Online Heat Pattern Control of a Shaft Furnace Based on a Real-time Visualization by Particle Filter

Abstract

In the steel works, direct observation of the internal states of many processes, such as the blast furnace, is difficult. Automation of such processes based on process visualization is an urgent issue. Because the number of sensors is limited, the state estimation utilizing partial sensor information is necessary. We developed a technique which visualizes the entire temperature distribution of a shaft furnace by means of the particle filter, which combines the sensor information and a nonlinear model calculation. This state estimation was incorporated in the heat pattern control logic based on future prediction, in which the estimated heat pattern is set as the initial condition. The control logic was implemented in a ferro-coke pilot plant. As a result, the control accuracy of 10°C was achieved. Furthermore, the operational condition was adjusted based on the correlation between the estimated heat pattern and the product strength. In consequence, the product strength improved by 0.5 points (Drum Index 150/15 mm, DI¹⁵⁰15).

1. Introduction

In the steel works, direct observation of the internal states of many processes which involves shaft furnaces, such as the blast furnace, is difficult. Such processes are operated manually depending on the operator’s ability and experience. Hence, automation based on process visualization is an urgent issue.

There have been many approaches to the visualization of internal state by physical model calculations. For instance, complicated models which take into account fluid motion, reaction, and heat transfer have been developed.¹⁾ However, because these models employ fixed parameters, they cannot deal with the transient phenomena caused by fluctuations of unknown parameters of materials characteristics, and so on.

In order to adapt to such situations, many studies have attempted to assimilate the model calculation with partial information from sensors, and compensate for modeling errors. Examples of conventional techniques are the Kalman filter,²⁾ which is based on a linear approximation of the model, and the particle filter with simplified models based on a lumped element approximation.^3,4) In the field of process control, there have been a small number of studies that retain the feature of the model, which directly reflects nonlinear and complicated phenomena as a distributed element model, while making the best use of sensor information.

On the other hand, in the field of meteorology, there have been numerous studies of data assimilation in which large-scale numerical simulations are assimilated with observation data. Data assimilation can be classified into the sequential type and the non-sequential type. The former includes the particle filter⁵⁾ and the ensemble Kalman filter;⁶⁾ an example of the latter is the adjoint method.⁷⁾ The former has the advantages that the implementation is relatively easy and the probability distribution of the state variable can be obtained. In particular, the particle filter features robustness and a clear physical interpretation.

In this research, nonlinear models of a shaft furnace assuming various unknown parameters are calculated online, based on the concept of the particle filter. The weight of each model is updated with the degree of coincidence with the actual data, and the unknown parameters are estimated online. This enables flexible modeling which can follow changes in plant characteristics with a clear interpretation.

In general, a shaft furnace containing a packed bed has a relatively long time constant, because of its huge heat capacity. Moreover, a long response delay also exists due to the material descent from the furnace top to the bottom. Therefore, simple feedback control based on the actual values is not adequate, and a control law which includes future prediction is necessary. In such cases, model predictive control with a physical model is effective.⁸⁾ Control accuracy is expected to improve by setting the estimated heat pattern with the particle filter as the initial condition of the future prediction.

The heat pattern control logic combined with real time estimation by the particle filter as outlined above was implemented in a ferro-coke furnace. Ferro-coke is a mixture of coal and iron ore with the ratio of 7:3.⁹⁾ Owing to the catalytic effect of metallic Fe, the coke gasification reaction starts at a lower temperature compared with normal coke.¹⁰⁾ This reduces the temperature of thermal reserve zone in the blast furnace, enabling low coke ratio operation. The ferro-coke manufacturing process consists of mixing, molding, and coking. The target of this research is the heat pattern of a ferro-coke furnace during the coking process.

The ferro-coke furnace is a continuous process in which the solid material is charged from the top, and discharged from the bottom. The residence time of the material is roughly 12 hours. There are several constraints on the heat pattern of the furnace, such as the temperature rising rate, coking time, and cooling condition. For example, a higher temperature rising rate enhances the fluidity of coal grains, resulting in better product strength. The holding time in the coking zone should be controlled in order to improve product strength and reactivity.

In spite of the necessity of the online heat pattern control, the number of sensors is limited. In addition, unknown parameters, such as the heat loss from the oven surface and the specific heat of the solid, exist in the process which cannot be detected online. Therefore, application of a control logic based on the online estimation with the particle filter is an appropriate approach. In the previous report, the estimation accuracy of the logic has been confirmed.¹¹⁾ As the next step, this paper focuses on how to utilize the estimated heat pattern in the heat pattern control.

The framework of this paper is as follows. In Section 2, the mathematical modeling of the ferro-coke furnace and the design of the particle filter are reviewed. The design of the model predictive control is presented in Section 3. An evaluation of the logic in the actual operation at a pilot plant is explained in Section 4. Improvement of the heat pattern based on the correlation between the estimated heat pattern and the product strength is discussed in Section 5. Finally, we conclude this paper in Section 6.

2. State Estimation Based on Particle Filter

2.1. Mathematical Modeling of the Shaft Furnace

As shown in Fig. 1, several tuyeres for coking and cooling are arranged symmetrically. There are three kinds of tuyeres, which are termed low temperature tuyere, hot tuyere, and cooling tuyere. The low temperature tuyere is used to adjust the temperature rising rate. The holding time in coking zone is achieved by the hot tuyere. The cooling tuyere and discharge device are installed at the bottom of the furnace. Ferro-coke briquette are charged from the top of the furnace, and heated up by the heat exchange between the solid and the gas. After the coking process near the hot tuyere, the final product is released from the bottom. Thermocouples TI (1)–TI (5) are arranged on either side of the oven wall, which can monitor the temperature continuously. Hereafter, average temperature of the two thermocouples at the same height is defined as the actual wall temperature.

Fig. 1.

Structure of the ferro-coke furnace.

A transient 2D model was developed for the visualization of temperature distribution, taking into account the reaction, the fluid motion, and the heat transfer. For example, the heat transfer model, which describes the heat exchange between the solid and the gas, and the reaction heat, can be expressed as Eqs. (1), (2). We simplified the heat transfer between the gas and the atmosphere through the oven wall as a boundary condition of Eq. (3). The total heat transfer coefficient h includes the thermal resistance between the gas and oven wall, heat conductivity of the oven wall, and the heat radiation to the atmosphere. This heat sink was incorporated in the gas heat calculation as a source term. Further details of the model can be found in the previous report.¹¹⁾ The variables are listed in Table 1. The coordinate x-y is defined in Fig. 1.   

$$\begin{array}{l}\frac{\partial ({\rho }_g{C}_g{T}_g)}{\partial t}+\frac{\partial (C_g{u}_g{T}_g)}{\partial x}+\frac{\partial (C_g{v}_g{T}_g)}{\partial y}=S\alpha (T_s-T_g)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}+R\mathrm{\Delta }{H}_R{\eta }_1+q\end{array}$$(1)

  

$$\frac{\partial ({\rho }_s{C}_s{T}_s)}{\partial t}+\frac{\partial ({\rho }_s{C}_s{v}_s{T}_s)}{\partial y}=S\alpha (T_g-T_s)+R\mathrm{\Delta }{H}_R{\eta }_2$$(2)

  

$$q=-h(T_g-T_{out})$$(3)

Table 1. Variables in the model.

Symbol	Notes	Dimension
ug	Mass velocity of the gas (Horizontal)	[kg/m2·s]
vg	Mass velocity of the gas (Vertical)	[kg/m2·s]
ρs	Density of the solid	[kg/m3]
vs	Velocity of the solid	[m/s]
R	Reaction rate	[kg/m3·s]
Tg	Gas temperature	[K]
Ts	Solid temperature	[K]
Cg	Specific heat of gas	[J/kg·K]
Cs	Specific heat of solid	[J/kg·K]
ΔHR	Reaction heat	[J/kg]
η1	Reaction heat distribution rate (gas)	[−]
η2	Reaction heat distribution rate (solid)	[−]
Tout	Atmosphere temperature	[K]
h	Total heat transfer coefficient	[J/m2·s·K]
α	Heat exchange coefficient	[J/m2·s·K]
ρg	Density of gas	[kg/m3]
S	Specific surface area	[m2/m3]

These differential equations are discretized by the finite volume method. The time step was 10 minutes. The discretized equations can be expressed in the form of Eq. (4), where T_s(k) and T_g(k) are the temperature distribution of the solid and the gas at time step k, respectively, u(k) is the model input, such as the inflow gas volume and temperature, and A(k) is the set of unknown parameters, which were assumed to fluctuate. We calculated the 1/2 region of the furnace, considering the structural symmetry of the furnace. The mesh number was 8 in horizontal direction and 120 in height direction.   

$$\left({\mathbf{T}}_s(k+1),{\mathbf{T}}_g(k+1)\right)=f\left({\mathbf{T}}_s(k),{\mathbf{T}}_g(k),\mathbf{u}(k),\mathbf{A}(k)\right)$$(4)

2.2. Algorithm of Particle Filter

In this section, the algorithm of the particle filter, which assimilates the sensor information and model calculation, is explained. Summarizing the logic, various models assuming different parameter are prepared, and the temperature distribution is calculated in parallel. Then, the fitness of each model with the actual data is evaluated by the actual sensor data, and the number of copies of the model for the next time step is determined by the fitness. As shown in Fig. 2, the procedure consisting of model prediction, evaluation, and making copies is repeated at every time step. This way, the accuracy of the model is retained. The details of the algorithm consist of five steps, as follows.

Fig. 2.

The algorithm of particle filter.

Step (1): As the initial guess of the unknown parameters, various sets of the parameters are prepared. Here, we assume that the fluctuating parameters are the specific heat of the solid, and the heat radiation coefficient of the furnace wall. In spite of the fact that the heat exchange coefficient α entails an uncertainty in general, we assessed that the variation of α has small impact on the heat pattern. It is because the heat exchange between the solid and gas was so rapid that the temperature of the two was almost identical. Hereafter, each set of the unknown parameters is to be called “particle”. The number of the particles was 25, considering the calculation time of each model and the control cycle time. It has been confirmed that 25 particles can estimate the two unknown parameters separately in the simulation experiment.¹¹⁾

The weight of i th particle at time step k is defined as w_i(k). The initial weight was set to be equal as shown in Eq. (5), where N is the number of particles.   

$$w_i(1)=1/N$$(5)

Step (2): Based on the unknown parameters of each particle, the temperature distribution is predicted using the transient model as shown in Eq. (6), where T_s,i(k) is the temperature distribution of the solid at time step k, and T_g,i(k) is the temperature distribution of the solid at time step k, with respect to i th particle.   

$$\left({\mathbf{T}}_{s,i}(k),{\mathbf{T}}_{g,i}(k)\right)=f\left({\mathbf{T}}_{s,i}(k-1),{\mathbf{T}}_{g,i}(k-1),\mathbf{u}(k-1),{\mathbf{A}}_i(k-1)\right)$$(6)

As this step is conducted independently for each particle, it is helpful to organize the transient model into the form as described in Section 2.1.

Step (3): The fitness between the actual data and the predicted temperature at the sensor locations is evaluated for each particle. First, the temperature prediction of the model of the i th particle at the sensor position can be obtained by Eq. (7), where C is the observation matrix, which extracts the value at the sensor positions from the calculated temperature distribution. In this case, we assumed that the thermocouples measure the temperature of the gas, because the thermocouples are placed on the internal surface of the oven wall.   

$${\mathbf{y}}_i(k)=\mathbf{C}{\mathbf{T}}_{g,i}(k)$$(7)

The definition of the fitness was defined as Eq. (8), where the suffix act means the actual value from the sensors. σ was set to the root square mean error of the particles, as described in Eq. (9).   

$${\theta }_i(k)=exp\left(-\frac{{\left|{\mathbf{y}}_i(k)-{\mathbf{y}}_{act}(k)\right|}^2}{{\sigma }^2}\right)$$(8)

  

$${\sigma }^2=\sum _{i=1}^N\frac{{\left|{\mathbf{y}}_i(k)-{\mathbf{y}}_{act}(k)\right|}^2}{N}$$(9)

Step (4): The weight of each particle is updated with the fitness, based on Bayes’ theorem.   

$$w_i(k)\propto w_i(k-1){\theta }_i(k)$$(10)

  

$$\sum _i{w}_i(k)=1$$(11)

The weight w_i(k) is updated by multiplication by the fitness θ_i(k), and normalized so that the total weight is unity. The estimation of temperature distribution and the unknown parameters at time step k can be expressed as the weighted average of the particle, as shown in Eqs. (12), (13), (14).   

$${\mathbf{T}}_s^a=\sum _i{w}_i(k)\cdot {\mathbf{T}}_{s,i}(k)$$(12)

  

$${\mathbf{T}}_g^a=\sum _i{w}_i(k)\cdot {\mathbf{T}}_{g,i}(k)$$(13)

  

$${\mathbf{A}}^a=\sum _i{w}_i(k)\cdot {\mathbf{A}}_i(k)$$(14)

Step (5): The copies of the particles are generated with the probability proportional to the weight of each particle. Thus, a particle with a larger weight has a greater chance of leaving more copies for the next time step. After that, the unknown parameters are slightly adjusted with random numbers to avoid making completely identical particles. In this case, an arbitrary number was selected from 0.995 to 1.005, and the unknown parameters were adjusted by multiplying the number. Then, the weight of each particle is set to unity.

Online estimation of unknown parameters is possible by conducting Step (2)–Step (5) at each time step. Therefore, higher accuracy is achievable, compared with the calculation by fixed parameters. The estimation accuracy improved by 30% by this method, as can be seen in previous report.¹¹⁾

3. Design of the Heat Pattern Control

3.1. Selection of Controlled Variables and Manipulated Variables

As the critical factors to be controlled online, furnace top heat, the discharged product temperature, and the internal temperature were selected, as shown in Fig. 3. First, the furnace top heat has a strong influence on the temperature rising rate of the material, which affects the product strength. In general, the furnace top heat depends on the heat flow ratio in a counter flow heat exchange process.¹²⁾ Therefore, the furnace top heat rises by increasing not only the hot tuyere flow rate but also the cooling tuyere flow rate. Hence, a control logic which incorporates the interference among the tuyeres is necessary. Secondly, the internal temperature should be controlled to reduce the variance of the high temperature zone for the coking process. Since this temperature cannot be measured online, the estimated temperature by the particle filter is utilized. Thirdly, as the discharged temperature, the product must be cooled sufficiently to prevent the ignition by the reaction with the oxygen in the air.

Fig. 3.

Selection of controlled variables and manipulated variables.

On the other hand, the possible manipulated variables to achieve the ideal heat pattern are the gas temperature of the hot tuyure, flow rate of the hot tuyure, the flow rate of the cooling tuyure, the flow rate of the low temperature tuyere, and the production rate. The production rate was excluded because it should be kept constant. The gas temperature was also excluded because changes in this variable may lead to an unstable coking reaction. For the time being, the flow rate of the low temperature tuyere was also kept constant for an operational reason. The remaining variables are the flow rates of the hot tuyere and the cooling tuyere.

3.2. Algorithm of the Model Predictive Control

The model predictive control consists of the following three steps as shown in Fig. 4. In summary, the future heat pattern is predicted assuming that the plant is left under the present boundary condition, followed by the calculation of the step response in the case where the manipulated variable is changed. Then, the optimal manipulation for achieving the target heat pattern is calculated. The control cycle time was 10 minutes. In the following, MV₁ and MV₂ correspond to the flow rates of the hot tuyere and the cooling tuyere, and CV₁, CV₂ and CV₃ mean the furnace top heat, the discharged temperature, and the internal temperature, respectively.

Fig. 4.

Algorithm of the model predictive control.

Step (1): Prediction of controlled variables

The time evolution of each controlled variable is calculated assuming that the present boundary condition continues in the future, as described in Eq. (15), where t is the time step whose starting point is present. The manipulated variable u(t) and the unknown parameters A(t) in the future are assumed to be identical with the present value at t = 0. The initial condition of the prediction is set to the estimated heat pattern by Eqs. (12) and (13), and the estimated unknown parameter by Eq. (14) is utilized, as shown in Eq. (16). The controlled variable in the future is calculated by Eq. (17), where H is the linear operator which extracts the controlled variable from the calculated heat pattern. Hereafter, the trajectory of the controlled variable is denoted as free response.   

$$\left({\mathbf{T}}_s(t+1),{\mathbf{T}}_g(t+1)\right)=f\left({\mathbf{T}}_s(t),{\mathbf{T}}_g(t),\mathbf{u}(0),\mathbf{A}(0)\right)$$(15)

  

$$\begin{array}{l}{\mathbf{T}}_s(0)={\mathbf{T}}_s^a\\ {\mathbf{T}}_g(0)={\mathbf{T}}_g^a\\ \mathbf{A}(0)={\mathbf{A}}^a\end{array}$$(16)

  

$$\left(\begin{array}{c}C{V}_{1,free}(t)\\ C{V}_{2,free}(t)\\ C{V}_{3,free}(t)\end{array}\right)=\mathbf{H}\cdot {\mathbf{T}}_g(t)$$(17)

Step (2): Calculation of step responses

The trajectory of the controlled variables is calculated in the case where each manipulated variable is changed by a unit volume. In Step 1, the controlled variables are predicted with the present manipulated variable. The influence of the manipulated variable can be extracted by taking the difference between the two cases, as shown in Fig. 5. The step response of CV_j at time step t in the case MV_i is changed is denoted as $St{p}_i^j(t)$.

Fig. 5.

Calculation of step response.

In general, a fixed step response is adopted in the field of model predictive control. In the case of a ferro-coke furnace, however, the step response greatly depends on the operational condition and unknown parameters. To deal with this nonlinearity, the step response is updated in each control cycle.

Step (3): Optimization of manipulated variables

The manipulated variables are optimized so that the controlled variables coincide with the target value in the future. In other words, the control error in the future is compensated by the linear combination of the step responses. In general, two parameters exist when applying the model predictive control, these being the prediction horizon and the control horizon.⁸⁾ In this case, the prediction horizon was set to 500 minutes (50 control cycles), considering that the residence time of the material inside the furnace is roughly 10 hours. The control horizon was set to 1 step for the simplicity of the control logic. The decision variable, evaluation function, and the constraint are as follows. In this way, the model predictive control can be reduced to a standard quadratic programming problem.

Step (3-1): Decision variables

The change of the manipulated variables (ΔMV₁, ΔMV₂) is calculated. After the optimization procedure, the flow rates of the tuyeres are updated with the optimization result.

Step (3-2): Evaluation function

The evaluation function is as follows, which consists of the weighted square sum of the deviation from the target value (CV_1,ref and CV_2,ref), and the weighted square sum of the change of the manipulated variable, as show in Eq. (18). From the viewpoint of calculation cost, the deviation of the controlled value at every 5 steps was added. CV_1,pre and CV_2,pre are the prediction values of the controlled variables, which can be approximated by the summation of the free response and the linear combination of step response, under the condition that the changes of manipulated variables are small. The decision variables are determined so that the controlled variables approach the target values, and at the same time, excessive actions are avoided.   

$$\begin{array}{l}J=a_1\cdot \sum _{s=1}^{10}{\left(C{V}_{1,ref}-C{V}_{1,pre}(5s)\right)}^2\\ +a_2\cdot \sum _{s=1}^{10}{\left(C{V}_{2,ref}-C{V}_{2,pre}(5s)\right)}^2+b_1\cdot {(\mathrm{\Delta }M{V}_1)}^2+b_2\cdot {(\mathrm{\Delta }M{V}_2)}^2\end{array}$$(18)

  

$$\begin{array}{l}C{V}_{1,pre}(t)=C{V}_{1,free}(t)+\mathrm{\Delta }M{V}_1\cdot St{p}_1^1(t)+\mathrm{\Delta }M{V}_2\cdot St{p}_2^1(t)\\ C{V}_{2,pre}(t)=C{V}_{2,free}(t)+\mathrm{\Delta }M{V}_1\cdot St{p}_1^2(t)+\mathrm{\Delta }M{V}_2\cdot St{p}_2^2(t)\end{array}$$(19)

Step (3-3): Constraints

The linear constraint that the internal temperature must be more than the lower limit was imposed, as presented in Eq. (20), where CV_3,lower is the lower limit of the internal temperature. CV₃ was treated as the constraint to ensure that the coking reaction proceeds in the middle of the furnace.   

$$\begin{array}{l}C{V}_{3,pre}(t)\ge C{V}_{3,lower}\\ C{V}_{3,pre}(t)=C{V}_{3,free}(t)+\mathrm{\Delta }M{V}_1\cdot St{p}_1^3(t)+\mathrm{\Delta }M{V}_2\cdot St{p}_2^3(t)\end{array}$$(20)

4. Evaluation in the Actual Operation

In this section, the experimental results of the model predictive control base on the particle filter are presented. The logic was implemented at the operation room of a ferro-coke plant. The information of the thermocouples at the four different height positions (TI (1), TI (3), TI (4), TI (5) in Fig. 1) were used for the input of the particle filter. The remaining one, TI (2) was used for validation of the logic. The results of the estimation of the heat pattern and the unknown parameters can be found in the previous report.¹¹⁾

The valve opening positons of the tuyeres were adjusted manually to realize the optimal flow rate given by the control logic. The variances of the controlled variables were compared in the case where the flow rate was changed with the control logic (guidance period in Fig. 6), and the case without using the logic. As shown in Fig. 6, the furnace top heat and the discharged temperature were kept near the set point without significant error during the guidance period, compared with the period without the control logic. The temperature in the figure is scaled by the deviation from the set point. Moreover, both values were controlled within the range of almost 10 degrees even if the production rate, which is the disturbance for the heat pattern control, was changed from 80% to 90%. The internal temperature was kept above the lower limit.

Fig. 6.

Experimental results of model predictive control.

As mentioned in Section 3.2, the model predictive control has a function to compensate for the influence of disturbances by predicting the future state. The predicted trajectory of the controlled variables at the timing when the production rate was increased is shown in Fig. 7. The two lines in the predicted horizon correspond to the case without action and the case with the optimal action. It can be seen that the decrease of the furnace top heat and the increase of the discharge temperature were predicted. This result is intuitively true because the furnace top heat decreases when more briquettes at room temperature are loaded and the discharged temperature increases due to insufficient cooling. The proper action to modify the trajectory was calculated. These prediction results were displayed to the operators continuously to enhance the interpretation of the control logic.

Fig. 7.

Predicted trajectories of controlled variables at timing of production rate change.

5. Improvement of Heat Pattern Based on Correlation between Estimated Heat Pattern and Product Quality

As the next step, the correlation between the estimated heat pattern and product strength was analyzed in order to identify the dominant factors which strongly affect the product strength.

The material temperature history was calculated by tracking the temperature during the descent inside the furnace as shown in Fig. 8, where the temperature is scaled by the maximum possible temperature. Holding time in high temperature zone, where the solid temperature exceeds 70%, can be calculated by this temperature history. In order to consider the variance within the cross section, the holding time was calculated independently in the four areas, and the correlation between the averaged value of the four areas and product strength was investigated.

Fig. 8.

Analysis of material temperature history.

As a result, it was found that there was a negative correlation between the product strength and the holding time in the high temperature zone, as shown in Fig. 9. The null hypothesis that there was no correlation between them was discarded based on the p-value of 0.014. The strength of normal coke is enhanced by prolonging the coking time because the coke micro-structure achieves the graphite structure. On the contrary, the strength of ferro-coke may deteriorate if the coking time is excessive, because the coke is partially consumed by the direct reduction reaction with the iron ore.

Fig. 9.

Correlation between holding time in high temperature zone and product strength.

Based on the correlation analysis, the temperature distribution was simulated in the case where the flow rate of the tuyeres was changed as shown in Table 2. It was predicted that the holding time in the high temperature zone could be reduced by 0.7 hour, by means of increasing the flow rate of the low temperature tuyere and decreasing the flow rate of the hot tuyere (Fig. 10).

Table 2. Condition of tuyere flow rate.

	Case1 (Base)	Case2 (Improved)
Low temp. tuyere (~550°C)	50 Nm^3/hr	300 Nm^3/hr
Hot tuyere (~850°C)	2050 Nm^3/hr	1920 Nm^3/hr
Cooling tuyere (~50°C)	2400 Nm^3/hr	2400 Nm^3/hr
Holding time in high temperature zone	3.2 hr	2.5 hr

Fig. 10.

Estimated heat pattern by changing the flow rate of tuyeres. Case1 (Left), Case2 (Right).

The experiment was conducted to realize the improved heat pattern. As shown in Fig. 11, the flow rates were adjusted in the two steps, which resulted in the improvement of the product strength by 0.5 points (Drum Index 150/15 mm). The null hypothesis that the average values of the two groups are identical was discarded based on the p-value of 0.04. These results demonstrate the validity of our approach.

Fig. 11.

Experimental results of the heat pattern improvement.

6. Conclusion

In this research, a heat pattern control of the shaft furnace was developed, which combines online state estimation logic based on particle filter logic and model predictive control. As a result of an evaluation in actual operation, the control accuracy of 10 degrees was achieved. Furthermore, the operational condition was adjusted based on the correlation between the estimated heat pattern and product strength. In consequence, product strength improved by 0.5 point (Drum Index 150/15 mm). As future work, the heat pattern control of other shaft furnaces such as the blast furnace will be developed.

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