Introduction

The competition in the mineral processing industry is increasingly fierce, the beneficiation plant not only improves the production efficiency, but also paid attention to the workshop environment. Khaled Ali Abuhasel1 noted that even in modern plant are inseparable from manual inspection and operation. Scholars have studied the single occupational hazard factors for the beneficiation plant in the past , such as dust and noise in the working environment. Bhadani2 studied the dust generation point of the beneficiation plant, Rohollah Fallah Madvari3 analyzed the causes and hazards of noise in the broken miners. Scholars soon realised that the workshop environment of the concentrator was complex, there are noise, dust, microclimate and many other influencing factors in the workshop working environment. Bieliatynskyi Andrii4 noted the effect of noise and dust in the workshop environment on the workers. Wen Fu5 considered that dust, noise and toxic gas were the main factors which damage the health of workers in beneficiation plants after investigated.

Syurin Sergei A6 studied the development trend of occupational diseases, he believed that it is urgent to establish a comprehensive evaluation method that covers all relevant factors in the environment to comprehensively evaluate the workshop environment. Xue Yawei7 used the element analysis method evaluated the current situation of the power grid, the element analysis model does not need a lot of sample, so this method effectively avoids the error brought in the learning process. The element analysis method, which has been improved by scholars in practical application over the years, this approach is very flexible and can be used in combination with other theories. Yanting Ji8 established a break model useing the improved element analysis, which combined element analysis with extension theory, this way can evaluate the membership of things relative to a certain evaluation level more scientifically and comprehensively. Jianhong Chen9 established the object element extension analysis model to analyse the mine safety , this model not only expands the value range of the correlation function, but also changes the evaluation index from a single determined value to an interval value, which can make the analysis results more credible. Therefore, this paper will establish the element extension model by element analysis method.

It is very necessary to choose the weight analysis method in the multi-index evaluation. Dan Liu10 used the entropy weight method to construct the object analysis model of tourism carrying capacity, he combined the object analysis method with the objective allocation method. The entropy weight method is a common multi-index evaluation method, but this method needs a large number of objective data, and the conclusions are not comprehensive, nevertheless, the G1 method is a subjective empowerment method to solve the multi-index problem. Seyedmohammadi11 combined the G1 method with the hierarchical analysis method to evaluate the suitability of agricultural land. Haiji Zhao12 applied the G1 method to the comprehensive evaluation of the economic benefits of the power plant, and the results show that the G1 method is superior in solving practical problems. Ang Chen13 founded that single assignment method cannot get exact membership grade, Wang Zhichao14 found the way to combine subjective and objective empowerment mode can successfully construct the evaluation model with higher reliability. Ming Jin15 established a comprehensive evaluation method for the whole data link based on the G1method and the entropy weight method, the comprehensive score reflects both the expert level and experience and the actual situation-related data. Qingqi Zhao16 combined the G1 method and entropy weight method to analyse the energy flow of the school integrated energy system, the evaluation model reflects the subjectivity and objectivity of evaluation. In recent years, a large number of scholars have applied the G1 entropy Method in the fields of natural sciences, social sciences and medicine17,18,19,20,21. Therefore, this project will combine the G1 method and entropy weight method to determine the weight of each evaluation index in the element analysis method, and establish the object extension model of the workshop environment of beneficiation plant, the conclusion can be used for reference by enterprises.

Establishment of the index system

The beneficiation plant includes breaking workshop, screening workshop, culling workshop, grinding workshop, culling yard, auxiliary facility, ancillary building. It will produce a lot of dust during breaking, screening, grinding, grading, screening and other process. And due to the poor ventilation, dust is easy to accumulate, the operating environment conditions are poor22. It will produce high intensity noise during the operation of equipment, such as crusher, vibrating screen, ball mill, hydraulic cyclone. The temperature and the concentration of benzene, toluene, xylene, in the workshops are high, there are the laboratory environment of occupational disease hazard factors statistics in Table 1. According to the investigation results, this paper selected 7 factors as the evaluation indexes, such as dust, noise, light environment, microclimate, benzene, toluene and xylene. As the units of each evaluation indices are different, the measurement data of all evaluation indexes should be dimensionless processed before calculation.

Table 1 Occupational-disease-inductive factors of the beneficiation plant.
Full size table

Determination of the weights

The results related to the weight of the evaluation index. It is important to insure the weight scientific and reasonable. At present, there are many methods to obtain the weights of the evaluation index, which can be divided into two kinds, subjective empowerment method and objective empowerment method. Subjective methods include the hierarchical analysis method, the expert research method, the G1 method, etc., while objective methods include the entropy weight method, the coefficient of variation method, etc. Considering the advantages and disadvantages of subjective and objective methods, this paper used the G1 method and the entropy weight method to obtain the weight of each evaluation index.

Calculated the subjective by the G1 method

The G1 method greatly reduces the process of determining the weight of multiple evaluation indicators does not need to construct the judgement matrix and perform the consistency test, so it is easy to apply23. The calculation steps are shown as follows.

First, rank the evaluation indicators according to the experts Second, determine the importance ratio value of the two adjacent evaluation indicators, rk, The formula for the importance ratio is shown in (1). The ω*k is the index weight of Ck, k = m, m-1,…, 3,2. The assignment of rk is from1.0 to 1.8, 1.0 is the minimum, 1.8 is the maximum, the higher the assignment, the greater the relation. Then calculate the weight of other indicators, Xm, Xm-1. m = 2, 3, 4, ….

$$r_{k} = \frac{{\omega_{k - 1}^{*} }}{{\omega_{k}^{*} }}$$
(1)
$$r_{k - 1} > \frac{1}{{r_{k} }}$$
(2)
$$\omega_{m}^{*} = \frac{1}{{1 + \sum\nolimits_{k = 1}^{m - 1} {\prod\nolimits_{i = k}^{m - 1} {r_{i} } } }}$$
(3)
$$\omega_{m - 1}^{*} = r_{m - 1} \omega_{m}^{*}$$
(4)

Calculated the objective weight by the entropy weight method

The entropy weighting method is an objective value assignment method, which calculate the weight of the index based on research objects. The meaning of the message is opposite to the entropy, the message is a measure of order of the system, while the entropy is a measure of the degree of disorder of the system24. Therefore, the smaller the entropy of an evaluation index, the greater the information provided by the index,, and its weight should be greater25. Therefore, the entropy weight method can be used to calculate the weight of each index in the research object, through the corresponding calculation formulas are shown as follows.

  1. (1)

    Construct an m × n matrix, the column vector is the data value of each evaluation index, the matrix is shown as follows.

    $$\left| {\begin{array}{*{20}c} {a_{11} } & {a_{12} } & \cdots & {a_{1n} } \\ {a_{21} } & {a_{22} } & \cdots & {a_{2n} } \\ \vdots & \vdots & \cdots & \vdots \\ {a_{m1} } & {a_{m2} } & \cdots & {a_{mn} } \\ \end{array} } \right|$$
    (5)
  2. (2)

    Calculate the value of the Pij., j is the ordinal number of the index, i stand for the ordinal number of the data, the formula is shown as follows.

    $$p_{ij} = \frac{{x_{ij} }}{{\sum\nolimits_{i = 1}^{n} {x_{ij} } }}$$
    (6)

    the n is the number of the data, which covered by the jth index.

  3. (3)

    Calculate the entropy value of the evaluation index. The formula is shown as follows.

    $$e_{j} = - \frac{1}{\ln n} \times \left( {\sum\limits_{i = 1}^{n} {p_{ij} \ln p_{ij} } } \right)$$
    (7)
  4. (4)

    Calculate the entropy right of the jth evaluation index. The formula is shown as follows.

    $$\omega_{j} = \frac{{1 - e_{j} }}{{\sum\nolimits_{j = 1}^{m} {\left( {1 - e_{j} } \right)} }}$$
    (8)

The m is the number of evaluation indicators, and ωj stand for the weight of the jth index, 0 ≤ ωj ≤ 1, the formula is shown as follows.

$$\sum\limits_{j = 1}^{m} {\omega_{j} = 1}$$
(9)

Determination of the comprehensive weight

In order to calculate the comprehensive weight, this paper adopts the distance function, which can represent the difference between the entropy weight method and the the G1 method, The comprehensive empowerment can eliminate the differences26. For the jth index, ω*j, represents the weight calculated by the G1 method while ωj, represents the weight calculated by the entropy weight method, the steps are shown as follows.

  1. (1)

    Calculate the distance function of the weight between the G1 method and the entropy weight method, make d stand for the conclusion, the formula is shown as follows.

    $$d = \left[ {\frac{1}{2}\sum\limits_{j = 1}^{m} {\left( {\omega_{j}^{*} - \omega_{j} } \right)^{2} } } \right]^{\frac{1}{2}}$$
    (10)
  2. (2)

    Calculate the proportion coefficient A and B (A > B), A stand for the weight calculated by the G1 method and B stand for the weight calculated by the entropy weight method, the formula is shown as follows.

    $$d^{2} = \left( {A - B} \right)^{2}$$
    (11)
    $$A + B = 1$$
    (12)
  3. (3)

    Calculate the comprehensive weight, the formula is shown as follows.

    $$a_{j} = A\omega_{j}^{*} + B\omega_{j}$$
    (13)

Establish the element analysis model

First the classic ___domain element matrix and segment ___domain element matrix are established, and then the correlation function is used to calculate the features and the evaluation level of correlation, then the comprehensive correlation of the evaluation level is calculated based on the weight of the research object, and finally the evaluation level of the research object is obtained27,28.

Determination of the element analysis matrix

The element matrix of classical ___domain objects is formed by the range of the quantity value corresponding to the feature in each evaluation level. Taking N0 as an example, make ci stand for one of features, make vij stand for the value of it, if vij ∈ (a0i,b0i) . The element matrix of the corresponding classical ___domain is shown as follows.

$$R_{0} = \left( {N_{0} ,c,v} \right) = \left| {\begin{array}{*{20}c} {N_{0} } & {c_{1} } & {\left( {a_{01} ,b_{01} } \right)} \\ {} & {c_{2} } & {\left( {a_{02} ,b_{02} } \right)} \\ {} & \cdots & \cdots \\ {} & {c_{n} } & {\left( {a_{0n} ,b_{0n} } \right)} \\ \end{array} } \right|$$
(14)

If each feature meets the above conditions, the corresponding node matrix is shown as follows.

$$R_{p} = \left( {N_{p} ,c,v_{p} } \right) = \left| {\begin{array}{*{20}c} {N_{p} } & {c_{1} } & {\left( {a_{p1} ,b_{p1} } \right)} \\ {} & {c_{2} } & {\left( {a_{p2} ,b_{p2} } \right)} \\ {} & \cdots & \cdots \\ {} & {c_{n} } & {\left( {a_{pn} ,b_{pn} } \right)} \\ \end{array} } \right|$$
(15)

Determination of the correlation degree

Use the association function to measure the degree of correlation between the measured value of each feature and its quantity value interval. The calculation formulas are shown as follows.

$$\overline{{v_{i} }} = \frac{{\sum\nolimits_{j = 1}^{n} {v_{ij} } }}{n}$$
(16)
$$K_{x} \left( {\overline{{v_{i} }} } \right) = - \frac{{\rho \left( {\overline{{v_{i} }} ,v_{0i} } \right)}}{{\left| {\overline{{v_{i} }} } \right|}},\overline{{v_{i} }} \in v_{0i}$$
(17)
$$K_{x} \left( {\overline{{v_{i} }} } \right) = \frac{{\rho \left( {\overline{{v_{i} }} ,v_{0i} } \right)}}{{\rho \left( {\overline{{v_{i} }} ,v_{pi} } \right) - \rho \left( {\overline{{v_{i} }} ,v_{0i} } \right)}},\overline{{v_{i} }} \notin v_{0i}$$
(18)

Kx(vi) represents the connection between the characteristics and the evaluation rating, ρ(vi,v0i) represents the distance between average value of characteristics and the v0i region. ρ(vi,vpi) represents the distance between average value of characteristics and the vpi-region, vi represents the average value of ci. The calculation formulas are shown as follows.

$$\rho \left( {\overline{{v_{i} }} ,v_{0i} } \right) = \left| {\overline{{v_{i} }} - \frac{1}{2}\left( {a_{0i} + b_{0i} } \right)} \right| - \frac{1}{2}\left( {b_{0i} - a_{0i} } \right)$$
(19)
$$\rho \left( {\overline{{v_{i} }} ,v_{pi} } \right) = \left| {\overline{{v_{i} }} - \frac{1}{2}\left( {a_{pi} + b_{pi} } \right)} \right| - \frac{1}{2}\left( {b_{pi} - a_{pi} } \right)$$
(20)

Calculation of evaluation grade

Evaluate the comprehensive correlation degree, where αi represents the comprehensive weight of the characteristic N. The calculation formula is shown as follows.

$$K_{x} \left( N \right) = \sum\limits_{i = 1}^{n} {\alpha_{i} K_{x} \left( {\overline{{v_{i} }} } \right)}$$
(21)

Use the formula (22) to evaluate evaluation grade, Kx(N) is the comprehensive correlation of the evaluation levels of xth.

$$K_{x0} \left( N \right) = \max \left( {K_{x} \left( N \right)} \right),\quad x = 1,\;2,\; \ldots ,\;n$$
(22)

Kx(N) represents the degree of conformity between the evaluation object and a certain evaluation level, When 0 < Kx(N) ≤ 1, it means that the evaluation meets the level, and the larger the value the closer the evaluation. When − 1 < Kx(N) ≤ 0, it means that the evaluation does not meet the evaluation level, but the closer the value to 0 the closer the lower of the evaluation level, the easier it is to convert into the evaluation level.

Instance application

Classification criteria of evaluation indicators

Divided the environment grade of beneficiation plant into 5 evaluation grades, excellent (grade I), good (grade II), medium (grade III), qualified (grade IV) and unqualified (grade V). The standard is from the relevant national or industrial standards. The standards of the workshop evaluation index are shown in Table2.

Table 2 Standards of the workshop evaluation index.
Full size table

Data of evaluation indicators

The evaluation indicators of the workshops were measured. The measured data are shown in Table 3, and the unmeasured data are shown in Table 4.

Table 3 Measured data of each evaluation index.
Full size table
Table 4 Measured data of all evaluation indexes.
Full size table

Element analysis model of the beneficiation plant

According to the results of the experts, the weight of each evaluation index based on the G1 method is shown in Table 5.

Table 5 Indexes based on the weight of G1 method.
Full size table

The entropy weighting method was used to calculate the weight of each evaluation index, using the data from Table 4. The weight of the evaluation index based on the entropy weighting method is shown in Table 6.

Table 6 Indexes based on the weight of entropy weight method.
Full size table

Using formulae (10), (11) and (12) to calculate the proportion coefficient in the total weight, and then using formula (13) to calculate the total weight A is the result of the G1 method and A is the result of the entropy weight method The calculation results are shown in Table 7.

Table 7 Comprehensive weight of each evaluation index of the workshop operating environment.
Full size table

Construct the element matrix according to the measured data, and use formula (16), (17), (18), (19), (20) and (21) to calculate the correlation between each evaluation index and each evaluation grade. Finally, use the formula (22) evaluation to determine the grade of each workshop. The evaluation results are shown in Table 8.

Table 8 Evaluation results.
Full size table

Kx(N) is the comprehensive correlation of the xth evaluation level. As it was shown in Table 8, that the evaluation level of the breaking workshop and the auxiliary facilities are unqualified, the auxiliary facility is qualified, the culling workshop, the culling yard and accessory building are medium, the screening workshop and grinding workshop are good.

Conclusion

  1. (1)

    This paper analyzed the characteristics of the workshop environment, established the evaluation index system of the working environment and the comprehensive evaluation model.

  2. (2)

    Based on the extension mathematics, this paper summarised the practical problems as compatibility and incompatibility problems, and then used the object analysis method to carry out. This paper expanded the value range of the correlation function from − ∞ to + ∞. It integrated all the information of various factors, ensured the integrity of the information.

  3. (3)

    This paper adopted both the subjective and objective method to calculate the weight of each evaluation index. The G1 method was used to assign the value, the entropy weight method was used to assign the value, and then the method of weight integration was used to make the comprehensive weight, so that the results are more scientific and reasonable, and the evaluation results are more accurate.

  4. (4)

    Taking a beneficiation plan as an example, a material analysis model was established. The results show that the evaluation level of the breaking workshop and the auxiliary facilities are unqualified (grade V), the auxiliary facility is qualified (grade IV), the culling workshop, culling yard and accessory building are medium (grade III), the screening workshop and grinding workshop are good (grade II). The evaluation results are consistent with the actual situation, indicating that the model has strong practical value and provides an effective technical way to establish the environmental evaluation model for beneficiation plant.