Fault Diagnosis for Blast Furnace Ironmaking Process Based on Two-stage Principal Component Analysis

Abstract

Monitoring an ironmaking process is a very challenging task as it often fluctuates frequently and lacks of direct measurements. Principal component analysis (PCA) technique has been widely used in various industrial fields, mainly due to its advantage of not requiring the information about the principle knowledge of the process and faults. However, the PCA based application results in ironmaking process are still limited. In this paper, based on the dataset collected from a real blast furnace with a volume of 2000 m³, a fault diagnosis method by incorporating the PCA technique in two stages will be presented. To overcome the adverse effects of the peak-like disturbances caused by switching between two distinct hot-blast stoves, they are identified and removed from the dataset through the first-stage PCA. Experimental results show that our method outperforms the existing algorithm and the operators’ monitoring in detecting the getting cold accident of the blast furnace.

1. Introduction

Blast furnaces are a class of huge high-temperature reactors producing molten iron for primary steelmaking in modern iron and steel industry.^1,2,3) In a typical ironmaking process,^2,3) iron-bearing materials (including iron ores, sinters, pellets, etc.), cokes and flux (such as limestone and dolomite) are continuously dumped into the blast furnace from the top, while dry air, enriching oxygen, moisture, fuels like tar or pulverized coal are blasted into the furnace from the bottom. The output consisting of slag and molten iron flows out of the furnace from the bottom. Thus the chemical reactions in the blast furnace are quite complex with one stream downward and the other upward.

In order to keep a blast furnace working at its normal status steadily,^1,3) prompt detection of different abnormality conditions is vitally important. However, monitoring the status of a blast furnace is exceptionally difficult due to the lacks of its accurate mathematical model and the direct measurements for its internal states.

Most of the existing fault diagnosis methods for the blast furnaces are based on expert systems.^4,5,6) But they could deliver desired performances only when comprehensive rules and sufficient historical fault information are available. In recent years, some data-driven methods have been proposed, including Support Vector Machine (SVM),^{7,8,9,10,11,12)} neural network^4,13,14,15) and state space model¹⁶⁾ assisted approaches. However, most of them require that a large amount of a priori information about the faults can be obtained,¹⁶⁾ which is not an easy task in real ironmaking process.

It is known that multivariate statistical process control (MSPC) is an important class of data-driven methods. The main advantage of such schemes with comparison to the aforementioned approaches is that neither a priori fault information nor the system model is necessary. Although there are some results reported on MSPC based applications in ironmaking field, they are mainly focused on the prediction of silicon content^17,18,19) and modeling^20,21,22) problems.

It is worth mentioning that Gamero’s work²³⁾ and Vanhatalo’s work²⁴⁾ are the representative of limited works on fault diagnosis of the ironmaking process by adopting PCA, which is a typical MPSC technique. In Gamero’s work, the qualitative trend analysis was addressed.²³⁾ In Vanhatalo’s work, an experimental blast furnace was considered.²⁴⁾ In fact, PCA based methods have been widely used for process control and fault diagnosis in chemical industry. MacGregor et al. first used PCA for process monitoring in industrial applications.²⁵⁾ Dunia and Qin employed PCA technique to realize sensor fault diagnosis.²⁶⁾ In the field of steel production, Dudzic et al. applied PCA to process monitoring and quality control.^27,28,29) Similar to the advantages of MSPC methods as discussed above, PCA technique is an attractive tool due to the following two reasons: i) it needs less principle knowledge and causal relationship of the process compared with those model-based approaches; ii) in contrast to the expert systems and SVM based methods, it does not require a priori information of the faults.

Inspired by related literature,^23,24) and the successful applications of PCA in other process control fields, we adopt the PCA technique for solving the problem of detecting the getting cold accidents for a real blast furnace with a volume of 2000 m³. Note that the data collected from the blast furnace in this paper is disturbed by the switching between any two distinct hot-blast stoves for blowing the hot air into the blast furnace. This constitutes the main difference between our work and earlier work.^23,24) To discriminate the disturbances caused by stove switching and the real abnormal status, we adopt a two-stage PCA based monitoring method. The first-stage PCA is used to identify, locate and remove the switching disturbances, while the second stage PCA adopts the new dataset by removing the stove switching invoked disturbances to build the process model. Then the Hotelling’s T² and SPE statistics are utilized to monitor the process online. It is known that T² statistic reflects the variation in each observation within the model by calculating squared Mahalanobis distance³⁰⁾ projected in the principal space between the observation and sample center. SPE statistic refers to the squared prediction error from the residual space, which measures the difference between an observation and its projection into the principal space retained in the PCA model.

2. A Brief Introduction to PCA Based Fault Diagnosis

Let X∈R^L×p be a data matrix, where the L rows are the observations and the p columns denote the variables. Normally in practice, the k^th row of X represents the measurement of all variables collected at the k^th sampling instant. Suppose that each column is mean centered and scaled,²⁵⁾ i.e. it is obtained by subtracting the sample mean from each individual sample and then dividing the difference by the sample standard deviation. With the PCA technique, X can be decomposed as follows,³¹⁾   

$$X=T{P}^T=\sum _{i=1}^p{t}_i{p}_i^T=\sum _{i=1}^s{t}_i{p}_i^T+E,$$(1)

where p_i∈R^p is a loading vector which is defined as the right singular vector of X corresponding to the i^th largest singular value; t_i is a score vector which is defined as the values of the i^th principal components for the L observation vector (i.e., t_i = $X{p}_i^T$ , i = 1,2,···, p). E is the residual matrix. s can be determined by   

$$\frac{\sum _{i=1}^s{\mathrm{\sigma }}_i^2}{\sum _{i=1}^p{\mathrm{\sigma }}_i^2}\times 100\%>95\%,$$(2)

where σ_i is the i^th singular value of X. Inequality (2) indicates that more than 95% of the total variance of the data is covered by the first s principal loadings.³¹⁾

Hotelling T² statistic and SPE statistic are two statistics, which have been widely used in the PCA based online process monitoring methods. They are defined, respectively, as²⁵⁾   

$$T_k^2=x_k^T{P}_s{\Sigma }_s^{-2}{P}_s^T{x}_k$$(3)

and   

$$SP{E}_k=r_k^T{r}_k,\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{r}_k=x_k-{\hat{x}}_k,\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{\hat{x}}_k=P_s{P}_s^T{x}_k,$$(4)

where x_k denotes a new-coming observation at sampling instant k, P_s is a matrix composed of the first s columns of P (i.e. p_i for 1 ≤ i ≤ s), Σ_s is a diagonal matrix composed of the s largest singular values of P_s.

Given a confidence level α, the thresholds for monitoring T² and SPE statistics can be calculated as below^25,31)   

$$T_{\alpha }^2=\frac{s(L-1)(L+1)}{L(L-s)}{F}_{\alpha }(s,L-s)$$(5)

  

$$SP{E}_{\alpha }={\theta }_1{\left[\frac{c_{\alpha }{(2{\theta }_2{h}_0^2)}^{1/2}}{{\theta }_1}+1+\frac{{\theta }_2{h}_0(h_0-1)}{{\theta }_1^2}\right]}^{1/h_0},$$(6)

where F_α (s, L – s) is the critical value of the F-distribution with s and L – s degrees of freedom for the α significance level, c_α is the normal deviate corresponding to the upper (1–α) percentile, ${\theta }_i=\sum _{j=\alpha +1}^n{\mathrm{\sigma }}_j^{2i}$ for i = 1,2,3 and $h_0=1-2{\theta }_1{\theta }_3/(3{\theta }_2^2)$ .

Note that when the SPE statistic exceeds its threshold, the contribution plot²⁵⁾ which reflects the contribution of each variable to deviations in the SPE statistic within a given sampling interval, can be used to diagnose which variables may be the cause of the faults. The contribution of the i^th variable to the SPE statistic at instant t is defined as³²⁾   

$$c_i(t)={(x_i(t)-{\hat{x}}_i(t))}^2=r_k{(t)}^2,\mathrm{\hspace{0.17em} }\hspace{0.17em}i=1,\cdots ,p.$$(7)

The contribution of the i^th variable to the SPE statistic between the instants k₁ and k₂ can be further calculated as   

$$C_i=\sum _{t=k_1}^{k_2}{c}_i(t).$$(8)

3. Methodology and Case Study

3.1. Description of the Data Set

In this paper, part of the historical data collected from No. 3 Blast Furnace with a volume of 2000 m³ in Liuzhou Iron&Steel Co. Ltd. is used as the data set. The dataset includes 103680 samples (corresponding to 12 days’ data with the sampling time of 10 seconds) for 29 main monitored variables, which are now listed in Table 1. An overview of the data is given in Fig. 1. It can be seen that the data set is divided into two parts, i.e. Part 1 and Part 2. Part 1 with 40000 samples were collected under normal condition and will be used as the training set to build the PCA based process-in-control model. Part 2 with 63680 samples will be used as the test set. According to the event log provided by the blast furnace operators, the data collected from the 85553rd sampling instant to the 103680th sampling instant (i.e. the part between the two adjacent red dotted lines in Fig. 1) corresponds to the process of a getting cold accident of the blast furnace. The remaining samples in Part 2 were collected under normal condition.

Table 1. Variable list of the data set.

1	Oxygen enrichment rate (%)	16	Enriching oxygen pressure (MPa)
2	Blast furnace permeability index	17	Cold blast pressure (MPa)
3	CO volume (%)	18	total pressure drop (Kpa)
4	H2 volume (%)	19	Hot blast pressure (MPa)
5	CO2 volume (%)	20	Actual blast velocity (m/s)
6	Blast velocity at tuyere of blast furnace (m/s)	21	Hot blast temperature (°C)
7	Enriching oxygen flow (m3/h)	22	Top temperature (1) (°C)
8	Cold blast flow (104 m3/h)	23	Top temperature (2) (°C)
9	Blast momentum (KJ)	24	Top temperature (3) (°C)
10	Blast furnace bosh gas volume (m3)	25	Top temperature (4) (°C)
11	BF bosh gas index	26	Drag coefficient
12	Theoretical combustion temperature (°C)	27	Coal injection set value (T/h)
13	Blast furnace top gas pressure (1) (°C)	28	Actual coal injection rate (T/h)
14	Blast furnace top gas pressure (2) (°C)	29	Actual coal injection in last hour (T)
15	Blast furnace top gas pressure (3) (°C)

Fig. 1.

An overview of the original data.

Remark 1: It is worth mentioning that all the 29 variables are plotted in Fig. 1 with their original amplitudes. Thus some variables appear overlapped at the bottom of Fig. 1, because their amplitudes are relatively small with comparison to the red, black, blue, pink and green ones, which correspond to blast furnace bosh gas volume, enriching oxygen flow, cold blast flow, theoretical combustion temperature and hot blast temperature, respectively. For the same reason, only the five variables are marked in the legend of Fig. 1. The units of the rest variables can be found in Table 1. Nevertheless, the data will be mean centered and scaled before they are used in the modeling and monitoring procedures. More details will be given in Section 3.2.

Different from the experimental blast furnace mentioned in literature,²⁴⁾ there are four stoves blowing the hot air into the blast furnace in turn in Liuzhou Iron&Steel Co., Ltd. Each switching between two distinct stoves would cause a peak-like disturbance as shown in the measured signals in Fig. 2, which enlarges the data of Part 1 in Fig. 1 from sampling instants k = 52500 to k = 55000. Since the switching time has not been recorded in the event log and there is no signal in the historical database can directly indicate the switching operation, the starting and ending time of the aforementioned disturbances are unknown to us. These switching invoked disturbances may severely influence the performance of process monitoring.

Fig. 2.

Original data from k = 52500 to k = 55000.

3.2. Two-stage PCA Based Process Monitoring for Ironmaking

3.2.1. Basic Idea

To overcome the effects of the aforementioned peak-like disturbances due to stove switching, a two-stage PCA based method is presented in this paper. In the first stage, those strong disturbances are identified based on PCA and a new training dataset is constructed by removing the identified switching disturbances. In the second stage, the standard PCA based process monitoring method²⁵⁾ is utilized. More concretely, a PCA model for the normal ironmaking process of the blast furnace is firstly built based on the training dataset constructed in the preceding stage. Then the T² and SPE statistics for each newly arrived sample in the test dataset are calculated and monitored to simulate a real online monitoring procedure. It is worth noting that the presented method in this paper is different from the standard PCA based method on the decision rule for generating fault alarms as will be discussed in Remark 4.

3.2.2. Stage 1: PCA Based Method for Removing the Data Corresponding to Stove Switching Operations

As mentioned above, a PCA based algorithm is proposed in the first stage to remove the peak-like disturbances from the training dataset which are caused by stove switching operations. The details, are summarized as follows.

Algorithm 1:

• Step 1: Pre-process the raw training data set ( $\tilde{X}$ _{tr_ori}) to obtain the mean centered and scaled measurements²⁵⁾ (X_{tr_ori}).

• Step 2: Let X = X_{tr_ori}, build the PCA model for X_{tr_ori} according to (1) and select the number of principal components, s according to (2).

• Step 3: For each sample x_j in X_{tr_ori}, where j denotes the sampling instant, derive the T² statistic, $T_j^2$ from (3).

• Step 4: For each instant k, calculate the mean value μ_k and standard deviation σ_k of $T_j^2$ for k – 100 ≤ j ≤ k – 50.

• Step 5: If $T_k^2$ < μ_k + 3σ_k, regard x_k as a normal sample; otherwise, identify x_k as a sample related to a stove switching operation. The starting and ending time of the switching operation are determined as follows. Find the nearest instants k – m and k + n from k such that $T_{k-m}^2$ < μ_k + σ_k and $T_{k+n}^2$ < μ_k + σ_k are satisfied, respectively, where m and n are both positive constants and m < k. The data sampled between instants k – m and k + n are regarded as peak-like disturbances.

• Step 6: Construct a new training data set (X_{tr_new}) by first removing the data corresponding to the disturbances identified in Step 5, and then re-processing the data to obtain the mean centered and scaled measurements.

Remark 2: Note that μ_k + 3σ_k, which is adopted at the beginning of Step 4 in Algorithm 1, is normally selected as the threshold to judge whether the T² statistic has an obvious change in the sense of hypothesis-test. In contrast to this, μ_k + σ_k is used for locating the starting and ending points of the peak. This indicates that when $T_k^2$ statistic falls below μ_k + σ_k, the samples would be treated to be normal. The effectiveness of such selections will be demonstrated by the experimental results given in Section 3.3.

Remark 3: In processing the historical data, we find that the stove switching operation would cause large fluctuations in T² statistic. This implies that a switching may change the relationships of the variables in a process and it can be described by T² statistic. However, it is hardly to be described by a single variable. Therefore, although some variables including blast velocity at tuyere and hot blast pressure are strongly related to the stove switching operations, T² statistic is adopted in Algorithm 1 of this paper rather than a single variable to identify the peak-like disturbances invoked by stove switching operations. Moreover, it will be observed from the results of historical data processing presented in Section 3.3 that the SPE statistic is not as sensitive as the T² statistic to the switching disturbances.

3.2.3. Stage 2: PCA Based Status Abnormality Monitoring

We now use the standard PCA based method²⁵⁾ presented in Section 2 to monitor the occurrences of abnormality during the ironmaking process. The following two procedures will be involved: (i) the PCA based modeling; (ii) the T² and SPE statistics based monitoring.

Note that the modeling procedure is similar to Step 2 of Algorithm 1, i.e. let X = X_{tr_new}, build the PCA model for X_{tr_new} according to (1), and select the number of principal components s according to (2).

In the following, the T² and SPE statistics are calculated and monitored for each sample in the test dataset,²⁵⁾ to simulate the real online monitoring process for each newly arrived sample.

Algorithm 2:

• Step 1: Based on X_{tr_new}, set the threshold, i.e. the upper control limit (UCL), $T_{UCL}^2$ for the T² statistic and the threshold SPE_UCL for the SPE statistic according to (5) and (6), respectively. Set another threshold W from the distribution of the width of the identified peak-like switching disturbances obtained by performing Algorithm 1.

• Step 2: Recalling that there are 40000 samples in the original training set X_{tr_ori}. From (3) and (4), calculate $T_k^2$ and SPE_k for each sample x_k for k = 40000 + 1,..., 40000 + W (i.e. the first W samples in the test dataset X_test).

• Step 3: Calculate $T_k^2$ and SPE_k for each newly arrived sample x_k, for k = 40000 + W + 1,..., 103680. Then make a decision according to the following rules.

(i) If $T_i^2$ ≥ $T_{UCL}^2$ and SPE_i ≥ SPE_UCL hold simultaneously, for i = k – W + 1, k – W + 2,..., k, it is concluded that the blast furnace has been operated under an abnormal condition.

(ii) If $T_i^2$ ≥ $T_{UCL}^2$ and SPE_i ≥ SPE_UCL hold simultaneously only for the time instants k smaller than W, it is concluded that the abnormal T² and SPE statistics are caused by the peak-like switching disturbances.

(iii) Otherwise, it is concluded that the ironmaking process has been operated under normal condition.

• Step 4: If the blast furnace is judged to be operated under an abnormal condition, i.e. the conditions in Step 3 (i) are satisfied, a fault alarm is generated and the contributions for SPE statistic are further calculated from (8).

Remark 4: In most of the existing PCA based monitoring algorithms,²⁵⁾ the process is judged as in abnormal condition regarded that T² and/or SPE statistics exceed their respective thresholds. In contrast to this, Step 3 (i) of Algorithm 2 in this paper indicates that only if both the T² and SPE statistics have exceeded their thresholds for a period longer than W, it is concluded that an abnormal status has occurred in the blast furnace. This will inevitably results in a detection delay of W sampling instants. However, such delay may last only several minutes, thus it is negligible with comparison to the settling times of an ironmaking process which are normally several hours. Moreover, W in Algorithm 2 can be selected according to the distribution of the widths of the identified switching disturbances by Algorithm 1. In the experiments of this paper, it is set as 0.9 W_m where W_m is the maximal width of the identified disturbances.

3.3. Experimental Results

3.3.1. Results of Peak-like Disturbances Removing

In this part, the experimental results of the first stage of our PCA based process monitoring method are provided. By performing Algorithm 1 on the original training dataset X_{tr_ori}, a new training dataset X_{tr_new} is obtained with the peak-like disturbances removed.

Figure 3 shows the percentages of the variance, which are accounted for by 29 principal components. It can be seen that more than 95% of the variance in the data set are captured by the first 12 principal components. Thus the number of principal components, s, is set to 12. In other words, only the first 12 principal components are adopted to build the PCA model in Step 2 of Stage 1.

Fig. 3.

Variance accounted for by the components of first-stage PCA model.

We select the confidence level α as α =1×10^–5. According to (5) and (6), $T_{UCL}^2$ and SPE_UCL are set as $T_{UCL}^2$  = 45.1095 and SPE_UCL = 6.9504.

The T² statistic of X_{tr_ori} obtained by performing Step 3 of Algorithm 1 is given in Fig. 4 where the peak-like disturbances identified by Algorithm 1 are also indicated.

Fig. 4.

Switching disturbances identified in the training set.

To verify that the T² statistic outperforms the SPE statistic in identifying the switching disturbances, we also calculate SPE_k for each sample in X_{tr_ori} as shown in Fig. 5. Clearly, the SPE statistic is not as sensitive as the T² statistic to the switching disturbances.

Fig. 5.

SPE statistic of the first-stage PCA model for training set.

3.3.2. Results of PCA Based Status Abnormality Monitoring

In this part, a PCA based model is firstly rebuilt based on the new training dataset X_{tr_new} obtained in Stage 1. Then Algorithm 2 is performed on the test data X_test to simulate the real online monitoring process for each newly arrived sample.

By following similar procedures of selecting s in Stage 1, s is also set to 12 in the second stage of PCA modeling. And the thresholds $T_{UCL}^2$ and SPE_UCL for process monitoring are set to 45.1109 and 6.2149 for the confidence level α = 1×10^–5 according to (5) and (6), respectively.

The distribution of the widths of the switching disturbances identified by Algorithm 1 is plotted in Fig. 6, where “frequency” in vertical axis is specifically the number of times that the widths fall within a given interval. It can be seen that the maximal width W_m is 40 instants. Then the threshold W is set as 0.9W_m, i.e. 36 instants which correspond to 6 minutes. Therefore, in Step 3 of Algorithm 2, if both the two statistics have exceeded their respective thresholds for a period longer than 36 instants, an alarm for abnormality will be generated. If both the statistics exceeds the thresholds, whereas the lasting period is shorter than 36 instants, the samples will be treated as disturbances caused by stove switching.

Fig. 6.

The distribution of the widths of switching disturbances.

An overview of the T² statistic and SPE statistic for the test set X_test by performing Step 2 and Step 3 of Algorithm 2 in this paper is provided in Figs. 7(b) and 7(c). The blue, green and red parts of the line are judged as normal status, disturbances and abnormal status, respectively. The grey dotted line represents the thresholds. Besides, the yellow dotted vertical line indicates the starting time of the accident reported in the event log, while the red dotted vertical line indicates the time of fault alarm generated by Algorithm 2. It can be seen that with the monitoring method presented in this paper, the alarm of the getting cold accident can be generated in advance of the time reported in the event log. Furthermore, there is no false alarm beforehand. Note that the red part of the line near time instant 70000 alarmed by our method corresponds to a scheduled blast furnace blowing down.

Fig. 7.

T² and SPE statistics of two-stage PCA and direct PCA models in test set.

By enlarging part of Fig. 7 from k = 84600 to k = 85600 in Fig. 8 the advantages of our two-stage PCA monitoring method in generating the accident alarm become more apparent. From Figs. 8(a), 8(b) and 8(c), it can be seen that the alarm is generated 396 instants (approximately 1.1 hours) earlier than the instant recorded in the event log. In fact, most of the serious faults are evolved gradually from tiny faults, which leads to the gradual increase of the T² and SPE statistics. This constitutes the main reason that PCA based monitoring method can detect a fault in its incipient stage.

Fig. 8.

Comparison of the alarm time by different monitoring methods.

Observing Figs. 8(d) and 8(e), we find the T² statistic of the direct PCA method generates the fault alarm at almost the same time as the two-stage PCA based method. However, its SPE statistic fails to generate an alarm earlier than the time recorded in the event log. As mentioned in Remark 4, different from our presented monitoring algorithm, the operational status of the process is normally judged according to T² and/or SPE statistics in direct PCA method. Thus the advantages of the two-stage PCA can be concluded based on Fig. 8 from the following two aspects:

1) If T² statistic is adopted in direct PCA to monitor the process, it can be seen that the direct PCA generates the alarm 3 instants (30 seconds) earlier than the two-stage PCA method. However, such negligible superiority in alarm generation time, is gained at a cost of higher false alarm rate. More concretely, direct PCA method leads to false alarms of 106 instants (17.7 minutes), whereas no false alarm is generated by the two-stage PCA method.

2) If SPE statistic is employed in direct PCA to avoid false alarms, the two-stage PCA method alarms at the 85156th instant, and the direct PCA method alarms at the 85553rd instant. Thus the two-stage PCA method alarms 397 instants (approximately 1.1 hours) earlier than the direct PCA method.

As mentioned in Section 2, once an alarm is generated, contribution plot can be further used to analyze which variables contributes the most to the change of the SPE statistic. The contributions of the 29 main variables to the SPE statistic given by our two-stage PCA model and the direct PCA model are plotted in Figs. 9(a) and 9(b), respectively. We focus on the time interval from instant 85156 to 85300 due to the following reasons. 1) During this period, the fault had developed gradually. However, it has not become so severe that the PCA model needs to be adjusted. 2) There is no stove switching procedure during this period.

Fig. 9.

Contributions of variables between instants 85156 and 85300 (i.e. 0.4 hours).

In Figs. 9(a) and 9(b), the contribution plots of the 2-stage PCA and direct PCA methods are given, respectively. In (b), the 12th variable (corresponding to theoretical combustion temperature) contributes the most to the deviation of the SPE statistic. However in (a), the 6th and 8th variable (corresponding to blast velocity at tuyere of blast furnace and cold blast flow) contribute more than theoretical combustion temperature.

The main reason to such difference of the contribution plots is that in contrast to direct PCA, switching disturbances have been removed in the training stage of the two-stage PCA. Since the blast velocities at tuyere of blast furnace and cold blast flow are hidden in the switching disturbances, the SPE statistic of direct PCA is much less sensitive to the two variables than that of two-stage PCA.

Remark 5: Note that the contribution plot of the two-stage PCA method is consistent with the operators’ empirical judgments and the analysis in the accident report provided by Liuzhou Iron&Steel Company.

4. Conclusion

This paper focuses on process monitoring and fault diagnosis for the blast furnace ironmaking process. A two-stage PCA method is used to monitor the process. In the first stage, the peak-like disturbances caused by the stove switchings are removed. In the second stage, the monitoring model is first rebuilt based on dataset with the switching disturbances removed. Then the process is monitored based on the T² statistic and the SPE statistic with a modified decision logic. Experiment results based on the historical data collected from a real blast furnace with a volume of 2000 m³ validate the advantages of our two-stage PCA method in detecting the getting cold accident with comparison to the direct PCA method and operators’ monitoring.

Acknowledgements

The work was supported by National Natural Science Foundation of China under grant 61290324 and 61203068.

References

• 1)   J.  Peacey and  W.  Davenport: The Iron Blast Furnace: Theory and Practice, Pergamon Press, Oxford and New York, (1979), 34.
• 2)   D. H.  Wakelin: The Making, Shaping, and Treating of Steel, Ironmaking Volume, 11th Edition, The AISE Steel Foundation, Pittsburgh, (1999), 229.
• 3)   C.  Van der Vliet: Modern Blast Furnace Ironmaking: An Introduction, IOS Press, Amsterdam, (2009), 16, 104.
• 4)   H.  Lu,  B.  Gao,  L.  Zhao,  H.  Guo and  T.  Yang: J. Univ. Sci. Technol. Beijing, 3 (2002), 013.
• 5)   L. J. W.  Shuqing: J. Iron Steel Res., 5 (1998).
• 6)   S.  Amano,  T.  Takarabe,  T.  Nakamori,  H.  Oda,  M.  Taira,  S.  Watanabe and  T.  Seki: ISIJ Int., 30 (1990), 105.
• 7)   A.  Wang,  L.  Zhang,  N.  Gao and  M.  Wang: Sixth World Cong. on Intelligent Control and Automation 2006, IEEE, Piscataway, NJ, (2006), 5615.
• 8)   A.  Wang,  L.  Zhang and  N.  Gao: 3rd Int. IEEE Conf. on Intelligent Systems 2006, IEEE, Piscataway, NJ, (2006), 571.
• 9)   H. X.  Tian and  A. N.  Wang: ISIJ Int., 50 (2010), 738.
• 10)   L. M.  Liu,  A. N.  Wang,  M.  Sha and  F. Y.  Zhao: J. Iron Steel Res. Int., 18 (2011), 17.
• 11)   L. M.  Liu,  A. N.  Wang,  M.  Sha,  X. Y.  Sun and  Y. L.  Li: ISIJ Int., 51 (2011), 1474.
• 12)   L.  Liu,  A.  Wang,  M.  Sha and  F.  Zhao: J. Iron Steel Res. Int., 18 (2011), 17.
• 13)   J.  Chen: Eng. Appl. Artif. Intel., 14 (2001), 77.
• 14)   V.  Radhakrishnan and  A.  Mohamed: J. Process Contr., 10 (2000), 509.
• 15)   L.  Pan and  X.  Hui: Adv. Mater. Res., 204 (2011), 1254.
• 16)   J.  Cai,  J.  Zeng and  S.  Luo: ISIJ Int., 52 (2012), 2194.
• 17)   T.  Bhattacharya: ISIJ Int., 45 (2005), 1943.
• 18)   W.  Wang: 2nd Int. Symp. on Intelligent Information Technology Application 2008, IEEE, Piscataway, NJ, (2008), 42.
• 19)   W.  Wang and  J.  Ma: Fifth Int. Conf. on Natural Computation 2009, IEEE, Piscataway, NJ, (2009), 590.
• 20)   X.  Liu and  W.  Wang: Int. Conf. on Multimedia Technology 2011, IEEE, Piscataway, NJ, (2011), 2789.
• 21)   Z.  Jiu-sun,  L.  Xiang-guan,  G.  Chuan-hou and  L.  Shi-hua: American Control Conf. 2008, IEEE, Piscataway, NJ, (2008), 2481.
• 22)   D.  Noskievičová: Metalurgija, 48 (2009), 281.
• 23)   F. I.  Gamero,  J.  Colomer,  J.  Meléndez and  P.  Warren: Eng. Appl. Artif. Intel., 19 (2006), 103.
• 24)   E.  Vanhatalo: Qual. Reliab. Eng. Int., 26 (2009), 495.
• 25)   J.  MacGregor and  T.  Kourti: Contr. Eng. Pract., 3 (1995), 403.
• 26)   R.  Dunia,  S. J.  Qin,  T. F.  Edgar and  T. J.  McAvoy: AIChE J., 42 (1996), 2797.
• 27)   M.  Dudzic and  I.  Miletic: Proc. of American Control Conf. 2002, IEEE, Piscataway, NJ, (2002), 600.
• 28)   M.  Dudzic and  Y.  Zhang: Dynamics And Control of Process Systems 2004, Elsevier Science, Oxford, (2005), 269.
• 29)   Y.  Zhang and  M. S.  Dudzic: J. Process Contr., 16 (2006), 819.
• 30)   P. C.  Mahalanobis: Proc. of National Institute of Sciences, Baptist Mission Press, Calcutta, (1936), 49.
• 31)   I. T.  Jolliffe: Principal Component Analysis, 2nd Edition, Springer, New York, (2002).
• 32)   P.  Miller,  R.  Swanson and  C. E.  Heckler: Appl. Math. Comput. Sci., 8 (1998), 775.