High Quality Steel Casting by Using Advanced Mathematical Methods

Round  1

Reviewer 1 Report

The assurance and improvement of steel quality in the continuous casting process is a big topic up today. The design of a control mechanism for a real caster with the goal of adjusting an optimal surface temperature profile for reducing the cracks in the shell due to the unbending is therefore of great interest. The paper describes a two-step model to adjust the steel shell surface temperature accordingly. First, a three-dimensional numerical model calculates the actual surface temperature due to the casting parameters and the temperature dependent material properties of the steel. Afterwards, a fuzzy controller adjusts the cooling rates of all the different cooling systems to get the desired temperature profile along the shell surface. The combination of simulation and fuzzy controller represents a kind of Model Predictive Control, which provides the necessary input data for the controller, which would be not accessible by direct measurements. The desired temperature data is retrieved from historical plant data.

For me, one main question arises while reading the text. The cracking and quality issue was related to the local surface temperature measurement just at one location: the bending point (Figure 5). There should be an explanation, why to make the expensive numerical simulations to get further temperature values, when already one measured value was sufficient to distinguish between good and bad heats. Otherwise: Shouldn’t it be also possible to set up a fuzzy controller with the measured temperature at the bending point as input data and then adjusting the cooling conditions as output data? Isn’t the shell thickness together with the surface temperature profile somehow already contained in the historical data which was used to design the fuzzy controller? It might be good to get some more information and benefits of taking the additional effort of making a whole 3D-simulation, e.g. in the introduction.

Section 4 suddenly demands for several regulation points for the fuzzy controller where the temperature is kept within an optimal temperature range. The reasoning for that and the finding and setting of these ranges is promised for section 5. However there is no statement in section 5 about the finding these optimal temperature ranges along the casting strand. Section 5 is about material composition, temperature dependent material properties and statistical evaluation of optimal surface temperature, but only at one location: for the unbending area! So please give the promised information why and how these additional temperature ranges were obtained. Are there further data series like in Figure 7 for other locations at the strand?

Boundary condition (2): The pouring temperature is for my understanding the highest temperature of the steel in the mould, i.e. where it enters the mould (which is when the melt leaves the nozzle ports). On the way to the free surface, the melt has already cooled down a little bit. By this, the term pouring temperature seems to be not correct for the boundary condition of the free surface temperature.

No fuzzy sets of no other rules of the fuzzy controller are presented or described in this article. What is the purpose of mentioning just the one for the modification of cooling rate? I would suggest omitting the sentence in line 192-193 and the whole Table 2. For my feeling it is distracting the reader too much in trying to understand the rules, new variables and dependencies – especially as it is already described sufficiently in words in the text before and afterwards. Either the whole fuzzy controller is described in more detail or it is left out of scope in this paper.

Figure 5: Although this Figure is correctly illustrating the historical data, it seems to be not the best way to show the desired optimal operation window. The historical evolution of the heats over time is of no specific interest, isn’t it? It is even raising other questions, like: Why is there a slight slope of temperature with increasing heat number, as it is also manifested by the given linear regression with a slope unequal to zero? What shall the linear regression illustrate? What does this trend mean for the future of this caster? Is it slightly running into bad operation condition? I would suggest to plot the data as a histogram with surface temperature ranges on the abscissa and the absolute or relative occurrence on the ordinate. Further it would be better to split the bad data into a part with higher surface temperature than the good one, and one part with lower surface temperature than the good one. In the end it could look like a set of three Gaussian curves: the good one with optimal surface temperatures in the middle surrounded by a bad one at the left and a bad one at the right. This leads to a further question in the text of line 228-230: What is the meaning of the higher average value of the bad heats and the higher standard deviation? I would interpret this value in that way that the historical heats were operated with a trend to higher temperatures compared to the optimal surface temperature. Does this have any evidence for the design of the controller or is there any other meaning behind this value? Next, the increase in standard deviation due to the cutting out of the good values in the middle and leaving only the spread values outside of it, is an inevitable consequence. What further shall this value illustrate?

Line 229-230 “The statistical results were used as the input for FL-BrDSM.”: How exactly were the statistical results used as input? Is it as a kind of look up table of historical data correlating different casting parameters or is it just as the finding of an optimal surface temperature region? Although mentioned on other occurrences in the text, this is not exactly explained in the paper.

First paragraph of section 6: Meniscus temperature and heat flux are only taken from history data (line 247)? What about the actual meniscus temperature and the actual heat flux in the mould? At the moment it sounds like the actual data were omitted, but I guess that was not the case, wasn’t it?

Figure 7: Please add a legend to the Figure. The red and the black curve are not described (just the secondary Ordinate as a hint is not enough). Further, the line types are not associated to the colour / location at the slab. In the plotted curves the colours are a little bit difficult to distinguish.

Lines 261 ff.: Now the terms “zones” and “loops” are introduced in combination with some numbers without an explanation or description of their location. This is quite confusing and it is hard to understand what is the statement of this paragraph.

Line 266: What is the maximum allowed cooling intensity? Where is it retrieved from?

Table 4: A doubling of parameters in the table (loops and casting speed) with different cooling intensities given at the top and at the bottom - without explanation of the differences in the settings. Still, the physical representation / location of “loop” is still nebulous.

Minor remarks:

Label of boundary condition / equation (7): Does “free surface” mean the solidified shell surface or the free surface at the meniscus? Although one has a guess, please name it unambiguous at this point.

Line 78: the symbol of the water mass flow rate is missing the dot above the m.

Line 84-85: Please check grammar of this sentence.

Line 96: the word “wall” might be to much here?

Table 1: Please use the same precision for all numbers! Otherwise it is irritating and hinder an easy overview and comparison of the values.

Author Response

We appreciate the reviewers’ careful reading of our manuscript and their comments. The revisions and additions in our revised manuscript are highlighted in "Track Changes" directly in the text.

All suggestions and recommendations have been considered and incorporated into the manuscript. We address the reviewers’ questions/comments point by point below:

For me, one main question arises while reading the text. The cracking and quality issue was related to the local surface temperature measurement just at one location: the bending point (Figure 5). There should be an explanation, why to make the expensive numerical simulations to get further temperature values, when already one measured value was sufficient to distinguish between good and bad heats. Otherwise: Shouldn’t it be also possible to set up a fuzzy controller with the measured temperature at the bending point as input data and then adjusting the cooling conditions as output data? Isn’t the shell thickness together with the surface temperature profile somehow already contained in the historical data which was used to design the fuzzy controller? It might be good to get some more information and benefits of taking the additional effort of making a whole 3D-simulation, e.g. in the introduction.

- Combination of 3D numerical model and fuzzy regulator not only find a cooling conditions to reach the optimal temperatures at unbending point, but also ensure smooth decreasing temperature profile through the caster, which increase the final steel quality. Another thing is that the model predictive control system needs the calculation of future temperatures. This is not possible without solidification model. Thus, solidification model is important part of optimal control algorithm.

Section 4 suddenly demands for several regulation points for the fuzzy controller where the temperature is kept within an optimal temperature range. The reasoning for that and the finding and setting of these ranges is promised for section 5. However there is no statement in section 5 about the finding these optimal temperature ranges along the casting strand. Section 5 is about material composition, temperature dependent material properties and statistical evaluation of optimal surface temperature, but only at one location: for the unbending area! So please give the promised information why and how these additional temperature ranges were obtained. Are there further data series like in Figure 7 for other locations at the strand?

- Section 5 has been extended for the information how to set temperature intervals for all control points along the caster, see lines 233-241.

Boundary condition (2): The pouring temperature is for my understanding the highest temperature of the steel in the mould, i.e. where it enters the mould (which is when the melt leaves the nozzle ports). On the way to the free surface, the melt has already cooled down a little bit. By this, the term pouring temperature seems to be not correct for the boundary condition of the free surface temperature.

- This is true and I agree with you. But the temperature difference is too small, so we set the pouring temperature on the meniscus (Dirichlet boundary condition). We also have the CFD model which calculates turbulent fluid flow in mold and this model also shows that temperature in the meniscus (free surface) is almost equal to the prescribed pouring temperature due to the liquid streams which go directly up from submerged entry nozzle. Finally 3D solidification model has been also validated by the pyrometer placed just below the mold and the match with the solidification model was more than sufficient. So yes there is a space to modify the model a little bit, but we can not expect a significant improvement.

No fuzzy sets of no other rules of the fuzzy controller are presented or described in this article. What is the purpose of mentioning just the one for the modification of cooling rate? I would suggest omitting the sentence in line 192-193 and the whole Table 2. For my feeling it is distracting the reader too much in trying to understand the rules, new variables and dependencies – especially as it is already described sufficiently in words in the text before and afterwards. Either the whole fuzzy controller is described in more detail or it is left out of scope in this paper.

- The sentence in line 192-193 and the Table 2 were omitted.

Figure 5: Although this Figure is correctly illustrating the historical data, it seems to be not the best way to show the desired optimal operation window. The historical evolution of the heats over time is of no specific interest, isn’t it? It is even raising other questions, like: Why is there a slight slope of temperature with increasing heat number, as it is also manifested by the given linear regression with a slope unequal to zero? What shall the linear regression illustrate? What does this trend mean for the future of this caster? Is it slightly running into bad operation condition? I would suggest to plot the data as a histogram with surface temperature ranges on the abscissa and the absolute or relative occurrence on the ordinate. Further it would be better to split the bad data into a part with higher surface temperature than the good one, and one part with lower surface temperature than the good one. In the end it could look like a set of three Gaussian curves: the good one with optimal surface temperatures in the middle surrounded by a bad one at the left and a bad one at the right. This leads to a further question in the text of line 228-230: What is the meaning of the higher average value of the bad heats and the higher standard deviation? I would interpret this value in that way that the historical heats were operated with a trend to higher temperatures compared to the optimal surface temperature. Does this have any evidence for the design of the controller or is there any other meaning behind this value? Next, the increase in standard deviation due to the cutting out of the good values in the middle and leaving only the spread values outside of it, is an inevitable consequence. What further shall this value illustrate?

- There is no special interest to evaluate heats over the time. The slight slope is probably only the coincidence. I checked the original data and over the time the average casting speed has raised a little bit. So this is probably the cause that the average surface temperature grew after the time. But this is not related to the article scope. I changed the Figure 5 to box plot, which illustrates difference between heats without and heats with defect. In the case of heats without crack, mean value and standard deviation were used for setting the optimal temperature intervals at unbending point.

Line 229-230 “The statistical results were used as the input for FL-BrDSM.”: How exactly were the statistical results used as input? Is it as a kind of look up table of historical data correlating different casting parameters or is it just as the finding of an optimal surface temperature region? Although mentioned on other occurrences in the text, this is not exactly explained in the paper.

- Optimal temperature intervals obtained by way in lines 234-242 are used as the input parameters for FL-BrDSM.

First paragraph of section 6: Meniscus temperature and heat flux are only taken from history data (line 247)? What about the actual meniscus temperature and the actual heat flux in the mould? At the moment it sounds like the actual data were omitted, but I guess that was not the case, wasn’t it?

- No they were not. The historical data are used in the case of off-line simulations. While in the case of on-line simulations the actual casting data are used from level 2 control system. Correction in lines 259-260.

Figure 7: Please add a legend to the Figure. The red and the black curve are not described (just the secondary Ordinate as a hint is not enough). Further, the line types are not associated to the colour / location at the slab. In the plotted curves the colours are a little bit difficult to distinguish.

- The legend was added in Figure 8

Lines 261 ff.: Now the terms “zones” and “loops” are introduced in combination with some numbers without an explanation or description of their location. This is quite confusing and it is hard to understand what is the statement of this paragraph.

- In the text the cooling zone is the same as cooling loop, which is the part of secondary cooling. Cooling zones were replaced by cooling loops to make it more clear for the reader. Figure 7 with cooling loops positions were added.

Line 266: What is the maximum allowed cooling intensity? Where is it retrieved from?

- physical limitations of pumps, line 283.

Table 4: A doubling of parameters in the table (loops and casting speed) with different cooling intensities given at the top and at the bottom - without explanation of the differences in the settings. Still, the physical representation / location of “loop” is still nebulous.

- It was only error caused by editing the table. Loops 7-12 were incorrectly listed as loops 1-6.

Label of boundary condition / equation (7): Does “free surface” mean the solidified shell surface or the free surface at the meniscus? Although one has a guess, please name it unambiguous at this point.

- the solidified shell free surface. Corrected.

Line 78: the symbol of the water mass flow rate is missing the dot above the m.

- corrected

Line 84-85: Please check grammar of this sentence.

-reformulated

Line 96: the word “wall” might be to much here?

-reformulated, line 97.

Table 1: Please use the same precision for all numbers! Otherwise it is irritating and hinder an easy overview and comparison of the values.

- corrected

Reviewer 2 Report

Affiliation:

Since both authors belong to the same institution, please delete “1” after authors’ name.

Flick et al. [1]… should be: Flick and  Stoiber [1]…

Mauder et al. [6]… should be: Mauder and Novotny [6]…

Mosayebidorcheh et al. [9]… should be: Mosayebidorcheh and Bandpy [9]…

Miettinen et al. [11]. should be: Miettinen [11].

Fluid flow of the liquid steel can be calculated by the CFD techniques.

Please modify as (if necessary): Fluid flow of the liquid steel can be calculated by the computational fluid dynamics (CFD) techniques.

3 Numerical formulation… should be: 3. Numerical formulation…

Figure 3 Calculaition of… should be: Calculation of…

Table 3 0.16-018 should be: 0.16-0.18

Figure 6a likvidus should be: liquidus

Table 4 Please check and modify the loop sequences (5th line):

loop 1 should be loop 7,

loop 2 should be loop 8, …

loop 6 should be loop 12.

Author Response

We appreciate the reviewers’ careful reading of our manuscript and their comments. The revisions and additions in our revised manuscript are highlighted in "Track Changes" directly in the text.

All suggestions and recommendations have been considered and incorporated into the manuscript.

Round  2

Reviewer 1 Report

Thanks for the explanations and comments to the questions.

Just again one remark to the new Figure 5:
The dispensable time trend is eliminated now. However, I still recommend to split the “bad” data part into two. In the chosen style, that would mean one box for the defects with higher surface temperature than the good ones and one box for the defects with lower surface temperatures than the good ones. Now it looks like it is also possible to get surface defects with temperatures in the range of the optimal temperature, because the box of the bad heats is also stretching over the good temperature range!

Beside of that, the text needs only some additional proof reading, e.g.:

·         precision of computational times is still very different in Table 1

·         line 195: empty table

·         line 233: missing letter in the word first

Author Response

Thanks for the additional remarks and careful reading.

Just again one remark to the new Figure 5:
The dispensable time trend is eliminated now. However, I still recommend to split the “bad” data part into two. In the chosen style, that would mean one box for the defects with higher surface temperature than the good ones and one box for the defects with lower surface temperatures than the good ones. Now it looks like it is also possible to get surface defects with temperatures in the range of the optimal temperature, because the box of the bad heats is also stretching over the good temperature range!

-good point, the figure 5 have been replace by new graph, with separated heats with defects and Gauss fitting of heats without defects. I hope it will be more clear this time.

Beside of that, the text needs only some additional proof reading, e.g.:

·         precision of computational times is still very different in Table 1

-corrected

·         line 195: empty table

-corrected

·         line 233: missing letter in the word first

-corrected