Case-based reasoning method based on mechanistic model correction for predicting endpoint sulphur content of molten iron in KR desulphurization

Abstract

In order to improve the control on sulphur content at the endpoint of Kanbara Reactor (KR) desulphurization process, the case-based reasoning (CBR) method based on mechanistic model correction is used to predict the endpoint sulphur content of molten iron. First, the KR desulphurization process is analysed to determine its kinetic mechanistic model, and partial derivatives are obtained for different attributes. Then, according to the analysis ofthe attributes, the corrected model is determined by the method of selecting the attributes, determining the reasonable weights and fitting the calculation results. Finally, the CBR method, the Back Propagation Neural Network (BPNN) and the corrected model are used to predict the endpoint sulphur content at KR desulphurization. The experiment results indicate that the prediction accuracy of corrected model is significantly higher than that of BPNN and mechanistic model.

Introduction

As the sulphur is generally harmful to most steel grades in the steel materials, it is necessary to strictly control the sulphur content in steel so as to ensure the mechanical and process properties of steel. At present, the sulphur is mainly removed by molten iron pretreatment for most steel grades, and Ladle Furnace (LF) refining is required by only a few of steel grades for deep desulphurization. In the desulphurization process of molten iron pretreatment, Kanbara Reactor (KR) stirring method and injecting magnesium method are the most widely used. With the increased power of the stirring equipment and the improvement of the process, the KR stirring method has become the most mainstream method for the desulphurization of molten iron in China and Japan.

The purpose of the KR stirring method is to remove the sulphur element in the molten iron and to supply molten iron that has qualified sulphur content for the converter steelmaking, so it is very important to effectively improve the control on the endpoint sulphur content in molten iron in KR desulphurization. However, in the actual production, the endpoint sulphur content in molten iron in the KR desulphurization process is obtained by sampling and testing, which not only prolongs the process time, but also increases the sampling and testing cost. Therefore, more and more researches attempt to solve the control problem of the endpoint sulphur content by means of prediction.

The case-based reasoning (CBR) method based on mechanistic model correction is proposed to control the endpoint sulphur content in KR desulphurization. First, the mechanistic model of KR desulphurization process is established. Then, the influence degree of each attribute on the objective function is analysed by obtaining the partial derivative for the attribute in the mechanistic model, and the corrected model is determined by selecting the attribute, determining the reasonable weight and fitting the calculation results. Finally, the prediction accuracy of the corrected model is verified using actual production data and shows good result. This model can provide a reference for the actual production to improve the control accuracy of the endpoint sulphur content.

Section ‘literature review’ reviews the related literatures. CBR method based on Mechanistic Model correction is proposed in Section ‘CBR method based on mechanistic model correction’. Experiment and results are obtained in Section ‘Experiment and results’, and conclusion is made in Section ‘Conclusions’.

Literature review

In the study of steel production, the models for sulphur content prediction at the endpoint of the smelting process include mechanistic model and data model.

As for mechanistic model, its research on desulphurization reaction mainly focuses on process optimization. Shougang research institute of technology established a kinetic model of the 60% Mg and 40% CaO injection desulphurization. By analysing the model, the desulphurization process of high sulphur molten iron had three stages, incubation stage, rapid desulphurization stage and slow desulphurization stage [1]. Wuhan University of Science and Technology established a mathematical model about the variation of sulphur content in liquid steel during a 300 t RH refining process based on the consideration of thermodynamics, kinetics of desulphurization and conditions of practical production. The effects of initial sulphur content in the liquid steel, powder injection rate, particle size of powder, flow rate of RH driving gas and initial temperature of the bath on the temperature drop were taken into account. Sulphur content in the steel bath during desulphurization process and the final sulphur content in the liquid steel were analysed. The model can be used to predict desulphurization process [2]. The accurate parameter setting and the data collection of all influencing factors are required in the application of the mechanistic model, which greatly limits the application of this model in the actual production.

As for the data model, there are many studies on the endpoint compositions and temperature prediction of the monomer process. To improve the control precision of endpoint because of the constraints of economy and technology, Yue proposed a method to solve the problem that the small and middle converters unable to introduce the sublance detection technology. The method combined the pedigree cluster and neural network. Simulation results show that the multi-neural network model has better prediction results [3]. By means of combining the methods of multivariate regression analysis and multi-level recursive completely, the multi-level recursive regression model, which was established based on large amount of production data, was used to complete the prediction of endpoint phosphorus content during BOF steelmaking process [4]. A mathematical model has been developed to predict nitrogen content in steel melt with respect to blowing time for making different grades of stainless steel using AOD converter. This mathematical model will be effective and beneficial because nitrogen prediction by this model corresponds well with actual measured values collected from steel plant [5]. An anti-jamming endpoint prediction model is proposed to predict the endpoint parameters of molten steel. The model is constructed on the parameters of extreme learning machine adaptively adjusted by the evolutionary membrane algorithm with the global optimization ability. The model has good prediction accuracy and robustness in the data with noise [6]. Ahmad proposes a procedure to predict the probability distribution of molten steel temperature in a tundish by integrating a grey-box model and a bootstrap filter to cope with uncertainties of the process. The derived probability distribution is used not only to predict molten steel temperature in a tundish but also to evaluate the reliability of prediction [7]. An improved PSO algorithm of reducing inertia weight and adding the constriction factor combined with BP neural network is presented for endpoint prediction in BOF to accurately predict the endpoint temperature and the carbon content [8]. The multi-objective optimization technique was adopted for addressing important issue of achieving low phosphorus content along with high-end blow temperature in basic oxygen steel making process. The meta-models have been created using evolutionary neural network algorithm through training of a data set containing 120 steel plant data entries concerning different input as well as output variables [9]. A discrete wavelet transfer-based backpropagation neural network (BPNN) model was built to predict the carbon efficiency of an iron ore sintering process. Actual run data were collected to verify the validity of the predictive model [10]. However, there is no research on the prediction of endpoint sulphur content in the KR process.

Extensive attention has been given to the application of CBR methods to solve related problems in the research field of data model. The CBR is a machine learning method in which the similarity among the influencing factors is used to solve the problem. A better solution can always be obtained for cases that have too complicated/weak correlation between influencing factors, or cases whose influencing factors are seriously insufficient. An integrated CBR model composed of rough search and delicate search, is proposed to predict the endpoint temperature of molten steel in AOD [11]. Combining with the ultra-fast cooling process, a developed CBR model was proposed, which mainly improves the case representation, similarity relation and retrieval module. Retrieval process was simplified and retrieval efficiency is improved apparently by the windmill retrieval algorithm. The proposed CBR model was used for predicting the case of cooling strategy and its capability is superior to the traditional process model [12]. A combined method of CBR and Bayesian belief network (BBN) has been proposed. The evaluation of the reliability of cases is conducted by applying BBN for the assessment which the CBR method lacks in [13]. The establishment based on CBR and radial basis function neural network of coke oven flue temperature intelligent prediction model, realize the real-time prediction of the temperature, and help to realize the coke oven production process of intelligent optimization control [14]. A two-step CBR method using genetic algorithm to find the optimal attributes subset based on the evaluation method of Correlation-based Feature Selection was proposed for predicting the endpoint phosphorus content in BOF efficiently [15]. To be simulate dynamics of cold tandem rolling processes, a novel hybrid intelligent dynamic modelling approach is proposed based on the combination of a linearized state space model derived from various mechanism equations, a CBR algorithm for multi-state space models selection, a genetic algorithm for optimization of case attributes, an adaptive fractal filtering algorithm for the identification of state space model parameters, a neural network-based simulation error compensation model for the strip exit velocity [16]. CBR based on two-step retrieval approach and the correlation-based feature weighting method was proposed for predicting end temperature of molten steel in LF [17].

At present, the research of CBR mainly focuses on the case classification processing of case store and the similarity algorithm improvement, but the necessary mechanistic analysis for the researched problems is absent. Better prediction accuracy can be obtained using the mechanistic model to correct the similarity of influencing factors in the CBR method. The mechanistic model is established to characterize the correlation between the influencing factors and the target factors. If the mechanistic model characterizing the correlation between the influencing factors and the target factors is established to correct the solution provided in the CBR method for the similarity among the influencing factors, a better prediction accuracy will be obtained. The research in this paper is based on this idea.

CBR method based on the mechanistic model correction

Arithmetic process of CBR

The CBR is a method to obtain solutions using the similarity between current problems and existing cases in the case store. The standard CBR model often consists of four processes: case representation, case retrieval, case reuse and case retain. Among them, case retrieval is the core of CBR.

Before the case retrieval, it is generally necessary to pre-process the case store and the current problem. The 0–1 normalization is used for data preprocess in this paper.

A typical retrieval method is to perform retrieval with the similarity between attributes. The grey distance similarity calculation method is used in this paper. Grey distance is an analysis method based on grey relational space theory, which integrates the characteristics of distance space and topological space. Its basic idea is to judge the degree of correlation between factors according to the similarity of the magnitude changes between the factor curves. Because it does not need the typical distribution law of data, and can combine qualitative analysis with quantitative analysis, it has been widely used in different fields.

Given that the problem case is , the existing case store is , m is the number of existing cases, , is the value on j-th attribute of and respectively, , n is the number of attributes in the case. The weight of j-th influencing factor is , in which .

Then the formula for calculating the similarity of the grey distance between the problem case and the case in case store is: (1)

In formula (1), is the identification coefficient, generally .

The case results obtained by the similarity calculation are reused to solve the problem case. The cases can be sorted by similarity which is calculated using the similarity calculation method. If there are k cases with the maximum similarities, the result of the problem case is computed as follows: (2)

In which G_i is the similarity between the new problem and the i-th case, and T_i is the result in the i-th stored case. The value of m will be 4 in the paper.

The CBR method is based on the similarity between the case attributes to obtain the result of the problem case, but the consideration of the relationship between the attribute and the result is absent. As far as the most practical problems are concerned, this correlation cannot be ignored. Therefore, a method is proposed in this paper to correct CBR calculation process using the mechanistic model.

The correction on the CBR method using the mechanistic model

The CBR is to realize case reuse to solve new problems by analysing and calculating the attribute similarity between existing case and new problem. Only the influence degree of different attributes on the target in the attribute weight of the similarity algorithm is considered in this method, but the inspection on the degree of necessity of attributes is absent. At the same time, it is impossible to compare and analyse the coupling relationship between attributes. Therefore, it is necessary to study the degree of necessity of related attributes and the coupling relationship between different attributes by means of the mechanistic model of the studied problem, and then correct the CBR method to obtain more accurate results.

The objective function is determined according to the specific problem in the study of the mechanistic model, where, the objective function is a function with related attributes, is the -th attribute. Meanwhile, the set is constructed, in which , and each attribute is taken at the average value of such attribute in the case store, then represents influence degree of attribute on the objective function in the value range centred on the average value in this problem.

The correction by mechanistic model on the CBR method includes the following three aspects:

Attribute selection: By comparing the size of each attribute , when influence degree of an attribute is too small, it can be deemed that such attribute has no influence on objective function, thus removing it from the CBR method. That is: when , the attribute is deemed to have no influence on objective function, and it is removed from the CBR method, is a threshold set according to a specific problem.

Determining the weight: the weight determination method based on the mechanistic model is to determine the corresponding weight according to the size of each attribute . The larger , the higher weight of such attribute, and total weight is 1. The specific value-taking process is: among the attributes whose values have not been taken, the attribute with the largest takes half of the remaining weight, by parity of reasoning, until there is only one attribute left, and such attribute takes the remaining weight. That is: among all the attributes, the attribute with the largest takes the weight of 0.5, the second largest attribute takes the weight of 0.25, and the third largest attribute takes the weight of 0.125, by parity of reasoning. The attributes with the smallest and the second smallest one take the same weight.

Fitting of calculation results: for the new problem, the CBR method and the mechanistic model are used for calculation respectively, and then the result of the two methods are fitted. The related fitting parameters are determined by the method of case store verification, then more accurate results are obtained. That is: the correction model is constructed as , in which, is the result of the CBR method, and is the result of the mechanistic model.

After the correction by the mechanistic model, the specific process of the CBR method is shown in Figure 1:

Figure 1.

Process of CBR model corrected by mechanistic model.

Experiment and results

Experiment data

Production performance data collected from a steel plant in the process of KR desulphurization production were used as the data source for CBR calculation and verification. The KR mechanical stirring method is a method in which the refractory stirrer is immersed into the molten iron pool by a certain depth, and then the desulphurizing agent is uniformly dispersed into the molten iron by the vortex arising from stirring, so that the solid and liquid are fully contacted, and high-efficiency desulphurization is achieved. The lime-based desulphurizer is used in KR desulphurization in this plant (CaO content is 80%, SiO₂ content is 3%, fluorite content is 8%, other ingredients content is 9%), and particles with diameter of 0.3–1.2 mm account for 80%. The operation flow of the KR desulphurization process is: entry → first sampling and temperature measurement → first slag removal → desulphurizer is added and stirred for desulphurization → stop stirring → second slag removal → second sampling and temperature measurement → exit. In this paper, 5701 sets of production data for 3 months of this plant are selected to conduct experiments. Four thousand sets of data are randomly selected as case store data, and the remaining 1701 sets of data are used as test data.

After the analysis on the measurement data in the production process, the data distribution of the influencing factors on the endpoint sulphur content in KR desulphurization are obtained, as shown in Table 1:

Table 1.

Data distribution of influencing factors on endpoint sulphur content at KR desulphurization.

Influencing factors	Data range	Average	Standard deviation
Entry [S] content/10⁻⁵	10–119	37.04	13.48
Entry temperature°C	1247–1461	1380.80	37.71
Weight of molten iron/ t	188.2–223.8	212.96	6.88
Consumption of desulphurizer/kg	659–3580	1439.44	331.90
Stirring time/min	8–29	14.86	2.03

Note: The [S] content in molten iron is measured as mass percentage.

Based on this data, the sulphur content at KR endpoint is predicted.

The predictive results are obtained based on back-propagation (BP) neural network. This neural network is implemented in Matlab. It is a three-layer network with input, hidden, and output layer. The input layer consists of 5 nodes representing the 5 attributes. The hidden layer also has 5 nodes with transig as transfer function. The output layer is composed of just one node representing the predicted the sulphur content with purelin as transfer function. The max epoch is 1500. The hit rate of predicting is illustrated in Figure 2(a).

Figure 2.

Hit rate of endpoint sulphur content prediction in KR process ((a) BPNN; (b) the ordinary CBR).

According to the CBR method described in Section ‘Arithmetic process of CBR’. The final predictive results were obtained based on ordinary CBR that used GRD with average weight and on a case base that contained 4000 sets of data. The distribution of its hit rate is illustrated in Figure 2(b).

The prediction results of both BPNN and ordinary CBR methods are summarized and compared in details, as shown in Table 2.

Table 2.

Hit rates of endpoint sulphur content prediction in KR processwith BPNN and ordinary CBR.

Error range/10⁻⁵	[−1,1]	[−2,2]	[−3,3]	[−4,4]	[−5,5]	[−6,6]	[−7,7]	[−8,8]
BPNN	20.34%	42.45%	62.20%	79.95%	91.24%	95.30%	96.18%	96.53%
Ordinary CBR	30.45%	47.62%	61.20%	73.72%	82.13%	89.36%	93.24%	95.59%

It can be seen from the comparison between BPNN and ordinary CBR that, BPNN, as a method of identifying data correlation between attributes and targets, has high prediction accuracy when the prediction error range is large, such as the prediction results within the error range of [−4, 4], [ −5,5] and [−6,6]. However, CBR, as a method of identifying attribute similarity between cases, has a high prediction accuracy when the prediction error range is small, such as the prediction results within the error range of [−1, 1] and [−2, 2]. This indicates that, for the prediction of endpoint sulphur content in KR desulphurization, only when both the relationship between the attribute and the target and the similarity of the attributes between the cases have been considered, overall better prediction result can be obtained.

Kinetic mechanistic model of KR desulphurization

In order to obtain a better prediction result, it is necessary to analyse the relationship between the endpoint sulphur content and its influencing factors by means of mechanistic analysis.

The KR stirring desulphurization reaction equation and the corresponding standard free energy are as follows: (3)

According to the thermodynamic calculation, the endpoint sulphur content at different molten iron temperatures at the point of desulphurization reaction equilibrium is shown in Table 3:

Table 3.

Relationship between molten iron temperature and endpoint sulphur content at the point of desulphurization reaction equilibrium.

T/K	1673	1623	1573
Endpoint [S] content/ 10⁻⁷	2.22	1.18	0.6

In the actual production, the average endpoint sulphur content in KR desulphurization is 6.44×10⁻⁵, which indicates that the reaction is far from equilibrium, so the endpoint sulphur content depends on the kinetic conditions of the reaction process.

Complicated mass transfer process and interfacial reaction are involved in the KR desulphurization process. According to the slag ion structure theory, the control element of the desulphurization reaction is the diffusion process of sulphur from molten iron to slag. The desulphurization rate is: (4) where is the contact area of slag iron, m²; is the volume of molten iron, m³; is the density of molten iron, kg/m³; is density of lime particles, kg/m³; is the mass transfer coefficient; is the distribution ratio of sulphur in slag-iron; is the initial sulphur content.

Considering the lime particles as spherical solid particles, the mass transfer coefficient is , in which, is the average diameter of lime particles, is the diffusion coefficient of sulphur in the molten iron, T is the temperature of molten iron measured in K Sherwood number , Reynolds number , is the flow velocity of molten iron, is the kinematic viscosity of molten iron; Schmidt number .

Arrange the above formula, bring in the corresponding parameters: , , , , and integrate the time parameters, the following is obtained: (5) where is the sulphur content in molten iron after time t.

The slagging agent composition and the slagging process of the KR desulphurization process in this plant are relatively stable, so can be deemed as a constant. The life and erosion of stirring head is fully considered in stirring head rotation speed control during the desulphurization process, which can provide a stable stirring light intensity, so can be deemed as a constant. is linear with the quantity of molten iron. is related to the consumption of desulphurizer and the particle size of the desulphurizer. The particle size of desulphurizer is stable, so is considered to be linear with desulphurization consumption. Rearrange the formula (5) to get: (6) where coefficient

is the consumption of desulphurizer, is the quantity of molten iron.

By fitting the actual production data, we obtain , bring it into formula (6) to obtain the mechanistic model of KR desulphurization.

Prediction result of CBR based on the mechanistic model correction

Based on the KR desulphurization kinetic model, as shown in formula (6), the partial derivatives of , , , and are obtained, and the average value of each parameter statistics in Table 1 is brought in to evaluate the influence degree of such parameter on endpoint sulphur content. The results are as follows:

According to the method in Section ‘The correction on CBR method using mechanistic model’ of this paper, the CBR method is corrected based on the above results:

Attribute selection:

According to the KR desulphurization model, if the threshold is set , the influence of temperature T and desulphurizer consumption on the endpoint sulphur content is negligible and can be removed from the attribute parameters of CBR.

The influence of the molten iron temperature T on the endpoint sulphur content is negligible, because the temperature change of the molten iron has little influence on the kinetic conditions of the desulphurization reaction during the KR desulphurization process. The desulphurizer consumption has negligible influence on the endpoint sulphur content, because the desulphurization reaction is far from reaching equilibrium, and according to the calculation through formula (3), the utilization rate of the desulphurizer is only 20%.

Through the attribute selection, the five influencing factors can be reduced to three influencing factors, namely the entry sulphur content , molten iron mass and stirring time .

Determine the weight

According to the results of partial derivatives for each factor, the weights of the relevant factors are calculated for the five factors and three factors scenarios respectively, as shown in Table 4:

Table 4.

Relevant factors weight for five and three factors scenarios.

Influencing factors	Entry [S]content	Entry temperature	Molten iron mass	Desulphurizer consumption	Stirring time
5 factors	0.25	0.0625	0.125	0.0625	0.5
3 factors	0.25	–	0.25	–	0.5

The CBR method is used to predict the endpoint sulphur content in KR desulphurization for the mechanistic model weight of five factors, the average weight of three factors and the mechanistic model weight of three factors, and the prediction results are as shown in Figure 3 (a–c). The mechanistic model is used to predict the endpoint sulphur content in KR desulphurization for the five factors and three factors, respectively. When the endpoint sulphur content is predicted by the three-factor mechanistic model, the other parameters in formula (6) are taken at the average value, and the prediction results are as shown in Figure 3(d,e).

Figure 3.

Hit rate of predicting endpoint sulphur content in KR process ((a) CBR.-5 factor-mechanistic model weight; (b) CBR.-3 factor-average weight; (c) CBR.-3 factor-mechanistic model weight; (d) mechanistic model-5 factor; (e) mechanistic model-3 factor).

Detailed statistics of the above prediction results are summarized in Table 5.

Table 5.

Hit rates of predicting endpoint sulphur content in KR process under five scenarios.

Error range/10⁻⁵	[−1,1]	[−2,2]	[−3,3]	[−4,4]	[−5,5]	[−6,6]	[−7,7]	[−8,8]
CBR.-5 factor-mechanistic model weight	30.04%	46.85%	62.26%	73.78%	82.60%	89.12%	93.18%	95.24%
CBR.-3 factor-average weight	30.81%	47.62%	62.32%	74.37%	84.36%	90.53%	93.71%	95.41%
CBR.-3 factor-mechanistic model weight	31.16%	48.56%	63.43%	75.66%	84.83%	90.48%	93.65%	95.36%
mechanistic model-5 factor	21.87%	41.80%	60.91%	75.25%	85.48%	91.18%	94.42%	95.88%
mechanistic model-3 factor	23.46%	45.97%	65.08%	77.43%	86.89%	93.30%	96.12%	97.47%

It can be seen from Table 5 that, the prediction results of the CBR.−3 factor-mechanistic model weight are overall better than that of other CBR. At the same time, the prediction accuracy of the mechanistic model-3 factors is also higher than that of the mechanistic model-5 factors comprehensively. This indicates that the unnecessary influencing factors can be removed from the attribute selection and attribute weight determination based on the mechanistic model, thus avoiding the influence of fluctuation of this factor on prediction accuracy. At the same time, the relative importance of each attribute can be determined, thus effectively improving the accuracy of CBR method.

Fitting of the calculation results

In order to further improve the prediction accuracy, a corrected model of the prediction results is constructed , and the following are obtained by data fitting of case store: , , , so the corrected model is: (7)

The prediction results of the corrected model (7) on the endpoint sulphur content are as shown in Figure 4:

Figure 4.

Hit rate of predicting endpoint sulphur content in KR process using the corrected model.

The detailed statistics of the prediction results of the corrected model are summarized, and the prediction results of CBR.-3 factor-mechanistic model weight, the mechanistic model-3 factor, ordinary CBR and BPNN are compared, as shown in Table 6:

Table 6.

Comparison of prediction hit rates of endpoint sulphur content in KR process using the corrected model and other methods.

Error range/10⁻⁵	[−1,1]	[−2,2]	[−3,3]	[−4,4]	[−5,5]	[−6,6]	[−7,7]	[−8,8]
Corrected model	24.57%	45.80%	68.61%	86.77%	95.06%	96.88%	97.24%	97.59%
CBR.-3 factor-mechanistic model weight	31.16%	48.56%	63.43%	75.66%	84.83%	90.48%	93.65%	95.36%
Mechanistic model-3 factor	23.46%	45.97%	65.08%	77.43%	86.89%	93.30%	96.12%	97.47%
Ordinary CBR	30.45%	47.62%	61.20%	73.72%	82.13%	89.36%	93.24%	95.59%
BPNN	20.34%	42.45%	62.20%	79.95%	91.24%	95.30%	96.18%	96.53%

It can be seen from the above test that, compared with other CBR methods, although the prediction hit rate of corrected model is lowered in smaller error range, its prediction hit rates in other error ranges are greatly improved. For example, in the error range from −3×10⁻⁵ to 3×10⁻⁵, the prediction hit rate of the corrected model has improved 5.18% than CBR.-3 factor-mechanistic model weight, and 7.41% higher than the ordinary CBR method. In the error range from −4×10⁻⁵ to 4×10⁻⁵, the corrected model has improved 11.11% than CBR.-3 factor-mechanistic model weight, and 13.05% higher than the ordinary case reasoning method. In the error range from −5×10⁻⁵ to 5×10⁻⁵, the corrected model has improved 10.23% than CBR.-3 factor-mechanistic model weight, and 12.93% higher than the ordinary case reasoning method. Considering that the actual measured accuracy of sulphur content of molten iron in KR desulphurization process is 1×10⁻⁵, and the reduction of prediction accuracy in error range from −1×10⁻⁵ to 1×10⁻⁵ and from −2×10⁻⁵ to 2×10⁻⁵ is acceptable.

As compared with the mechanistic model, although basically there is no change in the prediction hit rate within small error range of the corrected model, its hit rate in other error ranges is significantly improved. For example, in the error range from −3×10⁻⁵ to 3×10⁻⁵, the corrected model has improved 3.53% than mechanistic model-3 factors. In the error range from −4×10⁻⁵ to 4×10⁻⁵, the corrected model has improved 9.34% than mechanistic model-3 factors. In the error range from −5×10⁻⁵ to 5×10⁻⁵, the corrected model has improved 8.17% than mechanistic model -3 factors

As compared with BPNN, the prediction hit rate of corrected model in all error ranges has improved. For example, in the error range from −1×10⁻⁵ to 1×10⁻⁵, the corrected model has improved 4.23% than BPNN. In the error range from −3×10⁻⁵ to 3×10⁻⁵, the corrected model has improved 6.41% than BPNN. In the error range from −5×10⁻⁵ to 5×10⁻⁵, the corrected model has improved 3.82% than BPNN.

Conclusions

In this paper, a CBR method based on mechanistic model correction is proposed to predict the endpoint sulphur content of molten iron in the KR desulphurization process.

Based on the analysis of the kinetic mechanism of KR desulphurization process, and using the actual data to fit the relevant parameters, the kinetic mechanistic model of KR desulphurization process is established, and the partial derivative of each influencing factor is obtained to characterize its influence degree on the endpoint sulphur content.

Based on the kinetic mechanistic model and the analysis of the necessity of influencing factors, the CBR is corrected by the method of attribute selection, determining the reasonable attribute weight and the fitting of the calculation result, and finally, the corrected model of KR desulphurization is determined.

The CBR method (for the three factors, five factors, average weighting and mechanistic model weight, respectively), the mechanistic model (for the three factors and five factors respectively), BPNN and the corrected model are separately used to predict the endpoint sulphur content in KR desulphurization. The results show that the prediction accuracy of the corrected model is significantly higher than that of the BPNN and the mechanistic model. At the same time, the prediction accuracy of the corrected model is significantly improved as compared with the prediction results of all CBR methods in respect of the error ranges of the actual production process. The result is can be reference in instructing the production process.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the authors.

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