%
Univariate abnormal interval detection	61.19%
Multivariable process monitoring	65.59%

There are 63 True Positives, showing their production process is normal. Figure 11 shows the ladle No. 2032001489. The four variables are controlled smoothly, and there is no univariate abnormal interval. In addition, the reconstruction error of all time points is less than the control limit in the multivariable monitoring chart, indicating that the overall process is under control. Finally, the inclusion score is 41.667, which indicates that there are only a few inclusions in the cast slab.

Fig. 11.

The detection result of the ladle No. 2032001489, with an inclusion score of 41.667 (From top to bottom, there are multi-variable monitoring chart, single-variable monitoring chart of casting speed, mold level, SEN depth and tundish temperature. The red solid line represents the control limit, and the green area represents the control range determined by the process specification.). (Online version in color.)

There are 161 True Negatives, all of which have various types of abnormalities. In the ladle shown in Fig. 12, there are 86 time points exceeding the control limits in the multivariate monitoring chart. The total number of time points in this ladle is 2620, so the multivariate monitoring score S_mul in Eq. (6) is 3.282. At the same time, the multi-scale CNN-LSTM network detects that there are multiple abnormal intervals in the casting speed, as shown in the yellow area in Fig. 12. In summary, the ladle with the anomaly score of 10.282 is determined to be abnormal. The inclusion score of 125.25 indicates that there are serious inclusions. Furthermore, it can be seen that the results of multi-variable monitoring and univariate detection have a corresponding relationship in the time dimension, showing that the abnormal casting speed causes the multi-variable monitoring point to exceed the control limit. This inference is verified by the variable contribution chart of the abnormal point shown in Fig. 13, because the error contribution rate of casting speed is the largest among the four variables. In actual production, abnormal fluctuations of the casting speed will reduce the floating time of the inclusions in the molten steel and form inclusions in the cast slab.

Fig. 12.

The detection result of the ladle No. 2031002081, with an inclusion score of 125.25. (Online version in color.)

Fig. 13.

The variable contribution chart of the abnormal points. (Online version in color.)

Another ladle in True Negatives is shown in Fig. 14. The ladle with the anomaly score of 16 is judged to be abnormal, and the inclusion score is 186.6. Multiple abnormal intervals in a single variable are detected, and their information is listed in Table 8. Multiple impulse-type abnormal intervals of the casting speed indicate that the speed control is unstable, which further disturbs the stability of the flow field in the mold. It is hard for the inclusions in the molten steel to float up, which intensifies the formation of inclusions. In addition, the sudden decrease of SEN depth also affects the stable state of casting in a short time. The comprehensive anomaly detection results are fused in Fig. 15, where the type and location of the anomaly are shown. The green area represents outliers detected by multivariate process monitoring. The four variables are all controlled stably and no abnormal interval is detected at the time corresponding to these outliers marked in Fig. 14 with black dashed lines. It can be concluded that the abnormal coupling relationship between variables caused the multivariate statistical value to exceed the control limit. This further clarifies the necessity of fusion analysis for univariate abnormal interval detection and multivariate process monitoring.

Fig. 14.

The detection result of the ladle No. 2031006547, with an inclusion score of 186.6. (Online version in color.)

Table 8. Abnormal interval information in the ladle No. 2031006547.

No.	Variable	Type	Start time (s)	Duration (s)
1	Casting speed (m/min)	impulse	21	10
2	Casting speed (m/min)	impulse	130	31
3	Casting speed (m/min)	impulse	238	18
4	Casting speed (m/min)	impulse	379	33
5	SEN depth (mm)	Step descent	513	117
6	Tundish temperature (°C)	slowly-varying	634	146
7	Tundish temperature (°C)	Step descent	973	42

Fig. 15.

Fusion of univariate and multivariate anomaly detection results (The gray cuboid represents the slab, and different colored areas indicate various types of abnormalities detected.). (Online version in color.)

False Positives and False Negatives in Table 6 mean wrong anomaly detection results. The reason for False Positives may be that inclusions formed in the ironmaking and steelmaking processes, so inclusions cannot be detected via continuous casting process data. There are two possible reasons for False Negatives. On the one hand, the abnormality of the process may be too slight to form inclusions. On the other hand, the randomness of sampling casting billet and sampling location causes the existing inclusions may not be found.

5. Conclusion

In this paper, a time series anomaly detection scheme is proposed to detect abnormal patterns related to inclusions in the continuous casting process. The scheme consists of the multi-scale CNN-LSTM network and the autoencoder model. The key variables of continuous casting such as casting speed, mold level, SEN depth and tundish temperature are detected. Experimental results show that the proposed anomaly detection scheme has outstanding performance with a recall of 93.06%. It can not only effectively detect a variety of univariate abnormal intervals, but also perform multi-variable process monitoring with consideration of variable nonlinear coupling. Furthermore, the error contribution chart and the feature information of the abnormal interval are employed for causes analysis.

The data-driven detection scheme put forward new ideas for anomaly detection in actual production. High-cost manual analysis can be gradually replaced by efficient automatic detection algorithms, and post-event quality random inspections are gradually transformed into in-process quality control.

Acknowledgements

This research is supported by the National Key Technology R&D Program of China (Grant no. 2018YFB0704304) and the Fundamental Research Funds for the Central Universities (Grant no. FRF-AT-20-04).

References

• 1)   S.  Hore,  S. K.  Das,  M. M.  Humane and  A. K.  Peethala: Trans. Indian Inst. Met., 72 (2019), 3015.
• 2)   L.  Zhang,  C.  Guo,  W.  Yang,  Y.  Ren and  H.  Ling: Metall. Mater. Trans. B, 49 (2018), 803.
• 3)   K.  Wang,  M.  Jiang,  X.  Wang,  W.  Wan and  Y.  Wang: Metall. Mater. Trans. B, 51 (2020), 95.
• 4)   J. L.  Lei,  Z. L.  Xue,  H. Y.  Zhu and  Y. D.  Jiang: J. Iron Steel Res., 30 (2018), 847 (in Chinese).
• 5)   B.  Bandi,  B.  Santillana,  W.  Tiekink,  N.  Koura,  M.  Williams and  P.  Srirangam: Ironmaking Steelmaking, 47 (2020), 47.
• 6)   X.  Li,  N.  Wang,  M.  Chen and  T.  Ma: ISIJ Int., 61 (2021), 2074.
• 7)   R.  Sakaguchi,  T.  Shiraiwa,  P.  Chivavibul,  T.  Kasuya,  M.  Enoki,  N.  Yamashita,  H.  Yokota,  Y.  Matsui,  A.  Kazama,  K.  Ozaki and  H.  Takamatsu: ISIJ Int., 60 (2020), 1714.
• 8)   D.  You,  S. K.  Michelic,  P.  Presoly,  J.  Liu and  C.  Bernhard: Metals, 7 (2017), 460.
• 9)   A. L. V.  da Costa e Silva: J. Mater. Res. Technol., 7 (2018), 283.
• 10)   X.  Zhang,  Y.  Ren and  L.  Zhang: Metall. Mater. Trans. A, 49 (2018), 5469.
• 11)   P.  Fei,  Y.  Min,  C.-j.  Liu and  M.-f.  Jiang: Int. J. Miner. Metall. Mater., 26 (2019), 186.
• 12)   H.  Ling,  L.  Zhang and  H.  Li: Metall. Mater. Trans. B, 47 (2016), 2991.
• 13)   H.  Li,  X.  Bu,  X.  Liu,  X.  Li,  H.  Li,  F.  Liu and  Q.  Lyu: ISIJ Int., 61 (2021), 108.
• 14)   M.  Cuartas,  E.  Ruiz,  D.  Ferreño,  J.  Setién,  V.  Arroyo and  F.  Gutiérrez-Solana: J. Intell. Manuf., 32 (2021), 1739.
• 15)   Y. J.  Zhou,  K.  Xu,  F.  He and  D.  He: Control Eng. Pract., 101 (2020), 104514.
• 16)   Y.  Ma,  X. D.  Wang,  X. Y.  Zang,  M.  Yao,  L.  Zhang and  S. H.  Ye: Ironmaking Steelmaking, 35 (2008), 396.
• 17)   P.  Kaushik,  H.  Pielet and  H.  Yin: Ironmaking Steelmaking, 36 (2009), 561.
• 18)   Q. Y.  Zhang and  X. H.  Wang: J. Iron Steel Res. Int., 17 (2010), 15.
• 19)   X. J.  Zuo and  L. F.  Zhang: Spec. Steel, 3 (2011), 37 (in Chinese).
• 20)   M.  Nawaz,  A. S.  Maulud,  H.  Zabiri,  S. A. A.  Taqvi and  A.  Idris: Chin. J. Chem. Eng., 29 (2021), 253.
• 21)   F.  Karim,  S.  Majumdar,  H.  Darabi and  S.  Harford: Neural Netw., 116 (2019), 237.
• 22)   Y. H.  Li,  N. Y.  Wang,  J. P.  Shi,  X. D.  Hou and  J. Y.  Liu: Pattern Recognit., 80 (2018), 109.
• 23)   S.  Hahn and  H.  Choi: Neurocomputing, 398 (2020), 64.
• 24)   S.  Yu and  J. C.  Príncipe: Neural Netw., 117 (2019), 104.
• 25)   Z. Y.  Hu,  X. H.  Chen,  P.  Tang and  Z. B.  Hou: Contin. Cast., 42 (2017), 12 (in Chinese).
• 26)   J.  Ma,  B.  Wang,  D.  Zhang and  W.  Song: ISIJ Int., 58 (2018), 915.
• 27)   S.  Ayesha,  M. K.  Hanif and  R.  Talib: Inf. Fusion, 59 (2020), 44.
• 28)   T.  Zhang,  H.  Ye,  W.  Wang and  H.  Zhang: ISIJ Int., 54 (2014), 2334.