2.2.1. Material Flows Analysis Model

Material flows analysis model is established on the basis of the material balance in BFIMP (as shown in Figure 2).

$$\sum\_{j=1}^{m} P\_{x,i} + P\_a + P\_{f, \emptyset} = P\_{\emptyset} + P\_{\text{hot}} + P\_{\text{slag}} + P\_{\text{Lo1}}.\tag{1}$$

**Figure 2.** Material flows analysis model

In which,

*Px*,*i*: The amount of various materials, t/t;

*Pa* and *Pf g*: The amount of blast and fuel injection into the furnace, respectively, t/t;

*Pg*, *Phot* and *Pslag*: The mount of gas, hot metal and slag, respectively, t/t, and *Pg* = *Ppg* + *PLo*2;

*Ppg*: The mount of gas after purification, t/t;

*PLo*<sup>1</sup> and *PLo*2: The loss amount of various systems, t/t.

#### 2.2.2. Energy Flows Analysis Model

The energy flows analysis model is established based on the thermal equilibrium in BFIMP. In this paper, the BF body and BS, which are the major energy consumption regions, were only in consideration (as shown in Figure 3).

**Figure 3.** Energy flows analysis model.

Energy flows analysis model of BS is:

$$\sum\_{j=1}^{n} Q\_{s,j} = \sum\_{k=1}^{q} Q\_{r,k} + Q\_{Lo1}.\tag{2}$$

Energy flows analysis model of BF Body is:

$$\sum\_{l=1}^{s} Q\_{\mathbb{S},l} + Q\_{r,1} = \sum\_{r=1}^{t} Q\_{l,r} + Q\_{l,0}.\tag{3}$$

In which,

*Qs*,*<sup>j</sup>* and *Qr*,*k*: The input heat items and the output heat items of the BS, kgce/t (kgce: Kilogram coal equivalent);

*Qg*,*<sup>l</sup>* and *Qh*,*r*: The input heat items and the output heat items of the BF Body, kgce/t;

*QLo*<sup>1</sup> and *QLo*2: The loss heat items of the BS and the BF Body, kgce/t.

#### 2.2.3. The Key Operation Parameters

Several factors such as sintering grade and the quality of coke could be measured by using the proposed model. Additionally, operation parameters, which directly reflect the coupling quality between material flows and energy flows, have an important impact on the energy consumption in BFIMP, too. Therefore, these operation parameters should also be sought out, such as the blast temperature and blast pressure.

Generally, these influence factors on energy consumption should be divided into three categories: Material flows factors (the name of the material variable starts with '*P*', as shown in Figure 2); energy flows factors (the name of the energy variable starts with '*Q*', as shown in Figure 3) and operation parameters (the name of the operation variable starts with '*C*', such as blast volume and blast temperature).

#### *2.3. All-FactorsAnalysis on Energy Consumption in BFIMP*

#### 2.3.1. Data Pre-Processing

The data pre-treatment mainly included as follows:

(1) Some data were recorded manually. Inevitably, there would be some mistakes in the recording process, such as unrecorded, omitted and incorrectly annotated. Therefore, these data should be eliminated or modified.


#### 2.3.2. PCA

A simple correlation analysis (SCA) is a common method of statistical analysis between two random variables. However, all variables may affect each other in general when the number of variables is more than two items. Unfortunately, this mutual influence is not taken into account in SCA. Consequently, SCA was not applicable to the all-factors analysis on energy consumption in this paper, whereas there is an effective way to avoid this problem: PCA [32].This method can achieve the actual relevance of any two variables while eliminating the influence of other variables. Therefore, partial correlation coefficient (PCC) between energy consumption and other parameters can be obtained through the definition of partial correlation algorithm.

#### 2.3.3. MLR Model

First of all, relevant variables should be redefined. *Px* represents the *x*th variable of material flows, the total number of material flows variables is *M* after all-factors PCA processing. *Qy* represents the *y*th variable of energy flows and the total number of energy flows variables is *N* after all-factors PCA processing. *Cz* represents the *z*th variable of operation parameters and the total number of operation parameters variables is *R* after all-factors PCA processing. In addition, the number of samples is *S*, and *i* = 1, 2, ··· , *S*. Therefore, there are the following two regression models. A simple example of the PCC between *e* and *P*<sup>1</sup> is given to describe calculation process.

$$\varepsilon\_{i}\varepsilon\_{i} = \varepsilon\_{0} + \varepsilon\_{P,2}P\_{i,2} + \dots + \varepsilon\_{P,M}P\_{i,M} + \varepsilon\_{Q,1}Q\_{i,1} + \dots + \varepsilon\_{Q,N}Q\_{i,N} + \varepsilon\_{C,1}C\_{i,1} + \dots + \varepsilon\_{C,R}C\_{i,R} + \varepsilon'\_{i}.\tag{4}$$

*Pi*,1 = *d*<sup>0</sup> + *dP*,2·*Pi*,2 + ··· + *dP*,*M*·*Pi*,*<sup>M</sup>* + *dQ*,1·*Qi*,1 + ··· + *dQ*,*N*·*Qi*,*<sup>N</sup>* + *dC*,1·*Ci*,1 + ··· + *dC*,*R*·*Ci*,*<sup>R</sup>* + ε *<sup>i</sup>* . (5)

In which,

*ei*: Energy consumption of the *i*th group sample, kgce/t;


*cP*,2, ··· , *cP*,*M*, *cQ*,1, ··· , *cQ*,*N*, *cC*,1, ··· , *cC*,*R*, *dP*,2, ··· , *dP*,*M*, *dQ*,1, ··· , *dQ*,*N*, *dC*,1, ··· and *dC*,*R*: Regression coefficient;

ε *i* and ε *<sup>i</sup>* : Error term.

Then, the two fitting models can be achieved by the least square method. Meanwhile, the residuals are as follows between them:

$$u\_i = \varepsilon\_i - \left(\varepsilon\_0 + \varepsilon\_{P,2}^\* P\_{i,2} + \dots + \varepsilon\_{P,M}^\* P\_{i,M} + \varepsilon\_{Q,1}^\* Q\_{i,1} + \dots + \varepsilon\_{Q,N}^\* Q\_{i,N} + \varepsilon\_{\hat{\mathbb{C}},1}^\* \mathbb{C}\_{i,1} + \dots + \varepsilon\_{\hat{\mathbb{C}},K}^\* \mathbb{C}\_{i,K}\right). \tag{6}$$

$$v\_i = P\_{i,1} - \left(d\_0 + d\_{P,2}^\* P\_{i,2} + \dots + d\_{P,M}^\* P\_{i,M} + d\_{Q,1}^\* Q\_{i,1} + \dots + d\_{Q,N}^\* Q\_{i,N} + d\_{\hat{\mathbb{C}},1}^\* \mathbb{C}\_{i,1} + \dots + d\_{\hat{\mathbb{C}},K}^\* \mathbb{C}\_{i,K}\right). \tag{7}$$

In which,

*ui*: The residual of the *i*th group sample between *ei* and its fitting model;

*vi*: The residual of the *i*th group sample between *Pi*,1 and its fitting model;

Then, simple correlation coefficient between *u* vector (*u* = (*u*1, *u*2, ··· , *uS*) ) and *v* vector (*v* = (*v*1, *v*2, ··· , *vS*) ) can be obtained by calculation. This coefficient, which is denoted *re*,*P*<sup>1</sup> (as shown in Equation (8)), is called the PCC between *e* and *P*1. The calculation process of the other PCC is so as well.

$$r\_{\mathfrak{c},P1} = \frac{Cov(\mathfrak{u}, \mathfrak{v})}{\sqrt{Var[\mathfrak{u}] \cdot Var[\mathfrak{v}]}} \,. \tag{8}$$

In which,

*Cov*(*u*, *v*): The covariance between the *u* vector and *v* vector;

*Var*[*u*]: The variance of the *u* vector;

*Var*[*v*]: The variance of the *v* vector.

In this paper, the PCC between *e* and influence factors can be obtained by the SPSS software package due to its powerful statistical calculations function. Meanwhile, the significance level (*p* value) of them can also be achieved by SPSS software. There is a higher significance level between *e* and an influence factor if their *p* value is less than 0.05, and vice versa. Consequently, all influence factors with a high significance level can be achieved through related data processing. MLR model between *e* and these main influence factors can be established.

#### **3. Results and Discussion**

#### *3.1. Data Sources and Related Instructions*

In this paper, the data source is the production data of a steel enterprise's BFIMP from 2013 to 2014.In order to ensure the validity of the discussion, the pretreatments of these data should be carried out before application. After data pretreatment processes, the effective samples 104 groups of invalid samples were eliminated from the data of the 730 groups, and 626 groups were obtained.
